- Author:
- Michael Clerx <michael.clerx@cs.ox.ac.uk>
- Date:
- 2020-10-15 17:17:11+01:00
- Desc:
- Fix to pdf
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/605/rawfile/0eac6f2330f9ed2ed5a458ac1f6fe8cfc8b7998d/tentusscher_noble_noble_panfilov_2004_endo.cellml
<?xml version='1.0'?>
<!--
This CellML file was generated on 05/11/2007 at 17:00:27 using:
COR (0.9.31.801)
Copyright 2002-2007 Dr Alan Garny
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this cellular model
http://www.CellML.org/
-->
<model cmeta:id="tentusscher_2004_endo_cell" name="tentusscher_2004_endo_cell" 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#">
<units name="micrometre">
<unit prefix="micro" units="metre"/>
</units>
<units name="micrometre3">
<unit exponent="3" prefix="micro" units="metre"/>
</units>
<units name="millisecond">
<unit prefix="milli" units="second"/>
</units>
<units name="per_millisecond">
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<units name="millivolt">
<unit prefix="milli" units="volt"/>
</units>
<units name="millivolt_square">
<unit exponent="2" prefix="milli" units="volt"/>
</units>
<units name="per_millivolt">
<unit exponent="-1" prefix="milli" units="volt"/>
</units>
<units name="nanoS_per_picoF">
<unit prefix="nano" units="siemens"/>
<unit exponent="-1" prefix="pico" units="farad"/>
</units>
<units name="microF">
<unit prefix="micro" units="farad"/>
</units>
<units name="picoF">
<unit prefix="pico" units="farad"/>
</units>
<units name="picoA">
<unit prefix="pico" units="ampere"/>
</units>
<units name="picoA_per_picoF">
<unit prefix="pico" units="ampere"/>
<unit exponent="-1" prefix="pico" units="farad"/>
</units>
<units name="nanoA_per_millimolar">
<unit prefix="nano" units="ampere"/>
<unit exponent="-1" units="millimolar"/>
</units>
<units name="millimolar">
<unit prefix="milli" units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="millimolar_per_millisecond">
<unit units="millimolar"/>
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<units name="joule_per_mole_kelvin">
<unit units="joule"/>
<unit exponent="-1" units="mole"/>
<unit exponent="-1" units="kelvin"/>
</units>
<units name="coulomb_per_millimole">
<unit units="coulomb"/>
<unit exponent="-1" prefix="milli" units="mole"/>
</units>
<units name="cm2">
<unit exponent="2" prefix="centi" units="metre"/>
</units>
<units name="microF_per_cm2">
<unit units="microF"/>
<unit exponent="-1" units="cm2"/>
</units>
<units name="litre_per_farad_second">
<unit units="litre"/>
<unit exponent="-1" units="farad"/>
<unit exponent="-1" units="second"/>
</units>
<component name="environment">
<variable name="time" public_interface="out" units="millisecond"/>
</component>
<component cmeta:id="id_00001" name="membrane">
<variable initial_value="-86.2" name="V" public_interface="out" units="millivolt"/>
<variable initial_value="8.314" name="R" public_interface="out" units="joule_per_mole_kelvin"/>
<variable initial_value="310" name="T" public_interface="out" units="kelvin"/>
<variable initial_value="96.485" name="F" public_interface="out" units="coulomb_per_millimole"/>
<variable initial_value="185" name="Cm" public_interface="out" units="picoF"/>
<variable initial_value="16404" name="V_c" public_interface="out" units="micrometre3"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="i_K1" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_to" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_Kr" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_Ks" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_CaL" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_NaK" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_Na" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_b_Na" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_NaCa" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_b_Ca" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_p_K" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_p_Ca" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_Stim" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="10" name="stim_start" units="millisecond"/>
<variable initial_value="1000" name="stim_period" units="millisecond"/>
<variable initial_value="1" name="stim_duration" units="millisecond"/>
<variable initial_value="-52" name="stim_amplitude" units="picoA_per_picoF"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Stim</ci>
<piecewise>
<piece>
<ci>stim_amplitude</ci>
<apply>
<and/>
<apply>
<geq/>
<apply>
<minus/>
<ci>time</ci>
<apply>
<times/>
<apply>
<floor/>
<apply>
<divide/>
<ci>time</ci>
<ci>stim_period</ci>
</apply>
</apply>
<ci>stim_period</ci>
</apply>
</apply>
<ci>stim_start</ci>
</apply>
<apply>
<leq/>
<apply>
<minus/>
<ci>time</ci>
<apply>
<times/>
<apply>
<floor/>
<apply>
<divide/>
<ci>time</ci>
<ci>stim_period</ci>
</apply>
</apply>
<ci>stim_period</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>stim_start</ci>
<ci>stim_duration</ci>
</apply>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="picoA_per_picoF">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>V</ci>
</apply>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_K1</ci>
<ci>i_to</ci>
<ci>i_Kr</ci>
<ci>i_Ks</ci>
<ci>i_CaL</ci>
<ci>i_NaK</ci>
<ci>i_Na</ci>
<ci>i_b_Na</ci>
<ci>i_NaCa</ci>
<ci>i_b_Ca</ci>
<ci>i_p_K</ci>
<ci>i_p_Ca</ci>
<ci>i_Stim</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00002" name="reversal_potentials">
<variable name="E_Na" public_interface="out" units="millivolt"/>
<variable name="E_K" public_interface="out" units="millivolt"/>
<variable name="E_Ks" public_interface="out" units="millivolt"/>
<variable name="E_Ca" public_interface="out" units="millivolt"/>
<variable initial_value="0.03" name="P_kna" units="dimensionless"/>
<variable name="K_o" public_interface="in" units="millimolar"/>
<variable name="Na_o" public_interface="in" units="millimolar"/>
<variable name="K_i" public_interface="in" units="millimolar"/>
<variable name="Na_i" public_interface="in" units="millimolar"/>
<variable name="Ca_o" public_interface="in" units="millimolar"/>
<variable name="Ca_i" public_interface="in" units="millimolar"/>
<variable name="R" public_interface="in" units="joule_per_mole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_millimole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_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_o</ci>
<ci>Na_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>E_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_o</ci>
<ci>K_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>E_Ks</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<apply>
<plus/>
<ci>K_o</ci>
<apply>
<times/>
<ci>P_kna</ci>
<ci>Na_o</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>K_i</ci>
<apply>
<times/>
<ci>P_kna</ci>
<ci>Na_i</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>E_Ca</ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<ci>R</ci>
<ci>T</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci>Ca_o</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00015" name="inward_rectifier_potassium_current">
<variable name="i_K1" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="5.405" name="g_K1" units="nanoS_per_picoF"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="K_o" public_interface="in" units="millimolar"/>
<variable name="E_K" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="xK1_inf" units="dimensionless"/>
<variable name="alpha_K1" units="per_millisecond"/>
<variable name="beta_K1" units="per_millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_K1</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">0.1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.06</cn>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<cn cellml:units="millivolt">200</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_K1</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond">3</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.0002</cn>
<apply>
<plus/>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<cn cellml:units="millivolt">100</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond">1</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.1</cn>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.5</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>xK1_inf</ci>
<apply>
<divide/>
<ci>alpha_K1</ci>
<apply>
<plus/>
<ci>alpha_K1</ci>
<ci>beta_K1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_K1</ci>
<apply>
<times/>
<ci>g_K1</ci>
<ci>xK1_inf</ci>
<apply>
<root/>
<apply>
<divide/>
<ci>K_o</ci>
<cn cellml:units="millimolar">5.4</cn>
</apply>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00016" name="rapid_time_dependent_potassium_current">
<variable name="i_Kr" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="0.096" name="g_Kr" units="nanoS_per_picoF"/>
<variable name="E_K" public_interface="in" units="millivolt"/>
<variable name="K_o" public_interface="in" units="millimolar"/>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="Xr1" private_interface="in" units="dimensionless"/>
<variable name="Xr2" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Kr</ci>
<apply>
<times/>
<ci>g_Kr</ci>
<apply>
<root/>
<apply>
<divide/>
<ci>K_o</ci>
<cn cellml:units="millimolar">5.4</cn>
</apply>
</apply>
<ci>Xr1</ci>
<ci>Xr2</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00017" name="rapid_time_dependent_potassium_current_Xr1_gate">
<variable initial_value="0" name="Xr1" public_interface="out" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="xr1_inf" units="dimensionless"/>
<variable name="alpha_xr1" units="dimensionless"/>
<variable name="beta_xr1" units="dimensionless"/>
<variable name="tau_xr1" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>xr1_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">26</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">7</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_xr1</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">450</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">45</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_xr1</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">6</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">30</cn>
</apply>
<cn cellml:units="millivolt">11.5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_xr1</ci>
<apply>
<times/>
<cn cellml:units="millisecond">1</cn>
<ci>alpha_xr1</ci>
<ci>beta_xr1</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Xr1</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>xr1_inf</ci>
<ci>Xr1</ci>
</apply>
<ci>tau_xr1</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00018" name="rapid_time_dependent_potassium_current_Xr2_gate">
<variable initial_value="1" name="Xr2" public_interface="out" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="xr2_inf" units="dimensionless"/>
<variable name="alpha_xr2" units="dimensionless"/>
<variable name="beta_xr2" units="dimensionless"/>
<variable name="tau_xr2" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>xr2_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">88</cn>
</apply>
<cn cellml:units="millivolt">24</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_xr2</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">3</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">60</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_xr2</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1.12</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">60</cn>
</apply>
<cn cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_xr2</ci>
<apply>
<times/>
<cn cellml:units="millisecond">1</cn>
<ci>alpha_xr2</ci>
<ci>beta_xr2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Xr2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>xr2_inf</ci>
<ci>Xr2</ci>
</apply>
<ci>tau_xr2</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00019" name="slow_time_dependent_potassium_current">
<variable name="i_Ks" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="0.245" name="g_Ks" units="nanoS_per_picoF"/>
<variable name="E_Ks" public_interface="in" units="millivolt"/>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="Xs" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Ks</ci>
<apply>
<times/>
<ci>g_Ks</ci>
<apply>
<power/>
<ci>Xs</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ks</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00020" name="slow_time_dependent_potassium_current_Xs_gate">
<variable initial_value="0" name="Xs" public_interface="out" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="xs_inf" units="dimensionless"/>
<variable name="alpha_xs" units="dimensionless"/>
<variable name="beta_xs" units="dimensionless"/>
<variable name="tau_xs" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>xs_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">5</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">14</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_xs</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1100</cn>
<apply>
<root/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">10</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_xs</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">60</cn>
</apply>
<cn cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_xs</ci>
<apply>
<times/>
<cn cellml:units="millisecond">1</cn>
<ci>alpha_xs</ci>
<ci>beta_xs</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Xs</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>xs_inf</ci>
<ci>Xs</ci>
</apply>
<ci>tau_xs</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00003" name="fast_sodium_current">
<variable name="i_Na" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="14.838" name="g_Na" units="nanoS_per_picoF"/>
<variable name="E_Na" public_interface="in" units="millivolt"/>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="m" private_interface="in" units="dimensionless"/>
<variable name="h" private_interface="in" units="dimensionless"/>
<variable name="j" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Na</ci>
<apply>
<times/>
<ci>g_Na</ci>
<apply>
<power/>
<ci>m</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>h</ci>
<ci>j</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00004" name="fast_sodium_current_m_gate">
<variable initial_value="0" name="m" public_interface="out" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="m_inf" units="dimensionless"/>
<variable name="alpha_m" units="dimensionless"/>
<variable name="beta_m" units="dimensionless"/>
<variable name="tau_m" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>m_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">56.86</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">9.03</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_m</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">60</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_m</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">35</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">50</cn>
</apply>
<cn cellml:units="millivolt">200</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_m</ci>
<apply>
<times/>
<cn cellml:units="millisecond">1</cn>
<ci>alpha_m</ci>
<ci>beta_m</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>m</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>m_inf</ci>
<ci>m</ci>
</apply>
<ci>tau_m</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00005" name="fast_sodium_current_h_gate">
<variable initial_value="0.75" name="h" public_interface="out" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="h_inf" units="dimensionless"/>
<variable name="alpha_h" units="per_millisecond"/>
<variable name="beta_h" units="per_millisecond"/>
<variable name="tau_h" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>h_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">71.55</cn>
</apply>
<cn cellml:units="millivolt">7.43</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_h</ci>
<piecewise>
<piece>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.057</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">80</cn>
</apply>
</apply>
<cn cellml:units="millivolt">6.8</cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>beta_h</ci>
<piecewise>
<piece>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="per_millisecond">2.7</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.079</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond">310000</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.3485</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<cn cellml:units="per_millisecond">0.77</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.13</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">10.66</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">11.1</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>tau_h</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_h</ci>
<ci>beta_h</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>h</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>h_inf</ci>
<ci>h</ci>
</apply>
<ci>tau_h</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00006" name="fast_sodium_current_j_gate">
<variable initial_value="0.75" name="j" public_interface="out" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="j_inf" units="dimensionless"/>
<variable name="alpha_j" units="per_millisecond"/>
<variable name="beta_j" units="per_millisecond"/>
<variable name="tau_j" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>j_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">71.55</cn>
</apply>
<cn cellml:units="millivolt">7.43</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_j</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millisecond">25428</cn>
</apply>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.2444</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="per_millisecond" type="e-notation">6.948<sep/>-6</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.04391</cn>
</apply>
<ci>V</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">37.78</cn>
</apply>
</apply>
<cn cellml:units="millivolt">1</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.311</cn>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">79.23</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_millisecond">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>beta_j</ci>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.02424</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.01052</cn>
</apply>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.1378</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">40.14</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">40</cn>
</apply>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millisecond">0.6</cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="per_millivolt">0.057</cn>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="per_millivolt">0.1</cn>
</apply>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">32</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>tau_j</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_j</ci>
<ci>beta_j</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>j</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>j_inf</ci>
<ci>j</ci>
</apply>
<ci>tau_j</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00014" name="sodium_background_current">
<variable name="i_b_Na" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="0.00029" name="g_bna" units="nanoS_per_picoF"/>
<variable name="E_Na" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="V" public_interface="in" units="millivolt"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_b_Na</ci>
<apply>
<times/>
<ci>g_bna</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00034" name="L_type_Ca_current">
<variable name="i_CaL" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="0.175" name="g_CaL" units="litre_per_farad_second"/>
<variable name="Ca_o" public_interface="in" units="millimolar"/>
<variable name="Ca_i" private_interface="out" public_interface="in" units="millimolar"/>
<variable name="R" public_interface="in" units="joule_per_mole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_millimole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="d" private_interface="in" public_interface="out" units="dimensionless"/>
<variable name="f" private_interface="in" units="dimensionless"/>
<variable name="fCa" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_CaL</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>g_CaL</ci>
<ci>d</ci>
<ci>f</ci>
<ci>fCa</ci>
<cn cellml:units="dimensionless">4</cn>
<ci>V</ci>
<apply>
<power/>
<ci>F</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>Ca_i</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.341</cn>
<ci>Ca_o</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00035" name="L_type_Ca_current_d_gate">
<variable initial_value="0" name="d" public_interface="out" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="d_inf" units="dimensionless"/>
<variable name="alpha_d" units="dimensionless"/>
<variable name="beta_d" units="dimensionless"/>
<variable name="gamma_d" units="millisecond"/>
<variable name="tau_d" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>d_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">5</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">7.5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>alpha_d</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">1.4</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="millivolt">35</cn>
</apply>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">13</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.25</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_d</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1.4</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">5</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>gamma_d</ci>
<apply>
<divide/>
<cn cellml:units="millisecond">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">50</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">20</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_d</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">1</cn>
<ci>alpha_d</ci>
<ci>beta_d</ci>
</apply>
<ci>gamma_d</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>d</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>d_inf</ci>
<ci>d</ci>
</apply>
<ci>tau_d</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00036" name="L_type_Ca_current_f_gate">
<variable initial_value="1" name="f" public_interface="out" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="f_inf" units="dimensionless"/>
<variable name="tau_f" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">20</cn>
</apply>
<cn cellml:units="millivolt">7</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">1125</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">27</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="millivolt_square">240</cn>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">80</cn>
<apply>
<divide/>
<cn cellml:units="millisecond">165</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">25</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f_inf</ci>
<ci>f</ci>
</apply>
<ci>tau_f</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00037" name="L_type_Ca_current_fCa_gate">
<variable initial_value="1" name="fCa" public_interface="out" units="dimensionless"/>
<variable name="Ca_i" public_interface="in" units="millimolar"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="alpha_fCa" units="dimensionless"/>
<variable name="beta_fCa" units="dimensionless"/>
<variable name="gama_fCa" units="dimensionless"/>
<variable name="fCa_inf" units="dimensionless"/>
<variable name="tau_fCa" units="millisecond"/>
<variable name="d_fCa" units="per_millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_fCa</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.000325</cn>
</apply>
<cn cellml:units="dimensionless">8</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_fCa</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.0005</cn>
</apply>
<cn cellml:units="millimolar">0.0001</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>gama_fCa</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.2</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.00075</cn>
</apply>
<cn cellml:units="millimolar">0.0008</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>fCa_inf</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>alpha_fCa</ci>
<ci>beta_fCa</ci>
<ci>gama_fCa</ci>
<cn cellml:units="dimensionless">0.23</cn>
</apply>
<cn cellml:units="dimensionless">1.46</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_fCa</ci>
<cn cellml:units="millisecond">2</cn>
</apply>
<apply>
<eq/>
<ci>d_fCa</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>fCa_inf</ci>
<ci>fCa</ci>
</apply>
<ci>tau_fCa</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>fCa</ci>
</apply>
<piecewise>
<piece>
<cn cellml:units="per_millisecond">0</cn>
<apply>
<and/>
<apply>
<gt/>
<ci>fCa_inf</ci>
<ci>fCa</ci>
</apply>
<apply>
<gt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">60</cn>
</apply>
</apply>
</apply>
</piece>
<otherwise>
<ci>d_fCa</ci>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component cmeta:id="id_00051" name="calcium_background_current">
<variable name="i_b_Ca" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="0.000592" name="g_bca" units="nanoS_per_picoF"/>
<variable name="E_Ca" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="V" public_interface="in" units="millivolt"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_b_Ca</ci>
<apply>
<times/>
<ci>g_bca</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Ca</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00052" name="transient_outward_current">
<variable name="i_to" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="0.073" name="g_to" units="nanoS_per_picoF"/>
<variable name="E_K" public_interface="in" units="millivolt"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<variable name="time" private_interface="out" public_interface="in" units="millisecond"/>
<variable name="s" private_interface="in" units="dimensionless"/>
<variable name="r" private_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_to</ci>
<apply>
<times/>
<ci>g_to</ci>
<ci>r</ci>
<ci>s</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00053" name="transient_outward_current_s_gate">
<variable initial_value="1" name="s" public_interface="out" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="s_inf" units="dimensionless"/>
<variable name="tau_s" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>s_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">28</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_s</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">1000</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">67</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="millivolt_square">1000</cn>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">8</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>s</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>s_inf</ci>
<ci>s</ci>
</apply>
<ci>tau_s</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00054" name="transient_outward_current_r_gate">
<variable initial_value="0" name="r" public_interface="out" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="r_inf" units="dimensionless"/>
<variable name="tau_r" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>r_inf</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">20</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_r</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">9.5</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">40</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="millivolt_square">1800</cn>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">0.8</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>r</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>r_inf</ci>
<ci>r</ci>
</apply>
<ci>tau_r</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00058" name="sodium_potassium_pump_current">
<variable name="i_NaK" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="1.362" name="P_NaK" units="picoA_per_picoF"/>
<variable initial_value="1" name="K_mk" units="millimolar"/>
<variable initial_value="40" name="K_mNa" units="millimolar"/>
<variable name="K_o" public_interface="in" units="millimolar"/>
<variable name="Na_i" public_interface="in" units="millimolar"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="R" public_interface="in" units="joule_per_mole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_millimole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="V" private_interface="out" public_interface="in" units="millivolt"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaK</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>P_NaK</ci>
<ci>K_o</ci>
</apply>
<apply>
<plus/>
<ci>K_o</ci>
<ci>K_mk</ci>
</apply>
</apply>
<ci>Na_i</ci>
</apply>
<apply>
<plus/>
<ci>Na_i</ci>
<ci>K_mNa</ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">0.1245</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless">0.1</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">0.0353</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>V</ci>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00060" name="sodium_calcium_exchanger_current">
<variable name="i_NaCa" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="1000" name="K_NaCa" units="picoA_per_picoF"/>
<variable initial_value="0.1" name="K_sat" units="dimensionless"/>
<variable initial_value="2.5" name="alpha" units="dimensionless"/>
<variable initial_value="0.35" name="gamma" units="dimensionless"/>
<variable initial_value="1.38" name="Km_Ca" units="millimolar"/>
<variable initial_value="87.5" name="Km_Nai" units="millimolar"/>
<variable name="Na_i" public_interface="in" units="millimolar"/>
<variable name="Na_o" public_interface="in" units="millimolar"/>
<variable name="Ca_i" public_interface="in" units="millimolar"/>
<variable name="Ca_o" public_interface="in" units="millimolar"/>
<variable name="R" public_interface="in" units="joule_per_mole_kelvin"/>
<variable name="F" public_interface="in" units="coulomb_per_millimole"/>
<variable name="T" public_interface="in" units="kelvin"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaCa</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K_NaCa</ci>
<apply>
<minus/>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci>gamma</ci>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_o</ci>
</apply>
<apply>
<times/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>gamma</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci>Na_o</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>Ca_i</ci>
<ci>alpha</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<apply>
<plus/>
<apply>
<power/>
<ci>Km_Nai</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<apply>
<power/>
<ci>Na_o</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<apply>
<plus/>
<ci>Km_Ca</ci>
<ci>Ca_o</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>K_sat</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>gamma</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<ci>V</ci>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00038" name="calcium_pump_current">
<variable name="i_p_Ca" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="0.825" name="g_pCa" units="picoA_per_picoF"/>
<variable initial_value="0.0005" name="K_pCa" units="millimolar"/>
<variable name="Ca_i" public_interface="in" units="millimolar"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_p_Ca</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>g_pCa</ci>
<ci>Ca_i</ci>
</apply>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>K_pCa</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00021" name="potassium_pump_current">
<variable name="i_p_K" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="0.0146" name="g_pK" units="nanoS_per_picoF"/>
<variable name="E_K" public_interface="in" units="millivolt"/>
<variable name="V" public_interface="in" units="millivolt"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_p_K</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>g_pK</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">25</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">5.98</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00039" name="calcium_dynamics">
<variable initial_value="0.0002" name="Ca_i" public_interface="out" units="millimolar"/>
<variable initial_value="2" name="Ca_o" public_interface="out" units="millimolar"/>
<variable initial_value="0.2" name="Ca_SR" units="millimolar"/>
<variable name="i_rel" units="millimolar_per_millisecond"/>
<variable name="i_up" units="millimolar_per_millisecond"/>
<variable name="i_leak" units="millimolar_per_millisecond"/>
<variable initial_value="1" name="g" units="dimensionless"/>
<variable initial_value="2" name="tau_g" units="millisecond"/>
<variable name="g_inf" units="dimensionless"/>
<variable initial_value="0.016464" name="a_rel" units="millimolar_per_millisecond"/>
<variable initial_value="0.25" name="b_rel" units="millimolar"/>
<variable initial_value="0.008232" name="c_rel" units="millimolar_per_millisecond"/>
<variable initial_value="0.00025" name="K_up" units="millimolar"/>
<variable initial_value="8e-5" name="V_leak" units="per_millisecond"/>
<variable initial_value="0.000425" name="Vmax_up" units="millimolar_per_millisecond"/>
<variable name="ddt_Ca_i_total" units="millimolar_per_millisecond"/>
<variable name="ddt_Ca_sr_total" units="millimolar_per_millisecond"/>
<variable name="f_JCa_i_free" units="dimensionless"/>
<variable name="f_JCa_sr_free" units="dimensionless"/>
<variable initial_value="0.15" name="Buf_c" units="millimolar"/>
<variable initial_value="0.001" name="K_buf_c" units="millimolar"/>
<variable initial_value="10" name="Buf_sr" units="millimolar"/>
<variable initial_value="0.3" name="K_buf_sr" units="millimolar"/>
<variable initial_value="1094" name="V_sr" units="micrometre3"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="V_c" public_interface="in" units="micrometre3"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="d" public_interface="in" units="dimensionless"/>
<variable name="F" public_interface="in" units="coulomb_per_millimole"/>
<variable name="Cm" public_interface="in" units="picoF"/>
<variable name="i_CaL" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_NaCa" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_p_Ca" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_b_Ca" public_interface="in" units="picoA_per_picoF"/>
<variable name="d_g" units="per_millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_rel</ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci>a_rel</ci>
<apply>
<power/>
<ci>Ca_SR</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>b_rel</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>Ca_SR</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<ci>c_rel</ci>
</apply>
<ci>d</ci>
<ci>g</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>i_up</ci>
<apply>
<divide/>
<ci>Vmax_up</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<power/>
<ci>K_up</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>Ca_i</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_leak</ci>
<apply>
<times/>
<ci>V_leak</ci>
<apply>
<minus/>
<ci>Ca_SR</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>g_inf</ci>
<piecewise>
<piece>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.00035</cn>
</apply>
<cn cellml:units="dimensionless">6</cn>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.00035</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_i</ci>
<cn cellml:units="millimolar">0.00035</cn>
</apply>
<cn cellml:units="dimensionless">16</cn>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>d_g</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>g_inf</ci>
<ci>g</ci>
</apply>
<ci>tau_g</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>g</ci>
</apply>
<piecewise>
<piece>
<cn cellml:units="per_millisecond">0</cn>
<apply>
<and/>
<apply>
<gt/>
<ci>g_inf</ci>
<ci>g</ci>
</apply>
<apply>
<gt/>
<ci>V</ci>
<apply>
<minus/>
<cn cellml:units="millivolt">60</cn>
</apply>
</apply>
</apply>
</piece>
<otherwise>
<ci>d_g</ci>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>ddt_Ca_i_total</ci>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_CaL</ci>
<ci>i_b_Ca</ci>
<ci>i_p_Ca</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V_c</ci>
<ci>F</ci>
</apply>
</apply>
<ci>Cm</ci>
</apply>
<ci>i_leak</ci>
</apply>
<ci>i_up</ci>
</apply>
<ci>i_rel</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>ddt_Ca_sr_total</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>V_c</ci>
<ci>V_sr</ci>
</apply>
<apply>
<minus/>
<ci>i_up</ci>
<apply>
<plus/>
<ci>i_rel</ci>
<ci>i_leak</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>f_JCa_i_free</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>Buf_c</ci>
<ci>K_buf_c</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>Ca_i</ci>
<ci>K_buf_c</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>f_JCa_sr_free</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>Buf_sr</ci>
<ci>K_buf_sr</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>Ca_SR</ci>
<ci>K_buf_sr</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_i</ci>
</apply>
<apply>
<times/>
<ci>ddt_Ca_i_total</ci>
<ci>f_JCa_i_free</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_SR</ci>
</apply>
<apply>
<times/>
<ci>ddt_Ca_sr_total</ci>
<ci>f_JCa_sr_free</ci>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00007" name="sodium_dynamics">
<variable initial_value="11.6" name="Na_i" public_interface="out" units="millimolar"/>
<variable initial_value="140" name="Na_o" public_interface="out" units="millimolar"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="F" public_interface="in" units="coulomb_per_millimole"/>
<variable name="Cm" public_interface="in" units="picoF"/>
<variable name="V_c" public_interface="in" units="micrometre3"/>
<variable name="i_Na" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_NaCa" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_NaK" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_b_Na" public_interface="in" units="picoA_per_picoF"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Na_i</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_Na</ci>
<ci>i_b_Na</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaK</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">3</cn>
<ci>i_NaCa</ci>
</apply>
</apply>
</apply>
<ci>Cm</ci>
</apply>
<apply>
<times/>
<ci>V_c</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component cmeta:id="id_00033" name="potassium_dynamics">
<variable initial_value="138.3" name="K_i" public_interface="out" units="millimolar"/>
<variable initial_value="5.4" name="K_o" public_interface="out" units="millimolar"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="F" public_interface="in" units="coulomb_per_millimole"/>
<variable name="Cm" public_interface="in" units="picoF"/>
<variable name="V_c" public_interface="in" units="micrometre3"/>
<variable name="i_K1" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_to" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_NaK" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_Kr" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_Ks" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_p_K" public_interface="in" units="picoA_per_picoF"/>
<variable name="i_Stim" public_interface="in" units="picoA_per_picoF"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>K_i</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<ci>i_K1</ci>
<ci>i_to</ci>
<ci>i_Kr</ci>
<ci>i_Ks</ci>
<ci>i_p_K</ci>
<ci>i_Stim</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>i_NaK</ci>
</apply>
</apply>
</apply>
<ci>Cm</ci>
</apply>
<apply>
<times/>
<ci>V_c</ci>
<ci>F</ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref cmeta:id="id_00008" component="fast_sodium_current">
<component_ref cmeta:id="id_00009" component="fast_sodium_current_m_gate"/>
<component_ref cmeta:id="id_00010" component="fast_sodium_current_h_gate"/>
<component_ref cmeta:id="id_00011" component="fast_sodium_current_j_gate"/>
</component_ref>
<component_ref cmeta:id="id_00040" component="L_type_Ca_current">
<component_ref cmeta:id="id_00041" component="L_type_Ca_current_d_gate"/>
<component_ref cmeta:id="id_00042" component="L_type_Ca_current_f_gate"/>
<component_ref cmeta:id="id_00043" component="L_type_Ca_current_fCa_gate"/>
</component_ref>
<component_ref cmeta:id="id_00032" component="inward_rectifier_potassium_current"/>
<component_ref cmeta:id="id_00022" component="rapid_time_dependent_potassium_current">
<component_ref cmeta:id="id_00023" component="rapid_time_dependent_potassium_current_Xr1_gate"/>
<component_ref cmeta:id="id_00024" component="rapid_time_dependent_potassium_current_Xr2_gate"/>
</component_ref>
<component_ref component="slow_time_dependent_potassium_current">
<component_ref component="slow_time_dependent_potassium_current_Xs_gate"/>
</component_ref>
<component_ref cmeta:id="id_00013" component="sodium_background_current"/>
<component_ref cmeta:id="id_00049" component="calcium_background_current"/>
<component_ref cmeta:id="id_00055" component="transient_outward_current">
<component_ref cmeta:id="id_00056" component="transient_outward_current_s_gate"/>
<component_ref cmeta:id="id_00057" component="transient_outward_current_r_gate"/>
</component_ref>
<component_ref cmeta:id="id_00059" component="sodium_potassium_pump_current"/>
<component_ref cmeta:id="id_00061" component="sodium_calcium_exchanger_current"/>
<component_ref cmeta:id="id_00050" component="calcium_pump_current"/>
<component_ref cmeta:id="id_00025" component="potassium_pump_current"/>
<component_ref cmeta:id="id_00044" component="calcium_dynamics"/>
<component_ref cmeta:id="id_00012" component="sodium_dynamics"/>
<component_ref cmeta:id="id_00026" component="potassium_dynamics"/>
<component_ref component="reversal_potentials"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref cmeta:id="id_00062" component="fast_sodium_current">
<component_ref cmeta:id="id_00063" component="fast_sodium_current_m_gate"/>
<component_ref cmeta:id="id_00064" component="fast_sodium_current_h_gate"/>
<component_ref cmeta:id="id_00065" component="fast_sodium_current_j_gate"/>
</component_ref>
<component_ref cmeta:id="id_00045" component="L_type_Ca_current">
<component_ref cmeta:id="id_00046" component="L_type_Ca_current_d_gate"/>
<component_ref cmeta:id="id_00047" component="L_type_Ca_current_f_gate"/>
<component_ref cmeta:id="id_00048" component="L_type_Ca_current_fCa_gate"/>
</component_ref>
<component_ref cmeta:id="id_00027" component="rapid_time_dependent_potassium_current">
<component_ref cmeta:id="id_00028" component="rapid_time_dependent_potassium_current_Xr1_gate"/>
<component_ref cmeta:id="id_00029" component="rapid_time_dependent_potassium_current_Xr2_gate"/>
</component_ref>
<component_ref cmeta:id="id_00030" component="slow_time_dependent_potassium_current">
<component_ref cmeta:id="id_00031" component="slow_time_dependent_potassium_current_Xs_gate"/>
</component_ref>
<component_ref cmeta:id="id_00066" component="transient_outward_current">
<component_ref cmeta:id="id_00067" component="transient_outward_current_s_gate"/>
<component_ref cmeta:id="id_00068" component="transient_outward_current_r_gate"/>
</component_ref>
</group>
<connection>
<map_components component_1="membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="reversal_potentials" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="fast_sodium_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="L_type_Ca_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="rapid_time_dependent_potassium_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="slow_time_dependent_potassium_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="inward_rectifier_potassium_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="sodium_background_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="calcium_background_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="transient_outward_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="sodium_potassium_pump_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="sodium_calcium_exchanger_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="calcium_dynamics" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="sodium_dynamics" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="potassium_dynamics" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="reversal_potentials"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="fast_sodium_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_Na" variable_2="i_Na"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="L_type_Ca_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_CaL" variable_2="i_CaL"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="rapid_time_dependent_potassium_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_Kr" variable_2="i_Kr"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="slow_time_dependent_potassium_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_Ks" variable_2="i_Ks"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="transient_outward_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_to" variable_2="i_to"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="inward_rectifier_potassium_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_K1" variable_2="i_K1"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="sodium_background_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_b_Na" variable_2="i_b_Na"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="calcium_background_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_b_Ca" variable_2="i_b_Ca"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="sodium_potassium_pump_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_NaK" variable_2="i_NaK"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="sodium_calcium_exchanger_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_NaCa" variable_2="i_NaCa"/>
<map_variables variable_1="R" variable_2="R"/>
<map_variables variable_1="T" variable_2="T"/>
<map_variables variable_1="F" variable_2="F"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="calcium_pump_current"/>
<map_variables variable_1="i_p_Ca" variable_2="i_p_Ca"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="potassium_pump_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_p_K" variable_2="i_p_K"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="calcium_dynamics"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="V_c" variable_2="V_c"/>
<map_variables variable_1="Cm" variable_2="Cm"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="sodium_dynamics"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="V_c" variable_2="V_c"/>
<map_variables variable_1="Cm" variable_2="Cm"/>
</connection>
<connection>
<map_components component_1="membrane" component_2="potassium_dynamics"/>
<map_variables variable_1="F" variable_2="F"/>
<map_variables variable_1="V_c" variable_2="V_c"/>
<map_variables variable_1="Cm" variable_2="Cm"/>
<map_variables variable_1="i_Stim" variable_2="i_Stim"/>
</connection>
<connection>
<map_components component_1="reversal_potentials" component_2="sodium_background_current"/>
<map_variables variable_1="E_Na" variable_2="E_Na"/>
</connection>
<connection>
<map_components component_1="reversal_potentials" component_2="inward_rectifier_potassium_current"/>
<map_variables variable_1="E_K" variable_2="E_K"/>
</connection>
<connection>
<map_components component_1="reversal_potentials" component_2="rapid_time_dependent_potassium_current"/>
<map_variables variable_1="E_K" variable_2="E_K"/>
</connection>
<connection>
<map_components component_1="reversal_potentials" component_2="transient_outward_current"/>
<map_variables variable_1="E_K" variable_2="E_K"/>
</connection>
<connection>
<map_components component_1="reversal_potentials" component_2="potassium_pump_current"/>
<map_variables variable_1="E_K" variable_2="E_K"/>
</connection>
<connection>
<map_components component_1="reversal_potentials" component_2="slow_time_dependent_potassium_current"/>
<map_variables variable_1="E_Ks" variable_2="E_Ks"/>
</connection>
<connection>
<map_components component_1="reversal_potentials" component_2="calcium_background_current"/>
<map_variables variable_1="E_Ca" variable_2="E_Ca"/>
</connection>
<connection>
<map_components component_1="reversal_potentials" component_2="fast_sodium_current"/>
<map_variables variable_1="E_Na" variable_2="E_Na"/>
</connection>
<connection>
<map_components component_1="reversal_potentials" component_2="calcium_dynamics"/>
<map_variables variable_1="Ca_o" variable_2="Ca_o"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
</connection>
<connection>
<map_components component_1="reversal_potentials" component_2="potassium_dynamics"/>
<map_variables variable_1="K_o" variable_2="K_o"/>
<map_variables variable_1="K_i" variable_2="K_i"/>
</connection>
<connection>
<map_components component_1="reversal_potentials" component_2="sodium_dynamics"/>
<map_variables variable_1="Na_o" variable_2="Na_o"/>
<map_variables variable_1="Na_i" variable_2="Na_i"/>
</connection>
<connection>
<map_components component_1="inward_rectifier_potassium_current" component_2="potassium_dynamics"/>
<map_variables variable_1="i_K1" variable_2="i_K1"/>
<map_variables variable_1="K_o" variable_2="K_o"/>
</connection>
<connection>
<map_components component_1="rapid_time_dependent_potassium_current" component_2="potassium_dynamics"/>
<map_variables variable_1="i_Kr" variable_2="i_Kr"/>
<map_variables variable_1="K_o" variable_2="K_o"/>
</connection>
<connection>
<map_components component_1="slow_time_dependent_potassium_current" component_2="potassium_dynamics"/>
<map_variables variable_1="i_Ks" variable_2="i_Ks"/>
</connection>
<connection>
<map_components component_1="fast_sodium_current" component_2="sodium_dynamics"/>
<map_variables variable_1="i_Na" variable_2="i_Na"/>
</connection>
<connection>
<map_components component_1="sodium_background_current" component_2="sodium_dynamics"/>
<map_variables variable_1="i_b_Na" variable_2="i_b_Na"/>
</connection>
<connection>
<map_components component_1="L_type_Ca_current" component_2="calcium_dynamics"/>
<map_variables variable_1="Ca_o" variable_2="Ca_o"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
<map_variables variable_1="d" variable_2="d"/>
<map_variables variable_1="i_CaL" variable_2="i_CaL"/>
</connection>
<connection>
<map_components component_1="calcium_pump_current" component_2="calcium_dynamics"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
<map_variables variable_1="i_p_Ca" variable_2="i_p_Ca"/>
</connection>
<connection>
<map_components component_1="calcium_background_current" component_2="calcium_dynamics"/>
<map_variables variable_1="i_b_Ca" variable_2="i_b_Ca"/>
</connection>
<connection>
<map_components component_1="sodium_potassium_pump_current" component_2="potassium_dynamics"/>
<map_variables variable_1="i_NaK" variable_2="i_NaK"/>
<map_variables variable_1="K_o" variable_2="K_o"/>
</connection>
<connection>
<map_components component_1="sodium_potassium_pump_current" component_2="sodium_dynamics"/>
<map_variables variable_1="i_NaK" variable_2="i_NaK"/>
<map_variables variable_1="Na_i" variable_2="Na_i"/>
</connection>
<connection>
<map_components component_1="sodium_calcium_exchanger_current" component_2="calcium_dynamics"/>
<map_variables variable_1="i_NaCa" variable_2="i_NaCa"/>
<map_variables variable_1="Ca_i" variable_2="Ca_i"/>
<map_variables variable_1="Ca_o" variable_2="Ca_o"/>
</connection>
<connection>
<map_components component_1="sodium_calcium_exchanger_current" component_2="sodium_dynamics"/>
<map_variables variable_1="i_NaCa" variable_2="i_NaCa"/>
<map_variables variable_1="Na_i" variable_2="Na_i"/>
<map_variables variable_1="Na_o" variable_2="Na_o"/>
</connection>
<connection>
<map_components component_1="rapid_time_dependent_potassium_current" component_2="rapid_time_dependent_potassium_current_Xr1_gate"/>
<map_variables variable_1="Xr1" variable_2="Xr1"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
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<title xmlns="http://cellml.org/tmp-documentation">A Model For Human Ventricular Tissue</title>
<author xmlns="http://cellml.org/tmp-documentation">
<firstname xmlns="http://cellml.org/tmp-documentation">Catherine</firstname>
<surname xmlns="http://cellml.org/tmp-documentation">Lloyd</surname>
<affiliation xmlns="http://cellml.org/tmp-documentation">
<shortaffil xmlns="http://cellml.org/tmp-documentation">Auckland Bioengineering Institute, University of Auckland</shortaffil>
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<title xmlns="http://cellml.org/tmp-documentation">Model Status</title>
<para xmlns="http://cellml.org/tmp-documentation">
This variant of the model was created by Penny Noble of Oxford University, and represents the parameters given for the endocardial cell variant in Ten Tusscher et al. 2004. A stimulus protocol component has been added to the model to allow simulation of trains of action potentials. This file is known to run in OpenCell and COR to recreate the published results. The units have been checked and they are consistent.
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<title xmlns="http://cellml.org/tmp-documentation">Model Structure</title>
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ABSTRACT: The experimental and clinical possibilities for studying cardiac arrhythmias in human ventricular myocardium are very limited. Therefore, the use of alternative methods such as computer simulations is of great importance. In this article we introduce a mathematical model of the action potential of human ventricular cells that, while including a high level of electrophysiological detail, is computationally cost-effective enough to be applied in large-scale spatial simulations for the study of reentrant arrhythmias. The model is based on recent experimental data on most of the major ionic currents: the fast sodium, L-type calcium, transient outward, rapid and slow delayed rectifier, and inward rectifier currents. The model includes a basic calcium dynamics, allowing for the realistic modeling of calcium transients, calcium current inactivation, and the contraction staircase. We are able to reproduce human epicardial, endocardial, and M cell action potentials and show that differences can be explained by differences in the transient outward and slow delayed rectifier currents. Our model reproduces the experimentally observed data on action potential duration restitution, which is an important characteristic for reentrant arrhythmias. The conduction velocity restitution of our model is broader than in other models and agrees better with available data. Finally, we model the dynamics of spiral wave rotation in a two-dimensional sheet of human ventricular tissue and show that the spiral wave follows a complex meandering pattern and has a period of 265 ms. We conclude that the proposed model reproduces a variety of electrophysiological behaviors and provides a basis for studies of reentrant arrhythmias in human ventricular tissue.
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The original paper reference is cited below:
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<para xmlns="http://cellml.org/tmp-documentation">
A model for human ventricular tissue, K.H.W.J. ten Tusscher, D. Noble, P.J. Noble, and A.V. Panfilov, 2004,
<emphasis xmlns="http://cellml.org/tmp-documentation">American Journal of Physiology</emphasis>
, 286, H1573-H1589. <ulink xmlns="http://cellml.org/tmp-documentation" url="http://www.ncbi.nlm.nih.gov/pubmed/14656705">PubMed ID: 14656705</ulink>
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<title xmlns="http://cellml.org/tmp-documentation">cell diagram</title>
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<caption xmlns="http://cellml.org/tmp-documentation">A schematic diagram of the Ten Tusscher <emphasis xmlns="http://cellml.org/tmp-documentation">et al.</emphasis> 2004 mathematical model of the human ventricular myocyte.</caption>
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