<?xml version="1.0" encoding="utf-8"?>
<model
name="muscle_O2_delivery_CellML1_0_model"
cmeta:id="muscle_O2_delivery_CellML1_0_model"
xmlns="http://www.cellml.org/cellml/1.1#"
xmlns:cellml="http://www.cellml.org/cellml/1.1#"
xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
xmlns:xlink="http://www.w3.org/1999/xlink">
<!-- ======================================== DOCUMENTATION ============================================= -->
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Guyton Model: muscle_O2_delivery</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
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.
</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>
The tissues of the body are divided into non-muscle tissues and muscle tissues, and the delivery of oxygen to each one of these
is calculated separately. The principal reason for this separation is that during muscle activity, the delivery of oxygen to
the muscles increases tremendously and correspondingly affects the blood flow through the muscles. This particular CellML model
describes the delivery of oxygen to the muscle, and several aspects of local cellular usage of oxygen are also calculated.
</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="muscle_O2_delivery_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="m_o2.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>
Circulation: Overall Regulation, A.C. Guyton, T.G. Coleman, and H.J. Granger, 1972,
<emphasis>Annual Review of Physiology</emphasis>
, 34, 13-44. <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>
<!-- ======================================================= CITATION AND KEYWORD METADATA ================================================== -->
<rdf:RDF
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:bqs="http://www.cellml.org/bqs/1.0#"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
<rdf:Description rdf:about="#muscle_O2_delivery_CellML1_0_model">
<bqs:reference rdf:parseType="Resource">
<bqs:JournalArticle rdf:parseType="Resource">
<dc:creator>
<rdf:Seq>
<rdf:li rdf:parseType="Resource">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person" />
<vCard:N rdf:parseType="Resource">
<vCard:Family>Guyton</vCard:Family>
<vCard:Given></vCard:Given>
<vCard:Other></vCard:Other>
</vCard:N>
</rdf:li>
<rdf:li rdf:parseType="Resource">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person" />
<vCard:N rdf:parseType="Resource">
<vCard:Family>Muscle Oxygen Delivery</vCard:Family>
<vCard:Given></vCard:Given>
<vCard:Other></vCard:Other>
</vCard:N>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title>Description of Guyton muscle oxygen delivery module</dc:title>
<bqs:volume />
<bqs:first_page />
<bqs:last_page />
<bqs:Journal rdf:parseType="Resource">
<dc:title></dc:title>
</bqs:Journal>
<dcterms:issued rdf:parseType="Resource">
<dcterms:W3CDTF>2008-00-00 00:00</dcterms:W3CDTF>
</dcterms:issued>
</bqs:JournalArticle>
</bqs:reference>
<bqs:reference rdf:parseType="Resource">
<dc:subject rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>physiology</rdf:li>
<rdf:li>organ systems</rdf:li>
<rdf:li>cardiovascular circulation</rdf:li>
<rdf:li>muscle oxygen</rdf:li>
<rdf:li>Guyton</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
<!-- ======================================================= UNITS ================================================== -->
<units name="minute">
<unit multiplier="60" units="second"/>
</units>
<units name="per_minute">
<unit units="minute" exponent="-1"/>
</units>
<units name="mmHg">
<unit multiplier="133.322" units="newton"/>
<unit units="metre" exponent="-2"/>
</units>
<units name="per_mmHg">
<unit units="mmHg" exponent="-1"/>
</units>
<units name="mmHg_per_mL">
<unit units="mmHg"/>
<unit units="mL" exponent="-1"/>
</units>
<units name="per_mmHg2">
<unit units="mmHg" exponent="-2"/>
</units>
<units name="mmHg3">
<unit units="mmHg" exponent="3"/>
</units>
<units name="monovalent_mEq">
<unit units="mole" prefix="milli"/>
</units>
<units name="monovalent_mEq_per_minute">
<unit units="mole" prefix="milli"/>
<unit units="minute" exponent="-1"/>
</units>
<units name="monovalent_mEq_per_litre">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="monovalent_mEq_per_litre_per_minute">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
<unit units="minute" exponent="-1"/>
</units>
<units name="litre2_per_monovalent_mEq_per_minute">
<unit units="litre" exponent="2"/>
<unit units="mole" prefix="milli" exponent="-1"/>
<unit units="minute" exponent="-1"/>
</units>
<units name="L_per_minute">
<unit units="litre"/>
<unit units="minute" exponent="-1"/>
</units>
<units name="mL">
<unit units="litre" prefix="milli"/>
</units>
<units name="mL_per_L">
<unit units="litre" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="mL_per_minute">
<unit units="mL"/>
<unit units="minute" exponent="-1"/>
</units>
<units name="L_per_minute_per_mmHg">
<unit units="litre"/>
<unit units="minute" exponent="-1"/>
<unit units="mmHg" exponent="-1"/>
</units>
<!-- ================================================================================================================ -->
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#muscle_O2_delivery_CellML1_0_model">
<rdf:value>
The tissues of the body are divided into non-muscle tissues and muscle tissues,
and the delivery of oxygen to each one of these is calculated separately. The
principal reason for this separation is that during muscle activity, the delivery
of oxygen to the muscles increases tremendously and correspondingly affects the
blood flow through the muscles. Several aspects of local cellular usage of oxygen
are also calculated.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- ======================================== ENVIRONMENT COMPONENT ============================================= -->
<component name="environment">
<variable cmeta:id="environment_time"
name="time" units="minute" private_interface="none" public_interface="out"/>
</component>
<!-- ======================================== INITIAL_GUESSES ============================================= -->
<rdf:RDF xmlns:sh="http://www.cellml.org/metadata/simulation/solverhints/1.0#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#muscle_O2_delivery_CellML1_0_model">
<sh:solverHint rdf:parseType="Resource">
<sh:initialValue>57.064</sh:initialValue>
<sh:degree>0</sh:degree>
<sh:variable rdf:resource="#delivery_of_O2_to_M_tissues_RMO" />
</sh:solverHint>
<sh:solverHint rdf:parseType="Resource">
<sh:initialValue>39.9701</sh:initialValue>
<sh:degree>0</sh:degree>
<sh:variable rdf:resource="#M_venous_O2_content_PVO" />
</sh:solverHint>
<sh:solverHint rdf:parseType="Resource">
<sh:initialValue>48.0702</sh:initialValue>
<sh:degree>0</sh:degree>
<sh:variable rdf:resource="#volume_of_O2_in_M_tissue_QOM" />
</sh:solverHint>
<sh:solverHint rdf:parseType="Resource">
<sh:initialValue>38.0558</sh:initialValue>
<sh:degree>0</sh:degree>
<sh:variable rdf:resource="#pressure_of_O2_in_M_tissue_cells_PMO" />
</sh:solverHint>
<sh:solverHint rdf:parseType="Resource">
<sh:initialValue>57.1</sh:initialValue>
<sh:degree>0</sh:degree>
<sh:variable rdf:resource="#metabolic_O2_consumption_by_M_tissue_MMO" />
</sh:solverHint>
<sh:solverHint rdf:parseType="Resource">
<sh:initialValue>38.0</sh:initialValue>
<sh:degree>0</sh:degree>
<sh:variable rdf:resource="#metabolic_O2_consumption_by_M_tissue_P2O" />
</sh:solverHint>
<sh:solverHint rdf:parseType="Resource">
<sh:initialValue>0.699673</sh:initialValue>
<sh:degree>0</sh:degree>
<sh:variable rdf:resource="#M_venous_O2_content_OVS" />
</sh:solverHint>
</rdf:Description>
</rdf:RDF>
<!-- ======================================== MUSCLE O2 DELIVERY TOP-LEVEL COMPONENT ============================================= -->
<component name="muscle_O2_delivery"
cmeta:id="muscle_O2_delivery">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#muscle_O2_delivery">
<rdf:value>
Encapsulation grouping component containing all the components in the Muscle Oxygen Delivery Model.
The inputs and outputs of the Muscle Oxygen Delivery Model must be passed by this component.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<variable name="time" units="minute" private_interface="out" public_interface="in"/>
<!-- Inputs from components in other models -->
<variable name="BFM" initial_value="0.989949" units="L_per_minute" private_interface="out" public_interface="none"/>
<variable name="OVA" initial_value="204.497" units="mL_per_L" private_interface="out" public_interface="none"/>
<variable name="HM" initial_value="40.0381" units="dimensionless" private_interface="out" public_interface="none"/>
<variable name="AOM" initial_value="1.00002" units="dimensionless" private_interface="out" public_interface="none"/>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="muscle_O2_delivery" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- ==================================================== MUSCLE O2 BLOOD SUPPLY ========================================================= -->
<component name="M_O2_blood_supply"
cmeta:id="M_O2_blood_supply">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#M_O2_blood_supply">
<rdf:value>
OM1:
The volume of oxygen in the arterial blood flowing to the muscles each minute (02ARTM)
is equal to the volume of oxygen in each liter of arterial blood (OVA) times the muscle
blood flow (BFM).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#OM1">
<rdf:value>
OM1:
The volume of oxygen in the arterial blood flowing to the muscles each minute (02ARTM)
is equal to the volume of oxygen in each liter of arterial blood (OVA) times the muscle
blood flow (BFM).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="OVA" units="mL_per_L" private_interface="none" public_interface="in"/>
<variable name="BFM" units="L_per_minute" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="O2ARTM" units="mL_per_minute" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="OM1">
<eq/>
<ci>O2ARTM</ci>
<apply>
<times/>
<ci>OVA</ci>
<ci>BFM</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="M_O2_blood_supply" component_2="muscle_O2_delivery"/>
<map_variables variable_1="OVA" variable_2="OVA"/>
<map_variables variable_1="BFM" variable_2="BFM"/>
</connection>
<!-- ======================================== MUSCLE VENOUS O2 CONTENT ============================================= -->
<component name="M_venous_O2_content"
cmeta:id="M_venous_O2_content">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#M_venous_O2_content">
<rdf:value>
OM2:
The volume of oxygen in the venous blood flowing away from the muscles
each minute (O2VENM) is equal to the volume of blood flowing into the muscles
from the arteries (O2ARTM) minus the rate of uptake of oxygen by the muscles
per minute (RMO).
OM3 and OM4:
The venous oxygen saturation in the muscles (OVS) is equal to the volume of oxygen
transported to the muscle veins each minute (O2VENM) divided by the blood flow
through the muscles per minute (BFM), divided by the hematocrit of the blood (HM),
and divided by a constant that relates volume of oxygen in the blood to hematocrit.
Damping of the oxygen venous saturation (OVS) is provided by Block OM4 and is controlled
by the damping constant (Z6).
OM5 and OM5A:
The pressure of the oxygen in the venous blood of the muscles (PVO) is equal to the
saturation of the oxygen in the venous blood of the muscles (OVS) times a constant
and times a factor related exponentially (EXCXP2) to the level of exercise (EXC)
caused by changes in tissue fluid products that affect oxygen combination with
hemoglobin.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#OM2_to_OM4">
<rdf:value>
OM2:
The volume of oxygen in the venous blood flowing away from the muscles
each minute (O2VENM) is equal to the volume of blood flowing into the muscles
from the arteries (O2ARTM) minus the rate of uptake of oxygen by the muscles
per minute (RMO).
OM3 and OM4:
The venous oxygen saturation in the muscles (OVS) is equal to the volume of oxygen
transported to the muscle veins each minute (O2VENM) divided by the blood flow
through the muscles per minute (BFM), divided by the hematocrit of the blood (HM),
and divided by a constant that relates volume of oxygen in the blood to hematocrit.
Damping of the oxygen venous saturation (OVS) is provided by Block OM4 and is controlled
by the damping constant (Z6).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#OM5_and_OM5A">
<rdf:value>
OM5 and OM5A:
The pressure of the oxygen in the venous blood of the muscles (PVO) is equal to the
saturation of the oxygen in the venous blood of the muscles (OVS) times a constant
and times a factor related exponentially (EXCXP2) to the level of exercise (EXC)
caused by changes in tissue fluid products that affect oxygen combination with
hemoglobin.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="O2ARTM" units="mL_per_minute" private_interface="none" public_interface="in"/>
<variable name="RMO" units="mL_per_minute" private_interface="none" public_interface="in"/>
<variable name="BFM" units="L_per_minute" private_interface="none" public_interface="in"/>
<variable name="HM" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="time" units="minute" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable cmeta:id="M_venous_O2_content_PVO" name="PVO" units="mmHg" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="EXC" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="EXCXP2" units="dimensionless" private_interface="none" public_interface="in"/>
<!-- Internal variables -->
<variable name="OVS"
cmeta:id="M_venous_O2_content_OVS" units="dimensionless" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="OM2_to_OM4">
<eq/>
<ci>OVS</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>O2ARTM</ci>
<ci>RMO</ci>
</apply>
<apply>
<times/>
<ci>HM</ci>
<cn cellml:units="dimensionless">5.25</cn>
<ci>BFM</ci>
</apply>
</apply>
</apply>
<apply id="OM5_and_OM5A">
<eq/>
<ci>PVO</ci>
<apply>
<times/>
<cn cellml:units="mmHg">57.14</cn>
<ci>OVS</ci>
<apply>
<power/>
<ci>EXC</ci>
<ci>EXCXP2</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="M_venous_O2_content" component_2="M_O2_blood_supply"/>
<map_variables variable_1="O2ARTM" variable_2="O2ARTM"/>
</connection>
<connection>
<map_components component_1="M_venous_O2_content" component_2="delivery_of_O2_to_M_tissues"/>
<map_variables variable_1="RMO" variable_2="RMO"/>
<map_variables variable_1="PVO" variable_2="PVO"/>
</connection>
<connection>
<map_components component_1="M_venous_O2_content" component_2="muscle_O2_delivery"/>
<map_variables variable_1="BFM" variable_2="BFM"/>
<map_variables variable_1="HM" variable_2="HM"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="M_venous_O2_content" component_2="parameter_values"/>
<map_variables variable_1="EXC" variable_2="EXC"/>
<map_variables variable_1="EXCXP2" variable_2="EXCXP2"/>
</connection>
<!-- ======================================== AUTONOMIC EFFECT ON MUSCLE O2 CONSUMPTION ============================================= -->
<!-- THIS COMPONENT IS THE SAME AS THE AUTONOMICS EQUATIONS NUMBERS 47 AND 48!!!
<component name="autonomic_effect_on_M_O2_consumption"
cmeta:id="autonomic_effect_on_M_O2_consumption">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#autonomic_effect_on_M_O2_consumption">
<rdf:value>
OM24 and OM25:
Calculation of autonomic stimulation of muscle usage of oxygen (AOM) based
on the current level of whole-body autonomic stimulation (AUO) times a
proportionality factor (O2A).
</rdf:value>
</rdf:Description>
</rdf:RDF>
</component>
-->
<!-- ======================================== METABOLIC O2 CONSUMPTION BY MUSCLE TISSUE CELLS ============================================= -->
<component name="metabolic_O2_consumption_by_M_tissue"
cmeta:id="metabolic_O2_consumption_by_M_tissue">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#metabolic_O2_consumption_by_M_tissue">
<rdf:value>
OM17, OM18, OM19, OM20, OM21, OM22, and OM23:
Calculation of the rate of metabolic usage of oxygen by the muscle cells (MMO)
from several factors: the oxygen pressure in the muscle cells (PMO), the basal
level of oxygen utilization by the muscle cells (OMM), the effect of autonomic
stimulation on muscle usage of oxygen (AOM), and the effect of exercise on the
metabolic usage of oxygen by the muscles (EXC). Blocks OM17 and OM18 cause the
metabolic usage of oxygen to reach a maximum at any time that the average muscle
cellular oxygen level is above the value of 38 mmHg pressure. The constants in
the various blocks are curve-shaping constants to relate cellular oxygen
pressure (PMO) to the metabolic usage of oxygen.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#OM17_and_OM18">
<rdf:value>
OM17, OM18, OM19, OM20, OM21, OM22, and OM23:
Calculation of the rate of metabolic usage of oxygen by the muscle cells (MMO)
from several factors: the oxygen pressure in the muscle cells (PMO), the basal
level of oxygen utilization by the muscle cells (OMM), the effect of autonomic
stimulation on muscle usage of oxygen (AOM), and the effect of exercise on the
metabolic usage of oxygen by the muscles (EXC). Blocks OM17 and OM18 cause the
metabolic usage of oxygen to reach a maximum at any time that the average muscle
cellular oxygen level is above the value of 38 mmHg pressure. The constants in
the various blocks are curve-shaping constants to relate cellular oxygen
pressure (PMO) to the metabolic usage of oxygen.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#OM19_to_OM23">
<rdf:value>
OM17, OM18, OM19, OM20, OM21, OM22, and OM23:
Calculation of the rate of metabolic usage of oxygen by the muscle cells (MMO)
from several factors: the oxygen pressure in the muscle cells (PMO), the basal
level of oxygen utilization by the muscle cells (OMM), the effect of autonomic
stimulation on muscle usage of oxygen (AOM), and the effect of exercise on the
metabolic usage of oxygen by the muscles (EXC). Blocks OM17 and OM18 cause the
metabolic usage of oxygen to reach a maximum at any time that the average muscle
cellular oxygen level is above the value of 38 mmHg pressure. The constants in
the various blocks are curve-shaping constants to relate cellular oxygen
pressure (PMO) to the metabolic usage of oxygen.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="PMO" units="mmHg" private_interface="none" public_interface="in"/>
<variable name="AOM" units="dimensionless" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable cmeta:id="metabolic_O2_consumption_by_M_tissue_MMO"
name="MMO" units="mL_per_minute" private_interface="none" public_interface="out"/>
<variable cmeta:id="metabolic_O2_consumption_by_M_tissue_P2O"
name="P2O" units="mmHg" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="OMM" units="mL_per_minute" private_interface="none" public_interface="in"/>
<variable name="EXC" units="dimensionless" private_interface="none" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="OM17_and_OM18">
<eq/>
<ci>P2O</ci>
<piecewise>
<piece>
<cn cellml:units="mmHg">38</cn>
<apply>
<gt/>
<ci>PMO</ci>
<cn cellml:units="mmHg">38</cn>
</apply>
</piece>
<otherwise>
<ci>PMO</ci>
</otherwise>
</piecewise>
</apply>
<apply id="OM19_to_OM23">
<eq/>
<ci>MMO</ci>
<apply>
<times/>
<ci>AOM</ci>
<ci>OMM</ci>
<ci>EXC</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<power/>
<apply>
<minus/>
<cn cellml:units="mmHg">38.0001</cn>
<ci>P2O</ci>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
<cn cellml:units="mmHg3">54872</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="metabolic_O2_consumption_by_M_tissue" component_2="pressure_of_O2_in_M_tissue_cells"/>
<map_variables variable_1="PMO" variable_2="PMO"/>
</connection>
<connection>
<map_components component_1="metabolic_O2_consumption_by_M_tissue" component_2="muscle_O2_delivery"/>
<map_variables variable_1="AOM" variable_2="AOM"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="metabolic_O2_consumption_by_M_tissue" component_2="parameter_values"/>
<map_variables variable_1="OMM" variable_2="OMM"/>
<map_variables variable_1="EXC" variable_2="EXC"/>
</connection>
<!-- ======================================== DELIVERY OF O2 TO MUSCLE TISSUES ============================================= -->
<component name="delivery_of_O2_to_M_tissues"
cmeta:id="delivery_of_O2_to_M_tissues">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#delivery_of_O2_to_M_tissues">
<rdf:value>
OM6:
The pressure gradient for delivery of oxygen from the muscle capillaries to the
muscle cells (PGRM) is equal to the pressure of the oxygen remaining in the
muscle venous blood (PVO) minus the pressure of the oxygen in the muscle cells (PMO).
OM8:
Rate of delivery of oxygen to the muscles (RMO) is equal to the blood flow to
the muscles (BFM) times the pressure gradient between the muscle capillary blood
and the muscle cells (PGRM) times a constant (PM5) that can be varied to represent
such factors as changes in muscle capillarity or so forth.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#OM6_and_OM8">
<rdf:value>
OM6:
The pressure gradient for delivery of oxygen from the muscle capillaries to the
muscle cells (PGRM) is equal to the pressure of the oxygen remaining in the
muscle venous blood (PVO) minus the pressure of the oxygen in the muscle cells (PMO).
OM8:
Rate of delivery of oxygen to the muscles (RMO) is equal to the blood flow to
the muscles (BFM) times the pressure gradient between the muscle capillary blood
and the muscle cells (PGRM) times a constant (PM5) that can be varied to represent
such factors as changes in muscle capillarity or so forth.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="PMO" units="mmHg" private_interface="none" public_interface="in"/>
<variable name="PVO" units="mmHg" private_interface="none" public_interface="in"/>
<variable name="BFM" units="L_per_minute" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable cmeta:id="delivery_of_O2_to_M_tissues_RMO"
name="RMO" units="mL_per_minute" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="PM5" units="per_mmHg" private_interface="none" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="OM6_and_OM8">
<eq/>
<ci>RMO</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>PVO</ci>
<ci>PMO</ci>
</apply>
<ci>PM5</ci>
<ci>BFM</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="delivery_of_O2_to_M_tissues" component_2="pressure_of_O2_in_M_tissue_cells"/>
<map_variables variable_1="PMO" variable_2="PMO"/>
</connection>
<connection>
<map_components component_1="delivery_of_O2_to_M_tissues" component_2="muscle_O2_delivery"/>
<map_variables variable_1="BFM" variable_2="BFM"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="delivery_of_O2_to_M_tissues" component_2="parameter_values"/>
<map_variables variable_1="PM5" variable_2="PM5"/>
</connection>
<!-- ======================================== VOLUME OF O2 IN MUSCLE TISSUE ============================================= -->
<component name="volume_of_O2_in_M_tissue"
cmeta:id="volume_of_O2_in_M_tissue">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#volume_of_O2_in_M_tissue">
<rdf:value>
OM9:
The rate of change of stored oxygen in the muscle (DO2M) is equal to the
rate of delivery of oxygen to the muscles by the blood (RMO) minus the rate
of metabolic usage of oxygen by the muscle cells (MMO).
OM10:
The instantaneous volume of oxygen dissolved in all of the muscles (QOM) is
calculated by integrating with respect to time the rate of change of oxygen
in the muscles (DO2M).
OM11:
This sets a lower limit for QOM in the muscle tissue.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#OM9">
<rdf:value>
OM9:
The rate of change of stored oxygen in the muscle (DO2M) is equal to the
rate of delivery of oxygen to the muscles by the blood (RMO) minus the rate
of metabolic usage of oxygen by the muscle cells (MMO).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#OM10">
<rdf:value>
OM10:
The instantaneous volume of oxygen dissolved in all of the muscles (QOM) is
calculated by integrating with respect to time the rate of change of oxygen
in the muscles (DO2M).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#OM11">
<rdf:value>
OM11:
This sets a lower limit for QOM in the muscle tissue.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="RMO" units="mL_per_minute" private_interface="none" public_interface="in"/>
<variable name="MMO" units="mL_per_minute" private_interface="none" public_interface="in"/>
<variable name="time" units="minute" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable cmeta:id="volume_of_O2_in_M_tissue_QOM"
name="QOM" units="mL" private_interface="none" public_interface="out"/>
<!-- Internal variables -->
<variable name="DO2M" units="mL_per_minute" private_interface="none" public_interface="none"/>
<variable name="QOM1" initial_value="48.0839" units="mL" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="OM9">
<eq/>
<ci>DO2M</ci>
<apply>
<minus/>
<ci>RMO</ci>
<ci>MMO</ci>
</apply>
</apply>
<apply id="OM10">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>QOM1</ci>
</apply>
<ci>DO2M</ci>
</apply>
<apply id="OM11">
<eq/>
<ci>QOM</ci>
<piecewise>
<piece>
<cn cellml:units="mL">0.0001</cn>
<apply>
<lt/>
<ci>QOM1</ci>
<cn cellml:units="mL">0.0001</cn>
</apply>
</piece>
<otherwise>
<ci>QOM1</ci>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="volume_of_O2_in_M_tissue" component_2="delivery_of_O2_to_M_tissues"/>
<map_variables variable_1="RMO" variable_2="RMO"/>
</connection>
<connection>
<map_components component_1="volume_of_O2_in_M_tissue" component_2="metabolic_O2_consumption_by_M_tissue"/>
<map_variables variable_1="MMO" variable_2="MMO"/>
</connection>
<connection>
<map_components component_1="volume_of_O2_in_M_tissue" component_2="muscle_O2_delivery"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- ======================================== PRESSURE OF O2 IN MUSCLE TISSUE CELLS ============================================= -->
<component name="pressure_of_O2_in_M_tissue_cells"
cmeta:id="pressure_of_O2_in_M_tissue_cells">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#pressure_of_O2_in_M_tissue_cells">
<rdf:value>
OM12:
Calculation of the pressure of oxygen in the muscle cells (PMO) from the
volume of oxygen in the muscles (QOM).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#OM12">
<rdf:value>
OM12:
Calculation of the pressure of oxygen in the muscle cells (PMO) from the
volume of oxygen in the muscles (QOM).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="QOM" units="mL" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable cmeta:id="pressure_of_O2_in_M_tissue_cells_PMO"
name="PMO" units="mmHg" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="PK2" units="mmHg_per_mL" private_interface="none" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="OM12">
<eq/>
<ci>PMO</ci>
<apply>
<times/>
<ci>PK2</ci>
<ci>QOM</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="pressure_of_O2_in_M_tissue_cells" component_2="volume_of_O2_in_M_tissue"/>
<map_variables variable_1="QOM" variable_2="QOM"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="pressure_of_O2_in_M_tissue_cells" component_2="parameter_values"/>
<map_variables variable_1="PK2" variable_2="PK2"/>
</connection>
<!-- ========================================================== PARAMETER VALUES ================================================================ -->
<component name="parameter_values"
cmeta:id="parameter_values">
<variable name="EXC" units="dimensionless" initial_value="1" private_interface="none" public_interface="out"/> <!-- level of exercise activity [P] -->
<variable name="EXCXP2" units="dimensionless" initial_value="0.17" private_interface="none" public_interface="out"/> <!-- exponent factor of exercise on muscle metabolism [P] -->
<variable name="OMM" units="mL_per_minute" initial_value="57.1" private_interface="none" public_interface="out"/> <!-- basic O2 utilization in muscle tissues (at rest) [P] -->
<variable name="PM5" units="per_mmHg" initial_value="30" private_interface="none" public_interface="out"/> <!-- constant, to change muscle capillarity [P] -->
<variable name="PK2" units="mmHg_per_mL" initial_value="0.79167" private_interface="none" public_interface="out"/> <!-- proportionality constant, muscle tissue PO2 [P] -->
</component>
<!-- ============================================================ GROUPING =============================================================== -->
<group>
<relationship_ref relationship="containment"/>
<component_ref component="muscle_O2_delivery">
<component_ref component="M_O2_blood_supply"/>
<component_ref component="M_venous_O2_content"/>
<component_ref component="metabolic_O2_consumption_by_M_tissue"/>
<component_ref component="delivery_of_O2_to_M_tissues"/>
<component_ref component="volume_of_O2_in_M_tissue"/>
<component_ref component="pressure_of_O2_in_M_tissue_cells"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="muscle_O2_delivery">
<component_ref component="parameter_values"/>
<component_ref component="M_O2_blood_supply"/>
<component_ref component="M_venous_O2_content"/>
<component_ref component="metabolic_O2_consumption_by_M_tissue"/>
<component_ref component="delivery_of_O2_to_M_tissues"/>
<component_ref component="volume_of_O2_in_M_tissue"/>
<component_ref component="pressure_of_O2_in_M_tissue_cells"/>
</component_ref>
</group>
<!-- SIMULATION METADATA -->
<RDF:RDF xmlns:RDF="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<RDF:Description RDF:about="M_O2_delivery_1-0.cellml#muscle_O2_delivery_CellML1_0_model">
<NS1:simulation xmlns:NS1="http://www.cellml.org/metadata/simulation/1.0#" RDF:resource="rdf:#$QQv43"/>
</RDF:Description>
<RDF:Description RDF:about="rdf:#$4SdBX3">
<RDF:first RDF:resource="rdf:#$5SdBX3"/>
<RDF:rest RDF:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/>
</RDF:Description>
<RDF:Description RDF:about="rdf:#$3SdBX3">
<NS1:boundIntervals xmlns:NS1="http://www.cellml.org/metadata/simulation/1.0#" RDF:resource="rdf:#$4SdBX3"/>
</RDF:Description>
<RDF:Description xmlns:NS1="http://www.cellml.org/metadata/simulation/1.0#" RDF:about="rdf:#$5SdBX3" NS1:endingValue="100"/>
<RDF:Description xmlns:NS1="http://www.cellml.org/metadata/simulation/1.0#" RDF:about="rdf:#$SQv43" NS1:endingValue="100" NS1:nonstandard-pointDensity="1000"/>
<RDF:Description xmlns:NS1="http://www.cellml.org/metadata/simulation/1.0#" RDF:about="rdf:#$d2Cb93" NS1:nonstandard-pointDensity="1000"/>
<RDF:Description RDF:about="M_O2_delivery_1-0.cellml#muscle_O2_delivery_CellML1_0_model#LfY7zdZ%60EYs">
<NS1:simulation xmlns:NS1="http://www.cellml.org/metadata/simulation/1.0#" RDF:resource="rdf:#$b2Cb93"/>
<NS1:simulation xmlns:NS1="http://www.cellml.org/metadata/simulation/1.0#" RDF:resource="rdf:#$3SdBX3"/>
</RDF:Description>
<RDF:Description RDF:about="rdf:#$QQv43">
<NS1:boundIntervals xmlns:NS1="http://www.cellml.org/metadata/simulation/1.0#" RDF:resource="rdf:#$RQv43"/>
</RDF:Description>
<RDF:Description RDF:about="rdf:#$RQv43">
<RDF:first RDF:resource="rdf:#$SQv43"/>
<RDF:rest RDF:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/>
</RDF:Description>
<RDF:Description RDF:about="rdf:#$b2Cb93">
<NS1:boundIntervals xmlns:NS1="http://www.cellml.org/metadata/simulation/1.0#" RDF:resource="rdf:#$c2Cb93"/>
</RDF:Description>
<RDF:Description RDF:about="rdf:#$c2Cb93">
<RDF:first RDF:resource="rdf:#$d2Cb93"/>
<RDF:rest RDF:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/>
</RDF:Description>
</RDF:RDF>
</model>
