Guyton Model: Angiotensin
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This CellML model has been validated. 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). This may effect the transient behaviour of the model, however the steady-state behaviour would remain
the same. The equations in this file and the steady-state output from the model conform to the results from the MODSIM program.
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.
This particular CellML model describes 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.
model diagram
A systems analysis diagram for the full Guyton model describing circulation regulation.
model diagram
A schematic diagram of the components and processes described in the current CellML model.
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. (A PDF version of the article are available to journal subscribers on the Annual Review of Physiology website.) PubMed ID: 4334846
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.
$\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.
$\mathrm{ANX}=(\mathrm{ANGSCR}-1)\mathrm{ANXM}\frac{d \mathrm{ANX1}}{d \mathrm{time}}=\frac{\mathrm{ANX}-\mathrm{ANX1}}{\mathrm{ANV}}$
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.
$\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.
$\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.
$\frac{d \mathrm{ANC}}{d \mathrm{time}}=\frac{\mathrm{ANPR1}-\mathrm{ANC}}{\mathrm{ANT}}$
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.
$\mathrm{ANM}=\mathrm{ANMUL}-\frac{\mathrm{ANMUL}-1}{\frac{\mathrm{ANMLL}-1}{\mathrm{ANMLL}-\mathrm{ANMUL}}(\mathrm{ANC}-1)\mathrm{ANCSNS}+1}$
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).
$\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.
$\mathrm{ANUVN}=\mathrm{ANU}\mathrm{ANUVM}+1$
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.
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.
100
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.
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).
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.
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.
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.
10000
100
AN20, AN21, and AN22:
Calculation of the effect of angiotensin on venous constriction (ANUVN), with
sensitivity controlled by ANUVM in Block 21.
100000
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.
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.