Guyton Model: Kidney
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 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.
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
Guyton
Kidney
Description of Guyton kidney module
2008-00-00 00:00
keyword
physiology
organ systems
cardiovascular circulation
kidney
Guyton
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.
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40.0
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0.6
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42.4737
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42.4737
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84.8171
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1.22057
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37.8383
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1.20569
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1.20569
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51.842
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0.125006
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6.00368
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1.00005
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1.00051
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1.00051
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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!!!
$\mathrm{VUD}=\mathrm{VUDN}\mathrm{REK}$