<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 08/09/2017 at 12:34:21 using:
COR (0.9.31.1409)
Copyright 2002-2017 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk
CellML 1.0 was used to generate this model
http://www.cellml.org/
-->
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<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Slow Conduction in the Border Zones of Patchy Fibrosis Stabilizes the Drivers for Atrial Fibrillation: Insights from Multi-Scale Human Atrial Modeling
</title>
<author>
<firstname>Oleg</firstname>
<surname>Aslanidi</surname>
<affiliation>
<shortaffil>King's College London</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML version of the model has been checked in both PCEnv and COR and it runs to recreate the published results. The units have been checked and they balance. We would like to thank the original model author Oleg Aslanidi for his help in the final stages of model curation.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: TBC
</para>
<para>
The original paper is available at: <ulink url="http://journal.frontiersin.org/article/10.3389/fphys.2016.00474/full">http://journal.frontiersin.org/article/10.3389/fphys.2016.00474/full</ulink>
</para>
</sect1>
</article>
</documentation>
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<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">43.1</cn>
</apply>
<cn cellml:units="millivolt">5.3</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_oi</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">15</cn>
<apply>
<plus/>
<ci>alpha_oi</ci>
<ci>beta_oi</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>oi</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>oi_inf</ci>
<ci>oi</ci>
</apply>
<ci>tau_oi</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="ultra_rapid_K_current">
<variable name="i_Kur" units="picoA_per_picoF" public_interface="out"/>
<variable name="g_Kur" units="nanoS_per_picoF" initial_value="0.6"/>
<variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="E_K" units="millivolt" public_interface="in"/>
<variable name="ua" units="dimensionless" private_interface="in"/>
<variable name="ui" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_Kur</ci>
<apply>
<times/>
<apply>
<plus/>
<apply>
<times/>
<ci>g_Kur</ci>
<cn cellml:units="dimensionless">0.005</cn>
</apply>
<apply>
<divide/>
<cn cellml:units="nanoS_per_picoF">0.05</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">15</cn>
</apply>
</apply>
<cn cellml:units="millivolt">13</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<power/>
<ci>ua</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>ui</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_K</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="ultra_rapid_K_current_ua_gate">
<variable name="ua" units="dimensionless" initial_value="0.9933" public_interface="out"/>
<variable name="alpha_ua" units="per_millisecond"/>
<variable name="beta_ua" units="per_millisecond"/>
<variable name="tau_ua" units="millisecond"/>
<variable name="ua_inf" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_ua</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">0.65</cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">10</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">8.5</cn>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">30</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">59</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_ua</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">0.65</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">2.5</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">82</cn>
</apply>
<cn cellml:units="millivolt">17</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ua_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">33.3</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">9.6</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_ua</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>alpha_ua</ci>
<ci>beta_ua</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ua</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>ua_inf</ci>
<ci>ua</ci>
</apply>
<ci>tau_ua</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="ultra_rapid_K_current_ui_gate">
<variable name="ui" units="dimensionless" initial_value="0.0999" public_interface="out"/>
<variable name="alpha_ui" units="per_millisecond"/>
<variable name="beta_ui" units="per_millisecond"/>
<variable name="tau_ui" units="millisecond"/>
<variable name="ui_inf" units="dimensionless"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>alpha_ui</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">21</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">185</cn>
</apply>
<cn cellml:units="millivolt">28</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_ui</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">1</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<ci>V</ci>
<cn cellml:units="millivolt">158</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">16</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>ui_inf</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">99.45</cn>
</apply>
<cn cellml:units="millivolt">27.48</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_ui</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">5</cn>
<apply>
<plus/>
<ci>alpha_ui</ci>
<ci>beta_ui</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>ui</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>ui_inf</ci>
<ci>ui</ci>
</apply>
<ci>tau_ui</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="inward_rectifier">
<variable name="i_K1" units="picoA_per_picoF" public_interface="out"/>
<variable name="g_K1" units="nanoS_per_picoF" initial_value="0.03"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_K1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>g_K1</ci>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">86.75</cn>
</apply>
</apply>
<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">20</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="background_currents">
<variable name="i_b_Na" units="picoA_per_picoF" public_interface="out"/>
<variable name="g_b_Na" units="nanoS_per_picoF" initial_value="0.00607"/>
<variable name="E_Na" units="millivolt" public_interface="out"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="RToF" units="millivolt" public_interface="in"/>
<variable name="Na_i" units="millimolar" public_interface="in"/>
<variable name="Na_c" units="millimolar" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_Na</ci>
<apply>
<times/>
<ci>RToF</ci>
<apply>
<ln/>
<apply>
<divide/>
<ci>Na_c</ci>
<ci>Na_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_b_Na</ci>
<apply>
<times/>
<ci>g_b_Na</ci>
<apply>
<minus/>
<ci>V</ci>
<ci>E_Na</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="sodium_potassium_pump">
<variable name="i_NaK" units="picoA_per_picoF" public_interface="out"/>
<variable name="k_NaK_K" units="millimolar" initial_value="1"/>
<variable name="k_NaK_Na" units="millimolar" initial_value="11"/>
<variable name="i_NaK_max" units="picoA_per_picoF" initial_value="2.002"/>
<variable name="V_rev" units="millivolt" initial_value="-150"/>
<variable name="B" units="millivolt" initial_value="-200"/>
<variable name="K_c" units="millimolar" public_interface="in"/>
<variable name="Na_i" units="millimolar" public_interface="in"/>
<variable name="V" units="millivolt" public_interface="in"/>
<variable name="time" units="millisecond" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_NaK</ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>i_NaK_max</ci>
<ci>K_c</ci>
</apply>
<apply>
<plus/>
<ci>K_c</ci>
<ci>k_NaK_K</ci>
</apply>
</apply>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>Na_i</ci>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
<apply>
<power/>
<ci>k_NaK_Na</ci>
<cn cellml:units="dimensionless">1.5</cn>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>V_rev</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>V</ci>
<ci>B</ci>
</apply>
</apply>
</apply>
</math>
</component>
<group xmlns="http://www.cellml.org/cellml/1.0#">
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="transient_outward_K_current">
<component_ref component="transient_outward_K_current_oa_gate"/>
<component_ref component="transient_outward_K_current_oi_gate"/>
</component_ref>
<component_ref component="ultra_rapid_K_current">
<component_ref component="ultra_rapid_K_current_ua_gate"/>
<component_ref component="ultra_rapid_K_current_ui_gate"/>
</component_ref>
<component_ref component="non_specific_current"/>
<component_ref component="inward_rectifier"/>
<component_ref component="background_currents"/>
<component_ref component="sodium_potassium_pump"/>
</component_ref>
</group>
<group xmlns="http://www.cellml.org/cellml/1.0#">
<relationship_ref relationship="encapsulation"/>
<component_ref component="transient_outward_K_current">
<component_ref component="transient_outward_K_current_oa_gate"/>
<component_ref component="transient_outward_K_current_oi_gate"/>
</component_ref>
<component_ref component="ultra_rapid_K_current">
<component_ref component="ultra_rapid_K_current_ua_gate"/>
<component_ref component="ultra_rapid_K_current_ui_gate"/>
</component_ref>
</group>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="transient_outward_K_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="ultra_rapid_K_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="non_specific_current" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="inward_rectifier" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="background_currents" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="sodium_potassium_pump" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="transient_outward_K_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="RToF" variable_2="RToF"/>
<map_variables variable_1="K_i" variable_2="K_i"/>
<map_variables variable_1="K_c" variable_2="K_c"/>
<map_variables variable_1="i_to" variable_2="i_to"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="ultra_rapid_K_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_Kur" variable_2="i_Kur"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="non_specific_current"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_ns" variable_2="i_ns"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="inward_rectifier"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="i_K1" variable_2="i_K1"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="background_currents"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="Na_i" variable_2="Na_i"/>
<map_variables variable_1="Na_c" variable_2="Na_c"/>
<map_variables variable_1="RToF" variable_2="RToF"/>
<map_variables variable_1="i_b_Na" variable_2="i_b_Na"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="membrane" component_2="sodium_potassium_pump"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="Na_i" variable_2="Na_i"/>
<map_variables variable_1="K_c" variable_2="K_c"/>
<map_variables variable_1="i_NaK" variable_2="i_NaK"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="transient_outward_K_current" component_2="ultra_rapid_K_current"/>
<map_variables variable_1="E_K" variable_2="E_K"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="transient_outward_K_current" component_2="transient_outward_K_current_oa_gate"/>
<map_variables variable_1="oa" variable_2="oa"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="transient_outward_K_current" component_2="transient_outward_K_current_oi_gate"/>
<map_variables variable_1="oi" variable_2="oi"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="ultra_rapid_K_current" component_2="ultra_rapid_K_current_ua_gate"/>
<map_variables variable_1="ua" variable_2="ua"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="ultra_rapid_K_current" component_2="ultra_rapid_K_current_ui_gate"/>
<map_variables variable_1="ui" variable_2="ui"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
</model>
