Rendering of the source text

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<model 
	name="stress_relaxation_CellML1_0_model"
	cmeta:id="stress_relaxation_CellML1_0_model"
	
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<!-- ========================================	DOCUMENTATION	============================================= -->

<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Guyton Model: stress_relaxation</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 affect 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>
This particular CellML model describes the effect of stress relaxation on basic venous volume (V0).  This model calculates the effect over 
a period of time caused by excess volume (or too little volume) in the venous tree to cause changes in the volume holding capacity of the 
venous tree when it is fully filled with blood but at zero pressure.  In this model, there are two separate parallel stress relaxations of 
the veins.  One of these has a short time constant (SRK) and the other has a long time constant (SRK2).
</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="stress_relaxation_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>model diagram</title>
    </objectinfo>
    <imagedata fileref="stress.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&amp;cmd=Retrieve&amp;dopt=AbstractPlus&amp;list_uids=4334846&amp;query_hl=1&amp;itool=pubmed_docsum">PubMed ID: 4334846</ulink>
</para>

</sect1>
</article>
</documentation> 

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								<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person" />
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					<dc:title>Description of Guyton stress relaxation module</dc:title>
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      <unit units="mole" prefix="milli"/>
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      <unit units="mole" prefix="milli"/>
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      <unit units="litre"/>
      <unit units="minute" exponent="-1"/>
      <unit units="mmHg" exponent="-1"/>
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<!-- ============================================================================================================ -->

	
	<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
		<rdf:Description rdf:about="#stress_relaxation_CellML1_0_model">
			<rdf:value>
			Effect of Stress Relaxation on Basic Venous Volume (V0)
			This section calculates the effect over a period of time caused by excess volume 
			(or too little volume) in the venous tree to cause changes in the volume holding 
			capacity of the venous tree when it is fully filled with blood but at zero pressure.  
			In this model, there are two separate parallel stress relaxations of the veins.  
			One of these has a short time constant (SRK) and the other has a long time constant (SRK2).
			</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>

<!-- ========================================	STRESS RELAXATION TOP-LEVEL COMPONENT	============================================= -->
	<component 	name="stress_relaxation" 
				cmeta:id="stress_relaxation">
		<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
			<rdf:Description rdf:about="#stress_relaxation">
				<rdf:value>
				Encapsulation grouping component containing all the components in the Stress Relaxation Model. The inputs and 
				outputs of the Stress Relaxation 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="VVE"	initial_value="0.743224"	units="litre" private_interface="out" public_interface="none"/>
	</component>

<!-- INPUT CONNECTIONS -->
	<connection>
		<map_components component_1="stress_relaxation" component_2="environment"/>
		<map_variables variable_1="time" variable_2="time"/>
	</connection>

<!-- ========================================	SHORT-TERM STRESS RELAXATION	============================================= -->
	<component 	name="short_term_stress_relaxation" 
				cmeta:id="short_term_stress_relaxation">
		<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
			<rdf:Description rdf:about="#short_term_stress_relaxation">
				<rdf:value>
				SR1 and SR2:  
				Calculation of the ultimate degree of change in basic venous volume to 
				be caused by the short-term stress relaxation factor with input to the 
				system equal to the instantaneous excess venous volume (VVE); a multiplier 
				factor controls the degree of stress relaxation that will occur (SR).

				SR3, SR4, and SR5:  
				This is a delay circuit having a short time constant (SRK).  The output of 
				this circuit (VV7) approaches the ultimate degree of stress relaxation 
				caused by short-term stress relaxation as calculated from Block SR2.
				NB - REMOVED THE DAMPING FROM THE INTEGRAL!!!
				</rdf:value>
			</rdf:Description>
			<rdf:Description rdf:about="#SR1_to_SR5">
				<rdf:value>
				SR1 and SR2:  
				Calculation of the ultimate degree of change in basic venous volume to 
				be caused by the short-term stress relaxation factor with input to the 
				system equal to the instantaneous excess venous volume (VVE); a multiplier 
				factor controls the degree of stress relaxation that will occur (SR).

				SR3, SR4, and SR5:  
				This is a delay circuit having a short time constant (SRK).  The output of 
				this circuit (VV7) approaches the ultimate degree of stress relaxation 
				caused by short-term stress relaxation as calculated from Block SR2.
				NB - REMOVED THE DAMPING FROM THE INTEGRAL!!!
				</rdf:value>
			</rdf:Description>
		</rdf:RDF>
		
<!-- Inputs from other components -->
		<variable name="VVE"	units="litre" private_interface="none" public_interface="in"/>
		<variable name="time"	units="minute"	private_interface="none" public_interface="in"/>

<!-- Outputs to other components -->
		<variable	cmeta:id="short_term_stress_relaxation_VV7"
					name="VV7" 	initial_value="0.00366525"	units="litre" private_interface="none" public_interface="out"/>

<!-- Parameters from parameter_file -->
		<variable name="SR"		units="dimensionless" private_interface="none" public_interface="in"/>
		<variable name="SRK"	units="minute" private_interface="none" public_interface="in"/>

		<math xmlns="http://www.w3.org/1998/Math/MathML">
			<apply id="SR1_to_SR5">
				<eq/>
				<apply>
					<diff/>
					<bvar>
						<ci>time</ci>
					</bvar>
					<ci>VV7</ci>
				</apply>
				<apply>
					<divide/>
					<apply>
						<minus/>
						<apply>
							<times/>
							<apply>
								<minus/>
								<ci>VVE</ci>
								<cn cellml:units="litre">0.74</cn>
							</apply>
							<ci>SR</ci>
						</apply>
						<ci>VV7</ci>
					</apply>
					<ci>SRK</ci>
				</apply>
			</apply>
		</math>
	</component>

<!-- INPUT CONNECTIONS -->
	<connection>
		<map_components component_1="short_term_stress_relaxation" component_2="stress_relaxation"/>
		<map_variables variable_1="VVE" variable_2="VVE"/>
		<map_variables variable_1="time" variable_2="time"/>
	</connection>

<!-- PARAMETER CONNECTIONS -->
	<connection>
		<map_components component_1="short_term_stress_relaxation" component_2="parameter_values"/>
		<map_variables variable_1="SR" variable_2="SR"/>
		<map_variables variable_1="SRK" variable_2="SRK"/>
	</connection>

<!-- ========================================	LONG-TERM STRESS RELAXATION	============================================= -->
	<component 	name="long_term_stress_relaxation" 
				cmeta:id="long_term_stress_relaxation">
		<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
			<rdf:Description rdf:about="#long_term_stress_relaxation">
				<rdf:value>
				SR1A, SR2A, SR3A, AR4A, and SR5A:  
				Similar calculations to the above but this time with a long time constant 
				for stress relaxation (SRK2), and also having a separate variable for control 
				of the ultimate degree of the stress relaxation (SR2).  The output of this 
				long time constant stress relaxation (VV6) along with the output from the 
				short time constant stress relaxation (VV7) are subtracted from the actual 
				venous volume (VVS) in Block CD15 in the hemodynamic section of the model.
				</rdf:value>
			</rdf:Description>
			<rdf:Description rdf:about="#SR1A_to_SR5A">
				<rdf:value>
				SR1A, SR2A, SR3A, AR4A, and SR5A:  
				Similar calculations to the above but this time with a long time constant 
				for stress relaxation (SRK2), and also having a separate variable for control 
				of the ultimate degree of the stress relaxation (SR2).  The output of this 
				long time constant stress relaxation (VV6) along with the output from the 
				short time constant stress relaxation (VV7) are subtracted from the actual 
				venous volume (VVS) in Block CD15 in the hemodynamic section of the model.
				</rdf:value>
			</rdf:Description>
		</rdf:RDF>
		
<!-- Inputs from other components -->
		<variable name="VVE"	units="litre" private_interface="none" public_interface="in"/>
		<variable name="time"	units="minute" private_interface="none" public_interface="in"/>

<!-- Outputs to other components -->
		<variable 	cmeta:id="long_term_stress_relaxation_VV6"
					name="VV6" 	initial_value="0.0101913"	units="litre" private_interface="none" public_interface="out"/>

<!-- Parameters from parameter_file -->
		<variable name="SR2"	units="dimensionless" private_interface="none" public_interface="in"/>
		<variable name="SRK2"	units="minute" private_interface="none" public_interface="in"/>

		<math xmlns="http://www.w3.org/1998/Math/MathML">
			<apply id="SR1A_to_SR5A">
				<eq/>
				<apply>
					<diff/>
					<bvar>
						<ci>time</ci>
					</bvar>
					<ci>VV6</ci>
				</apply>
				<apply>
					<divide/>
					<apply>
						<minus/>
						<apply>
							<times/>
							<apply>
								<minus/>
								<ci>VVE</ci>
								<cn cellml:units="litre">0.74</cn>
							</apply>
							<ci>SR2</ci>
						</apply>
						<ci>VV6</ci>
					</apply>
					<ci>SRK2</ci>
				</apply>
			</apply>
		</math>
	</component>

<!-- INPUT CONNECTIONS -->
	<connection>
		<map_components component_1="long_term_stress_relaxation" component_2="stress_relaxation"/>
		<map_variables variable_1="VVE" variable_2="VVE"/>
		<map_variables variable_1="time" variable_2="time"/>
	</connection>

<!-- PARAMETER CONNECTIONS -->
	<connection>
		<map_components component_1="long_term_stress_relaxation" component_2="parameter_values"/>
		<map_variables variable_1="SR2" variable_2="SR2"/>
		<map_variables variable_1="SRK2" variable_2="SRK2"/>
	</connection>

<!-- ==========================================================	PARAMETER VALUES	================================================================ -->
	<component 	name="parameter_values"
				cmeta:id="parameter_values">
		<variable name="SR" 		units="dimensionless" 	initial_value="1"			private_interface="none"	public_interface="out"/>	<!-- sensitivity controller, short-term stress relaxation [P] -->
		<variable name="SR2" 		units="dimensionless" 	initial_value="1"			private_interface="none"	public_interface="out"/>	<!-- sensitivity controller, long-term stress relaxation [P] -->
		<variable name="SRK" 		units="minute" 	initial_value="5"			private_interface="none"	public_interface="out"/>	<!-- short time constant for stress relaxation [P] -->
		<variable name="SRK2" 		units="minute" 	initial_value="10000"		private_interface="none"	public_interface="out"/>	<!-- long time constant for stress relaxation [P] -->
	</component>
	
<!-- ============================================================		GROUPING		=============================================================== -->

	<group>
		<relationship_ref relationship="containment"/>
		<component_ref component="stress_relaxation">
			<component_ref component="short_term_stress_relaxation"/>
			<component_ref component="long_term_stress_relaxation"/>
		</component_ref>
	</group>

	
	<group>
		<relationship_ref relationship="encapsulation"/>
		<component_ref component="stress_relaxation">
			<component_ref component="parameter_values"/>
			<component_ref component="short_term_stress_relaxation"/>
			<component_ref component="long_term_stress_relaxation"/>
		</component_ref>
	</group>


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