- Author:
- jonna <devnull@localhost>
- Date:
- 2009-07-16 14:53:59+12:00
- Desc:
- Added General Files. Changed links of dependencies so can open from web-browser. Added RDF metadata for citation and keywords, removed publication link from documentation.
- Permanent Source URI:
- https://models.cellml.org/workspace/guyton_capillary_dynamics_2008/rawfile/5cd018cc55bbd6d2141555788ee59b7914b58f50/guyton_capillary_dynamics_2008.cellml
<?xml version="1.0" encoding="utf-8"?>
<model
name="capillary_dynamics_CellML1_0_model"
cmeta:id="capillary_dynamics_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: Capillary Dynamics</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>
This particular CellML model describes the the movement of fluid and protein through the capillary membrane. It also calculates the volumes of
fluid in the free fluid space of the interstitium and in the gel fluid space. It calculates the pressures in both of these fluids as well as
the so-called solid tissue pressure caused by the compression of solid elements against other portions of the interstitium. In addition, the
quantities of proteins and their concentrations in both the free fluid and the gel fluid are calculated. And, finally, the flow of both fluid
and proteins in the lymph system are computed, as well as the overall body protein balance.
</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="capillary_dynamics_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="capillary_dynamics.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="#capillary_dynamics_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>Capillary Dynamics</vCard:Family>
<vCard:Given></vCard:Given>
<vCard:Other></vCard:Other>
</vCard:N>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title>Description of Guyton capillary dynamics 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>capillary dynamics</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="mmHg_L">
<unit units="mmHg"/>
<unit units="litre"/>
</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="gram_per_L">
<unit units="gram"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="L_mmHg_per_gram">
<unit units="litre"/>
<unit units="mmHg"/>
<unit units="gram" exponent="-1"/>
</units>
<units name="L2_mmHg_per_gram2">
<unit units="litre" exponent="2"/>
<unit units="mmHg"/>
<unit units="gram" exponent="-2"/>
</units>
<units name="mmHg_minute_per_L">
<unit units="minute"/>
<unit units="mmHg"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="gram_per_minute">
<unit units="gram"/>
<unit units="minute" exponent="-1"/>
</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="#capillary_dynamics_CellML1_0_model">
<rdf:value>
CAPILLARY DYNAMICS, TISSUE FLUID, AND TISSUE PROTEIN
This portion of the model calculates the movement of fluid and protein through the
capillary membrane. It also calculates the volumes of fluid in the free fluid space
of the interstitium and in the gel fluid space. It calculates the pressures in both
of these fluids as well as the so-called solid tissue pressure caused by the compression
of solid elements against other portions of the interstitium. In addition, the quantities
of proteins and their concentrations in both the free fluid and the gel fluid are calculated.
And, finally, the flow of both fluid and proteins in the lymph system are computed, as well
as the overall body protein balance.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- ======================================== ENVIRONMENT COMPONENT ============================================= -->
<component name="environment">
<variable name="time" units="minute" private_interface="none" public_interface="out"/>
</component>
<!-- ======================================== CAPILLARY DYNAMICS TOP-LEVEL COMPONENT ============================================= -->
<component name="capillary_dynamics"
cmeta:id="capillary_dynamics">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#capillary_dynamics">
<rdf:value>
Encapsulation grouping component containing all the components in the Capillary Dynamics Model. The inputs and
outputs of the Capillary Dynamics Model must be passed by this component.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<variable cmeta:id="environment_time"
name="time" units="minute" private_interface="out" public_interface="in"/>
<!-- Inputs from components in other models -->
<variable name="VEC" initial_value="14.8548" units="litre" private_interface="out" public_interface="none"/>
<variable name="PPD" initial_value="4.4805e-06" units="gram_per_minute" private_interface="out" public_interface="none"/>
<variable name="RVS" initial_value="2.77751" units="mmHg_minute_per_L" private_interface="out" public_interface="none"/>
<variable name="DFP" initial_value="-4.078e-07" units="L_per_minute" private_interface="out" public_interface="none"/>
<variable name="VPF" initial_value="0.0123238" units="litre" private_interface="out" public_interface="none"/>
<variable name="BFN" initial_value="2.79521" units="L_per_minute" private_interface="out" public_interface="none"/>
<variable name="PVS" initial_value="3.71612" units="mmHg" private_interface="out" public_interface="none"/>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="capillary_dynamics" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- ======================================== CAPILLARY MEMBRANE DYNAMICS ============================================= -->
<component name="capillary_membrane_dynamics"
cmeta:id="capillary_membrane_dynamics">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#capillary_membrane_dynamics">
<rdf:value>
Containment grouping component for "capillary_pressure" and
"rate_of_fluid_out_of_capillaries".
</rdf:value>
</rdf:Description>
</rdf:RDF>
</component>
<!-- ======================================== CAPILLARY PRESSURE ============================================= -->
<component name="capillary_pressure"
cmeta:id="capillary_pressure">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#capillary_pressure">
<rdf:value>
CP1 and CP2:
The capillary pressure (PC) is equal to the resistance to blood flow in the
small veins (RVS) times the blood flow in the small veins (BFN), times a constant
to represent the additional normal flow through the muscles and kidneys, plus
the pressure in the large vein circulation. The value of the capillary pressure (PC)
is assumed to be the same in all tissues of the body.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP1_and_CP2">
<rdf:value>
CP1 and CP2:
The capillary pressure (PC) is equal to the resistance to blood flow in the
small veins (RVS) times the blood flow in the small veins (BFN), times a constant
to represent the additional normal flow through the muscles and kidneys, plus
the pressure in the large vein circulation. The value of the capillary pressure (PC)
is assumed to be the same in all tissues of the body.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="RVS" units="mmHg_minute_per_L" private_interface="none" public_interface="in"/>
<variable name="BFN" units="L_per_minute" private_interface="none" public_interface="in"/>
<variable name="PVS" units="mmHg" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable cmeta:id="capillary_pressure_PC"
name="PC" units="mmHg" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP1_and_CP2">
<eq/>
<ci>PC</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>RVS</ci>
<cn cellml:units="dimensionless">1.7</cn>
<ci>BFN</ci>
</apply>
<ci>PVS</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="capillary_pressure" component_2="capillary_dynamics"/>
<map_variables variable_1="RVS" variable_2="RVS"/>
<map_variables variable_1="BFN" variable_2="BFN"/>
<map_variables variable_1="PVS" variable_2="PVS"/>
</connection>
<!-- ======================================== RATE OF FLUID OUT OF CAPILLARIES ============================================= -->
<component name="rate_of_fluid_out_of_capillaries"
cmeta:id="rate_of_fluid_out_of_capillaries">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#rate_of_fluid_out_of_capillaries">
<rdf:value>
CP3:
The pressure gradient for filtration of fluid across the capillary membranes (PCGR)
is equal to the capillary pressure (PC), plus the colloid osmotic pressure of the
tissue gel (PTC), minus the plasma colloid osmotic pressure (PPC), minus the hydrostatic
pressure of the gel (PGH).
CP4:
The rate of filtration of fluid out of the capillaries of the systemic circulation (CFILTR)
is equal to the pressure gradient across the capillary membranes (PCGR) times the capillary
filtration coefficient (CFC).
CP5:
The total rate of movement of fluid out of all the systemic capillaries of the body (VTC) is
equal to the rate of filtration from the systemic capillaries (CFILTR) plus the rate of
leakage of whole plasma though leaky capillaries (VTCPL).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP3_to_CP5">
<rdf:value>
CP3:
The pressure gradient for filtration of fluid across the capillary membranes (PCGR)
is equal to the capillary pressure (PC), plus the colloid osmotic pressure of the
tissue gel (PTC), minus the plasma colloid osmotic pressure (PPC), minus the hydrostatic
pressure of the gel (PGH).
CP4:
The rate of filtration of fluid out of the capillaries of the systemic circulation (CFILTR)
is equal to the pressure gradient across the capillary membranes (PCGR) times the capillary
filtration coefficient (CFC).
CP5:
The total rate of movement of fluid out of all the systemic capillaries of the body (VTC) is
equal to the rate of filtration from the systemic capillaries (CFILTR) plus the rate of
leakage of whole plasma though leaky capillaries (VTCPL).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="PC" units="mmHg" private_interface="none" public_interface="in"/>
<variable name="PGH" units="mmHg" private_interface="none" public_interface="in"/>
<variable name="PTC" units="mmHg" private_interface="none" public_interface="in"/>
<variable name="PPC" units="mmHg" private_interface="none" public_interface="in"/>
<variable name="VTCPL" units="L_per_minute" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="VTC" units="L_per_minute" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="CFC" units="L_per_minute_per_mmHg" private_interface="none" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP3_to_CP5">
<eq/>
<ci>VTC</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>PC</ci>
<ci>PPC</ci>
</apply>
<ci>PGH</ci>
</apply>
<ci>PTC</ci>
</apply>
<ci>CFC</ci>
</apply>
<ci>VTCPL</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="rate_of_fluid_out_of_capillaries" component_2="capillary_pressure"/>
<map_variables variable_1="PC" variable_2="PC"/>
</connection>
<connection>
<map_components component_1="rate_of_fluid_out_of_capillaries" component_2="hydrostatic_pressure_of_tissue_gel"/>
<map_variables variable_1="PGH" variable_2="PGH"/>
</connection>
<connection>
<map_components component_1="rate_of_fluid_out_of_capillaries" component_2="total_osmotic_pressure_of_tissue_gel"/>
<map_variables variable_1="PTC" variable_2="PTC"/>
</connection>
<connection>
<map_components component_1="rate_of_fluid_out_of_capillaries" component_2="plasma_colloid_osmotic_pressure"/>
<map_variables variable_1="PPC" variable_2="PPC"/>
</connection>
<connection>
<map_components component_1="rate_of_fluid_out_of_capillaries" component_2="plasma_leakage"/>
<map_variables variable_1="VTCPL" variable_2="VTCPL"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="rate_of_fluid_out_of_capillaries" component_2="parameter_values"/>
<map_variables variable_1="CFC" variable_2="CFC"/>
</connection>
<!-- ======================================== PLASMA VOLUME AND PROTEIN ============================================= -->
<component name="plasma_volume_and_protein"
cmeta:id="plasma_volume_and_protein">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#plasma_volume_and_protein">
<rdf:value>
Containment grouping component for "plasma_volume", "plasma_protein_concentration",
"protein_destruction_and_formation", "plasma_leakage", "protein_influx_into_interstitium",
"total_plasma_protein" and "plasma_colloid_osmotic_pressure".
</rdf:value>
</rdf:Description>
</rdf:RDF>
</component>
<!-- ======================================== PLASMA VOLUME ============================================= -->
<component name="plasma_volume"
cmeta:id="plasma_volume">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#plasma_volume">
<rdf:value>
CP10:
The rate of change of plasma volume (VPD) is equal to the rate of inflow of
fluid into the plasma by way of the lymph (VTL) minus the rate of loss of
fluid from the systemic tissue capillaries (VTC), minus the rate of loss of
fluid from the pulmonary capillaries (DFP), and plus any rate of transfusion
of plasma into the circulation.
CP11:
The plasma volume (VP) is determined by integrating the rate of change of the
plasma volume (VPD) with respect to time.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP10">
<rdf:value>
CP10:
The rate of change of plasma volume (VPD) is equal to the rate of inflow of
fluid into the plasma by way of the lymph (VTL) minus the rate of loss of
fluid from the systemic tissue capillaries (VTC), minus the rate of loss of
fluid from the pulmonary capillaries (DFP), and plus any rate of transfusion
of plasma into the circulation.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP11">
<rdf:value>
CP11:
The plasma volume (VP) is determined by integrating the rate of change of the
plasma volume (VPD) with respect to time.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="DFP" units="L_per_minute" private_interface="none" public_interface="in"/>
<variable name="VTC" units="L_per_minute" private_interface="none" public_interface="in"/>
<variable name="VTL" units="L_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="plasma_volume_VP"
name="VP" initial_value="3.00449" units="litre" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="TRPL" units="L_per_minute" private_interface="none" public_interface="in"/>
<!-- Internal variables -->
<variable name="VPD" units="L_per_minute" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP10">
<eq/>
<ci>VPD</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>VTL</ci>
<ci>VTC</ci>
</apply>
<ci>DFP</ci>
</apply>
<ci>TRPL</ci>
</apply>
</apply>
<apply id="CP11">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>VP</ci>
</apply>
<ci>VPD</ci>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="plasma_volume" component_2="capillary_dynamics"/>
<map_variables variable_1="DFP" variable_2="DFP"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="plasma_volume" component_2="rate_of_fluid_out_of_capillaries"/>
<map_variables variable_1="VTC" variable_2="VTC"/>
</connection>
<connection>
<map_components component_1="plasma_volume" component_2="lymph_flow"/>
<map_variables variable_1="VTL" variable_2="VTL"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="plasma_volume" component_2="parameter_values"/>
<map_variables variable_1="TRPL" variable_2="TRPL"/>
</connection>
<!-- ======================================== PLASMA PROTEIN CONCENTRATION ============================================= -->
<component name="plasma_protein_concentration"
cmeta:id="plasma_protein_concentration">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#plasma_protein_concentration">
<rdf:value>
CP35:
The concentration of protein in the plasma (CPP) is equal to the total quantity
of protein in the plasma (RPR) divided by the plasma volume (VP).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP35">
<rdf:value>
CP35:
The concentration of protein in the plasma (CPP) is equal to the total quantity
of protein in the plasma (RPR) divided by the plasma volume (VP).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="PRP" units="gram" private_interface="none" public_interface="in"/>
<variable name="VP" units="litre" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable cmeta:id="plasma_protein_concentration_CPP"
name="CPP" units="gram_per_L" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP35">
<eq/>
<ci>CPP</ci>
<apply>
<divide/>
<ci>PRP</ci>
<ci>VP</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="plasma_protein_concentration" component_2="total_plasma_protein"/>
<map_variables variable_1="PRP" variable_2="PRP"/>
</connection>
<connection>
<map_components component_1="plasma_protein_concentration" component_2="plasma_volume"/>
<map_variables variable_1="VP" variable_2="VP"/>
</connection>
<!-- ======================================== PROTEIN DESTRUCTION AND FORMATION ============================================= -->
<component name="protein_destruction_and_formation"
cmeta:id="protein_destruction_and_formation">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#protein_destruction_and_formation">
<rdf:value>
CP37 and CP38:
A factor related to the rate of destruction of protein by the liver (CPPD) is
equal to plasma protein concentration CPP) minus a critical protein limiting value (CPR).
Block CP38 limits the rate of destruction of protein by the liver to a lower limit of zero.
CP39 and CP40:
Curve-fitting blocks to calculate the rate of destruction of protein by the
liver (LPPRDS) from the factor (CPPD) calculated in Block 37. The curve-fitting
constants are LPDE and LPK.
CP41:
Net rate of protein exchange between the liver and the plasma (DLP) is equal to the
rate of production of protein by the liver (LPPR) minus the rate of destruction of
protein by the liver (LPPRDS).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP37_and_CP38">
<rdf:value>
CP37 and CP38:
A factor related to the rate of destruction of protein by the liver (CPPD) is
equal to plasma protein concentration CPP) minus a critical protein limiting value (CPR).
Block CP38 limits the rate of destruction of protein by the liver to a lower limit of zero.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP39_to_CP41">
<rdf:value>
CP39 and CP40:
Curve-fitting blocks to calculate the rate of destruction of protein by the
liver (LPPRDS) from the factor (CPPD) calculated in Block 37. The curve-fitting
constants are LPDE and LPK.
CP41:
Net rate of protein exchange between the liver and the plasma (DLP) is equal to the
rate of production of protein by the liver (LPPR) minus the rate of destruction of
protein by the liver (LPPRDS).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="CPP" units="gram_per_L" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="DLP" units="gram_per_minute" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="CPR" units="gram_per_L" private_interface="none" public_interface="in"/>
<variable name="LPPR" units="gram_per_minute" private_interface="none" public_interface="in"/>
<variable name="LPDE" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="LPK" units="L_per_minute" private_interface="none" public_interface="in"/>
<!-- Internal variables -->
<variable name="CPPD" units="gram_per_L" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP37_and_CP38">
<eq/>
<ci>CPPD</ci>
<piecewise>
<piece>
<cn cellml:units="gram_per_L">0</cn>
<apply>
<lt/>
<apply>
<minus/>
<ci>CPP</ci>
<ci>CPR</ci>
</apply>
<cn cellml:units="gram_per_L">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<minus/>
<ci>CPP</ci>
<ci>CPR</ci>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="CP39_to_CP41">
<eq/>
<ci>DLP</ci>
<apply>
<minus/>
<ci>LPPR</ci>
<apply>
<times/>
<apply>
<power/>
<ci>CPPD</ci>
<ci>LPDE</ci>
</apply>
<ci>LPK</ci>
</apply>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="protein_destruction_and_formation" component_2="plasma_protein_concentration"/>
<map_variables variable_1="CPP" variable_2="CPP"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="protein_destruction_and_formation" component_2="parameter_values"/>
<map_variables variable_1="CPR" variable_2="CPR"/>
<map_variables variable_1="LPPR" variable_2="LPPR"/>
<map_variables variable_1="LPDE" variable_2="LPDE"/>
<map_variables variable_1="LPK" variable_2="LPK"/>
</connection>
<!-- ======================================== PLASMA LEAKAGE ============================================= -->
<component name="plasma_leakage"
cmeta:id="plasma_leakage">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#plasma_leakage">
<rdf:value>
CP25 and CP26:
Calculation of a pressure gradient to cause whole plasma leakage through the
capillary membranes (PRCD), calculated by adding the capillary pressure (PC) and
subtracting a critical capillary pressure (PCR) below which no whole plasma will leak.
Block CP26 limits the rate of plasma leakage (PRCD) to a lower level of zero.
CP27 and CP28:
The rate of leakage of whole plasma through the capillary membrane (VTCPL) is equal
to the pressure gradient for leakage of plasma (PRCD) times a constant (CPK) and this
product raised to a power (PCE).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP25_and_CP26">
<rdf:value>
CP25 and CP26:
Calculation of a pressure gradient to cause whole plasma leakage through the
capillary membranes (PRCD), calculated by adding the capillary pressure (PC) and
subtracting a critical capillary pressure (PCR) below which no whole plasma will leak.
Block CP26 limits the rate of plasma leakage (PRCD) to a lower level of zero.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP27_and_CP28">
<rdf:value>
CP27 and CP28:
The rate of leakage of whole plasma through the capillary membrane (VTCPL) is equal
to the pressure gradient for leakage of plasma (PRCD) times a constant (CPK) and this
product raised to a power (PCE).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="PC" units="mmHg" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="VTCPL" units="L_per_minute" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="PCR" units="mmHg" private_interface="none" public_interface="in"/>
<variable name="CPK" units="L_per_minute_per_mmHg" private_interface="none" public_interface="in"/>
<variable name="PCE" units="dimensionless" private_interface="none" public_interface="in"/>
<!-- Internal variables -->
<variable name="PRCD" units="mmHg" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP25_and_CP26">
<eq/>
<ci>PRCD</ci>
<piecewise>
<piece>
<cn cellml:units="mmHg">0</cn>
<apply>
<lt/>
<apply>
<minus/>
<ci>PC</ci>
<ci>PCR</ci>
</apply>
<cn cellml:units="mmHg">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<minus/>
<ci>PC</ci>
<ci>PCR</ci>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="CP27_and_CP28">
<eq/>
<ci>VTCPL</ci>
<apply>
<power/>
<apply>
<times/>
<ci>PRCD</ci>
<ci>CPK</ci>
</apply>
<ci>PCE</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="plasma_leakage" component_2="capillary_pressure"/>
<map_variables variable_1="PC" variable_2="PC"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="plasma_leakage" component_2="parameter_values"/>
<map_variables variable_1="PCR" variable_2="PCR"/>
<map_variables variable_1="CPK" variable_2="CPK"/>
<map_variables variable_1="PCE" variable_2="PCE"/>
</connection>
<!-- ======================================== PROTEIN INFLUX INTO INTERSTITIUM ============================================= -->
<component name="protein_influx_into_interstitium"
cmeta:id="protein_influx_into_interstitium">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#protein_influx_into_interstitium">
<rdf:value>
CP29:
Rate of leakage of plasma protein in the leaking whole plasma into the interstitium
from the circulating plasma (TVCPL) equals the volume of plasma leaking (VTCPL)
times the concentration of protein in the plasma (CPP).
CP30 and CP31:
The rate of diffusion of protein through the capillary pores (PLPRDF) is equal
to the difference between plasma concentration of protein (CPP) minus the concentration
of protein in the interstitial free fluid (CPI) times a constant in Block CP31.
CP32:
Rate of influx of protein into the interstitium from the plasma in the capillaries (DPC)
is equal to the rate of protein leaking in the whole plasma (VTCPL) plus the rate of
diffusion of protein through the capillary pores (PLPRDF).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP29_to_CP32">
<rdf:value>
CP29:
Rate of leakage of plasma protein in the leaking whole plasma into the interstitium
from the circulating plasma (TVCPL) equals the volume of plasma leaking (VTCPL)
times the concentration of protein in the plasma (CPP).
CP30 and CP31:
The rate of diffusion of protein through the capillary pores (PLPRDF) is equal
to the difference between plasma concentration of protein (CPP) minus the concentration
of protein in the interstitial free fluid (CPI) times a constant in Block CP31.
CP32:
Rate of influx of protein into the interstitium from the plasma in the capillaries (DPC)
is equal to the rate of protein leaking in the whole plasma (VTCPL) plus the rate of
diffusion of protein through the capillary pores (PLPRDF).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="VTCPL" units="L_per_minute" private_interface="none" public_interface="in"/>
<variable name="CPP" units="gram_per_L" private_interface="none" public_interface="in"/>
<variable name="CPI" units="gram_per_L" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="DPC" units="gram_per_minute" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP29_to_CP32">
<eq/>
<ci>DPC</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>VTCPL</ci>
<ci>CPP</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>CPP</ci>
<ci>CPI</ci>
</apply>
<cn cellml:units="L_per_minute">0.00104</cn>
</apply>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="protein_influx_into_interstitium" component_2="plasma_leakage"/>
<map_variables variable_1="VTCPL" variable_2="VTCPL"/>
</connection>
<connection>
<map_components component_1="protein_influx_into_interstitium" component_2="plasma_protein_concentration"/>
<map_variables variable_1="CPP" variable_2="CPP"/>
</connection>
<connection>
<map_components component_1="protein_influx_into_interstitium" component_2="interstitial_protein_concentration"/>
<map_variables variable_1="CPI" variable_2="CPI"/>
</connection>
<!-- ======================================== TOTAL PLASMA PROTEIN ============================================= -->
<component name="total_plasma_protein"
cmeta:id="total_plasma_protein">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#total_plasma_protein">
<rdf:value>
CP33: The rate of change of the quantity of protein in the plasma (DPP)
is equal to the net rate of formation of protein by the liver (DLP), plus
the rate of return of protein to the circulation in the lymph (DPL), minus
the loss of protein from the circulation into the systemic interstitium (DPC),
minus the rate of loss of protein through the pulmonary capillary membranes (PPD).
CP34:
The total quantity of protein in the plasma (PRP) is determined by integrating
the rate of change of the protein in the plasma (DPP) with respect to time.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP33">
<rdf:value>
CP33: The rate of change of the quantity of protein in the plasma (DPP)
is equal to the net rate of formation of protein by the liver (DLP), plus
the rate of return of protein to the circulation in the lymph (DPL), minus
the loss of protein from the circulation into the systemic interstitium (DPC),
minus the rate of loss of protein through the pulmonary capillary membranes (PPD).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP34">
<rdf:value>
CP34:
The total quantity of protein in the plasma (PRP) is determined by integrating
the rate of change of the protein in the plasma (DPP) with respect to time.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="DPC" units="gram_per_minute" private_interface="none" public_interface="in"/>
<variable name="PPD" units="gram_per_minute" private_interface="none" public_interface="in"/>
<variable name="DPL" units="gram_per_minute" private_interface="none" public_interface="in"/>
<variable name="DLP" units="gram_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="PRP" initial_value="216.243" units="gram" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="TRPL" units="L_per_minute" private_interface="none" public_interface="in"/>
<!-- Internal variables -->
<variable name="DPP" units="gram_per_minute" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP33">
<eq/>
<ci>DPP</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>DLP</ci>
<ci>DPL</ci>
</apply>
<ci>DPC</ci>
</apply>
<ci>PPD</ci>
</apply>
<apply>
<times/>
<ci>TRPL</ci>
<cn cellml:units="gram_per_L">72</cn>
</apply>
</apply>
</apply>
<apply id="CP34">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>PRP</ci>
</apply>
<ci>DPP</ci>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="total_plasma_protein" component_2="protein_influx_into_interstitium"/>
<map_variables variable_1="DPC" variable_2="DPC"/>
</connection>
<connection>
<map_components component_1="total_plasma_protein" component_2="lymph_protein_flow"/>
<map_variables variable_1="DPL" variable_2="DPL"/>
</connection>
<connection>
<map_components component_1="total_plasma_protein" component_2="protein_destruction_and_formation"/>
<map_variables variable_1="DLP" variable_2="DLP"/>
</connection>
<connection>
<map_components component_1="total_plasma_protein" component_2="capillary_dynamics"/>
<map_variables variable_1="PPD" variable_2="PPD"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="total_plasma_protein" component_2="parameter_values"/>
<map_variables variable_1="TRPL" variable_2="TRPL"/>
</connection>
<!-- ======================================== PLASMA COLLOID OSMOTIC PRESSURE ============================================= -->
<component name="plasma_colloid_osmotic_pressure"
cmeta:id="plasma_colloid_osmotic_pressure">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#plasma_colloid_osmotic_pressure">
<rdf:value>
CP36:
The plasma colloid osmotic pressure (PPC) is calculated in this block from
the concentration of protein in the plasma (CPP).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP36">
<rdf:value>
CP36:
The plasma colloid osmotic pressure (PPC) is calculated in this block from
the concentration of protein in the plasma (CPP).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="CPP" units="gram_per_L" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable cmeta:id="plasma_colloid_osmotic_pressure_PPC"
name="PPC" units="mmHg" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP36">
<eq/>
<ci>PPC</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="L_mmHg_per_gram">0.28</cn>
<ci>CPP</ci>
</apply>
<apply>
<times/>
<cn cellml:units="L2_mmHg_per_gram2">0.0019</cn>
<apply>
<power/>
<ci>CPP</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="plasma_colloid_osmotic_pressure" component_2="plasma_protein_concentration"/>
<map_variables variable_1="CPP" variable_2="CPP"/>
</connection>
<!-- ======================================== SYSTEMIC TISSUE FLUID VOLUME AND PROTEIN ============================================= -->
<component name="systemic_tissue_fluid_volume_and_protein"
cmeta:id="systemic_tissue_fluid_volume_and_protein">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#systemic_tissue_fluid_volume_and_protein">
<rdf:value>
Containment grouping component for "total_systemic_fluid_volume",
"interstitial_fluid_volume", "total_interstitial_protein",
"interstitial_protein_concentration", "interstitial_colloid_osmotic_pressure"
and "lymph_protein_flow".
</rdf:value>
</rdf:Description>
</rdf:RDF>
</component>
<!-- ======================================== TOTAL SYSTEMIC FLUID VOLUME ============================================= -->
<component name="total_systemic_fluid_volume"
cmeta:id="total_systemic_fluid_volume">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#total_systemic_fluid_volume">
<rdf:value>
CP6:
The total fluid volume in the systemic circulation portion of the body (VTS)
is equal to the total extracellular fluid volume (VEC) minus plasma volume (VP)
and minus pulmonary extracellular fluid volume (VPF).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP6">
<rdf:value>
CP6:
The total fluid volume in the systemic circulation portion of the body (VTS)
is equal to the total extracellular fluid volume (VEC) minus plasma volume (VP)
and minus pulmonary extracellular fluid volume (VPF).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="VEC" units="litre" private_interface="none" public_interface="in"/>
<variable name="VP" units="litre" private_interface="none" public_interface="in"/>
<variable name="VPF" units="litre" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="VTS" units="litre" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP6">
<eq/>
<ci>VTS</ci>
<apply>
<minus/>
<apply>
<minus/>
<ci>VEC</ci>
<ci>VP</ci>
</apply>
<ci>VPF</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="total_systemic_fluid_volume" component_2="capillary_dynamics"/>
<map_variables variable_1="VEC" variable_2="VEC"/>
<map_variables variable_1="VPF" variable_2="VPF"/>
</connection>
<connection>
<map_components component_1="total_systemic_fluid_volume" component_2="plasma_volume"/>
<map_variables variable_1="VP" variable_2="VP"/>
</connection>
<!-- ======================================== INTERSTITIAL FLUID VOLUME ============================================= -->
<component name="interstitial_fluid_volume"
cmeta:id="interstitial_fluid_volume">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#interstitial_fluid_volume">
<rdf:value>
CP7, CP7A, CP7B, CP7C, CP7D, and CP7E:
Calculation of the effect of tissue space stress relaxation on volume of fluid
in the interstitial space (VTS1) after higher or lower than normal volumes
(VTS greater or lower than 12) have existed in the tissue spaces for prolonged
periods of time. The sensitivity control for the extent of tissue space stress
relaxation is TSSLML, and the reciprocal of the time constant of the effect
is TSSLTC.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP7_to_CP7D">
<rdf:value>
CP7, CP7A, CP7B, CP7C, CP7D, and CP7E:
Calculation of the effect of tissue space stress relaxation on volume of fluid
in the interstitial space (VTS1) after higher or lower than normal volumes
(VTS greater or lower than 12) have existed in the tissue spaces for prolonged
periods of time. The sensitivity control for the extent of tissue space stress
relaxation is TSSLML, and the reciprocal of the time constant of the effect
is TSSLTC.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP7E">
<rdf:value>
CP7, CP7A, CP7B, CP7C, CP7D, and CP7E:
Calculation of the effect of tissue space stress relaxation on volume of fluid
in the interstitial space (VTS1) after higher or lower than normal volumes
(VTS greater or lower than 12) have existed in the tissue spaces for prolonged
periods of time. The sensitivity control for the extent of tissue space stress
relaxation is TSSLML, and the reciprocal of the time constant of the effect
is TSSLTC.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="VTS" units="litre" private_interface="none" public_interface="in"/>
<variable name="time" units="minute" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="VTS1" units="litre" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="TSSLML" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="TSSLTC" units="per_minute" private_interface="none" public_interface="in"/>
<!-- Internal variables -->
<variable name="VTS2" initial_value="0.0" units="litre" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP7_to_CP7D">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>VTS2</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci>VTS</ci>
<cn cellml:units="litre">12</cn>
</apply>
<ci>TSSLML</ci>
</apply>
<ci>VTS2</ci>
</apply>
<ci>TSSLTC</ci>
</apply>
</apply>
<apply id="CP7E">
<eq/>
<ci>VTS1</ci>
<apply>
<minus/>
<ci>VTS</ci>
<ci>VTS2</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="interstitial_fluid_volume" component_2="total_systemic_fluid_volume"/>
<map_variables variable_1="VTS" variable_2="VTS"/>
</connection>
<connection>
<map_components component_1="interstitial_fluid_volume" component_2="capillary_dynamics"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="interstitial_fluid_volume" component_2="parameter_values"/>
<map_variables variable_1="TSSLML" variable_2="TSSLML"/>
<map_variables variable_1="TSSLTC" variable_2="TSSLTC"/>
</connection>
<!-- ======================================== TOTAL INTERSTITIAL PROTEIN ============================================= -->
<component name="total_interstitial_protein"
cmeta:id="total_interstitial_protein">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#total_interstitial_protein">
<rdf:value>
CP42:
The rate of change of protein in the systemic interstitium (DPI) is equal to
the rate of leakage from the plasma of protein through the systemic capillary
membranes (DPC) minus the rate of return of the protein from the systemic
interstitium by way of the lymphatics (DPL).
CP43:
The total tissue protein (TSP) is calculated by integrating the rate of
change of protein in the interstitium (DPI) with respect to time.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP42">
<rdf:value>
CP42:
The rate of change of protein in the systemic interstitium (DPI) is equal to
the rate of leakage from the plasma of protein through the systemic capillary
membranes (DPC) minus the rate of return of the protein from the systemic
interstitium by way of the lymphatics (DPL).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP43">
<rdf:value>
CP43:
The total tissue protein (TSP) is calculated by integrating the rate of
change of protein in the interstitium (DPI) with respect to time.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="DPC" units="gram_per_minute" private_interface="none" public_interface="in"/>
<variable name="DPL" units="gram_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="TSP" initial_value="279.945" units="gram" private_interface="none" public_interface="out"/>
<!-- Internal variables -->
<variable name="DPI" units="gram_per_minute" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP42">
<eq/>
<ci>DPI</ci>
<apply>
<minus/>
<ci>DPC</ci>
<ci>DPL</ci>
</apply>
</apply>
<apply id="CP43">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>TSP</ci>
</apply>
<ci>DPI</ci>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="total_interstitial_protein" component_2="lymph_protein_flow"/>
<map_variables variable_1="DPL" variable_2="DPL"/>
</connection>
<connection>
<map_components component_1="total_interstitial_protein" component_2="protein_influx_into_interstitium"/>
<map_variables variable_1="DPC" variable_2="DPC"/>
</connection>
<connection>
<map_components component_1="total_interstitial_protein" component_2="capillary_dynamics"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<!-- ======================================== INTERSTITIAL PROTEIN CONCENTRATION ============================================= -->
<component name="interstitial_protein_concentration"
cmeta:id="interstitial_protein_concentration">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#interstitial_protein_concentration">
<rdf:value>
CP44:
The concentration of protein in the interstitium (CPI) is equal to the total
quantity of protein in the interstitium (TSP) divided by the total volume of
fluid in the systemic interstitium (VTS).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP44">
<rdf:value>
CP44:
The concentration of protein in the interstitium (CPI) is equal to the total
quantity of protein in the interstitium (TSP) divided by the total volume of
fluid in the systemic interstitium (VTS).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="TSP" units="gram" private_interface="none" public_interface="in"/>
<variable name="VTS" units="litre" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="CPI" units="gram_per_L" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP44">
<eq/>
<ci>CPI</ci>
<apply>
<divide/>
<ci>TSP</ci>
<ci>VTS</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="interstitial_protein_concentration" component_2="total_interstitial_protein"/>
<map_variables variable_1="TSP" variable_2="TSP"/>
</connection>
<connection>
<map_components component_1="interstitial_protein_concentration" component_2="total_systemic_fluid_volume"/>
<map_variables variable_1="VTS" variable_2="VTS"/>
</connection>
<!-- ======================================== INTERSTITIAL COLLOID OSMOTIC PRESSURE ============================================= -->
<component name="interstitial_colloid_osmotic_pressure"
cmeta:id="interstitial_colloid_osmotic_pressure">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#interstitial_colloid_osmotic_pressure">
<rdf:value>
CP45:
The colloid osmotic pressure of the free fluid in the interstitium (PTCPR) is
calculated in this block from the concentration of protein in the interstitium (CPI).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP45">
<rdf:value>
CP45:
The colloid osmotic pressure of the free fluid in the interstitium (PTCPR) is
calculated in this block from the concentration of protein in the interstitium (CPI).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="CPI" units="gram_per_L" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="PTCPR" units="mmHg" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP45">
<eq/>
<ci>PTCPR</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="L_mmHg_per_gram">0.28</cn>
<ci>CPI</ci>
</apply>
<apply>
<times/>
<cn cellml:units="L2_mmHg_per_gram2">0.0019</cn>
<apply>
<power/>
<ci>CPI</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="interstitial_colloid_osmotic_pressure" component_2="interstitial_protein_concentration"/>
<map_variables variable_1="CPI" variable_2="CPI"/>
</connection>
<!-- ======================================== LYMPH PROTEIN FLOW ============================================= -->
<component name="lymph_protein_flow"
cmeta:id="lymph_protein_flow">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#lymph_protein_flow">
<rdf:value>
CP46:
The rate of return of protein to the circulation by way of the lymph (DPL) is
equal to the concentration of protein in the systemic interstitium (CPI) times
the rate of lymph flow from the interstitium (VTL).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP46">
<rdf:value>
CP46:
The rate of return of protein to the circulation by way of the lymph (DPL) is
equal to the concentration of protein in the systemic interstitium (CPI) times
the rate of lymph flow from the interstitium (VTL).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="CPI" units="gram_per_L" private_interface="none" public_interface="in"/>
<variable name="VTL" units="L_per_minute" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="DPL" units="gram_per_minute" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP46">
<eq/>
<ci>DPL</ci>
<apply>
<times/>
<ci>CPI</ci>
<ci>VTL</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="lymph_protein_flow" component_2="interstitial_protein_concentration"/>
<map_variables variable_1="CPI" variable_2="CPI"/>
</connection>
<connection>
<map_components component_1="lymph_protein_flow" component_2="lymph_flow"/>
<map_variables variable_1="VTL" variable_2="VTL"/>
</connection>
<!-- ======================================== TISSUE GEL AND FLUID, AND LYMPH FLOW ============================================= -->
<component name="tissue_gel_and_fluid_and_lymph_flow"
cmeta:id="tissue_gel_and_fluid_and_lymph_flow">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#tissue_gel_and_fluid_and_lymph_flow">
<rdf:value>
Containment grouping component for "hydrostatic_pressure_of_tissue_gel",
"total_osmotic_pressure_of_tissue_gel", "total_tissue_pressure",
"interstial_free_fluid_pressure", "interstitial_solid_tissue_pressure",
"lymph_flow", "interstitial_gel_volume" and "interstitial_free_fluid_volume".
</rdf:value>
</rdf:Description>
</rdf:RDF>
</component>
<!-- ======================================== HYDROSTATIC PRESSURE OF TISSUE GEL ============================================= -->
<component name="hydrostatic_pressure_of_tissue_gel"
cmeta:id="hydrostatic_pressure_of_tissue_gel">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#hydrostatic_pressure_of_tissue_gel">
<rdf:value>
CP13 and CP14:
Calculation of the concentration of hyaluronic acid in the interstitium (CHY)
from the total quantity of hyaluronic acid in the interstitium (HYL) and the
total volume of fluid in the interstitium (VTS). The exponent CMPTSS describes
the non-linearity of this effect.
CP15 and CP16:
Calculation of the hydrostatic pressure in the tissue gel (PGH) from the
concentration of hyaluronic acid in the interstitium (CHY) and the total
tissue pressure (PTT). (The hyaluronic acid acts as an elastic body that
expands, and, therefore, creates a negative pressure.)
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP13_and_CP14">
<rdf:value>
CP13 and CP14:
Calculation of the concentration of hyaluronic acid in the interstitium (CHY)
from the total quantity of hyaluronic acid in the interstitium (HYL) and the
total volume of fluid in the interstitium (VTS). The exponent CMPTSS describes
the non-linearity of this effect.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP15_and_CP16">
<rdf:value>
CP15 and CP16:
Calculation of the hydrostatic pressure in the tissue gel (PGH) from the
concentration of hyaluronic acid in the interstitium (CHY) and the total
tissue pressure (PTT). (The hyaluronic acid acts as an elastic body that
expands, and, therefore, creates a negative pressure.)
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="VTS" units="litre" private_interface="none" public_interface="in"/>
<variable name="PTT" units="mmHg" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="CHY" units="gram_per_L" private_interface="none" public_interface="out"/>
<variable name="PGH" units="mmHg" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="HYL" units="gram" private_interface="none" public_interface="in"/>
<variable name="CMPTSS" units="dimensionless" private_interface="none" public_interface="in"/>
<variable name="PGHF" units="L_mmHg_per_gram" private_interface="none" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP13_and_CP14">
<eq/>
<ci>CHY</ci>
<apply>
<power/>
<apply>
<divide/>
<apply>
<divide/>
<ci>HYL</ci>
<ci>VTS</ci>
</apply>
<cn cellml:units="dimensionless">5</cn>
</apply>
<ci>CMPTSS</ci>
</apply>
</apply>
<apply id="CP15_and_CP16">
<eq/>
<ci>PGH</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>CHY</ci>
<ci>PGHF</ci>
</apply>
<ci>PTT</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="hydrostatic_pressure_of_tissue_gel" component_2="total_tissue_pressure"/>
<map_variables variable_1="PTT" variable_2="PTT"/>
</connection>
<connection>
<map_components component_1="hydrostatic_pressure_of_tissue_gel" component_2="total_systemic_fluid_volume"/>
<map_variables variable_1="VTS" variable_2="VTS"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="hydrostatic_pressure_of_tissue_gel" component_2="parameter_values"/>
<map_variables variable_1="HYL" variable_2="HYL"/>
<map_variables variable_1="CMPTSS" variable_2="CMPTSS"/>
<map_variables variable_1="PGHF" variable_2="PGHF"/>
</connection>
<!-- ======================================== TOTAL OSMOTIC PRESSURE OF TISSUE GEL ============================================= -->
<component name="total_osmotic_pressure_of_tissue_gel"
cmeta:id="total_osmotic_pressure_of_tissue_gel">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#total_osmotic_pressure_of_tissue_gel">
<rdf:value>
CP17:
The osmotic pressure caused by the hyaluronic acid in the gel (POSHYL)
is equal to the concentration of hyaluronic acid in the gel (CHY) times
a constant.
CP18:
The total osmotic pressure of the tissue gel (PTC) is equal to the osmotic
pressure caused by the hyaluronic acid in the gel (POSHYL) times the colloid
osmotic pressure caused by the plasma protein in the free fluid of the
interstitium (PTCPR) times a constant (GCOPF).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP17">
<rdf:value>
CP17:
The osmotic pressure caused by the hyaluronic acid in the gel (POSHYL)
is equal to the concentration of hyaluronic acid in the gel (CHY) times
a constant.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP18">
<rdf:value>
CP18:
The total osmotic pressure of the tissue gel (PTC) is equal to the osmotic
pressure caused by the hyaluronic acid in the gel (POSHYL) times the colloid
osmotic pressure caused by the plasma protein in the free fluid of the
interstitium (PTCPR) times a constant (GCOPF).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="CHY" units="gram_per_L" private_interface="none" public_interface="in"/>
<variable name="PTCPR" units="mmHg" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="POSHYL" units="mmHg" private_interface="none" public_interface="out"/>
<variable name="PTC" units="mmHg" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="GCOPF" units="per_mmHg" private_interface="none" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP17">
<eq/>
<ci>POSHYL</ci>
<apply>
<times/>
<ci>CHY</ci>
<cn cellml:units="L_mmHg_per_gram">2</cn>
</apply>
</apply>
<apply id="CP18">
<eq/>
<ci>PTC</ci>
<apply>
<times/>
<ci>POSHYL</ci>
<ci>PTCPR</ci>
<ci>GCOPF</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="total_osmotic_pressure_of_tissue_gel" component_2="hydrostatic_pressure_of_tissue_gel"/>
<map_variables variable_1="CHY" variable_2="CHY"/>
</connection>
<connection>
<map_components component_1="total_osmotic_pressure_of_tissue_gel" component_2="interstitial_colloid_osmotic_pressure"/>
<map_variables variable_1="PTCPR" variable_2="PTCPR"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="total_osmotic_pressure_of_tissue_gel" component_2="parameter_values"/>
<map_variables variable_1="GCOPF" variable_2="GCOPF"/>
</connection>
<!-- ======================================== TOTAL TISSUE PRESSURE ============================================= -->
<component name="total_tissue_pressure"
cmeta:id="total_tissue_pressure">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#total_tissue_pressure">
<rdf:value>
CP12:
Calculation of the total tissue pressure (PTT) as a function of the total
interstitial fluid volume (VTS1).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP12">
<rdf:value>
CP12:
Calculation of the total tissue pressure (PTT) as a function of the total
interstitial fluid volume (VTS1).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="VTS1" units="litre" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="PTT" units="mmHg" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="VTSF" units="litre" private_interface="none" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP12">
<eq/>
<ci>PTT</ci>
<apply>
<times/>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<ci>VTS1</ci>
<ci>VTSF</ci>
</apply>
<ci>VTSF</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<cn cellml:units="mmHg">1</cn>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="total_tissue_pressure" component_2="interstitial_fluid_volume"/>
<map_variables variable_1="VTS1" variable_2="VTS1"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="total_tissue_pressure" component_2="parameter_values"/>
<map_variables variable_1="VTSF" variable_2="VTSF"/>
</connection>
<!-- ======================================== INTERSTITIAL FREE FLUID PRESSURE ============================================= -->
<component name="interstial_free_fluid_pressure"
cmeta:id="interstial_free_fluid_pressure">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#interstial_free_fluid_pressure">
<rdf:value>
CP19:
The pressure in the free interstitial fluid (PIF) is equal to the hydrostatic
pressure in the tissue gel (PGH) minus the colloid osmotic pressure of the
hyaluronic acid in the tissue gel (POSHYL).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP19">
<rdf:value>
CP19:
The pressure in the free interstitial fluid (PIF) is equal to the hydrostatic
pressure in the tissue gel (PGH) minus the colloid osmotic pressure of the
hyaluronic acid in the tissue gel (POSHYL).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="PGH" units="mmHg" private_interface="none" public_interface="in"/>
<variable name="POSHYL" units="mmHg" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="PIF" units="mmHg" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP19">
<eq/>
<ci>PIF</ci>
<apply>
<minus/>
<ci>PGH</ci>
<ci>POSHYL</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="interstial_free_fluid_pressure" component_2="total_osmotic_pressure_of_tissue_gel"/>
<map_variables variable_1="POSHYL" variable_2="POSHYL"/>
</connection>
<connection>
<map_components component_1="interstial_free_fluid_pressure" component_2="hydrostatic_pressure_of_tissue_gel"/>
<map_variables variable_1="PGH" variable_2="PGH"/>
</connection>
<!-- ======================================== INTERSTITIAL SOLID TISSUE PRESSURE ============================================= -->
<component name="interstitial_solid_tissue_pressure"
cmeta:id="interstitial_solid_tissue_pressure">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#interstitial_solid_tissue_pressure">
<rdf:value>
CP20:
The solid tissue pressure of the interstitium (PTS) is equal to the total
tissue pressure (PTT) minus the pressure in the free fluid of the interstitium (PIF).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP20">
<rdf:value>
CP20:
The solid tissue pressure of the interstitium (PTS) is equal to the total
tissue pressure (PTT) minus the pressure in the free fluid of the interstitium (PIF).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="PIF" units="mmHg" private_interface="none" public_interface="in"/>
<variable name="PTT" units="mmHg" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="PTS" units="mmHg" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP20">
<eq/>
<ci>PTS</ci>
<apply>
<minus/>
<ci>PTT</ci>
<ci>PIF</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="interstitial_solid_tissue_pressure" component_2="interstial_free_fluid_pressure"/>
<map_variables variable_1="PIF" variable_2="PIF"/>
</connection>
<connection>
<map_components component_1="interstitial_solid_tissue_pressure" component_2="total_tissue_pressure"/>
<map_variables variable_1="PTT" variable_2="PTT"/>
</connection>
<!-- ======================================== LYMPH FLOW ============================================= -->
<component name="lymph_flow"
cmeta:id="lymph_flow">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#lymph_flow">
<rdf:value>
CP21 and CP22:
The pressure gradient that promotes lymph flow (PLD) is equal to a constant (PLDF)
that is determined by the pumping action of the lymphatics plus the interstitial
free fluid pressure (PIF), minus the total tissue pressure (PTT). Block CP22
limits the upper level of this pressure gradient.
CP23 and CP24:
The rate of lymph flow (VTL) is equal to the pressure gradient that causes
lymph flow (PLD) times a constant representing lymphatic conductance.
Block CP24 limits the lower level of lymph flow to zero.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP21">
<rdf:value>
CP21:
The pressure gradient that promotes lymph flow (PLD) is equal to a constant (PLDF)
that is determined by the pumping action of the lymphatics plus the interstitial
free fluid pressure (PIF), minus the total tissue pressure (PTT).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP22">
<rdf:value>
CP22:
Block CP22 limits the upper level of this pressure gradient.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP23_and_CP24">
<rdf:value>
] CP23 and CP24:
The rate of lymph flow (VTL) is equal to the pressure gradient that causes
lymph flow (PLD) times a constant representing lymphatic conductance.
Block CP24 limits the lower level of lymph flow to zero.
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="PIF" units="mmHg" private_interface="none" public_interface="in"/>
<variable name="PTT" units="mmHg" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="VTL" units="L_per_minute" private_interface="none" public_interface="out"/>
<!-- Parameters from parameter_file -->
<variable name="PLDF" units="mmHg" private_interface="none" public_interface="in"/>
<!-- Internal variables -->
<variable name="PLD1" units="mmHg" private_interface="none" public_interface="none"/>
<variable name="PLD" units="mmHg" private_interface="none" public_interface="none"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP21">
<eq/>
<ci>PLD1</ci>
<apply>
<minus/>
<apply>
<plus/>
<ci>PIF</ci>
<ci>PLDF</ci>
</apply>
<ci>PTT</ci>
</apply>
</apply>
<apply id="CP22">
<eq/>
<ci>PLD</ci>
<piecewise>
<piece>
<cn cellml:units="mmHg">7</cn>
<apply>
<gt/>
<ci>PLD1</ci>
<cn cellml:units="mmHg">7</cn>
</apply>
</piece>
<otherwise>
<ci>PLD1</ci>
</otherwise>
</piecewise>
</apply>
<apply id="CP23_and_CP24">
<eq/>
<ci>VTL</ci>
<piecewise>
<piece>
<cn cellml:units="L_per_minute">0</cn>
<apply>
<lt/>
<ci>PLD</ci>
<cn cellml:units="mmHg">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci>PLD</ci>
<cn cellml:units="L_per_minute_per_mmHg">0.02</cn>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="lymph_flow" component_2="interstial_free_fluid_pressure"/>
<map_variables variable_1="PIF" variable_2="PIF"/>
</connection>
<connection>
<map_components component_1="lymph_flow" component_2="total_tissue_pressure"/>
<map_variables variable_1="PTT" variable_2="PTT"/>
</connection>
<!-- PARAMETER CONNECTIONS -->
<connection>
<map_components component_1="lymph_flow" component_2="parameter_values"/>
<map_variables variable_1="PLDF" variable_2="PLDF"/>
</connection>
<!-- ======================================== INTERSTITIAL GEL VOLUME ============================================= -->
<component name="interstitial_gel_volume"
cmeta:id="interstitial_gel_volume">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#interstitial_gel_volume">
<rdf:value>
CP8:
This block gives a function curve that relates the volume of the tissue gel (VG)
to the total interstitial fluid volume (VTS).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP8">
<rdf:value>
CP8:
This block gives a function curve that relates the volume of the tissue gel (VG)
to the total interstitial fluid volume (VTS).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="VTS" units="litre" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="VG" units="litre" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP8">
<eq/>
<ci>VG</ci>
<piecewise>
<piece>
<cn cellml:units="litre">0</cn>
<apply>
<leq/>
<ci>VTS</ci>
<cn cellml:units="litre">0</cn>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="litre">0</cn>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">11.4</cn>
<cn cellml:units="dimensionless">0</cn>
</apply>
<apply>
<minus/>
<ci>VTS</ci>
<cn cellml:units="litre">0</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">12</cn>
<cn cellml:units="dimensionless">0</cn>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<gt/>
<ci>VTS</ci>
<cn cellml:units="litre">0</cn>
</apply>
<apply>
<leq/>
<ci>VTS</ci>
<cn cellml:units="litre">12</cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="litre">11.4</cn>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">14</cn>
<cn cellml:units="dimensionless">11.4</cn>
</apply>
<apply>
<minus/>
<ci>VTS</ci>
<cn cellml:units="litre">12</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">15</cn>
<cn cellml:units="dimensionless">12</cn>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<gt/>
<ci>VTS</ci>
<cn cellml:units="litre">12</cn>
</apply>
<apply>
<leq/>
<ci>VTS</ci>
<cn cellml:units="litre">15</cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="litre">14</cn>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">16</cn>
<cn cellml:units="dimensionless">14</cn>
</apply>
<apply>
<minus/>
<ci>VTS</ci>
<cn cellml:units="litre">15</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">18</cn>
<cn cellml:units="dimensionless">15</cn>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<gt/>
<ci>VTS</ci>
<cn cellml:units="litre">15</cn>
</apply>
<apply>
<leq/>
<ci>VTS</ci>
<cn cellml:units="litre">18</cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="litre">16</cn>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">17.3</cn>
<cn cellml:units="dimensionless">16</cn>
</apply>
<apply>
<minus/>
<ci>VTS</ci>
<cn cellml:units="litre">18</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">21</cn>
<cn cellml:units="dimensionless">18</cn>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<gt/>
<ci>VTS</ci>
<cn cellml:units="litre">18</cn>
</apply>
<apply>
<leq/>
<ci>VTS</ci>
<cn cellml:units="litre">21</cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<plus/>
<cn cellml:units="litre">17.3</cn>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">18</cn>
<cn cellml:units="dimensionless">17.3</cn>
</apply>
<apply>
<minus/>
<ci>VTS</ci>
<cn cellml:units="litre">21</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">24</cn>
<cn cellml:units="dimensionless">21</cn>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<gt/>
<ci>VTS</ci>
<cn cellml:units="litre">21</cn>
</apply>
<apply>
<leq/>
<ci>VTS</ci>
<cn cellml:units="litre">24</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="litre">18</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="interstitial_gel_volume" component_2="total_systemic_fluid_volume"/>
<map_variables variable_1="VTS" variable_2="VTS"/>
</connection>
<!-- ======================================== INTERSTITIAL FREE FLUID VOLUME ============================================= -->
<component name="interstitial_free_fluid_volume"
cmeta:id="interstitial_free_fluid_volume">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#interstitial_free_fluid_volume">
<rdf:value>
CP9:
The volume of free fluid in the interstitium (VIF) is equal to the total
interstitial fluid volume (VTS) minus the volume of fluid in the tissue gel (VG).
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="#CP9">
<rdf:value>
CP9:
The volume of free fluid in the interstitium (VIF) is equal to the total
interstitial fluid volume (VTS) minus the volume of fluid in the tissue gel (VG).
</rdf:value>
</rdf:Description>
</rdf:RDF>
<!-- Inputs from other components -->
<variable name="VTS" units="litre" private_interface="none" public_interface="in"/>
<variable name="VG" units="litre" private_interface="none" public_interface="in"/>
<!-- Outputs to other components -->
<variable name="VIF" units="litre" private_interface="none" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="CP9">
<eq/>
<ci>VIF</ci>
<apply>
<minus/>
<ci>VTS</ci>
<ci>VG</ci>
</apply>
</apply>
</math>
</component>
<!-- INPUT CONNECTIONS -->
<connection>
<map_components component_1="interstitial_free_fluid_volume" component_2="total_systemic_fluid_volume"/>
<map_variables variable_1="VTS" variable_2="VTS"/>
</connection>
<connection>
<map_components component_1="interstitial_free_fluid_volume" component_2="interstitial_gel_volume"/>
<map_variables variable_1="VG" variable_2="VG"/>
</connection>
<!-- ============================================================ PARAMETER VALUES =============================================================== -->
<component name="parameter_values"
cmeta:id="parameter_values">
<variable name="CFC" units="L_per_minute_per_mmHg" initial_value="0.01167" private_interface="none" public_interface="out"/> <!-- capillary filtration coefficient [P] -->
<variable name="TRPL" units="L_per_minute" initial_value="0" private_interface="none" public_interface="out"/> <!-- transfusion coefficient [P] -->
<variable name="CPR" units="gram_per_L" initial_value="40" private_interface="none" public_interface="out"/> <!-- critical plasma protein conc for protein destruction [P] -->
<variable name="LPDE" units="dimensionless" initial_value="8" private_interface="none" public_interface="out"/> <!-- curve fitting coefficient, liver protein destruction [P] -->
<variable name="PCE" units="dimensionless" initial_value="1" private_interface="none" public_interface="out"/> <!-- curve fitting exponent, capillary leakage [P] -->
<variable name="PCR" units="mmHg" initial_value="15" private_interface="none" public_interface="out"/> <!-- critical capillary pressure for protein leakage [P] -->
<variable name="LPK" units="L_per_minute" initial_value="2.728e-14" private_interface="none" public_interface="out"/> <!-- curve fitting coefficient, liver protein destruction [P] -->
<variable name="LPPR" units="gram_per_minute" initial_value="0.03" private_interface="none" public_interface="out"/> <!-- rate of liver protein production [P] -->
<variable name="CPK" units="L_per_minute_per_mmHg" initial_value="0.000253" private_interface="none" public_interface="out"/> <!-- curve fitting exponent, , capillary leakage [P] -->
<variable name="TSSLML" units="dimensionless" initial_value="0.15" private_interface="none" public_interface="out"/> <!-- sensitivity controller of VTS [P] -->
<variable name="TSSLTC" units="per_minute" initial_value="0.005" private_interface="none" public_interface="out"/> <!-- VTS1 time constant [P] -->
<variable name="HYL" units="gram" initial_value="60" private_interface="none" public_interface="out"/> <!-- quantity of hyaluronic acid in tissues -->
<variable name="CMPTSS" units="dimensionless" initial_value="2" private_interface="none" public_interface="out"/> <!-- curve fitting exponent, calculation of CHY [P] -->
<variable name="PGHF" units="L_mmHg_per_gram" initial_value="-2" private_interface="none" public_interface="out"/> <!-- proportionality coefficent, CHY to PGH [P] -->
<variable name="GCOPF" units="per_mmHg" initial_value="0.8092" private_interface="none" public_interface="out"/> <!-- coefficient, calculation of PTC [P] -->
<variable name="VTSF" units="litre" initial_value="6" private_interface="none" public_interface="out"/> <!-- curve fitting coefficient, PTT [P] -->
<variable name="PLDF" units="mmHg" initial_value="4.2" private_interface="none" public_interface="out"/> <!-- constant pressure, computation of PLD [P] -->
</component>
<!-- ============================================================ GROUPING =============================================================== -->
<group>
<relationship_ref relationship="containment"/>
<component_ref component="capillary_dynamics">
<component_ref component="capillary_membrane_dynamics">
<component_ref component="capillary_pressure"/>
<component_ref component="rate_of_fluid_out_of_capillaries"/>
</component_ref>
<component_ref component="plasma_volume_and_protein">
<component_ref component="plasma_volume"/>
<component_ref component="plasma_protein_concentration"/>
<component_ref component="protein_destruction_and_formation"/>
<component_ref component="plasma_leakage"/>
<component_ref component="protein_influx_into_interstitium"/>
<component_ref component="total_plasma_protein"/>
<component_ref component="plasma_colloid_osmotic_pressure"/>
</component_ref>
<component_ref component="systemic_tissue_fluid_volume_and_protein">
<component_ref component="total_systemic_fluid_volume"/>
<component_ref component="interstitial_fluid_volume"/>
<component_ref component="total_interstitial_protein"/>
<component_ref component="interstitial_protein_concentration"/>
<component_ref component="interstitial_colloid_osmotic_pressure"/>
<component_ref component="lymph_protein_flow"/>
</component_ref>
<component_ref component="tissue_gel_and_fluid_and_lymph_flow">
<component_ref component="hydrostatic_pressure_of_tissue_gel"/>
<component_ref component="total_osmotic_pressure_of_tissue_gel"/>
<component_ref component="total_tissue_pressure"/>
<component_ref component="interstial_free_fluid_pressure"/>
<component_ref component="interstitial_solid_tissue_pressure"/>
<component_ref component="lymph_flow"/>
<component_ref component="interstitial_gel_volume"/>
<component_ref component="interstitial_free_fluid_volume"/>
</component_ref>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="capillary_dynamics">
<component_ref component="parameter_values"/>
<component_ref component="capillary_membrane_dynamics"/>
<component_ref component="capillary_pressure"/>
<component_ref component="rate_of_fluid_out_of_capillaries"/>
<component_ref component="plasma_volume_and_protein"/>
<component_ref component="plasma_volume"/>
<component_ref component="plasma_protein_concentration"/>
<component_ref component="protein_destruction_and_formation"/>
<component_ref component="plasma_leakage"/>
<component_ref component="protein_influx_into_interstitium"/>
<component_ref component="total_plasma_protein"/>
<component_ref component="plasma_colloid_osmotic_pressure"/>
<component_ref component="systemic_tissue_fluid_volume_and_protein"/>
<component_ref component="total_systemic_fluid_volume"/>
<component_ref component="interstitial_fluid_volume"/>
<component_ref component="total_interstitial_protein"/>
<component_ref component="interstitial_protein_concentration"/>
<component_ref component="interstitial_colloid_osmotic_pressure"/>
<component_ref component="lymph_protein_flow"/>
<component_ref component="tissue_gel_and_fluid_and_lymph_flow"/>
<component_ref component="hydrostatic_pressure_of_tissue_gel"/>
<component_ref component="total_osmotic_pressure_of_tissue_gel"/>
<component_ref component="total_tissue_pressure"/>
<component_ref component="interstial_free_fluid_pressure"/>
<component_ref component="interstitial_solid_tissue_pressure"/>
<component_ref component="lymph_flow"/>
<component_ref component="interstitial_gel_volume"/>
<component_ref component="interstitial_free_fluid_volume"/>
</component_ref>
</group>
</model>
