Guyton Model: Antidiuretic Hormone
Catherine
Lloyd
Auckland 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 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).
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
Antidiuretic Hormone
Description of Guyton antidiuretic hormone module
2008-00-00 00:00
keyword
physiology
organ systems
cardiovascular circulation
antidiuretic hormone
Guyton
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}$