- Author:
- GIPL\mv12 <marta.varela@kcl.ac.uk>
- Date:
- 2017-09-07 15:16:18+01:00
- Desc:
- no message
- Permanent Source URI:
- https://models.cellml.org/workspace/4be/rawfile/545655a249edec71c6b1de2d57780acf4dbfbd3c/Morgan atrial fbroblast 2016.cellml
<?xml version="1.0" encoding="utf-8"?>
<!--
This CellML file was generated on 07/09/2017 at 14:37:47 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/
-->
<model xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" name="morgan_atrial_fibroblast_2016" cmeta:id="morgan_atrial_fibroblast_2016" 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#">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Optimal velocity and safety of discontinuous conduction through the heterogeneous Purkinje-ventricular junction
</title>
<author>
<firstname>Penny</firstname>
<surname>Noble</surname>
<affiliation>
<shortaffil>University of Oxford</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: Experimental evidence suggests that regional differences in action potential (AP) morphology can provide a substrate for initiation and maintenance of reentrant arrhythmias in the right atrium (RA), but the relationships between the complex electrophysiological and anatomical organization of the RA and the genesis of reentry are unclear. In this study, a biophysically detailed three-dimensional computer model of the right atrial tissue was constructed to study the role of tissue heterogeneity and anisotropy in arrhythmogenesis. The model of Lindblad et al. for a rabbit atrial cell was modified to incorporate experimental data on regional differences in several ionic currents (primarily, I(Na), I(CaL), I(K1), I(to), and I(sus)) between the crista terminalis and pectinate muscle cells. The modified model was validated by its ability to reproduce the AP properties measured experimentally. The anatomical model of the rabbit RA (including tissue geometry and fiber orientation) was based on a recent histological reconstruction. Simulations with the resultant electrophysiologically and anatomically detailed three-dimensional model show that complex organization of the RA tissue causes breakdown of regular AP conduction patterns at high pacing rates (>11.75 Hz): as the AP in the crista terminalis cells is longer, and electrotonic coupling transverse to fibers of the crista terminalis is weak, high-frequency pacing at the border between the crista terminalis and pectinate muscles results in a unidirectional conduction block toward the crista terminalis and generation of reentry. Contributions of the tissue heterogeneity and anisotropy to reentry initiation mechanisms are quantified by measuring action potential duration (APD) gradients at the border between the crista terminalis and pectinate muscles: the APD gradients are high in areas where both heterogeneity and anisotropy are high, such that intrinsic APD differences are not diminished by electrotonic interactions. Thus, our detailed computer model reconstructs complex electrical activity in the RA, and provides new insights into the mechanisms of transition from focal atrial tachycardia into reentry.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Mechanisms of transition from normal to reentrant electrical activity in a model of rabbit atrial tissue: interaction of tissue heterogeneity and anisotropy, Oleg V. Aslanidi, Mark R. Boyett, Halina Dobrzynski, and Henggui Zhang, 2009, <emphasis>Biophysical Journal</emphasis>, 96, 798-817. <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=19186122&dopt=Abstract">PubMed ID: 19186122</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>schematic diagram</title>
</objectinfo>
<imagedata fileref="aslanidi_2009b.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram describing the atrial cell model.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"><rdf:Description rdf:nodeID="n1"><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Bag"/></rdf:type><rdf:_1 xml:lang="en">atrial cell</rdf:_1><rdf:_2 xml:lang="en">cardiac</rdf:_2><rdf:_3 xml:lang="en">electrophysiology</rdf:_3></rdf:Description><rdf:Description rdf:nodeID="n2"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">V</Other><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">O</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Aslanidi</Family></rdf:Description><rdf:Description rdf:nodeID="n3"><FN xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine Lloyd</FN></rdf:Description><rdf:Description rdf:nodeID="n4"><maximumStepSize xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">.1</maximumStepSize><pointDensity xmlns="http://www.cellml.org/metadata/simulation/1.0#nonstandard-" xml:lang="en">10000</pointDensity><endingValue xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">5</endingValue></rdf:Description><rdf:Description rdf:nodeID="n5"><rdf:type><rdf:Description rdf:about="http://www.example.org/foo/bar/bazfoo"/></rdf:type></rdf:Description><rdf:Description rdf:nodeID="n6"><Orgname xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">The University of Oxford</Orgname><Orgunit xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Department of Physiology, Anatomy and Genetics</Orgunit></rdf:Description><rdf:Description rdf:nodeID="n7"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n8"/></Person></rdf:Description><rdf:Description rdf:nodeID="n9"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n10"/></Person></rdf:Description><rdf:Description rdf:about=""><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n11"/></creator><created xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:nodeID="n12"/></created></rdf:Description><rdf:Description rdf:nodeID="n13"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n2"/></N></rdf:Description><rdf:Description rdf:nodeID="n11"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n14"/></N><EMAIL xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n15"/></EMAIL><ORG xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n6"/></ORG></rdf:Description><rdf:Description rdf:nodeID="n16"><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n3"/></creator><rdf:value xml:lang="en">
This is the CellML description of Aslanidi et al.'s mathematical
model of membrane action potentials in rabbit atrial cells
</rdf:value></rdf:Description><rdf:Description rdf:nodeID="n14"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Penny</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Noble</Family></rdf:Description><rdf:Description rdf:nodeID="n15"><rdf:type><rdf:Description rdf:about="http://imc.org/vCard/3.0#internet"/></rdf:type><rdf:value xml:lang="en">penny.noble@dpag.ox.ac.uk</rdf:value></rdf:Description><rdf:Description rdf:nodeID="n17"><Pubmed_id xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">19186122</Pubmed_id><JournalArticle xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n18"/></JournalArticle></rdf:Description><rdf:Description rdf:nodeID="n19"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n20"/></Person></rdf:Description><rdf:Description rdf:about="#aslanidi_atrial_model_2009"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
The Aslanidi et al. 2009 Model of Rabbit Atrial Cells
</title><cmeta:species xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xml:lang="en">Rabbit</cmeta:species><cmeta:bio_entity xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xml:lang="en">atrial cell</cmeta:bio_entity><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n17"/></reference><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n21"/></reference><cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#"><rdf:Description rdf:nodeID="n16"/></cmeta:comment><simulation xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n22"/></simulation></rdf:Description><rdf:Description rdf:nodeID="n23"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">H</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Dobrzynski</Family></rdf:Description><rdf:Description rdf:nodeID="n24"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Biophysical Journal</title></rdf:Description><rdf:Description rdf:nodeID="n25"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">J</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Li</Family></rdf:Description><rdf:Description rdf:nodeID="n8"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n23"/></N></rdf:Description><rdf:Description rdf:nodeID="n26"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n27"/></Person></rdf:Description><rdf:Description rdf:nodeID="n18"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
Mechanisms of transition from normal to reentrant electrical activity in a model of rabbit atrial tissue: interaction of tissue heterogeneity and anisotropy
</title><issued xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:nodeID="n28"/></issued><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n29"/></creator><volume xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">96</volume><first_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">798</first_page><last_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">817</last_page><Journal xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n24"/></Journal></rdf:Description><rdf:Description rdf:nodeID="n28"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2009-02</W3CDTF></rdf:Description><rdf:Description rdf:nodeID="n30"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">H</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Zhang</Family></rdf:Description><rdf:Description rdf:nodeID="n29"><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Seq"/></rdf:type><rdf:_5><rdf:Description rdf:nodeID="n9"/></rdf:_5><rdf:_4><rdf:Description rdf:nodeID="n26"/></rdf:_4><rdf:_1><rdf:Description rdf:nodeID="n31"/></rdf:_1><rdf:_2><rdf:Description rdf:nodeID="n19"/></rdf:_2><rdf:_3><rdf:Description rdf:nodeID="n7"/></rdf:_3></rdf:Description><rdf:Description rdf:nodeID="n21"><subject xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:nodeID="n32"/></subject></rdf:Description><rdf:Description rdf:nodeID="n20"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n33"/></N></rdf:Description><rdf:Description rdf:nodeID="n27"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n25"/></N></rdf:Description><rdf:Description rdf:nodeID="n31"><Person xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:nodeID="n13"/></Person></rdf:Description><rdf:Description rdf:nodeID="n32"><rdf:value><rdf:Description rdf:nodeID="n1"/></rdf:value><subject_type xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">keyword</subject_type></rdf:Description><rdf:Description rdf:nodeID="n34"><rdf:first><rdf:Description rdf:nodeID="n4"/></rdf:first><rdf:rest><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/></rdf:rest></rdf:Description><rdf:Description rdf:nodeID="n22"><boundIntervals xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n34"/></boundIntervals></rdf:Description><rdf:Description rdf:nodeID="n10"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:nodeID="n30"/></N></rdf:Description><rdf:Description rdf:nodeID="n33"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">R</Other><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">M</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Boyett</Family></rdf:Description><rdf:Description rdf:nodeID="n12"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2009-09-28</W3CDTF></rdf:Description></rdf:RDF> <units xmlns="http://www.cellml.org/cellml/1.0#" name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="per_millisecond">
<unit units="millisecond" exponent="-1"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="picoA">
<unit units="ampere" prefix="pico"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="picoF">
<unit units="farad" prefix="pico"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="picoA_per_picoF">
<unit units="ampere" prefix="pico"/>
<unit units="picoF" exponent="-1"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="nanoS">
<unit units="siemens" prefix="nano"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="nanoS_per_picoF">
<unit units="siemens" prefix="nano"/>
<unit units="picoF" exponent="-1"/>
</units>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="environment">
<variable name="time" units="millisecond" public_interface="out"/>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="membrane">
<variable name="V" units="millivolt" initial_value="-50" public_interface="out"/>
<variable name="RToF" units="millivolt" initial_value="26.54" public_interface="out"/>
<variable name="K_c" units="millimolar" initial_value="5.4" public_interface="out"/>
<variable name="K_i" units="millimolar" initial_value="139" public_interface="out"/>
<variable name="Na_c" units="millimolar" initial_value="140" public_interface="out"/>
<variable name="Na_i" units="millimolar" initial_value="11.2" public_interface="out"/>
<variable name="time" units="millisecond" public_interface="in"/>
<variable name="i_ns" units="picoA_per_picoF" public_interface="in"/>
<variable name="i_to" units="picoA_per_picoF" public_interface="in"/>
<variable name="i_K1" units="picoA_per_picoF" public_interface="in"/>
<variable name="i_Kur" units="picoA_per_picoF" public_interface="in"/>
<variable name="i_b_Na" units="picoA_per_picoF" public_interface="in"/>
<variable name="i_NaK" units="picoA_per_picoF" public_interface="in"/>
<variable name="i_Stim" units="picoA_per_picoF"/>
<variable name="stim_start" units="millisecond" initial_value="100"/>
<variable name="stim_end" units="millisecond" initial_value="10000"/>
<variable name="stim_period" units="millisecond" initial_value="500"/>
<variable name="stim_duration" units="millisecond" initial_value="2"/>
<variable name="stim_amplitude" units="picoA_per_picoF" initial_value="-100"/>
<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/>
<ci>time</ci>
<ci>stim_start</ci>
</apply>
<apply>
<leq/>
<ci>time</ci>
<ci>stim_end</ci>
</apply>
<apply>
<leq/>
<apply>
<minus/>
<apply>
<minus/>
<ci>time</ci>
<ci>stim_start</ci>
</apply>
<apply>
<times/>
<apply>
<floor/>
<apply>
<divide/>
<apply>
<minus/>
<ci>time</ci>
<ci>stim_start</ci>
</apply>
<ci>stim_period</ci>
</apply>
</apply>
<ci>stim_period</ci>
</apply>
</apply>
<ci>stim_duration</ci>
</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_ns</ci>
<ci>i_Kur</ci>
<ci>i_to</ci>
<ci>i_K1</ci>
<ci>i_b_Na</ci>
<ci>i_NaK</ci>
<ci>i_Stim</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="non_specific_current">
<variable name="i_ns" units="picoA_per_picoF" public_interface="out"/>
<variable name="g_ns" units="nanoS_per_picoF" initial_value="0.018"/>
<variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>i_ns</ci>
<apply>
<times/>
<ci>g_ns</ci>
<ci>V</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="transient_outward_K_current">
<variable name="i_to" units="picoA_per_picoF" public_interface="out"/>
<variable name="E_K" units="millivolt" public_interface="out"/>
<variable name="g_to" units="nanoS_per_picoF" initial_value="0.01652"/>
<variable name="time" units="millisecond" public_interface="in" private_interface="out"/>
<variable name="V" units="millivolt" public_interface="in" private_interface="out"/>
<variable name="RToF" units="millivolt" public_interface="in"/>
<variable name="K_c" units="millimolar" public_interface="in"/>
<variable name="K_i" units="millimolar" public_interface="in"/>
<variable name="oa" units="dimensionless" private_interface="in"/>
<variable name="oi" units="dimensionless" private_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>E_K</ci>
<apply>
<times/>
<ci>RToF</ci>
<apply>
<ln/>
<apply>
<divide/>
<ci>K_c</ci>
<ci>K_i</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>i_to</ci>
<apply>
<times/>
<ci>g_to</ci>
<apply>
<power/>
<ci>oa</ci>
<cn cellml:units="dimensionless">3</cn>
</apply>
<ci>oi</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="transient_outward_K_current_oa_gate">
<variable name="oa" units="dimensionless" initial_value="0.2488" public_interface="out"/>
<variable name="alpha_oa" units="per_millisecond"/>
<variable name="beta_oa" units="per_millisecond"/>
<variable name="tau_oa" units="millisecond"/>
<variable name="oa_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_oa</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_oa</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>oa_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">20.47</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">17.54</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>tau_oa</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">15</cn>
<apply>
<plus/>
<ci>alpha_oa</ci>
<ci>beta_oa</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>oa</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>oa_inf</ci>
<ci>oa</ci>
</apply>
<ci>tau_oa</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="transient_outward_K_current_oi_gate">
<variable name="oi" units="dimensionless" initial_value="0.1866" public_interface="out"/>
<variable name="alpha_oi" units="per_millisecond"/>
<variable name="beta_oi" units="per_millisecond"/>
<variable name="tau_oi" units="millisecond"/>
<variable name="oi_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_oi</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">18.53</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">113.7</cn>
</apply>
<cn cellml:units="millivolt">10.95</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>beta_oi</ci>
<apply>
<divide/>
<cn cellml:units="per_millisecond">1</cn>
<apply>
<plus/>
<cn cellml:units="dimensionless">35.56</cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci>V</ci>
<cn cellml:units="millivolt">1.26</cn>
</apply>
<apply>
<minus/>
<cn cellml:units="millivolt">7.44</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>oi_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">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>
