This is the CellML 1.0 Guyton Model.
Guyton Model
Jonna
Terkildsen
Auckland Bioengineering Institute, University of Auckland
Model Status
This CellML model has not been completely validated as yet. The output from the model may not conform
to the results from the MODSIM program. Due to the differences between procedural
code (in this case C-code) and declarative languages (CellML), some aspects of the original model were not
able to be encapsulated by the CellML model (such as the damping of variables). Work is underway to fix these
omissions and validate the CellML model. We also anticipate that many of these problems will be fixed when
the CellML 1.0 models are combined in a CellML 1.1 format.
Model Structure
Arthur Guyton (1919-2003) was an American physiologist who became famous for his 1950s experiments in which he studied
the physiology of cardiac output and its relationship with the peripheral circulation. The results of these experiments
challenged the conventional wisdom that it was the heart itself that controlled cardiac output. Instead Guyton
demonstrated that it was the need of the body tissues for oxygen which was the real regulator of cardiac output.
The "Guyton Curves" describe the relationship between right atrial pressures and cardiac output, and they form a
foundation for understanding the physiology of circulation.
The Guyton model of fluid, electrolyte, and circulatory regulation is an extensive mathematical model of human circulatory
physiology, capable of simulating a variety of experimental conditions, and contains a number of linked subsystems relating
to circulation and its neuroendocrine control.
This is a CellML translation of the Guyton model of the regulation of the circulatory system. The complete model consists
of separate modules each of which characterise a separate physiological subsystems. The Circulation Dynamics is the primary
system, to which other modules/blocks are connected. The other modules characterise the dynamics of the kidney,
electrolytes and cell water, thirst and drinking, hormone regulation, autonomic regulation, cardiovascular system etc,
and these feedback on the central circulation model. The CellML code in these modules is based on the C code from the
programme C-MODSIM created by Dr Jean-Pierre Montani.
model diagram
A systems analysis diagram for the full Guyton model describing circulation regulation.
There are several publications referring to the Guyton model. One of these papers is cited below:
Circulation: Overall Regulation, A.C. Guyton, T.G. Coleman, and H.J. Granger, 1972,
Annual Review of Physiology
, 34, 13-44. PubMed ID: 4334846
Terkildsen
Jonna
j.terkildsen@auckland.ac.nz
The University of Auckland
Auckland Bioengineering Institute
2008-04-03
The University of Auckland, Auckland Bioengineering Institute
Guyton
Cardiovascular
Circulation
Description of Guyton 1992 Full Cardiovascular Circulation Model
2008-00-00 00:00
keyword
physiology
organ systems
cardiovascular circulation
Guyton
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Temp component setting MYOGRS, PAMKRN and PAMK to 1.
ALDOSTERONE AND ITS FEEDBACK CONTROL FUNCTIONS FOR MODIFICATION OF THE CIRCULATION
Two inputs are used for controlling aldosterone secretion, the potassium concentration in the
extracellular fluids (CKE) and the effect of angiotensin (ANM) on aldosterone secretion.
In turn, multiplier effects for aldosterone control of potassium (AMK) and sodium (AMNA) transport
through cell membranes, especially through the kidney tubule membranes are calculated.
Encapsulation grouping component containing all the components in the Aldosterone Model.
The inputs and outputs of the Aldosterone Model must be passed by this component.
AL1, AL2, and AL3:
Calculation of the partial effect of angiotensin on aldosterone secretion (ANMAL)
based on the general angiotensin multiplier (ANM). The sensitivity of this effect
is controlled by the sensitivity control variable (ANMALD) in Block AL2.
AL1, AL2, and AL3:
Calculation of the partial effect of angiotensin on aldosterone secretion (ANMAL)
based on the general angiotensin multiplier (ANM). The sensitivity of this effect
is controlled by the sensitivity control variable (ANMALD) in Block AL2.
$\mathrm{ANMAL}=\mathrm{ANM}\mathrm{ANMALD}+1$
AL4:
Calculation of the driving force of potassium extracellular fluid concentration (CKE)
on aldosterone secretion by subtracting the constant 3.3 from CKE.
AL4:
Calculation of the driving force of potassium extracellular fluid concentration (CKE)
on aldosterone secretion by subtracting the constant 3.3 from CKE.
$\mathrm{OSMAL}=\frac{\mathrm{CKE}-3.3}{1.0}$
AL5:
Calculation of the basic rate of secretion of aldosterone (AMRBSC) by multiplying
the potassium drive for secretion from Block AL4 times the angiotensin drive for
aldosterone secretion (ANMAL).
AL6, AL7, AL8, and AL9:
These blocks calculate the aldosterone secretion rate (AMR). Blocks AL6, AL7,
and AL8 represent a sensitivity controller for the control of aldosterone secretion rate.
The sensitivity control variable is AMKMUL in Block AL7. Block AL9 sets a lower limit
to the aldosterone secretion equal to zero.
AL9A:
Provision is made here for infusion of aldosterone to perform infusion experiments (ALDINF).
AL9B:
Provision is made here to set the rate of aldosterone entering the circulatory system (AMR1)
to a constant value (ALDKNS) irrespective of all other changes at earlier stages in this
calculation.
AL5:
Calculation of the basic rate of secretion of aldosterone (AMRBSC) by multiplying
the potassium drive for secretion from Block AL4 times the angiotensin drive for
aldosterone secretion (ANMAL).
AL6, AL7, AL8:
These blocks calculate the aldosterone secretion rate (AMR). Blocks AL6, AL7,
and AL8 represent a sensitivity controller for the control of aldosterone secretion rate.
The sensitivity control variable is AMKMUL in Block AL7.
AL9:
Block AL9 sets a lower limit to the aldosterone secretion equal to zero.
AL9A:
Provision is made here for infusion of aldosterone to perform infusion experiments (ALDINF).
AL9B:
Provision is made here to set the rate of aldosterone entering the circulatory system (AMR1)
to a constant value (ALDKNS) irrespective of all other changes at earlier stages in this
calculation.
$\mathrm{AMRBSC}=\mathrm{ANMAL}\times 0.909\mathrm{OSMAL}\mathrm{AMRT}=\mathrm{AMRBSC}\mathrm{AMKMUL}+1\mathrm{AMR}=\begin{cases}0 & \text{if $\mathrm{AMRT}< 0$}\\ \mathrm{AMRT} & \text{otherwise}\end{cases}\mathrm{AMR1}=\begin{cases}\mathrm{ALDKNS} & \text{if $\mathrm{ALDKNS}> 0$}\\ \mathrm{AMR}+\mathrm{ALDINF} & \text{otherwise}\end{cases}$
AL10, AL11, and AL12:
Calculation of aldosterone concentration (AMC), allowing for a time delay in the
build-up of the aldosterone. The time constant for the time delay is AMT in Block AL12.
AL10, AL11, and AL12:
Calculation of aldosterone concentration (AMC), allowing for a time delay in the
build-up of the aldosterone. The time constant for the time delay is AMT in Block AL12.
$\frac{d \mathrm{AMC}}{d \mathrm{time}}=\frac{\mathrm{AMR1}-\mathrm{AMC}}{\mathrm{AMT}}$
AL13:
This block calculates, based on the input of aldosterone concentration (AMC),
an output factor (AM1) for the physiological multiplying effect of aldosterone
on different physiological mechanisms. This is a temporary aldosterone multiplier
effect. It is calculated as shown in the block, with AM1LL equal to the lower
limit of AM1 and AM1UL equal to the upper limit.
AL14, AL15, and AL16:
These are a sensitivity controller; the control variable for sensitivity is ALDMM in
Block AL15, and the output AM is a general aldosterone multiplier.
AL13:
This block calculates, based on the input of aldosterone concentration (AMC),
an output factor (AM1) for the physiological multiplying effect of aldosterone
on different physiological mechanisms. This is a temporary aldosterone multiplier
effect. It is calculated as shown in the block, with AM1LL equal to the lower
limit of AM1 and AM1UL equal to the upper limit.
AL14, AL15, and AL16:
These are a sensitivity controller; the control variable for sensitivity is ALDMM in
Block AL15, and the output AM is a general aldosterone multiplier.
$\mathrm{AM1}=\mathrm{AM1UL}-\frac{\mathrm{AM1UL}-1}{\frac{\mathrm{AM1LL}-1}{\mathrm{AM1LL}-\mathrm{AM1UL}}(\mathrm{AMC}-1)\mathrm{AMCSNS}+1}\mathrm{AM}=\mathrm{AM1}\mathrm{ALDMM}+1$
AL17, AL18, AL19, and AL20:
This is an additional sensitivity control circuit for controlling the aldosterone
multiplier effect on potassium transport through cell membranes (AMK), especially
in the kidney tubules. The input to this system is the general aldosterone multiplier (AM),
and the sensitivity controller is the variable AMKM in Block AL18. The lower limit to
AMK is set by Block AL20.
AL17, AL18 and AL19:
This is an additional sensitivity control circuit for controlling the aldosterone
multiplier effect on potassium transport through cell membranes (AMK), especially
in the kidney tubules. The input to this system is the general aldosterone multiplier (AM),
and the sensitivity controller is the variable AMKM in Block AL18.
AL20:
The lower limit to AMK is set by Block AL20.
$\mathrm{AMKT}=\mathrm{AM}\mathrm{AMKM}+1\mathrm{AMK}=\begin{cases}0.2 & \text{if $\mathrm{AMKT}< 0.2$}\\ \mathrm{AMKT} & \text{otherwise}\end{cases}$
AL21, AL22, AL23, AL24, and AL25:
This circuit calculates an aldosterone multiplier factor for control of sodium
transport through cell membranes (AMNA), with the input to the circuit equal to
the generalized aldosterone multiplier (AM) and a sensitivity controller (AMNAM)
in Block AL22. The upper and lower limits for the controlling effect on sodium
transport are set by variables AMNAUL and AMNALL in Blocks AL24 and AL25 respectively.
AL21, AL22 and AL23:
This circuit calculates an aldosterone multiplier factor for control of sodium
transport through cell membranes (AMNA), with the input to the circuit equal to
the generalized aldosterone multiplier (AM) and a sensitivity controller (AMNAM)
in Block AL22.
AL24, and AL25:
The upper and lower limits for the controlling effect on sodium
transport are set by variables AMNAUL and AMNALL in Blocks AL24 and AL25 respectively.
$\mathrm{AMNAT}=\mathrm{AM}\mathrm{AMNAM}+1\mathrm{AMNA}=\begin{cases}\mathrm{AMNALL} & \text{if $\mathrm{AMNAT}< \mathrm{AMNALL}$}\\ \mathrm{AMNAUL} & \text{if $\mathrm{AMNAT}> \mathrm{AMNAUL}$}\\ \mathrm{AMNAT} & \text{otherwise}\end{cases}$
This section calculates the control functions of angiotensin, beginning with the
control of angiotensin formation by the kidneys in response to changes in the rate
of flow of fluid in the renal tubules at the macula densa (MDFLW), and extending
through a series of curve-fitting and sensitivity controlled equations to determine
the multiple feedback effects of angiotensin to control the various aspects of
circulatory function.
Encapsulation grouping component containing all the components in the Angiotensin Model.
The inputs and outputs of the Angiotensin Model must be passed by this component.
AN1:
This block damps the variations in rate of fluid flow in the renal tubules at
the macula densa (MDFLW). The damped outflow is the variable MDFLW3.
NB - REMOVED DAMPING FORM AN1!!!!
AN2:
This block calculates the formation rate of angiotensin (ANGSCR) at different
levels of MDFLW3.
AN1:
This block damps the variations in rate of fluid flow in the renal tubules at
the macula densa (MDFLW). The damped outflow is the variable MDFLW3.
NB - REMOVED DAMPING FORM AN1!!!!
AN2:
This block calculates the formation rate of angiotensin (ANGSCR) at different
levels of MDFLW3.
$\mathrm{MDFLW3}=\mathrm{MDFLW}\mathrm{ANGSCR}=\begin{cases}\frac{1}{1-\mathrm{MDFLW3}\times 72} & \text{if $\mathrm{MDFLW3}> 1$}\\ 10-\frac{9}{1-1\times 8} & \text{otherwise}\end{cases}$
AN4, AN5, AN6, AN7, and AN8:
Calculation of additional formation of angiotensin caused after a long-term delay.
That is, when the JG cells are stimulated over long periods of time, in addition to
their acute effects on secretion rate of renin and subsequent formation of angiotensin,
there is a long-term increase in numbers of active JG cells to give a long-term delayed
response over a period of days. The variable ANXM adjusts the magnitude of this
delayed response. ANX is the total response without regard to the time delay. ANV is
the time-constant of the time delay. ANX1 is the total extra secretion after factoring
in the time delay effects of blocks 6, 7, and 8.
AN4, AN5, AN6, AN7, and AN8:
Calculation of additional formation of angiotensin caused after a long-term delay.
That is, when the JG cells are stimulated over long periods of time, in addition to
their acute effects on secretion rate of renin and subsequent formation of angiotensin,
there is a long-term increase in numbers of active JG cells to give a long-term delayed
response over a period of days. The variable ANXM adjusts the magnitude of this
delayed response. ANX is the total response without regard to the time delay. ANV is
the time-constant of the time delay. ANX1 is the total extra secretion after factoring
in the time delay effects of blocks 6, 7, and 8.
AN4, AN5, AN6, AN7, and AN8:
Calculation of additional formation of angiotensin caused after a long-term delay.
That is, when the JG cells are stimulated over long periods of time, in addition to
their acute effects on secretion rate of renin and subsequent formation of angiotensin,
there is a long-term increase in numbers of active JG cells to give a long-term delayed
response over a period of days. The variable ANXM adjusts the magnitude of this
delayed response. ANX is the total response without regard to the time delay. ANV is
the time-constant of the time delay. ANX1 is the total extra secretion after factoring
in the time delay effects of blocks 6, 7, and 8.
$\mathrm{ANX}=(\mathrm{ANGSCR}-1)\mathrm{ANXM}\frac{d \mathrm{ANX1}}{d \mathrm{time}}=\frac{\mathrm{ANX}-\mathrm{ANX1}}{\mathrm{ANV}}$
AN9:
Summation of instantaneous formation of angiotensin (ANGSCR) plus the time delayed
formation of angiotensin (ANX1).
AN10:
Calculation of the total rate of formation of angiotensin (ANPR) in case some of
the renal mass (and therefore some of the JG cells) has been removed or destroyed.
Factor REK is equal to the proportion of kidney mass that is still functional.
AN11:
This sets the lower limit of ANPR to a very low level, almost zero, below which
this cannot fall. The reason for this is to prevent a negative value from appearing.
AN9:
Summation of instantaneous formation of angiotensin (ANGSCR) plus the time delayed
formation of angiotensin (ANX1).
AN10:
Calculation of the total rate of formation of angiotensin (ANPR) in case some of
the renal mass (and therefore some of the JG cells) has been removed or destroyed.
Factor REK is equal to the proportion of kidney mass that is still functional.
AN11:
This sets the lower limit of ANPR to a very low level, almost zero, below which
this cannot fall. The reason for this is to prevent a negative value from appearing.
$\mathrm{ANPRT}=(\mathrm{ANGSCR}+\mathrm{ANX1})\mathrm{REK}\mathrm{ANPR}=\begin{cases}0.00001 & \text{if $\mathrm{ANPRT}< 0.00001$}\\ \mathrm{ANPRT} & \text{otherwise}\end{cases}$
AN11A:
This block allows the addition of infused angiotensin (ANGINF) to the amount of
angiotensin that is formed in the body (ANPR).
AN11B:
This block allows one to disregard all the previous blocks and to set the total
rate of angiotensin entering the circulatory system (ANPR1) to a constant level, ANGKNS.
When ANGKNS is equal to zero or less, then Block 11B is ineffective.
AN11A:
This block allows the addition of infused angiotensin (ANGINF) to the amount of
angiotensin that is formed in the body (ANPR).
AN11B:
This block allows one to disregard all the previous blocks and to set the total
rate of angiotensin entering the circulatory system (ANPR1) to a constant level, ANGKNS.
When ANGKNS is equal to zero or less, then Block 11B is ineffective.
$\mathrm{ANPR1}=\begin{cases}\mathrm{ANGKNS} & \text{if $\mathrm{ANGKNS}> 0$}\\ \mathrm{ANPR}+\mathrm{ANGINF} & \text{otherwise}\end{cases}$
AN12, AN13, and AN14:
These blocks convert the rate of entry of angiotensin into the body fluids (ANPR1),
into the concentration of angiotensin (ANC) considering the normal value to be the
numeral 1. The value ANT is the time constant for rate of change of angiotensin
concentration in the body fluids. The value Z12 is a damping coefficient to allow
damping of this conversion so that the model can be run faster for long-term simulations.
AN12, AN13, and AN14:
These blocks convert the rate of entry of angiotensin into the body fluids (ANPR1),
into the concentration of angiotensin (ANC) considering the normal value to be the
numeral 1. The value ANT is the time constant for rate of change of angiotensin
concentration in the body fluids. The value Z12 is a damping coefficient to allow
damping of this conversion so that the model can be run faster for long-term simulations.
$\frac{d \mathrm{ANC}}{d \mathrm{time}}=\frac{\mathrm{ANPR1}-\mathrm{ANC}}{\mathrm{ANT}}$
AN15:
This is an equation that allows one to convert the concentration of angiotensin (ANC)
into an angiotensin multiplier (ANM) which describes the multiplicative effect of
angiotensin on various physiological functions, assuming the normal value of ANM
to be 1.0. The value ANMUL is the upper limit to the level of ANM. ANMLL is the
lower limit of ANM. And the value ANCSNS is a sensitivity value for adjusting the
quantitative effect of ANC on ANM.
AN15:
This is an equation that allows one to convert the concentration of angiotensin (ANC)
into an angiotensin multiplier (ANM) which describes the multiplicative effect of
angiotensin on various physiological functions, assuming the normal value of ANM
to be 1.0. The value ANMUL is the upper limit to the level of ANM. ANMLL is the
lower limit of ANM. And the value ANCSNS is a sensitivity value for adjusting the
quantitative effect of ANC on ANM.
$\mathrm{ANM}=\mathrm{ANMUL}-\frac{\mathrm{ANMUL}-1}{\frac{\mathrm{ANMLL}-1}{\mathrm{ANMLL}-\mathrm{ANMUL}}(\mathrm{ANC}-1)\mathrm{ANCSNS}+1}$
AN16, AN17, and AN18:
These blocks are a sensitivity controller for converting the basic effect of the
angiotensin multiplier (ANM) on other functional systems of the circulation (ANU).
The sensitivity adjustment is the factor ANUM in Block 17.
AN19:
This block sets the lower limit to which ANU can fall (ANULL).
AN16, AN17, and AN18:
These blocks are a sensitivity controller for converting the basic effect of the
angiotensin multiplier (ANM) on other functional systems of the circulation (ANU).
The sensitivity adjustment is the factor ANUM in Block 17.
AN19:
This block sets the lower limit to which ANU can fall (ANULL).
$\mathrm{ANU1}=\mathrm{ANM}\mathrm{ANUM}+1\mathrm{ANU}=\begin{cases}\mathrm{ANULL} & \text{if $\mathrm{ANU1}< \mathrm{ANULL}$}\\ \mathrm{ANU1} & \text{otherwise}\end{cases}$
AN20, AN21, and AN22:
Calculation of the effect of angiotensin on venous constriction (ANUVN), with
sensitivity controlled by ANUVM in Block 21.
AN20, AN21, and AN22:
Calculation of the effect of angiotensin on venous constriction (ANUVN), with
sensitivity controlled by ANUVM in Block 21.
$\mathrm{ANUVN}=\mathrm{ANU}\mathrm{ANUVM}+1$
Antidiuretic Hormone and its control functions.
This section calculates the control of antidiuretic hormone secretion and also
calculates multiplier factors for control of other aspects of circulatory function
by antidiuretic hormone. The major factors that are considered to affect the rate
of antidiuretic hormone secretion are (1) a feedback effect of osmotic concentration
in the extracellular fluids as determined from the concentration of sodium (CNA),
and (2) a feedback effect of arterial pressure (PA).
Encapsulation grouping component containing all the components in the Anti-Diuretic Hormone Model.
The inputs and outputs of the Anti-Diuretic Hormone Model must be passed by this component.
AD1, AD2, and AD3:
Calculation of a multiplier factor (ADHNA) that determines the effect of the
concentration of sodium in the extracellular fluid (CNA) on the secretion of ADH.
The lower limit of CNA at which the normal stimulating effect of changes in CNA
will affect antidiuretic hormone secretion is equal to CNR. The mathematical
steps in Blocks AD1, AD2, and AD3 provide curve shaping effects for the relationship
between CNA and ADHNA.
AD8:
The effect of sodium concentration on ADH secretion (ADHNA) is not allowed
to go below zero.
AD1, AD2, and AD3:
Calculation of a multiplier factor (ADHNA) that determines the effect of the
concentration of sodium in the extracellular fluid (CNA) on the secretion of ADH.
The lower limit of CNA at which the normal stimulating effect of changes in CNA
will affect antidiuretic hormone secretion is equal to CNR. The mathematical
steps in Blocks AD1, AD2, and AD3 provide curve shaping effects for the relationship
between CNA and ADHNA.
AD8:
The effect of sodium concentration on ADH secretion (ADHNA) is not allowed
to go below zero.
$\mathrm{ADHNA1}=\frac{\mathrm{CNA}-\mathrm{CNR}}{142-\mathrm{CNR}}\mathrm{ADHNA}=\begin{cases}0 & \text{if $\mathrm{ADHNA1}< 0$}\\ \mathrm{ADHNA1} & \text{otherwise}\end{cases}$
AD4, AD5, AD6, and AD7:
Calculation of the effect of low levels of arterial pressure to cause secretion
of antidiuretic hormone. The mathematical steps in these blocks provide appropriate
curve shaping. Zero effect of pressure on ADH secretion occurs whenever the arterial
pressure is greater than 85 mm Hg. The factor ADHPAM is the sensitivity control for
the overall effect. The output of this set of blocks is ADHPR.
AD4, AD5, AD6, and AD7:
Calculation of the effect of low levels of arterial pressure to cause secretion
of antidiuretic hormone. The mathematical steps in these blocks provide appropriate
curve shaping. Zero effect of pressure on ADH secretion occurs whenever the arterial
pressure is greater than 85 mm Hg. The factor ADHPAM is the sensitivity control for
the overall effect. The output of this set of blocks is ADHPR.
AD4, AD5, AD6, and AD7:
Calculation of the effect of low levels of arterial pressure to cause secretion
of antidiuretic hormone. The mathematical steps in these blocks provide appropriate
curve shaping. Zero effect of pressure on ADH secretion occurs whenever the arterial
pressure is greater than 85 mm Hg. The factor ADHPAM is the sensitivity control for
the overall effect. The output of this set of blocks is ADHPR.
$\mathrm{ADHPA}=\begin{cases}\mathrm{ADHPUL} & \text{if $\mathrm{PA1}> \mathrm{ADHPUL}$}\\ \mathrm{PA1} & \text{otherwise}\end{cases}\mathrm{ADHPR}=(\mathrm{ADHPUL}-\mathrm{ADHPA})^{2}\mathrm{ADHPAM}$
AD9:
Calculation of the net rate of ADH entry into the body fluids (ADH) by adding
the partial effect of ADHNA for osmotic control of ADH secretion plus the partial
effect ADHPR for pressure control of secretion, plus ADHINF for any rate of
infusion of ADH.
AD9:
Calculation of the net rate of ADH entry into the body fluids (ADH) by adding
the partial effect of ADHNA for osmotic control of ADH secretion plus the partial
effect ADHPR for pressure control of secretion, plus ADHINF for any rate of
infusion of ADH.
$\mathrm{ADH1}=\mathrm{ADHNA}+\mathrm{ADHPR}+\mathrm{ADHINF}\mathrm{ADH}=\begin{cases}0 & \text{if $\mathrm{ADH1}< 0$}\\ \mathrm{ADH1} & \text{otherwise}\end{cases}$
AD10, AD11, AD12, and AD13:
Calculation of instantaneous antidiuretic hormone concentration in the blood (ADHC)
by integrating in Block 12 the rate of hormone entry into the fluids (ADH) with
respect to time. A time constant for the integration (Block 11) is equal to ADHTC.
Block 13 damps the response of this integration to prevent oscillation when very
long iteration intervals are used in providing long-term solutions for the model.
AD10, AD11, AD12, and AD13:
Calculation of instantaneous antidiuretic hormone concentration in the blood (ADHC)
by integrating in Block 12 the rate of hormone entry into the fluids (ADH) with
respect to time. A time constant for the integration (Block 11) is equal to ADHTC.
Block 13 damps the response of this integration to prevent oscillation when very
long iteration intervals are used in providing long-term solutions for the model.
$\frac{d \mathrm{ADHC}}{d \mathrm{time}}=\frac{\mathrm{ADH}-\mathrm{ADHC}}{\mathrm{ADHTC}}$
AD14 and AD15:
Calculation from the instantaneous concentration of ADH in the plasma (ADHC)
of a multiplier factor (ADHMV) to describe the effect of antidiuretic hormone
in causing contraction of many of the blood vessels of the body. Block 15 sets
a lower limit for ADHMV equal to ADHVLL, and the upper limit is ADHVUL.
AD14:
Calculation from the instantaneous concentration of ADH in the plasma (ADHC)
of a multiplier factor (ADHMV) to describe the effect of antidiuretic hormone
in causing contraction of many of the blood vessels of the body.
AD15:
Block 15 sets a lower limit for ADHMV equal to ADHVLL, and the upper limit is ADHVUL.
$\mathrm{ADHMV1}=\mathrm{ADHVUL}-\frac{\mathrm{ADHVUL}-1}{\frac{\mathrm{ADHVLL}-1}{\mathrm{ADHVLL}-\mathrm{ADHVUL}}(\mathrm{ADHC}-1)+1}\mathrm{ADHMV}=\begin{cases}\mathrm{ADHVLL} & \text{if $\mathrm{ADHMV1}< \mathrm{ADHVLL}$}\\ \mathrm{ADHMV1} & \text{otherwise}\end{cases}$
AD16 and AD17:
Calculation from the plasma concentration of ADH (ADHC) of a multiplier factor (ADHMK)
to describe the effect of the ADH in affecting the kidney. Block 17 gives a lower limit
to ADHMK equal to ADHKLL, and Block 16 gives an upper limit equal to AMKUL.
AD16:
Calculation from the plasma concentration of ADH (ADHC) of a multiplier factor (ADHMK)
to describe the effect of the ADH in affecting the kidney.
AD17:
Block 17 gives a lower limit to ADHMK equal to ADHKLL, and Block 16 gives an upper limit equal to AMKUL.
$\mathrm{ADHMK1}=\mathrm{ADHKUL}-\frac{\mathrm{ADHKUL}-1}{\frac{\mathrm{ADHKLL}-1}{\mathrm{ADHKLL}-\mathrm{ADHKUL}}(\mathrm{ADHC}-1)+1}\mathrm{ADHMK}=\begin{cases}\mathrm{ADHKLL} & \text{if $\mathrm{ADHMK1}< \mathrm{ADHKLL}$}\\ \mathrm{ADHMK1} & \text{otherwise}\end{cases}$
This section calculates the control of atrial natriuretic peptide secretion by the
left and right atria of the heart. It also calculates a multiplier factor for
controlling the resistance of the afferent arterioles (AAR) of the kidneys.
Encapsulation grouping component containing all the components in the Atrial Natriuretic
Peptide Model. The inputs and outputs of the Atrial Natriuretic Peptide Model must be passed
by this component.
ANP1, ANP2, ANP3, ANP3A, and ANP4:
Calculation of the total amount of atrial natriuretic peptide secreted at
any given time. Block ANP1 determines the pressure level at which changes
in left atrial pressure (PLA) will begin to affect atrinatriuretic peptide
secretion. Block 1A sets a lower limit of zero for this secretion.
Block ANP2 calculates from the pressure level in the right atrium (PRA) the
stimulation of ANP output by the right atrium. Block 3 multiplies the
output of the right atrium by two-fold (against a one-fold amount secreted
by the left atrium). Block 3A sets a lower limit of zero for right atrial
output. Block 4 adds the outputs from the left atrium and right atrium.
ANP5:
Block 5 normalizes the ANP secretion under normal conditions to a value of 1.
ANP1, ANP2, ANP3 and ANP3A:
Calculation of the total amount of atrial natriuretic peptide secreted at
any given time. Block ANP1 determines the pressure level at which changes
in left atrial pressure (PLA) will begin to affect atrinatriuretic peptide
secretion. Block 1A sets a lower limit of zero for this secretion.
Block ANP2 calculates from the pressure level in the right atrium (PRA) the
stimulation of ANP output by the right atrium. Block 3 multiplies the
output of the right atrium by two-fold (against a one-fold amount secreted
by the left atrium). Block 3A sets a lower limit of zero for right atrial
output.
ANP1, ANP2, ANP3 and ANP3A:
Calculation of the total amount of atrial natriuretic peptide secreted at
any given time. Block ANP1 determines the pressure level at which changes
in left atrial pressure (PLA) will begin to affect atrinatriuretic peptide
secretion. Block 1A sets a lower limit of zero for this secretion.
Block ANP2 calculates from the pressure level in the right atrium (PRA) the
stimulation of ANP output by the right atrium. Block 3 multiplies the
output of the right atrium by two-fold (against a one-fold amount secreted
by the left atrium). Block 3A sets a lower limit of zero for right atrial
output.
ANP4 and ANP5:
Block 4 adds the outputs from the left atrium and right atrium. Block 5 normalizes
the ANP secretion under normal conditions to a value of 1.
$\mathrm{ANPL}=\begin{cases}0 & \text{if $(\mathrm{PLA}-1)\times 1< 0$}\\ (\mathrm{PLA}-1)\times 1 & \text{otherwise}\end{cases}\mathrm{ANPR2}=\begin{cases}0 & \text{if $(\mathrm{PRA}+1)\times 2< 0$}\\ (\mathrm{PRA}+1)\times 2 & \text{otherwise}\end{cases}\mathrm{ANP}=\frac{\mathrm{ANPL}+\mathrm{ANPR2}}{3}$
ANP 7:
This block allows infusion of ANP into the circulation (ANPINF). The output
of the block is ANP1 which is the total rate of ANP entering the circulation
at any given time.
ANP 7:
This block allows infusion of ANP into the circulation (ANPINF). The output
of the block is ANP1 which is the total rate of ANP entering the circulation
at any given time.
$\mathrm{ANP1}=\begin{cases}\mathrm{ANPKNS} & \text{if $\mathrm{ANPKNS}> 0$}\\ \mathrm{ANP}+\mathrm{ANPINF} & \text{otherwise}\end{cases}$
ANP8, ANP9, and ANP10:
Calculation of the concentration of ANP in the plasma (ANPC) from the rate of
entry of ANP into the plasma (ANP1). The time constant for build-up of ANP in
the circulation is determined by ANPTC in Block 9. ANPC is normalized to 1.
ANP8, ANP9, and ANP10:
Calculation of the concentration of ANP in the plasma (ANPC) from the rate of
entry of ANP into the plasma (ANP1). The time constant for build-up of ANP in
the circulation is determined by ANPTC in Block 9. ANPC is normalized to 1.
$\frac{d \mathrm{ANPC}}{d \mathrm{time}}=\frac{\mathrm{ANP1}-\mathrm{ANPC}}{\mathrm{ANPTC}}$
ANP11:
This curve calculates a multiplier factor (ANPX) for determining the effect
of ANP on the afferent arteriolar resistance of the kidneys. The upper limit
of ANPX is ANPXUL.
ANP 12:
This block sets the lower limit of ANPX equal to -1.
ANP11:
This curve calculates a multiplier factor (ANPX) for determining the effect
of ANP on the afferent arteriolar resistance of the kidneys. The upper limit
of ANPX is ANPXUL.
ANP 12:
This block sets the lower limit of ANPX equal to -1.
$\mathrm{ANPX1}=\mathrm{ANPXUL}-\frac{\mathrm{ANPXUL}}{0.5555556(1+\mathrm{ANPC})}\mathrm{ANPX}=\begin{cases}-1 & \text{if $\mathrm{ANPX1}< -1$}\\ \mathrm{ANPX1} & \text{otherwise}\end{cases}$
Autonomic Control Of The Circulation
Autonomic control of the circulation primarily operates through the sympathetic
system, though to a slight extent through parasympathetic signals to the heart.
These have been lumped together, and there are basically three separate feedback
mechanisms in this computational block. These are: (1) feedback from the
baroreceptor control system; (2) feedback from the peripheral chemoreceptors in
the carotid and aortic bodies,; and (3) feedback control of the circulatory system
caused by central nervous system ischemia, that is, ischemia of the vasomotor center
of the brainstem. Several other inputs that affect the autonomic nervous system are
also included. These are: activation of the autonomic nervous system during exercise;
baroreceptor feedback effects from pulmonary artery pressure (PPA), left atrial
pressure (PLA), and an effect of low blood PO2 (PO2ART).
Note: Not shown in the diagram is also a variable (STA) that is normally zero.
When it is set to any level above zero, the value of the general autonomic multiplier (AU)
becomes fixed to the value of STA.
WHERE DO I PUT THIS NOTE?????
Encapsulation grouping component containing all the components in the Autonomics Model. The inputs and
outputs of the Autonomics Model must be passed by this component.
AU1:
Calculation of the effective systemic arterial pressure (PA1) by subtracting
any pressure drop (EXE) between the output point of the heart where the pressure
is equal to PA and the remainder of the aortic tree where the pressure will be
equal to PA1. This block allows simulation of aortic constriction at its root.
AU2:
A block that will allow one to set the effective systemic arterial pressure (PA1)
to any constant value desired by increasing the value CRRFLX to any value above zero.
As long as it remains at zero, there is no effect.
AU1:
Calculation of the effective systemic arterial pressure (PA1) by subtracting
any pressure drop (EXE) between the output point of the heart where the pressure
is equal to PA and the remainder of the aortic tree where the pressure will be
equal to PA1. This block allows simulation of aortic constriction at its root.
AU2:
A block that will allow one to set the effective systemic arterial pressure (PA1)
to any constant value desired by increasing the value CRRFLX to any value above zero.
As long as it remains at zero, there is no effect.
$\mathrm{PA1}=\begin{cases}\mathrm{CRRFLX} & \text{if $\mathrm{CRRFLX}> 0.0000001$}\\ \mathrm{PA}-\mathrm{EXE} & \text{otherwise}\end{cases}$
AU4:
Calculation of the nervous output from the chemoreceptors (AUC) at the
different systemic arterial pressure levels (PA1).
AU19:
Sensitivity control for increasing or decreasing the degree of response of
AUC to chemoreceptor nervous output.
AU4:
Calculation of the nervous output from the chemoreceptors (AUC) at the
different systemic arterial pressure levels (PA1).
AU19:
Sensitivity control for increasing or decreasing the degree of response of
AUC to chemoreceptor nervous output.
$\mathrm{AUC}=\begin{cases}0.005(80-\mathrm{PA1})\mathrm{AUC1} & \text{if $(\mathrm{PA1}< 80)\land (\mathrm{PA1}\ge 40)$}\\ 0.2\mathrm{AUC1} & \text{if $\mathrm{PA1}< 40$}\\ 0 & \text{otherwise}\end{cases}$
AU20:
Calculation of a nervous factor (AUC2) for effecting autonomic control of
the circulation depending on the peripheral level of oxygen in the blood (PO2ART).
O2CHMO is a sensitivity controller.
AU21:
Addition of the chemoreflex output (AUC) caused by activation of the chemoreceptors
by low arterial pressure plus the chemoreceptor output (AUC2) caused by reduced
arterial oxygen saturation (PO2ART). The output of Block 21 is equal to AUC3.
AU20:
Calculation of a nervous factor (AUC2) for effecting autonomic control of
the circulation depending on the peripheral level of oxygen in the blood (PO2ART).
O2CHMO is a sensitivity controller.
AU21:
Addition of the chemoreflex output (AUC) caused by activation of the chemoreceptors
by low arterial pressure plus the chemoreceptor output (AUC2) caused by reduced
arterial oxygen saturation (PO2ART). The output of Block 21 is equal to AUC3.
$\mathrm{AUC2}=\begin{cases}\mathrm{O2CHMO}(80-\mathrm{PO2ART}) & \text{if $(\mathrm{PO2ART}< 80)\land (\mathrm{PO2ART}\ge 40)$}\\ \mathrm{O2CHMO}\times 40 & \text{if $\mathrm{PO2ART}< 40$}\\ 0 & \text{otherwise}\end{cases}\mathrm{AUC3}=\mathrm{AUC}+\mathrm{AUC2}$
AU3:
Calculation of the nervous output from the baroreceptors (AUB) at the different
systemic arterial pressure levels (PA1).
AU6, AU7, and AU8:
Sensitivity control of the effect of baroreceptor reflex output (AUB) on the
autonomic nervous system. The output of this sensitivity controller is AU6A,
and the degree of sensitivity control is equal to AUX.
AU9, AU10, and AU11:
Time delay in the buildup of sympathetic output (AU6) that results from changes
in baroreceptor reflex nervous output (AU6A). The time constant of this delay
circuit is equal to BAROTC.
AU14, AU15, and AU16:
Calculation of adaptation of the baroreceptor feedback mechanism (AU4) over a
period of hours. The time constant of this adaptation is equal to AUK.
THIS IS COMMENTED OUT BECAUSE IT IS NOT IN THE MODSIM CODE
AU17:
This block sets AU6 equal to AU6A irrespective of the time constant for buildup
of the nervous effect of the baroreceptor reflex when the iteration interval for
solution of the equations is greater than .16666. This prevents some instability
when the equations are being calculated for long-term instead of short-term changes.
AU18:
Damping of baroreceptor autonomic feedback output (AU6) when long-term solutions are
being calculated, to prevent oscillation in the circuit. The output after the damping
is AU6C. MDMP sets the degree of damping.
AU3:
Calculation of the nervous output from the baroreceptors (AUB) at the different
systemic arterial pressure levels (PA1).
AU6, AU7, and AU8:
Sensitivity control of the effect of baroreceptor reflex output (AUB) on the
autonomic nervous system. The output of this sensitivity controller is AU6A,
and the degree of sensitivity control is equal to AUX.
AU6, AU7, and AU8:
Sensitivity control of the effect of baroreceptor reflex output (AUB) on the
autonomic nervous system. The output of this sensitivity controller is AU6A,
and the degree of sensitivity control is equal to AUX.
AU9, AU10, and AU11:
Time delay in the buildup of sympathetic output (AU6) that results from changes
in baroreceptor reflex nervous output (AU6A). The time constant of this delay
circuit is equal to BAROTC.
AU14, AU15, and AU16:
Calculation of adaptation of the baroreceptor feedback mechanism (AU4) over a
period of hours. The time constant of this adaptation is equal to AUK.
THIS IS COMMENTED OUT BECAUSE IT IS NOT IN THE MODSIM CODE
AU18:
Damping of baroreceptor autonomic feedback output (AU6) when long-term solutions are
being calculated, to prevent oscillation in the circuit. The output after the damping
is AU6C. MDMP sets the degree of damping.
$\mathrm{AUB}=\begin{cases}0.016667(160-\mathrm{PA1}) & \text{if $(\mathrm{PA1}< 160)\land (\mathrm{PA1}\ge 80)$}\\ 1.3336 & \text{if $\mathrm{PA1}< 80$}\\ 0 & \text{otherwise}\end{cases}\mathrm{A1B}=\mathrm{AUB}\mathrm{AUX}+1\mathrm{AU6A}=\mathrm{A1B}-\mathrm{AU4}\frac{d \mathrm{AU6}}{d \mathrm{time}}=\frac{\mathrm{AU6A}-\mathrm{AU6}}{\mathrm{BAROTC}}\mathrm{AU6C}=\mathrm{AU6}$
AU5:
Calculation of the nervous output (AUN) caused by activation of the central
nervous system ischemic reflex, resulting from reduced systemic arterial
pressure (PA1).
AU22:
Control of the sensitivity of the CNS ischemic reflex output by the sensitivity
controller AUN1.
AU5:
Calculation of the nervous output (AUN) caused by activation of the central
nervous system ischemic reflex, resulting from reduced systemic arterial
pressure (PA1).
AU22:
Control of the sensitivity of the CNS ischemic reflex output by the sensitivity
controller AUN1.
$\mathrm{AUN}=\begin{cases}0.04(40-\mathrm{PA1})\mathrm{AUN1} & \text{if $\mathrm{PA1}< 40$}\\ 0 & \text{otherwise}\end{cases}$
AU24, AU25, AU26, AU27, and AU28:
Calculation of an additional factor (AULP) that affects the total autonomic
response, caused by stretch receptors in the pulmonary vasculature. These
are in response to left atrial pressure (PLA), right atrial pressure (PRA),
and pulmonary arterial pressure (PPA). The sensitivity controller for these
effects is AULPM in Block 27.
AU24, AU25, AU26, AU27, and AU28:
Calculation of an additional factor (AULP) that affects the total autonomic
response, caused by stretch receptors in the pulmonary vasculature. These
are in response to left atrial pressure (PLA), right atrial pressure (PRA),
and pulmonary arterial pressure (PPA). The sensitivity controller for these
effects is AULPM in Block 27.
$\mathrm{AULP}=\frac{15}{\mathrm{PLA}+\mathrm{PRA}+\mathrm{PPA}}\mathrm{AULPM}+1$
AU29, AU30, AU31, and AU32:
Effect of the exercise nervous signal (EXC) on autonomic output. The
exponent (EXCXP) in Block 29 provides a curve fitting effect of exercise on the
autonomic output, and the factor (EXCML) is a sensitivity multiplier effect.
AU29, AU30, AU31, and AU32:
Effect of the exercise nervous signal (EXC) on autonomic output. The
exponent (EXCXP) in Block 29 provides a curve fitting effect of exercise on the
autonomic output, and the factor (EXCML) is a sensitivity multiplier effect.
$\mathrm{AUEX}=\mathrm{EXC}^{\mathrm{EXCXP}}$
AU23:
Summation of the different nervous output controls of autonomic stimulation, AUC3
from the chemoreceptor component, AU6C from the arterial baroreceptor reflex component,
and the output of Block 22 from the CNS ischemic reflex component.
AU33:
Summation of all of the different factors affecting autonomic stimulation
of the circulation, giving a total output of AUTTL.
AU34:
Limitation of the lower level of autonomic stimulation of the circulatory system
so that this cannot fall below the level of zero.
AU23:
Summation of the different nervous output controls of autonomic stimulation, AUC3
from the chemoreceptor component, AU6C from the arterial baroreceptor reflex component,
and the output of Block 22 from the CNS ischemic reflex component.
AU33:
Summation of all of the different factors affecting autonomic stimulation
of the circulation, giving a total output of AUTTL.
AU34:
Limitation of the lower level of autonomic stimulation of the circulatory system
so that this cannot fall below the level of zero.
$\mathrm{AUTTL1}=\mathrm{AUEX}\mathrm{AULP}(\mathrm{AUC3}+\mathrm{AU6C}+\mathrm{AUN})\mathrm{EXCML}+1\mathrm{AUTTL}=\begin{cases}0 & \text{if $\mathrm{AUTTL1}< 0$}\\ \mathrm{AUTTL1} & \text{otherwise}\end{cases}$
AU35, AU36, and AU37:
This is a time-delay circuit to delay the peripheral changes that occur in the
circulatory system for a fraction of a minute after changes in the nervous component
take place. This results from the need to build up autonomic transmitter substance
and for the different organs to respond. The output after this delay circuit is AU1.
The time constant of the delay is AUDMP.
AU38:
This is a curve fitting step to fit the output strength of functional reaction to
sympathetic stimulation (AU) to the input level of nervous stimulation (AU1).
The maximum level of AU is set by the equation in this block to equal AUMAX.
AUSLPC determines the slope of the relationship.
AU39:
This sets the minimum level of AU (the output functional reaction) equal to a
minimum value of AUMIN.
AU35, AU36, and AU37:
This is a time-delay circuit to delay the peripheral changes that occur in the
circulatory system for a fraction of a minute after changes in the nervous component
take place. This results from the need to build up autonomic transmitter substance
and for the different organs to respond. The output after this delay circuit is AU1.
The time constant of the delay is AUDMP.
AU35, AU36, and AU37:
This is a time-delay circuit to delay the peripheral changes that occur in the
circulatory system for a fraction of a minute after changes in the nervous component
take place. This results from the need to build up autonomic transmitter substance
and for the different organs to respond. The output after this delay circuit is AU1.
The time constant of the delay is AUDMP.
AU38:
This is a curve fitting step to fit the output strength of functional reaction to
sympathetic stimulation (AU) to the input level of nervous stimulation (AU1).
The maximum level of AU is set by the equation in this block to equal AUMAX.
AUSLPC determines the slope of the relationship.
AU39:
This sets the minimum level of AU (the output functional reaction) equal to a
minimum value of AUMIN.
$\mathrm{DAU}=\frac{\mathrm{AUTTL}-\mathrm{AU1}}{\mathrm{AUDMP}}\frac{d \mathrm{AU1}}{d \mathrm{time}}=\mathrm{DAU}\mathrm{AUT}=\mathrm{AUMAX}-\frac{\mathrm{AUMAX}-1}{e^{\mathrm{AUSLP}(\mathrm{AU1}-1)}}\mathrm{AU}=\begin{cases}\mathrm{AUMIN} & \text{if $\mathrm{AUT}< \mathrm{AUMIN}$}\\ \mathrm{AUT} & \text{otherwise}\end{cases}$
AU40 and AU41:
Calculation of the effect on venous vascular resistance (VVR) of different
levels of autonomic functional reaction (AU). The sensitivity control is AUL,
and VV9 determines the range.
AU42:
A step to reduce the output effect of normal autonomic reaction (AU) equal to
zero (AUO) so that differences from control levels can be activated in
Blocks 43, 45, 47, 50, and 53.
AU43 and AU44:
Sensitivity control for the autonomic effect on the heart (AUH). The sensitivity
is controlled by AUV.
AU45 and AU46:
Sensitivity control of the autonomic effect on heart rate (AUR). The sensitivity
is controlled by AUS.
AU47 and AU48:
Calculation of the autonomic effect on muscle metabolism (AOM). The sensitivity
control for this variable is O2A.
AU50, AU51, and AU52:
Calculation of an autonomic multiplier effect that is used at multiple points in
the circulatory system (AUM). The values AUM1 and AUM2 are curve fitting controls.
AU53 and AU54:
Sensitivity control for adjusting the autonomic multiplier effect on the
venous tree (AVE). The variable (AUY) controls the sensitivity.
AU40 and AU41:
Calculation of the effect on venous vascular resistance (VVR) of different
levels of autonomic functional reaction (AU). The sensitivity control is AUL,
and VV9 determines the range.
AU42:
A step to reduce the output effect of normal autonomic reaction (AU) equal to
zero (AUO) so that differences from control levels can be activated in
Blocks 43, 45, 47, 50, and 53.
AU43 and AU44:
Sensitivity control for the autonomic effect on the heart (AUH). The sensitivity
is controlled by AUV.
AU45 and AU46:
Sensitivity control of the autonomic effect on heart rate (AUR). The sensitivity
is controlled by AUS.
AU47 and AU48:
Calculation of the autonomic effect on muscle metabolism (AOM). The sensitivity
control for this variable is O2A.
AU50, AU51, and AU52:
Calculation of an autonomic multiplier effect that is used at multiple points in
the circulatory system (AUM). The values AUM1 and AUM2 are curve fitting controls.
AU53 and AU54:
Sensitivity control for adjusting the autonomic multiplier effect on the
venous tree (AVE). The variable (AUY) controls the sensitivity.
$\mathrm{VVR}=\mathrm{VV9}-\mathrm{AU}\mathrm{AUL}+\mathrm{AUL}\mathrm{AUO}=\mathrm{AU}-1\mathrm{AUH}=\mathrm{AUO}\mathrm{AUV}+1\mathrm{AUR}=\mathrm{AUO}\mathrm{AUS}+1\mathrm{AOM}=\mathrm{AUO}\mathrm{O2A}+1\mathrm{AUM}=(\mathrm{AUO}\mathrm{AUM1}+1)^{\mathrm{AUM2}}\mathrm{AVE}=\mathrm{AUO}\mathrm{AUY}+1$
CAPILLARY DYNAMICS, TISSUE FLUID, AND TISSUE PROTEIN
This portion of the model calculates the movement of fluid and protein through the
capillary membrane. It also calculates the volumes of fluid in the free fluid space
of the interstitium and in the gel fluid space. It calculates the pressures in both
of these fluids as well as the so-called solid tissue pressure caused by the compression
of solid elements against other portions of the interstitium. In addition, the quantities
of proteins and their concentrations in both the free fluid and the gel fluid are calculated.
And, finally, the flow of both fluid and proteins in the lymph system are computed, as well
as the overall body protein balance.
Encapsulation grouping component containing all the components in the Capillary Dynamics Model. The inputs and
outputs of the Capillary Dynamics Model must be passed by this component.
Containment grouping component for "capillary_pressure" and
"rate_of_fluid_out_of_capillaries".
CP1 and CP2:
The capillary pressure (PC) is equal to the resistance to blood flow in the
small veins (RVS) times the blood flow in the small veins (BFN), times a constant
to represent the additional normal flow through the muscles and kidneys, plus
the pressure in the large vein circulation. The value of the capillary pressure (PC)
is assumed to be the same in all tissues of the body.
CP1 and CP2:
The capillary pressure (PC) is equal to the resistance to blood flow in the
small veins (RVS) times the blood flow in the small veins (BFN), times a constant
to represent the additional normal flow through the muscles and kidneys, plus
the pressure in the large vein circulation. The value of the capillary pressure (PC)
is assumed to be the same in all tissues of the body.
$\mathrm{PC}=\mathrm{RVS}\times 1.7\mathrm{BFN}+\mathrm{PVS}$
CP3:
The pressure gradient for filtration of fluid across the capillary membranes (PCGR)
is equal to the capillary pressure (PC), plus the colloid osmotic pressure of the
tissue gel (PTC), minus the plasma colloid osmotic pressure (PPC), minus the hydrostatic
pressure of the gel (PGH).
CP4:
The rate of filtration of fluid out of the capillaries of the systemic circulation (CFILTR)
is equal to the pressure gradient across the capillary membranes (PCGR) times the capillary
filtration coefficient (CFC).
CP5:
The total rate of movement of fluid out of all the systemic capillaries of the body (VTC) is
equal to the rate of filtration from the systemic capillaries (CFILTR) plus the rate of
leakage of whole plasma though leaky capillaries (VTCPL).
CP3:
The pressure gradient for filtration of fluid across the capillary membranes (PCGR)
is equal to the capillary pressure (PC), plus the colloid osmotic pressure of the
tissue gel (PTC), minus the plasma colloid osmotic pressure (PPC), minus the hydrostatic
pressure of the gel (PGH).
CP4:
The rate of filtration of fluid out of the capillaries of the systemic circulation (CFILTR)
is equal to the pressure gradient across the capillary membranes (PCGR) times the capillary
filtration coefficient (CFC).
CP5:
The total rate of movement of fluid out of all the systemic capillaries of the body (VTC) is
equal to the rate of filtration from the systemic capillaries (CFILTR) plus the rate of
leakage of whole plasma though leaky capillaries (VTCPL).
$\mathrm{VTC}=(\mathrm{PC}-\mathrm{PPC}-\mathrm{PGH}+\mathrm{PTC})\mathrm{CFC}+\mathrm{VTCPL}$
Containment grouping component for "plasma_volume", "plasma_protein_concentration",
"protein_destruction_and_formation", "plasma_leakage", "protein_influx_into_interstitium",
"total_plasma_protein" and "plasma_colloid_osmotic_pressure".
CP10:
The rate of change of plasma volume (VPD) is equal to the rate of inflow of
fluid into the plasma by way of the lymph (VTL) minus the rate of loss of
fluid from the systemic tissue capillaries (VTC), minus the rate of loss of
fluid from the pulmonary capillaries (DFP), and plus any rate of transfusion
of plasma into the circulation.
CP11:
The plasma volume (VP) is determined by integrating the rate of change of the
plasma volume (VPD) with respect to time.
CP10:
The rate of change of plasma volume (VPD) is equal to the rate of inflow of
fluid into the plasma by way of the lymph (VTL) minus the rate of loss of
fluid from the systemic tissue capillaries (VTC), minus the rate of loss of
fluid from the pulmonary capillaries (DFP), and plus any rate of transfusion
of plasma into the circulation.
CP11:
The plasma volume (VP) is determined by integrating the rate of change of the
plasma volume (VPD) with respect to time.
$\mathrm{VPD}=\mathrm{VTL}-\mathrm{VTC}-\mathrm{DFP}+\mathrm{TRPL}\frac{d \mathrm{VP}}{d \mathrm{time}}=\mathrm{VPD}$
CP35:
The concentration of protein in the plasma (CPP) is equal to the total quantity
of protein in the plasma (RPR) divided by the plasma volume (VP).
CP35:
The concentration of protein in the plasma (CPP) is equal to the total quantity
of protein in the plasma (RPR) divided by the plasma volume (VP).
$\mathrm{CPP}=\frac{\mathrm{PRP}}{\mathrm{VP}}$
CP37 and CP38:
A factor related to the rate of destruction of protein by the liver (CPPD) is
equal to plasma protein concentration CPP) minus a critical protein limiting value (CPR).
Block CP38 limits the rate of destruction of protein by the liver to a lower limit of zero.
CP39 and CP40:
Curve-fitting blocks to calculate the rate of destruction of protein by the
liver (LPPRDS) from the factor (CPPD) calculated in Block 37. The curve-fitting
constants are LPDE and LPK.
CP41:
Net rate of protein exchange between the liver and the plasma (DLP) is equal to the
rate of production of protein by the liver (LPPR) minus the rate of destruction of
protein by the liver (LPPRDS).
CP37 and CP38:
A factor related to the rate of destruction of protein by the liver (CPPD) is
equal to plasma protein concentration CPP) minus a critical protein limiting value (CPR).
Block CP38 limits the rate of destruction of protein by the liver to a lower limit of zero.
CP39 and CP40:
Curve-fitting blocks to calculate the rate of destruction of protein by the
liver (LPPRDS) from the factor (CPPD) calculated in Block 37. The curve-fitting
constants are LPDE and LPK.
CP41:
Net rate of protein exchange between the liver and the plasma (DLP) is equal to the
rate of production of protein by the liver (LPPR) minus the rate of destruction of
protein by the liver (LPPRDS).
$\mathrm{CPPD}=\begin{cases}0 & \text{if $\mathrm{CPP}-\mathrm{CPR}< 0$}\\ \mathrm{CPP}-\mathrm{CPR} & \text{otherwise}\end{cases}\mathrm{DLP}=\mathrm{LPPR}-\mathrm{CPPD}^{\mathrm{LPDE}}\mathrm{LPK}$
CP25 and CP26:
Calculation of a pressure gradient to cause whole plasma leakage through the
capillary membranes (PRCD), calculated by adding the capillary pressure (PC) and
subtracting a critical capillary pressure (PCR) below which no whole plasma will leak.
Block CP26 limits the rate of plasma leakage (PRCD) to a lower level of zero.
CP27 and CP28:
The rate of leakage of whole plasma through the capillary membrane (VTCPL) is equal
to the pressure gradient for leakage of plasma (PRCD) times a constant (CPK) and this
product raised to a power (PCE).
CP25 and CP26:
Calculation of a pressure gradient to cause whole plasma leakage through the
capillary membranes (PRCD), calculated by adding the capillary pressure (PC) and
subtracting a critical capillary pressure (PCR) below which no whole plasma will leak.
Block CP26 limits the rate of plasma leakage (PRCD) to a lower level of zero.
CP27 and CP28:
The rate of leakage of whole plasma through the capillary membrane (VTCPL) is equal
to the pressure gradient for leakage of plasma (PRCD) times a constant (CPK) and this
product raised to a power (PCE).
$\mathrm{PRCD}=\begin{cases}0 & \text{if $\mathrm{PC}-\mathrm{PCR}< 0$}\\ \mathrm{PC}-\mathrm{PCR} & \text{otherwise}\end{cases}\mathrm{VTCPL}=(\mathrm{PRCD}\mathrm{CPK})^{\mathrm{PCE}}$
CP29:
Rate of leakage of plasma protein in the leaking whole plasma into the interstitium
from the circulating plasma (TVCPL) equals the volume of plasma leaking (VTCPL)
times the concentration of protein in the plasma (CPP).
CP30 and CP31:
The rate of diffusion of protein through the capillary pores (PLPRDF) is equal
to the difference between plasma concentration of protein (CPP) minus the concentration
of protein in the interstitial free fluid (CPI) times a constant in Block CP31.
CP32:
Rate of influx of protein into the interstitium from the plasma in the capillaries (DPC)
is equal to the rate of protein leaking in the whole plasma (VTCPL) plus the rate of
diffusion of protein through the capillary pores (PLPRDF).
CP29:
Rate of leakage of plasma protein in the leaking whole plasma into the interstitium
from the circulating plasma (TVCPL) equals the volume of plasma leaking (VTCPL)
times the concentration of protein in the plasma (CPP).
CP30 and CP31:
The rate of diffusion of protein through the capillary pores (PLPRDF) is equal
to the difference between plasma concentration of protein (CPP) minus the concentration
of protein in the interstitial free fluid (CPI) times a constant in Block CP31.
CP32:
Rate of influx of protein into the interstitium from the plasma in the capillaries (DPC)
is equal to the rate of protein leaking in the whole plasma (VTCPL) plus the rate of
diffusion of protein through the capillary pores (PLPRDF).
$\mathrm{DPC}=\mathrm{VTCPL}\mathrm{CPP}-\mathrm{CPP}\times 0.00104$
CP33: The rate of change of the quantity of protein in the plasma (DPP)
is equal to the net rate of formation of protein by the liver (DLP), plus
the rate of return of protein to the circulation in the lymph (DPL), minus
the loss of protein from the circulation into the systemic interstitium (DPC),
minus the rate of loss of protein through the pulmonary capillary membranes (PPD).
CP34:
The total quantity of protein in the plasma (PRP) is determined by integrating
the rate of change of the protein in the plasma (DPP) with respect to time.
CP33: The rate of change of the quantity of protein in the plasma (DPP)
is equal to the net rate of formation of protein by the liver (DLP), plus
the rate of return of protein to the circulation in the lymph (DPL), minus
the loss of protein from the circulation into the systemic interstitium (DPC),
minus the rate of loss of protein through the pulmonary capillary membranes (PPD).
CP34:
The total quantity of protein in the plasma (PRP) is determined by integrating
the rate of change of the protein in the plasma (DPP) with respect to time.
$\mathrm{DPP}=\mathrm{DLP}+\mathrm{DPL}-\mathrm{DPC}-\mathrm{PPD}+\mathrm{TRPL}\times 72\frac{d \mathrm{PRP}}{d \mathrm{time}}=\mathrm{DPP}$
CP36:
The plasma colloid osmotic pressure (PPC) is calculated in this block from
the concentration of protein in the plasma (CPP).
CP36:
The plasma colloid osmotic pressure (PPC) is calculated in this block from
the concentration of protein in the plasma (CPP).
$\mathrm{PPC}=0.28\mathrm{CPP}+0.0019\mathrm{CPP}^{2}$
Containment grouping component for "total_systemic_fluid_volume",
"interstitial_fluid_volume", "total_interstitial_protein",
"interstitial_protein_concentration", "interstitial_colloid_osmotic_pressure"
and "lymph_protein_flow".
CP6:
The total fluid volume in the systemic circulation portion of the body (VTS)
is equal to the total extracellular fluid volume (VEC) minus plasma volume (VP)
and minus pulmonary extracellular fluid volume (VPF).
CP6:
The total fluid volume in the systemic circulation portion of the body (VTS)
is equal to the total extracellular fluid volume (VEC) minus plasma volume (VP)
and minus pulmonary extracellular fluid volume (VPF).
$\mathrm{VTS}=\mathrm{VEC}-\mathrm{VP}-\mathrm{VPF}$
CP7, CP7A, CP7B, CP7C, CP7D, and CP7E:
Calculation of the effect of tissue space stress relaxation on volume of fluid
in the interstitial space (VTS1) after higher or lower than normal volumes
(VTS greater or lower than 12) have existed in the tissue spaces for prolonged
periods of time. The sensitivity control for the extent of tissue space stress
relaxation is TSSLML, and the reciprocal of the time constant of the effect
is TSSLTC.
CP7, CP7A, CP7B, CP7C, CP7D, and CP7E:
Calculation of the effect of tissue space stress relaxation on volume of fluid
in the interstitial space (VTS1) after higher or lower than normal volumes
(VTS greater or lower than 12) have existed in the tissue spaces for prolonged
periods of time. The sensitivity control for the extent of tissue space stress
relaxation is TSSLML, and the reciprocal of the time constant of the effect
is TSSLTC.
CP7, CP7A, CP7B, CP7C, CP7D, and CP7E:
Calculation of the effect of tissue space stress relaxation on volume of fluid
in the interstitial space (VTS1) after higher or lower than normal volumes
(VTS greater or lower than 12) have existed in the tissue spaces for prolonged
periods of time. The sensitivity control for the extent of tissue space stress
relaxation is TSSLML, and the reciprocal of the time constant of the effect
is TSSLTC.
$\frac{d \mathrm{VTS2}}{d \mathrm{time}}=((\mathrm{VTS}-12)\mathrm{TSSLML}-\mathrm{VTS2})\mathrm{TSSLTC}\mathrm{VTS1}=\mathrm{VTS}-\mathrm{VTS2}$
CP42:
The rate of change of protein in the systemic interstitium (DPI) is equal to
the rate of leakage from the plasma of protein through the systemic capillary
membranes (DPC) minus the rate of return of the protein from the systemic
interstitium by way of the lymphatics (DPL).
CP43:
The total tissue protein (TSP) is calculated by integrating the rate of
change of protein in the interstitium (DPI) with respect to time.
CP42:
The rate of change of protein in the systemic interstitium (DPI) is equal to
the rate of leakage from the plasma of protein through the systemic capillary
membranes (DPC) minus the rate of return of the protein from the systemic
interstitium by way of the lymphatics (DPL).
CP43:
The total tissue protein (TSP) is calculated by integrating the rate of
change of protein in the interstitium (DPI) with respect to time.
$\mathrm{DPI}=\mathrm{DPC}-\mathrm{DPL}\frac{d \mathrm{TSP}}{d \mathrm{time}}=\mathrm{DPI}$
CP44:
The concentration of protein in the interstitium (CPI) is equal to the total
quantity of protein in the interstitium (TSP) divided by the total volume of
fluid in the systemic interstitium (VTS).
CP44:
The concentration of protein in the interstitium (CPI) is equal to the total
quantity of protein in the interstitium (TSP) divided by the total volume of
fluid in the systemic interstitium (VTS).
$\mathrm{CPI}=\frac{\mathrm{TSP}}{\mathrm{VTS}}$
CP45:
The colloid osmotic pressure of the free fluid in the interstitium (PTCPR) is
calculated in this block from the concentration of protein in the interstitium (CPI).
CP45:
The colloid osmotic pressure of the free fluid in the interstitium (PTCPR) is
calculated in this block from the concentration of protein in the interstitium (CPI).
$\mathrm{PTCPR}=0.28\mathrm{CPI}+0.0019\mathrm{CPI}^{2}$
CP46:
The rate of return of protein to the circulation by way of the lymph (DPL) is
equal to the concentration of protein in the systemic interstitium (CPI) times
the rate of lymph flow from the interstitium (VTL).
CP46:
The rate of return of protein to the circulation by way of the lymph (DPL) is
equal to the concentration of protein in the systemic interstitium (CPI) times
the rate of lymph flow from the interstitium (VTL).
$\mathrm{DPL}=\mathrm{CPI}\mathrm{VTL}$
Containment grouping component for "hydrostatic_pressure_of_tissue_gel",
"total_osmotic_pressure_of_tissue_gel", "total_tissue_pressure",
"interstial_free_fluid_pressure", "interstitial_solid_tissue_pressure",
"lymph_flow", "interstitial_gel_volume" and "interstitial_free_fluid_volume".
CP13 and CP14:
Calculation of the concentration of hyaluronic acid in the interstitium (CHY)
from the total quantity of hyaluronic acid in the interstitium (HYL) and the
total volume of fluid in the interstitium (VTS). The exponent CMPTSS describes
the non-linearity of this effect.
CP15 and CP16:
Calculation of the hydrostatic pressure in the tissue gel (PGH) from the
concentration of hyaluronic acid in the interstitium (CHY) and the total
tissue pressure (PTT). (The hyaluronic acid acts as an elastic body that
expands, and, therefore, creates a negative pressure.)
CP13 and CP14:
Calculation of the concentration of hyaluronic acid in the interstitium (CHY)
from the total quantity of hyaluronic acid in the interstitium (HYL) and the
total volume of fluid in the interstitium (VTS). The exponent CMPTSS describes
the non-linearity of this effect.
CP15 and CP16:
Calculation of the hydrostatic pressure in the tissue gel (PGH) from the
concentration of hyaluronic acid in the interstitium (CHY) and the total
tissue pressure (PTT). (The hyaluronic acid acts as an elastic body that
expands, and, therefore, creates a negative pressure.)
$\mathrm{CHY}=\left(\frac{\frac{\mathrm{HYL}}{\mathrm{VTS}}}{5}\right)^{\mathrm{CMPTSS}}\mathrm{PGH}=\mathrm{CHY}\mathrm{PGHF}+\mathrm{PTT}$
CP17:
The osmotic pressure caused by the hyaluronic acid in the gel (POSHYL)
is equal to the concentration of hyaluronic acid in the gel (CHY) times
a constant.
CP18:
The total osmotic pressure of the tissue gel (PTC) is equal to the osmotic
pressure caused by the hyaluronic acid in the gel (POSHYL) times the colloid
osmotic pressure caused by the plasma protein in the free fluid of the
interstitium (PTCPR) times a constant (GCOPF).
CP17:
The osmotic pressure caused by the hyaluronic acid in the gel (POSHYL)
is equal to the concentration of hyaluronic acid in the gel (CHY) times
a constant.
CP18:
The total osmotic pressure of the tissue gel (PTC) is equal to the osmotic
pressure caused by the hyaluronic acid in the gel (POSHYL) times the colloid
osmotic pressure caused by the plasma protein in the free fluid of the
interstitium (PTCPR) times a constant (GCOPF).
$\mathrm{POSHYL}=\mathrm{CHY}\times 2\mathrm{PTC}=\mathrm{POSHYL}\mathrm{PTCPR}\mathrm{GCOPF}$
CP12:
Calculation of the total tissue pressure (PTT) as a function of the total
interstitial fluid volume (VTS1).
CP12:
Calculation of the total tissue pressure (PTT) as a function of the total
interstitial fluid volume (VTS1).
$\mathrm{PTT}=\left(\frac{\mathrm{VTS1}-\mathrm{VTSF}}{\mathrm{VTSF}}\right)^{2}\times 1$
CP19:
The pressure in the free interstitial fluid (PIF) is equal to the hydrostatic
pressure in the tissue gel (PGH) minus the colloid osmotic pressure of the
hyaluronic acid in the tissue gel (POSHYL).
CP19:
The pressure in the free interstitial fluid (PIF) is equal to the hydrostatic
pressure in the tissue gel (PGH) minus the colloid osmotic pressure of the
hyaluronic acid in the tissue gel (POSHYL).
$\mathrm{PIF}=\mathrm{PGH}-\mathrm{POSHYL}$
CP20:
The solid tissue pressure of the interstitium (PTS) is equal to the total
tissue pressure (PTT) minus the pressure in the free fluid of the interstitium (PIF).
CP20:
The solid tissue pressure of the interstitium (PTS) is equal to the total
tissue pressure (PTT) minus the pressure in the free fluid of the interstitium (PIF).
$\mathrm{PTS}=\mathrm{PTT}-\mathrm{PIF}$
CP21 and CP22:
The pressure gradient that promotes lymph flow (PLD) is equal to a constant (PLDF)
that is determined by the pumping action of the lymphatics plus the interstitial
free fluid pressure (PIF), minus the total tissue pressure (PTT). Block CP22
limits the upper level of this pressure gradient.
CP23 and CP24:
The rate of lymph flow (VTL) is equal to the pressure gradient that causes
lymph flow (PLD) times a constant representing lymphatic conductance.
Block CP24 limits the lower level of lymph flow to zero.
CP21:
The pressure gradient that promotes lymph flow (PLD) is equal to a constant (PLDF)
that is determined by the pumping action of the lymphatics plus the interstitial
free fluid pressure (PIF), minus the total tissue pressure (PTT).
CP22:
Block CP22 limits the upper level of this pressure gradient.
] CP23 and CP24:
The rate of lymph flow (VTL) is equal to the pressure gradient that causes
lymph flow (PLD) times a constant representing lymphatic conductance.
Block CP24 limits the lower level of lymph flow to zero.
$\mathrm{PLD1}=\mathrm{PIF}+\mathrm{PLDF}-\mathrm{PTT}\mathrm{PLD}=\begin{cases}7 & \text{if $\mathrm{PLD1}> 7$}\\ \mathrm{PLD1} & \text{otherwise}\end{cases}\mathrm{VTL}=\begin{cases}0 & \text{if $\mathrm{PLD}< 0$}\\ \mathrm{PLD}\times 0.02 & \text{otherwise}\end{cases}$
CP8:
This block gives a function curve that relates the volume of the tissue gel (VG)
to the total interstitial fluid volume (VTS).
CP8:
This block gives a function curve that relates the volume of the tissue gel (VG)
to the total interstitial fluid volume (VTS).
$\mathrm{VG}=\begin{cases}0 & \text{if $\mathrm{VTS}\le 0$}\\ 0+\frac{(11.4-0)(\mathrm{VTS}-0)}{12-0} & \text{if $(\mathrm{VTS}> 0)\land (\mathrm{VTS}\le 12)$}\\ 11.4+\frac{(14-11.4)(\mathrm{VTS}-12)}{15-12} & \text{if $(\mathrm{VTS}> 12)\land (\mathrm{VTS}\le 15)$}\\ 14+\frac{(16-14)(\mathrm{VTS}-15)}{18-15} & \text{if $(\mathrm{VTS}> 15)\land (\mathrm{VTS}\le 18)$}\\ 16+\frac{(17.3-16)(\mathrm{VTS}-18)}{21-18} & \text{if $(\mathrm{VTS}> 18)\land (\mathrm{VTS}\le 21)$}\\ 17.3+\frac{(18-17.3)(\mathrm{VTS}-21)}{24-21} & \text{if $(\mathrm{VTS}> 21)\land (\mathrm{VTS}\le 24)$}\\ 18 & \text{otherwise}\end{cases}$
CP9:
The volume of free fluid in the interstitium (VIF) is equal to the total
interstitial fluid volume (VTS) minus the volume of fluid in the tissue gel (VG).
CP9:
The volume of free fluid in the interstitium (VIF) is equal to the total
interstitial fluid volume (VTS) minus the volume of fluid in the tissue gel (VG).
$\mathrm{VIF}=\mathrm{VTS}-\mathrm{VG}$
This section calculates the flow of blood around the circuit from arteries, to veins,
to heart, to lungs, and back to heart again. It also calculates the resistances and
the effect of various factors on the resistances. In other words, this section
presents the basic hemodynamics of the circulatory system.
Encapsulation grouping component containing all the components in the Circulatory Dynamics Model.
The inputs and outputs of the Circulatory Dynamics Model must be passed by this component.
CD75:
The blood volume change that must be distributed to the different segments of the
circulation since the last iteration (VBD) is calculated by subtracting the volumes
of the various vascular segments (VAS, VVS, VRA, VLA, and VPA) from the total blood
volume, that is, plasma volume (VP) plus red cell volume (VRC).
CD75:
The blood volume change that must be distributed to the different segments of the
circulation since the last iteration (VBD) is calculated by subtracting the volumes
of the various vascular segments (VAS, VVS, VRA, VLA, and VPA) from the total blood
volume, that is, plasma volume (VP) plus red cell volume (VRC).
$\mathrm{VBD}=\frac{\mathrm{VP}+\mathrm{VRC}-\mathrm{VVS1}-\mathrm{VAS1}-\mathrm{VLA1}-\mathrm{VPA1}-\mathrm{VRA1}}{2}$
Containment grouping component for "right_atrial_blood_volume", "right_atrial_pressure",
and "autonomic_stimulation_effect_on_right_atrial_pressure".
CD20:
The rate of change of blood volume in the right atrium (DRA) is equal to the rate
of blood flow into the right atrium from the veins (QVO) minus the rate of outflow
of blood from the right atrium through the right heart (QRO).
CD21:
A temporary value for the volume of blood in the right atrium is calculated by
integrating the rate of change of blood volume in the right atrium (DRA).
CD22:
The portion of any change in total blood volume (VBD) that is ascribable to the
right atrium is calculated by multiplying the total blood volume change (VBD)
since the last iteration times a constant.
CD23:
The instantaneous volume of blood in the right atrium (VRA) is equal to the
temporary value calculated in CD21 plus the volume of blood caused by a change
in blood volume as calculated in CD22.
CD20:
The rate of change of blood volume in the right atrium (DRA) is equal to the rate
of blood flow into the right atrium from the veins (QVO) minus the rate of outflow
of blood from the right atrium through the right heart (QRO).
CD21:
A temporary value for the volume of blood in the right atrium is calculated by
integrating the rate of change of blood volume in the right atrium (DRA).
CD22:
The portion of any change in total blood volume (VBD) that is ascribable to the
right atrium is calculated by multiplying the total blood volume change (VBD)
since the last iteration times a constant.
CD23:
The instantaneous volume of blood in the right atrium (VRA) is equal to the
temporary value calculated in CD21 plus the volume of blood caused by a change
in blood volume as calculated in CD22.
$\mathrm{DRA}=\mathrm{QVO}-\mathrm{QRO}\frac{d \mathrm{VRA1}}{d \mathrm{time}}=\mathrm{DRA}\mathrm{VRA}=\mathrm{VRA1}+\mathrm{VBD}\times 0.0574$
CD24:
The volume of excess blood in the right atrium (VRE) is equal to the
instantaneous volume of blood in the right atrium (VRA) minus a constant value
which represents the volume of blood in the right atrium when the atrium is
filled to a level that will cause no increase in atrial pressure and the
pressure is still zero.
CD25:
Temporary right atrial pressure (PRA) at normal level of autonomic stimulation (AU=1)
is equal to the excess volume of blood in the right atrium (VRE) divided by a constant
value which represents the capacitance of the right atrium.
CD24:
The volume of excess blood in the right atrium (VRE) is equal to the
instantaneous volume of blood in the right atrium (VRA) minus a constant value
which represents the volume of blood in the right atrium when the atrium is
filled to a level that will cause no increase in atrial pressure and the
pressure is still zero.
CD25:
Temporary right atrial pressure (PRA) at normal level of autonomic stimulation (AU=1)
is equal to the excess volume of blood in the right atrium (VRE) divided by a constant
value which represents the capacitance of the right atrium.
$\mathrm{VRE}=\mathrm{VRA}-0.1\mathrm{PRA}=\frac{\mathrm{VRE}}{0.005}$
CD25C, CD25D, CD25E, and CD25F:
Calculation of the shift of the temporary calculated right atrial pressure of PRA
to its actual value of PRA1 when the level of autonomic stimulation AU) changes to
some other value besides the normal value of 1.0. The value of HTAUML determines
the ratio of the slope of changing PRA1 to slope of changing PRA.
CD25C, CD25D, CD25E, and CD25F:
Calculation of the shift of the temporary calculated right atrial pressure of PRA
to its actual value of PRA1 when the level of autonomic stimulation AU) changes to
some other value besides the normal value of 1.0. The value of HTAUML determines
the ratio of the slope of changing PRA1 to slope of changing PRA.
$\mathrm{PRA1}=(\mathrm{PRA}+8)(\mathrm{HTAUML}(\mathrm{AU}-1)+1)-8$
Containment grouping component for "pressure_effect_on_right_ventricular_pumping",
"pumping_effectiveness_of_right_ventricle" and "right_ventricular_output".
CD68:
Calculation of a multiplier factor (PP2) from three factors that affect the
ability of the right heart to withstand increasing output loads: The effect
of the pulmonary arterial pressure itself (PPA), the effect of changes in heart
arterial oxygen saturation in the coronary blood flow (OSA), and the effect of
sympathetic stimulation (AUH).
CD69:
Function curve relating the multiplier factor from CD68 (PP2) to a multiplier
factor for pumping strength of the right heart musculature (RVM).
CD68:
Calculation of a multiplier factor (PP2) from three factors that affect the
ability of the right heart to withstand increasing output loads: The effect
of the pulmonary arterial pressure itself (PPA), the effect of changes in heart
arterial oxygen saturation in the coronary blood flow (OSA), and the effect of
sympathetic stimulation (AUH).
CD69:
Function curve relating the multiplier factor from CD68 (PP2) to a multiplier
factor for pumping strength of the right heart musculature (RVM).
$\mathrm{PP2}=\frac{\frac{\mathrm{PPA}}{\mathrm{AUH}}}{\mathrm{OSA}}\mathrm{RVM}=\begin{cases}1.06 & \text{if $\mathrm{PP2}\le 0$}\\ 1.06+\frac{(0.97-1.06)(\mathrm{PP2}-0)}{32-0} & \text{if $(\mathrm{PP2}> 0)\land (\mathrm{PP2}\le 32)$}\\ 0.97+\frac{(0.93-0.97)(\mathrm{PP2}-32)}{38.4-32} & \text{if $(\mathrm{PP2}> 32)\land (\mathrm{PP2}\le 38.4)$}\\ 0.93+\frac{(0.8-0.93)(\mathrm{PP2}-38.4)}{48-38.4} & \text{if $(\mathrm{PP2}> 38.4)\land (\mathrm{PP2}\le 48)$}\\ 0.8+\frac{(0.46-0.8)(\mathrm{PP2}-48)}{60.8-48} & \text{if $(\mathrm{PP2}> 48)\land (\mathrm{PP2}\le 60.8)$}\\ 0.46+\frac{(0-0.46)(\mathrm{PP2}-60.8)}{72-60.8} & \text{if $(\mathrm{PP2}> 60.8)\land (\mathrm{PP2}\le 72)$}\\ 0 & \text{otherwise}\end{cases}$
CD70 and CD71:
Calculation of the proportion of the pumping effectiveness of the right heart that is
caused by left heart contraction. This is determined by the normal proportion (QRF)
times the instantaneous output of the left heart (QLO) and divided by the normalized
output of the left heart (QLN) when all factors affecting left heart strength are normal.
CD72 and CD73:
Calculation of the proportion of the right heart pumping effectiveness that is caused
by right heart musculature contraction itself, calculated from multiple factors that
affect right heart pumping including the normal proportion of right heart pumping that
is caused by left heart pumping (QRF), the strength of the right heart (HSR) relative
to its normal strength, the loading effect of pulmonary arterial pressure on the
right heart (RVM), the effect of autonomic stimulation on right heart strength (AUH),
the effect of possible deterioration of the right heart from shock and other factors (HMD),
and the effect on right heart strength caused by hypertrophy of the right heart (HPR).
CD74:
Calculation of the pumping effectiveness of the right heart (HPEF) by adding the
proportion of the pumping effectiveness caused by left heart function as calculated
from CD71 plus the proportion caused by pumping by the right heart as calculated
from CD73.
CD70 and CD71:
Calculation of the proportion of the pumping effectiveness of the right heart that is
caused by left heart contraction. This is determined by the normal proportion (QRF)
times the instantaneous output of the left heart (QLO) and divided by the normalized
output of the left heart (QLN) when all factors affecting left heart strength are normal.
CD72 and CD73:
Calculation of the proportion of the right heart pumping effectiveness that is caused
by right heart musculature contraction itself, calculated from multiple factors that
affect right heart pumping including the normal proportion of right heart pumping that
is caused by left heart pumping (QRF), the strength of the right heart (HSR) relative
to its normal strength, the loading effect of pulmonary arterial pressure on the
right heart (RVM), the effect of autonomic stimulation on right heart strength (AUH),
the effect of possible deterioration of the right heart from shock and other factors (HMD),
and the effect on right heart strength caused by hypertrophy of the right heart (HPR).
CD74:
Calculation of the pumping effectiveness of the right heart (HPEF) by adding the
proportion of the pumping effectiveness caused by left heart function as calculated
from CD71 plus the proportion caused by pumping by the right heart as calculated
from CD73.
$\mathrm{HPEF}=1\mathrm{AUH}\mathrm{RVM}\mathrm{HSR}\mathrm{HMD}\mathrm{HPR}+\frac{\mathrm{QRF}\mathrm{QLO}}{\mathrm{QLN}}$
CD26:
Function curve that gives the output from the right heart (QRN) for any given
level of right atrial pressure (PRA1) when all conditions of the right heart
are normal.
CD27: Calculation of the actual output from the right heart (QRO) by multiplying
the normalized value for the output (QRN) times a value that represents the
instantaneous pumping effectiveness of the right heart (HPEF).
CD26:
Function curve that gives the output from the right heart (QRN) for any given
level of right atrial pressure (PRA1) when all conditions of the right heart
are normal.
CD27: Calculation of the actual output from the right heart (QRO) by multiplying
the normalized value for the output (QRN) times a value that represents the
instantaneous pumping effectiveness of the right heart (HPEF).
$\mathrm{QRN}=\begin{cases}0 & \text{if $\mathrm{PRA1}\le -8$}\\ 0+\frac{(0.75-0)(\mathrm{PRA1}--8)}{-6--8} & \text{if $(\mathrm{PRA1}> -8)\land (\mathrm{PRA1}\le -6)$}\\ 0.75+\frac{(2.6-0.75)(\mathrm{PRA1}--6)}{-2--6} & \text{if $(\mathrm{PRA1}> -6)\land (\mathrm{PRA1}\le -2)$}\\ 2.6+\frac{(9.8-2.6)(\mathrm{PRA1}--2)}{4--2} & \text{if $(\mathrm{PRA1}> -2)\land (\mathrm{PRA1}\le 4)$}\\ 9.8+\frac{(13.5-9.8)(\mathrm{PRA1}-4)}{12-4} & \text{if $(\mathrm{PRA1}> 4)\land (\mathrm{PRA1}\le 12)$}\\ 13.5 & \text{otherwise}\end{cases}\mathrm{QRO}=\mathrm{QRN}\mathrm{HPEF}$
Containment grouping component for "pulmonary_vasculature_blood_volume",
"pulmonary_vasculature_pressure", "pulmonary_arterial_resistance",
"pulmonary_venous_resistance", "total_pulmonary_vasculature_resistance",
"pressure_gradient_through_the_lungs" and
"rate_of_blood_flow_from_pulmonary_veins_to_left_atrium".
CD28:
Rate of change of blood volume in the pulmonary arterial tree (DPA) is equal to the
rate of blood flow into the pulmonary arterial tree (QRO) minus the rate of blood flow
from the pulmonary arterial tree to the pulmonary venous tree (QPO).
CD29:
A temporary value for the instantaneous volume of blood in the pulmonary arterial
tree is calculated by integrating the rate of change of blood volume in the pulmonary
arterial tree (DPA).
CD30:
The portion ascribable to the pulmonary arteries of any total blood volume change (VBD)
that has occurred since the last iteration is calculated by multiplying the total volume
change since the last iteration (VBD) times a constant proportionality factor.
CD31:
The instantaneous volume of blood in the pulmonary arteria tree (VPA) is equal to the
temporary value calculated from Block CD29 plus the additional blood resulting from a
blood volume change as calculated in CD30.
CD28:
Rate of change of blood volume in the pulmonary arterial tree (DPA) is equal to the
rate of blood flow into the pulmonary arterial tree (QRO) minus the rate of blood flow
from the pulmonary arterial tree to the pulmonary venous tree (QPO).
CD29:
A temporary value for the instantaneous volume of blood in the pulmonary arterial
tree is calculated by integrating the rate of change of blood volume in the pulmonary
arterial tree (DPA).
CD30:
The portion ascribable to the pulmonary arteries of any total blood volume change (VBD)
that has occurred since the last iteration is calculated by multiplying the total volume
change since the last iteration (VBD) times a constant proportionality factor.
CD31:
The instantaneous volume of blood in the pulmonary arteria tree (VPA) is equal to the
temporary value calculated from Block CD29 plus the additional blood resulting from a
blood volume change as calculated in CD30.
$\mathrm{DPA}=\mathrm{QRO}-\mathrm{QPO}\frac{d \mathrm{VPA1}}{d \mathrm{time}}=\mathrm{DPA}\mathrm{VPA}=\mathrm{VPA1}+\mathrm{VBD}\times 0.155$
CD32:
Excess volume of blood in the pulmonary arterial tree (VPE) is equal to the
instantaneous volume of blood in the pulmonary tree (VPA) minus a constant value
which represents the volume of blood in the pulmonary arterial tree when it is
filled but still at zero pressure.
CD33:
The pulmonary arterial pressure (PPA) is equal to the excess volume of blood in
the pulmonary arterial tree (VPE) divided by a constant which is equal to the
capacitance of the pulmonary arterial tree.
CD32:
Excess volume of blood in the pulmonary arterial tree (VPE) is equal to the
instantaneous volume of blood in the pulmonary tree (VPA) minus a constant value
which represents the volume of blood in the pulmonary arterial tree when it is
filled but still at zero pressure.
CD33:
The pulmonary arterial pressure (PPA) is equal to the excess volume of blood in
the pulmonary arterial tree (VPE) divided by a constant which is equal to the
capacitance of the pulmonary arterial tree.
$\mathrm{VPE}=\mathrm{VPA}-0.30625\mathrm{PPA}=\frac{\mathrm{VPE}}{0.0048}$
CD59, CD60, CD61, and CD62:
Calculation of the resistance through the pulmonary arterioles (RPA) caused by
changes in pulmonary arterial pressure (PPA). CD60 gives a limit value for one
of the intermediate calculations, and CD61 gives an exponential effect of pressure
on natriuresis.
CD59, CD60, CD61, and CD62:
Calculation of the resistance through the pulmonary arterioles (RPA) caused by
changes in pulmonary arterial pressure (PPA). CD60 gives a limit value for one
of the intermediate calculations, and CD61 gives an exponential effect of pressure
on natriuresis.
CD59, CD60, CD61, and CD62:
Calculation of the resistance through the pulmonary arterioles (RPA) caused by
changes in pulmonary arterial pressure (PPA). CD60 gives a limit value for one
of the intermediate calculations, and CD61 gives an exponential effect of pressure
on natriuresis.
CD59, CD60, CD61, and CD62:
Calculation of the resistance through the pulmonary arterioles (RPA) caused by
changes in pulmonary arterial pressure (PPA). CD60 gives a limit value for one
of the intermediate calculations, and CD61 gives an exponential effect of pressure
on natriuresis.
CD59, CD60, CD61, and CD62:
Calculation of the resistance through the pulmonary arterioles (RPA) caused by
changes in pulmonary arterial pressure (PPA). CD60 gives a limit value for one
of the intermediate calculations, and CD61 gives an exponential effect of pressure
on natriuresis.
$\mathrm{PP1T}=0.026\mathrm{PPA}\mathrm{PP1}=\begin{cases}0.00001 & \text{if $\mathrm{PP1T}< 0.00001$}\\ \mathrm{PP1T} & \text{otherwise}\end{cases}\mathrm{CPA}=\mathrm{PP1}^{0.5}\mathrm{RPA}=\frac{1}{\mathrm{CPA}}$
CD63 and CD64:
Calculation of the resistance of blood flow through the pulmonary veins (RPV) as
a function of the left atrial pressure (PLA). Basically an increase in left
atrial pressure distends the pulmonary veins and reduces the resistance.
CD63 and CD64:
Calculation of the resistance of blood flow through the pulmonary veins (RPV) as
a function of the left atrial pressure (PLA). Basically an increase in left
atrial pressure distends the pulmonary veins and reduces the resistance.
CD63 and CD64:
Calculation of the resistance of blood flow through the pulmonary veins (RPV) as
a function of the left atrial pressure (PLA). Basically an increase in left
atrial pressure distends the pulmonary veins and reduces the resistance.
$\mathrm{PL1}=\mathrm{PLA}+18\mathrm{RPV}=\frac{1}{\mathrm{PL1}\times 0.0357}$
CD65:
The total resistance in the pulmonary circuit (RPT) is equal to the sum of the
pulmonary arterial resistance (RPA) plus the pulmonary venous resistance (RPV).
CD65:
The total resistance in the pulmonary circuit (RPT) is equal to the sum of the
pulmonary arterial resistance (RPA) plus the pulmonary venous resistance (RPV).
$\mathrm{RPT}=\mathrm{RPV}+\mathrm{RPA}$
CD34:
The pressure gradient through the lungs from the pulmonary arteries to the
pulmonary veins (PGL) is equal to the pressure in the pulmonary arteries (PPA)
minus the pressure in the left atrium (PLA).
CD34:
The pressure gradient through the lungs from the pulmonary arteries to the
pulmonary veins (PGL) is equal to the pressure in the pulmonary arteries (PPA)
minus the pressure in the left atrium (PLA).
$\mathrm{PGL}=\mathrm{PPA}-\mathrm{PLA}$
CD35:
Rate of outflow of blood from the pulmonary arterial tree (QPO) is equal to
the pressure gradient through the lungs (PGL) divided by the resistance to
blood flow through the lungs (RPT).
CD35A:
Damping of QPO to allow rapid computation of long-term hemodynamics. When
the value U equals 1.0 there is no damping. Any larger value for U provides
proportionate damping.
CD35:
Rate of outflow of blood from the pulmonary arterial tree (QPO) is equal to
the pressure gradient through the lungs (PGL) divided by the resistance to
blood flow through the lungs (RPT).
CD35A:
Damping of QPO to allow rapid computation of long-term hemodynamics. When
the value U equals 1.0 there is no damping. Any larger value for U provides
proportionate damping.
$\mathrm{QPO}=\frac{\mathrm{PGL}}{\mathrm{RPT}}$
Containment grouping component for "left_atrial_blood_volume", "left_atrial_pressure"
and "autonomic_stimulation_effect_on_left_atrial_pressure".
CD36:
The rate of change of blood volume in the left atrium (DLA) is equal to the rate
of blood flow into the left atrium from the pulmonary circulation (QPO) minus the
rate of blood flow out of the left atrium through the left heart (QLO).
CD37:
Calculation of a temporary value for the instantaneous volume of blood in the
left atrium by integrating the rate of blood volume change in the left atrium (DLA).
CD38:
Calculation of the proportion of any blood volume change (VBD) that has occurred
since the last iteration that is distributed to the left atrium, calculated by
multiplying by a porprotionality constant.
CD39:
The instantaneous volume of blood in the left atrium (VLA) is equal to the
temporary value calculated in CD37 plus the proportion of any blood volume
change that is attributable to the left atrium as calculated in CD38.
CD36:
The rate of change of blood volume in the left atrium (DLA) is equal to the rate
of blood flow into the left atrium from the pulmonary circulation (QPO) minus the
rate of blood flow out of the left atrium through the left heart (QLO).
CD37:
Calculation of a temporary value for the instantaneous volume of blood in the
left atrium by integrating the rate of blood volume change in the left atrium (DLA).
CD38:
Calculation of the proportion of any blood volume change (VBD) that has occurred
since the last iteration that is distributed to the left atrium, calculated by
multiplying by a porprotionality constant.
CD39:
The instantaneous volume of blood in the left atrium (VLA) is equal to the
temporary value calculated in CD37 plus the proportion of any blood volume
change that is attributable to the left atrium as calculated in CD38.
$\mathrm{DLA}=\mathrm{QPO}-\mathrm{QLO}\frac{d \mathrm{VLA1}}{d \mathrm{time}}=\mathrm{DLA}\mathrm{VLA}=\mathrm{VLA1}+\mathrm{VBD}\times 0.128$
CD40:
The excess blood volume in the left atrium (VLE) is equal to the instantaneous
volume of blood in the left atrium (VLA) minus a constant value which is the
volume of blood in the left atrium when it is filled with the pressure at zero.
CD41:
The pressure in the left atrium (PLE) is equal to the instantaneous exces volume
in the left atrium (VLE) divided by a constant which is equal to the capacitance
of the left atrium.
CD40:
The excess blood volume in the left atrium (VLE) is equal to the instantaneous
volume of blood in the left atrium (VLA) minus a constant value which is the
volume of blood in the left atrium when it is filled with the pressure at zero.
CD41:
The pressure in the left atrium (PLE) is equal to the instantaneous exces volume
in the left atrium (VLE) divided by a constant which is equal to the capacitance
of the left atrium.
$\mathrm{VLE}=\mathrm{VLA}-0.38\mathrm{PLA}=\frac{\mathrm{VLE}}{0.01}$
CD41A, CD41B, CD41C, and CD41D:
These blocks serve the same functions for the left heart that Blocks CD25C, CD25D,
CD25E, and CD25F serve for the right ventricle. The value AU in Block CD41D is the
level of autonomic stimulation of the heart, and HTAUML is the multiplier constant
for calculating the effect of changes in AU on the shift of left atrial pressure
effect from PLA to PLA1.
CD41A, CD41B, CD41C, and CD41D:
These blocks serve the same functions for the left heart that Blocks CD25C, CD25D,
CD25E, and CD25F serve for the right ventricle. The value AU in Block CD41D is the
level of autonomic stimulation of the heart, and HTAUML is the multiplier constant
for calculating the effect of changes in AU on the shift of left atrial pressure
effect from PLA to PLA1.
$\mathrm{PLA1}=(\mathrm{PLA}+4)(\mathrm{HTAUML}(\mathrm{AU}-1)+1)-4$
Containment grouping component for "pumping_effectiveness_of_left_ventricle",
and "left_ventricular_output".
CD66:
A temporary multiplier function (PA2) for the effectiveness of left heart pumping
is calculated from three factors: Stimulation of the left heart by the autonomic
nervous system (AUH), effect on heart pumping caused by changes in arterial oxygen
saturation (OSA), effect on heart pumping caused by the loading effect of systemic
arterial pressure (PA).
CD67:
Function curve relating the pumping effectiveness of the left heart (LVM) to the
multiplier function calculated in CD66 (PA2).
CD66:
A temporary multiplier function (PA2) for the effectiveness of left heart pumping
is calculated from three factors: Stimulation of the left heart by the autonomic
nervous system (AUH), effect on heart pumping caused by changes in arterial oxygen
saturation (OSA), effect on heart pumping caused by the loading effect of systemic
arterial pressure (PA).
CD67:
Function curve relating the pumping effectiveness of the left heart (LVM) to the
multiplier function calculated in CD66 (PA2).
$\mathrm{PA2}=\frac{\mathrm{PA}}{\mathrm{AUH}\mathrm{OSA}}\mathrm{LVM}=\begin{cases}1.04 & \text{if $\mathrm{PA2}\le 0$}\\ 1.04+\frac{(1.025-1.04)(\mathrm{PA2}-0)}{60-0} & \text{if $(\mathrm{PA2}> 0)\land (\mathrm{PA2}\le 60)$}\\ 1.025+\frac{(0.97-1.025)(\mathrm{PA2}-60)}{125-60} & \text{if $(\mathrm{PA2}> 60)\land (\mathrm{PA2}\le 125)$}\\ 0.97+\frac{(0.88-0.97)(\mathrm{PA2}-125)}{160-125} & \text{if $(\mathrm{PA2}> 125)\land (\mathrm{PA2}\le 160)$}\\ 0.88+\frac{(0.59-0.88)(\mathrm{PA2}-160)}{200-160} & \text{if $(\mathrm{PA2}> 160)\land (\mathrm{PA2}\le 200)$}\\ 0.59+\frac{(0-0.59)(\mathrm{PA2}-200)}{240-200} & \text{if $(\mathrm{PA2}> 200)\land (\mathrm{PA2}\le 240)$}\\ 0 & \text{otherwise}\end{cases}$
CD42:
Function curve that gives the normalized rate of output of the left ventricle (QLN)
when the left ventricle is operating at a normal level of pumping effectiveness for
any given left atrial pressure (PLA).
CD43:
The actual rate of output from the left ventricle (QLO) when the normalized rate (QLN)
is multiplied by various factors that alter the pumping effectiveness of the heart:
A multiplier that reduces the effectiveness because of pressure load on the heart (LVM),
a factor that changes the effectiveness of the heart because of abnormal left heart
strength (HSL), a factor that increases the effectiveness of the heart because of
hypertrophy (HPL), a factor that decreases the strength of the heart because of
deterioration of the heart in low blood flow states (HMD), and a factor that alters
the strength of the heart by increases or decreases in autonomic stimulation (AUH).
CD42:
Function curve that gives the normalized rate of output of the left ventricle (QLN)
when the left ventricle is operating at a normal level of pumping effectiveness for
any given left atrial pressure (PLA).
CD43:
The actual rate of output from the left ventricle (QLO) when the normalized rate (QLN)
is multiplied by various factors that alter the pumping effectiveness of the heart:
A multiplier that reduces the effectiveness because of pressure load on the heart (LVM),
a factor that changes the effectiveness of the heart because of abnormal left heart
strength (HSL), a factor that increases the effectiveness of the heart because of
hypertrophy (HPL), a factor that decreases the strength of the heart because of
deterioration of the heart in low blood flow states (HMD), and a factor that alters
the strength of the heart by increases or decreases in autonomic stimulation (AUH).
CD43:
The actual rate of output from the left ventricle (QLO) when the normalized rate (QLN)
is multiplied by various factors that alter the pumping effectiveness of the heart:
A multiplier that reduces the effectiveness because of pressure load on the heart (LVM),
a factor that changes the effectiveness of the heart because of abnormal left heart
strength (HSL), a factor that increases the effectiveness of the heart because of
hypertrophy (HPL), a factor that decreases the strength of the heart because of
deterioration of the heart in low blood flow states (HMD), and a factor that alters
the strength of the heart by increases or decreases in autonomic stimulation (AUH).
CD43:
The actual rate of output from the left ventricle (QLO) when the normalized rate (QLN)
is multiplied by various factors that alter the pumping effectiveness of the heart:
A multiplier that reduces the effectiveness because of pressure load on the heart (LVM),
a factor that changes the effectiveness of the heart because of abnormal left heart
strength (HSL), a factor that increases the effectiveness of the heart because of
hypertrophy (HPL), a factor that decreases the strength of the heart because of
deterioration of the heart in low blood flow states (HMD), and a factor that alters
the strength of the heart by increases or decreases in autonomic stimulation (AUH).
$\mathrm{QLN}=\begin{cases}0.01 & \text{if $\mathrm{PLA1}\le -2$}\\ 0.01+\frac{(3.6-0.01)(\mathrm{PLA1}--2)}{1--2} & \text{if $(\mathrm{PLA1}> -2)\land (\mathrm{PLA1}\le 1)$}\\ 3.6+\frac{(9.4-3.6)(\mathrm{PLA1}-1)}{5-1} & \text{if $(\mathrm{PLA1}> 1)\land (\mathrm{PLA1}\le 5)$}\\ 9.4+\frac{(11.6-9.4)(\mathrm{PLA1}-5)}{8-5} & \text{if $(\mathrm{PLA1}> 5)\land (\mathrm{PLA1}\le 8)$}\\ 11.6+\frac{(13.5-11.6)(\mathrm{PLA1}-8)}{12-8} & \text{if $(\mathrm{PLA1}> 8)\land (\mathrm{PLA1}\le 12)$}\\ 13.5 & \text{otherwise}\end{cases}\mathrm{QLOT}=\mathrm{LVM}\mathrm{QLN}\mathrm{AUH}\mathrm{HSL}\mathrm{HMD}\mathrm{HPL}\mathrm{QLO1}=\frac{\mathrm{PLA}-\mathrm{PA}}{3}\mathrm{QLO}=\begin{cases}\mathrm{QLOT}+\mathrm{QLO1} & \text{if $\mathrm{QLO1}> 0$}\\ \mathrm{QLOT} & \text{otherwise}\end{cases}$
Containment grouping component for "venous_blood_volume",
"angiotensin_induced_venous_constriction", "venous_excess_volume",
"venous_average_pressure", "venous_outflow_pressure_into_heart",
"resistance_from_veins_to_right_atrium", "rate_of_blood_flow_from_veins_to_right_atrium",
"venous_resistance" and "NM_NR_venous_resistance".
CD11:
The rate of change of blood volume in the systemic veins (DVS) is equal to the
rate of blood flow into the veins from the arterial tree (QAO) minus the rate
of blood flow out of the veins (QVO).
CD12:
A temporary value is calculated for the instantaneous volume of blood in the
veins by integrating the rate of change of the volume in the veins (DVS).
CD13:
The portion of any change in blood volume that has occurred since the last iteration
that is ascribable to volume change in the veins is calculated by multiplying the
total volume change (VBD) times a constant.
CD14:
The instantaneous volume of blood in the veins (VVS) is the sum of the temporary
calculation of instantaneous venous volume from CD12 plus the additional venous
volume change caused by change in total blood volume as calculated in CD13.
CD11:
The rate of change of blood volume in the systemic veins (DVS) is equal to the
rate of blood flow into the veins from the arterial tree (QAO) minus the rate
of blood flow out of the veins (QVO).
CD12:
A temporary value is calculated for the instantaneous volume of blood in the
veins by integrating the rate of change of the volume in the veins (DVS).
CD13:
The portion of any change in blood volume that has occurred since the last iteration
that is ascribable to volume change in the veins is calculated by multiplying the
total volume change (VBD) times a constant.
CD14:
The instantaneous volume of blood in the veins (VVS) is the sum of the temporary
calculation of instantaneous venous volume from CD12 plus the additional venous
volume change caused by change in total blood volume as calculated in CD13.
$\mathrm{DVS}=\mathrm{QAO}-\mathrm{QVO}\frac{d \mathrm{VVS1}}{d \mathrm{time}}=\mathrm{DVS}\mathrm{VVS}=\mathrm{VVS1}+\mathrm{VBD}\times 0.3986$
CD76 and CD77:
Calculation of the decrease in excess venous volume caused by angiotensin
constriction based on two factors: A multiplier factor caused by changes in
concentration of angiotensin in the circulating blood (ANU) and a
sensitivity adjustment (ANY).
CD76 and CD77:
Calculation of the decrease in excess venous volume caused by angiotensin
constriction based on two factors: A multiplier factor caused by changes in
concentration of angiotensin in the circulating blood (ANU) and a
sensitivity adjustment (ANY).
$\mathrm{VVA}=(\mathrm{ANU}-1)\mathrm{ANY}$
CD15:
The excess volume in the veins (VVE) is calculated by subtracting the maximum
volume of blood at zero venous pressure from the actual volume of blood in the
systemic venous system (VVS). The maximum volume of blood in the venous system
at zero pressure is equal to the sum of several variable factors: a basic volume
when all other factors are normal (VVR), changes caused by atrial volume
receptor feedback (ATRVFB), changes caused by stress relaxation (VV6 and VV7),
and a change in basic volume of the venous system caused by constriction of the
venous system in response to circulating angiotensin from block CD77.
CD15:
The excess volume in the veins (VVE) is calculated by subtracting the maximum
volume of blood at zero venous pressure from the actual volume of blood in the
systemic venous system (VVS). The maximum volume of blood in the venous system
at zero pressure is equal to the sum of several variable factors: a basic volume
when all other factors are normal (VVR), changes caused by atrial volume
receptor feedback (ATRVFB), changes caused by stress relaxation (VV6 and VV7),
and a change in basic volume of the venous system caused by constriction of the
venous system in response to circulating angiotensin from block CD77.
$\mathrm{VVE1}=\mathrm{VVS}-\mathrm{VVR}-\mathrm{VVA}-\mathrm{VV7}-\mathrm{VV6}-\mathrm{ATRVFB}\mathrm{VVE}=\begin{cases}0.0001 & \text{if $\mathrm{VVE1}< 0.0001$}\\ \mathrm{VVE1} & \text{otherwise}\end{cases}$
CD16, CD16A, and CD16B:
The average pressure in the venous system (PVS) is equal to the excess volume of
blood in the veins (VVE) divided by the capacitance of the venous system (CV).
The mathematics in these blocks are arranged so that when CV in block CD16A is
changed, the blood volume in the venous system does not change at the normal venous
pressure level of PVS (+ 3.7 mm Hg).
CD16D:
This block prevents the average venous pressure (PVS) from falling below .001 mm Hg.
CD16, CD16A, and CD16B:
The average pressure in the venous system (PVS) is equal to the excess volume of
blood in the veins (VVE) divided by the capacitance of the venous system (CV).
The mathematics in these blocks are arranged so that when CV in block CD16A is
changed, the blood volume in the venous system does not change at the normal venous
pressure level of PVS (+ 3.7 mm Hg).
CD16D:
This block prevents the average venous pressure (PVS) from falling below .001 mm Hg.
$\mathrm{PVS1}=3.7+\frac{\mathrm{VVE}-0.74}{\mathrm{CV}}\mathrm{PVS}=\begin{cases}0.0001 & \text{if $\mathrm{PVS1}< 0.0001$}\\ \mathrm{PVS1} & \text{otherwise}\end{cases}$
CD25A and CD25B:
Calculation of the outflow pressure from the systemic veins into the chest (PR1)
which is used for calculating the blood flow through the venous system in CD17.
This corrects for the collapse of veins that might occur at entry to the chest
when the right atrial pressure is negative, thus maintaining the output pressure
from the venous system above a minimum pressure level corresponding to the pressure
at which the veins collapse (PRILL).
CD25A and CD25B:
Calculation of the outflow pressure from the systemic veins into the chest (PR1)
which is used for calculating the blood flow through the venous system in CD17.
This corrects for the collapse of veins that might occur at entry to the chest
when the right atrial pressure is negative, thus maintaining the output pressure
from the venous system above a minimum pressure level corresponding to the pressure
at which the veins collapse (PRILL).
$\mathrm{PR1}=\begin{cases}\mathrm{PR1LL} & \text{if $\mathrm{PRA}< \mathrm{PR1LL}$}\\ \mathrm{PRA} & \text{otherwise}\end{cases}$
CD18, CD18A, and CD18B:
These blocks calculate the resistance from the large veins to the right atrium (RVS).
Block CD18 takes into consideration the effect of the viscosity of the blood (VIM) when
the normal value for the viscosity is considered to be 1.0. Block CD18A considers that
the resistance (RVS) decreases in proportion to the square root of the level of large
vein pressure (PVS). The numerical values in Blocks CD18 and CD18B are proportionality
constants. This group of blocks is especially concerned with the reduction of venous
resistance when pressure increases the diameter of the veins.
CD18, CD18A, and CD18B:
These blocks calculate the resistance from the large veins to the right atrium (RVS).
Block CD18 takes into consideration the effect of the viscosity of the blood (VIM) when
the normal value for the viscosity is considered to be 1.0. Block CD18A considers that
the resistance (RVS) decreases in proportion to the square root of the level of large
vein pressure (PVS). The numerical values in Blocks CD18 and CD18B are proportionality
constants. This group of blocks is especially concerned with the reduction of venous
resistance when pressure increases the diameter of the veins.
$\mathrm{RVG}=\frac{0.74}{\left(\frac{\mathrm{PVS}}{\mathrm{VIM}\times 3.7}\right)^{0.5}}$
CD17:
The temporary pressure gradient (PGV) from the midpoint of the veins to the exit
of the veins into the chest equals the venous pressure (PVS) minus the pressure
at the exit point (PR1).
CD19:
The rate of blood flow out of the veins into the right atrium (QVO) is equal to
the pressure gradient through the venous system (PGV) divided by the resistance
to blood flow through the venous system (RVS).
CD19A:
This block provides damping of the value QVO when running on the computer.
A damping value of X of 1.0 is no damping. Any higher value causes damping.
The value should be equal to 1.0 when studying rapid changes in circulatory
dynamics.
CD17:
The temporary pressure gradient (PGV) from the midpoint of the veins to the exit
of the veins into the chest equals the venous pressure (PVS) minus the pressure
at the exit point (PR1).
CD19:
The rate of blood flow out of the veins into the right atrium (QVO) is equal to
the pressure gradient through the venous system (PGV) divided by the resistance
to blood flow through the venous system (RVS).
CD19A:
This block provides damping of the value QVO when running on the computer.
A damping value of X of 1.0 is no damping. Any higher value causes damping.
The value should be equal to 1.0 when studying rapid changes in circulatory
dynamics.
$\mathrm{PGV}=\mathrm{PVS}-\mathrm{PR1}\mathrm{QVO}=\frac{\mathrm{PGV}}{\mathrm{RVG}}$
CD50, CD51, CD52, CD53, CD54, and CD55:
A curve-shaping series to calculate a resistance multiplier factor (RV1) from the
effect of vascular stretch in the venous system, based on two factors: the input
pressure to the venous system from the capillaries (PC) and a basal systemic venous
multiplier (RVSM). The damping factor in CD54 slows the response and prevents
oscillation of the system.
NB - The damping in CD54 has not been coded!!!!
CD56:
Calculation of the venous resistance (RVS) after modification of the basic venous
resistance multiplier factor (RV1) by various other multiplier factors: a multiplier
factor for the effect of angiotensin (ANUVN), a multiplier factor for the effect of
the autonomic nervous system (AVE), and a multiplier factor for the effect of blood
viscosity on venous resistance (VIM).
CD50, CD51, CD52, CD53, CD54, and CD55:
A curve-shaping series to calculate a resistance multiplier factor (RV1) from the
effect of vascular stretch in the venous system, based on two factors: the input
pressure to the venous system from the capillaries (PC) and a basal systemic venous
multiplier (RVSM). The damping factor in CD54 slows the response and prevents
oscillation of the system.
NB - The damping in CD54 has not been coded!!!!
CD50, CD51, CD52, CD53, CD54, and CD55:
A curve-shaping series to calculate a resistance multiplier factor (RV1) from the
effect of vascular stretch in the venous system, based on two factors: the input
pressure to the venous system from the capillaries (PC) and a basal systemic venous
multiplier (RVSM). The damping factor in CD54 slows the response and prevents
oscillation of the system.
NB - The damping in CD54 has not been coded!!!!
CD56:
Calculation of the venous resistance (RVS) after modification of the basic venous
resistance multiplier factor (RV1) by various other multiplier factors: a multiplier
factor for the effect of angiotensin (ANUVN), a multiplier factor for the effect of
the autonomic nervous system (AVE), and a multiplier factor for the effect of blood
viscosity on venous resistance (VIM).
$\mathrm{CN3}=(\mathrm{PC}\mathrm{CN7}+17)\mathrm{CN2}\mathrm{RV1}=\frac{\mathrm{RVSM}}{\mathrm{CN3}}\mathrm{RVS}=\mathrm{AVE}\mathrm{RV1}\mathrm{VIM}\mathrm{ANUVN}$
CD57:
Calculation of that proportion of the renal venous resistance that is ascribable
to blood flow through the systemic circulation besides the muscles and the kidneys,
by multiplying the actual venous resistance (RVS) times a proportionality factor.
CD57:
Calculation of that proportion of the renal venous resistance that is ascribable
to blood flow through the systemic circulation besides the muscles and the kidneys,
by multiplying the actual venous resistance (RVS) times a proportionality factor.
$\mathrm{NNRVR}=\mathrm{RVS}\times 1.79$
Containment grouping component for "arterial_blood_volume",
"arterial_pressure_and_pressure_gradient", "pressure_effect_on_arterial_distention",
"NR_systemic_arterial_resistance_multiplier" and "NM_NR_arterial_resistance".
CD1:
The rate of change of blood volume in the aorta (DAS) is equal to the rate of
inflow to the aorta from the heart (QLO) minus the rate of outflow from the
aorta through the systemic circulation (QAO) plus any flow that occurs passively
through the left ventricle (QLO1) because of a left atrial pressure that is
greater than aortic pressure, as occurs in the last stages of left ventricular
failure.
CD2:
Integration of the rate of change of volume in the aorta (DAS) gives an output
which is a temporary value for the volume of blood in the systemic arteries at
any given instant.
CD3:
This block calculates the portion of any change in blood volume that has occurred
since the last iteration (VBD) that is partitioned into the arteries. The remainder
is partitioned into other sections of the circulation.
CD4:
The volume of blood in the arterial tree at any given instant (VAS) is equal to the
temporary calculation in volume of blood as described in CD2 plus the portion of a
blood volume change as calculated in CD3.
CD1:
The rate of change of blood volume in the aorta (DAS) is equal to the rate of
inflow to the aorta from the heart (QLO) minus the rate of outflow from the
aorta through the systemic circulation (QAO) plus any flow that occurs passively
through the left ventricle (QLO1) because of a left atrial pressure that is
greater than aortic pressure, as occurs in the last stages of left ventricular
failure.
CD2:
Integration of the rate of change of volume in the aorta (DAS) gives an output
which is a temporary value for the volume of blood in the systemic arteries at
any given instant.
CD3:
This block calculates the portion of any change in blood volume that has occurred
since the last iteration (VBD) that is partitioned into the arteries. The remainder
is partitioned into other sections of the circulation.
CD4:
The volume of blood in the arterial tree at any given instant (VAS) is equal to the
temporary calculation in volume of blood as described in CD2 plus the portion of a
blood volume change as calculated in CD3.
$\mathrm{DAS}=\mathrm{QLO}-\mathrm{QAO}\frac{d \mathrm{VAS1}}{d \mathrm{time}}=\mathrm{DAS}\mathrm{VAS}=\mathrm{VAS1}+\mathrm{VBD}\times 0.261$
CD5:
The excess volume in the arterial tree (VAE) over and above the volume that is
required to barely fill the aorta at zero pressure is calculated by subtracting
a constant (which is equal to "VO") from the instantaneous volume in the aorta (VAS).
CD6:
Arterial pressure (PA) is equal to the excess volume in the arterial tree (VAE)
divided by a constant which is the capacitance of the arterial tree.
CD78:
The output of this block is the total pressure gradient from the arterial pressure (PA)
to the right atrial pressure (PRA).
CD5:
The excess volume in the arterial tree (VAE) over and above the volume that is
required to barely fill the aorta at zero pressure is calculated by subtracting
a constant (which is equal to "VO") from the instantaneous volume in the aorta (VAS).
CD6:
Arterial pressure (PA) is equal to the excess volume in the arterial tree (VAE)
divided by a constant which is the capacitance of the arterial tree.
CD78:
The output of this block is the total pressure gradient from the arterial pressure (PA)
to the right atrial pressure (PRA).
$\mathrm{VAE}=\mathrm{VAS}-0.495\mathrm{PA}=\frac{\mathrm{VAE}}{0.00355}\mathrm{PAG}=\mathrm{PA}-\mathrm{PRA}$
CD44 and CD45:
Calculation of the effect of arterial vascular distension on resistance caused by
the arterial pressure itself (PA), giving a multiplier output (PAM) that is then
used to calculate the effect of distension on systemic resistance. The exponential
factor (PAEX) modifies the extent to which pressure affects the degree of distension
on an exponential basis.
CD44 and CD45:
Calculation of the effect of arterial vascular distension on resistance caused by
the arterial pressure itself (PA), giving a multiplier output (PAM) that is then
used to calculate the effect of distension on systemic resistance. The exponential
factor (PAEX) modifies the extent to which pressure affects the degree of distension
on an exponential basis.
$\mathrm{PAM}=\left(\frac{\mathrm{PA}}{100}\right)^{\mathrm{PAEX}}$
CD46 and CD47:
Calculation of the effect of multiple factors on systemic arterial resistance in
the muscles and in the soft tissues besides the kidneys to give a multiplier
factor (R1). The input factors that contribute to this multiplier factor are:
a multiplier factor for the degree of sympathetic stimulation (AUM), a multiplier
factor for blood viscosity (VIM), a multiplier factor for the effect of angiotensin
on vascular resistance (ANU), a multiplier factor for the effect of antidiuretic
hormone (ADHMV), a division factor for the effect of feedback from the atrial stretch
receptors (ATRRFB), a division factor caused by dilation of the arteries in response
to changes in arterial pressure (PAM), and a multiplier factor (PAMK) for any other
effect that might constrict the arteries.
CD46 and CD47:
Calculation of the effect of multiple factors on systemic arterial resistance in
the muscles and in the soft tissues besides the kidneys to give a multiplier
factor (R1). The input factors that contribute to this multiplier factor are:
a multiplier factor for the degree of sympathetic stimulation (AUM), a multiplier
factor for blood viscosity (VIM), a multiplier factor for the effect of angiotensin
on vascular resistance (ANU), a multiplier factor for the effect of antidiuretic
hormone (ADHMV), a division factor for the effect of feedback from the atrial stretch
receptors (ATRRFB), a division factor caused by dilation of the arteries in response
to changes in arterial pressure (PAM), and a multiplier factor (PAMK) for any other
effect that might constrict the arteries.
$\mathrm{R1}=\frac{\frac{\mathrm{ANU}\mathrm{ADHMV}\mathrm{AUM}\mathrm{VIM}\mathrm{PAMK}}{\mathrm{PAM}}}{\mathrm{ATRRFB}}$
CD49:
Modification of the resistance multiplier factor (R1) in the tissues of the
body besides the muscles and the kidneys caused by the basic resistance
through these tissues (RAR), times the degree of effect of an autoregulation
multiplier factor (ARM) caused by autoregulation in these tissues, times
RMULT1 for experiments on postulations of very rapid autoregulation, and
times MYOGRS for resistance changes caused by myogenic autoregulation.
CD49:
Modification of the resistance multiplier factor (R1) in the tissues of the
body besides the muscles and the kidneys caused by the basic resistance
through these tissues (RAR), times the degree of effect of an autoregulation
multiplier factor (ARM) caused by autoregulation in these tissues, times
RMULT1 for experiments on postulations of very rapid autoregulation, and
times MYOGRS for resistance changes caused by myogenic autoregulation.
$\mathrm{NNRAR}=\mathrm{RAR}\mathrm{ARM}\mathrm{R1}\mathrm{MYOGRS}\mathrm{RMULT1}$
CD7:
The pressure gradient from the aorta to the major veins in the systemic circulation (PGS)
is equal to the pressure in the aorta (PA) minus the average pressure in the major veins (PVS).
CD7:
The pressure gradient from the aorta to the major veins in the systemic circulation (PGS)
is equal to the pressure in the aorta (PA) minus the average pressure in the major veins (PVS).
$\mathrm{PGS}=\mathrm{PA}-\mathrm{PVS}$
CD48:
Calculation of the resistance through the systemic muscles (RSM) by multiplying
the basic resistance through the muscles (RAM) times the multiplier factor
calculated in CD47 (R1), times another multiplier factor resulting from local
tissue blood flow autoregulation in the muscles (AMM), times RMULT1 for experiments
on postulations of very rapid autoregulation, and times MYOGRS for resistance
changes caused by possible myogenic autoregulation.
CD48:
Calculation of the resistance through the systemic muscles (RSM) by multiplying
the basic resistance through the muscles (RAM) times the multiplier factor
calculated in CD47 (R1), times another multiplier factor resulting from local
tissue blood flow autoregulation in the muscles (AMM), times RMULT1 for experiments
on postulations of very rapid autoregulation, and times MYOGRS for resistance
changes caused by possible myogenic autoregulation.
$\mathrm{RSM}=\mathrm{RAM}\mathrm{AMM}\mathrm{R1}\mathrm{MYOGRS}\mathrm{RMULT1}$
CD58:
Calculation of the resistance to blood flow through the nonmuscular and nonkidney
portions of the systemic vasculature (RSN) by adding the arterial portion of the
resistance as calculated from CD49 and the venous portion of the resistance
calculated from CD57.
CD58:
Calculation of the resistance to blood flow through the nonmuscular and nonkidney
portions of the systemic vasculature (RSN) by adding the arterial portion of the
resistance as calculated from CD49 and the venous portion of the resistance
calculated from CD57.
$\mathrm{RSN}=\mathrm{NNRAR}+\mathrm{NNRVR}$
CD9:
The blood flow through the muscles (BFM) is equal to the pressure gradient through
the systemic circulation to the major veins (PGS) divided by the resistance to the
blood flow through the muscles (RSM).
CD9:
The blood flow through the muscles (BFM) is equal to the pressure gradient through
the systemic circulation to the major veins (PGS) divided by the resistance to the
blood flow through the muscles (RSM).
$\mathrm{BFM}=\frac{\mathrm{PGS}}{\mathrm{RSM}}$
CD8:
Blood flow through the nonmuscular portions of the body besides the kidneys (BFN)
is equal to the pressure gradient through the systemic circulation (PGS) divided by
the resistance through the nonmuscular portions of the body besides the kidneys (RSN).
CD8:
Blood flow through the nonmuscular portions of the body besides the kidneys (BFN)
is equal to the pressure gradient through the systemic circulation (PGS) divided by
the resistance through the nonmuscular portions of the body besides the kidneys (RSN).
$\mathrm{BFN}=\frac{\mathrm{PGS}}{\mathrm{RSN}}$
CD79:
Calculation of the rate of blood flow through a fistula (FISFLO) by multiplying
a conductance factor for the fistula (FIS) times the pressure difference from the
arteries to the right atrium as calculated by Block CD78.
CD79:
Calculation of the rate of blood flow through a fistula (FISFLO) by multiplying
a conductance factor for the fistula (FIS) times the pressure difference from the
arteries to the right atrium as calculated by Block CD78.
$\mathrm{FISFLO}=\mathrm{PAG}\mathrm{FIS}$
CD10:
The rate of blood flow out of the arterial tree (QAO) is equal to the blood flow
through the muscles (BFM), the blood flow through the nonmuscular portions of
the body (BFN), the blood flow through the kidneys (RBF) and the blood flow
through any artificial AV fistulas (FISFLO).
CD10:
The rate of blood flow out of the arterial tree (QAO) is equal to the blood flow
through the muscles (BFM), the blood flow through the nonmuscular portions of
the body (BFN), the blood flow through the kidneys (RBF) and the blood flow
through any artificial AV fistulas (FISFLO).
$\mathrm{SYSFLO}=\mathrm{BFM}+\mathrm{BFN}+\mathrm{RBF}\mathrm{QAO}=\mathrm{SYSFLO}+\mathrm{FISFLO}$
CD80:
The total peripheral resistance (RTP) is equal to the total pressure drop from
the arteries to the right atrium (from Block CD78) divided by the total blood
flow through the systemic circulation (QAO).
CD80:
The total peripheral resistance (RTP) is equal to the total pressure drop from
the arteries to the right atrium (from Block CD78) divided by the total blood
flow through the systemic circulation (QAO).
$\mathrm{RTP}=\frac{\mathrm{PAG}}{\mathrm{QAO}}$
Extracellular and intracellular fluid electrolytes and volumes.
Encapsulation grouping component containing all the components in the Electrolytes Model. The inputs and
outputs of the Electrolytes Model must be passed by this component.
EL1, EL2, and EL3:
The rate of intake of sodium (NAINT) is equal to the normal rate of sodium intake (NID)
times a salt appetite multiplier factor (STH). The rate of change of sodium in the
extracellular fluid (NED) is equal to the rate of intake of sodium (NAINT), minus the
rate of excretion of sodium in the urine (NOD), plus sodium entering the body in
transfused plasma (TRPL).
EL4:
The instantaneous quantity of sodium in the extracellular fluid (NAE) is calculated
by integrating with respect to time the rate of change of sodium in the
extracellular fluid (NED).
EL5:
The concentration of sodium in the extracellular fluid (CNA) is equal to the quantity
of sodium in the extracellular fluid (NAE) divided by the extracellular fluid volume (VEC).
EL1, EL2, and EL3:
The rate of intake of sodium (NAINT) is equal to the normal rate of sodium intake (NID)
times a salt appetite multiplier factor (STH). The rate of change of sodium in the
extracellular fluid (NED) is equal to the rate of intake of sodium (NAINT), minus the
rate of excretion of sodium in the urine (NOD), plus sodium entering the body in
transfused plasma (TRPL).
EL4:
The instantaneous quantity of sodium in the extracellular fluid (NAE) is calculated
by integrating with respect to time the rate of change of sodium in the
extracellular fluid (NED).
EL5:
The concentration of sodium in the extracellular fluid (CNA) is equal to the quantity
of sodium in the extracellular fluid (NAE) divided by the extracellular fluid volume (VEC).
$\mathrm{NED}=\mathrm{NID}\mathrm{STH}-\mathrm{NOD}+\mathrm{TRPL}\times 142\frac{d \mathrm{NAE}}{d \mathrm{time}}=\mathrm{NED}\mathrm{CNA}=\frac{\mathrm{NAE}}{\mathrm{VEC}}$
EL9, EL10, and EL11:
Calculation of an aldosterone multiplier factor for the effect of aldosterone (AMK)
on the distribution of potassium across the cell membranes. The variable (ALCLK) is
a sensitivity control for adjusting the effect of the aldosterone on the cellular
membrane distribution relationship of potassium on the two sides of the cell membranes.
EL9, EL10, and EL11:
Calculation of an aldosterone multiplier factor for the effect of aldosterone (AMK)
on the distribution of potassium across the cell membranes. The variable (ALCLK) is
a sensitivity control for adjusting the effect of the aldosterone on the cellular
membrane distribution relationship of potassium on the two sides of the cell membranes.
$\mathrm{AMK1}=\mathrm{AMK}\mathrm{ALCLK}+1$
EL6:
The rate of change of the total quantity of potassium in all of the body fluids (KTOTD)
is equal to the rate of intake of potassium (KID) minus the rate of excretion of
potassium in the urine (KOD).
EL7:
The total quantity of potassium in all the body fluids at any given time (KTOT)
is calculated by integrating with respect to time the rate of change of the potassium
in all of the body fluids (KTOTD).
EL7A:
Calculation of the freely mobile potassium in the body (approximately 616) by
subtracting the relatively fixed potassium in all the cells of the body
(approximately 3000) from the total potassium of the body (KTOT).
EL7B:
Calculation of the total potassium in the extracellular fluid of the body (KE) by
dividing the total freely mobile calcium from Block EL7A by a constant factor of
9.3333 (which is a distribution relationship of the freely mobile potassium between
the intracellular and extracellular fluid), and divided by a factor from Block EL11
that determines the activity of aldosterone on the distribution relationship of
potassium across the cell membranes.
EL8:
The concentration of potassium in the extracellular fluid (CKE) is equal to the
quantity of potassium in the extracellular fluid (KE) divided by the volume of
extracellular fluid (VEC).
EL6:
The rate of change of the total quantity of potassium in all of the body fluids (KTOTD)
is equal to the rate of intake of potassium (KID) minus the rate of excretion of
potassium in the urine (KOD).
EL7:
The total quantity of potassium in all the body fluids at any given time (KTOT)
is calculated by integrating with respect to time the rate of change of the potassium
in all of the body fluids (KTOTD).
EL7A:
Calculation of the freely mobile potassium in the body (approximately 616) by
subtracting the relatively fixed potassium in all the cells of the body
(approximately 3000) from the total potassium of the body (KTOT).
EL7B:
Calculation of the total potassium in the extracellular fluid of the body (KE) by
dividing the total freely mobile calcium from Block EL7A by a constant factor of
9.3333 (which is a distribution relationship of the freely mobile potassium between
the intracellular and extracellular fluid), and divided by a factor from Block EL11
that determines the activity of aldosterone on the distribution relationship of
potassium across the cell membranes.
EL8:
The concentration of potassium in the extracellular fluid (CKE) is equal to the
quantity of potassium in the extracellular fluid (KE) divided by the volume of
extracellular fluid (VEC).
$\mathrm{KTOTD}=\mathrm{KID}-\mathrm{KOD}\frac{d \mathrm{KTOT}}{d \mathrm{time}}=\mathrm{KTOTD}\mathrm{KE}=\frac{\mathrm{KTOT}-3000}{\mathrm{AMK1}\times 9.3333}\mathrm{CKE}=\frac{\mathrm{KE}}{\mathrm{VEC}}$
EL12:
Calculation of the total potassium inside all the cells of the body (KI) by
subtracting the potassium in the extracellular fluids (KE) from the total potassium
in the body (KTOT).
EL13:
Calculation of the concentration of potassium inside the cells of the body (CKI)
by dividing the total potassium inside all the cells (KI) by the volume of fluid
inside all the cells (VIC).
EL12:
Calculation of the total potassium inside all the cells of the body (KI) by
subtracting the potassium in the extracellular fluids (KE) from the total potassium
in the body (KTOT).
EL13:
Calculation of the concentration of potassium inside the cells of the body (CKI)
by dividing the total potassium inside all the cells (KI) by the volume of fluid
inside all the cells (VIC).
$\mathrm{KI}=\mathrm{KTOT}-\mathrm{KE}\mathrm{CKI}=\frac{\mathrm{KI}}{\mathrm{VIC}}$
EL14 and EL15:
Calculation of the rate of change of volume inside all the cells of the body (VID)
caused in Block EL14 by differences in osmotic effect of sodium concentration (CNA)
outside the cells and potassium concentration (CKI) inside the cells. The rate of
transfer of this fluid (VID) is determined by a proportionality factor (VIDML).
EL16:
Calculation of the changing level of intracellular fluid volume in the entire body (VIC)
by integrating the rate of change of this fluid volume (VID).
EL14 and EL15:
Calculation of the rate of change of volume inside all the cells of the body (VID)
caused in Block EL14 by differences in osmotic effect of sodium concentration (CNA)
outside the cells and potassium concentration (CKI) inside the cells. The rate of
transfer of this fluid (VID) is determined by a proportionality factor (VIDML).
EL14 and EL15:
Calculation of the rate of change of volume inside all the cells of the body (VID)
caused in Block EL14 by differences in osmotic effect of sodium concentration (CNA)
outside the cells and potassium concentration (CKI) inside the cells. The rate of
transfer of this fluid (VID) is determined by a proportionality factor (VIDML).
EL16:
Calculation of the changing level of intracellular fluid volume in the entire body (VIC)
by integrating the rate of change of this fluid volume (VID).
$\mathrm{CCD}=\mathrm{CKI}-\mathrm{CNA}\mathrm{VID}=\mathrm{CCD}\mathrm{VIDML}\frac{d \mathrm{VIC}}{d \mathrm{time}}=\mathrm{VID}$
EL17:
The rate of change of total volume of water in the body (DVTW) is equal to the
rate of intake of water (TVD) minus the rate of output of water in the urine (VUD).
EL18:
The total volume of water in the body at any given instant (VTW) is determined
by integrating with respect times the rate of change of total water volume (DVTW).
EL17:
The rate of change of total volume of water in the body (DVTW) is equal to the
rate of intake of water (TVD) minus the rate of output of water in the urine (VUD).
EL18:
The total volume of water in the body at any given instant (VTW) is determined
by integrating with respect times the rate of change of total water volume (DVTW).
$\frac{d \mathrm{VTW}}{d \mathrm{time}}=\mathrm{TVD}-\mathrm{VUD}$
EL19:
The extracellular fluid volume (VEC) is equal to the total volume of water in the
body (VTW) minus the total volume of water inside all of the cells of the body (VIC).
EL19:
The extracellular fluid volume (VEC) is equal to the total volume of water in the
body (VTW) minus the total volume of water inside all of the cells of the body (VIC).
$\mathrm{VEC}=\mathrm{VTW}-\mathrm{VIC}$
Effect of heart hypertrophy or heart deterioration on heart pumping capability.
Encapsulation grouping component containing all the components in the Heart Hypertrophy or Deterioration Model.
The inputs and outputs of the Model must be passed by this component.
HH1A, HH1, and HH2:
Calculation of a quantitative value (output of Block HH2) which is a multiplier
that is approached asymptotically in response to three factors that cause left
ventricular hypertrophy, (1) the arterial pressure (PA), (2) the cardiac output (QAO),
and (3) the basic strength of the heart (HSL). The degree of hypertrophy in response
to the input factors is controlled by the exponent (Z13) in Block HH2.
HH3, HH4, and HH5:
Calculation of the actual degree of hypertrophy of the left ventricle (HPL) that
results over a period of time in response to arterial pressure (PA), cardiac output (QAO),
and basic left ventricular strength (HSL). The value HPL approaches the output value
from Block HH2 asymptotically with a time constant equal to the input variable at the
side of Block HH4.
HH1A, HH1, and HH2:
Calculation of a quantitative value (output of Block HH2) which is a multiplier
that is approached asymptotically in response to three factors that cause left
ventricular hypertrophy, (1) the arterial pressure (PA), (2) the cardiac output (QAO),
and (3) the basic strength of the heart (HSL). The degree of hypertrophy in response
to the input factors is controlled by the exponent (Z13) in Block HH2.
HH3, HH4, and HH5:
Calculation of the actual degree of hypertrophy of the left ventricle (HPL) that
results over a period of time in response to arterial pressure (PA), cardiac output (QAO),
and basic left ventricular strength (HSL). The value HPL approaches the output value
from Block HH2 asymptotically with a time constant equal to the input variable at the
side of Block HH4.
$\frac{d \mathrm{HPL}}{d \mathrm{time}}=\frac{\left(\frac{\mathrm{PA}\mathrm{QAO}}{500\mathrm{HSL}}\right)^{\mathrm{Z13}}-\mathrm{HPL}}{57600}$
HH6A, HH6, HH7, HH8, HH9, and HH10:
Calculation of the degree of hypertrophy of the right ventricle (HPR) according
to the same scheme as noted above for left ventricular hypertrophy, but with different
inputs: pulmonary arterial pressure (PPA), cardiac output (QAO), and basic normal
strength of the right heart (HSR).
HH6A, HH6, HH7, HH8, HH9, and HH10:
Calculation of the degree of hypertrophy of the right ventricle (HPR) according
to the same scheme as noted above for left ventricular hypertrophy, but with different
inputs: pulmonary arterial pressure (PPA), cardiac output (QAO), and basic normal
strength of the right heart (HSR).
$\frac{d \mathrm{HPR}}{d \mathrm{time}}=\frac{\left(\frac{\mathrm{PPA}\mathrm{QAO}}{75\mathrm{HSR}}\right)^{\mathrm{Z13}}-\mathrm{HPR}}{57600}$
HH11, HH12, HH13, and HH14:
Calculation of a multiplier factor that decreases cardiac pumping effectiveness (HMD)
when the cellular P02 of the heart muscle cells (POT) falls too low. The sensitivity
control is DHDTR, and the effect is limited by Block HH14 so that no change in HMD
occurs until the cell PO2 falls below the input value to the side of Block HH11.
HH11, HH12, HH13, and HH14:
Calculation of a multiplier factor that decreases cardiac pumping effectiveness (HMD)
when the cellular P02 of the heart muscle cells (POT) falls too low. The sensitivity
control is DHDTR, and the effect is limited by Block HH14 so that no change in HMD
occurs until the cell PO2 falls below the input value to the side of Block HH11.
HH11, HH12, HH13, and HH14:
Calculation of a multiplier factor that decreases cardiac pumping effectiveness (HMD)
when the cellular P02 of the heart muscle cells (POT) falls too low. The sensitivity
control is DHDTR, and the effect is limited by Block HH14 so that no change in HMD
occurs until the cell PO2 falls below the input value to the side of Block HH11.
HH11, HH12, HH13, and HH14:
Calculation of a multiplier factor that decreases cardiac pumping effectiveness (HMD)
when the cellular P02 of the heart muscle cells (POT) falls too low. The sensitivity
control is DHDTR, and the effect is limited by Block HH14 so that no change in HMD
occurs until the cell PO2 falls below the input value to the side of Block HH11.
$\mathrm{DHM}=(\mathrm{POT}-10)\mathrm{DHDTR}\frac{d \mathrm{HMD1}}{d \mathrm{time}}=\mathrm{DHM}\mathrm{HMD}=\begin{cases}1 & \text{if $\mathrm{HMD1}> 1$}\\ \mathrm{HMD1} & \text{otherwise}\end{cases}$
The heart rate (HR) and stroke volume output (SVO) are controlled by
autonomic stimulation (AUR), by a direct effect of right atrial pressure (PRA)
on the sinus rhythm of the heart, and by an effect of any degree of deterioration
of the heart (HMD) on heart rate control.
Encapsulation grouping component containing all the components in the Heart Rate and Stroke Volume Model.
The inputs and outputs of the Heart Rate and Stroke Volume Model must be passed by this component.
HR1:
Calculation of the portion of the heart rate that is controlled by
autonomic stimulation. Autonomic input is the variable (AUR).
HR1:
Calculation of the portion of the heart rate that is controlled by
autonomic stimulation. Autonomic input is the variable (AUR).
$\mathrm{AUHR}=72\mathrm{AUR}$
HR1A, HR1B, and HR2:
Calculation of the portion of the heart rate that is controlled by direct
effect of changes in right atrial pressure (PRA) on the sinus nodal rhythm.
Block HR1B limits the effect to positive atrial pressure (PRA) values.
HR1A, HR1B, and HR2:
Calculation of the portion of the heart rate that is controlled by direct
effect of changes in right atrial pressure (PRA) on the sinus nodal rhythm.
Block HR1B limits the effect to positive atrial pressure (PRA) values.
$\mathrm{PRHR}=\mathrm{PR1LL}^{0.5}\times 5$
HR4, HR5, and HR6:
Sensitivity control for the effect of any deterioration of heart function (HMD)
on heart rate. The sensitivity factor is the side input to Block HR5.
HR4, HR5, and HR6:
Sensitivity control for the effect of any deterioration of heart function (HMD)
on heart rate. The sensitivity factor is the side input to Block HR5.
$\mathrm{HDHR}=\mathrm{HMD}\times 0.5+1$
HR3:
Calculation of a temporary value for heart rate based on the control effects
of autonomic stimulation and right atrial pressure.
HR7: Calculation of heart rate (HR) by multiplying the heart deterioration
multiplier effect (output from Block HR6) times the temporary basic heart rate
calculated from Block HR3.
HR3:
Calculation of a temporary value for heart rate based on the control effects
of autonomic stimulation and right atrial pressure.
HR7: Calculation of heart rate (HR) by multiplying the heart deterioration
multiplier effect (output from Block HR6) times the temporary basic heart rate
calculated from Block HR3.
$\mathrm{HR}=(\mathrm{AUHR}+\mathrm{PRHR})\mathrm{HDHR}$
HR8:
Calculation of stroke volume output (SVO) by dividing minute left ventricular output (QLO)
by heart rate (HR).
HR8:
Calculation of stroke volume output (SVO) by dividing minute left ventricular output (QLO)
by heart rate (HR).
$\mathrm{SVO}=\frac{\mathrm{QLO}}{\mathrm{HR}}$
The circulatory system is divided into three separate parts for blood flow control:
(1) the kidneys which are presented in an entirely separate section of this model;
(2) non-muscle local blood flow control; and (3) muscle local blood flow control.
Muscle Autoregulatory Local Blood Flow Control
Autoregulation in the muscles is similar to that in the non-muscle tissues except
that only two parallel autoregulatory circuits are given. One of these is an
extremely short-term autoregulatory circuit that allows rapid adjustment of muscle
blood flow to muscle metabolism during muscle activity, and the other is a very
long-term autoregulatory circuit.
Encapsulation grouping component containing all the components in the Muscle Autoregulatory Local Blood
Flow Control Model. The inputs and outputs of the Muscle Autoregulatory Local Blood Flow Control Model
must be passed by this component.
ARM1:
Calculation of the driving force for autoregulation in the muscles (PDO) by subtracting
a set-point value from the pressure of oxygen in the muscle tissues (PMO).
ARM1:
Calculation of the driving force for autoregulation in the muscles (PDO) by subtracting
a set-point value from the pressure of oxygen in the muscle tissues (PMO).
$\mathrm{PDO}=\mathrm{PMO}-38$
Containment grouping component for "M_ST_sensitivity_control" and "M_ST_time_delay_and_damping".
ARM2 and ARM3:
Sensitivity control for the short-term muscle autoregulation, controlled by the
variable (POM), and the driving output oxygen pressure is the variable POE.
ARM2 and ARM3:
Sensitivity control for the short-term muscle autoregulation, controlled by the
variable (POM), and the driving output oxygen pressure is the variable POE.
$\mathrm{POE}=\mathrm{PDO}\mathrm{POM}+1$
ARM5, ARM6, and ARM7:
Time delay mechanism for the rapid autoregulation, allowing the output of
Block ARM7 (AMM1) to approach POE with a time constant of A4K.
ARM7A:
This sets a lower limit (AMM4) for the variable AMM1.
ARM5, ARM6, and ARM7:
Time delay mechanism for the rapid autoregulation, allowing the output of
Block ARM7 (AMM1) to approach POE with a time constant of A4K.
ARM7A:
This sets a lower limit (AMM4) for the variable AMM1.
$\frac{d \mathrm{AMM1T}}{d \mathrm{time}}=\frac{\mathrm{POE}\times 1-\mathrm{AMM1T}}{\mathrm{A4K}}\mathrm{AMM1}=\begin{cases}\mathrm{AMM4} & \text{if $\mathrm{AMM1T}< \mathrm{AMM4}$}\\ \mathrm{AMM1T} & \text{otherwise}\end{cases}$
Containment grouping component for "M_LT_sensitivity_control" and
"M_LT_time_delay".
ARM8:
Sensitivity control for controlling the long-term autoregulation in the muscles.
The variable that controls the sensitivity is POM2.
ARM8:
Sensitivity control for controlling the long-term autoregulation in the muscles.
The variable that controls the sensitivity is POM2.
$\mathrm{POF}=\mathrm{POM2}\mathrm{PDO}+1$
ARM9, ARM10, and ARM11:
Time delay system for long-term autoregulation in muscle with a time constant
equal to A4K2 and an output of AMM2.
ARM9, ARM10, and ARM11:
Time delay system for long-term autoregulation in muscle with a time constant
equal to A4K2 and an output of AMM2.
$\frac{d \mathrm{AMM2}}{d \mathrm{time}}=\frac{\mathrm{POF}\times 1-\mathrm{AMM2}}{\mathrm{A4K2}}$
ARM12:
Multiplication of the outputs of the two parallel muscle autoregulatory
systems (AMM1 and AMM2) to given an overall multiplier factor for muscle
autoregulation (AMM) that in turn controls vascular resistance in the muscles.
ARM12:
Multiplication of the outputs of the two parallel muscle autoregulatory
systems (AMM1 and AMM2) to given an overall multiplier factor for muscle
autoregulation (AMM) that in turn controls vascular resistance in the muscles.
$\mathrm{AMM}=\mathrm{AMM1}\mathrm{AMM2}$
The tissues of the body are divided into non-muscle tissues and muscle tissues,
and the delivery of oxygen to each one of these is calculated separately. The
principal reason for this separation is that during muscle activity, the delivery
of oxygen to the muscles increases tremendously and correspondingly affects the
blood flow through the muscles. Several aspects of local cellular usage of oxygen
are also calculated.
Encapsulation grouping component containing all the components in the Muscle Oxygen Delivery Model.
The inputs and outputs of the Muscle Oxygen Delivery Model must be passed by this component.
OM1:
The volume of oxygen in the arterial blood flowing to the muscles each minute (02ARTM)
is equal to the volume of oxygen in each liter of arterial blood (OVA) times the muscle
blood flow (BFM).
OM1:
The volume of oxygen in the arterial blood flowing to the muscles each minute (02ARTM)
is equal to the volume of oxygen in each liter of arterial blood (OVA) times the muscle
blood flow (BFM).
$\mathrm{O2ARTM}=\mathrm{OVA}\mathrm{BFM}$
OM2:
The volume of oxygen in the venous blood flowing away from the muscles
each minute (O2VENM) is equal to the volume of blood flowing into the muscles
from the arteries (O2ARTM) minus the rate of uptake of oxygen by the muscles
per minute (RMO).
OM3 and OM4:
The venous oxygen saturation in the muscles (OVS) is equal to the volume of oxygen
transported to the muscle veins each minute (O2VENM) divided by the blood flow
through the muscles per minute (BFM), divided by the hematocrit of the blood (HM),
and divided by a constant that relates volume of oxygen in the blood to hematocrit.
Damping of the oxygen venous saturation (OVS) is provided by Block OM4 and is controlled
by the damping constant (Z6).
OM5 and OM5A:
The pressure of the oxygen in the venous blood of the muscles (PVO) is equal to the
saturation of the oxygen in the venous blood of the muscles (OVS) times a constant
and times a factor related exponentially (EXCXP2) to the level of exercise (EXC)
caused by changes in tissue fluid products that affect oxygen combination with
hemoglobin.
OM2:
The volume of oxygen in the venous blood flowing away from the muscles
each minute (O2VENM) is equal to the volume of blood flowing into the muscles
from the arteries (O2ARTM) minus the rate of uptake of oxygen by the muscles
per minute (RMO).
OM3 and OM4:
The venous oxygen saturation in the muscles (OVS) is equal to the volume of oxygen
transported to the muscle veins each minute (O2VENM) divided by the blood flow
through the muscles per minute (BFM), divided by the hematocrit of the blood (HM),
and divided by a constant that relates volume of oxygen in the blood to hematocrit.
Damping of the oxygen venous saturation (OVS) is provided by Block OM4 and is controlled
by the damping constant (Z6).
OM5 and OM5A:
The pressure of the oxygen in the venous blood of the muscles (PVO) is equal to the
saturation of the oxygen in the venous blood of the muscles (OVS) times a constant
and times a factor related exponentially (EXCXP2) to the level of exercise (EXC)
caused by changes in tissue fluid products that affect oxygen combination with
hemoglobin.
$\mathrm{OVS}=\frac{\mathrm{O2ARTM}-\mathrm{RMO}}{\mathrm{HM}\times 5.25\mathrm{BFM}}\mathrm{PVO}=57.14\mathrm{OVS}\mathrm{EXC}^{\mathrm{EXCXP2}}$
OM17, OM18, OM19, OM20, OM21, OM22, and OM23:
Calculation of the rate of metabolic usage of oxygen by the muscle cells (MMO)
from several factors: the oxygen pressure in the muscle cells (PMO), the basal
level of oxygen utilization by the muscle cells (OMM), the effect of autonomic
stimulation on muscle usage of oxygen (AOM), and the effect of exercise on the
metabolic usage of oxygen by the muscles (EXC). Blocks OM17 and OM18 cause the
metabolic usage of oxygen to reach a maximum at any time that the average muscle
cellular oxygen level is above the value of 38 mmHg pressure. The constants in
the various blocks are curve-shaping constants to relate cellular oxygen
pressure (PMO) to the metabolic usage of oxygen.
OM17, OM18, OM19, OM20, OM21, OM22, and OM23:
Calculation of the rate of metabolic usage of oxygen by the muscle cells (MMO)
from several factors: the oxygen pressure in the muscle cells (PMO), the basal
level of oxygen utilization by the muscle cells (OMM), the effect of autonomic
stimulation on muscle usage of oxygen (AOM), and the effect of exercise on the
metabolic usage of oxygen by the muscles (EXC). Blocks OM17 and OM18 cause the
metabolic usage of oxygen to reach a maximum at any time that the average muscle
cellular oxygen level is above the value of 38 mmHg pressure. The constants in
the various blocks are curve-shaping constants to relate cellular oxygen
pressure (PMO) to the metabolic usage of oxygen.
OM17, OM18, OM19, OM20, OM21, OM22, and OM23:
Calculation of the rate of metabolic usage of oxygen by the muscle cells (MMO)
from several factors: the oxygen pressure in the muscle cells (PMO), the basal
level of oxygen utilization by the muscle cells (OMM), the effect of autonomic
stimulation on muscle usage of oxygen (AOM), and the effect of exercise on the
metabolic usage of oxygen by the muscles (EXC). Blocks OM17 and OM18 cause the
metabolic usage of oxygen to reach a maximum at any time that the average muscle
cellular oxygen level is above the value of 38 mmHg pressure. The constants in
the various blocks are curve-shaping constants to relate cellular oxygen
pressure (PMO) to the metabolic usage of oxygen.
$\mathrm{P2O}=\begin{cases}38 & \text{if $\mathrm{PMO}> 38$}\\ \mathrm{PMO} & \text{otherwise}\end{cases}\mathrm{MMO}=\mathrm{AOM}\mathrm{OMM}\mathrm{EXC}(1-\frac{(38.0001-\mathrm{P2O})^{3}}{54872})$
OM6:
The pressure gradient for delivery of oxygen from the muscle capillaries to the
muscle cells (PGRM) is equal to the pressure of the oxygen remaining in the
muscle venous blood (PVO) minus the pressure of the oxygen in the muscle cells (PMO).
OM8:
Rate of delivery of oxygen to the muscles (RMO) is equal to the blood flow to
the muscles (BFM) times the pressure gradient between the muscle capillary blood
and the muscle cells (PGRM) times a constant (PM5) that can be varied to represent
such factors as changes in muscle capillarity or so forth.
OM6:
The pressure gradient for delivery of oxygen from the muscle capillaries to the
muscle cells (PGRM) is equal to the pressure of the oxygen remaining in the
muscle venous blood (PVO) minus the pressure of the oxygen in the muscle cells (PMO).
OM8:
Rate of delivery of oxygen to the muscles (RMO) is equal to the blood flow to
the muscles (BFM) times the pressure gradient between the muscle capillary blood
and the muscle cells (PGRM) times a constant (PM5) that can be varied to represent
such factors as changes in muscle capillarity or so forth.
$\mathrm{RMO}=(\mathrm{PVO}-\mathrm{PMO})\mathrm{PM5}\mathrm{BFM}$
OM9:
The rate of change of stored oxygen in the muscle (DO2M) is equal to the
rate of delivery of oxygen to the muscles by the blood (RMO) minus the rate
of metabolic usage of oxygen by the muscle cells (MMO).
OM10:
The instantaneous volume of oxygen dissolved in all of the muscles (QOM) is
calculated by integrating with respect to time the rate of change of oxygen
in the muscles (DO2M).
OM11:
This sets a lower limit for QOM in the muscle tissue.
OM9:
The rate of change of stored oxygen in the muscle (DO2M) is equal to the
rate of delivery of oxygen to the muscles by the blood (RMO) minus the rate
of metabolic usage of oxygen by the muscle cells (MMO).
OM10:
The instantaneous volume of oxygen dissolved in all of the muscles (QOM) is
calculated by integrating with respect to time the rate of change of oxygen
in the muscles (DO2M).
OM11:
This sets a lower limit for QOM in the muscle tissue.
$\mathrm{DO2M}=\mathrm{RMO}-\mathrm{MMO}\frac{d \mathrm{QOM1}}{d \mathrm{time}}=\mathrm{DO2M}\mathrm{QOM}=\begin{cases}0.0001 & \text{if $\mathrm{QOM1}< 0.0001$}\\ \mathrm{QOM1} & \text{otherwise}\end{cases}$
OM12:
Calculation of the pressure of oxygen in the muscle cells (PMO) from the
volume of oxygen in the muscles (QOM).
OM12:
Calculation of the pressure of oxygen in the muscle cells (PMO) from the
volume of oxygen in the muscles (QOM).
$\mathrm{PMO}=\mathrm{PK2}\mathrm{QOM}$
The circulatory system is divided into three separate parts for blood flow control:
(1) the kidneys which are presented in an entirely separate section of this model;
(2) non-muscle local blood flow control; and (3) muscle local blood flow control.
Non-muscle Autoregulatory Local Blood Flow Control
This portion of the circulation has three separate parallel autoregulatory processes,
one of which occurs in a matter of minutes, another over a period of tens of minutes,
and a third over a period of weeks. All of these are considered to respond to changes
in tissue oxygen level. The first two are rapid metabolic feedback effects, one almost
instantaneous and the other occurring over a period of tens of minutes to an hour or so.
The third is considered to be structural changes that result over a period of weeks and
may be a consequence of the vasodilation or vasoconstriction that occurs during the two
short-term metabolic stages.
Encapsulation grouping component containing all the components in the Non-Muscle Autoregulatory Local Blood
Flow Control Model. The inputs and outputs of the Non-Muscle Autoregulatory Local Blood Flow Control Model
must be passed by this component.
ARN1:
The driving force that causes an autoregulatory response in non-muscle
tissues (POD) is equal to the pressure of the oxygen in tissues (POT) minus
the set-point for the autoregulatory response (POR).
ARN1:
The driving force that causes an autoregulatory response in non-muscle
tissues (POD) is equal to the pressure of the oxygen in tissues (POT) minus
the set-point for the autoregulatory response (POR).
$\mathrm{POD}=\mathrm{POT}-\mathrm{POR}$
Containment grouping component for "ST_sensitivity_control" and
"ST_time_delay_and_damping".
ARN2 and ARN3:
Sensitivity control for short-term autoregulation, with the sensitivity
controlled by the variable POK and the output of these two blocks equal
to the variable POB.
ARN2 and ARN3:
Sensitivity control for short-term autoregulation, with the sensitivity
controlled by the variable POK and the output of these two blocks equal
to the variable POB.
$\mathrm{POB}=\mathrm{POD}\mathrm{POK}+1$
ARN5, ARN6, and ARN7:
An integrative time delay system which allows the output from Block ARN7 (AR1)
to approach the value POB with a time constant of (A1K).
ARN7A:
Damping of output from Block ARN7 to prevent oscillation when the iteration
interval for computer solution of the model is long.
ARN5, ARN6, and ARN7:
An integrative time delay system which allows the output from Block ARN7 (AR1)
to approach the value POB with a time constant of (A1K).
ARN7A:
Damping of output from Block ARN7 to prevent oscillation when the iteration
interval for computer solution of the model is long.
$\frac{d \mathrm{AR1T}}{d \mathrm{time}}=\frac{\mathrm{POB}\times 1-\mathrm{AR1T}}{\mathrm{A1K}}\mathrm{AR1}=\begin{cases}0.5 & \text{if $\mathrm{AR1T}< 0.5$}\\ \mathrm{AR1T} & \text{otherwise}\end{cases}$
Containment grouping component for "NM_I_sensitivity_control" and
"NM_I_time_delay_and_limit".
ARN8 and ARN9:
Sensitivity control for the intermediate time autoregulation controlled by
variable (PON). The input is POD, and the output is POA.
ARN8 and ARN9:
Sensitivity control for the intermediate time autoregulation controlled by
variable (PON). The input is POD, and the output is POA.
$\mathrm{POA}=\mathrm{PON}\mathrm{POD}+1$
ARN11, ARN12, and ARN13:
A time delay mechanism for the intermediate autoregulation which allows the
output of Block ARN13 (AR2) to approach (POA) with a time constant of A2K.
ARN13A:
This sets a lower limit for AR2.
ARN11, ARN12, and ARN13:
A time delay mechanism for the intermediate autoregulation which allows the
output of Block ARN13 (AR2) to approach (POA) with a time constant of A2K.
ARN13A:
This sets a lower limit for AR2.
$\frac{d \mathrm{AR2T}}{d \mathrm{time}}=\frac{\mathrm{POA}\times 1-\mathrm{AR2T}}{\mathrm{A2K}}\mathrm{AR2}=\begin{cases}0.5 & \text{if $\mathrm{AR2T}< 0.5$}\\ \mathrm{AR2T} & \text{otherwise}\end{cases}$
Containment grouping component for "NM_LT_sensitivity_control" and
"NM_LT_time_delay_and_limit".`
ARN14:
Calculation of the relationship between the driving force for overall
autoregulatory control (POD) and that for long-term autoregulatory control (POC).
The sensitivity control is variable (POZ).
ARN14:
Calculation of the relationship between the driving force for overall
autoregulatory control (POD) and that for long-term autoregulatory control (POC).
The sensitivity control is variable (POZ).
$\mathrm{POC}=\mathrm{POZ}\mathrm{POD}+1$
ARN15, ARN16, and ARN17:
Time delay system that allows the output of Block ARN17 (AR3) to approach POC
with a time constant equal to the variable (A3K).
ARN17A:
This sets the lower limit for AR3.
ARN15, ARN16, and ARN17:
Time delay system that allows the output of Block ARN17 (AR3) to approach POC
with a time constant equal to the variable (A3K).
ARN17A:
This sets the lower limit for AR3.
$\frac{d \mathrm{AR3T}}{d \mathrm{time}}=\frac{\mathrm{POC}\times 1-\mathrm{AR3T}}{\mathrm{A3K}}\mathrm{AR3}=\begin{cases}0.3 & \text{if $\mathrm{AR3T}< 0.3$}\\ \mathrm{AR3T} & \text{otherwise}\end{cases}$
ARN18:
Multiplication of the outputs of the three different autoregulation mechanisms
by multiplying AR3, AR2, and AR1 times each other, giving a total output of the
non-muscle autoregulatory system equal to the variable (ARM1).
ARN18:
Multiplication of the outputs of the three different autoregulation mechanisms
by multiplying AR3, AR2, and AR1 times each other, giving a total output of the
non-muscle autoregulatory system equal to the variable (ARM1).
$\mathrm{ARM1}=\mathrm{AR1}\mathrm{AR2}\mathrm{AR3}$
ARN19, ARN20, and ARN21:
Sensitivity control for the total autoregulatory output for non-muscle, non-renal
tissues. The input is ARM1, the sensitivity control is AUTOSN, and the final output
is a non-muscle autoregulatory multiplier factor (ARM) that controls non-muscle vascular
resistance.
ARN19, ARN20, and ARN21:
Sensitivity control for the total autoregulatory output for non-muscle, non-renal
tissues. The input is ARM1, the sensitivity control is AUTOSN, and the final output
is a non-muscle autoregulatory multiplier factor (ARM) that controls non-muscle vascular
resistance.
$\mathrm{ARM}=\mathrm{ARM1}\mathrm{AUTOSN}+1$
The tissues of the body are divided into non-muscle tissues and muscle tissues,
and the delivery of oxygen to each one of these is calculated separately. The
principal reason for this separation is that during muscle activity, the delivery
of oxygen to the muscles increases tremendously and correspondingly affects the
blood flow through the muscles. Several aspects of local cellular usage of oxygen
are also calculated.
Encapsulation grouping component containing all the components in the Non-Muscle Oxygen Delivery Model.
The inputs and outputs of the Non-Muscle Oxygen Delivery Model must be passed by this component.
ONM1:
The quantity of oxygen in the arterial blood entering the non-muscle
tissues per minute (O2ARTN) is equal to the oxygen volume in each liter of
arterial blood (OVA) times the blood flow to the non-muscle tissues (BFN).
ONM1:
The quantity of oxygen in the arterial blood entering the non-muscle
tissues per minute (O2ARTN) is equal to the oxygen volume in each liter of
arterial blood (OVA) times the blood flow to the non-muscle tissues (BFN).
$\mathrm{O2ARTN}=\mathrm{OVA}\mathrm{BFN}$
ONM2:
The volume of oxygen remaining in the effluent venous blood from the non-muscle
tissues per minute (O2VENN) is equal to the volume of oxygen in the entering
arterial blood (O2ARTN) minus the rate of delivery of oxygen to the non-muscle
tissues per minute (DOB).
ONM3 and ONM4:
The oxygen saturation of the venous blood leaving the non-muscle tissues (OSV)
is calculated from the volume of oxygen in this venous blood (O2VENN) divided by
three different factors: the rate of blood flow through the non-muscle tissues (BFN),
the hematocrit (HM), and a constant factor for converting volume of oxygen to saturation.
Block ONM4 provides damping to prevent too rapid changes which could cause computational
oscillation; the degree of damping can be altered by altering the damping factor (Z7).
ONM5:
The pressure of oxygen in the venous blood (POV) is calculated by multiplying the venous
blood saturation (OSV) times a constant.
ONM2:
The volume of oxygen remaining in the effluent venous blood from the non-muscle
tissues per minute (O2VENN) is equal to the volume of oxygen in the entering
arterial blood (O2ARTN) minus the rate of delivery of oxygen to the non-muscle
tissues per minute (DOB).
ONM3 and ONM4:
The oxygen saturation of the venous blood leaving the non-muscle tissues (OSV)
is calculated from the volume of oxygen in this venous blood (O2VENN) divided by
three different factors: the rate of blood flow through the non-muscle tissues (BFN),
the hematocrit (HM), and a constant factor for converting volume of oxygen to saturation.
Block ONM4 provides damping to prevent too rapid changes which could cause computational
oscillation; the degree of damping can be altered by altering the damping factor (Z7).
ONM5:
The pressure of oxygen in the venous blood (POV) is calculated by multiplying the venous
blood saturation (OSV) times a constant.
$\mathrm{OSV}=\frac{\mathrm{O2ARTN}-\mathrm{DOB}}{\mathrm{HM}\times 5.25\mathrm{BFN}}\mathrm{POV}=\mathrm{OSV}\times 57.14$
ONM14, ONM15, ONM16, ONM17, ONM18, ONM19, and ONM20:
Calculation of the rate of oxygen usage by the non-muscle tissues (M02) based on
three input factors: the normal rate of oxygen usage by these tissues when all
other factors are normal (02M), a decreasing effect on tissue utilization of oxygen
caused by very low tissue PO2's (POT) resulting mainly from failure of flow of the
oxygen to the places where it is needed within the tissue (Blocks 14, 15, 16, 17, 18,
and 19), and a multiplying effect on oxygen usage caused by autonomic stimulation (AOM).
In addition, there is a limit set by Block ONM15 which causes the tissue oxygen level not
to affect metabolism once its level is above a set value.
ONM14, ONM15, ONM16, ONM17, ONM18, ONM19, and ONM20:
Calculation of the rate of oxygen usage by the non-muscle tissues (M02) based on
three input factors: the normal rate of oxygen usage by these tissues when all
other factors are normal (02M), a decreasing effect on tissue utilization of oxygen
caused by very low tissue PO2's (POT) resulting mainly from failure of flow of the
oxygen to the places where it is needed within the tissue (Blocks 14, 15, 16, 17, 18,
and 19), and a multiplying effect on oxygen usage caused by autonomic stimulation (AOM).
In addition, there is a limit set by Block ONM15 which causes the tissue oxygen level not
to affect metabolism once its level is above a set value.
ONM14, ONM15, ONM16, ONM17, ONM18, ONM19, and ONM20:
Calculation of the rate of oxygen usage by the non-muscle tissues (M02) based on
three input factors: the normal rate of oxygen usage by these tissues when all
other factors are normal (02M), a decreasing effect on tissue utilization of oxygen
caused by very low tissue PO2's (POT) resulting mainly from failure of flow of the
oxygen to the places where it is needed within the tissue (Blocks 14, 15, 16, 17, 18,
and 19), and a multiplying effect on oxygen usage caused by autonomic stimulation (AOM).
In addition, there is a limit set by Block ONM15 which causes the tissue oxygen level not
to affect metabolism once its level is above a set value.
$\mathrm{P1O}=\begin{cases}35 & \text{if $\mathrm{POT}> 35$}\\ \mathrm{POT} & \text{otherwise}\end{cases}\mathrm{MO2}=\mathrm{AOM}\mathrm{O2M}(1-\frac{(35.0001-\mathrm{P1O})^{3}}{42875})$
ONM6:
The pressure gradient of the oxygen between the venous or capillary blood of the
non-muscle tissues and the tissue cells themselves (PGRN) is equal to the pressure
of the oxygen in the venous blood (POV) minus the pressure in the non-muscle
tissue cells (POT).
ONM7:
The delivery of oxygen to the non-muscle tissues (DOB) is equal to blood flow to
the tissues (BFN) times the oxygen pressure gradient between the venous or capillary
blood and the tissues (PGRN) times a numerical factor for conductance of oxygen from
the capillaries to the tissue cells.
ONM6:
The pressure gradient of the oxygen between the venous or capillary blood of the
non-muscle tissues and the tissue cells themselves (PGRN) is equal to the pressure
of the oxygen in the venous blood (POV) minus the pressure in the non-muscle
tissue cells (POT).
ONM7:
The delivery of oxygen to the non-muscle tissues (DOB) is equal to blood flow to
the tissues (BFN) times the oxygen pressure gradient between the venous or capillary
blood and the tissues (PGRN) times a numerical factor for conductance of oxygen from
the capillaries to the tissue cells.
$\mathrm{DOB}=(\mathrm{POV}-\mathrm{POT})\times 12.857\mathrm{BFN}$
ONM8:
The rate of change of oxygen in the non-muscle tissues (DO2N) is equal to the rate
of delivery of oxygen to the non-muscle tissues (DOB) minus the rate of metabolism
of oxygen in the tissues (MO2).
ONM9:
Limitation in the use of oxygen by the tissues (MO2) when tissue oxygenation (Q02)
falls very low.
ONM10:
The instantaneous quantity of oxygen in the tissues (Q02) is calculated by integrating
the rate of change of the oxygen in these tissues (D02N).
ONM8:
The rate of change of oxygen in the non-muscle tissues (DO2N) is equal to the rate
of delivery of oxygen to the non-muscle tissues (DOB) minus the rate of metabolism
of oxygen in the tissues (MO2).
ONM9:
Limitation in the use of oxygen by the tissues (MO2) when tissue oxygenation (Q02)
falls very low.
ONM10:
The instantaneous quantity of oxygen in the tissues (Q02) is calculated by integrating
the rate of change of the oxygen in these tissues (D02N).
ONM10:
The instantaneous quantity of oxygen in the tissues (Q02) is calculated by integrating
the rate of change of the oxygen in these tissues (D02N).
$\mathrm{DO2N1}=\mathrm{DOB}-\mathrm{MO2}\mathrm{DO2N}=\begin{cases}\mathrm{DO2N1}\times 0.1 & \text{if $(\mathrm{QO2}< 6)\land (\mathrm{DO2N1}< 0)$}\\ \mathrm{DO2N1} & \text{otherwise}\end{cases}\frac{d \mathrm{QO2T}}{d \mathrm{time}}=\mathrm{DO2N}\mathrm{QO2}=\begin{cases}0 & \text{if $\mathrm{QO2T}< 0$}\\ \mathrm{QO2T} & \text{otherwise}\end{cases}$
ONM11:
The pressure of the oxygen in the tissue cells of the non-muscle tissues (POT)
is equal to the quantity of oxygen in the tissues (Q02) times a constant.
ONM11:
The pressure of the oxygen in the tissue cells of the non-muscle tissues (POT)
is equal to the quantity of oxygen in the tissues (Q02) times a constant.
$\mathrm{POT}=\mathrm{QO2}\times 0.48611$
This is a highly simplified analysis of pulmonary fluid dynamics. In general, the gel
portion of the pulmonary fluid is ignored, so that the pulmonary fluid volume (VPF) is
in reality an approximation of the amount of fluid that is relatively freely mobile.
Though this fluid is called "interstitial fluid," it includes fluid in the respiratory
passages. Likewise, the pressure-volume curve of the pulmonary interstitium is highly
simplified, as well as the control of lymph flow. Nevertheless, for many purposes, this
simplified analysis serves quite well.
Encapsulation grouping component containing all the components in the Pulmonary Fluid Dynamics Model.
The inputs and outputs of the Pulmonary Fluid Dynamics Model must be passed by this component.
PD1, PD2, PD2A, and PD3:
Calculation of pulmonary capillary pressure (PCP) from the pulmonary arterial
pressure (PPA) and left atrial pressure (PLA), and also from the vascular
resistances in the arterial (RPA) and venous (RPV) sides of the pulmonary
capillaries. The arterial resistance is set to be 1.6 times the venous
resistance.
PD1, PD2, PD2A, and PD3:
Calculation of pulmonary capillary pressure (PCP) from the pulmonary arterial
pressure (PPA) and left atrial pressure (PLA), and also from the vascular
resistances in the arterial (RPA) and venous (RPV) sides of the pulmonary
capillaries. The arterial resistance is set to be 1.6 times the venous
resistance.
$\mathrm{PCP}=\frac{(\mathrm{PPA}-\mathrm{PLA})\mathrm{RPV}}{\mathrm{RPV}+\mathrm{RPA}}+\mathrm{PLA}$
PD4:
The pressure gradient across the pulmonary capillary membrane (PGRPCM) is equal
to the pulmonary capillary pressure (PCP), plus the colloid osmotic pressure of
the pulmonary interstitial fluid (POS), minus the pulmonary interstitial fluid
pressure (PPI), minus the plasma colloid osmotic pressure (PPC).
PD5:
Rate of filtration of fluid outward through the pulmonary capillary membranes
into the interstitium (PFI) is equal to the pressure gradient across the
pulmonary capillary membrane (PGRPCM) times the pulmonary capillary filtration
coefficient (CPF).
PD4:
The pressure gradient across the pulmonary capillary membrane (PGRPCM) is equal
to the pulmonary capillary pressure (PCP), plus the colloid osmotic pressure of
the pulmonary interstitial fluid (POS), minus the pulmonary interstitial fluid
pressure (PPI), minus the plasma colloid osmotic pressure (PPC).
PD5:
Rate of filtration of fluid outward through the pulmonary capillary membranes
into the interstitium (PFI) is equal to the pressure gradient across the
pulmonary capillary membrane (PGRPCM) times the pulmonary capillary filtration
coefficient (CPF).
$\mathrm{PFI}=(\mathrm{PCP}-\mathrm{PPI}+\mathrm{POS}-\mathrm{PPC})\mathrm{CPF}$
PD5A, PD5B, and PD5C:
The rate of change of the fluid volume in the lungs (DFP) is equal to the rate
of filtration of fluid out of the pulmonary capillary membranes (PFI), minus the
rate of return of fluid to the circulation from the pulmonary interstitium by way
of the pulmonary lymphatics (PLF). Blocks 5B and 5C are computational blocks for
preventing oscillation and for preventing overshoot of the iteration. The damping
factor (Z) is used at multiple points in the model.
PD6:
Calculation of the volume of free fluid in the pulmonary interstitium (and
respiratory passageways) (VPF) by integrating the rate of change of the free fluid
in the lungs (DFP).
NB: - Damping in PD5B has been removed so that DFP = DFZ.
- PD5C has been rearranged so that "if" statement is dependent on VPF which may alter
the DFP output. (DFP IMPORTED INTO CP10 - Capillary Dynamics! CHECK THIS!!!).
PD5A, PD5B, and PD5C:
The rate of change of the fluid volume in the lungs (DFP) is equal to the rate
of filtration of fluid out of the pulmonary capillary membranes (PFI), minus the
rate of return of fluid to the circulation from the pulmonary interstitium by way
of the pulmonary lymphatics (PLF). Blocks 5B and 5C are computational blocks for
preventing oscillation and for preventing overshoot of the iteration. The damping
factor (Z) is used at multiple points in the model.
NB: - Damping in PD5B has been removed so that DFP = DFZ.
- PD5C has been rearranged so that "if" statement is dependent on VPF which may alter
the DFP output. (DFP IMPORTED INTO CP10 - Capillary Dynamics! CHECK THIS!!!).
PD5A, PD5B, and PD5C:
The rate of change of the fluid volume in the lungs (DFP) is equal to the rate
of filtration of fluid out of the pulmonary capillary membranes (PFI), minus the
rate of return of fluid to the circulation from the pulmonary interstitium by way
of the pulmonary lymphatics (PLF). Blocks 5B and 5C are computational blocks for
preventing oscillation and for preventing overshoot of the iteration. The damping
factor (Z) is used at multiple points in the model.
NB: - Damping in PD5B has been removed so that DFP = DFZ.
- PD5C has been rearranged so that "if" statement is dependent on VPF which may alter
the DFP output. (DFP IMPORTED INTO CP10 - Capillary Dynamics! CHECK THIS!!!).
PD5A, PD5B, and PD5C:
The rate of change of the fluid volume in the lungs (DFP) is equal to the rate
of filtration of fluid out of the pulmonary capillary membranes (PFI), minus the
rate of return of fluid to the circulation from the pulmonary interstitium by way
of the pulmonary lymphatics (PLF). Blocks 5B and 5C are computational blocks for
preventing oscillation and for preventing overshoot of the iteration. The damping
factor (Z) is used at multiple points in the model.
NB: - Damping in PD5B has been removed so that DFP = DFZ.
- PD5C has been rearranged so that "if" statement is dependent on VPF which may alter
the DFP output. (DFP IMPORTED INTO CP10 - Capillary Dynamics! CHECK THIS!!!).
PD6:
Calculation of the volume of free fluid in the pulmonary interstitium (and
respiratory passageways) (VPF) by integrating the rate of change of the free fluid
in the lungs (DFP).
$\mathrm{DFZ}=\mathrm{PFI}-\mathrm{PLF}\mathrm{DFP}=\mathrm{DFZ}\frac{d \mathrm{VPF1}}{d \mathrm{time}}=\mathrm{DFP}\mathrm{VPF}=\begin{cases}0.001 & \text{if $\mathrm{VPF1}< 0.001$}\\ \mathrm{VPF1} & \text{otherwise}\end{cases}$
PD10 and PD11:
Curve-fitting blocks to calculate the pulmonary interstitial fluid pressure (PPI)
from the pulmonary interstitial fluid volume (VPF).
PD10 and PD11:
Curve-fitting blocks to calculate the pulmonary interstitial fluid pressure (PPI)
from the pulmonary interstitial fluid volume (VPF).
$\mathrm{PPI}=2-\frac{0.15}{\mathrm{VPF}}$
PD15, PD15A, and PD15B:
The rate of change of the total quantity of protein in the pulmonary interstitium (PPD)
is equal to the rate of influx of protein into the interstitium as a result of protein
leakage through the pulmonary capillary membrane (PPN) minus the rate of return of protein
to the circulation from the interstitium by way of the lymphatics (PPO). Blocks 15A and
15B are computational blocks for the purpose of preventing overshoot of an iteration and
for preventing oscillation. The factor (Z) is a damping factor that is used widely
throughout the model.
NB: - Damping in PF15A has been removed so that PPD = PPZ.
- PD15B has been rearranged so that "if" statement is dependent on PPR which may alter
the PPD output. (PPD IMPORTED INTO CP33 - Capillary Dynamics! CHECK THIS!!!).
PD16:
The total quantity of protein in the pulmonary interstital free fluid (PPR) is calculated
by integrating with respect to time the rate of change of protein in the pulmonary
interstitium (PPD).
PD17:
The concentration of protein in the pulmonary interstitium (CPN) is equal to the total
quantity of protein in the interstitium (PPR) divided by the volume of interstitial
fluid (VPF).
PD15, PD15A, and PD15B:
The rate of change of the total quantity of protein in the pulmonary interstitium (PPD)
is equal to the rate of influx of protein into the interstitium as a result of protein
leakage through the pulmonary capillary membrane (PPN) minus the rate of return of protein
to the circulation from the interstitium by way of the lymphatics (PPO). Blocks 15A and
15B are computational blocks for the purpose of preventing overshoot of an iteration and
for preventing oscillation. The factor (Z) is a damping factor that is used widely
throughout the model.
NB: - Damping in PF15A has been removed so that PPD = PPZ.
- PD15B has been rearranged so that "if" statement is dependent on PPR which may alter
the PPD output. (PPD IMPORTED INTO CP33 - Capillary Dynamics! CHECK THIS!!!).
PD15, PD15A, and PD15B:
The rate of change of the total quantity of protein in the pulmonary interstitium (PPD)
is equal to the rate of influx of protein into the interstitium as a result of protein
leakage through the pulmonary capillary membrane (PPN) minus the rate of return of protein
to the circulation from the interstitium by way of the lymphatics (PPO). Blocks 15A and
15B are computational blocks for the purpose of preventing overshoot of an iteration and
for preventing oscillation. The factor (Z) is a damping factor that is used widely
throughout the model.
NB: - Damping in PF15A has been removed so that PPD = PPZ.
- PD15B has been rearranged so that "if" statement is dependent on PPR which may alter
the PPD output. (PPD IMPORTED INTO CP33 - Capillary Dynamics! CHECK THIS!!!).
PD15, PD15A, and PD15B:
The rate of change of the total quantity of protein in the pulmonary interstitium (PPD)
is equal to the rate of influx of protein into the interstitium as a result of protein
leakage through the pulmonary capillary membrane (PPN) minus the rate of return of protein
to the circulation from the interstitium by way of the lymphatics (PPO). Blocks 15A and
15B are computational blocks for the purpose of preventing overshoot of an iteration and
for preventing oscillation. The factor (Z) is a damping factor that is used widely
throughout the model.
NB: - Damping in PF15A has been removed so that PPD = PPZ.
- PD15B has been rearranged so that "if" statement is dependent on PPR which may alter
the PPD output. (PPD IMPORTED INTO CP33 - Capillary Dynamics! CHECK THIS!!!).
PD16:
The total quantity of protein in the pulmonary interstital free fluid (PPR) is calculated
by integrating with respect to time the rate of change of protein in the pulmonary
interstitium (PPD).
PD17:
The concentration of protein in the pulmonary interstitium (CPN) is equal to the total
quantity of protein in the interstitium (PPR) divided by the volume of interstitial
fluid (VPF).
$\mathrm{PPZ}=\mathrm{PPN}-\mathrm{PPO}\mathrm{PPD}=\mathrm{PPZ}\frac{d \mathrm{PPR1}}{d \mathrm{time}}=\mathrm{PPD}\mathrm{PPR}=\begin{cases}0.025 & \text{if $\mathrm{PPR1}< 0.025$}\\ \mathrm{PPR1} & \text{otherwise}\end{cases}\mathrm{CPN}=\frac{\mathrm{PPR}}{\mathrm{VPF}}$
PD18:
The colloid osmotic pressure of the pulmonary interstitial fluid (POS) is equal to
the concentration of protein in the pulmonary interstitium (CPN) times a constant.
PD18:
The colloid osmotic pressure of the pulmonary interstitial fluid (POS) is equal to
the concentration of protein in the pulmonary interstitium (CPN) times a constant.
$\mathrm{POS}=\mathrm{CPN}\times 0.4$
PD19 and PD20:
The rate of leakage of protein through the pulmonary capillary membrane into the pulmonary
interstitium (PPN) is equal to the concentration of protein in the plasma (CPP), minus the
concentration of protein in the pulmonary interstitium (CPN) times a constant.
PD19 and PD20:
The rate of leakage of protein through the pulmonary capillary membrane into the pulmonary
interstitium (PPN) is equal to the concentration of protein in the plasma (CPP), minus the
concentration of protein in the pulmonary interstitium (CPN) times a constant.
$\mathrm{PPN}=(\mathrm{CPP}-\mathrm{CPN})\times 0.000225$
PD12 and PD13:
Curve-fitting blocks to calculate the rate of pulmonary lymph flow (PLF) from the
pulmonary interstitial fluid pressure (PPI).
PD14:
Rate of return of protein from the pulmonary interstitium to the circulation in
the pulmonary lymph (PPO) is equal to the concentration of protein in the
pulmonary interstitial fluid (CPN) times the rate of pulmonary lymph flow (PLF).
PD12 and PD13:
Curve-fitting blocks to calculate the rate of pulmonary lymph flow (PLF) from the
pulmonary interstitial fluid pressure (PPI).
PD14:
Rate of return of protein from the pulmonary interstitium to the circulation in
the pulmonary lymph (PPO) is equal to the concentration of protein in the
pulmonary interstitial fluid (CPN) times the rate of pulmonary lymph flow (PLF).
$\mathrm{PLF}=(\mathrm{PPI}+11)\times 0.0003\mathrm{PPO}=\mathrm{PLF}\mathrm{CPN}$
This section calculates the dynamics of oxygen uptake by the lungs, and calculates
also the combination of the oxygen with the hemoglobin of the blood.
Encapsulation grouping component containing all the components in the Pulmonary Oxygen Uptake Model.
The inputs and outputs of the Pulmonary Oxygen Uptake Model must be passed by this component.
PO1:
Calculation of total oxygen utilization by the body (O2UTIL) by adding the oxygen
usage by the muscles (RMO) plus oxygen usage by non-muscle parts of the body (DOB).
PO1:
Calculation of total oxygen utilization by the body (O2UTIL) by adding the oxygen
usage by the muscles (RMO) plus oxygen usage by non-muscle parts of the body (DOB).
$\mathrm{O2UTIL}=\mathrm{DOB}+\mathrm{RMO}$
PO2:
Calculation of alveolar ventilation (ALVENT). The details of this block will
be discussed in relation to blocks 14 through 24.
PO2:
Calculation of alveolar ventilation (ALVENT). The details of this block will
be discussed in relation to blocks 14 through 24.
$\mathrm{ALVENT}=\mathrm{O2UTIL}\mathrm{VNTSTM}\times 0.026667\mathrm{O2VTS2}\mathrm{O2VAD2}$
PO3 and PO4:
The output of block 3 is the decrease in oxygen pressure between the humidified
air breathed into the trachea and the PO2 in the alveoli. It is calculated by
dividing the rate of oxygen utilization (O2UTIL) by the rate of alveolar
ventilation (ALVENT) and by a constant. Block PO4 calculates the alveolar PO2 (PO2ALV)
by subtracting the PO2 decrease (output of block 3) from the PO2 of ambient
humidified air (PO2AMB) entering the trachea.
PO3 and PO4:
The output of block 3 is the decrease in oxygen pressure between the humidified
air breathed into the trachea and the PO2 in the alveoli. It is calculated by
dividing the rate of oxygen utilization (O2UTIL) by the rate of alveolar
ventilation (ALVENT) and by a constant. Block PO4 calculates the alveolar PO2 (PO2ALV)
by subtracting the PO2 decrease (output of block 3) from the PO2 of ambient
humidified air (PO2AMB) entering the trachea.
$\mathrm{PO2ALV}=\mathrm{PO2AMB}-\frac{\frac{\mathrm{O2UTIL}}{\mathrm{ALVENT}}}{0.761}$
PO5: Calculation of the pressure difference between alveolar PO2 (PO2ALV) and
arterialized blood PO2 (PO2ART) leaving the lungs.
PO6 and PO7:
Calculation of the respiratory diffusion coefficient (RSPDFC) for diffusion of
oxygen between the alveoli and the blood leaving the pulmonary capillaries.
Block PO6 calculates a resistance to oxygen diffusion that varies in proportion
to the amount of free fluid in the alveoli (VPF) and the amount of pulmonary tissue
through which the oxygen must diffuse (VPTISS). Block 7 calculates the respiratory
diffusion coefficient (RSPDFC) by dividing a constant (PL2) by the resistance to
diffusion as calculated from block 6.
PO8:
Calculation of the rate of oxygen diffusion through the pulmonary membrane into
the capillaries (O2DFS) by multiplying the pressure difference (output of Block PO5)
between the alveoli and the pulmonary arterialized capillary blood times the respiratory
diffusion coefficient (RSPDFC).
PO6 and PO7:
Calculation of the respiratory diffusion coefficient (RSPDFC) for diffusion of
oxygen between the alveoli and the blood leaving the pulmonary capillaries.
Block PO6 calculates a resistance to oxygen diffusion that varies in proportion
to the amount of free fluid in the alveoli (VPF) and the amount of pulmonary tissue
through which the oxygen must diffuse (VPTISS). Block 7 calculates the respiratory
diffusion coefficient (RSPDFC) by dividing a constant (PL2) by the resistance to
diffusion as calculated from block 6.
PO5: Calculation of the pressure difference between alveolar PO2 (PO2ALV) and
arterialized blood PO2 (PO2ART) leaving the lungs.
PO8:
Calculation of the rate of oxygen diffusion through the pulmonary membrane into
the capillaries (O2DFS) by multiplying the pressure difference (output of Block PO5)
between the alveoli and the pulmonary arterialized capillary blood times the respiratory
diffusion coefficient (RSPDFC).
$\mathrm{RSPDFC}=\frac{\mathrm{PL2}}{\mathrm{VPTISS}+\mathrm{VPF}}\mathrm{O2DFS}=(\mathrm{PO2ALV}-\mathrm{PO2ART})\mathrm{RSPDFC}$
PO9:
Calculation of the difference between oxygen diffusion into the capillary blood
of the lungs (O2DFS) and the rate of oxygen utilization by the body (O2UTIL).
PO10:
Calculation of the rate of change of oxygen per liter of blood passing through
the lungs (DOVA) by dividing the rate of change of total amount of oxygen entering
the arterial blood per minute (output of Block 9) by the rate of blood flow through
the lungs (QRO).
PO11:
Calculation of the volume of oxygen in milliliters in each liter of arterial blood (OVA)
leaving the left ventricle by integrating the rate of change of oxygen in the
arterial blood (DOVA) with respect to time.
PO9:
Calculation of the difference between oxygen diffusion into the capillary blood
of the lungs (O2DFS) and the rate of oxygen utilization by the body (O2UTIL).
PO10:
Calculation of the rate of change of oxygen per liter of blood passing through
the lungs (DOVA) by dividing the rate of change of total amount of oxygen entering
the arterial blood per minute (output of Block 9) by the rate of blood flow through
the lungs (QRO).
PO11:
Calculation of the volume of oxygen in milliliters in each liter of arterial blood (OVA)
leaving the left ventricle by integrating the rate of change of oxygen in the
arterial blood (DOVA) with respect to time.
$\mathrm{DOVA}=\frac{\mathrm{O2DFS}-\mathrm{O2UTIL}}{\mathrm{QRO}\times 1.0}\frac{d \mathrm{OVA}}{d \mathrm{time}}=\mathrm{DOVA}$
PO12:
Calculation of the arterial oxygen saturation (OSA) by dividing concentration
of arterial oxygen in the arterial blood (OVA) by the hematocrit (HM) and by a
constant that relates the saturation to oxygen content.
PO13:
Calculation of PO2 in the arterial blood (PO2ART) at each level of arterial
hemoglobin oxygen saturation (OSA).
PO12:
Calculation of the arterial oxygen saturation (OSA) by dividing concentration
of arterial oxygen in the arterial blood (OVA) by the hematocrit (HM) and by a
constant that relates the saturation to oxygen content.
PO13:
Calculation of PO2 in the arterial blood (PO2ART) at each level of arterial
hemoglobin oxygen saturation (OSA).
$\mathrm{OSA}=\frac{\frac{\mathrm{OVA}}{\mathrm{HM}}}{5.25}\mathrm{PO2ART}=\begin{cases}114-\mathrm{OSA}\times 6667 & \text{if $\mathrm{OSA}> 1$}\\ 74-\mathrm{OSA}\times 625 & \text{if $(\mathrm{OSA}> 0.936)\land (\mathrm{OSA}\le 1)$}\\ 46-\mathrm{OSA}\times 205.882 & \text{if $(\mathrm{OSA}> 0.8)\land (\mathrm{OSA}\le 0.936)$}\\ \mathrm{OSA}\times 57.5 & \text{otherwise}\end{cases}$
Containment grouping component for "acute_chemoreceptor_adaptation_of_alveolar_ventilation"
and "progressive_chemoreceptor_adaptation_of_alveolar_ventilation".
PO14, PO15, PO16, PO17, PO18, PO19, PO20, PO21, PO22, PO23, PO24, and PO22:
This system of blocks calculates the effect of the O2 chemoreceptors in the carotid
and aortic bodies on alveoli ventilation (ALVENT). That is, when the arterial PO2
from Block 13 (PO2ART) falls below normal, this increases the alveolar ventilation
because of increased chemoreceptor stimulation. The increase in ventilation occurs
in two stages. One of these is an acute stage (calculated in Blocks 14-18) which
becomes fully activated within a few minutes. The second stage is a progressive
adaptation of this chemoreceptor control mechanism to increase pulmonary ventilation
another several fold over 1 to 3 days (calculated in Blocks 19-24).
The output of Block 18 (O2VTS2) is the initial acute adjustment of ventilation.
Blocks 16 and 17 set the upper and lower limits to this acute response to low oxygen.
The delayed effect on ventilation is the output of Block 24 (O2VAD2). Blocks 19, 20,
and 21 adjust the sensitivity of this delayed response. Block 22 provides the time
constant for this response. Block 2 multiplies the short-time constant response (O2VST2)
times the long-time constant response (O2VAD2). Another input to Block 2 is the rate
of oxygen utilization by the body [O2UTIL]. Physiologically, this is not a stimulus
to ventilation. However, in this model we do not calculate CO2 in the blood which is
a powerful stimulant of ventilation. Since the amount of carbon dioxide that is formed
over a period of minutes is approximately proportional to the rate of oxygen utilization,
we have used this O2UTIL factor as one of the normalized stimulatory factors of alveolar
ventilation in Block 2, but realizing that this is simply a substitute for rate of carbon
dioxide formation if the model were worked out in much greater detail. Still another input
is a special factor (VNTSTM) which allows the overall level of alveolar ventilation to be
increased or decreased artificially.
See description in "chemoreceptor_adaptation_of_alveolar_ventilation".
$\mathrm{O2VTST1}=\frac{\mathrm{PO2ART}-67}{30}\mathrm{O2VTST}=\begin{cases}1 & \text{if $\mathrm{O2VTST1}> 1$}\\ 0.6 & \text{if $\mathrm{O2VTST1}< 0.6$}\\ \mathrm{O2VTST1} & \text{otherwise}\end{cases}\mathrm{O2VTS2}=\frac{1}{\mathrm{O2VTST}}$
See description in chemoreceptor_adaptation_of_alveolar_ventilation.
$\mathrm{DO2VAD}=((\mathrm{O2VTS2}-1)\times 3-\mathrm{O2VAD1})\times 0.0005\frac{d \mathrm{O2VAD1}}{d \mathrm{time}}=\mathrm{DO2VAD}\mathrm{O2VAD2}=\mathrm{O2VAD1}+1$
The red cell volume is considered to be controlled by two principal factors that
control the production of erythropoietin:
(1) the arterial blood oxygen saturation (OSA) and renal function as determined by
renal blood flow (RFN), and
(2) the fraction (REK) of the renal mass that is functional.
Encapsulation grouping component containing all the components in the Red Cells and Viscosity Model.
The inputs and outputs of the Red Cells and Viscosity Model must be passed by this component.
Containment grouping component for "hematocrit_fraction", "viscosity_due_to_RBCs"
and "blood_viscosity".
RC6:
Calculation of blood volume (VB) by adding the volume of the red blood cells (VRC)
to the plasma volume (VP).
RC7:
The fraction of the blood that is composed of red blood cells (HM1) is equal to
the volume of red blood cells (VRC) divided by the blood volume (VB).
RC8:
The hematocrit (HM) equals the fraction of the blood that is red cells (HM1)
times 100.
RC6:
Calculation of blood volume (VB) by adding the volume of the red blood cells (VRC)
to the plasma volume (VP).
RC7:
The fraction of the blood that is composed of red blood cells (HM1) is equal to
the volume of red blood cells (VRC) divided by the blood volume (VB).
RC8:
The hematocrit (HM) equals the fraction of the blood that is red cells (HM1)
times 100.
$\mathrm{VB}=\mathrm{VP}+\mathrm{VRC}\mathrm{HM1}=\frac{\mathrm{VRC}}{\mathrm{VB}}\mathrm{HM}=100\mathrm{HM1}$
RC9, RC10, and RC11:
Curve-fitting blocks to calculate the portion of the viscosity of the blood that
is caused by red blood cells (VIE). The two variables (HMK and HKM) are
curve-fitting constants.
RC9, RC10, and RC11:
Curve-fitting blocks to calculate the portion of the viscosity of the blood that
is caused by red blood cells (VIE). The two variables (HMK and HKM) are
curve-fitting constants.
$\mathrm{VIE}=\frac{\mathrm{HM}}{(\mathrm{HMK}-\mathrm{HM})\mathrm{HKM}}$
RC12:
The viscosity of the blood (VIB) when calculated as a multiple of the viscosity
of water is equal to the viscosity effect caused by the red cells (VIE) plus a
constant determined by the viscosity of the plasma.
RC13:
Calculation of a normalized viscosity multiplier factor (VIM) that is used elsewhere
in the circulation to calculate the effect of changes in the viscosity from normal
(assumed to be 1.0) on various circulatory effects.
RC12:
The viscosity of the blood (VIB) when calculated as a multiple of the viscosity
of water is equal to the viscosity effect caused by the red cells (VIE) plus a
constant determined by the viscosity of the plasma.
RC13:
Calculation of a normalized viscosity multiplier factor (VIM) that is used elsewhere
in the circulation to calculate the effect of changes in the viscosity from normal
(assumed to be 1.0) on various circulatory effects.
$\mathrm{VIB}=\mathrm{VIE}+1.5\mathrm{VIM}=0.3333\mathrm{VIB}$
Containment grouping component for "oxygen_stimulation", "RBC_production",
"RBC_destruction" and "blood_viscosity".
RC1, RC1A, RC1B, RC1C, RC1D, RC2, RC2C, and RC2D:
Calculation of the effect of atmospheric O2 pressure (PO2AMB) on the
driving force (HM7) for production of red blood cells. RC1A, RC1B, and RC1D
calculate the effect of pressures below the level of 80 mmHg, and RC1 the effect
of pressures above 80. Blocks RC2, RC2C, and RC2D provide limits to the effects.
RC1, RC1A, RC1B, RC1C, RC1D, RC2, RC2C, and RC2D:
Calculation of the effect of atmospheric O2 pressure (PO2AMB) on the
driving force (HM7) for production of red blood cells. RC1A, RC1B, and RC1D
calculate the effect of pressures below the level of 80 mmHg, and RC1 the effect
of pressures above 80. Blocks RC2, RC2C, and RC2D provide limits to the effects.
RC1, RC1A, RC1B, RC1C, RC1D, RC2, RC2C, and RC2D:
Calculation of the effect of atmospheric O2 pressure (PO2AMB) on the
driving force (HM7) for production of red blood cells. RC1A, RC1B, and RC1D
calculate the effect of pressures below the level of 80 mmHg, and RC1 the effect
of pressures above 80. Blocks RC2, RC2C, and RC2D provide limits to the effects.
RC1, RC1A, RC1B, RC1C, RC1D, RC2, RC2C, and RC2D:
Calculation of the effect of atmospheric O2 pressure (PO2AMB) on the
driving force (HM7) for production of red blood cells. RC1A, RC1B, and RC1D
calculate the effect of pressures below the level of 80 mmHg, and RC1 the effect
of pressures above 80. Blocks RC2, RC2C, and RC2D provide limits to the effects.
RC1, RC1A, RC1B, RC1C, RC1D, RC2, RC2C, and RC2D:
Calculation of the effect of atmospheric O2 pressure (PO2AMB) on the
driving force (HM7) for production of red blood cells. RC1A, RC1B, and RC1D
calculate the effect of pressures below the level of 80 mmHg, and RC1 the effect
of pressures above 80. Blocks RC2, RC2C, and RC2D provide limits to the effects.
RC1, RC1A, RC1B, RC1C, RC1D, RC2, RC2C, and RC2D:
Calculation of the effect of atmospheric O2 pressure (PO2AMB) on the
driving force (HM7) for production of red blood cells. RC1A, RC1B, and RC1D
calculate the effect of pressures below the level of 80 mmHg, and RC1 the effect
of pressures above 80. Blocks RC2, RC2C, and RC2D provide limits to the effects.
$\mathrm{PO2AM1}=\begin{cases}80 & \text{if $\mathrm{PO2AMB}> 80$}\\ \mathrm{PO2AMB} & \text{otherwise}\end{cases}\mathrm{HM3}=(\mathrm{PO2AM1}-40)\mathrm{HM}\mathrm{HM4}=\mathrm{PO2AMB}-40\mathrm{HM5}=\begin{cases}0 & \text{if $\mathrm{HM3}+\mathrm{HM4}< 0$}\\ \mathrm{HM3}+\mathrm{HM4} & \text{otherwise}\end{cases}\mathrm{HM7}=\mathrm{HM6}-\mathrm{HM5}$
RC2A, RC2B, and RC2E:
Calculation of the rate of red blood cell production (RC1), with a lower limit
of zero set by Block RC2E, and the rate of production partly determined by the
amount of kidney mass available (REK) to produce erythropoition.
RC2A, RC2B, and RC2E:
Calculation of the rate of red blood cell production (RC1), with a lower limit
of zero set by Block RC2E, and the rate of production partly determined by the
amount of kidney mass available (REK) to produce erythropoition.
$\mathrm{RC1}=\begin{cases}0 & \text{if $\mathrm{HM7}\mathrm{HM8}\mathrm{REK}+0.000005< 0$}\\ \mathrm{HM7}\mathrm{HM8}\mathrm{REK}+0.000005 & \text{otherwise}\end{cases}$
RC5:
Calculation of the rate of red cell volume destruction (RC2) caused by the presence
of an already large red cell volume (VRC). The rate factor for this effect is (RKC).
Also increased blood viscosity is considered to cause increased destruction.
RC5:
Calculation of the rate of red cell volume destruction (RC2) caused by the presence
of an already large red cell volume (VRC). The rate factor for this effect is (RKC).
Also increased blood viscosity is considered to cause increased destruction.
$\mathrm{RC2}=\mathrm{VRC}\mathrm{RKC}\mathrm{VIM}$
RC3:
Calculation of the rate of change of red blood cell volume (RCD) by adding
the rate of RBC production (RC1) and subtracting the rate of destruction (RC2).
NB - Parameter TRRBC is not in diagram.
RC4:
Calculation of the instantaneous volume of red blood cells by integrating the rate
of change in total volume of red cells (RCD).
RC3:
Calculation of the rate of change of red blood cell volume (RCD) by adding
the rate of RBC production (RC1) and subtracting the rate of destruction (RC2).
NB - Parameter TRRBC is not in diagram.
RC4:
Calculation of the instantaneous volume of red blood cells by integrating the rate
of change in total volume of red cells (RCD).
$\mathrm{RCD}=\mathrm{RC1}-\mathrm{RC2}+\mathrm{TRRBC}\frac{d \mathrm{VRC}}{d \mathrm{time}}=\mathrm{RCD}$
Effect of Stress Relaxation on Basic Venous Volume (V0)
This section calculates the effect over a period of time caused by excess volume
(or too little volume) in the venous tree to cause changes in the volume holding
capacity of the venous tree when it is fully filled with blood but at zero pressure.
In this model, there are two separate parallel stress relaxations of the veins.
One of these has a short time constant (SRK) and the other has a long time constant (SRK2).
Encapsulation grouping component containing all the components in the Stress Relaxation Model.
The inputs and outputs of the Stress Relaxation Model must be passed by this component.
SR1 and SR2:
Calculation of the ultimate degree of change in basic venous volume to
be caused by the short-term stress relaxation factor with input to the
system equal to the instantaneous excess venous volume (VVE); a multiplier
factor controls the degree of stress relaxation that will occur (SR).
SR3, SR4, and SR5:
This is a delay circuit having a short time constant (SRK). The output of
this circuit (VV7) approaches the ultimate degree of stress relaxation
caused by short-term stress relaxation as calculated from Block SR2.
NB - REMOVED THE DAMPING FROM THE INTEGRAL!!!
SR1 and SR2:
Calculation of the ultimate degree of change in basic venous volume to
be caused by the short-term stress relaxation factor with input to the
system equal to the instantaneous excess venous volume (VVE); a multiplier
factor controls the degree of stress relaxation that will occur (SR).
SR3, SR4, and SR5:
This is a delay circuit having a short time constant (SRK). The output of
this circuit (VV7) approaches the ultimate degree of stress relaxation
caused by short-term stress relaxation as calculated from Block SR2.
NB - REMOVED THE DAMPING FROM THE INTEGRAL!!!
$\frac{d \mathrm{VV7}}{d \mathrm{time}}=\frac{(\mathrm{VVE}-0.74)\mathrm{SR}-\mathrm{VV7}}{\mathrm{SRK}}$
SR1A, SR2A, SR3A, AR4A, and SR5A:
Similar calculations to the above but this time with a long time constant
for stress relaxation (SRK2), and also having a separate variable for control
of the ultimate degree of the stress relaxation (SR2). The output of this
long time constant stress relaxation (VV6) along with the output from the
short time constant stress relaxation (VV7) are subtracted from the actual
venous volume (VVS) in Block CD15 in the hemodynamic section of the model.
SR1A, SR2A, SR3A, AR4A, and SR5A:
Similar calculations to the above but this time with a long time constant
for stress relaxation (SRK2), and also having a separate variable for control
of the ultimate degree of the stress relaxation (SR2). The output of this
long time constant stress relaxation (VV6) along with the output from the
short time constant stress relaxation (VV7) are subtracted from the actual
venous volume (VVS) in Block CD15 in the hemodynamic section of the model.
$\frac{d \mathrm{VV6}}{d \mathrm{time}}=\frac{(\mathrm{VVE}-0.74)\mathrm{SR2}-\mathrm{VV6}}{\mathrm{SRK2}}$
The salt appetite is considered in this model to be related to the adequacy
of body metabolism, as measured by the PO2 level in the non-muscle tissue
cells (POT). Also, when the concentration of angiotensin increases (ANM),
this, too, increases salt intake. For instance, in circulatory shock, when
the adequacy of metabolism falls, the person develops a salt appetite. For
lack of information, no control function of salt concentration per se has
been assumed, merely that when the body salt falls, circulatory effectiveness
falls, angiotensin increases, and a salt appetite develops.
Three separate factors are assumed to drive the thirst mechanism, the
concentration of antidiuretic hormone, which in turn is driven by changes
in electrolyte composition (as detailed in another section) and second, the
effect of angiotensin on thirst, and third, the effect of the salt appetite
stimulation on thirst.
Encapsulation grouping component containing all the components in the Thirst, Drinking
and Salt Appetite Model. The inputs and outputs of the Thirst, Drinking and Salt Appetite
Model must be passed by this component.
TS1, TS1A, TS2, TS2A, TS2B, TS2C, TS3, and TS4:
These are curve-fitting blocks to derive a value for salt appetite and for partial control of
thirst (STH) based on the input values of PO2 in the non-muscle tissue cells (POT) and the
angiotensin multiplier effect (ANM). The constant ANMSLT sets the sensitivity of salt appetite
to angiotensin, and the constant Z10 sets the PO2 level below which POT exerts its effects.
TS1, TS1A, TS2, TS2A, TS2B, TS2C, TS3, and TS4:
These are curve-fitting blocks to derive a value for salt appetite and for partial control of
thirst (STH) based on the input values of PO2 in the non-muscle tissue cells (POT) and the
angiotensin multiplier effect (ANM). The constant ANMSLT sets the sensitivity of salt appetite
to angiotensin, and the constant Z10 sets the PO2 level below which POT exerts its effects.
TS1, TS1A, TS2, TS2A, TS2B, TS2C, TS3, and TS4:
These are curve-fitting blocks to derive a value for salt appetite and for partial control of
thirst (STH) based on the input values of PO2 in the non-muscle tissue cells (POT) and the
angiotensin multiplier effect (ANM). The constant ANMSLT sets the sensitivity of salt appetite
to angiotensin, and the constant Z10 sets the PO2 level below which POT exerts its effects.
TS1, TS1A, TS2, TS2A, TS2B, TS2C, TS3, and TS4:
These are curve-fitting blocks to derive a value for salt appetite and for partial control of
thirst (STH) based on the input values of PO2 in the non-muscle tissue cells (POT) and the
angiotensin multiplier effect (ANM). The constant ANMSLT sets the sensitivity of salt appetite
to angiotensin, and the constant Z10 sets the PO2 level below which POT exerts its effects.
$\mathrm{ANMSML}=\mathrm{ANM}\mathrm{ANMSLT}+1\mathrm{STH1}=(\mathrm{Z10}-\mathrm{POT})^{2}\mathrm{Z11}\mathrm{ANMSML}\mathrm{STH}=\begin{cases}0.8 & \text{if $\mathrm{STH1}< 0.8$}\\ 8 & \text{if $\mathrm{STH1}> 8$}\\ \mathrm{STH1} & \text{otherwise}\end{cases}$
TS5, TS6, and TS7:
These blocks are a sensitivity controller for calculating a multiplier effect
of antidiuretic hormone on thirst (AHCM) from an antidiuretic hormone
concentration factor in the circulating body fluids (ADHC). The sensitivity is
controlled by the control factor (AHTHM).
TS5, TS6, and TS7:
These blocks are a sensitivity controller for calculating a multiplier effect
of antidiuretic hormone on thirst (AHCM) from an antidiuretic hormone
concentration factor in the circulating body fluids (ADHC). The sensitivity is
controlled by the control factor (AHTHM).
$\mathrm{AHCM}=\mathrm{ADHC}\mathrm{AHTHM}+1$
TS10 and TS11:
Calculation of the drive to stimulate thirst caused by angiotensin (ANMH) from
the generalized angiotensin multiplier (ANM). The sensitivity of this calculation
is controlled by the angiotensin-thirst sensitivity control variable (ANMTM).
TS10 and TS11:
Calculation of the drive to stimulate thirst caused by angiotensin (ANMH) from
the generalized angiotensin multiplier (ANM). The sensitivity of this calculation
is controlled by the angiotensin-thirst sensitivity control variable (ANMTM).
$\mathrm{ANMTH}=(\mathrm{ANM}-1)\mathrm{ANMTM}\times 0.001$
TS8 and TS9:
Calculation of a thirst drive (AHTH) based on antidiuretic hormone and salt
appetite by multiplying three factors, the salt appetite drive (STH), the antidiuretic
hormone concentration multiplier (AHCM), and a constant. Block TS9 sets a lower limit
to AHTH equal to zero.
TS12 and TS13:
A temporary calculation for rate of intake of fluid by the body (TVZ) is equal to the
drinking drive (AHTH) caused by the product of the salt appetite drive (STH) and the
antidiuretic-thirst drive (AHTH), plus the angiotensin-thirst drive (ANMTH). Block
TS13 sets the lower limit of (TVZ) to zero.
TS14, TS15, and TS16:
This is a delay circuit which causes the actual rate of fluid intake (TVD) to be delayed
with respect to changes in the temporarily calculated rate of fluid intake (TVZ) by a
time constant TVDLL. Also shown in Block TS14 is a variable (DR) that can be used for
forced input of water over and above the natural drinking desires; this can be used for
intravenous infusion of water as well.
TS8:
Calculation of a thirst drive (AHTH) based on antidiuretic hormone and salt
appetite by multiplying three factors, the salt appetite drive (STH), the antidiuretic
hormone concentration multiplier (AHCM), and a constant.
TS9:
Block TS9 sets a lower limit to AHTH equal to zero.
TS12:
A temporary calculation for rate of intake of fluid by the body (TVZ) is equal to the
drinking drive (AHTH) caused by the product of the salt appetite drive (STH) and the
antidiuretic-thirst drive (AHTH), plus the angiotensin-thirst drive (ANMTH).
TS13:
Block TS13 sets the lower limit of (TVZ) to zero.
TS14, TS15, and TS16:
This is a delay circuit which causes the actual rate of fluid intake (TVD) to be delayed
with respect to changes in the temporarily calculated rate of fluid intake (TVZ) by a
time constant TVDLL. Also shown in Block TS14 is a variable (DR) that can be used for
forced input of water over and above the natural drinking desires; this can be used for
intravenous infusion of water as well.
$\mathrm{AHTH1}=\mathrm{AHCM}\mathrm{STH}\times 0.001\mathrm{AHTH}=\begin{cases}0 & \text{if $\mathrm{AHTH1}< 0$}\\ \mathrm{AHTH1} & \text{otherwise}\end{cases}\mathrm{TVZ1}=(\mathrm{ANMTH}+\mathrm{AHTH})\times 1\mathrm{TVZ}=\begin{cases}0 & \text{if $\mathrm{TVZ1}< 0$}\\ \mathrm{TVZ1} & \text{otherwise}\end{cases}\frac{d \mathrm{TVD}}{d \mathrm{time}}=\frac{\mathrm{TVZ}+\mathrm{DR}-\mathrm{TVD}}{\mathrm{TVDDL}}$
The volume receptor nervous feedback mechanism:
The volume receptors are considered to be activated by right atrial pressure (PRA),
and feedback is provided to control non-muscle arterial resistance and venous tone.
Encapsulation grouping component containing all the components in the Volume Receptors Model.
The inputs and outputs of the Volume Receptors Model must be passed by this component.
VR1 and VR2:
The function curve in Block VR1 and sensitivity control in VR2 (controlled by
variable AH9) provide a relationship between right atrial pressure (PRA) and an
intermediate factor (AHZ) that controls the degree of nervous feedback.
VR1 and VR2:
The function curve in Block VR1 and sensitivity control in VR2 (controlled by
variable AH9) provide a relationship between right atrial pressure (PRA) and an
intermediate factor (AHZ) that controls the degree of nervous feedback.
VR1 and VR2:
The function curve in Block VR1 and sensitivity control in VR2 (controlled by
variable AH9) provide a relationship between right atrial pressure (PRA) and an
intermediate factor (AHZ) that controls the degree of nervous feedback.
$\mathrm{AHZ1}=\left|\mathrm{PRA}\right|^{\mathrm{AH10}}\mathrm{AH9}\mathrm{AHZ}=\begin{cases}-\mathrm{AHZ1} & \text{if $\mathrm{PRA}< 0$}\\ \mathrm{AHZ1} & \text{otherwise}\end{cases}$
VR3, VR4, and VR5:
Series of blocks to provide autoresetting of the volume receptors back
toward zero with time. The degree of reset is the variable (AHY), and
the time constant for resetting is the variable (AH11).
VR3, VR4, and VR5:
Series of blocks to provide autoresetting of the volume receptors back
toward zero with time. The degree of reset is the variable (AHY), and
the time constant for resetting is the variable (AH11).
$\frac{d \mathrm{AHY}}{d \mathrm{time}}=\frac{\mathrm{AHZ}-\mathrm{AHY}}{\mathrm{AH11}}$
VR6:
The final degree of effect of the volume nervous feedback mechanism is
the output from block VR6 (AH7).
VR6:
The final degree of effect of the volume nervous feedback mechanism is
the output from block VR6 (AH7).
$\mathrm{AH7}=\mathrm{AHZ}-\mathrm{AHY}$
VR7 and VR8:
Sensitivity control for the volume receptor nervous feedback effect on the
non-muscle arterial resistance. The output multiplier effect for feedback
to the arteries is the variable (ATRRFB) and the sensitivity controller is
the variable (ATRFBM).
VR7 and VR8:
Sensitivity control for the volume receptor nervous feedback effect on the
non-muscle arterial resistance. The output multiplier effect for feedback
to the arteries is the variable (ATRRFB) and the sensitivity controller is
the variable (ATRFBM).
$\mathrm{ATRRFB}=\mathrm{AH7}\mathrm{ATRFBM}+1$
VR9:
Sensitivity control for volume receptor feedback to the venous system.
The output of Block 9 (ATRVFB) controls V0 of the venous tree. The sensitivity
controller is the variable (ATRVM).
VR9:
Sensitivity control for volume receptor feedback to the venous system.
The output of Block 9 (ATRVFB) controls V0 of the venous tree. The sensitivity
controller is the variable (ATRVM).
$\mathrm{ATRVFB}=\mathrm{AH7}\mathrm{ATRVM}$
FUNCTION OF THE KIDNEY
This section is a highly simplified analysis of renal function, including analysis of
blood flow through the kidney and of the formation of glomerular filtrate. Then the
changes that occur in the filtrate as it passes through the tubules are calculated.
However, only four substances are considered as they pass through the tubules:
sodium, potassium, urea, and water.
The control effects of angiotensin, aldosterone, antidiuretic hormone, and nervous
signals are also presented.
Encapsulation grouping component containing all the components in the Kidney Model. The inputs and
outputs of the Kidney Model must be passed by this component.
KD1:
The perfusion pressure of the kidneys (PAR) is calculated by subtracting any
pressure gradient caused by renal arterial constriction (GBL) from the systemic
arterial pressure (PA). This block allows one to simulate Goldblatt hypertension.
KD2:
This block allows one to simulate other experiments. The factor (RAPRSP), when
set to any value besides zero, will fix the renal perfusion pressure (PAR) to an
exact value that will not change regardless of changes in systemic arterial pressure.
The factor (RFCDFT) allows one to test the hypothetical condition that function of
the kidney over a long period of time asymptotically approaches normal output
function regardless of changes in arterial pressure. That is, PAR drifts continually
back toward the normal mean value of 100 rather than being determined by the systemic
arterial pressure, simulating shift of the renal function curve. This is used to test
theories that in the long run kidney output function can be independent of arterial
pressure.
KD2:
This block allows one to simulate other experiments. The factor (RAPRSP), when
set to any value besides zero, will fix the renal perfusion pressure (PAR) to an
exact value that will not change regardless of changes in systemic arterial pressure.
The factor (RFCDFT) allows one to test the hypothetical condition that function of
the kidney over a long period of time asymptotically approaches normal output
function regardless of changes in arterial pressure. That is, PAR drifts continually
back toward the normal mean value of 100 rather than being determined by the systemic
arterial pressure, simulating shift of the renal function curve. This is used to test
theories that in the long run kidney output function can be independent of arterial
pressure.
KD1:
The perfusion pressure of the kidneys (PAR) is calculated by subtracting any
pressure gradient caused by renal arterial constriction (GBL) from the systemic
arterial pressure (PA). This block allows one to simulate Goldblatt hypertension.
KD2:
This block allows one to simulate other experiments. The factor (RAPRSP), when
set to any value besides zero, will fix the renal perfusion pressure (PAR) to an
exact value that will not change regardless of changes in systemic arterial pressure.
The factor (RFCDFT) allows one to test the hypothetical condition that function of
the kidney over a long period of time asymptotically approaches normal output
function regardless of changes in arterial pressure. That is, PAR drifts continually
back toward the normal mean value of 100 rather than being determined by the systemic
arterial pressure, simulating shift of the renal function curve. This is used to test
theories that in the long run kidney output function can be independent of arterial
pressure.
$\frac{d \mathrm{PAR1}}{d \mathrm{time}}=\frac{100-\mathrm{PA}\mathrm{RCDFPC}-\mathrm{PAR1}}{\mathrm{RCDFDP}}\mathrm{PAR}=\begin{cases}\mathrm{RAPRSP} & \text{if $(\mathrm{RAPRSP}> 0)\land (\mathrm{RFCDFT}\le 0)$}\\ \mathrm{PAR1} & \text{if $\mathrm{RFCDFT}> 0$}\\ \mathrm{PA}-\mathrm{GBL} & \text{otherwise}\end{cases}$
KD57, KD58, KD59, KD60, KD61, KD62, KD63, KD64, KD65, KD66, and KD67:
Calculation of an autoregulatory feedback factor that affects the degree of constriction
of both afferent and efferent arterioles (RNAUG2) which is the output of Block 64.
This feedback effect, and the resistance of the afferent and efferent arterioles,
increases in proportion to the calculation from these blocks and in response to the
flow rate of fluid in the tubules at the macula densa (MDFLW) which is the input to
Block 57. Blocks 57, 58, and 59 calculate the sensitivity of this feedback mechanism,
and the sensitivity control factor is RNAUGN in Block 58. Blocks 60 and 61 calculate
the time constant of development of this feedback in the arterioles after any change in
rate of flow (MDFLW) at the macula densa. The time constant of this feedback response
is RNAGTC in Block 60. The value RNAULL is the lower limit to the autoregulatory
response (RNAUG1) as set by Block 62. RNAUUL is the upper limit, as set by Block 63.
Block 65, 66, and 67 calculate obliterative adaptation of this feedback response in case
such as this does occur. The sensitivity of this, RNAUAD, in Block 66 is set at zero
because many persons believe there is no such decay of this feedback response. Yet others
have postulated such a feedback response, in which case RNAUAD would then become the factor
that sets the time constant of the loss of the feedback response with time. The output of
this total system from Block 14 is RNAUG2.
NB - REMOVED DAMPING FROM KD57-KD61!!!!!!!!!
KD57, KD58, KD59, KD60 and KD61:
Calculation of an autoregulatory feedback factor that affects the degree of constriction
of both afferent and efferent arterioles (RNAUG2) which is the output of Block 64.
This feedback effect, and the resistance of the afferent and efferent arterioles,
increases in proportion to the calculation from these blocks and in response to the
flow rate of fluid in the tubules at the macula densa (MDFLW) which is the input to
Block 57. Blocks 57, 58, and 59 calculate the sensitivity of this feedback mechanism,
and the sensitivity control factor is RNAUGN in Block 58. Blocks 60 and 61 calculate
the time constant of development of this feedback in the arterioles after any change in
rate of flow (MDFLW) at the macula densa. The time constant of this feedback response
is RNAGTC in Block 60.
KD62 and KD63:
The value RNAULL is the lower limit to the autoregulatory response (RNAUG1) as set by Block 62.
RNAUUL is the upper limit, as set by Block 63.
KD64:
Calculation of an autoregulatory feedback factor that affects the degree of constriction
of both afferent and efferent arterioles (RNAUG2) which is the output of Block 64.
This feedback effect, and the resistance of the afferent and efferent arterioles,
increases in proportion to the calculation from these blocks and in response to the
flow rate of fluid in the tubules at the macula densa (MDFLW) which is the input to
Block 57.
KD65, KD66, and KD67:
Block 65, 66, and 67 calculate obliterative adaptation of this feedback response in case
such as this does occur. The sensitivity of this, RNAUAD, in Block 66 is set at zero
because many persons believe there is no such decay of this feedback response. Yet others
have postulated such a feedback response, in which case RNAUAD would then become the factor
that sets the time constant of the loss of the feedback response with time. The output of
this total system from Block 14 is RNAUG2.
NB - REMOVED DAMPING FROM KD57-KD61!!!!!!!!!
$\mathrm{RNAUG1T}=\mathrm{MDFLW}\mathrm{RNAUGN}+1\mathrm{RNAUG1}=\begin{cases}\mathrm{RNAULL} & \text{if $\mathrm{RNAUG1T}< \mathrm{RNAULL}$}\\ \mathrm{RNAUUL} & \text{if $\mathrm{RNAUG1T}> \mathrm{RNAUUL}$}\\ \mathrm{RNAUG1T} & \text{otherwise}\end{cases}\mathrm{RNAUG2}=\mathrm{RNAUG1}-\mathrm{RNAUG3}\frac{d \mathrm{RNAUG3}}{d \mathrm{time}}=(\mathrm{RNAUG2}-1)\mathrm{RNAUAD}$
Containment grouping component for "autonomic_effect_on_AAR", "angiotensin_effect_on_AAR",
"AAR_calculation" and "atrial_natriuretic_peptide_effect_on_AAR".
KD10, KD11, KD12, and KD13:
Calculation of the effect of autonomic stimulation (AUM) on afferent arteriolar
resistance (AUMK). A sensitivity controller for this is in Block 11 (ARF). A
limit is in Block 13 equal to 0.8.
KD10, KD11, KD12, and KD13:
Calculation of the effect of autonomic stimulation (AUM) on afferent arteriolar
resistance (AUMK). A sensitivity controller for this is in Block 11 (ARF). A
limit is in Block 13 equal to 0.8.
KD10, KD11, KD12, and KD13:
Calculation of the effect of autonomic stimulation (AUM) on afferent arteriolar
resistance (AUMK). A sensitivity controller for this is in Block 11 (ARF). A
limit is in Block 13 equal to 0.8.
$\mathrm{AUMKT}=\mathrm{AUM}\mathrm{ARF}+1\mathrm{AUMK}=\begin{cases}0.8 & \text{if $\mathrm{AUMKT}< 0.8$}\\ \mathrm{AUMKT} & \text{otherwise}\end{cases}$
KD3, KD7 and KD8:
Calculation of a temporary value for the effect of angiotensin on the afferent arteriolar
resistance (ANMAR). The angiotensin-related factors that affect the afferent arteriolar
resistance are an angiotensin multiplier factor (ANM), and an angiotensin multiplier sensitivity
controller (ANMAM).
KD3, KD7 and KD8:
Calculation of a temporary value for the effect of angiotensin on the afferent arteriolar
resistance (ANMAR). The angiotensin-related factors that affect the afferent arteriolar
resistance are an angiotensin multiplier factor (ANM), and an angiotensin multiplier sensitivity
controller (ANMAM).
KD3, KD7 and KD8:
Calculation of a temporary value for the effect of angiotensin on the afferent arteriolar
resistance (ANMAR). The angiotensin-related factors that affect the afferent arteriolar
resistance are an angiotensin multiplier factor (ANM), and an angiotensin multiplier sensitivity
controller (ANMAM).
$\mathrm{ANMAR1}=\mathrm{ANM}\mathrm{ANMAM}+1\mathrm{ANMAR}=\begin{cases}\mathrm{ANMARL} & \text{if $\mathrm{ANMAR1}< \mathrm{ANMARL}$}\\ \mathrm{ANMAR1} & \text{otherwise}\end{cases}$
KD9:
Calculation of a temporary value for the afferent arteriolar resistance (AAR1), except for
the effect of atrial natriuretic peptide on this resistance which is calculated later.
The factors that affect the afferent arteriolar resistance are the angiotensin multiplier
on afferent arterioles (ANMAR), an autonomic multiplier factor for nervous control of afferent
resistance (AUMK), an autoregulatory feedback multiplier effect on afferent arteriolar
resistance (RNAUG2), a myogenic autoregulation factor (myogrs), and a basic afferent
arteriolar resistance factor (AAR1) which allows for intrarenal alterations.
KD9:
Calculation of a temporary value for the afferent arteriolar resistance (AAR1), except for
the effect of atrial natriuretic peptide on this resistance which is calculated later.
The factors that affect the afferent arteriolar resistance are the angiotensin multiplier
on afferent arterioles (ANMAR), an autonomic multiplier factor for nervous control of afferent
resistance (AUMK), an autoregulatory feedback multiplier effect on afferent arteriolar
resistance (RNAUG2), a myogenic autoregulation factor (myogrs), and a basic afferent
arteriolar resistance factor (AAR1) which allows for intrarenal alterations.
$\mathrm{AAR1}=\mathrm{AARK}\mathrm{PAMKRN}\mathrm{AUMK}\mathrm{RNAUG2}\mathrm{ANMAR}\times 40\mathrm{MYOGRS}$
KD21, KD22, and KD23:
Calculation of the effect of circulating atrial natriuretic peptide on afferent
arteriolar resistance (AAR). The input to this sequence is ANPX which is derived
from the atrial natriuretic peptide section diagram. Sensitivity is determined
by ANPXAF, and the lower limit of AAR is set by Block 23 to equal AARLL.
KD21 and KD22:
Calculation of the effect of circulating atrial natriuretic peptide on afferent
arteriolar resistance (AAR). The input to this sequence is ANPX which is derived
from the atrial natriuretic peptide section diagram. Sensitivity is determined
by ANPXAF.
KD23:
The lower limit of AAR is set by Block 23 to equal AARLL.
$\mathrm{AART}=\mathrm{AAR1}-\mathrm{ANPX}\mathrm{ANPXAF}+\mathrm{ANPXAF}\mathrm{AAR}=\begin{cases}\mathrm{AARLL} & \text{if $\mathrm{AART}< \mathrm{AARLL}$}\\ \mathrm{AART} & \text{otherwise}\end{cases}$
Containment grouping component for "autonomic_effect_on_EAR", "angiotensin_effect_on_EAR",
"effect_of_renal_autoregulatory_feedback_on_EAR" and "EAR_calculation".
KD14, KD15, and KD16:
Calculation from AUMK (the output of Block 13), the effect of autonomic stimulation
on efferent arteriolar resistance. The output of Block 16 multiplies efferent
arteriolar resistance in Block 6.
KD14, KD15, and KD16:
Calculation from AUMK (the output of Block 13), the effect of autonomic stimulation
on efferent arteriolar resistance. The output of Block 16 multiplies efferent
arteriolar resistance in Block 6.
$\mathrm{AUMK2}=\mathrm{AUMK}\mathrm{AUMK1}+1$
KD3, KD4 and KD5:
Calculation of a temporary value for the effect of angiotensin on the efferent arteriolar
resistance (ANMER). The angiotensin-related factors that affect the efferent arteriolar
resistance are an angiotensin multiplier (ANM), and a sensitivity control for the effect of
angiotensin on the efferent arterioles (ANMEM).
KD3, KD4 and KD5:
Calculation of a temporary value for the effect of angiotensin on the efferent arteriolar
resistance (ANMER). The angiotensin-related factors that affect the efferent arteriolar
resistance are an angiotensin multiplier (ANM), and a sensitivity control for the effect of
angiotensin on the efferent arterioles (ANMEM).
$\mathrm{ANMER}=\mathrm{ANM}\mathrm{ANMEM}+1$
KD17, KD18, and KD19:
Sensitivity control of the renal autoregulatory feedback on efferent arteriolar
resistance. The sensitivity is controlled by (EFAFR) in Block 18.
KD17, KD18, and KD19:
Sensitivity control of the renal autoregulatory feedback on efferent arteriolar
resistance. The sensitivity is controlled by (EFAFR) in Block 18.
$\mathrm{RNAUG4}=\mathrm{RNAUG2}\mathrm{EFAFR}+1$
KD6 and KD6A:
Calculation of the efferent arteriolar resistance of the kidneys (EAR). The various factors
that affect this are: the angiotensin multiplier on efferent arterioles (ANMER), the basic
efferent arteriolar resistance when all other factors are normal (EARK), a multiplier factor
from Block KD19 that determines feedback from the renal autoregulatory mechanism, a multiplier
factor from Block 16 that determines autonomic nervous signal control of efferent arteriolar
resistance, and a factor (MYOGRS) for any myogenic autoregulation that might occur in the
efferent arterioles. Block KD6A sets the lower limit for the efferent arteriolar resistance (EAR)
at a level equal to the factor (EARLL).
KD6:
Calculation of the efferent arteriolar resistance of the kidneys (EAR). The various factors
that affect this are: the angiotensin multiplier on efferent arterioles (ANMER), the basic
efferent arteriolar resistance when all other factors are normal (EARK), a multiplier factor
from Block KD19 that determines feedback from the renal autoregulatory mechanism, a multiplier
factor from Block 16 that determines autonomic nervous signal control of efferent arteriolar
resistance, and a factor (MYOGRS) for any myogenic autoregulation that might occur in the
efferent arterioles.
KD6A:
Block KD6A sets the lower limit for the efferent arteriolar resistance (EAR)
at a level equal to the factor (EARLL).
$\mathrm{EAR1}=43.333\mathrm{EARK}\mathrm{ANMER}\mathrm{RNAUG4}\mathrm{MYOGRS}\mathrm{AUMK2}\mathrm{EAR}=\begin{cases}\mathrm{EARLL} & \text{if $\mathrm{EAR1}< \mathrm{EARLL}$}\\ \mathrm{EAR1} & \text{otherwise}\end{cases}$
KD20:
Calculation of the total renal resistance (RR) by adding efferent arteriolar
resistance (EAR) to afferent resistance (AAR).
KD20:
Calculation of the total renal resistance (RR) by adding efferent arteriolar
resistance (EAR) to afferent resistance (AAR).
$\mathrm{RR}=\mathrm{AAR}+\mathrm{EAR}$
KD24A:
Renal perfusion pressure (PAR) divided by renal resistance (RR) equals the
renal blood flow for normal kidneys (RFN).
KD24A:
Renal perfusion pressure (PAR) divided by renal resistance (RR) equals the
renal blood flow for normal kidneys (RFN).
$\mathrm{RFN}=\frac{\mathrm{PAR}}{\mathrm{RR}}$
KD73:
Calculation of the actual renal blood flow (RBF) by multiplying the normalized
renal blood flow (RFN) for two normal kidneys times the fraction of normal kidney
mass present in the body (REK).
KD73:
Calculation of the actual renal blood flow (RBF) by multiplying the normalized
renal blood flow (RFN) for two normal kidneys times the fraction of normal kidney
mass present in the body (REK).
$\mathrm{RBF}=\mathrm{REK}\mathrm{RFN}$
Containment grouping component for "glomerular_colloid_osmotic_pressure",
"glomerular_pressure", "glomerular_filtration_rate".
KD68, KD69, KD70, KD71, KD71A, KD72, KD72A, and KD72B:
Calculation of the colloid osmotic pressure of the proteins in the plasma of the
fluid flowing through the glomerular capillaries (GLPC). This calculation is based
on four input factors, fractional hematocrit (HM1) in Block 68, normalized rate of
blood flow (RFN) in Block 69, normalized rate of flow through the two kidneys (GFN)
in Block 70, and plasma protein concentration in the blood elsewhere in the body (PPC)
in Block 72A. The output of Block 72A is damped in Block 72B by the damping factor GPPD;
this is to prevent oscillation in the feedback circuit.
NB - REMOVED DAMPING FROM KD72-KD72B!!!!
KD68, KD69, KD70, KD71, KD71A, KD72, KD72A, and KD72B:
Calculation of the colloid osmotic pressure of the proteins in the plasma of the
fluid flowing through the glomerular capillaries (GLPC). This calculation is based
on four input factors, fractional hematocrit (HM1) in Block 68, normalized rate of
blood flow (RFN) in Block 69, normalized rate of flow through the two kidneys (GFN)
in Block 70, and plasma protein concentration in the blood elsewhere in the body (PPC)
in Block 72A. The output of Block 72A is damped in Block 72B by the damping factor GPPD;
this is to prevent oscillation in the feedback circuit.
NB - REMOVED DAMPING FROM KD72-KD72B!!!!
KD68, KD69, KD70, KD71, KD71A, KD72, KD72A, and KD72B:
Calculation of the colloid osmotic pressure of the proteins in the plasma of the
fluid flowing through the glomerular capillaries (GLPC). This calculation is based
on four input factors, fractional hematocrit (HM1) in Block 68, normalized rate of
blood flow (RFN) in Block 69, normalized rate of flow through the two kidneys (GFN)
in Block 70, and plasma protein concentration in the blood elsewhere in the body (PPC)
in Block 72A. The output of Block 72A is damped in Block 72B by the damping factor GPPD;
this is to prevent oscillation in the feedback circuit.
NB - REMOVED DAMPING FROM KD72-KD72B!!!!
KD68, KD69, KD70, KD71, KD71A, KD72, KD72A, and KD72B:
Calculation of the colloid osmotic pressure of the proteins in the plasma of the
fluid flowing through the glomerular capillaries (GLPC). This calculation is based
on four input factors, fractional hematocrit (HM1) in Block 68, normalized rate of
blood flow (RFN) in Block 69, normalized rate of flow through the two kidneys (GFN)
in Block 70, and plasma protein concentration in the blood elsewhere in the body (PPC)
in Block 72A. The output of Block 72A is damped in Block 72B by the damping factor GPPD;
this is to prevent oscillation in the feedback circuit.
NB - REMOVED DAMPING FROM KD72-KD72B!!!!
$\mathrm{EFAFPR1}=\frac{\mathrm{RFN}(1-\mathrm{HM1})}{\mathrm{RFN}(1-\mathrm{HM1})-\mathrm{GFN}}\mathrm{EFAFPR}=\begin{cases}1 & \text{if $\mathrm{EFAFPR1}< 1$}\\ \mathrm{EFAFPR1} & \text{otherwise}\end{cases}\mathrm{GLPC}=\begin{cases}\mathrm{EFAFPR}^{1.35}\mathrm{PPC}\times 0.98 & \text{if $\mathrm{GLPCA}> 0$}\\ \mathrm{PPC}+4 & \text{otherwise}\end{cases}$
KD24:
Arterial pressure drop (APD) in the renal arteries and afferent arterioles
before the blood gets to the glomerulus equals RFN times efferent arterial
resistance (AAR).
KD25:
Calculation of glomerular pressure (GLP) by subtracting afferent pressure drop (APD)
from the input pressure to the kidney (PAR).
KD24:
Arterial pressure drop (APD) in the renal arteries and afferent arterioles
before the blood gets to the glomerulus equals RFN times efferent arterial
resistance (AAR).
KD25:
Calculation of glomerular pressure (GLP) by subtracting afferent pressure drop (APD)
from the input pressure to the kidney (PAR).
$\mathrm{APD}=\mathrm{AAR}\mathrm{RFN}\mathrm{GLP}=\mathrm{PAR}-\mathrm{APD}$
KD26:
Calculation of average filtration pressure through the glomerular
capillary walls (PFL) by subtracting intrarenal pressure (PXTP) and
colloid osmotic pressure of the glomerular plasma (GLPC) from the average
glomerular pressure (GLP).
KD27 and KD28:
Calculation of the normalized glomerular filtration rate (GFN) if both kidneys
are fully functional. This is calculated by multiplying the pressure drop
across the glomerular capillary membrane (PFL) times the glomerular filtration
coefficient (GFLC). The lower limit for glomerular filtration is set in Block 28
by the value GFNLL.
NB - DAMPING REMOVED FROM KD27!!!
KD51:
Calculation of the actual glomerular filtration rate (GFR) by multiplying the rate
that would be true if both kidneys were totally intact (GFN) times the fraction of
normal kidney mass actually functioning (REK).
KD26:
Calculation of average filtration pressure through the glomerular
capillary walls (PFL) by subtracting intrarenal pressure (PXTP) and
colloid osmotic pressure of the glomerular plasma (GLPC) from the average
glomerular pressure (GLP).
KD27:
Calculation of the normalized glomerular filtration rate (GFN) if both kidneys
are fully functional. This is calculated by multiplying the pressure drop
across the glomerular capillary membrane (PFL) times the glomerular filtration
coefficient (GFLC).
NB - DAMPING REMOVED FROM KD27!!!
KD28:
The lower limit for glomerular filtration is set in Block 28
by the value GFNLL.
KD51:
Calculation of the actual glomerular filtration rate (GFR) by multiplying the rate
that would be true if both kidneys were totally intact (GFN) times the fraction of
normal kidney mass actually functioning (REK).
$\mathrm{PFL}=\mathrm{GLP}-\mathrm{GLPC}-\mathrm{PXTP}\mathrm{GFN1}=\mathrm{PFL}\mathrm{GFLC}\mathrm{GFN}=\begin{cases}\mathrm{GFNLL} & \text{if $\mathrm{GFN1}< \mathrm{GFNLL}$}\\ \mathrm{GFN1} & \text{otherwise}\end{cases}\mathrm{GFR}=\mathrm{GFN}\mathrm{REK}$
KD29:
Calculation of normalized rate of flow of fluid out of the proximal tubules (PTFL)
making the assumption that this is directly proportional to the normalized glomerular
filtration rate (GFN). The value (1.0) is considered to be the normal flow of fluid
out of the proximal tubules when all functions of the kidneys are normal.
KD30, KD31, and KD32:
This is a sensitivity controller to determine the normalized rate of flow of tubular
fluid at the macula densa level in the kidneys (MDFLW) when the normalized rate of flow
out of the proximal tubules (PTFL) changes from the normalized mean value of 1. The
multiplier value MDFL1 in Block 31 determines how many times as much the normalized
value for macula densa flow (MDFLW) changes with respect to change in proximal tubular
outflow (PTFL).
KD33:
This block sets a lower limit of macula densa flow (MDFLW) equal to zero.
KD29:
Calculation of normalized rate of flow of fluid out of the proximal tubules (PTFL)
making the assumption that this is directly proportional to the normalized glomerular
filtration rate (GFN). The value (1.0) is considered to be the normal flow of fluid
out of the proximal tubules when all functions of the kidneys are normal.
KD30, KD31, and KD32:
This is a sensitivity controller to determine the normalized rate of flow of tubular
fluid at the macula densa level in the kidneys (MDFLW) when the normalized rate of flow
out of the proximal tubules (PTFL) changes from the normalized mean value of 1. The
multiplier value MDFL1 in Block 31 determines how many times as much the normalized
value for macula densa flow (MDFLW) changes with respect to change in proximal tubular
outflow (PTFL).
KD33:
This block sets a lower limit of macula densa flow (MDFLW) equal to zero.
$\mathrm{PTFL}=\mathrm{GFN}\times 8\mathrm{MDFLWT}=\mathrm{PTFL}\mathrm{MDFL1}+1\mathrm{MDFLW}=\begin{cases}0 & \text{if $\mathrm{MDFLWT}< 0$}\\ \mathrm{MDFLWT} & \text{otherwise}\end{cases}$
KD79, KD80, and KD81:
Calculation of the renal tissue fluid colloid osmotic pressure (RTSPPC) based on
the average colloid osmotic pressure of the plasma in the glomerulus (GLPC) times
a factor caused by reabsorption of fluid into the plasma flowing through the
capillaries surrounding the tubules (RTPPR), and minus a factor resulting from a
protein differential between the capillaries and the tissue spaces (RTPPRS). The
lower limit of RTSPPC is set to 1.0 by Block 81.
KD79 and KD80:
Calculation of the renal tissue fluid colloid osmotic pressure (RTSPPC) based on
the average colloid osmotic pressure of the plasma in the glomerulus (GLPC) times
a factor caused by reabsorption of fluid into the plasma flowing through the
capillaries surrounding the tubules (RTPPR), and minus a factor resulting from a
protein differential between the capillaries and the tissue spaces (RTPPRS).
KD81:
The lower limit of RTSPPC is set to 1.0 by Block 81.
$\mathrm{RTSPPC1}=\mathrm{GLPC}\mathrm{RTPPR}-\mathrm{RTPPRS}\mathrm{RTSPPC}=\begin{cases}1 & \text{if $\mathrm{RTSPPC1}< 1$}\\ \mathrm{RTSPPC1} & \text{otherwise}\end{cases}$
Containment grouping component for "plasma_urea_concentration",
"glomerular_urea_concentration".
KD53 and KD54:
Calculation of the concentration of urea in the glomerular filtrate and also in the plasma (PLURC).
Subtraction in Block 53 of the urinary output of urea (UROD) from rate of formation of urea in the body (URFORM)
and the result integrated in Block 54 calculates the total urea in the plasma and other body fluids (PLUR).
KD53 and KD54:
Calculation of the concentration of urea in the glomerular filtrate and also in the plasma (PLURC).
Subtraction in Block 53 of the urinary output of urea (UROD) from rate of formation of urea in the body (URFORM)
and the result integrated in Block 54 calculates the total urea in the plasma and other body fluids (PLUR).
$\frac{d \mathrm{PLUR}}{d \mathrm{time}}=\mathrm{URFORM}-\mathrm{UROD}$
KD55:
Calculation of the concentration of urea in the glomerular filtrate and also
in the plasma (PLURC).
KD55:
Calculation of the concentration of urea in the glomerular filtrate and also
in the plasma (PLURC).
$\mathrm{PLURC}=\frac{\mathrm{PLUR}}{\mathrm{VTW}}$
Containment grouping component for "peritubular_capillary_pressure" and
"peritubular_capillary_reabsorption_factor".
KD74, KD75, KD76, and KD77:
Calculation of renal peritubular capillary pressure. Blocks KD74, KD75 and KD76
are a sensitivity control to determine the effect of changes in RFN on the calculation.
In Block KD77, the output of Block KD76 is multiplied by a resistance from the
glomerulus back to the large veins (RVRS).
KD74, KD75, KD76, and KD77:
Calculation of renal peritubular capillary pressure. Blocks KD74, KD75 and KD76
are a sensitivity control to determine the effect of changes in RFN on the calculation.
In Block KD77, the output of Block KD76 is multiplied by a resistance from the
glomerulus back to the large veins (RVRS).
$\mathrm{RCPRS}=(\mathrm{RFN}\mathrm{RFABX}+1.2)\mathrm{RVRS}$
KD78:
The pressure difference for absorption of fluid into the peritubular
capillaries (RABSPR) is equal to the average colloid osmotic pressure
in the peritubular capillaries (RABSPR), which is equal to the average
colloid osmotic pressure in the glomerulus (GLPC), minus renal tissue
fluid colloid osmotic pressure (RTSPPC), minus the renal peritubular
capillary pressure (RCPRS), and plus the renal tissue fluid pressure (RTSPRS).
KD82:
A temporary distal tubular reabsorption factor (RFAB1) is calculated from
the peritubular capillary absorptive pressure difference (RABSPR) times the
renal peritubular capillary reabsorption coefficient (RABSC).
KD83:
This is a damping circuit to calculate the reabsorption factor (RFAB). The
damping coefficient is RFABDP. The purpose of this is to prevent
oscillation in the system.
NB - REMOVED DAMPING FROM KD83!!
KD84, KD85, KD86, and KD87:
Blocks 84, 85, and 86 are a sensitivity control for determining the effect
of the reabsorption factor RFAB on distal tubule reabsorption (RFABD). The
sensitivity is controlled by the factor in Block 85, RFABDM. Block 87 prevents
the value of RFABD from falling below a value of .0001.
KD78:
The pressure difference for absorption of fluid into the peritubular
capillaries (RABSPR) is equal to the average colloid osmotic pressure
in the peritubular capillaries (RABSPR), which is equal to the average
colloid osmotic pressure in the glomerulus (GLPC), minus renal tissue
fluid colloid osmotic pressure (RTSPPC), minus the renal peritubular
capillary pressure (RCPRS), and plus the renal tissue fluid pressure (RTSPRS).
KD82:
A temporary distal tubular reabsorption factor (RFAB1) is calculated from
the peritubular capillary absorptive pressure difference (RABSPR) times the
renal peritubular capillary reabsorption coefficient (RABSC).
KD83:
This is a damping circuit to calculate the reabsorption factor (RFAB). The
damping coefficient is RFABDP. The purpose of this is to prevent
oscillation in the system.
NB - REMOVED DAMPING FROM KD83!!
KD84, KD85, and KD86:
Blocks 84, 85, and 86 are a sensitivity control for determining the effect
of the reabsorption factor RFAB on distal tubule reabsorption (RFABD). The
sensitivity is controlled by the factor in Block 85, RFABDM.
KD87:
Block 87 prevents the value of RFABD from falling below a value of .0001.
$\mathrm{RABSPR}=\mathrm{GLPC}+\mathrm{RTSPRS}-\mathrm{RCPRS}-\mathrm{RTSPPC}\mathrm{RFAB1}=\mathrm{RABSPR}\mathrm{RABSC}\mathrm{RFAB}=\mathrm{RFAB1}\mathrm{RFABD1}=\mathrm{RFAB}\mathrm{RFABDM}+1\mathrm{RFABD}=\begin{cases}0.0001 & \text{if $\mathrm{RFABD1}< 0.0001$}\\ \mathrm{RFABD1} & \text{otherwise}\end{cases}$
Containment grouping component for "distal_tubular_Na_delivery",
"Na_reabsorption_into_distal_tubules",
"angiotensin_induced_Na_reabsorption_into_distal_tubules", "distal_tubular_K_delivery",
"effect_of_physical_forces_on_distal_K_reabsorption", "effect_of_fluid_flow_on_K_reabsorption",
"K_reabsorption_into_distal_tubules", "K_secretion_from_distal_tubules".
KD34:
Calculation of rate of delivery of sodium into the distal tubular system of
two normal kidneys in milliequivalents per minute (DTNAI), which is equal to
the normalized delivery of fluid into the distal tubules (MDFLW) times the
concentration of sodium in the tubules (CNA), times the factor 0.0061619.
KD34:
Calculation of rate of delivery of sodium into the distal tubular system of
two normal kidneys in milliequivalents per minute (DTNAI), which is equal to
the normalized delivery of fluid into the distal tubules (MDFLW) times the
concentration of sodium in the tubules (CNA), times the factor 0.0061619.
$\mathrm{DTNAI}=\mathrm{MDFLW}\mathrm{CNA}\times 0.0061619$
KD113, KD114, and KD115:
Calculation of the effect of an antidiuretic hormone multiplier constant (ADHMK)
on the absorption of sodium by the distal tubular-collecting duct system (output
of Block 115). The sensitivity of this ADH effect is adjusted by the sensitivity
factor AHMNAR in Block 114.
KD36 and KD37:
Calculation of the sodium reabsorbed in the distal tubules and collecting duct (DTNARA).
The different factors that affect this are the basic value for the normal state (DTNAR),
the basic blood capillary hemodynamics of the system (RFABD), the effect of antidiuretic
hormone (from Block 115), and the effect of an aldosterone multiplier effect to cause
reabsorption of sodium (AMNA) as determined from the output of Block 23 in the aldosterone
section of these diagrams. Block 37 sets the lower limit of DTNARA at zero. DIURET
allows one to simulate the effect of a diuretic.
KD113, KD114, and KD115:
Calculation of the effect of an antidiuretic hormone multiplier constant (ADHMK)
on the absorption of sodium by the distal tubular-collecting duct system (output
of Block 115). The sensitivity of this ADH effect is adjusted by the sensitivity
factor AHMNAR in Block 114.
KD36 and KD37:
Calculation of the sodium reabsorbed in the distal tubules and collecting duct (DTNARA).
The different factors that affect this are the basic value for the normal state (DTNAR),
the basic blood capillary hemodynamics of the system (RFABD), the effect of antidiuretic
hormone (from Block 115), and the effect of an aldosterone multiplier effect to cause
reabsorption of sodium (AMNA) as determined from the output of Block 23 in the aldosterone
section of these diagrams. Block 37 sets the lower limit of DTNARA at zero. DIURET
allows one to simulate the effect of a diuretic.
KD36 and KD37:
Calculation of the sodium reabsorbed in the distal tubules and collecting duct (DTNARA).
The different factors that affect this are the basic value for the normal state (DTNAR),
the basic blood capillary hemodynamics of the system (RFABD), the effect of antidiuretic
hormone (from Block 115), and the effect of an aldosterone multiplier effect to cause
reabsorption of sodium (AMNA) as determined from the output of Block 23 in the aldosterone
section of these diagrams. Block 37 sets the lower limit of DTNARA at zero. DIURET
allows one to simulate the effect of a diuretic.
$\mathrm{DTNARA1}=\frac{\mathrm{AMNA}\mathrm{RFABD}\mathrm{DTNAR}}{\mathrm{DIURET}}(\mathrm{ADHMK}\mathrm{AHMNAR}+1)\mathrm{DTNARA}=\begin{cases}\mathrm{DTNARL} & \text{if $\mathrm{DTNARA1}< \mathrm{DTNARL}$}\\ \mathrm{DTNARA1} & \text{otherwise}\end{cases}$
KD108, KD109, KD110, KD111, and KD112:
Calculation of the fraction of the distal tubular reabsorption of sodium that is
absorbed each minute that is dependent on the availability of angiotensin (DTNANG).
The input factor to this system of blocks, ANM, is the angiotensin multiplier.
Blocks 108, 109, and 110 adjust the sensitivity of the effect in accordance with
the sensitivity factor ANMNAM. Block 111 converts the output of Block 110 into
actual milliequivalents of sodium per minute, and Block 112 places a lower limit
on absorption of sodium in response to angiotensin to a level of zero.
KD108, KD109, KD110 and KD111:
Calculation of the fraction of the distal tubular reabsorption of sodium that is
absorbed each minute that is dependent on the availability of angiotensin (DTNANG).
The input factor to this system of blocks, ANM, is the angiotensin multiplier.
Blocks 108, 109, and 110 adjust the sensitivity of the effect in accordance with
the sensitivity factor ANMNAM. Block 111 converts the output of Block 110 into
actual milliequivalents of sodium per minute.
KD112:
Block 112 places a lower limit on absorption of sodium in response to angiotensin to a level of zero.
$\mathrm{DTNANG1}=(\mathrm{ANM}\mathrm{ANMNAM}+1)\times 0.1\mathrm{DTNANG}=\begin{cases}0 & \text{if $\mathrm{DTNANG1}< 0$}\\ \mathrm{DTNANG1} & \text{otherwise}\end{cases}$
KD101 and KD102:
Calculation of the rate of entry of potassium into the distal tubular system (DTKI)
based on the rate of sodium entry into the system (DTNAI), divided by the concentration
of sodium in the extracellular fluid (CNA), and multiplied by the concentration of
potassium in the extracellular fluid (CKE).
KD101 and KD102:
Calculation of the rate of entry of potassium into the distal tubular system (DTKI)
based on the rate of sodium entry into the system (DTNAI), divided by the concentration
of sodium in the extracellular fluid (CNA), and multiplied by the concentration of
potassium in the extracellular fluid (CKE).
$\mathrm{DTKI}=\frac{\mathrm{DTNAI}\mathrm{CKE}}{\mathrm{CNA}}$
KD99 and KD100:
Calculation of the effect of renal hemodynamics (RFABD) in affecting the
rate of reabsorption of potassium by the distal tubule-collecting duct
system (RFABK). The intensity of this effect is controlled by factor
RFABKM in Block 100.
KD99 and KD100:
Calculation of the effect of renal hemodynamics (RFABD) in affecting the
rate of reabsorption of potassium by the distal tubule-collecting duct
system (RFABK). The intensity of this effect is controlled by factor
RFABKM in Block 100.
$\mathrm{RFABK}=(\mathrm{RFABD}-1)\mathrm{RFABKM}$
KD88, KD89, KD90, and KD90A:
Calculation of a multiplier factor for the effect of rate of flow of fluid into
the distal tubular system (MDFLW) on the rate of reabsorption of potassium from
the distal tubules and collecting ducts (MDFLK). The sensitivity of this control
is MDFLKM in Block 89. The lower limit of the output MDFLK is set to .1 by
Block 90A.
KD88, KD89 and KD90:
Calculation of a multiplier factor for the effect of rate of flow of fluid into
the distal tubular system (MDFLW) on the rate of reabsorption of potassium from
the distal tubules and collecting ducts (MDFLK). The sensitivity of this control
is MDFLKM in Block 89.
KD90A:
The lower limit of the output MDFLK is set to .1 by Block 90A.
$\mathrm{MDFLK1}=\mathrm{MDFLW}\mathrm{MDFLKM}+1\mathrm{MDFLK}=\begin{cases}0.1 & \text{if $\mathrm{MDFLK1}< 0.1$}\\ \mathrm{MDFLK1} & \text{otherwise}\end{cases}$
KD104, KD105, KD106, and KD107:
The rate of reabsorption of potassium in the distal tubule-collecting duct
system DTKA is proportional to the urinary excretion rate of potassium (KODN)
times a proportionality factor, .0004519, and divided by the rate of output of
urine from the kidneys (VUDN). Blocks 105, 106, and 107 are a time delay circuit
to allow for the time required for this effect to develop. The time delay
constant is determined by factor I6 in Block 106.
KD104, KD105, KD106, and KD107:
The rate of reabsorption of potassium in the distal tubule-collecting duct
system DTKA is proportional to the urinary excretion rate of potassium (KODN)
times a proportionality factor, .0004519, and divided by the rate of output of
urine from the kidneys (VUDN). Blocks 105, 106, and 107 are a time delay circuit
to allow for the time required for this effect to develop. The time delay
constant is determined by factor I6 in Block 106.
$\frac{d \mathrm{DTKA}}{d \mathrm{time}}=(\frac{\mathrm{KODN}}{\mathrm{VUDN}}\times 0.0004518-\mathrm{DTKA})\times 1.0$
KD91, KD92, and KD93:
Calculation of a temporary rate of potassium secretion into the distal
tubular-collecting tubular system (DTKSC1) based on the concentration of
potassium in the plasma (CKE), which is first normalized to the value 1.0
in Block 91, then raised to a power (CKEEX) in Block 92. The result is
multiplied by the delivery of potassium into the tubular system at the
macula densa level of the distal tubule (MDFLK), and by a multiplier effect
depicting the effect of aldosterone on the secretion of potassium by the
tubular epithelium into the tubule (AMK).
KD94, KD95, KD96, KD97, and KD98:
Calculation of the actual rate of secretion of potassium into the distal
tubule-collecting duct system (DTKSC) by multiplying the temporary rate of
secretion from Block 93 (DTKSC1) times a multiplier factor based on
angiotensin concentration in the body fluids (ANMKE). ANMKE is calculated
from a generalized body angiotensin multiplier factor (ANM) times a controller
for the sensitivity of this effect (ANMKEM). ANMKE is limited to a lowest
value by ANMKEL in Block 97.
KD94, KD95 and KD96:
Calculation of the actual rate of secretion of potassium into the distal
tubule-collecting duct system (DTKSC) by multiplying the temporary rate of
secretion from Block 93 (DTKSC1) times a multiplier factor based on
angiotensin concentration in the body fluids (ANMKE). ANMKE is calculated
from a generalized body angiotensin multiplier factor (ANM) times a controller
for the sensitivity of this effect (ANMKEM).
KD97:
ANMKE is limited to a lowest value by ANMKEL in Block 97.
KD91, KD92, and KD93:
Calculation of a temporary rate of potassium secretion into the distal
tubular-collecting tubular system (DTKSC1) based on the concentration of
potassium in the plasma (CKE), which is first normalized to the value 1.0
in Block 91, then raised to a power (CKEEX) in Block 92. The result is
multiplied by the delivery of potassium into the tubular system at the
macula densa level of the distal tubule (MDFLK), and by a multiplier effect
depicting the effect of aldosterone on the secretion of potassium by the
tubular epithelium into the tubule (AMK).
$\mathrm{ANMKE1}=\mathrm{ANM}\mathrm{ANMKEM}+1\mathrm{ANMKE}=\begin{cases}\mathrm{ANMKEL} & \text{if $\mathrm{ANMKE1}< \mathrm{ANMKEL}$}\\ \mathrm{ANMKE1} & \text{otherwise}\end{cases}\mathrm{DTKSC}=\frac{\left(\frac{\mathrm{CKE}}{4.4}\right)^{\mathrm{CKEEX}}\mathrm{AMK}\times 0.08\mathrm{MDFLK}}{\mathrm{ANMKE}}$
Containment grouping component for "normal_Na_excretion", "normal_K_excretion",
"normal_urea_excretion", "normal_osmolar_and_water_excretion",
"normal_urine_volume", "actual_Na_exretion_rate", "actual_K_excretion_rate",
"actual_urea_excretion_rate", "actual_urine_volume".
KD35:
Calculation of the normalized rate of delivery of sodium into the urine (NODN)
if both kidneys are intact and normal. This is calculated by subtracting from
the rate of entry of sodium into the distal tubular system (DTNAI) the distal
tubular and collecting duct reabsorption of sodium caused by the presence of
angiotensin in the blood (DTNANG) and that caused by multiple other factors (DTNARA)
from Blocks 36 and 37.
KD38:
This sets a lower limit for the normalized output of sodium (NODN) to zero.
KD35:
Calculation of the normalized rate of delivery of sodium into the urine (NODN)
if both kidneys are intact and normal. This is calculated by subtracting from
the rate of entry of sodium into the distal tubular system (DTNAI) the distal
tubular and collecting duct reabsorption of sodium caused by the presence of
angiotensin in the blood (DTNANG) and that caused by multiple other factors (DTNARA)
from Blocks 36 and 37.
KD38:
This sets a lower limit for the normalized output of sodium (NODN) to zero.
$\mathrm{NODN1}=\mathrm{DTNAI}-\mathrm{DTNARA}-\mathrm{DTNANG}\mathrm{NODN}=\begin{cases}0.00000001 & \text{if $\mathrm{NODN1}< 0.00000001$}\\ \mathrm{NODN1} & \text{otherwise}\end{cases}$
KD103 and KD103A:
The normalized rate of excretion of potassium into the urine by two normal
kidneys (KODN) is equal to the rate of entry of potassium into the distal
tubular-collecting duct system (DTKI), minus any excess absorption caused
by abnormal renal hemodynamics (RFABK), plus the rate of secretion of
potassium by the tubular epithelium into the distal tubules and collecting
tubules (DTKSC), and minus the rate of absorption of potassium by all
portions of the distal tubule-collecting duct system DTKA. Block 103A sets
the lower limit of the excretion of potassium in the urine (KODN) at zero.
KD103:
The normalized rate of excretion of potassium into the urine by two normal
kidneys (KODN) is equal to the rate of entry of potassium into the distal
tubular-collecting duct system (DTKI), minus any excess absorption caused
by abnormal renal hemodynamics (RFABK), plus the rate of secretion of
potassium by the tubular epithelium into the distal tubules and collecting
tubules (DTKSC), and minus the rate of absorption of potassium by all
portions of the distal tubule-collecting duct system DTKA.
KD103A:
Block 103A sets the lower limit of the excretion of potassium in the urine (KODN) at zero.
$\mathrm{KODN1}=\mathrm{DTKI}+\mathrm{DTKSC}-\mathrm{DTKA}-\mathrm{RFABK}\mathrm{KODN}=\begin{cases}0 & \text{if $\mathrm{KODN1}< 0$}\\ \mathrm{KODN1} & \text{otherwise}\end{cases}$
KD52:
Calculation of the rate of excretion of urea if both kidneys were functionally
intact (DTURI) by multiplying the concentration of urea in the glomerular
filtrate (PLURC) times the square of glomerular filtration for the two normal
kidneys (GFN) times the numerical factor 3.84.
KD52:
Calculation of the rate of excretion of urea if both kidneys were functionally
intact (DTURI) by multiplying the concentration of urea in the glomerular
filtrate (PLURC) times the square of glomerular filtration for the two normal
kidneys (GFN) times the numerical factor 3.84.
$\mathrm{DTURI}=\mathrm{GFN}^{2}\mathrm{PLURC}\times 3.84$
KD40, KD41, and KD42:
Calculation of the normalized output of osmotic substances by the kidneys if
both kidneys are functioning totally and normally (OSMOPN) by adding together
in Block 40 the milliequivalents of sodium output (NODN) and potassium output (KODN),
then multiplying in Block 41 by a factor of 2 to include the anions that go with
the sodium and potassium cations, and addition in Block 42 of osmotic excretion in
the form of urea (DUTRI).
KD40, KD41, and KD42:
Calculation of the normalized output of osmotic substances by the kidneys if
both kidneys are functioning totally and normally (OSMOPN) by adding together
in Block 40 the milliequivalents of sodium output (NODN) and potassium output (KODN),
then multiplying in Block 41 by a factor of 2 to include the anions that go with
the sodium and potassium cations, and addition in Block 42 of osmotic excretion in
the form of urea (DUTRI).
$\mathrm{OSMOPN1}=\mathrm{DTURI}+2(\mathrm{NODN}+\mathrm{KODN})\mathrm{OSMOPN}=\begin{cases}0.6 & \text{if $\mathrm{OSMOPN1}> 0.6$}\\ \mathrm{OSMOPN1} & \text{otherwise}\end{cases}$
KD43, KD44, KD45, KD46, KD47, and KD48:
Calculation of the normalized output of urine volume if both kidneys are totally
intact (VUDN) as the output of Block 48. Blocks 43, 45, and 47 calculate the
portion of VUDN that is caused by excess of osmotic substances (OSMOP1) over and
above the normal amount (OSMOPN). Blocks 44 and 46 calculate the portion of VUDN
that is caused by that portion of OSMOPN that is below the normal value of .6.
The sensitivity of this portion of urine output varies markedly with the antidiuretic
hormone effect on the kidney (ADHMK). Block 48 summates the total VUDN caused by the
osmotic substances above the normal level of .6 plus those caused by the osmotic
substances below the normal level of .6.
KD43, KD44, KD45, KD46, KD47, and KD48:
Calculation of the normalized output of urine volume if both kidneys are totally
intact (VUDN) as the output of Block 48. Blocks 43, 45, and 47 calculate the
portion of VUDN that is caused by excess of osmotic substances (OSMOP1) over and
above the normal amount (OSMOPN). Blocks 44 and 46 calculate the portion of VUDN
that is caused by that portion of OSMOPN that is below the normal value of .6.
The sensitivity of this portion of urine output varies markedly with the antidiuretic
hormone effect on the kidney (ADHMK). Block 48 summates the total VUDN caused by the
osmotic substances above the normal level of .6 plus those caused by the osmotic
substances below the normal level of .6.
KD43, KD44, KD45, KD46, KD47, and KD48:
Calculation of the normalized output of urine volume if both kidneys are totally
intact (VUDN) as the output of Block 48. Blocks 43, 45, and 47 calculate the
portion of VUDN that is caused by excess of osmotic substances (OSMOP1) over and
above the normal amount (OSMOPN). Blocks 44 and 46 calculate the portion of VUDN
that is caused by that portion of OSMOPN that is below the normal value of .6.
The sensitivity of this portion of urine output varies markedly with the antidiuretic
hormone effect on the kidney (ADHMK). Block 48 summates the total VUDN caused by the
osmotic substances above the normal level of .6 plus those caused by the osmotic
substances below the normal level of .6.
KD43, KD44, KD45, KD46, KD47, and KD48:
Calculation of the normalized output of urine volume if both kidneys are totally
intact (VUDN) as the output of Block 48. Blocks 43, 45, and 47 calculate the
portion of VUDN that is caused by excess of osmotic substances (OSMOP1) over and
above the normal amount (OSMOPN). Blocks 44 and 46 calculate the portion of VUDN
that is caused by that portion of OSMOPN that is below the normal value of .6.
The sensitivity of this portion of urine output varies markedly with the antidiuretic
hormone effect on the kidney (ADHMK). Block 48 summates the total VUDN caused by the
osmotic substances above the normal level of .6 plus those caused by the osmotic
substances below the normal level of .6.
$\mathrm{OSMOP1T}=\mathrm{OSMOPN1}-0.6\mathrm{OSMOP1}=\begin{cases}0 & \text{if $\mathrm{OSMOP1T}< 0$}\\ \mathrm{OSMOP1T} & \text{otherwise}\end{cases}\mathrm{VUDN}=\frac{\mathrm{OSMOPN}}{600\mathrm{ADHMK}}+\frac{\mathrm{OSMOP1}}{360}$
KD39:
Calculation of the actual rate of sodium output from the kidneys (NOD) by
multiplying the normalized rate (NODN) times the percentage of normal kidney
mass that is present in the body (REK).
KD39:
Calculation of the actual rate of sodium output from the kidneys (NOD) by
multiplying the normalized rate (NODN) times the percentage of normal kidney
mass that is present in the body (REK).
$\mathrm{NOD}=\mathrm{NODN}\mathrm{REK}$
KD116:
Calculation of the actual rate of potassium output from the kidneys (KOD) by
multiplying the normalized rate (KODN) times the percentage of normal kidney
mass that is present in the body (REK).
KD116:
Calculation of the actual rate of potassium output from the kidneys (KOD) by
multiplying the normalized rate (KODN) times the percentage of normal kidney
mass that is present in the body (REK).
$\mathrm{KOD}=\mathrm{KODN}\mathrm{REK}$
KD56:
Calculation of rate of excretion of urea per minute in terms of osmoles (UROD),
which is equal to the rate of excretion if the kidneys were normal (DTURI) times
the actual fraction of normal kidney mass in the body (REK).
KD56:
Calculation of rate of excretion of urea per minute in terms of osmoles (UROD),
which is equal to the rate of excretion if the kidneys were normal (DTURI) times
the actual fraction of normal kidney mass in the body (REK).
$\mathrm{UROD}=\mathrm{DTURI}\mathrm{REK}$
KD49:
Actual rate of urinary output (VUD) calculated from the rate of output if
both kidneys were totally intact (VUDN) by multiplying VUDN by the fraction
of normal kidney mass that is functional in the body (REK).
KD50:
A stability test to test whether or not VUD is varying up and down too much
and if so making appropriate mathematical corrections. This is simply a
mathematical maneuver for allowing more rapid solution of the equations.
NB - This stability test has not been coded!!!
KD49:
Actual rate of urinary output (VUD) calculated from the rate of output if
both kidneys were totally intact (VUDN) by multiplying VUDN by the fraction
of normal kidney mass that is functional in the body (REK).
KD50:
A stability test to test whether or not VUD is varying up and down too much
and if so making appropriate mathematical corrections. This is simply a
mathematical maneuver for allowing more rapid solution of the equations.
NB - This stability test has not been coded!!!
$\mathrm{VUD}=\mathrm{VUDN}\mathrm{REK}$