<?xml version="1.0" encoding="utf-8"?>
<model
name="non_muscle_O2_delivery_CellML1_0_model"
cmeta:id="non_muscle_O2_delivery_CellML1_0_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">
<!-- ======================================== DOCUMENTATION ============================================= -->
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Guyton Model: non_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 non-muscle tissues, 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="non_muscle_O2_delivery_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="NM_O2_Delivery.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="#non_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>Non-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 non-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>non-muscle oxygen delivery</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="#non_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>
<!-- ======================================== NON-MUSCLE O2 DELIVERY TOP-LEVEL COMPONENT ============================================= -->
<component name="non_muscle_O2_delivery"
cmeta:id="non_muscle_O2_delivery">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#non_muscle_O2_delivery">
<rdf:value>
Encapsulation grouping component containing all the components in the Non-Muscle Oxygen Delivery Model.
The inputs and outputs of the Non-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="BFN" initial_value="2.79521" 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="non_muscle_O2_delivery" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- ==================================================== NON-MUSCLE O2 BLOOD SUPPLY ========================================================= -->
<component name="NM_O2_blood_supply"
cmeta:id="NM_O2_blood_supply">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#NM_O2_blood_supply">
<rdf:value>
ONM1:
The quantity of oxygen in the arterial blood entering the non-muscle
tissues per minute (O2ARTN) is equal to the oxygen volume in each liter of
arterial blood (OVA) times the blood flow to the non-muscle tissues (BFN).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ONM1">
<rdf:value>
ONM1:
The quantity of oxygen in the arterial blood entering the non-muscle
tissues per minute (O2ARTN) is equal to the oxygen volume in each liter of
arterial blood (OVA) times the blood flow to the non-muscle tissues (BFN).
</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="BFN" units="L_per_minute" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="O2ARTN" units="mL_per_minute" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ONM1">
<eq/>
<ci>O2ARTN</ci>
<apply>
<times/>
<ci>OVA</ci>
<ci>BFN</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="NM_O2_blood_supply" component_2="non_muscle_O2_delivery"/>
<map_variables variable_1="OVA" variable_2="OVA"/>
<map_variables variable_1="BFN" variable_2="BFN"/>
</connection>
<!-- ======================================== NON-MUSCLE VENOUS O2 CONTENT ============================================= -->
<component name="NM_venous_O2_content"
cmeta:id="NM_venous_O2_content">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#NM_venous_O2_content">
<rdf:value>
ONM2:
The volume of oxygen remaining in the effluent venous blood from the non-muscle
tissues per minute (O2VENN) is equal to the volume of oxygen in the entering
arterial blood (O2ARTN) minus the rate of delivery of oxygen to the non-muscle
tissues per minute (DOB).
ONM3 and ONM4:
The oxygen saturation of the venous blood leaving the non-muscle tissues (OSV)
is calculated from the volume of oxygen in this venous blood (O2VENN) divided by
three different factors: the rate of blood flow through the non-muscle tissues (BFN),
the hematocrit (HM), and a constant factor for converting volume of oxygen to saturation.
Block ONM4 provides damping to prevent too rapid changes which could cause computational
oscillation; the degree of damping can be altered by altering the damping factor (Z7).
ONM5:
The pressure of oxygen in the venous blood (POV) is calculated by multiplying the venous
blood saturation (OSV) times a constant.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ONM2_to_ONM4">
<rdf:value>
ONM2:
The volume of oxygen remaining in the effluent venous blood from the non-muscle
tissues per minute (O2VENN) is equal to the volume of oxygen in the entering
arterial blood (O2ARTN) minus the rate of delivery of oxygen to the non-muscle
tissues per minute (DOB).
ONM3 and ONM4:
The oxygen saturation of the venous blood leaving the non-muscle tissues (OSV)
is calculated from the volume of oxygen in this venous blood (O2VENN) divided by
three different factors: the rate of blood flow through the non-muscle tissues (BFN),
the hematocrit (HM), and a constant factor for converting volume of oxygen to saturation.
Block ONM4 provides damping to prevent too rapid changes which could cause computational
oscillation; the degree of damping can be altered by altering the damping factor (Z7).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ONM5">
<rdf:value>
ONM5:
The pressure of oxygen in the venous blood (POV) is calculated by multiplying the venous
blood saturation (OSV) times a constant.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="O2ARTN" units="mL_per_minute" private_interface="none" public_interface="in"/>
<variable name="DOB" units="mL_per_minute" private_interface="none" public_interface="in"/>
<variable name="BFN" 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="NM_venous_O2_content_POV"
name="POV" units="mmHg" private_interface="none" public_interface="out"/>
<!-- Internal variables -->
<variable name="OSV" units="dimensionless" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ONM2_to_ONM4">
<eq/>
<ci>OSV</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>O2ARTN</ci>
<ci>DOB</ci>
</apply>
<apply>
<times/>
<ci>HM</ci>
<cn cellml:units="dimensionless">5.25</cn>
<ci>BFN</ci>
</apply>
</apply>
</apply>
<apply id="ONM5">
<eq/>
<ci>POV</ci>
<apply>
<times/>
<ci>OSV</ci>
<cn cellml:units="mmHg">57.14</cn>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="NM_venous_O2_content" component_2="NM_O2_blood_supply"/>
<map_variables variable_1="O2ARTN" variable_2="O2ARTN"/>
</connection>
<connection>
<map_components component_1="NM_venous_O2_content" component_2="delivery_of_O2_to_NM_tissues"/>
<map_variables variable_1="DOB" variable_2="DOB"/>
<map_variables variable_1="POV" variable_2="POV"/>
</connection>
<connection>
<map_components component_1="NM_venous_O2_content" component_2="non_muscle_O2_delivery"/>
<map_variables variable_1="BFN" variable_2="BFN"/>
<map_variables variable_1="HM" variable_2="HM"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- ======================================== O2 CONSUMPTION BY NON-MUSCLE TISSUE CELLS ============================================= -->
<component name="O2_consumption_by_NM_tissue"
cmeta:id="O2_consumption_by_NM_tissue">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#O2_consumption_by_NM_tissue">
<rdf:value>
ONM14, ONM15, ONM16, ONM17, ONM18, ONM19, and ONM20:
Calculation of the rate of oxygen usage by the non-muscle tissues (M02) based on
three input factors: the normal rate of oxygen usage by these tissues when all
other factors are normal (02M), a decreasing effect on tissue utilization of oxygen
caused by very low tissue PO2's (POT) resulting mainly from failure of flow of the
oxygen to the places where it is needed within the tissue (Blocks 14, 15, 16, 17, 18,
and 19), and a multiplying effect on oxygen usage caused by autonomic stimulation (AOM).
In addition, there is a limit set by Block ONM15 which causes the tissue oxygen level not
to affect metabolism once its level is above a set value.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ONM14_and_ONM15">
<rdf:value>
ONM14, ONM15, ONM16, ONM17, ONM18, ONM19, and ONM20:
Calculation of the rate of oxygen usage by the non-muscle tissues (M02) based on
three input factors: the normal rate of oxygen usage by these tissues when all
other factors are normal (02M), a decreasing effect on tissue utilization of oxygen
caused by very low tissue PO2's (POT) resulting mainly from failure of flow of the
oxygen to the places where it is needed within the tissue (Blocks 14, 15, 16, 17, 18,
and 19), and a multiplying effect on oxygen usage caused by autonomic stimulation (AOM).
In addition, there is a limit set by Block ONM15 which causes the tissue oxygen level not
to affect metabolism once its level is above a set value.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ONM16_to_ONM20">
<rdf:value>
ONM14, ONM15, ONM16, ONM17, ONM18, ONM19, and ONM20:
Calculation of the rate of oxygen usage by the non-muscle tissues (M02) based on
three input factors: the normal rate of oxygen usage by these tissues when all
other factors are normal (02M), a decreasing effect on tissue utilization of oxygen
caused by very low tissue PO2's (POT) resulting mainly from failure of flow of the
oxygen to the places where it is needed within the tissue (Blocks 14, 15, 16, 17, 18,
and 19), and a multiplying effect on oxygen usage caused by autonomic stimulation (AOM).
In addition, there is a limit set by Block ONM15 which causes the tissue oxygen level not
to affect metabolism once its level is above a set value.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="POT" units="mmHg" private_interface="none" public_interface="in"/>
<variable name="AOM" units="dimensionless" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="MO2" units="mL_per_minute" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="O2M" units="mL_per_minute" private_interface="none" public_interface="in"/>
<!-- Internal variables -->
<variable name="P1O" units="mmHg" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ONM14_and_ONM15">
<eq/>
<ci>P1O</ci>
<piecewise>
<piece>
<cn cellml:units="mmHg">35</cn>
<apply>
<gt/>
<ci>POT</ci>
<cn cellml:units="mmHg">35</cn>
</apply>
</piece>
<otherwise>
<ci>POT</ci>
</otherwise>
</piecewise>
</apply>
<apply id="ONM16_to_ONM20">
<eq/>
<ci>MO2</ci>
<apply>
<times/>
<ci>AOM</ci>
<ci>O2M</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<power/>
<apply>
<minus/>
<cn cellml:units="mmHg">35.0001</cn>
<ci>P1O</ci>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
<cn cellml:units="mmHg3">42875</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="O2_consumption_by_NM_tissue" component_2="pressure_of_O2_in_NM_tissue_cells"/>
<map_variables variable_1="POT" variable_2="POT"/>
</connection>
<connection>
<map_components component_1="O2_consumption_by_NM_tissue" component_2="non_muscle_O2_delivery"/>
<map_variables variable_1="AOM" variable_2="AOM"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="O2_consumption_by_NM_tissue" component_2="parameter_values"/>
<map_variables variable_1="O2M" variable_2="O2M"/>
</connection>
<!-- ======================================== DELIVERY OF O2 TO NON-MUSCLE TISSUES ============================================= -->
<component name="delivery_of_O2_to_NM_tissues"
cmeta:id="delivery_of_O2_to_NM_tissues">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#delivery_of_O2_to_NM_tissues">
<rdf:value>
ONM6:
The pressure gradient of the oxygen between the venous or capillary blood of the
non-muscle tissues and the tissue cells themselves (PGRN) is equal to the pressure
of the oxygen in the venous blood (POV) minus the pressure in the non-muscle
tissue cells (POT).
ONM7:
The delivery of oxygen to the non-muscle tissues (DOB) is equal to blood flow to
the tissues (BFN) times the oxygen pressure gradient between the venous or capillary
blood and the tissues (PGRN) times a numerical factor for conductance of oxygen from
the capillaries to the tissue cells.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ONM6_and_ONM7">
<rdf:value>
ONM6:
The pressure gradient of the oxygen between the venous or capillary blood of the
non-muscle tissues and the tissue cells themselves (PGRN) is equal to the pressure
of the oxygen in the venous blood (POV) minus the pressure in the non-muscle
tissue cells (POT).
ONM7:
The delivery of oxygen to the non-muscle tissues (DOB) is equal to blood flow to
the tissues (BFN) times the oxygen pressure gradient between the venous or capillary
blood and the tissues (PGRN) times a numerical factor for conductance of oxygen from
the capillaries to the tissue cells.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="POT" units="mmHg" private_interface="none" public_interface="in"/>
<variable name="POV" units="mmHg" private_interface="none" public_interface="in"/>
<variable name="BFN" units="L_per_minute" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable cmeta:id="delivery_of_O2_to_NM_tissues_DOB"
name="DOB" units="mL_per_minute" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ONM6_and_ONM7">
<eq/>
<ci>DOB</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>POV</ci>
<ci>POT</ci>
</apply>
<cn cellml:units="per_mmHg">12.857</cn>
<ci>BFN</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="delivery_of_O2_to_NM_tissues" component_2="pressure_of_O2_in_NM_tissue_cells"/>
<map_variables variable_1="POT" variable_2="POT"/>
</connection>
<connection>
<map_components component_1="delivery_of_O2_to_NM_tissues" component_2="non_muscle_O2_delivery"/>
<map_variables variable_1="BFN" variable_2="BFN"/>
</connection>
<!-- ======================================== VOLUME OF O2 IN NON-MUSCLE TISSUE ============================================= -->
<component name="volume_of_O2_in_NM_tissue"
cmeta:id="volume_of_O2_in_NM_tissue">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#volume_of_O2_in_NM_tissue">
<rdf:value>
ONM8:
The rate of change of oxygen in the non-muscle tissues (DO2N) is equal to the rate
of delivery of oxygen to the non-muscle tissues (DOB) minus the rate of metabolism
of oxygen in the tissues (MO2).
ONM9:
Limitation in the use of oxygen by the tissues (MO2) when tissue oxygenation (Q02)
falls very low.
ONM10:
The instantaneous quantity of oxygen in the tissues (Q02) is calculated by integrating
the rate of change of the oxygen in these tissues (D02N).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ONM8">
<rdf:value>
ONM8:
The rate of change of oxygen in the non-muscle tissues (DO2N) is equal to the rate
of delivery of oxygen to the non-muscle tissues (DOB) minus the rate of metabolism
of oxygen in the tissues (MO2).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ONM9">
<rdf:value>
ONM9:
Limitation in the use of oxygen by the tissues (MO2) when tissue oxygenation (Q02)
falls very low.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ONM10">
<rdf:value>
ONM10:
The instantaneous quantity of oxygen in the tissues (Q02) is calculated by integrating
the rate of change of the oxygen in these tissues (D02N).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ONM10_cont">
<rdf:value>
ONM10:
The instantaneous quantity of oxygen in the tissues (Q02) is calculated by integrating
the rate of change of the oxygen in these tissues (D02N).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="DOB" units="mL_per_minute" private_interface="none" public_interface="in"/>
<variable name="MO2" 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 name="QO2" units="mL" private_interface="none" public_interface="out"/>
<!-- Internal variables -->
<variable name="DO2N" units="mL_per_minute" private_interface="none" public_interface="none"/>
<variable name="DO2N1" units="mL_per_minute" private_interface="none" public_interface="none"/>
<variable name="QO2T" initial_value="72.2362" units="mL" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ONM8">
<eq/>
<ci>DO2N1</ci>
<apply>
<minus/>
<ci>DOB</ci>
<ci>MO2</ci>
</apply>
</apply>
<apply id="ONM9">
<eq/>
<ci>DO2N</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>DO2N1</ci>
<cn cellml:units="dimensionless">0.1</cn>
</apply>
<apply>
<and/>
<apply>
<lt/>
<ci>QO2</ci>
<cn cellml:units="mL">6</cn>
</apply>
<apply>
<lt/>
<ci>DO2N1</ci>
<cn cellml:units="mL_per_minute">0</cn>
</apply>
</apply>
</piece>
<otherwise>
<ci>DO2N1</ci>
</otherwise>
</piecewise>
</apply>
<apply id="ONM10">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>QO2T</ci>
</apply>
<ci>DO2N</ci>
</apply>
<apply id="ONM10_cont">
<eq/>
<ci>QO2</ci>
<piecewise>
<piece>
<cn cellml:units="mL">0</cn>
<apply>
<lt/>
<ci>QO2T</ci>
<cn cellml:units="mL">0</cn>
</apply>
</piece>
<otherwise>
<ci>QO2T</ci>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="volume_of_O2_in_NM_tissue" component_2="delivery_of_O2_to_NM_tissues"/>
<map_variables variable_1="DOB" variable_2="DOB"/>
</connection>
<connection>
<map_components component_1="volume_of_O2_in_NM_tissue" component_2="O2_consumption_by_NM_tissue"/>
<map_variables variable_1="MO2" variable_2="MO2"/>
</connection>
<connection>
<map_components component_1="volume_of_O2_in_NM_tissue" component_2="non_muscle_O2_delivery"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- ======================================== PRESSURE OF O2 IN NON-MUSCLE TISSUE CELLS ============================================= -->
<component name="pressure_of_O2_in_NM_tissue_cells"
cmeta:id="pressure_of_O2_in_NM_tissue_cells">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#pressure_of_O2_in_NM_tissue_cells">
<rdf:value>
ONM11:
The pressure of the oxygen in the tissue cells of the non-muscle tissues (POT)
is equal to the quantity of oxygen in the tissues (Q02) times a constant.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ONM11">
<rdf:value>
ONM11:
The pressure of the oxygen in the tissue cells of the non-muscle tissues (POT)
is equal to the quantity of oxygen in the tissues (Q02) times a constant.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="QO2" units="mL" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="POT" units="mmHg" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ONM11">
<eq/>
<ci>POT</ci>
<apply>
<times/>
<ci>QO2</ci>
<cn cellml:units="mmHg_per_mL">0.48611</cn>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="pressure_of_O2_in_NM_tissue_cells" component_2="volume_of_O2_in_NM_tissue"/>
<map_variables variable_1="QO2" variable_2="QO2"/>
</connection>
<!-- ========================================================== PARAMETER VALUES ================================================================ -->
<component name="parameter_values"
cmeta:id="parameter_values">
<variable name="O2M" units="mL_per_minute" initial_value="164" private_interface="none" public_interface="out"/> <!-- basic O2 utilization in nonmuscle tissues -->
</component>
<!-- ============================================================ GROUPING =============================================================== -->
<group>
<relationship_ref relationship="containment"/>
<component_ref component="non_muscle_O2_delivery">
<component_ref component="NM_O2_blood_supply"/>
<component_ref component="NM_venous_O2_content"/>
<component_ref component="O2_consumption_by_NM_tissue"/>
<component_ref component="delivery_of_O2_to_NM_tissues"/>
<component_ref component="volume_of_O2_in_NM_tissue"/>
<component_ref component="pressure_of_O2_in_NM_tissue_cells"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="non_muscle_O2_delivery">
<component_ref component="parameter_values"/>
<component_ref component="NM_O2_blood_supply"/>
<component_ref component="NM_venous_O2_content"/>
<component_ref component="O2_consumption_by_NM_tissue"/>
<component_ref component="delivery_of_O2_to_NM_tissues"/>
<component_ref component="volume_of_O2_in_NM_tissue"/>
<component_ref component="pressure_of_O2_in_NM_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="#non_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:#$4SdBX3"/>
</RDF:Description>
<RDF:Description xmlns:NS1="http://www.cellml.org/metadata/simulation/1.0#" RDF:about="rdf:#$SQv43" NS1:endingValue="10" NS1:nonstandard-pointDensity="1000"/>
<RDF:Description RDF:about="#non_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>
