Guyton Model: Electrolytes
Catherine
Lloyd
Auckland Bioengineering Institute, University of Auckland
Model Status
This CellML model has not been validated. The equations in this file may contain errors and 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.
This particular CellML model describes the extracellular and intracellular fluid electrolytes and volumes.
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. PubMed ID: 4334846
Guyton
Electrolytes
Description of Guyton electrolytes module
2008-00-00 00:00
keyword
physiology
organ systems
cardiovascular circulation
electrolytes
Guyton
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).
$\mathrm{VEC}=\mathrm{VTW}-\mathrm{VIC}$