Guyton Model: red_cells_and_viscosity
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 how the red blood 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.
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
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).
$\mathrm{RCD}=\mathrm{RC1}-\mathrm{RC2}+\mathrm{TRRBC}\frac{d \mathrm{VRC}}{d \mathrm{time}}=\mathrm{RCD}$