- Author:
- Catherine Lloyd <c.lloyd@auckland.ac.nz>
- Date:
- 2010-05-06 14:37:45+12:00
- Desc:
- Updated documentation.
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/yi_fogelson_keener_peskin_2003/rawfile/47a473afd55a85e76b79221259e0df0bdf279744/yi_fogelson_keener_peskin_2003.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : yi_model_2003.xml
CREATED : 27th December 2002
LAST MODIFIED : 2nd May 2005
AUTHOR : Catherine Lloyd
The Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Yi et al's 2003 mathematical model of volume shifts and ionic concentration changes during ischemia and hypoxia.
CHANGES:
09/04/2003 - AAC - Added publication date information.
02/05/2005 - PJV - Changed unit dimensions to make them consistent.
-->
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="yi_2003" name="yi_2003">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling Volume Shifts and Ionic Concentration Changes during Ischemia and Hypoxia</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: The response of tissue to ischemia (cessation of blood flow and deprivation of oxygen) includes swelling of the intracellular space, shrinkage of the extracellular space, and an increase in the extracellular potassium concentration. The responses of cardiac and brain tissue to ischemia are qualitatively different in that cardiac tissue shows a rise in extracellular potassium over several minutes from about 5 to 10-12 mM followed by a plateau, while brain tissue shows a similar initial rise followed by a very rapid increase in extracellular potassium to levels of 50-80 mM. During hypoxia the flow of blood (or perfusate) is maintained and, while there is a substantial efflux of potassium from cells, there is little accumulation of potassium in the interstitium. A mathematical model is proposed and studied to try to elucidate the mechanism(s) underlying the increase in extracellular potassium, and the different time courses seen in neural and cardiac tissue. The model involves a Hodgkin-Huxley-type description of transmembrane ion currents, allows for ion concentrations as well as volumes to change for both the intracellular and extracellular space, and includes coupling of damaged tissue to nearby healthy tissue. The model produces a response to ischemia much like that seen in neural tissue, and the mechanism underlying this response in the model is determined. The same mechanism is not present in cardiac ion models, and this may explain the qualitative difference in response shown in cardiac tissue.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
A Mathematical Study of Volume Shifts and Ionic Concentration Changes during Ischemia and Hypoxia, Chung-Seon Yi, Aaron L. Fogelson, James P. Keener, and Charles S. Peskin, 2003, <emphasis>Theoretical Journal of Biology</emphasis>, 220, 83-106. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=12453453&dopt=Abstract">PubMed ID: 12453453</ulink>
</para>
<informalfigure float="0" id="fig_schematic_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>schematic diagram</title>
</objectinfo>
<imagedata fileref="yi_2003a.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the Yi <emphasis>et al.</emphasis> 2003 mathematical model. In the tissue damaged by ischemia or hypoxia there are three compartments: an intracellular space within a collection of homogeneous cells; the extracellular space surrounding these cells; and the capillary space serving the cells. In addition there is a fourth compartment which represents the extracellular space of the undamaged tissue. The cell membrane separates the intracellular and extracellular compartments, and the capillary wall separates the extracellular space from the capillary space.</caption>
</informalfigure>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="yi_2003b.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the ionic components of the Yi <emphasis>et al.</emphasis> 2003 mathematical model. Sodium, chloride and potassium ions are exchanged between the intracellular and extracellular environments through channels and via the sodium-potassium pump. Water is also passed between the various components.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
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<units name="micromole_per_minute">
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<unit units="millimolar"/>
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<variable units="cm3" public_interface="out" name="V_i" initial_value="3.80E-8"/>
<variable units="joule_per_mole_kelvin" public_interface="out" name="R" initial_value="8.314"/>
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<variable units="cm3_per_Pa_per_minute" public_interface="out" name="Lie_p" initial_value="1.21E12"/>
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<variable units="millivolt" name="delta_init"/>
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<variable units="micromole" name="X_i" initial_value="3.83E-6"/>
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<variable units="cm2" name="A_s" initial_value="7.67E-5"/>
<variable units="micromole" public_interface="in" name="X_e"/>
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</math>
</component>
<component name="intracellular_sodium">
<variable units="millimolar" public_interface="out" name="Na_i" initial_value="11.2"/>
<variable units="milliC_per_volt_per_minute" public_interface="out" name="g_Na"/>
<variable units="millivolt" public_interface="out" name="delta_Na"/>
<variable units="milliC_per_volt_per_minute" name="g_b_Na" initial_value="3.31E-5"/>
<variable units="milliC_per_volt_per_minute" name="g_Na_max" initial_value="3.69E-2"/>
<variable units="minute" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Na_e"/>
<variable units="micromole_per_minute" public_interface="in" name="P"/>
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<ci> Na_i </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="intracellular_sodium_m_gate">
<variable units="dimensionless" public_interface="out" name="m_infinity"/>
<variable units="first_order_rate_constant" name="A_m"/>
<variable units="first_order_rate_constant" name="B_m"/>
<variable units="millivolt" public_interface="in" name="delta"/>
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<variable units="milliC_per_volt_per_minute" public_interface="out" name="g_Cl" initial_value="2.81E-4"/>
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<variable units="minute" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Cl_e"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="delta"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Cl_i_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cl_i </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> g_Cl </ci>
<ci> F </ci>
</apply>
<apply>
<plus/>
<ci> delta </ci>
<ci> delta_Cl </ci>
</apply>
</apply>
</apply>
<apply id="delta_Cl_calculation">
<eq/>
<ci> delta_Cl </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Cl_e </ci>
<ci> Cl_i </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="extracellular_sodium">
<variable units="millimolar" public_interface="out" name="Na_e" initial_value="140.0"/>
<variable units="millivolt" public_interface="in" name="delta_Na"/>
<variable units="minute" public_interface="in" name="time"/>
<variable units="milliC_per_volt_per_minute" public_interface="in" name="g_Na"/>
<variable units="micromole_per_minute" public_interface="in" name="P"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="delta"/>
<variable units="cm3_millimolar_per_minute" public_interface="in" name="Jv_Na"/>
<variable units="cm3_millimolar_per_minute" public_interface="in" name="Jh_Na"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Na_e_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Na_e </ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<ci> g_Na </ci>
<ci> F </ci>
</apply>
<apply>
<minus/>
<ci> delta </ci>
<ci> delta_Na </ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> P </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Jv_Na </ci>
<ci> Jh_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="extracellular_potassium">
<variable units="millimolar" public_interface="out" name="K_e" initial_value="5.4"/>
<variable units="milliC_per_volt_per_minute" public_interface="in" name="g_K"/>
<variable units="millivolt" public_interface="in" name="delta_K"/>
<variable units="minute" public_interface="in" name="time"/>
<variable units="micromole_per_minute" public_interface="in" name="P"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="delta"/>
<variable units="cm3_millimolar_per_minute" public_interface="in" name="Jv_K"/>
<variable units="cm3_millimolar_per_minute" public_interface="in" name="Jh_K"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="K_e_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> K_e </ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<ci> g_K </ci>
<ci> F </ci>
</apply>
<apply>
<minus/>
<ci> delta </ci>
<ci> delta_K </ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> P </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Jv_K </ci>
<ci> Jh_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="extracellular_chloride">
<variable units="millimolar" public_interface="out" name="Cl_e" initial_value="110.0"/>
<variable units="milliC_per_volt_per_minute" public_interface="in" name="g_Cl"/>
<variable units="millivolt" public_interface="in" name="delta_Cl"/>
<variable units="minute" public_interface="in" name="time"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="delta"/>
<variable units="cm3_millimolar_per_minute" public_interface="in" name="Jv_Cl"/>
<variable units="cm3_millimolar_per_minute" public_interface="in" name="Jh_Cl"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Cl_e_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cl_e </ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<divide/>
<ci> g_Cl </ci>
<ci> F </ci>
</apply>
<apply>
<plus/>
<ci> delta </ci>
<ci> delta_Cl </ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<ci> Jv_Cl </ci>
<ci> Jh_Cl </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="extracellular_space">
<variable units="cm3" public_interface="out" name="V_e" initial_value="9.50E-9"/>
<variable units="millivolt" public_interface="out" name="delta_e"/>
<variable units="micromole" public_interface="out" name="X_e" initial_value="3.94E-9"/>
<variable units="dimensionless" name="z_e" initial_value="85.4"/>
<variable units="cm3_per_Pa_per_minute" public_interface="in" name="Lie_p"/>
<variable units="Pa" public_interface="in" name="pi_i"/>
<variable units="Pa" public_interface="in" name="pi_e"/>
<variable units="minute" public_interface="in" name="time"/>
<variable units="cm3_per_minute" public_interface="in" name="Jv_H2O"/>
<variable units="cm3_per_minute" public_interface="in" name="Jh_H2O"/>
<variable units="millimolar" public_interface="in" name="Cl_e"/>
<variable units="millimolar" public_interface="in" name="Na_e"/>
<variable units="millimolar" public_interface="in" name="K_e"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="V_e_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> V_e </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> Lie_p </ci>
<apply>
<minus/>
<ci> pi_e </ci>
<ci> pi_i </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> Jv_H2O </ci>
<ci> Jh_H2O </ci>
</apply>
</apply>
</apply>
<apply id="X_e_calculation">
<eq/>
<ci> X_e </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> V_e </ci>
<apply>
<minus/>
<apply>
<plus/>
<ci> Na_e </ci>
<ci> K_e </ci>
</apply>
<ci> Cl_e </ci>
</apply>
</apply>
<ci> z_e </ci>
</apply>
</apply>
</math>
</component>
<component name="water_flux">
<variable units="cm3_per_minute" public_interface="out" name="Jh_H2O" initial_value="0.0"/>
<variable units="cm3" name="V_infinity_e"/>
<variable units="cm3" name="V_infinity_T"/>
<variable units="minute" name="tau_1" initial_value="3.3"/>
<variable units="minute" name="tau_2" initial_value="33.0"/>
<variable units="cm3" public_interface="in" name="V_i"/>
<variable units="cm3" public_interface="in" name="V_e"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Jh_H2O_calculation">
<eq/>
<ci> Jh_H2O </ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> tau_1 </ci>
</apply>
<apply>
<minus/>
<ci> V_infinity_e </ci>
<ci> V_e </ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> tau_2 </ci>
</apply>
<apply>
<minus/>
<ci> V_infinity_T </ci>
<apply>
<plus/>
<ci> V_i </ci>
<ci> V_e </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_flux">
<variable units="cm3_millimolar_per_minute" public_interface="out" name="Jh_Na" initial_value="0.0"/>
<variable units="millimolar" name="Na_infinity_e"/>
<variable units="dimensionless" name="alpha_Na"/>
<variable units="millimolar" public_interface="in" name="Na_e"/>
<variable units="millivolt" public_interface="in" name="delta_eh"/>
<variable units="minute" public_interface="in" name="time"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="cm3_per_minute" public_interface="in" name="P_h"/>
<variable units="cm3_per_minute" public_interface="in" name="Jh_H2O"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Jh_Na_calculation">
<eq/>
<ci> Jh_Na </ci>
<apply>
<times/>
<ci> P_h </ci>
<ci> alpha_Na </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Na_infinity_e </ci>
<apply>
<times/>
<ci> Na_e </ci>
<apply>
<exp/>
<ci> alpha_Na </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<ci> alpha_Na </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_Na_calculation">
<eq/>
<ci> alpha_Na </ci>
<apply>
<minus/>
<apply>
<divide/>
<ci> Jh_H2O </ci>
<ci> P_h </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
<ci> delta_eh </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="potassium_flux">
<variable units="cm3_millimolar_per_minute" public_interface="out" name="Jh_K" initial_value="0.0"/>
<variable units="millimolar" name="K_infinity_e"/>
<variable units="dimensionless" name="alpha_K"/>
<variable units="millimolar" public_interface="in" name="K_e"/>
<variable units="millivolt" public_interface="in" name="delta_eh"/>
<variable units="minute" public_interface="in" name="time"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="cm3_per_minute" public_interface="in" name="P_h"/>
<variable units="cm3_per_minute" public_interface="in" name="Jh_H2O"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Jh_K_calculation">
<eq/>
<ci> Jh_K </ci>
<apply>
<times/>
<ci> P_h </ci>
<ci> alpha_K </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> K_infinity_e </ci>
<apply>
<times/>
<ci> K_e </ci>
<apply>
<exp/>
<ci> alpha_K </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<ci> alpha_K </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_K_calculation">
<eq/>
<ci> alpha_K </ci>
<apply>
<minus/>
<apply>
<divide/>
<ci> Jh_H2O </ci>
<ci> P_h </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
<ci> delta_eh </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="chloride_flux">
<variable units="cm3_millimolar_per_minute" public_interface="out" name="Jh_Cl" initial_value="0.0"/>
<variable units="millimolar" name="Cl_infinity_e"/>
<variable units="dimensionless" name="alpha_Cl"/>
<variable units="millimolar" public_interface="in" name="Cl_e"/>
<variable units="millivolt" public_interface="in" name="delta_eh"/>
<variable units="minute" public_interface="in" name="time"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="cm3_per_minute" public_interface="in" name="P_h"/>
<variable units="cm3_per_minute" public_interface="in" name="Jh_H2O"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Jh_Cl_calculation">
<eq/>
<ci> Jh_Cl </ci>
<apply>
<times/>
<ci> P_h </ci>
<ci> alpha_Cl </ci>
<apply>
<divide/>
<apply>
<minus/>
<ci> Cl_infinity_e </ci>
<apply>
<times/>
<ci> Cl_e </ci>
<apply>
<exp/>
<ci> alpha_Cl </ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<ci> alpha_Cl </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_Cl_calculation">
<eq/>
<ci> alpha_Cl </ci>
<apply>
<minus/>
<apply>
<divide/>
<ci> Jh_H2O </ci>
<ci> P_h </ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -1.0 </cn>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
<ci> delta_eh </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="capillary_compartment_sodium">
<variable units="millimolar" public_interface="out" name="Na_v" initial_value="136.7"/>
<variable units="millivolt" public_interface="out" name="delta_ev_Na"/>
<variable units="cm3_millimolar_per_minute" public_interface="out" name="Jv_Na" initial_value="0.0"/>
<variable units="minute" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Na_a"/>
<variable units="millimolar" public_interface="in" name="Na_e"/>
<variable units="cm3_per_minute" public_interface="in" name="Qv"/>
<variable units="cm3_per_minute" public_interface="in" name="Qa"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Na_v_calculation">
<eq/>
<ci> Na_v </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci> Qa </ci>
<ci> Na_a </ci>
</apply>
<ci> Jv_Na </ci>
</apply>
<ci> Qv </ci>
</apply>
</apply>
<apply id="delta_ev_Na_calculation">
<eq/>
<ci> delta_ev_Na </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Na_v </ci>
<ci> Na_e </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Jv_Na_calculation">
<eq/>
<ci> Jv_Na </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> Qv </ci>
<ci> Na_v </ci>
</apply>
<apply>
<times/>
<ci> Qa </ci>
<ci> Na_a </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="capillary_compartment_potassium">
<variable units="millimolar" public_interface="out" name="K_v" initial_value="5.27"/>
<variable units="millivolt" public_interface="out" name="delta_ev_K"/>
<variable units="cm3_millimolar_per_minute" public_interface="out" name="Jv_K" initial_value="0.0"/>
<variable units="minute" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="K_a"/>
<variable units="millimolar" public_interface="in" name="K_e"/>
<variable units="cm3_per_minute" public_interface="in" name="Qv"/>
<variable units="cm3_per_minute" public_interface="in" name="Qa"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="K_v_calculation">
<eq/>
<ci> K_v </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci> Qa </ci>
<ci> K_a </ci>
</apply>
<ci> Jv_K </ci>
</apply>
<ci> Qv </ci>
</apply>
</apply>
<apply id="delta_ev_K_calculation">
<eq/>
<ci> delta_ev_K </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> K_v </ci>
<ci> K_e </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Jv_K_calculation">
<eq/>
<ci> Jv_K </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> Qv </ci>
<ci> K_v </ci>
</apply>
<apply>
<times/>
<ci> Qa </ci>
<ci> K_a </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="capillary_compartment_chloride">
<variable units="millimolar" public_interface="out" name="Cl_v" initial_value="112.7"/>
<variable units="millivolt" public_interface="out" name="delta_ev_Cl"/>
<variable units="cm3_millimolar_per_minute" public_interface="out" name="Jv_Cl" initial_value="0.0"/>
<variable units="minute" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Cl_a"/>
<variable units="millimolar" public_interface="in" name="Cl_e"/>
<variable units="cm3_per_minute" public_interface="in" name="Qv"/>
<variable units="cm3_per_minute" public_interface="in" name="Qa"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Cl_v_calculation">
<eq/>
<ci> Cl_v </ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci> Qa </ci>
<ci> Cl_a </ci>
</apply>
<ci> Jv_Cl </ci>
</apply>
<ci> Qv </ci>
</apply>
</apply>
<apply id="delta_ev_Cl_calculation">
<eq/>
<ci> delta_ev_Cl </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Cl_v </ci>
<ci> Cl_e </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="Jv_Cl_calculation">
<eq/>
<ci> Jv_Cl </ci>
<apply>
<minus/>
<apply>
<times/>
<ci> Qv </ci>
<ci> Cl_v </ci>
</apply>
<apply>
<times/>
<ci> Qa </ci>
<ci> Cl_a </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="capillary_space">
<variable units="Pa" public_interface="out" name="pi_v"/>
<variable units="cm3_per_minute" public_interface="out" name="Qv" initial_value="3.6E-8"/>
<variable units="millimolar" public_interface="out" name="Pr_v" initial_value="1.45"/>
<variable units="cm3_per_minute" public_interface="out" name="Jv_H2O"/>
<variable units="dimensionless" name="z_v" initial_value="24.4"/>
<variable units="cm3_per_minute" public_interface="in" name="Qa"/>
<variable units="millimolar" public_interface="in" name="Na_v"/>
<variable units="millimolar" public_interface="in" name="K_v"/>
<variable units="millimolar" public_interface="in" name="Cl_v"/>
<variable units="Pa" public_interface="in" name="pi_e"/>
<variable units="minute" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Qv_calculation">
<eq/>
<ci> Qv </ci>
<apply>
<plus/>
<ci> Qa </ci>
<ci> Jv_H2O </ci>
</apply>
</apply>
<apply id="Jv_H2O_calculation">
<eq/>
<ci> Jv_H2O </ci>
<apply>
<minus/>
<ci> Qv </ci>
<ci> Qa </ci>
</apply>
</apply>
<apply id="pi_v_calculation">
<eq/>
<ci> pi_v </ci>
<apply>
<plus/>
<ci> Na_v </ci>
<ci> K_v </ci>
<ci> Cl_v </ci>
<ci> Pr_v </ci>
</apply>
</apply>
<apply id="Pr_v_calculation">
<eq/>
<ci> Pr_v </ci>
<apply>
<divide/>
<apply>
<plus/>
<ci> Na_v </ci>
<ci> K_v </ci>
<apply>
<minus/>
<ci> Cl_v </ci>
</apply>
</apply>
<ci> z_v </ci>
</apply>
</apply>
</math>
</component>
<component name="arterial_space">
<variable units="cm3_per_minute" public_interface="out" name="Qa" initial_value="3.6E-8"/>
<variable units="millimolar" public_interface="out" name="Na_a" initial_value="140.0"/>
<variable units="millimolar" public_interface="out" name="K_a" initial_value="5.4"/>
<variable units="millimolar" public_interface="out" name="Cl_a" initial_value="110.0"/>
<variable units="millimolar" name="Pr_a" initial_value="1.45"/>
<variable units="minute" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="Pr_v"/>
<variable units="cm3_per_minute" public_interface="in" name="Qv"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="Qa_calculation">
<eq/>
<ci> Qa </ci>
<apply>
<divide/>
<apply>
<times/>
<ci> Qv </ci>
<ci> Pr_v </ci>
</apply>
<ci> Pr_a </ci>
</apply>
</apply>
</math>
</component>
<component name="pump_rate">
<variable units="micromole_per_minute" public_interface="out" name="P"/>
<variable units="micromole_per_minute" name="P_max" initial_value="4.6E-8"/>
<variable units="millimolar" name="Km_Na_i" initial_value="10.0"/>
<variable units="millimolar" name="Km_K_e" initial_value="1.5"/>
<variable units="dimensionless" name="f_NaK"/>
<variable units="dimensionless" name="a_t"/>
<variable units="minute" public_interface="in" name="time"/>
<variable units="millimolar" public_interface="in" name="K_e"/>
<variable units="millimolar" public_interface="in" name="Na_i"/>
<variable units="millimolar" public_interface="in" name="Na_e"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="millivolt" public_interface="in" name="delta"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="P_calculation">
<eq/>
<ci> P </ci>
<apply>
<times/>
<ci> a_t </ci>
<ci> P_max </ci>
<ci> f_NaK </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<ci> Km_Na_i </ci>
<ci> Na_i </ci>
</apply>
<cn cellml:units="dimensionless"> 1.5 </cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> K_e </ci>
<apply>
<plus/>
<ci> Km_K_e </ci>
<ci> K_e </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="f_NaK_calculation">
<eq/>
<ci> f_NaK </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.1245 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.1 </cn>
<ci> delta </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0365 </cn>
<cn cellml:units="dimensionless"> 7.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.1 </cn>
<ci> delta </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<ci> Na_e </ci>
<cn cellml:units="millimolar"> 67.3 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
</apply>
<apply id="a_t_calculation">
<eq/>
<ci> a_t </ci>
<apply>
<power/>
<cn cellml:units="dimensionless"> 0.35 </cn>
<apply>
<divide/>
<ci> time </ci>
<cn cellml:units="minute"> 15.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="intracellular_sodium">
<component_ref component="intracellular_sodium_m_gate"/>
<component_ref component="intracellular_sodium_h_gate"/>
</component_ref>
<component_ref component="intracellular_potassium">
<component_ref component="intracellular_potassium_n_gate"/>
</component_ref>
</group>
<connection>
<map_components component_2="environment" component_1="intracellular_space"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_sodium"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_potassium"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="intracellular_chloride"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="extracellular_sodium"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="extracellular_potassium"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="extracellular_chloride"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="extracellular_space"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="water_flux"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="sodium_flux"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="potassium_flux"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="chloride_flux"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="capillary_compartment_sodium"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="capillary_compartment_potassium"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="capillary_compartment_chloride"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="capillary_space"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="arterial_space"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="environment" component_1="pump_rate"/>
<map_variables variable_2="time" variable_1="time"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium" component_1="intracellular_space"/>
<map_variables variable_2="Na_i" variable_1="Na_i"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="delta" variable_1="delta"/>
<map_variables variable_2="delta_eq" variable_1="delta_eq"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium" component_1="intracellular_space"/>
<map_variables variable_2="K_i" variable_1="K_i"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="delta" variable_1="delta"/>
<map_variables variable_2="delta_eq" variable_1="delta_eq"/>
</connection>
<connection>
<map_components component_2="intracellular_chloride" component_1="intracellular_space"/>
<map_variables variable_2="Cl_i" variable_1="Cl_i"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="delta" variable_1="delta"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium" component_1="intracellular_space"/>
<map_variables variable_2="Na_e" variable_1="Na_e"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="delta" variable_1="delta"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium" component_1="intracellular_space"/>
<map_variables variable_2="K_e" variable_1="K_e"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="delta" variable_1="delta"/>
</connection>
<connection>
<map_components component_2="extracellular_chloride" component_1="intracellular_space"/>
<map_variables variable_2="Cl_e" variable_1="Cl_e"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="delta" variable_1="delta"/>
</connection>
<connection>
<map_components component_2="extracellular_space" component_1="intracellular_space"/>
<map_variables variable_2="X_e" variable_1="X_e"/>
<map_variables variable_2="V_e" variable_1="V_e"/>
<map_variables variable_2="pi_e" variable_1="pi_e"/>
<map_variables variable_2="pi_i" variable_1="pi_i"/>
<map_variables variable_2="Lie_p" variable_1="Lie_p"/>
<map_variables variable_2="delta_e" variable_1="delta_e"/>
</connection>
<connection>
<map_components component_2="water_flux" component_1="intracellular_space"/>
<map_variables variable_2="V_i" variable_1="V_i"/>
</connection>
<connection>
<map_components component_2="sodium_flux" component_1="intracellular_space"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="P_h" variable_1="P_h"/>
<map_variables variable_2="delta_eh" variable_1="delta_eh"/>
</connection>
<connection>
<map_components component_2="potassium_flux" component_1="intracellular_space"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="P_h" variable_1="P_h"/>
<map_variables variable_2="delta_eh" variable_1="delta_eh"/>
</connection>
<connection>
<map_components component_2="chloride_flux" component_1="intracellular_space"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="P_h" variable_1="P_h"/>
<map_variables variable_2="delta_eh" variable_1="delta_eh"/>
</connection>
<connection>
<map_components component_2="capillary_compartment_sodium" component_1="intracellular_space"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="capillary_compartment_potassium" component_1="intracellular_space"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="capillary_compartment_chloride" component_1="intracellular_space"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
</connection>
<connection>
<map_components component_2="capillary_space" component_1="intracellular_space"/>
<map_variables variable_2="pi_e" variable_1="pi_e"/>
</connection>
<connection>
<map_components component_2="pump_rate" component_1="intracellular_space"/>
<map_variables variable_2="R" variable_1="R"/>
<map_variables variable_2="T" variable_1="T"/>
<map_variables variable_2="F" variable_1="F"/>
<map_variables variable_2="delta" variable_1="delta"/>
</connection>
<connection>
<map_components component_2="extracellular_sodium" component_1="intracellular_sodium"/>
<map_variables variable_2="Na_e" variable_1="Na_e"/>
<map_variables variable_2="g_Na" variable_1="g_Na"/>
<map_variables variable_2="delta_Na" variable_1="delta_Na"/>
</connection>
<connection>
<map_components component_2="pump_rate" component_1="intracellular_sodium"/>
<map_variables variable_2="Na_i" variable_1="Na_i"/>
<map_variables variable_2="P" variable_1="P"/>
</connection>
<connection>
<map_components component_2="pump_rate" component_1="intracellular_potassium"/>
<map_variables variable_2="P" variable_1="P"/>
</connection>
<connection>
<map_components component_2="extracellular_potassium" component_1="intracellular_potassium"/>
<map_variables variable_2="K_e" variable_1="K_e"/>
<map_variables variable_2="g_K" variable_1="g_K"/>
<map_variables variable_2="delta_K" variable_1="delta_K"/>
</connection>
<connection>
<map_components component_2="extracellular_chloride" component_1="intracellular_chloride"/>
<map_variables variable_2="Cl_e" variable_1="Cl_e"/>
<map_variables variable_2="g_Cl" variable_1="g_Cl"/>
<map_variables variable_2="delta_Cl" variable_1="delta_Cl"/>
</connection>
<connection>
<map_components component_2="sodium_flux" component_1="extracellular_sodium"/>
<map_variables variable_2="Na_e" variable_1="Na_e"/>
<map_variables variable_2="Jh_Na" variable_1="Jh_Na"/>
</connection>
<connection>
<map_components component_2="capillary_compartment_sodium" component_1="extracellular_sodium"/>
<map_variables variable_2="Na_e" variable_1="Na_e"/>
<map_variables variable_2="Jv_Na" variable_1="Jv_Na"/>
</connection>
<connection>
<map_components component_2="pump_rate" component_1="extracellular_sodium"/>
<map_variables variable_2="Na_e" variable_1="Na_e"/>
<map_variables variable_2="P" variable_1="P"/>
</connection>
<connection>
<map_components component_2="potassium_flux" component_1="extracellular_potassium"/>
<map_variables variable_2="K_e" variable_1="K_e"/>
<map_variables variable_2="Jh_K" variable_1="Jh_K"/>
</connection>
<connection>
<map_components component_2="capillary_compartment_potassium" component_1="extracellular_potassium"/>
<map_variables variable_2="K_e" variable_1="K_e"/>
<map_variables variable_2="Jv_K" variable_1="Jv_K"/>
</connection>
<connection>
<map_components component_2="pump_rate" component_1="extracellular_potassium"/>
<map_variables variable_2="K_e" variable_1="K_e"/>
<map_variables variable_2="P" variable_1="P"/>
</connection>
<connection>
<map_components component_2="chloride_flux" component_1="extracellular_chloride"/>
<map_variables variable_2="Cl_e" variable_1="Cl_e"/>
<map_variables variable_2="Jh_Cl" variable_1="Jh_Cl"/>
</connection>
<connection>
<map_components component_2="extracellular_space" component_1="extracellular_chloride"/>
<map_variables variable_2="Cl_e" variable_1="Cl_e"/>
</connection>
<connection>
<map_components component_2="extracellular_space" component_1="extracellular_potassium"/>
<map_variables variable_2="K_e" variable_1="K_e"/>
</connection>
<connection>
<map_components component_2="extracellular_space" component_1="extracellular_sodium"/>
<map_variables variable_2="Na_e" variable_1="Na_e"/>
</connection>
<connection>
<map_components component_2="capillary_compartment_chloride" component_1="extracellular_chloride"/>
<map_variables variable_2="Cl_e" variable_1="Cl_e"/>
<map_variables variable_2="Jv_Cl" variable_1="Jv_Cl"/>
</connection>
<connection>
<map_components component_2="water_flux" component_1="extracellular_space"/>
<map_variables variable_2="V_e" variable_1="V_e"/>
<map_variables variable_2="Jh_H2O" variable_1="Jh_H2O"/>
</connection>
<connection>
<map_components component_2="capillary_space" component_1="extracellular_space"/>
<map_variables variable_2="Jv_H2O" variable_1="Jv_H2O"/>
</connection>
<connection>
<map_components component_2="sodium_flux" component_1="water_flux"/>
<map_variables variable_2="Jh_H2O" variable_1="Jh_H2O"/>
</connection>
<connection>
<map_components component_2="potassium_flux" component_1="water_flux"/>
<map_variables variable_2="Jh_H2O" variable_1="Jh_H2O"/>
</connection>
<connection>
<map_components component_2="chloride_flux" component_1="water_flux"/>
<map_variables variable_2="Jh_H2O" variable_1="Jh_H2O"/>
</connection>
<connection>
<map_components component_2="arterial_space" component_1="capillary_compartment_sodium"/>
<map_variables variable_2="Na_a" variable_1="Na_a"/>
<map_variables variable_2="Qa" variable_1="Qa"/>
</connection>
<connection>
<map_components component_2="capillary_space" component_1="capillary_compartment_sodium"/>
<map_variables variable_2="Na_v" variable_1="Na_v"/>
<map_variables variable_2="Qv" variable_1="Qv"/>
</connection>
<connection>
<map_components component_2="arterial_space" component_1="capillary_compartment_potassium"/>
<map_variables variable_2="K_a" variable_1="K_a"/>
<map_variables variable_2="Qa" variable_1="Qa"/>
</connection>
<connection>
<map_components component_2="capillary_space" component_1="capillary_compartment_potassium"/>
<map_variables variable_2="K_v" variable_1="K_v"/>
<map_variables variable_2="Qv" variable_1="Qv"/>
</connection>
<connection>
<map_components component_2="arterial_space" component_1="capillary_compartment_chloride"/>
<map_variables variable_2="Cl_a" variable_1="Cl_a"/>
<map_variables variable_2="Qa" variable_1="Qa"/>
</connection>
<connection>
<map_components component_2="capillary_space" component_1="capillary_compartment_chloride"/>
<map_variables variable_2="Cl_v" variable_1="Cl_v"/>
<map_variables variable_2="Qv" variable_1="Qv"/>
</connection>
<connection>
<map_components component_2="arterial_space" component_1="capillary_space"/>
<map_variables variable_2="Qv" variable_1="Qv"/>
<map_variables variable_2="Qa" variable_1="Qa"/>
<map_variables variable_2="Pr_v" variable_1="Pr_v"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_m_gate" component_1="intracellular_sodium"/>
<map_variables variable_2="m_infinity" variable_1="m_infinity"/>
<map_variables variable_2="delta" variable_1="delta"/>
<map_variables variable_2="delta_eq" variable_1="delta_eq"/>
</connection>
<connection>
<map_components component_2="intracellular_sodium_h_gate" component_1="intracellular_sodium"/>
<map_variables variable_2="h_infinity" variable_1="h_infinity"/>
<map_variables variable_2="delta" variable_1="delta"/>
<map_variables variable_2="delta_eq" variable_1="delta_eq"/>
</connection>
<connection>
<map_components component_2="intracellular_potassium_n_gate" component_1="intracellular_potassium"/>
<map_variables variable_2="n_infinity" variable_1="n_infinity"/>
<map_variables variable_2="delta" variable_1="delta"/>
<map_variables variable_2="delta_eq" variable_1="delta_eq"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#08bb621a-e405-4bdf-9e7b-7ac4a855d8fa">
<rdf:li>Cardiac Myocyte</rdf:li>
<rdf:li>calcium dynamics</rdf:li>
<rdf:li>electrophysiology</rdf:li>
<rdf:li>ischemia</rdf:li>
<rdf:li>hypoxia</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#16325396-015a-44ea-a549-08edd2985cb2">
<rdf:li rdf:resource="rdf:#4a077e80-9899-4b66-854c-eb553bb1a8e9"/>
<rdf:li rdf:resource="rdf:#3f5975f8-d42a-43a9-8019-519ce17e525b"/>
<rdf:li rdf:resource="rdf:#df2f9b52-d291-4d37-92da-5800d0ee505b"/>
<rdf:li rdf:resource="rdf:#6a6b60fb-4680-4e5c-a118-933d10645121"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#ccb6b55e-7bf3-4d89-83f9-fa02a5bf7267">
<vCard:Given>Autumn</vCard:Given>
<vCard:Family>Cuellar</vCard:Family>
<vCard:Other>A</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#df2f9b52-d291-4d37-92da-5800d0ee505b">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#c99b3ea4-c51e-481d-9fb7-99c73907fab2"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#51aeae1c-eb6e-407a-890a-0629b0489470">
<dcterms:modified rdf:resource="rdf:#539be03f-f99d-4250-a195-655a15849aed"/>
<rdf:value>
Changed unit dimensions to make them consistent.
</rdf:value>
<cmeta:modifier rdf:resource="rdf:#6cacaee9-22d5-40c0-89d9-01be64cc81f5"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c99b3ea4-c51e-481d-9fb7-99c73907fab2">
<vCard:Given>James</vCard:Given>
<vCard:Family>Keener</vCard:Family>
<vCard:Other>P</vCard:Other>
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A Mathematical Study of Volume Shifts and Ionic Concentration
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