- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2008-04-03 02:24:17+13:00
- Desc:
- committing version01 of guyton_electrolytes_2008
- Permanent Source URI:
- http://models.cellml.org/workspace/guyton_electrolytes_2008/rawfile/dc9daa4bb135f3d5f5ff7e9ba9d5e980dc950eaa/guyton_electrolytes_2008.cellml
<?xml version='1.0' encoding='utf-8'?>
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:xlink="http://www.w3.org/1999/xlink" name="electrolytes_CellML1_0_model" cmeta:id="electrolytes_CellML1_0_model">
<!-- ======================================== DOCUMENTATION ============================================= -->
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Guyton Model: Electrolytes</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
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.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
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.
</para>
<para>
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.
</para>
<para>
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.
</para>
<para>
This particular CellML model describes the extracellular and intracellular fluid electrolytes and volumes.
</para>
<informalfigure float="0" id="full_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="full_model.png"/>
</imageobject>
</mediaobject>
<caption>A systems analysis diagram for the full Guyton model describing circulation regulation.</caption>
</informalfigure>
<informalfigure float="0" id="electrolytes_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="electrolytes.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the components and processes described in the current CellML model.</caption>
</informalfigure>
<para>
There are several publications referring to the Guyton model. One of these papers is cited below:
</para>
<para>
<ulink url="http://arjournals.annualreviews.org/doi/abs/10.1146/annurev.ph.34.030172.000305">Circulation: Overall Regulation</ulink>, A.C. Guyton, T.G. Coleman, and H.J. Granger, 1972, <ulink url="http://www.biophysj.org/">
<emphasis>Annual Review of Physiology</emphasis>
</ulink>, 34, 13-44. (A <ulink url="http://arjournals.annualreviews.org/doi/pdf/10.1146/annurev.ph.34.030172.000305?cookieSet=1">PDF</ulink> version of the article are available to journal subscribers on the <emphasis>Annual Review of Physiology</emphasis> website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=4334846&query_hl=1&itool=pubmed_docsum">PubMed ID: 4334846</ulink>
</para>
</sect1>
</article>
</documentation>
<!-- =================================================================================================================== -->
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#electrolytes_CellML1_0_model">
<rdf:value>
Extracellular and intracellular fluid electrolytes and volumes.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- ======================================== ENVIRONMENT COMPONENT ============================================= -->
<component name="environment">
<variable name="time" units="second" private_interface="none" public_interface="out"/>
</component>
<!-- ======================================== ELECTROLYTES TOP-LEVEL COMPONENT ============================================= -->
<component name="electrolytes" cmeta:id="electrolytes">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#electrolytes">
<rdf:value>
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.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<variable name="time" units="second" private_interface="out" public_interface="in"/>
<!-- Inputs from components in other models -->
<variable name="AMK" initial_value="1.037" units="dimensionless" private_interface="out" public_interface="none"/>
<variable name="TVD" initial_value="0.000980838" units="dimensionless" private_interface="out" public_interface="none"/>
<variable name="NOD" initial_value="0.0959449" units="dimensionless" private_interface="out" public_interface="none"/>
<variable name="STH" initial_value="0.977181" units="dimensionless" private_interface="out" public_interface="none"/>
<variable name="KOD" initial_value="0.0804374" units="dimensionless" private_interface="out" public_interface="none"/>
<variable name="VUD" initial_value="0.000989" units="dimensionless" private_interface="out" public_interface="none"/>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="electrolytes" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- ======================================== EXTRACELLULAR SODIUM CONCENTRATION ============================================= -->
<component name="extracellular_Na_concentration" cmeta:id="extracellular_Na_concentration">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#extracellular_Na_concentration">
<rdf:value>
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).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="STH" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="NOD" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="VEC" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="time" units="second" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="CNA" units="dimensionless" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="NID" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="TRPL" units="dimensionless" private_interface="none" public_interface="in"/>
<!-- Internal variables -->
<variable name="NED" units="dimensionless" private_interface="none" public_interface="none"/>
<variable name="NAE" initial_value="2109.91" units="dimensionless" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="EL1_to_EL3">
<eq/>
<ci>NED</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>NID</ci>
<ci>STH</ci>
</apply>
<ci>NOD</ci>
</apply>
<apply>
<times/>
<ci>TRPL</ci>
<cn cellml:units="dimensionless">142</cn>
</apply>
</apply>
</apply>
<apply id="EL4">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>NAE</ci>
</apply>
<ci>NED</ci>
</apply>
<apply id="EL5">
<eq/>
<ci>CNA</ci>
<apply>
<divide/>
<ci>NAE</ci>
<ci>VEC</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="extracellular_Na_concentration" component_2="electrolytes"/>
<map_variables variable_1="STH" variable_2="STH"/>
<map_variables variable_1="NOD" variable_2="NOD"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="extracellular_Na_concentration" component_2="extracellular_fluid_volume"/>
<map_variables variable_1="VEC" variable_2="VEC"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="extracellular_Na_concentration" component_2="parameter_values"/>
<map_variables variable_1="TRPL" variable_2="TRPL"/>
<map_variables variable_1="NID" variable_2="NID"/>
</connection>
<!-- ================================== ALDOSTERONE EFFECT ON CELLULAR POTASSIUM DISTRIBUTION ===================================== -->
<component name="aldosterone_effect_on_cellular_K_distribution" cmeta:id="aldosterone_effect_on_cellular_K_distribution">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#aldosterone_effect_on_cellular_K_distribution">
<rdf:value>
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.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="AMK" units="dimensionless" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="AMK1" units="dimensionless" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="ALCLK" units="dimensionless" private_interface="none" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="EL9_to_EL11">
<eq/>
<ci>AMK1</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>AMK</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>ALCLK</ci>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="aldosterone_effect_on_cellular_K_distribution" component_2="electrolytes"/>
<map_variables variable_1="AMK" variable_2="AMK"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="aldosterone_effect_on_cellular_K_distribution" component_2="parameter_values"/>
<map_variables variable_1="ALCLK" variable_2="ALCLK"/>
</connection>
<!-- ======================================== EXTRACELLULAR POTASSIUM CONCENTRATION ============================================= -->
<component name="extracellular_K_concentration" cmeta:id="extracellular_K_concentration">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#extracellular_K_concentration">
<rdf:value>
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).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="KOD" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="AMK1" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="VEC" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="time" units="second" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="CKE" units="dimensionless" private_interface="none" public_interface="out"/>
<variable name="KE" units="dimensionless" private_interface="none" public_interface="out"/>
<variable name="KTOT" initial_value="3622.54" units="dimensionless" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="KID" units="dimensionless" private_interface="none" public_interface="in"/>
<!-- Internal variables -->
<variable name="KTOTD" units="dimensionless" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="EL6">
<eq/>
<ci>KTOTD</ci>
<apply>
<minus/>
<ci>KID</ci>
<ci>KOD</ci>
</apply>
</apply>
<apply id="EL7">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>KTOT</ci>
</apply>
<ci>KTOTD</ci>
</apply>
<apply id="EL7A_and_EL7B">
<eq/>
<ci>KE</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>KTOT</ci>
<cn cellml:units="dimensionless">3000</cn>
</apply>
<apply>
<times/>
<ci>AMK1</ci>
<cn cellml:units="dimensionless">9.3333</cn>
</apply>
</apply>
</apply>
<apply id="EL8">
<eq/>
<ci>CKE</ci>
<apply>
<divide/>
<ci>KE</ci>
<ci>VEC</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="extracellular_K_concentration" component_2="electrolytes"/>
<map_variables variable_1="KOD" variable_2="KOD"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="extracellular_K_concentration" component_2="aldosterone_effect_on_cellular_K_distribution"/>
<map_variables variable_1="AMK1" variable_2="AMK1"/>
</connection>
<connection>
<map_components component_1="extracellular_K_concentration" component_2="extracellular_fluid_volume"/>
<map_variables variable_1="VEC" variable_2="VEC"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="extracellular_K_concentration" component_2="parameter_values"/>
<map_variables variable_1="KID" variable_2="KID"/>
</connection>
<!-- ======================================== INTRACELLULAR POTASSIUM CONCENTRATION ============================================= -->
<component name="intracellular_K_concentration" cmeta:id="intracellular_K_concentration">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#intracellular_K_concentration">
<rdf:value>
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).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="KTOT" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="KE" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="VIC" units="dimensionless" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="CKI" units="dimensionless" private_interface="none" public_interface="out"/>
<!-- Internal variables -->
<variable name="KI" units="dimensionless" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="EL12">
<eq/>
<ci>KI</ci>
<apply>
<minus/>
<ci>KTOT</ci>
<ci>KE</ci>
</apply>
</apply>
<apply id="EL13">
<eq/>
<ci>CKI</ci>
<apply>
<divide/>
<ci>KI</ci>
<ci>VIC</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="intracellular_K_concentration" component_2="extracellular_K_concentration"/>
<map_variables variable_1="KTOT" variable_2="KTOT"/>
<map_variables variable_1="KE" variable_2="KE"/>
</connection>
<connection>
<map_components component_1="intracellular_K_concentration" component_2="intracellular_fluid_volume"/>
<map_variables variable_1="VIC" variable_2="VIC"/>
<map_variables variable_1="CKI" variable_2="CKI"/>
</connection>
<!-- ======================================== INTRACELLULAR FLUID VOLUME ============================================= -->
<component name="intracellular_fluid_volume" cmeta:id="intracellular_fluid_volume">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#intracellular_fluid_volume">
<rdf:value>
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).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="CNA" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="CKI" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="time" units="second" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="VIC" initial_value="25.0404" units="dimensionless" private_interface="none" public_interface="out"/>
<variable name="VID" units="dimensionless" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="VIDML" units="dimensionless" private_interface="none" public_interface="in"/>
<!-- Internal variables -->
<variable name="CCD" units="dimensionless" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="EL14">
<eq/>
<ci>CCD</ci>
<apply>
<minus/>
<ci>CKI</ci>
<ci>CNA</ci>
</apply>
</apply>
<apply id="EL15">
<eq/>
<ci>VID</ci>
<apply>
<times/>
<ci>CCD</ci>
<ci>VIDML</ci>
</apply>
</apply>
<apply id="EL16">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>VIC</ci>
</apply>
<ci>VID</ci>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="intracellular_fluid_volume" component_2="extracellular_Na_concentration"/>
<map_variables variable_1="CNA" variable_2="CNA"/>
</connection>
<connection>
<map_components component_1="intracellular_fluid_volume" component_2="electrolytes"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="intracellular_fluid_volume" component_2="parameter_values"/>
<map_variables variable_1="VIDML" variable_2="VIDML"/>
</connection>
<!-- ======================================== TOTAL BODY WATER ============================================= -->
<component name="total_body_water" cmeta:id="total_body_water">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#total_body_water">
<rdf:value>
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).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="TVD" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="VUD" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="time" units="second" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="VTW" initial_value="39.8952" units="dimensionless" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="EL17_and_EL18">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>VTW</ci>
</apply>
<apply>
<minus/>
<ci>TVD</ci>
<ci>VUD</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="total_body_water" component_2="electrolytes"/>
<map_variables variable_1="TVD" variable_2="TVD"/>
<map_variables variable_1="VUD" variable_2="VUD"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- ======================================== EXTRACELLULAR FLUID VOLUME ============================================= -->
<component name="extracellular_fluid_volume" cmeta:id="extracellular_fluid_volume">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#extracellular_fluid_volume">
<rdf:value>
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).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="VIC" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="VTW" units="dimensionless" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="VEC" units="dimensionless" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="EL19">
<eq/>
<ci>VEC</ci>
<apply>
<minus/>
<ci>VTW</ci>
<ci>VIC</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="extracellular_fluid_volume" component_2="intracellular_fluid_volume"/>
<map_variables variable_1="VIC" variable_2="VIC"/>
</connection>
<connection>
<map_components component_1="extracellular_fluid_volume" component_2="total_body_water"/>
<map_variables variable_1="VTW" variable_2="VTW"/>
</connection>
<!-- ============================================================ PARAMETER VALUES =============================================================== -->
<component name="parameter_values" cmeta:id="parameter_values">
<variable name="TRPL" units="dimensionless" initial_value="0" private_interface="none" public_interface="out"/> <!-- transfusion coefficient [P] -->
<variable name="NID" units="dimensionless" initial_value="0.1" private_interface="none" public_interface="out"/> <!-- rate of sodium intake -->
<variable name="ALCLK" units="dimensionless" initial_value="0.3" private_interface="none" public_interface="out"/> <!-- sensitivity controller of AMK1 [P] -->
<variable name="KID" units="dimensionless" initial_value="0.08" private_interface="none" public_interface="out"/> <!-- rate of potassium intake -->
<variable name="VIDML" units="dimensionless" initial_value="0.01" private_interface="none" public_interface="out"/> <!-- proportionality constant, CCD to VID [P] -->
</component>
<!-- ============================================================ GROUPING =============================================================== -->
<group>
<relationship_ref relationship="containment"/>
<component_ref component="electrolytes">
<component_ref component="extracellular_Na_concentration"/>
<component_ref component="aldosterone_effect_on_cellular_K_distribution"/>
<component_ref component="extracellular_K_concentration"/>
<component_ref component="intracellular_K_concentration"/>
<component_ref component="intracellular_fluid_volume"/>
<component_ref component="total_body_water"/>
<component_ref component="extracellular_fluid_volume"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="electrolytes">
<component_ref component="parameter_values"/>
<component_ref component="extracellular_Na_concentration"/>
<component_ref component="aldosterone_effect_on_cellular_K_distribution"/>
<component_ref component="extracellular_K_concentration"/>
<component_ref component="intracellular_K_concentration"/>
<component_ref component="intracellular_fluid_volume"/>
<component_ref component="total_body_water"/>
<component_ref component="extracellular_fluid_volume"/>
</component_ref>
</group>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#extracellular_K_concentration">
<rdf:value>
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).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#intracellular_K_concentration">
<rdf:value>
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).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#aldosterone_effect_on_cellular_K_distribution">
<rdf:value>
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.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#total_body_water">
<rdf:value>
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).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#extracellular_Na_concentration">
<rdf:value>
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).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#extracellular_fluid_volume">
<rdf:value>
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).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#electrolytes">
<rdf:value>
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.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#electrolytes_CellML1_0_model">
<rdf:value>
Extracellular and intracellular fluid electrolytes and volumes.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#intracellular_fluid_volume">
<rdf:value>
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).
</rdf:value>
</rdf:Description>
</rdf:RDF>
</model>
