- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2009-11-18 12:37:53+13:00
- Desc:
- Added a third model to the workspace.
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/heldt_2002/rawfile/992273bd58b6473e1e692f76a30e79adacf39bea/lpc.cellml
<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 1/11/2009 at 11:25:38 at a.m. using:
COR (0.9.31.1329)
Copyright 2002-2009 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
-->
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<title>Computational modeling of cardiovascular response to orthostatic stress</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML model runs in both COR and PCEnv to reproduce the published results. The units have been checked and they balance. This is a lumped parameter model for cardiac activation based on the work of Heldt et al. 2002. This CellMl model represents the whole heart (all four chambers) connected to a lumped parameter model of the circulatory system including systemic circulation, a coronary circulation, and a pulmonary circulation. The model and results are exactly the same as the <ulink url="http://physiome.org/model/doku.php?id=Integrative_Physiology:Lumped_parameter_circulation:model_detail#Detailed_Description">JSim model</ulink> of the same name.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: The objective of this study is to develop a model of the cardiovascular system capable of simulating the short-term (less than or equal to 5 min) transient and steady-state hemodynamic responses to head-up tilt and lower body negative pressure. The model consists of a closed-loop lumped-parameter representation of the circulation connected to set-point models of the arterial and cardiopulmonary baroreflexes. Model parameters are largely based on literature values. Model verification was performed by comparing the simulation output under baseline conditions and at different levels of orthostatic stress to sets of population-averaged hemodynamic data reported in the literature. On the basis of experimental evidence, we adjusted some model parameters to simulate experimental data. Orthostatic stress simulations are not statistically different from experimental data (two-sided test of significance with Bonferroni adjustment for multiple comparisons). Transient response characteristics of heart rate to tilt also compare well with reported data. A case study is presented on how the model is intended to be used in the future to investigate the effects of post-spaceflight orthostatic intolerance.
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="heldt_2002b.png"/>
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<caption>Schematic diagram of the Heldt et al. 2002 circulation model.</caption>
</informalfigure>
<para>
The original paper reference is cited below:
</para>
<para>
Computational modeling of cardiovascular response to orthostatic stress, T. Heldt, E.B. Shim, R.D. Kamm, and R.G. Mark, 2002, <emphasis>Journal of Applied Physiology</emphasis>, 92, 1239-1254. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=11842064&query_hl=1&itool=pubmed_docsum">PubMed ID: 11842064</ulink>
</para>
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</article>
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This is the CellML description of Heldt et al.'s computational model of the heart. Specifically the left ventricle.
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Computational modeling of cardiovascular response to orthostatic stress
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<ci>HR</ci>
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<minus/>
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<ci>trela</ci>
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<ci>yla</ci>
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<divide/>
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<minus/>
<cn cellml:units="dimensionless">1</cn>
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<times/>
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<and/>
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<geq/>
<ci>trela</ci>
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<divide/>
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<plus/>
<cn cellml:units="dimensionless">1</cn>
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<divide/>
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<times/>
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<minus/>
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<ci>Tsa</ci>
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<and/>
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<lt/>
<ci>trela</ci>
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<times/>
<cn cellml:units="dimensionless">1.5</cn>
<ci>Tsa</ci>
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<geq/>
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<eq/>
<ci>yra</ci>
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<eq/>
<ci>ylv</ci>
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<piece>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
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<times/>
<pi/>
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<ci>Tsv</ci>
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<geq/>
<ci>trelv</ci>
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<leq/>
<ci>trelv</ci>
<ci>Tsv</ci>
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<divide/>
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<plus/>
<cn cellml:units="dimensionless">1</cn>
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<cos/>
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<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<pi/>
<apply>
<minus/>
<ci>trelv</ci>
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<ci>Tsv</ci>
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<lt/>
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<times/>
<cn cellml:units="dimensionless">1.5</cn>
<ci>Tsv</ci>
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<geq/>
<ci>trelv</ci>
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<eq/>
<ci>yrv</ci>
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<eq/>
<ci>Era</ci>
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<plus/>
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<times/>
<apply>
<minus/>
<ci>Emaxra</ci>
<ci>Eminra</ci>
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<ci>yra</ci>
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<ci>Eminra</ci>
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<eq/>
<ci>Erv</ci>
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<plus/>
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<times/>
<apply>
<minus/>
<ci>Emaxrv</ci>
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<ci>yrv</ci>
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<ci>Eminrv</ci>
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<eq/>
<ci>Ela</ci>
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<plus/>
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<times/>
<apply>
<minus/>
<ci>Emaxla</ci>
<ci>Eminla</ci>
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<ci>yla</ci>
</apply>
<ci>Eminla</ci>
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<eq/>
<ci>Elv</ci>
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<plus/>
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<times/>
<apply>
<minus/>
<ci>Emaxlv</ci>
<ci>Eminlv</ci>
</apply>
<ci>ylv</ci>
</apply>
<ci>Eminlv</ci>
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<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Faod</ci>
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<divide/>
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<minus/>
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<minus/>
<ci>Paodc</ci>
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<times/>
<ci>Faod</ci>
<ci>Raod</ci>
</apply>
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<ci>Psap</ci>
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<ci>Laod</ci>
</apply>
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<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Faop</ci>
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<times/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>Paopc</ci>
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<times/>
<ci>Faop</ci>
<ci>Raop</ci>
<cn cellml:units="dimensionless">16.66666666666667</cn>
</apply>
</apply>
<ci>Paodc</ci>
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<ci>Laop</ci>
</apply>
<cn cellml:units="dimensionless">0.059999999999999984</cn>
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<eq/>
<ci>Fcorao</ci>
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<divide/>
<apply>
<minus/>
<ci>Pcoraoc</ci>
<ci>Pcoreac</ci>
</apply>
<ci>Rcorao</ci>
</apply>
</apply>
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<eq/>
<ci>Fcorcap</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Pcorcapc</ci>
<ci>Pcorsvc</ci>
</apply>
<ci>Rcorcap</ci>
</apply>
</apply>
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<eq/>
<ci>Fcorea</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Pcoreac</ci>
<ci>Pcorlac</ci>
</apply>
<ci>Rcorea</ci>
</apply>
</apply>
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<eq/>
<ci>Fcorev</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Pcorevc</ci>
<ci>Prac</ci>
</apply>
<ci>Rcorev</ci>
</apply>
</apply>
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<eq/>
<ci>Fcorla</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Pcorlac</ci>
<ci>Pcorsac</ci>
</apply>
<ci>Rcorla</ci>
</apply>
</apply>
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<eq/>
<ci>Fcorlv</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Pcorlvc</ci>
<ci>Pcorevc</ci>
</apply>
<ci>Rcorlv</ci>
</apply>
</apply>
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<eq/>
<ci>Fcorsa</ci>
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<divide/>
<apply>
<minus/>
<ci>Pcorsac</ci>
<ci>Pcorcapc</ci>
</apply>
<ci>Rcorsa</ci>
</apply>
</apply>
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<eq/>
<ci>Fcorsv</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Pcorsvc</ci>
<ci>Pcorlvc</ci>
</apply>
<ci>Rcorsv</ci>
</apply>
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<eq/>
<ci>Fcrb</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Paodc</ci>
<ci>Pvcc</ci>
</apply>
<ci>Rcrb</ci>
</apply>
</apply>
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<eq/>
<ci>Fla</ci>
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<piece>
<apply>
<divide/>
<apply>
<minus/>
<ci>Plac</ci>
<ci>Plvc</ci>
</apply>
<ci>Rla</ci>
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<apply>
<gt/>
<ci>Plac</ci>
<ci>Plvc</ci>
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<cn cellml:units="flow">0</cn>
</otherwise>
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<eq/>
<ci>Flv</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<minus/>
<ci>Plvc</ci>
<ci>Paopc</ci>
</apply>
<ci>Rav</ci>
</apply>
<apply>
<gt/>
<ci>Plvc</ci>
<ci>Paopc</ci>
</apply>
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<cn cellml:units="flow">0</cn>
</otherwise>
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<eq/>
<ci>Fpa</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ppac</ci>
<ci>Ppcc</ci>
</apply>
<ci>Rpa</ci>
</apply>
</apply>
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<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Fpad</ci>
</apply>
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<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>Ppadc</ci>
<ci>Ppac</ci>
</apply>
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<times/>
<ci>Fpad</ci>
<ci>Rpad</ci>
</apply>
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<ci>Lpad</ci>
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<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Fpap</ci>
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<times/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>Ppapc</ci>
<ci>Ppadc</ci>
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<apply>
<times/>
<ci>Fpap</ci>
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<ci>Lpa</ci>
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<eq/>
<ci>Fpc</ci>
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<divide/>
<apply>
<minus/>
<ci>Ppcc</ci>
<ci>Ppvc</ci>
</apply>
<ci>Rpc</ci>
</apply>
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<eq/>
<ci>Fps</ci>
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<divide/>
<apply>
<minus/>
<ci>Ppac</ci>
<ci>Ppvc</ci>
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<ci>Rps</ci>
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<eq/>
<ci>Fpv</ci>
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<divide/>
<apply>
<minus/>
<ci>Ppvc</ci>
<ci>Plac</ci>
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<ci>Rpv</ci>
</apply>
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<eq/>
<ci>Fra</ci>
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<piece>
<apply>
<divide/>
<apply>
<minus/>
<ci>Prac</ci>
<ci>Prvc</ci>
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<ci>Rra</ci>
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<gt/>
<ci>Prac</ci>
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<ci>Frv</ci>
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<piece>
<apply>
<divide/>
<apply>
<minus/>
<ci>Prvc</ci>
<ci>Ppapc</ci>
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<ci>Rpuv</ci>
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<apply>
<gt/>
<ci>Prvc</ci>
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<cn cellml:units="flow">0</cn>
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<eq/>
<ci>Fsa</ci>
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<divide/>
<apply>
<minus/>
<ci>Psa</ci>
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</apply>
<ci>Rsa</ci>
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<eq/>
<ci>Fsap</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>Psap</ci>
<ci>Psa</ci>
</apply>
<ci>Rsap</ci>
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<eq/>
<ci>Fsc</ci>
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<divide/>
<apply>
<minus/>
<ci>Psc</ci>
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<ci>Rsc</ci>
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<eq/>
<ci>Fsv</ci>
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<divide/>
<apply>
<minus/>
<ci>Psv</ci>
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<ci>Rsv</ci>
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<eq/>
<ci>Fvc</ci>
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<divide/>
<apply>
<minus/>
<ci>Pvcc</ci>
<ci>Prac</ci>
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<ci>Rvc</ci>
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<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
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<ci>MAP</ci>
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<divide/>
<apply>
<minus/>
<ci>Psa</ci>
<ci>MAP</ci>
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<eq/>
<ci>P_QRSwave</ci>
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<cn cellml:units="mV">5</cn>
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<and/>
<apply>
<gt/>
<ci>t</ci>
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<lt/>
<ci>t</ci>
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<plus/>
<ci>beattime</ci>
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<cn cellml:units="mV">10</cn>
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<and/>
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<gt/>
<ci>t</ci>
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<plus/>
<ci>beattime</ci>
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<lt/>
<ci>t</ci>
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<plus/>
<ci>beattime</ci>
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<ci>Paod</ci>
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<eq/>
<ci>Paodc</ci>
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<divide/>
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<plus/>
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<plus/>
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<minus/>
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<times/>
<ci>Rtaod</ci>
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<ci>Rtaod</ci>
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<ci>Vaod</ci>
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<times/>
<ci>Rcrb</ci>
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<minus/>
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<exp/>
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<divide/>
<ci>Vaod</ci>
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<minus/>
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<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
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<ci>Paopc</ci>
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<minus/>
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<minus/>
<apply>
<minus/>
<ci>Flv</ci>
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<diff/>
<bvar>
<ci>t</ci>
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<ci>Vaop</ci>
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<divide/>
<cn cellml:units="dimensionless">1</cn>
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<divide/>
<ci>Px2</ci>
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<minus/>
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<exp/>
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<divide/>
<ci>Vcorao</ci>
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<eq/>
<ci>Pcoraoc</ci>
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<eq/>
<ci>Pcorcap</ci>
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<minus/>
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<divide/>
<ci>Vcorcap</ci>
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<divide/>
<apply>
<times/>
<ci>Px1</ci>
<cn cellml:units="dimensionless">1</cn>
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<divide/>
<ci>Vcorcap</ci>
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<cn cellml:units="dimensionless">1</cn>
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<ci>Pcorcapc</ci>
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<plus/>
<ci>Pcorcap</ci>
<ci>Pcorisfc</ci>
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<eq/>
<ci>Pcorea</ci>
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<minus/>
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<divide/>
<ci>Vcorea</ci>
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<divide/>
<apply>
<times/>
<ci>Px1</ci>
<cn cellml:units="dimensionless">1</cn>
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<divide/>
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<cn cellml:units="dimensionless">1</cn>
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<eq/>
<ci>Pcoreac</ci>
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<plus/>
<ci>Pcorea</ci>
<ci>Ppcdc</ci>
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<eq/>
<ci>Pcorev</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>Vcorev</ci>
<ci>Ccorev</ci>
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<divide/>
<apply>
<times/>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
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<minus/>
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<exp/>
<apply>
<divide/>
<ci>Vcorev</ci>
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<cn cellml:units="dimensionless">1</cn>
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<ci>Pcorevc</ci>
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<plus/>
<ci>Pcorev</ci>
<ci>Ppcdc</ci>
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<eq/>
<ci>Pcorisfc</ci>
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<abs/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Plvc</ci>
<ci>Ppcdc</ci>
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<cn cellml:units="dimensionless">2</cn>
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<eq/>
<ci>Pcorla</ci>
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<minus/>
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<divide/>
<ci>Vcorla</ci>
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<divide/>
<apply>
<times/>
<ci>Px1</ci>
<cn cellml:units="dimensionless">1</cn>
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<minus/>
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<exp/>
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<divide/>
<ci>Vcorla</ci>
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<cn cellml:units="dimensionless">1</cn>
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</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Pcorlac</ci>
<apply>
<plus/>
<ci>Pcorla</ci>
<ci>Pcorisfc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Pcorlv</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>Vcorlv</ci>
<ci>Ccorlv</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px1</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vcorlv</ci>
<ci>Vx1</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Pcorlvc</ci>
<apply>
<plus/>
<ci>Pcorlv</ci>
<ci>Ppcdc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Pcorsa</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>Vcorsa</ci>
<ci>Ccorsa</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px1</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vcorsa</ci>
<ci>Vx1</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Pcorsac</ci>
<apply>
<plus/>
<ci>Pcorsa</ci>
<ci>Pcorisfc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Pcorsv</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>Vcorsv</ci>
<ci>Ccorsv</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px1</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vcorsv</ci>
<ci>Vx1</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Pcorsvc</ci>
<apply>
<plus/>
<ci>Pcorsv</ci>
<ci>Ppcdc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Pla</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci>Vla</ci>
<ci>Vlar</ci>
</apply>
<ci>Ela</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vla</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Plac</ci>
<apply>
<plus/>
<ci>Pla</ci>
<ci>Ppcdc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Plv</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci>Vlv</ci>
<ci>Vlvr</ci>
</apply>
<ci>Elv</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vlv</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Plvc</ci>
<apply>
<plus/>
<ci>Plv</ci>
<ci>Ppcdc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppa</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>Vpa</ci>
<ci>Cpa</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vpa</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppac</ci>
<apply>
<plus/>
<ci>Ppa</ci>
<ci>Pplc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppad</ci>
<apply>
<minus/>
<ci>Ppadc</ci>
<ci>Pplc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppadc</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vpad</ci>
</apply>
<ci>Rtpad</ci>
</apply>
<ci>Pplc</ci>
<apply>
<divide/>
<ci>Vpad</ci>
<ci>Ctpad</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vpad</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppap</ci>
<apply>
<minus/>
<ci>Ppapc</ci>
<ci>Pplc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppapc1</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<times/>
<ci>Rpuv</ci>
<ci>Vpap</ci>
</apply>
<ci>Ctpap</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Rpuv</ci>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vpap</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Prvc</ci>
<ci>Rtpap</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Rpuv</ci>
<ci>Rtpap</ci>
<ci>Fpap</ci>
<cn cellml:units="dimensionless">16.666666666666668</cn>
</apply>
</apply>
<apply>
<times/>
<ci>Pplc</ci>
<ci>Rpuv</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>Rtpap</ci>
<ci>Rpuv</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppapc2</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<divide/>
<ci>Vpap</ci>
<ci>Ctpap</ci>
</apply>
<ci>Pplc</ci>
</apply>
<apply>
<times/>
<ci>Rtpap</ci>
<ci>Fpap</ci>
<cn cellml:units="dimensionless">16.666666666666668</cn>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vpap</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppapc</ci>
<piecewise>
<piece>
<ci>Ppapc1</ci>
<apply>
<gt/>
<ci>Prvc</ci>
<ci>Ppapc1</ci>
</apply>
</piece>
<otherwise>
<ci>Ppapc2</ci>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>Ppc</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>Vpc</ci>
<ci>Cpc</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vpc</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppcc</ci>
<apply>
<plus/>
<ci>Ppc</ci>
<ci>Pplc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppcd</ci>
<apply>
<minus/>
<apply>
<times/>
<ci>K_pcd</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Vpcd</ci>
<ci>Vpcd_o</ci>
</apply>
<ci>phi_pcd</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vpcd</ci>
<ci>Vx75</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppcdc</ci>
<apply>
<plus/>
<ci>Ppcd</ci>
<ci>Pplc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppl</ci>
<apply>
<minus/>
<ci>Pplc</ci>
<ci>Pbs</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppv</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>Vpv</ci>
<ci>Cpv</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vpv</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Ppvc</ci>
<apply>
<plus/>
<ci>Ppv</ci>
<ci>Pplc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Pra</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci>Vra</ci>
<ci>Vrar</ci>
</apply>
<ci>Era</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vra</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Prac</ci>
<apply>
<plus/>
<ci>Pra</ci>
<ci>Ppcdc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Prv</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci>Vrv</ci>
<ci>Vrvr</ci>
</apply>
<ci>Erv</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vrv</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Prvc</ci>
<apply>
<plus/>
<ci>Prv</ci>
<ci>Ppcdc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Psa_a</ci>
<apply>
<times/>
<ci>Kc</ci>
<apply>
<log/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Vsa</ci>
<ci>Vsa_o</ci>
</apply>
<ci>Do</ci>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Psa</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>F_vaso</ci>
<ci>Psa_a</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>F_vaso</ci>
</apply>
<ci>Psa_p</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Psa_p</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>Kp1</ci>
<apply>
<exp/>
<apply>
<times/>
<ci>tau_p</ci>
<apply>
<minus/>
<ci>Vsa</ci>
<ci>Vsa_o</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Kp2</ci>
<apply>
<power/>
<apply>
<minus/>
<ci>Vsa</ci>
<ci>Vsa_o</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Psap</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>Vsap</ci>
<ci>Csap</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vsap</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Psc</ci>
<apply>
<minus/>
<apply>
<divide/>
<ci>Vsc</ci>
<ci>Csc</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vsc</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Psv</ci>
<apply>
<times/>
<ci>Kv</ci>
<apply>
<log/>
<apply>
<minus/>
<apply>
<divide/>
<ci>Vmax_sv</ci>
<ci>Vsv</ci>
</apply>
<cn cellml:units="dimensionless">0.99</cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>PulArtVol</ci>
<apply>
<plus/>
<ci>Vpap</ci>
<ci>Vpad</ci>
<ci>Vpa</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>PulVenVol</ci>
<ci>Vpv</ci>
</apply>
<apply>
<eq/>
<ci>Pvc</ci>
<piecewise>
<piece>
<apply>
<minus/>
<apply>
<plus/>
<ci>D2</ci>
<apply>
<times/>
<ci>K2</ci>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vo</ci>
<ci>Vmin_vc</ci>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>K1</ci>
<apply>
<minus/>
<ci>Vvc</ci>
<ci>Vo</ci>
</apply>
</apply>
<cn cellml:units="capacitance">1</cn>
</apply>
</apply>
<apply>
<divide/>
<ci>Px2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vvc</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<apply>
<gt/>
<ci>Vvc</ci>
<ci>Vo</ci>
</apply>
</piece>
<otherwise>
<apply>
<minus/>
<apply>
<plus/>
<ci>D2</ci>
<apply>
<times/>
<ci>K2</ci>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vvc</ci>
<ci>Vmin_vc</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci>Px2</ci>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vvc</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>Pvcc</ci>
<apply>
<plus/>
<ci>Pvc</ci>
<ci>Pplc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Rsa</ci>
<apply>
<plus/>
<ci>Rsao</ci>
<apply>
<times/>
<ci>Kr</ci>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<ci>F_vaso</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>Kr</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Vsa_max</ci>
<ci>Vsa</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>Rvc</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>KR</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>Vmax_vc</ci>
<ci>Vvc</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<ci>Ro</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>SV</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>COutput</ci>
<ci>HR</ci>
</apply>
<cn cellml:units="dimensionless">60</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>SysArtVol</ci>
<apply>
<plus/>
<ci>Vaop</ci>
<ci>Vaod</ci>
<ci>Vsa</ci>
<ci>Vsap</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>SysVenVol</ci>
<apply>
<plus/>
<ci>Vsv</ci>
<ci>Vvc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>VBcirc</ci>
<apply>
<minus/>
<ci>Vtot</ci>
<ci>perifl</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vaod</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<apply>
<minus/>
<ci>Faop</ci>
<apply>
<times/>
<ci>Faod</ci>
<cn cellml:units="dimensionless">0.059999999999999984</cn>
</apply>
</apply>
<apply>
<times/>
<ci>Fcrb</ci>
<cn cellml:units="dimensionless">0.059999999999999984</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">16.66666666666667</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vaop</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<ci>Paopc</ci>
<apply>
<divide/>
<ci>Vaop</ci>
<ci>Caop</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Px2</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<ci>Vaop</ci>
<ci>Vx8</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
<ci>Rtaop</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vcorao</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<ci>Flv</ci>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vaop</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Faop</ci>
<cn cellml:units="dimensionless">16.66666666666667</cn>
</apply>
</apply>
<ci>Fcorao</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vcorcap</ci>
</apply>
<apply>
<minus/>
<ci>Fcorsa</ci>
<ci>Fcorcap</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Vcorcirc</ci>
<apply>
<plus/>
<ci>Vcorao</ci>
<ci>Vcorea</ci>
<ci>Vcorla</ci>
<ci>Vcorsa</ci>
<ci>Vcorcap</ci>
<ci>Vcorsv</ci>
<ci>Vcorlv</ci>
<ci>Vcorev</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vcorea</ci>
</apply>
<apply>
<minus/>
<ci>Fcorao</ci>
<ci>Fcorea</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vcorev</ci>
</apply>
<apply>
<minus/>
<ci>Fcorlv</ci>
<ci>Fcorev</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vcorla</ci>
</apply>
<apply>
<minus/>
<ci>Fcorea</ci>
<ci>Fcorla</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vcorlv</ci>
</apply>
<apply>
<minus/>
<ci>Fcorsv</ci>
<ci>Fcorlv</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vcorsa</ci>
</apply>
<apply>
<minus/>
<ci>Fcorla</ci>
<ci>Fcorsa</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vcorsv</ci>
</apply>
<apply>
<minus/>
<ci>Fcorcap</ci>
<ci>Fcorsv</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vla</ci>
</apply>
<apply>
<minus/>
<ci>Fpv</ci>
<ci>Fla</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Vlar</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>yla</ci>
</apply>
<apply>
<minus/>
<ci>Vlard</ci>
<ci>Vlars</ci>
</apply>
</apply>
<ci>Vlars</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vlv</ci>
</apply>
<apply>
<minus/>
<ci>Fla</ci>
<ci>Flv</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Vlvr</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>ylv</ci>
</apply>
<apply>
<minus/>
<ci>Vlvrd</ci>
<ci>Vlvrs</ci>
</apply>
</apply>
<ci>Vlvrs</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vpa</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<ci>Fpad</ci>
<ci>Fps</ci>
</apply>
<ci>Fpa</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vpad</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>Fpap</ci>
<apply>
<times/>
<ci>Fpad</ci>
<cn cellml:units="dimensionless">0.059999999999999984</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">16.66666666666667</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vpap</ci>
</apply>
<apply>
<minus/>
<ci>Frv</ci>
<apply>
<times/>
<ci>Fpap</ci>
<cn cellml:units="dimensionless">16.66666666666667</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vpc</ci>
</apply>
<apply>
<minus/>
<ci>Fpa</ci>
<ci>Fpc</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Vpcd</ci>
<apply>
<plus/>
<ci>Vrv</ci>
<ci>Vra</ci>
<ci>Vlv</ci>
<ci>Vla</ci>
<ci>perifl</ci>
<ci>Vmyo</ci>
<ci>Vcorcirc</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vpv</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>Fpc</ci>
<ci>Fps</ci>
</apply>
<ci>Fpv</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vra</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<ci>Fvc</ci>
<ci>Fra</ci>
</apply>
<ci>Fcorev</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Vrar</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>yra</ci>
</apply>
<apply>
<minus/>
<ci>Vrard</ci>
<ci>Vrars</ci>
</apply>
</apply>
<ci>Vrars</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vrv</ci>
</apply>
<apply>
<minus/>
<ci>Fra</ci>
<ci>Frv</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Vrvr</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>yrv</ci>
</apply>
<apply>
<minus/>
<ci>Vrvrd</ci>
<ci>Vrvrs</ci>
</apply>
</apply>
<ci>Vrvrs</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vsa</ci>
</apply>
<apply>
<minus/>
<ci>Fsap</ci>
<ci>Fsa</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vsap</ci>
</apply>
<apply>
<minus/>
<ci>Faod</ci>
<ci>Fsap</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vsc</ci>
</apply>
<apply>
<minus/>
<ci>Fsa</ci>
<ci>Fsc</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vsv</ci>
</apply>
<apply>
<minus/>
<ci>Fsc</ci>
<ci>Fsv</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Vtot</ci>
<apply>
<plus/>
<ci>Vra</ci>
<ci>Vrv</ci>
<ci>Vpap</ci>
<ci>Vpad</ci>
<ci>Vpa</ci>
<ci>Vpc</ci>
<ci>Vpv</ci>
<ci>Vla</ci>
<ci>Vlv</ci>
<ci>Vaop</ci>
<ci>Vaod</ci>
<ci>Vsa</ci>
<ci>Vsap</ci>
<ci>Vsc</ci>
<ci>Vsv</ci>
<ci>Vvc</ci>
<ci>perifl</ci>
<ci>Vcorcirc</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Vvc</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>Fsv</ci>
<ci>Fcrb</ci>
</apply>
<ci>Fvc</ci>
</apply>
</apply>
</math>
</component>
</model>
