- Author:
- Michael Clerx <michael.clerx@cs.ox.ac.uk>
- Date:
- 2020-10-15 17:17:25+01:00
- Desc:
- Fix to pdf
- Permanent Source URI:
- https://models.cellml.org/workspace/604/rawfile/de5a4e600b57c8b9b0bd477695648c82351bc6dd/ten_tusscher_model_2006_m.cellml
<?xml version='1.0'?>
<!--
This CellML file was generated on 05/11/2007 at 17:03:45 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_panfilov_2006_M_cell" name="tentusscher_panfilov_2006_M_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="-85.423" 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="0.0165" 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="0.473" 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="0.098" 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="0.0174" 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="0.00165" 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="0.749" 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="0.6788" 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="3.288e-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="0.7026" 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="0.9526" 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="0.9942" 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="0.294" 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="0.999998" 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">20</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">85</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<power/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">45</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="millivolt_square">320</cn>
</apply>
</apply>
</apply>
<apply>
<divide/>
<cn cellml:units="millisecond">5</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">20</cn>
</apply>
<cn cellml:units="millivolt">5</cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond">3</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="2.347e-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="0.000153" name="Ca_i" public_interface="out" units="millimolar"/>
<variable initial_value="2" name="Ca_o" public_interface="out" units="millimolar"/>
<variable initial_value="4.272" name="Ca_SR" units="millimolar"/>
<variable initial_value="0.00042" 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="0.8978" 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="10.132" 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="138.52" 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>
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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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<firstname xmlns="http://cellml.org/tmp-documentation">Noble</firstname>
<surname xmlns="http://cellml.org/tmp-documentation">Penny</surname>
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<title xmlns="http://cellml.org/tmp-documentation">Model Status</title>
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This is the M-CELL VARIANT of the model. This model was created by Penny Noble of Oxford University and is known to run 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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<title xmlns="http://cellml.org/tmp-documentation">Model Structure</title>
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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:type xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
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<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">Corrections to model name and stimulus current to enable running in COR.</rdf:value>
<cmeta:modifier xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#a935f454-9e1b-4040-8871-bf8bf7a68b3b" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
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<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2006-09-00 00:00</dcterms:W3CDTF>
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<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2008-05-14T00:00:00+00:00</dcterms:W3CDTF>
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<bqs:Pubmed_id xmlns:bqs="http://www.cellml.org/bqs/1.0#">16565318</bqs:Pubmed_id>
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<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#1cf69b20-de90-4f19-a673-169f6fdf475c">
<dcterms:W3CDTF xmlns:dcterms="http://purl.org/dc/terms/">2008-06-19T11:17:33+12:00</dcterms:W3CDTF>
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<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:resource="rdf:#fb9e7106-ef4a-4116-9fe3-00087b0a59cd" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
<rdf:value xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">The 2006 model is based on earlier ten Tusscher models, and incorporates recent experimental restitution data, an improved description of intracellular calcium dynamics - including subspace calcium dynamics which control L-type calcium current and calcium-induced calcium release (CICR,) by means of modelling CICR with a four-state Markov model for the ryanodine receptor - and incorporation of both fast and slow voltage-gated inactivation of the L-type calcium current.
This is the M-CELL VARIANT of the model. This model was created by Penny Noble of Oxford University and is known to run in COR and PCEnv.</rdf:value>
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<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Alternans and spiral breakup in a human ventricular tissue model.</dc:title>
<bqs:volume xmlns:bqs="http://www.cellml.org/bqs/1.0#">291</bqs:volume>
<bqs:first_page xmlns:bqs="http://www.cellml.org/bqs/1.0#">1088</bqs:first_page>
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<bqs:last_page xmlns:bqs="http://www.cellml.org/bqs/1.0#">1100</bqs:last_page>
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<vCard:EMAIL xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:resource="rdf:#972771a8-4a1e-42f7-99f4-38fa5965ec4a" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"/>
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<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#cb269275-0222-4565-9e0d-307e4ac3ebf8">
<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">James</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Lawson</vCard:Family>
<vCard:Other xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Richard</vCard:Other>
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<rdf:Description xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" rdf:about="rdf:#fb9e7106-ef4a-4116-9fe3-00087b0a59cd">
<vCard:FN xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Penny Noble</vCard:FN>
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<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">AV</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Panfilov</vCard:Family>
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<vCard:Given xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Penny</vCard:Given>
<vCard:Family xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Noble</vCard:Family>
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