- Author:
- Michael Clerx <michael.clerx@cs.ox.ac.uk>
- Date:
- 2020-10-15 14:07:04+01:00
- Desc:
- Added pdf explaining the unit changes, and how the concentration equations were derived.
- Permanent Source URI:
- http://models.cellml.org/workspace/604/rawfile/18404eb423a18da1ea892611d0a4ff8f129ad8fb/ten_tusscher_model_2006_endo.cellml
<?xml version='1.0'?>
<!--
This CellML file was generated on 21/05/2008 at 15:15:33 using:
COR (0.9.31.955)
Copyright 2002-2008 Dr Alan Garny
http://COR.physiol.ox.ac.uk/ - COR@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.CellML.org/
-->
<model cmeta:id="tentusscher_panfilov_2006_endo_cell" name="tentusscher_panfilov_2006_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="per_millimolar_per_millisecond">
<unit exponent="-1" units="millimolar"/>
<unit exponent="-1" prefix="milli" units="second"/>
</units>
<units name="per_millimolar2_per_millisecond">
<unit exponent="-2" 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 name="membrane">
<variable initial_value="-86.709" 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 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 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="dimensionless"/>
<variable name="beta_K1" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_K1</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">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="dimensionless">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>
<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>
<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 name="rapid_time_dependent_potassium_current">
<variable name="i_Kr" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="0.153" 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 name="rapid_time_dependent_potassium_current_Xr1_gate">
<variable initial_value="0.00448" 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 name="rapid_time_dependent_potassium_current_Xr2_gate">
<variable initial_value="0.476" 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 name="slow_time_dependent_potassium_current">
<variable name="i_Ks" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="0.392" 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 name="slow_time_dependent_potassium_current_Xs_gate">
<variable initial_value="0.0087" 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">1400</cn>
<apply>
<root/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">5</cn>
<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">35</cn>
</apply>
<cn cellml:units="millivolt">15</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_xs</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">1</cn>
<ci>alpha_xs</ci>
<ci>beta_xs</ci>
</apply>
<cn cellml:units="millisecond">80</cn>
</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 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 name="fast_sodium_current_m_gate">
<variable initial_value="0.00155" 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 name="fast_sodium_current_h_gate">
<variable initial_value="0.7573" 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 name="fast_sodium_current_j_gate">
<variable initial_value="0.7225" 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 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 name="L_type_Ca_current">
<variable name="i_CaL" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="0.0398" name="g_CaL" units="litre_per_farad_second"/>
<variable name="Ca_o" public_interface="in" units="millimolar"/>
<variable name="Ca_ss" 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="f2" private_interface="in" units="dimensionless"/>
<variable name="fCass" 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>f2</ci>
<ci>fCass</ci>
<cn cellml:units="dimensionless">4</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">15</cn>
</apply>
<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/>
<cn cellml:units="dimensionless">0.25</cn>
<ci>Ca_ss</ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">15</cn>
</apply>
<ci>F</ci>
</apply>
<apply>
<times/>
<ci>R</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
</apply>
<ci>Ca_o</ci>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">15</cn>
</apply>
<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 name="L_type_Ca_current_d_gate">
<variable initial_value="3.164e-5" 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">8</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 name="L_type_Ca_current_f_gate">
<variable initial_value="0.8009" 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">1102.5</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">225</cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="millisecond">200</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<cn cellml:units="millivolt">13</cn>
<ci>V</ci>
</apply>
<cn cellml:units="millivolt">10</cn>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="millisecond">180</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">10</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">20</cn>
</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 name="L_type_Ca_current_f2_gate">
<variable initial_value="0.9778" name="f2" public_interface="out" units="dimensionless"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="f2_inf" units="dimensionless"/>
<variable name="tau_f2" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>f2_inf</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.67</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">7</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.33</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_f2</ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="millisecond">562</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>
<apply>
<divide/>
<cn cellml:units="millisecond">31</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>
<divide/>
<cn cellml:units="millisecond">80</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">10</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>f2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>f2_inf</ci>
<ci>f2</ci>
</apply>
<ci>tau_f2</ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_Ca_current_fCass_gate">
<variable initial_value="0.9953" name="fCass" public_interface="out" units="dimensionless"/>
<variable name="Ca_ss" public_interface="in" units="millimolar"/>
<variable name="V" public_interface="in" units="millivolt"/>
<variable name="time" public_interface="in" units="millisecond"/>
<variable name="fCass_inf" units="dimensionless"/>
<variable name="tau_fCass" units="millisecond"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>fCass_inf</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless">0.6</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_ss</ci>
<cn cellml:units="millimolar">0.05</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless">0.4</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_fCass</ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="millisecond">80</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>Ca_ss</ci>
<cn cellml:units="millimolar">0.05</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">2</cn>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>fCass</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>fCass_inf</ci>
<ci>fCass</ci>
</apply>
<ci>tau_fCass</ci>
</apply>
</apply>
</math>
</component>
<component 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 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 name="transient_outward_current_s_gate">
<variable initial_value="0.3212" 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 name="transient_outward_current_r_gate">
<variable initial_value="2.235e-8" 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 name="sodium_potassium_pump_current">
<variable name="i_NaK" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="2.724" 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 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 name="calcium_pump_current">
<variable name="i_p_Ca" public_interface="out" units="picoA_per_picoF"/>
<variable initial_value="0.1238" 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 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 name="calcium_dynamics">
<variable initial_value="0.00013" name="Ca_i" public_interface="out" units="millimolar"/>
<variable initial_value="2" name="Ca_o" public_interface="out" units="millimolar"/>
<variable initial_value="3.715" name="Ca_SR" units="millimolar"/>
<variable initial_value="0.00036" name="Ca_ss" public_interface="out" 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 name="i_xfer" units="millimolar_per_millisecond"/>
<variable name="O" units="dimensionless"/>
<variable initial_value="0.9068" name="R_prime" units="dimensionless"/>
<variable name="k1" units="per_millimolar2_per_millisecond"/>
<variable name="k2" units="per_millimolar_per_millisecond"/>
<variable initial_value="0.15" name="k1_prime" units="per_millimolar2_per_millisecond"/>
<variable initial_value="0.045" name="k2_prime" units="per_millimolar_per_millisecond"/>
<variable initial_value="0.06" name="k3" units="per_millisecond"/>
<variable initial_value="0.005" name="k4" units="per_millisecond"/>
<variable initial_value="1.5" name="EC" units="millimolar"/>
<variable initial_value="2.5" name="max_sr" units="dimensionless"/>
<variable initial_value="1" name="min_sr" units="dimensionless"/>
<variable name="kcasr" units="dimensionless"/>
<variable initial_value="0.102" name="V_rel" units="per_millisecond"/>
<variable initial_value="0.0038" name="V_xfer" units="per_millisecond"/>
<variable initial_value="0.00025" name="K_up" units="millimolar"/>
<variable initial_value="0.00036" name="V_leak" units="per_millisecond"/>
<variable initial_value="0.006375" 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="ddt_Ca_ss_total" units="millimolar_per_millisecond"/>
<variable name="f_JCa_i_free" units="dimensionless"/>
<variable name="f_JCa_sr_free" units="dimensionless"/>
<variable name="f_JCa_ss_free" units="dimensionless"/>
<variable initial_value="0.2" 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="0.4" name="Buf_ss" units="millimolar"/>
<variable initial_value="0.00025" name="K_buf_ss" units="millimolar"/>
<variable initial_value="1094" name="V_sr" units="micrometre3"/>
<variable initial_value="54.68" name="V_ss" 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"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_rel</ci>
<apply>
<times/>
<ci>V_rel</ci>
<ci>O</ci>
<apply>
<minus/>
<ci>Ca_SR</ci>
<ci>Ca_ss</ci>
</apply>
</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>i_xfer</ci>
<apply>
<times/>
<ci>V_xfer</ci>
<apply>
<minus/>
<ci>Ca_ss</ci>
<ci>Ca_i</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>O</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k1</ci>
<apply>
<power/>
<ci>Ca_ss</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>R_prime</ci>
</apply>
<apply>
<plus/>
<ci>k3</ci>
<apply>
<times/>
<ci>k1</ci>
<apply>
<power/>
<ci>Ca_ss</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>R_prime</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<ci>k2</ci>
</apply>
<ci>Ca_ss</ci>
<ci>R_prime</ci>
</apply>
<apply>
<times/>
<ci>k4</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>R_prime</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>k1</ci>
<apply>
<divide/>
<ci>k1_prime</ci>
<ci>kcasr</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>k2</ci>
<apply>
<times/>
<ci>k2_prime</ci>
<ci>kcasr</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>kcasr</ci>
<apply>
<minus/>
<ci>max_sr</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>max_sr</ci>
<ci>min_sr</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<apply>
<divide/>
<ci>EC</ci>
<ci>Ca_SR</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ddt_Ca_i_total</ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<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>
<ci>Cm</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V_c</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>i_leak</ci>
<ci>i_up</ci>
</apply>
<ci>V_sr</ci>
</apply>
<ci>V_c</ci>
</apply>
<ci>i_xfer</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>ddt_Ca_sr_total</ci>
<apply>
<minus/>
<ci>i_up</ci>
<apply>
<plus/>
<ci>i_rel</ci>
<ci>i_leak</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ddt_Ca_ss_total</ci>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>i_CaL</ci>
</apply>
<ci>Cm</ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>V_ss</ci>
<ci>F</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>i_rel</ci>
<ci>V_sr</ci>
</apply>
<ci>V_ss</ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>i_xfer</ci>
<ci>V_c</ci>
</apply>
<ci>V_ss</ci>
</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/>
<ci>f_JCa_ss_free</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<times/>
<ci>Buf_ss</ci>
<ci>K_buf_ss</ci>
</apply>
<apply>
<power/>
<apply>
<plus/>
<ci>Ca_ss</ci>
<ci>K_buf_ss</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>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>Ca_ss</ci>
</apply>
<apply>
<times/>
<ci>ddt_Ca_ss_total</ci>
<ci>f_JCa_ss_free</ci>
</apply>
</apply>
</math>
</component>
<component name="sodium_dynamics">
<variable initial_value="10.355" 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>
<times/>
<apply>
<divide/>
<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>
<apply>
<times/>
<ci>V_c</ci>
<ci>F</ci>
</apply>
</apply>
<ci>Cm</ci>
</apply>
</apply>
</math>
</component>
<component name="potassium_dynamics">
<variable initial_value="138.4" 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>
<times/>
<apply>
<divide/>
<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>
<apply>
<times/>
<ci>V_c</ci>
<ci>F</ci>
</apply>
</apply>
<ci>Cm</ci>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
<component_ref component="fast_sodium_current_j_gate"/>
</component_ref>
<component_ref component="L_type_Ca_current">
<component_ref component="L_type_Ca_current_d_gate"/>
<component_ref component="L_type_Ca_current_f_gate"/>
<component_ref component="L_type_Ca_current_f2_gate"/>
<component_ref component="L_type_Ca_current_fCass_gate"/>
</component_ref>
<component_ref component="inward_rectifier_potassium_current"/>
<component_ref component="rapid_time_dependent_potassium_current">
<component_ref component="rapid_time_dependent_potassium_current_Xr1_gate"/>
<component_ref 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 component="sodium_background_current"/>
<component_ref component="calcium_background_current"/>
<component_ref component="transient_outward_current">
<component_ref component="transient_outward_current_s_gate"/>
<component_ref component="transient_outward_current_r_gate"/>
</component_ref>
<component_ref component="sodium_potassium_pump_current"/>
<component_ref component="sodium_calcium_exchanger_current"/>
<component_ref component="calcium_pump_current"/>
<component_ref component="potassium_pump_current"/>
<component_ref component="calcium_dynamics"/>
<component_ref component="sodium_dynamics"/>
<component_ref component="potassium_dynamics"/>
<component_ref component="reversal_potentials"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
<component_ref component="fast_sodium_current_j_gate"/>
</component_ref>
<component_ref component="L_type_Ca_current">
<component_ref component="L_type_Ca_current_d_gate"/>
<component_ref component="L_type_Ca_current_f_gate"/>
<component_ref component="L_type_Ca_current_f2_gate"/>
<component_ref component="L_type_Ca_current_fCass_gate"/>
</component_ref>
<component_ref component="rapid_time_dependent_potassium_current">
<component_ref component="rapid_time_dependent_potassium_current_Xr1_gate"/>
<component_ref 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 component="transient_outward_current">
<component_ref component="transient_outward_current_s_gate"/>
<component_ref 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"/>
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<title xmlns="http://cellml.org/tmp-documentation">Alternans and spiral breakup in a human ventricular tissue model</title>
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This is the ENDOCARDIAL CELL VARIANT of the model. This model was created by Penny Noble of Oxford University and is known to read in COR and PCEnv. A stimulus protocol has been added that allows the model to simulate multiple action potentials at 1Hz.
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ABSTRACT: Ventricular fibrillation (VF) is one of the main causes of death in the Western world. According to one hypothesis, the chaotic excitation dynamics during VF are the result of dynamical instabilities in action potential duration (APD) the occurrence of which requires that the slope of the APD restitution curve exceeds 1. Other factors such as electrotonic coupling and cardiac memory also determine whether these instabilities can develop. In this paper we study the conditions for alternans and spiral breakup in human cardiac tissue. Therefore, we develop a new version of our human ventricular cell model, which is based on recent experimental measurements of human APD restitution and includes a more extensive description of intracellular calcium dynamics. We apply this model to study the conditions for electrical instability in single cells, for reentrant waves in a ring of cells, and for reentry in two-dimensional sheets of ventricular tissue. We show that an important determinant for the onset of instability is the recovery dynamics of the fast sodium current. Slower sodium current recovery leads to longer periods of spiral wave rotation and more gradual conduction velocity restitution, both of which suppress restitution-mediated instability. As a result, maximum restitution slopes considerably exceeding 1 (up to 1.5) may be necessary for electrical instability to occur. Although slopes necessary for the onset of instabilities found in our study exceed 1, they are within the range of experimentally measured slopes. Therefore, we conclude that steep APD restitution-mediated instability is a potential mechanism for VF in the human heart.
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The original paper reference is cited below:
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Alternans and spiral breakup in a human ventricular tissue model, K.H.W.J. ten Tusscher, A.V. Panfilov, Sep 2006,
<emphasis xmlns="http://cellml.org/tmp-documentation">American Journal of Physiology, Heart and Circulatory Physiology</emphasis>, 291 3, H1088-1100. <ulink xmlns="http://cellml.org/tmp-documentation" url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=16565318&dopt=Abstract">PubMed ID: 16565318</ulink>
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<caption xmlns="http://cellml.org/tmp-documentation">A schematic diagram describing the ion movement across the cell surface membrane and the sarcoplasmic reticulum, which are described by the Ten Tusscher <emphasis xmlns="http://cellml.org/tmp-documentation">et al.</emphasis> 2006 mathematical model of the human ventricular myocyte.</caption>
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<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">Added simulation metadata to allow simulation for 5 seconds.
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<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xml:lang="en" xmlns:xml="http://www.w3.org/XML/1998/namespace">Corrections to model name and stimulus current to enable running in COR.</rdf:value>
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