<?xml version="1.0" encoding="utf-8"?>
<model
name="non_muscle_autoregulatory_local_blood_flow_control_CellML1_0_model"
cmeta:id="non_muscle_autoregulatory_local_blood_flow_control_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_autoregulatory_local_blood_flow_control</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 circulatory system is divided into three separate parts for blood flow control:(1) the kidneys which are presented in an entirely
separate CellML model; (2) non-muscle local blood flow control; and (3) muscle local blood flow control. This particular CellML model
describes non-muscle autoregulatory local blood flow control. This portion of the circulation has three separate parallel autoregulatory
processes, one of which occurs in a matter of minutes, another over a period of tens of minutes, and a third over a period of weeks.
All of these are considered to respond to changes in tissue oxygen level. The first two are rapid metabolic feedback effects, one almost
instantaneous and the other occurring over a period of tens of minutes to an hour or so. The third is considered to be structural changes
that result over a period of weeks and may be a consequence of the vasodilation or vasoconstriction that occurs during the two short-term
metabolic stages.
</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_autoregulatory_local_blood_flow_control_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="nm_blood_flow.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_autoregulatory_local_blood_flow_control_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 Blood Flow</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 local blood flow control 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 blood flow</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_L_per_mmHg">
<unit units="litre" prefix="milli"/>
<unit units="litre" exponent="-1"/>
<unit units="mmHg" exponent="-1"/>
</units>
<units name="mL_per_L_per_minute">
<unit units="litre" prefix="milli"/>
<unit units="litre" exponent="-1"/>
<unit units="minute" exponent="-1"/>
</units>
<units name="mL_per_minute_per_mmHg">
<unit units="litre" prefix="milli"/>
<unit units="minute" exponent="-1"/>
<unit units="mmHg" exponent="-1"/>
</units>
<units name="L_mL_per_minute_per_mmHg">
<unit units="litre"/>
<unit units="litre" prefix="milli"/>
<unit units="minute" exponent="-1"/>
<unit units="mmHg" exponent="-1"/>
</units>
<units name="L_per_mL">
<unit units="litre" prefix="milli" exponent="-1"/>
<unit units="litre"/>
</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_autoregulatory_local_blood_flow_control_CellML1_0_model">
<rdf:value>
The circulatory system is divided into three separate parts for blood flow control:
(1) the kidneys which are presented in an entirely separate section of this model;
(2) non-muscle local blood flow control; and (3) muscle local blood flow control.
Non-muscle Autoregulatory Local Blood Flow Control
This portion of the circulation has three separate parallel autoregulatory processes,
one of which occurs in a matter of minutes, another over a period of tens of minutes,
and a third over a period of weeks. All of these are considered to respond to changes
in tissue oxygen level. The first two are rapid metabolic feedback effects, one almost
instantaneous and the other occurring over a period of tens of minutes to an hour or so.
The third is considered to be structural changes that result over a period of weeks and
may be a consequence of the vasodilation or vasoconstriction that occurs during the two
short-term metabolic stages.
</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 AUTOREGULATORY LOCAL BLOOD FLOW CONTROL TOP-LEVEL COMPONENT ============================================= -->
<component name="non_muscle_autoregulatory_local_blood_flow_control"
cmeta:id="non_muscle_autoregulatory_local_blood_flow_control">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#non_muscle_autoregulatory_local_blood_flow_control">
<rdf:value>
Encapsulation grouping component containing all the components in the Non-Muscle Autoregulatory Local Blood
Flow Control Model. The inputs and outputs of the Non-Muscle Autoregulatory Local Blood Flow Control 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="POT" initial_value="35.1148" units="mmHg" private_interface="out" public_interface="none"/>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="non_muscle_autoregulatory_local_blood_flow_control" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- ======================================== AUTOREGULATORY DRIVING FORCE ============================================= -->
<component name="NM_autoregulatory_driving_force"
cmeta:id="NM_autoregulatory_driving_force">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#NM_autoregulatory_driving_force">
<rdf:value>
ARN1:
The driving force that causes an autoregulatory response in non-muscle
tissues (POD) is equal to the pressure of the oxygen in tissues (POT) minus
the set-point for the autoregulatory response (POR).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ARN1">
<rdf:value>
ARN1:
The driving force that causes an autoregulatory response in non-muscle
tissues (POD) is equal to the pressure of the oxygen in tissues (POT) minus
the set-point for the autoregulatory response (POR).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="POT" units="mmHg" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="POD" units="mmHg" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="POR" units="mmHg" private_interface="none" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ARN1">
<eq/>
<ci>POD</ci>
<apply>
<minus/>
<ci>POT</ci>
<ci>POR</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="NM_autoregulatory_driving_force" component_2="non_muscle_autoregulatory_local_blood_flow_control"/>
<map_variables variable_1="POT" variable_2="POT"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="NM_autoregulatory_driving_force" component_2="parameter_values"/>
<map_variables variable_1="POR" variable_2="POR"/>
</connection>
<!-- ======================================== NON-MUSCLE SHORT-TERM AUTOREGULATION ============================================= -->
<component name="NM_short_term_autoregulation"
cmeta:id="NM_short_term_autoregulation">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#NM_short_term_autoregulation">
<rdf:value>
Containment grouping component for "ST_sensitivity_control" and
"ST_time_delay_and_damping".
</rdf:value>
</rdf:Description>
</rdf:RDF>
</component>
<!-- ======================================== NON-MUSCLE SHORT_TERM SENSITIVITY CONTROL ============================================= -->
<component name="NM_ST_sensitivity_control"
cmeta:id="NM_ST_sensitivity_control">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#NM_ST_sensitivity_control">
<rdf:value>
ARN2 and ARN3:
Sensitivity control for short-term autoregulation, with the sensitivity
controlled by the variable POK and the output of these two blocks equal
to the variable POB.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ARN2_and_ARN3">
<rdf:value>
ARN2 and ARN3:
Sensitivity control for short-term autoregulation, with the sensitivity
controlled by the variable POK and the output of these two blocks equal
to the variable POB.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="POD" units="mmHg" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="POB" units="mmHg" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="POK" units="dimensionless" private_interface="none" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ARN2_and_ARN3">
<eq/>
<ci>POB</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>POD</ci>
<ci>POK</ci>
</apply>
<cn cellml:units="mmHg">1</cn>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="NM_ST_sensitivity_control" component_2="NM_autoregulatory_driving_force"/>
<map_variables variable_1="POD" variable_2="POD"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="NM_ST_sensitivity_control" component_2="parameter_values"/>
<map_variables variable_1="POK" variable_2="POK"/>
</connection>
<!-- ======================================== NON-MUSCLE SHORT-TERM TIME-DELAY AND DAMPING ============================================= -->
<component name="NM_ST_time_delay_and_damping"
cmeta:id="NM_ST_time_delay_and_damping">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#NM_ST_time_delay_and_damping">
<rdf:value>
ARN5, ARN6, and ARN7:
An integrative time delay system which allows the output from Block ARN7 (AR1)
to approach the value POB with a time constant of (A1K).
ARN7A:
Damping of output from Block ARN7 to prevent oscillation when the iteration
interval for computer solution of the model is long.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ARN5_to_ARN7">
<rdf:value>
ARN5, ARN6, and ARN7:
An integrative time delay system which allows the output from Block ARN7 (AR1)
to approach the value POB with a time constant of (A1K).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ARN7A">
<rdf:value>
ARN7A:
Damping of output from Block ARN7 to prevent oscillation when the iteration
interval for computer solution of the model is long.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="POB" units="mmHg" 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_ST_time_delay_and_damping_AR1"
name="AR1" units="dimensionless" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="A1K" units="minute" private_interface="none" public_interface="in"/>
<!-- Internal variables -->
<variable name="AR1T" initial_value="1.02127" units="dimensionless" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ARN5_to_ARN7">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>AR1T</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>POB</ci>
<cn cellml:units="per_mmHg">1</cn>
</apply>
<ci>AR1T</ci>
</apply>
<ci>A1K</ci>
</apply>
</apply>
<apply id="ARN7A">
<eq/>
<ci>AR1</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<lt/>
<ci>AR1T</ci>
<cn cellml:units="dimensionless">0.5</cn>
</apply>
</piece>
<otherwise>
<ci>AR1T</ci>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="NM_ST_time_delay_and_damping" component_2="NM_ST_sensitivity_control"/>
<map_variables variable_1="POB" variable_2="POB"/>
</connection>
<connection>
<map_components component_1="NM_ST_time_delay_and_damping" component_2="non_muscle_autoregulatory_local_blood_flow_control"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="NM_ST_time_delay_and_damping" component_2="parameter_values"/>
<map_variables variable_1="A1K" variable_2="A1K"/>
</connection>
<!-- ======================================== NON-MUSCLE INTERMEDIATE AUTOREGULATION ============================================= -->
<component name="NM_intermediate_autoregulation"
cmeta:id="NM_intermediate_autoregulation">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#NM_intermediate_autoregulation">
<rdf:value>
Containment grouping component for "NM_I_sensitivity_control" and
"NM_I_time_delay_and_limit".
</rdf:value>
</rdf:Description>
</rdf:RDF>
</component>
<!-- ======================================== NON-MUSCLE INTERMEDIATE SENSITIVITY CONTROL ============================================= -->
<component name="NM_I_sensitivity_control"
cmeta:id="NM_I_sensitivity_control">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#NM_I_sensitivity_control">
<rdf:value>
ARN8 and ARN9:
Sensitivity control for the intermediate time autoregulation controlled by
variable (PON). The input is POD, and the output is POA.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ARN8_and_ARN9">
<rdf:value>
ARN8 and ARN9:
Sensitivity control for the intermediate time autoregulation controlled by
variable (PON). The input is POD, and the output is POA.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="POD" units="mmHg" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="POA" units="mmHg" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="PON" units="dimensionless" private_interface="none" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ARN8_and_ARN9">
<eq/>
<ci>POA</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>PON</ci>
<ci>POD</ci>
</apply>
<cn cellml:units="mmHg">1</cn>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="NM_I_sensitivity_control" component_2="NM_autoregulatory_driving_force"/>
<map_variables variable_1="POD" variable_2="POD"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="NM_I_sensitivity_control" component_2="parameter_values"/>
<map_variables variable_1="PON" variable_2="PON"/>
</connection>
<!-- ======================================== NON-MUSCLE INTERMEDIATE TIME-DELAY AND LIMIT ============================================= -->
<component name="NM_I_time_delay_and_limit"
cmeta:id="NM_I_time_delay_and_limit">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#NM_I_time_delay_and_limit">
<rdf:value>
ARN11, ARN12, and ARN13:
A time delay mechanism for the intermediate autoregulation which allows the
output of Block ARN13 (AR2) to approach (POA) with a time constant of A2K.
ARN13A:
This sets a lower limit for AR2.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ARN11_to_ARN13">
<rdf:value>
ARN11, ARN12, and ARN13:
A time delay mechanism for the intermediate autoregulation which allows the
output of Block ARN13 (AR2) to approach (POA) with a time constant of A2K.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ARN13A">
<rdf:value>
ARN13A:
This sets a lower limit for AR2.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="POA" units="mmHg" 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_I_time_delay_and_limit_AR2"
name="AR2" units="dimensionless" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="A2K" units="minute" private_interface="none" public_interface="in"/>
<!-- Internal variables -->
<variable name="AR2T" initial_value="1.01179" units="dimensionless" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ARN11_to_ARN13">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>AR2T</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>POA</ci>
<cn cellml:units="per_mmHg">1</cn>
</apply>
<ci>AR2T</ci>
</apply>
<ci>A2K</ci>
</apply>
</apply>
<apply id="ARN13A">
<eq/>
<ci>AR2</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">0.5</cn>
<apply>
<lt/>
<ci>AR2T</ci>
<cn cellml:units="dimensionless">0.5</cn>
</apply>
</piece>
<otherwise>
<ci>AR2T</ci>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="NM_I_time_delay_and_limit" component_2="NM_I_sensitivity_control"/>
<map_variables variable_1="POA" variable_2="POA"/>
</connection>
<connection>
<map_components component_1="NM_I_time_delay_and_limit" component_2="non_muscle_autoregulatory_local_blood_flow_control"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="NM_I_time_delay_and_limit" component_2="parameter_values"/>
<map_variables variable_1="A2K" variable_2="A2K"/>
</connection>
<!-- ======================================== NON-MUSCLE LONG-TERM AUTOREGULATION ============================================= -->
<component name="NM_long_term_autoregulation"
cmeta:id="NM_long_term_autoregulation">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#NM_long_term_autoregulation">
<rdf:value>
Containment grouping component for "NM_LT_sensitivity_control" and
"NM_LT_time_delay_and_limit".`
</rdf:value>
</rdf:Description>
</rdf:RDF>
</component>
<!-- ======================================== NON-MUSCLE LONG-TERM SENSITIVITY CONTROL ============================================= -->
<component name="NM_LT_sensitivity_control"
cmeta:id="NM_LT_sensitivity_control">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#NM_LT_sensitivity_control">
<rdf:value>
ARN14:
Calculation of the relationship between the driving force for overall
autoregulatory control (POD) and that for long-term autoregulatory control (POC).
The sensitivity control is variable (POZ).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ARN14">
<rdf:value>
ARN14:
Calculation of the relationship between the driving force for overall
autoregulatory control (POD) and that for long-term autoregulatory control (POC).
The sensitivity control is variable (POZ).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="POD" units="mmHg" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="POC" units="mmHg" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="POZ" units="dimensionless" private_interface="none" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ARN14">
<eq/>
<ci>POC</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>POZ</ci>
<ci>POD</ci>
</apply>
<cn cellml:units="mmHg">1</cn>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="NM_LT_sensitivity_control" component_2="NM_autoregulatory_driving_force"/>
<map_variables variable_1="POD" variable_2="POD"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="NM_LT_sensitivity_control" component_2="parameter_values"/>
<map_variables variable_1="POZ" variable_2="POZ"/>
</connection>
<!-- ======================================== NON-MUSCLE LONG-TERM TIME DELAY AND LOWER LIMIT ============================================= -->
<component name="NM_LT_time_delay_and_limit"
cmeta:id="NM_LT_time_delay_and_limit">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#NM_LT_time_delay_and_limit">
<rdf:value>
ARN15, ARN16, and ARN17:
Time delay system that allows the output of Block ARN17 (AR3) to approach POC
with a time constant equal to the variable (A3K).
ARN17A:
This sets the lower limit for AR3.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ARN15_to_ARN17">
<rdf:value>
ARN15, ARN16, and ARN17:
Time delay system that allows the output of Block ARN17 (AR3) to approach POC
with a time constant equal to the variable (A3K).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ARN17A">
<rdf:value>
ARN17A:
This sets the lower limit for AR3.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="POC" units="mmHg" 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_LT_time_delay_and_limit_AR3"
name="AR3" units="dimensionless" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="A3K" units="minute" private_interface="none" public_interface="in"/>
<!-- Internal variables -->
<variable name="AR3T" initial_value="1.1448" units="dimensionless" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ARN15_to_ARN17">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>AR3T</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>POC</ci>
<cn cellml:units="per_mmHg">1</cn>
</apply>
<ci>AR3T</ci>
</apply>
<ci>A3K</ci>
</apply>
</apply>
<apply id="ARN17A">
<eq/>
<ci>AR3</ci>
<piecewise>
<piece>
<cn cellml:units="dimensionless">0.3</cn>
<apply>
<lt/>
<ci>AR3T</ci>
<cn cellml:units="dimensionless">0.3</cn>
</apply>
</piece>
<otherwise>
<ci>AR3T</ci>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="NM_LT_time_delay_and_limit" component_2="NM_LT_sensitivity_control"/>
<map_variables variable_1="POC" variable_2="POC"/>
</connection>
<connection>
<map_components component_1="NM_LT_time_delay_and_limit" component_2="non_muscle_autoregulatory_local_blood_flow_control"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="NM_LT_time_delay_and_limit" component_2="parameter_values"/>
<map_variables variable_1="A3K" variable_2="A3K"/>
</connection>
<!-- ======================================== TOTAL NON-MUSCLE AUTOREGULATION ============================================= -->
<component name="total_NM_autoregulation"
cmeta:id="total_NM_autoregulation">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#total_NM_autoregulation">
<rdf:value>
ARN18:
Multiplication of the outputs of the three different autoregulation mechanisms
by multiplying AR3, AR2, and AR1 times each other, giving a total output of the
non-muscle autoregulatory system equal to the variable (ARM1).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ARN18">
<rdf:value>
ARN18:
Multiplication of the outputs of the three different autoregulation mechanisms
by multiplying AR3, AR2, and AR1 times each other, giving a total output of the
non-muscle autoregulatory system equal to the variable (ARM1).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="AR1" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="AR2" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="AR3" units="dimensionless" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="ARM1" units="dimensionless" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ARN18">
<eq/>
<ci>ARM1</ci>
<apply>
<times/>
<ci>AR1</ci>
<ci>AR2</ci>
<ci>AR3</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="total_NM_autoregulation" component_2="NM_ST_time_delay_and_damping"/>
<map_variables variable_1="AR1" variable_2="AR1"/>
</connection>
<connection>
<map_components component_1="total_NM_autoregulation" component_2="NM_I_time_delay_and_limit"/>
<map_variables variable_1="AR2" variable_2="AR2"/>
</connection>
<connection>
<map_components component_1="total_NM_autoregulation" component_2="NM_LT_time_delay_and_limit"/>
<map_variables variable_1="AR3" variable_2="AR3"/>
</connection>
<!-- ======================================== GLOBAL NON-MUSCLE BLOOD FLOW AUTOREGULATION OUTPUT ============================================= -->
<component name="global_NM_blood_flow_autoregulation_output"
cmeta:id="global_NM_blood_flow_autoregulation_output">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#global_NM_blood_flow_autoregulation_output">
<rdf:value>
ARN19, ARN20, and ARN21:
Sensitivity control for the total autoregulatory output for non-muscle, non-renal
tissues. The input is ARM1, the sensitivity control is AUTOSN, and the final output
is a non-muscle autoregulatory multiplier factor (ARM) that controls non-muscle vascular
resistance.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#ARN19_to_ARN21">
<rdf:value>
ARN19, ARN20, and ARN21:
Sensitivity control for the total autoregulatory output for non-muscle, non-renal
tissues. The input is ARM1, the sensitivity control is AUTOSN, and the final output
is a non-muscle autoregulatory multiplier factor (ARM) that controls non-muscle vascular
resistance.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="ARM1" units="dimensionless" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable cmeta:id="global_NM_blood_flow_autoregulation_output_ARM"
name="ARM" units="dimensionless" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="AUTOSN" units="dimensionless" private_interface="none" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="ARN19_to_ARN21">
<eq/>
<ci>ARM</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>ARM1</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>AUTOSN</ci>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="global_NM_blood_flow_autoregulation_output" component_2="total_NM_autoregulation"/>
<map_variables variable_1="ARM1" variable_2="ARM1"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="global_NM_blood_flow_autoregulation_output" component_2="parameter_values"/>
<map_variables variable_1="AUTOSN" variable_2="AUTOSN"/>
</connection>
<!-- ========================================================== PARAMETER VALUES ================================================================ -->
<component name="parameter_values"
cmeta:id="parameter_values">
<variable name="POR" units="mmHg" initial_value="35" private_interface="none" public_interface="out"/> <!-- reference value of capillary PO2 in non-muscle tissue [P] -->
<variable name="POK" units="dimensionless" initial_value="0.1" private_interface="none" public_interface="out"/> <!-- sensitivity control, rapid nonmuscle autoregulation [P] -->
<variable name="A1K" units="minute" initial_value="0.5" private_interface="none" public_interface="out"/> <!-- time constant, rapid nonmuscle autoregulation [P] -->
<variable name="PON" units="dimensionless" initial_value="0.1" private_interface="none" public_interface="out"/> <!-- sensitivity control, intermediate nonmuscle autoregulation [P] -->
<variable name="A2K" units="minute" initial_value="60" private_interface="none" public_interface="out"/> <!-- time constant, intermediate nonmuscle autoregulation [P] -->
<variable name="A3K" units="minute" initial_value="40000" private_interface="none" public_interface="out"/> <!-- time constant, long-term nonmuscle autoregulation [P] -->
<variable name="POZ" units="dimensionless" initial_value="2" private_interface="none" public_interface="out"/> <!-- sensitivity control, long-term nonmuscle autoregulation [P] -->
<variable name="AUTOSN" units="dimensionless" initial_value="0.9" private_interface="none" public_interface="out"/> <!-- overall sensitivity controller, nonmuscle autoreg. [P] -->
</component>
<!-- ============================================================ GROUPING =============================================================== -->
<group>
<relationship_ref relationship="containment"/>
<component_ref component="non_muscle_autoregulatory_local_blood_flow_control">
<component_ref component="NM_autoregulatory_driving_force"/>
<component_ref component="NM_short_term_autoregulation">
<component_ref component="NM_ST_sensitivity_control"/>
<component_ref component="NM_ST_time_delay_and_damping"/>
</component_ref>
<component_ref component="NM_intermediate_autoregulation">
<component_ref component="NM_I_sensitivity_control"/>
<component_ref component="NM_I_time_delay_and_limit"/>
</component_ref>
<component_ref component="NM_long_term_autoregulation">
<component_ref component="NM_LT_sensitivity_control"/>
<component_ref component="NM_LT_time_delay_and_limit"/>
</component_ref>
<component_ref component="total_NM_autoregulation"/>
<component_ref component="global_NM_blood_flow_autoregulation_output"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="non_muscle_autoregulatory_local_blood_flow_control">
<component_ref component="parameter_values"/>
<component_ref component="NM_autoregulatory_driving_force"/>
<component_ref component="NM_short_term_autoregulation"/>
<component_ref component="NM_ST_sensitivity_control"/>
<component_ref component="NM_ST_time_delay_and_damping"/>
<component_ref component="NM_intermediate_autoregulation"/>
<component_ref component="NM_I_sensitivity_control"/>
<component_ref component="NM_I_time_delay_and_limit"/>
<component_ref component="NM_long_term_autoregulation"/>
<component_ref component="NM_LT_sensitivity_control"/>
<component_ref component="NM_LT_time_delay_and_limit"/>
<component_ref component="total_NM_autoregulation"/>
<component_ref component="global_NM_blood_flow_autoregulation_output"/>
</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_autoregulatory_local_blood_flow_control_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="200000" NS1:nonstandard-pointDensity="100000"/>
<RDF:Description RDF:about="#non_muscle_autoregulatory_local_blood_flow_control_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>
