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/Bioelectrics/Bidomain/jrw-1998.xml

http://github.com/xyan075/examples
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   1<?xml version="1.0" encoding="iso-8859-1"?>
   2
   3
   4<!--  FILE :  jafri_rice_winslow_model_1998.xml
   5
   6CREATED :  September 2001
   7
   8LAST MODIFIED : 30th July 2003
   9
  10AUTHOR :  Catherine Lloyd
  11          Department of Engineering Science
  12          The University of Auckland
  13          
  14MODEL STATUS :  This model conforms to the CellML 1.0 Specification released on
  1510th August 2001, and the CellML Metadata 1.0 Specification released on 16th
  16January, 2002.
  17
  18DESCRIPTION :  This file contains a CellML description of the mammalian
  19ventricular action potential based on the Jafri-Rice-Winslow model, 1998.  This
  20model is a development of the LR-II model.  In particular, it makes an accurate
  21model of the membrane currents and adds a more sophisticated model of calcium
  22ion handling.
  23
  24CHANGES: 
  25  19/10/2001 - CML - Removed document type definition as this is declared as
  26                     optional according to the W3C recommendation.  
  27  24/10/2001 - CML - Made changes to some of the metadata, bringing them up to
  28                     date with the most recent working draft (26th September) of
  29                     the Metadata specification.
  30  07/12/2001 - CML - Changed tau_y_calculation after checking mathml using the
  31                     validator.
  32  04/01/2002 - CML - Altered some of the connections.
  33  21/01/2002 - AAC - Updated metadata to conform to the 16/1/02 CellML Metadata
  34                     1.0 Specification.
  35  25/02/2002 - CML - Corrected several equations.
  36  28/02/2002 - CML - Corrected several equations, variable units and their 
  37                     initial values.
  38  06/05/2002 - CML - Added some initial values.
  39  22/07/2002 - CML - Added more metadata.
  40  09/04/2003 - AAC - Added publication date information.  
  41  04/06/2003 - CML - Fixed MathML in a few components.
  42  30/07/2003 - CML - Altered a few equations.
  43-->
  44
  45<model
  46    name="jafri_rice_winslow_model_1998"
  47    cmeta:id="jafri_rice_winslow_model_1998"
  48    xmlns="http://www.cellml.org/cellml/1.0#"
  49    xmlns:cellml="http://www.cellml.org/cellml/1.0#"
  50    xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
  51  <rdf:RDF
  52      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
  53      xmlns:cmeta="http://www.cellml.org/metadata/1.0#"
  54      xmlns:bqs="http://www.cellml.org/bqs/1.0#"
  55      xmlns:dc="http://purl.org/dc/elements/1.1/"
  56      xmlns:dcterms="http://purl.org/dc/terms/"
  57      xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
  58    <!--
  59      The following RDF block contains metadata that applies to this document
  60      as a whole, as indicated by the empty about attribute on the 
  61      <rdf:Description> element.
  62    -->
  63    <rdf:Description rdf:about="">
  64      <!--
  65        The Model Builder Metadata.  The Dublin Core "creator" element is used  
  66        to indicate the person who translated the model into CellML.
  67      -->
  68      <dc:creator rdf:parseType="Resource">
  69        <vCard:N rdf:parseType="Resource">
  70          <vCard:Family>Lloyd</vCard:Family>
  71          <vCard:Given>Catherine</vCard:Given>
  72          <vCard:Other>May</vCard:Other>
  73        </vCard:N>
  74        <vCard:EMAIL rdf:parseType="Resource">
  75          <rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
  76          <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet" />
  77        </vCard:EMAIL>
  78        <vCard:ORG rdf:parseType="Resource">
  79          <vCard:Orgname>The University of Auckland</vCard:Orgname>
  80          <vCard:Orgunit>The Bioengineering Research Group</vCard:Orgunit>
  81        </vCard:ORG>
  82      </dc:creator>
  83      
  84      <!--
  85        The Creation Date metadata. This is the date on which the model
  86        was translated into CellML.
  87      -->
  88      <dcterms:created rdf:parseType="Resource">
  89        <dcterms:W3CDTF>2001-09-24</dcterms:W3CDTF>
  90      </dcterms:created>
  91      
  92      <!--
  93        The Modification History metadata. This lists the changes that have been
  94        made to the document, who made the changes, and when they were made.
  95      -->
  96      <cmeta:modification rdf:parseType="Resource">
  97        <rdf:value>
  98          Corrected equations.
  99        </rdf:value>
 100        <cmeta:modifier rdf:parseType="Resource">
 101          <vCard:N rdf:parseType="Resource">
 102            <vCard:Family>Lloyd</vCard:Family>
 103            <vCard:Given>Catherine</vCard:Given>
 104            <vCard:Other>May</vCard:Other>
 105          </vCard:N>
 106        </cmeta:modifier>
 107        <dcterms:modified rdf:parseType="Resource"> 
 108          <dcterms:W3CDTF>2003-07-30</dcterms:W3CDTF>
 109        </dcterms:modified>
 110      </cmeta:modification>
 111      <cmeta:modification rdf:parseType="Resource">
 112        <rdf:value>
 113          Corrected equations: alpha_j_calculation and beta_j_calculation in 
 114          fast_sodium_current_j_gate, alpha_X_calculation and beta_X_calculation           in time_dependent_potassium_current_X_gate, and f_NaK_calculation and 
 115          i_NaK_calculation in Ca_release_current_from_JSR.
 116        </rdf:value>
 117        <cmeta:modifier rdf:parseType="Resource">
 118          <vCard:N rdf:parseType="Resource">
 119            <vCard:Family>Lloyd</vCard:Family>
 120            <vCard:Given>Catherine</vCard:Given>
 121            <vCard:Other>May</vCard:Other>
 122          </vCard:N>
 123        </cmeta:modifier>
 124        <dcterms:modified rdf:parseType="Resource"> 
 125          <dcterms:W3CDTF>2003-06-04</dcterms:W3CDTF>
 126        </dcterms:modified>
 127      </cmeta:modification>
 128      <cmeta:modification rdf:parseType="Resource">
 129        <rdf:value>
 130          Added some initial values from Penny Noble's documentation.
 131        </rdf:value>
 132        <cmeta:modifier rdf:parseType="Resource">
 133          <vCard:N rdf:parseType="Resource">
 134            <vCard:Family>Lloyd</vCard:Family>
 135            <vCard:Given>Catherine</vCard:Given>
 136            <vCard:Other>May</vCard:Other>
 137          </vCard:N>
 138        </cmeta:modifier>
 139        <dcterms:modified rdf:parseType="Resource">
 140          <dcterms:W3CDTF>2002-05-06</dcterms:W3CDTF>
 141        </dcterms:modified>
 142      </cmeta:modification>
 143      <cmeta:modification rdf:parseType="Resource">
 144        <rdf:value>
 145          Corrected several equations, variable units and their initial values.
 146        </rdf:value>
 147        <cmeta:modifier rdf:parseType="Resource">
 148          <vCard:N rdf:parseType="Resource">
 149            <vCard:Family>Lloyd</vCard:Family>
 150            <vCard:Given>Catherine</vCard:Given>
 151            <vCard:Other>May</vCard:Other>
 152          </vCard:N>
 153        </cmeta:modifier>
 154        <dcterms:modified rdf:parseType="Resource">
 155          <dcterms:W3CDTF>2002-02-28</dcterms:W3CDTF>
 156        </dcterms:modified>
 157      </cmeta:modification>  
 158      <cmeta:modification rdf:parseType="Resource">
 159        <rdf:value>
 160          Corrected several equations.
 161        </rdf:value>
 162        <cmeta:modifier rdf:parseType="Resource">
 163          <vCard:N rdf:parseType="Resource">
 164            <vCard:Family>Lloyd</vCard:Family>
 165            <vCard:Given>Catherine</vCard:Given>
 166            <vCard:Other>May</vCard:Other>
 167          </vCard:N>
 168        </cmeta:modifier>
 169        <dcterms:modified rdf:parseType="Resource">
 170          <dcterms:W3CDTF>2002-02-25</dcterms:W3CDTF>
 171        </dcterms:modified>
 172      </cmeta:modification>   
 173      <cmeta:modification rdf:parseType="Resource">
 174        <rdf:value>
 175          Altered some of the connections.
 176        </rdf:value>
 177        <cmeta:modifier rdf:parseType="Resource">
 178          <vCard:N rdf:parseType="Resource">
 179            <vCard:Family>Lloyd</vCard:Family>
 180            <vCard:Given>Catherine</vCard:Given>
 181            <vCard:Other>May</vCard:Other>
 182          </vCard:N>
 183        </cmeta:modifier>
 184        <dcterms:modified rdf:parseType="Resource">
 185          <dcterms:W3CDTF>2002-01-04</dcterms:W3CDTF>
 186        </dcterms:modified>
 187      </cmeta:modification>
 188      <cmeta:modification rdf:parseType="Resource">
 189        <rdf:value>
 190          Changed tau_y_calculation after checking mathml using the validator.
 191        </rdf:value>
 192        <cmeta:modifier rdf:parseType="Resource">
 193          <vCard:N rdf:parseType="Resource">
 194            <vCard:Family>Lloyd</vCard:Family>
 195            <vCard:Given>Catherine</vCard:Given>
 196            <vCard:Other>May</vCard:Other>
 197          </vCard:N>
 198        </cmeta:modifier>
 199        <dcterms:modified rdf:parseType="Resource">
 200          <dcterms:W3CDTF>2001-12-07</dcterms:W3CDTF>
 201        </dcterms:modified>
 202      </cmeta:modification>
 203      <cmeta:modification rdf:parseType="Resource">
 204        <rdf:value>
 205          Removed document type definition as this is declared as optional
 206          according to the W3C recommendation.
 207        </rdf:value>
 208        <cmeta:modifier rdf:parseType="Resource">
 209          <vCard:N rdf:parseType="Resource">
 210            <vCard:Family>Lloyd</vCard:Family>
 211            <vCard:Given>Catherine</vCard:Given>
 212            <vCard:Other>May</vCard:Other>
 213          </vCard:N>
 214        </cmeta:modifier>
 215        <dcterms:modified rdf:parseType="Resource">
 216          <dcterms:W3CDTF>2001-10-19</dcterms:W3CDTF>
 217        </dcterms:modified>
 218      </cmeta:modification>
 219      
 220      
 221      <!-- The Publisher metadata. -->
 222      <dc:publisher>
 223        The University of Auckland, Bioengineering Research Group
 224      </dc:publisher>
 225    </rdf:Description>
 226    
 227    <!--
 228      The following metadata refers to the model itself, as indicated by the
 229      reference to the ID "jafri_rice_winslow_model_1998", which is declared on 
 230      the <model> element.
 231    -->
 232    <rdf:Description rdf:about="#jafri_rice_winslow_model_1998">
 233      <!-- A human readable name for the model. -->
 234      <dc:title>
 235        The Jafri-Rice-Winslow Model for Calcium Regulation in the Ventricular
 236        Myocyte, 1997
 237      </dc:title>
 238      
 239      <!-- A comment regarding the model. -->
 240      <cmeta:comment rdf:parseType="Resource">
 241        <rdf:value>
 242          This is the CellML description of Jafri, Rice and Winslow's           
 243          mathematical model for calcium regulation in the ventricular myocyte. 
 244          It is based on an accurate model of the membrane currents and adds a  
 245          more sophisticated model of calcium handling.  The JRW model is based 
 246          on the LR-II model for ventricular action potentials, with several    
 247          modifications. 
 248        </rdf:value>
 249        <!-- The creator of the comment. -->
 250        <dc:creator rdf:parseType="Resource">
 251          <vCard:FN>Catherine Lloyd</vCard:FN>
 252        </dc:creator>
 253      </cmeta:comment>
 254      
 255      <!-- The model is relevant to all mammals. -->
 256      <cmeta:species>Mammalia</cmeta:species>
 257      
 258      <cmeta:bio_entity>Ventricular Myocyte</cmeta:bio_entity>
 259      
 260      <!-- 
 261        The CellML Metadata Specification recommends that bibliographic metadata
 262        is used to provide information about the original model reference.  The 
 263        "identifier" attribute on the "BibliographicReference" class provides an
 264        elegant way to identify a cited reference using a database identifier            such as Pubmed.  All associated data such as author, journal title,     
 265        date, etc can be looked up on the database.
 266      -->
 267      <bqs:reference rdf:parseType="Resource">
 268        <bqs:Pubmed_id>9512016</bqs:Pubmed_id>
 269        <bqs:JournalArticle rdf:parseType="Resource">
 270          <dc:creator>
 271            <rdf:Seq>
 272              <rdf:li rdf:parseType="Resource">
 273                <bqs:Person rdf:parseType="Resource">
 274                  <vCard:N rdf:parseType="Resource">
 275                    <vCard:Family>Jafri</vCard:Family>
 276                    <vCard:Given>M</vCard:Given>
 277                    <vCard:Other>Saleet</vCard:Other>
 278                  </vCard:N>
 279                </bqs:Person>
 280              </rdf:li>
 281              <rdf:li rdf:parseType="Resource">
 282                <bqs:Person rdf:parseType="Resource">
 283                  <vCard:N rdf:parseType="Resource">
 284                    <vCard:Family>Rice</vCard:Family>
 285                    <vCard:Given>John</vCard:Given>
 286                    <vCard:Other>Jeremy</vCard:Other>
 287                  </vCard:N>
 288                </bqs:Person>
 289              </rdf:li>
 290              <rdf:li rdf:parseType="Resource">
 291                <bqs:Person rdf:parseType="Resource">
 292                  <vCard:N rdf:parseType="Resource">
 293                    <vCard:Family>Winslow</vCard:Family>
 294                    <vCard:Given>Raimond</vCard:Given>
 295                    <vCard:Other>L</vCard:Other>
 296                  </vCard:N>
 297                </bqs:Person>
 298              </rdf:li>
 299            </rdf:Seq>
 300          </dc:creator>
 301          <dc:title>
 302            Cardiac Ca2+ Dynamics: The Roles of Ryanodine Receptor Adaptation 
 303            and Sarcoplasmic Reticulum Load
 304          </dc:title>
 305          <dcterms:issued rdf:parseType="Resource">
 306            <dcterms:W3CDTF>1998-03</dcterms:W3CDTF>
 307          </dcterms:issued>
 308          <bqs:Journal rdf:parseType="Resource">
 309            <dc:title>Biophysical Journal</dc:title>
 310          </bqs:Journal>
 311          <bqs:volume>74</bqs:volume>
 312          <bqs:first_page>1149</bqs:first_page>
 313          <bqs:last_page>1168</bqs:last_page>
 314        </bqs:JournalArticle>
 315      </bqs:reference>
 316    </rdf:Description>
 317  </rdf:RDF>
 318  
 319  <!--
 320    Below, we define some additional units for association with variables and
 321    constants within the model. The identifiers are fairly self-explanatory.
 322  -->
 323  <units name="ms">
 324    <unit prefix="milli" units="second" />
 325  </units>
 326  
 327  <units name="per_ms">
 328    <unit prefix="milli" units="second" exponent="-1" />
 329  </units>
 330  
 331  <units name="per_mm">
 332    <unit prefix="milli" units="metre" exponent="-1" />
 333  </units>
 334  
 335  <units name="mV">
 336    <unit prefix="milli" units="volt" />
 337  </units>
 338
 339  <units name="per_mV">
 340    <unit prefix="milli" units="volt" exponent="-1" />
 341  </units>
 342  
 343  <units name="per_mV_ms">
 344    <unit units="mV" exponent="-1" />
 345    <unit units="ms" exponent="-1" />
 346  </units>
 347  
 348  <units name="mS_per_mm2">
 349    <unit prefix="milli" units="siemens" />
 350    <unit prefix="milli" units="metre" exponent="-2" />
 351  </units>
 352  
 353  <units name="mm2">
 354    <unit prefix="milli" units="metre" exponent="2" />
 355  </units>
 356  
 357  <units name="mM">
 358    <unit prefix="nano" units="mole" />
 359    <unit prefix="milli" units="metre" exponent="-3" />
 360  </units>
 361  
 362  <units name="mM_per_ms">
 363    <unit units="mM" />
 364    <unit units="ms" exponent="-1" />
 365  </units>
 366  
 367  <units name="per_mM_per_ms">
 368    <unit units="mM" exponent="-1" />
 369    <unit units="ms" exponent="-1" />
 370  </units>
 371  
 372  <units name="per_mM3_per_ms">
 373    <unit units="mM" exponent="-3" />
 374    <unit units="ms" exponent="-1" />
 375  </units>
 376  
 377  <units name="per_mM4_per_ms">
 378    <unit units="mM" exponent="-4" />
 379    <unit units="ms" exponent="-1" />
 380  </units>
 381    
 382  <units name="uF_per_mm2">
 383    <unit prefix="micro" units="farad" />
 384    <unit prefix="milli" units="metre" exponent="-2" />
 385  </units>
 386
 387  <units name="uA_per_mm2">
 388    <unit prefix="micro" units="ampere" />
 389    <unit prefix="milli" units="metre" exponent="-2" />
 390  </units>
 391    
 392  <units name="mm_per_ms">
 393    <unit prefix="milli" units="metre" />
 394    <unit units="ms" exponent="-1" />
 395  </units>
 396  
 397  <units name="gas_constant_units">
 398    <unit prefix="pico" units="joule" />
 399    <unit prefix="nano" units="mole" exponent="-1" />
 400    <unit units="kelvin" exponent="-1" />
 401  </units>
 402  
 403  <units name="faradays_constant_units">
 404    <unit prefix="nano" units="coulomb" />
 405    <unit prefix="nano" units="mole" exponent="-1" />
 406  </units>
 407  
 408  
 409  <!--
 410    The "environment" component is used to declare variables that are used by
 411    all or most of the other components, in this case just "time".
 412  -->
 413  <component name="environment">
 414    <variable name="time" public_interface="out" units="ms" />
 415  </component>
 416
 417
 418  <!--
 419    The "membrane" component is really the `root' node of our model.
 420    It defines the action potential variable "V" among other things.
 421  -->
 422  <component name="membrane" cmeta:id="membrane">
 423    <rdf:RDF
 424      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 425      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 426      <rdf:Description rdf:about="#membrane">
 427        <cmeta:comment rdf:parseType="Resource">
 428          <rdf:value>
 429            The main component of the model which defines the action potential.
 430          </rdf:value>
 431        </cmeta:comment>
 432      </rdf:Description>
 433    </rdf:RDF>
 434
 435    <!-- These variables are defined here and used in other components. -->
 436    <variable
 437        name="V" public_interface="out"
 438        initial_value="-84.1638" units="mV" />
 439    <variable
 440        name="R" public_interface="out"
 441        initial_value="8.3145e3" units="gas_constant_units" />
 442    <variable
 443        name="T" public_interface="out"
 444        initial_value="310.0" units="kelvin" />
 445    <variable
 446        name="F" public_interface="out"
 447        initial_value="9.6845e4" units="faradays_constant_units" />
 448         
 449    <!-- These variables are imported from other components. -->
 450    <variable name="time" public_interface="in" units="ms" />
 451    <variable name="i_Na" public_interface="in" units="uA_per_mm2" />
 452    <variable name="i_Ca_L_Ca" public_interface="in" units="uA_per_mm2" />
 453    <variable name="i_Ca_L_K" public_interface="in" units="uA_per_mm2" />
 454    <variable name="i_K" public_interface="in" units="uA_per_mm2" />
 455    <variable name="i_K1" public_interface="in" units="uA_per_mm2" />
 456    <variable name="i_NaCa" public_interface="in" units="uA_per_mm2" />
 457    <variable name="i_Kp" public_interface="in" units="uA_per_mm2" />
 458    <variable name="i_p_Ca" public_interface="in" units="uA_per_mm2" />
 459    <variable name="i_Na_b" public_interface="in" units="uA_per_mm2" />
 460    <variable name="i_Ca_b" public_interface="in" units="uA_per_mm2" />
 461    <variable name="i_NaK" public_interface="in" units="uA_per_mm2" />
 462    <variable name="i_ns_Ca" public_interface="in" units="uA_per_mm2" />
 463    
 464    <!-- These variables is defined here and only used internally. -->
 465    <variable name="Cm" initial_value="0.01" units="uF_per_mm2" />
 466    <variable name="I_stim" units="uA_per_mm2" />
 467    
 468    <rdf:RDF
 469      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 470      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 471      <rdf:Description rdf:about="#membrane_voltage_diff_eq">
 472        <cmeta:comment rdf:parseType="Resource">
 473          <rdf:value>
 474            The kinetics of the transmembrane potential, defined as the sum of
 475            all the sarcolemmal currents and an applied stimulus current.
 476          </rdf:value>
 477        </cmeta:comment>
 478      </rdf:Description>
 479    </rdf:RDF>
 480    <math xmlns="http://www.w3.org/1998/Math/MathML"
 481      cmeta:id="membrane_voltage_diff_eq">
 482      <apply id="membrane_voltage_diff_eq"><eq />
 483        <apply><diff />
 484          <bvar><ci> time </ci></bvar>
 485          <ci> V </ci>
 486        </apply>
 487        <apply><divide />
 488          <apply><minus />
 489            <ci>I_stim</ci>
 490            <apply><plus />
 491              <ci> i_Na </ci>
 492              <ci> i_Ca_L_Ca </ci>
 493              <ci> i_Ca_L_K </ci>
 494              <ci> i_K </ci>
 495              <ci> i_NaCa </ci>
 496              <ci> i_K1 </ci>
 497              <ci> i_Kp </ci>
 498              <ci> i_p_Ca </ci>
 499              <ci> i_Na_b </ci>
 500              <ci> i_Ca_b </ci>
 501              <ci> i_NaK </ci>
 502              <ci> i_ns_Ca </ci>
 503            </apply>
 504          </apply>
 505          <ci> Cm </ci>
 506        </apply>
 507      </apply>
 508    </math>
 509    <rdf:RDF
 510      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 511      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 512      <rdf:Description rdf:about="#IStim_for_cmiss_eq">
 513        <cmeta:comment rdf:parseType="Resource">
 514          <rdf:value>
 515            This is a dummy equation that we simply use to make grabbing the
 516            value in CMISS much easier.
 517          </rdf:value>
 518        </cmeta:comment>
 519      </rdf:Description>
 520    </rdf:RDF>
 521    <variable name="IStimC" units="uA_per_mm2" public_interface="out"/>
 522    <math xmlns="http://www.w3.org/1998/Math/MathML" cmeta:id="IStim_for_cmiss_eq">
 523      <apply id="IStim_for_cmiss"><eq/>
 524        <ci>IStimC</ci>
 525        <ci>I_stim</ci>
 526      </apply>
 527    </math>
 528  </component>
 529  
 530  <component name="fast_sodium_current" cmeta:id="fast_sodium_current">
 531    <rdf:RDF
 532      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 533      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 534      <rdf:Description rdf:about="#fast_sodium_current">
 535        <cmeta:comment rdf:parseType="Resource">
 536          <rdf:value>
 537            The fast sodium current component contains the differential
 538            equations governing the influx of sodium ions through the cell
 539            surface membrane into the cell.
 540          </rdf:value>
 541        </cmeta:comment>
 542      </rdf:Description>
 543    </rdf:RDF>
 544
 545    <!-- These variables are defined here and used in other components. -->
 546    <variable name="i_Na" public_interface="out" units="uA_per_mm2" />
 547    <variable name="E_Na" public_interface="out" units="mV" />
 548    
 549    <!-- This variable is defined here and only used internally. -->
 550    <variable name="g_Na" initial_value="0.128" units="mS_per_mm2" />
 551    
 552    <!-- 
 553      Time is imported from the environment, and membrane potential is          
 554      imported from the membrane component.  These variables are used in the    
 555      "sodium_current" parent component, which also acts as an interface,       
 556      passing the variables to its encapsulated gate components. 
 557    -->
 558    <variable
 559        name="time" public_interface="in"
 560        private_interface="out" units="ms" />
 561    <variable
 562        name="V" public_interface="in"
 563        private_interface="out" units="mV" />
 564    <variable name="R" public_interface="in" units="gas_constant_units" />
 565    <variable name="T" public_interface="in" units="kelvin" />
 566    <variable name="F" public_interface="in" units="faradays_constant_units" />
 567    <variable name="Nai" public_interface="in" units="mM" />
 568    <variable name="Nao" public_interface="in" units="mM" />
 569    
 570    <!-- These variables are imported from encapsulated components. -->
 571    <variable name="m" private_interface="in" units="dimensionless" />
 572    <variable name="h" private_interface="in" units="dimensionless" />
 573    <variable name="j" private_interface="in" units="dimensionless" />
 574    
 575    <rdf:RDF
 576      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 577      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 578      <rdf:Description rdf:about="#i_Na_calculation_eq">
 579        <cmeta:comment rdf:parseType="Resource">
 580          <rdf:value>
 581            Calculation of the fast sodium current using the three
 582            Hodkin-Huxley type voltage-dependent gating variables m, h, and j.
 583          </rdf:value>
 584        </cmeta:comment>
 585      </rdf:Description>
 586    </rdf:RDF>
 587    <math xmlns="http://www.w3.org/1998/Math/MathML"
 588      cmeta:id="i_Na_calculation_eq">
 589      <apply id="i_Na_calculation"><eq />
 590        <ci> i_Na </ci>
 591        <apply><times />
 592          <ci> g_Na </ci>
 593          <apply><power />
 594            <ci> m </ci>
 595            <cn cellml:units="dimensionless"> 3.0 </cn>
 596          </apply>
 597          <ci> h </ci>
 598          <ci> j </ci>
 599          <apply><minus />
 600            <ci> V </ci>
 601            <ci> E_Na </ci>
 602          </apply>
 603        </apply>
 604      </apply>
 605    </math>
 606      
 607    <rdf:RDF
 608      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 609      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 610      <rdf:Description rdf:about="#E_Na_calculation_eq">
 611        <cmeta:comment rdf:parseType="Resource">
 612          <rdf:value>
 613            The sodium reversal potential.
 614          </rdf:value>
 615        </cmeta:comment>
 616      </rdf:Description>
 617    </rdf:RDF>
 618    <math xmlns="http://www.w3.org/1998/Math/MathML"
 619      cmeta:id="E_Na_calculation_eq">
 620      <apply id="E_Na_calculation"><eq />
 621        <ci> E_Na </ci>
 622        <apply><times />
 623          <apply><divide />
 624            <apply><times />
 625              <ci> R </ci>
 626              <ci> T </ci>
 627            </apply>
 628            <ci> F </ci>
 629          </apply>
 630          <apply><ln />
 631            <apply><divide />
 632              <ci> Nao </ci>
 633              <ci> Nai </ci>
 634            </apply>
 635          </apply>
 636        </apply>
 637      </apply>
 638    </math>
 639  </component>
 640     
 641  <!--
 642    The "fast_sodium_current_m_gate" is the m gate encapsulated inside the fast 
 643    sodium current. 
 644  -->
 645  <component name="fast_sodium_current_m_gate"
 646    cmeta:id="fast_sodium_current_m_gate">
 647    <rdf:RDF
 648      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 649      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 650      <rdf:Description rdf:about="#fast_sodium_current_m_gate">
 651        <cmeta:comment rdf:parseType="Resource">
 652          <rdf:value>
 653            The voltage-dependent activation gate for the fast sodium current -
 654            the m gate.
 655          </rdf:value>
 656        </cmeta:comment>
 657      </rdf:Description>
 658    </rdf:RDF>
 659    
 660    <!-- This variable is defined here and used in other components. -->
 661    <variable
 662        name="m" public_interface="out"
 663        initial_value="0.0328302" units="dimensionless" />
 664        
 665    <!-- These variables are defined here and only used internally. -->
 666    <variable name="alpha_m" units="per_ms" />
 667    <variable name="beta_m" units="per_ms" />
 668
 669    <!-- 
 670      These variables are imported from the environment and the membrane via    
 671      the "fast_sodium_current" component.
 672    -->
 673    <variable name="V" public_interface="in" units="mV" />
 674    <variable name="time" public_interface="in" units="ms" />
 675   
 676    <rdf:RDF
 677      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 678      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 679      <rdf:Description rdf:about="#alpha_m_calculation_eq">
 680        <cmeta:comment rdf:parseType="Resource">
 681          <rdf:value>
 682            The opening rate of the m gate.
 683          </rdf:value>
 684        </cmeta:comment>
 685      </rdf:Description>
 686    </rdf:RDF>
 687    <math xmlns="http://www.w3.org/1998/Math/MathML"
 688      cmeta:id="alpha_m_calculation_eq">
 689      <apply id="alpha_m_calculation"><eq />
 690        <ci> alpha_m </ci>
 691        <apply><divide />
 692          <apply><times />
 693            <cn cellml:units="per_mV_ms"> 0.32 </cn>
 694            <apply><plus />
 695              <ci> V </ci>
 696              <cn cellml:units="mV"> 47.13 </cn>
 697            </apply>
 698          </apply>
 699          <apply><minus />
 700            <cn cellml:units="dimensionless"> 1.0 </cn>
 701            <apply><exp />
 702              <apply><times />
 703                <cn cellml:units="per_mV"> -0.1 </cn>
 704                <apply><plus />
 705                  <ci> V </ci>
 706                  <cn cellml:units="mV"> 47.13 </cn>
 707                </apply>
 708              </apply>
 709            </apply>
 710          </apply>
 711        </apply>
 712      </apply>
 713    </math>
 714      
 715    <rdf:RDF
 716      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 717      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 718      <rdf:Description rdf:about="#beta_m_calculation_eq">
 719        <cmeta:comment rdf:parseType="Resource">
 720          <rdf:value>
 721            The closing rate of the m gate.
 722          </rdf:value>
 723        </cmeta:comment>
 724      </rdf:Description>
 725    </rdf:RDF>
 726    <math xmlns="http://www.w3.org/1998/Math/MathML"
 727      cmeta:id="beta_m_calculation_eq">
 728      <apply id="beta_m_calculation"><eq />
 729        <ci> beta_m </ci>
 730        <apply><times />
 731          <cn cellml:units="per_ms"> 0.08 </cn>
 732          <apply><exp />
 733            <apply><divide />
 734              <apply><minus />
 735                <ci> V </ci>
 736              </apply>
 737              <cn cellml:units="mV"> 11.0 </cn>
 738            </apply>
 739          </apply>
 740        </apply>
 741      </apply>
 742    </math>
 743      
 744    <rdf:RDF
 745      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 746      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 747      <rdf:Description rdf:about="#dm_dt_eq">
 748        <cmeta:comment rdf:parseType="Resource">
 749          <rdf:value>
 750            The kinetics of the m gate.
 751          </rdf:value>
 752        </cmeta:comment>
 753      </rdf:Description>
 754    </rdf:RDF>
 755    <math xmlns="http://www.w3.org/1998/Math/MathML"
 756      cmeta:id="dm_dt_eq">
 757      <apply id="dm_dt"><eq />
 758        <apply><diff />
 759          <bvar><ci> time </ci></bvar>
 760          <ci> m </ci>
 761        </apply>
 762        <apply><minus />
 763          <apply><times />
 764            <ci> alpha_m </ci>
 765            <apply><minus />
 766              <cn cellml:units="per_mV"> 1.0 </cn>
 767              <ci> m </ci>
 768            </apply>
 769          </apply>
 770          <apply><times />
 771            <ci> beta_m </ci>
 772            <ci> m </ci>
 773          </apply>
 774        </apply>
 775      </apply>
 776    </math>
 777  </component>
 778  
 779  <!--
 780    The "fast_sodium_current_h_gate" component is the h gate encapsulated in
 781    the fast sodium current.
 782  -->
 783  <component name="fast_sodium_current_h_gate"
 784    cmeta:id="fast_sodium_current_h_gate">
 785    <rdf:RDF
 786      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 787      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 788      <rdf:Description rdf:about="#fast_sodium_current_h_gate">
 789        <cmeta:comment rdf:parseType="Resource">
 790          <rdf:value>
 791            The voltage-dependent inactivation gate for the fast sodium current
 792            - the h gate.
 793          </rdf:value>
 794        </cmeta:comment>
 795      </rdf:Description>
 796    </rdf:RDF>
 797
 798    <!-- This variable is defined here and used in other components. -->
 799    <variable
 800        name="h" public_interface="out"
 801        initial_value="0.988354" units="dimensionless" />
 802        
 803    <!-- These variables are defined here and only used internally. -->
 804    <variable name="alpha_h" units="per_ms" />
 805    <variable name="beta_h" units="per_ms" />
 806
 807    <!-- 
 808      These variables are imported from the environment and the membrane via    
 809      the "fast_sodium_current" component.  
 810    -->
 811    <variable name="V" public_interface="in" units="mV" />
 812    <variable name="time" public_interface="in" units="ms" />
 813    
 814    <rdf:RDF
 815      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 816      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 817      <rdf:Description rdf:about="#alpha_h_calculation_eq">
 818        <cmeta:comment rdf:parseType="Resource">
 819          <rdf:value>
 820            The opening rate of the h gate.
 821          </rdf:value>
 822        </cmeta:comment>
 823      </rdf:Description>
 824    </rdf:RDF>
 825    <math xmlns="http://www.w3.org/1998/Math/MathML"
 826      cmeta:id="alpha_h_calculation_eq">
 827      <apply id="alpha_h_calculation"><eq />
 828        <ci> alpha_h </ci>
 829        <piecewise>
 830          <piece>
 831            <apply><times />
 832              <cn cellml:units="per_ms"> 0.135 </cn>
 833              <apply><exp />
 834                <apply><divide />
 835                  <apply><plus />
 836                    <cn cellml:units="mV"> 80.0 </cn>
 837                    <ci> V </ci>
 838                  </apply>
 839                  <cn cellml:units="mV"> -6.8 </cn>
 840                </apply>
 841              </apply>
 842            </apply>
 843            <apply><lt />
 844              <ci> V </ci> 
 845              <cn cellml:units="mV"> -40.0 </cn>
 846            </apply>
 847          </piece>
 848          <otherwise>
 849            <cn cellml:units="per_ms"> 0.0 </cn>
 850          </otherwise>
 851        </piecewise>
 852      </apply>
 853    </math>
 854       
 855    <rdf:RDF
 856      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 857      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 858      <rdf:Description rdf:about="#beta_h_calculation_eq">
 859        <cmeta:comment rdf:parseType="Resource">
 860          <rdf:value>
 861            The closing rate of the h gate.
 862          </rdf:value>
 863        </cmeta:comment>
 864      </rdf:Description>
 865    </rdf:RDF>
 866    <math xmlns="http://www.w3.org/1998/Math/MathML"
 867      cmeta:id="beta_h_calculation_eq">
 868      <apply id="beta_h_calculation"><eq />
 869        <ci> beta_h </ci>
 870        <piecewise>
 871          <piece>
 872            <apply><plus />
 873              <apply><times />
 874                <cn cellml:units="per_ms"> 3.56 </cn>
 875                <apply><exp />
 876                  <apply><times />
 877                    <cn cellml:units="mV"> 0.079 </cn>
 878                    <ci> V </ci>
 879                  </apply>
 880                </apply>
 881              </apply>
 882              <apply><times />
 883                <cn cellml:units="per_ms"> 310000.0 </cn>
 884                <apply><exp />
 885                  <apply><times />
 886                    <cn cellml:units="per_mV"> 0.35 </cn>
 887                    <ci> V </ci>
 888                  </apply>
 889                </apply>
 890              </apply>
 891            </apply>
 892            <apply><lt />
 893              <ci> V </ci>
 894              <cn cellml:units="mV"> -40.0 </cn>
 895            </apply>
 896          </piece>
 897          <otherwise>
 898            <apply><divide />
 899              <cn cellml:units="dimensionless"> 1.0 </cn>
 900              <apply><times />
 901                <cn cellml:units="ms"> 0.13 </cn>
 902                <apply><plus />
 903                  <cn cellml:units="dimensionless"> 1.0 </cn>
 904                  <apply><exp />
 905                    <apply><divide />
 906                      <apply><plus />
 907                        <ci> V </ci>
 908                        <cn cellml:units="mV"> 10.66 </cn>
 909                      </apply>
 910                      <cn cellml:units="mV"> -11.1 </cn>
 911                    </apply>
 912                  </apply>
 913                </apply>
 914              </apply>
 915            </apply>
 916          </otherwise>
 917        </piecewise>
 918      </apply>
 919    </math>
 920       
 921    <rdf:RDF
 922      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 923      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 924      <rdf:Description rdf:about="#dh_dt_eq">
 925        <cmeta:comment rdf:parseType="Resource">
 926          <rdf:value>
 927            The kinetics of the h gate.
 928          </rdf:value>
 929        </cmeta:comment>
 930      </rdf:Description>
 931    </rdf:RDF>
 932    <math xmlns="http://www.w3.org/1998/Math/MathML"
 933      cmeta:id="dh_dt_eq">
 934      <apply id="dh_dt"><eq />
 935        <apply><diff />
 936          <bvar><ci> time </ci></bvar>
 937          <ci> h </ci>
 938        </apply>
 939        <apply><minus />
 940          <apply><times />
 941            <ci> alpha_h </ci>
 942            <apply><minus />
 943              <cn cellml:units="dimensionless"> 1.0 </cn>
 944              <ci> h </ci>
 945            </apply>
 946          </apply>
 947          <apply><times />
 948            <ci> beta_h </ci>
 949            <ci> h </ci>
 950          </apply>
 951        </apply>
 952      </apply>
 953    </math>
 954  </component>
 955  
 956  <!--
 957    The "fast_sodium_current_j_gate" component is the j gate encapsulated in
 958    the fast sodium current.
 959  -->
 960  <component name="fast_sodium_current_j_gate"
 961    cmeta:id="fast_sodium_current_j_gate">
 962    <rdf:RDF
 963      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 964      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 965      <rdf:Description rdf:about="#fast_sodium_current_j_gate">
 966        <cmeta:comment rdf:parseType="Resource">
 967          <rdf:value>
 968            The voltage-dependent slow inactivation gate for the fast sodium
 969            current - the j gate.
 970          </rdf:value>
 971        </cmeta:comment>
 972      </rdf:Description>
 973    </rdf:RDF>
 974
 975    <!-- This variable is defined here and used in other components. -->
 976    <variable
 977        name="j" public_interface="out"
 978        initial_value="0.992540" units="dimensionless" />
 979        
 980    <!-- These variables are defined here and only used internally. -->
 981    <variable name="alpha_j" units="per_ms" />
 982    <variable name="beta_j" units="per_ms" />
 983    
 984    <!-- 
 985      These variables are imported from the environment and the membrane via    
 986      the "fast_sodium_current" component.  
 987    -->
 988    <variable name="V" public_interface="in" units="mV" />
 989    <variable name="time" public_interface="in" units="ms" />
 990    
 991    <rdf:RDF
 992      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
 993      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
 994      <rdf:Description rdf:about="#alpha_j_calculation_eq">
 995        <cmeta:comment rdf:parseType="Resource">
 996          <rdf:value>
 997            The opening rate of the j gate.
 998          </rdf:value>
 999        </cmeta:comment>
1000      </rdf:Description>
1001    </rdf:RDF>
1002    <math xmlns="http://www.w3.org/1998/Math/MathML"
1003      cmeta:id="alpha_j_calculation_eq">
1004      <apply id="alpha_j_calculation"><eq />
1005        <ci> alpha_j </ci>
1006        <piecewise>
1007          <piece>
1008            <apply><times />
1009              <apply><minus />
1010                <apply><times />
1011                  <cn cellml:units="per_mV_ms"> -127140.0 </cn>
1012                  <apply><exp />
1013                    <apply><times /> 
1014                      <cn cellml:units="per_mV"> 0.2444 </cn>
1015                      <ci> V </ci>
1016                    </apply>
1017                  </apply>
1018                </apply>
1019                <apply><times />
1020                  <cn cellml:units="per_mV_ms"> 0.00003474 </cn>
1021                  <apply><exp />
1022                    <apply><times />
1023                      <cn cellml:units="per_mV"> -0.04391 </cn>
1024                      <ci> V </ci>
1025                    </apply>
1026                  </apply>
1027                </apply>
1028              </apply>
1029              <apply><divide />
1030                <apply><plus />
1031                  <ci> V </ci>
1032                  <cn cellml:units="mV"> 37.78 </cn>
1033                </apply>
1034                <apply><plus />
1035                  <cn cellml:units="dimensionless"> 1.0 </cn>
1036                  <apply><exp />
1037                    <apply><times />
1038                      <cn cellml:units="per_mV"> 0.311 </cn>
1039                      <apply><plus />
1040                        <ci> V </ci>
1041                        <cn cellml:units="mV"> 79.23 </cn>
1042                      </apply>
1043                    </apply>
1044                  </apply>
1045                </apply>
1046              </apply>
1047            </apply>
1048            <apply><lt />
1049              <ci> V </ci>
1050              <cn cellml:units="mV"> -40.0 </cn>
1051            </apply>
1052          </piece>
1053          <otherwise>
1054            <cn cellml:units="per_ms"> 0.0 </cn>
1055          </otherwise>
1056        </piecewise>
1057      </apply>
1058    </math>
1059       
1060    <rdf:RDF
1061      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
1062      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
1063      <rdf:Description rdf:about="#beta_j_calculation_eq">
1064        <cmeta:comment rdf:parseType="Resource">
1065          <rdf:value>
1066            The closing rate of the j gate.
1067          </rdf:value>
1068        </cmeta:comment>
1069      </rdf:Description>
1070    </rdf:RDF>
1071    <math xmlns="http://www.w3.org/1998/Math/MathML"
1072      cmeta:id="beta_j_calculation_eq">
1073      <apply id="beta_j_calculation"><eq />
1074        <ci> beta_j </ci>
1075        <piecewise>
1076          <piece>
1077            <apply><times />
1078              <cn cellml:units="per_ms"> 0.1212 </cn>
1079              <apply><divide />
1080                <apply><exp />
1081                  <apply><times />
1082                    <cn cellml:units="per_mV"> -0.01052 </cn>
1083                    <ci> V </ci>
1084                  </apply>
1085                </apply>
1086                <apply><plus />
1087                  <cn cellml:units="dimensionless"> 1.0 </cn>
1088                  <apply><exp />
1089                    <apply><times />
1090                      <cn cellml:units="per_mV"> -0.1378 </cn>
1091                      <apply><plus />       
1092                        <ci> V </ci>
1093                        <cn cellml:units="mV"> 40.14 </cn>
1094                      </apply>
1095                    </apply>
1096                  </apply>
1097                </apply>
1098              </apply>
1099            </apply>
1100            <apply><lt />
1101              <ci> V </ci>
1102              <cn cellml:units="mV"> -40.0 </cn>
1103            </apply>
1104          </piece>
1105          <otherwise>
1106            <apply><times />
1107              <cn cellml:units="per_ms"> 0.3 </cn>
1108              <apply><divide />
1109                <apply><exp />
1110                  <apply><times />
1111                    <cn cellml:units="per_mV"> -0.0000002535 </cn>
1112                    <ci> V </ci>                                                
1113                  </apply>
1114                </apply>
1115                <apply><plus />
1116                  <cn cellml:units="dimensionless"> 1.0 </cn>
1117                  <apply><exp />
1118                    <apply><times />
1119                      <cn cellml:units="per_mV"> -0.1 </cn>
1120                      <apply><plus />
1121                        <ci> V </ci>
1122                        <cn cellml:units="mV"> 32.0 </cn>
1123                      </apply>
1124                    </apply>
1125                  </apply>
1126                </apply>
1127              </apply>
1128            </apply>                                                            
1129          </otherwise> 
1130        </piecewise>
1131      </apply>
1132    </math>
1133       
1134    <rdf:RDF
1135      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
1136      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
1137      <rdf:Description rdf:about="#dj_dt_eq">
1138        <cmeta:comment rdf:parseType="Resource">
1139          <rdf:value>
1140            The kinetics of the j gate.
1141          </rdf:value>
1142        </cmeta:comment>
1143      </rdf:Description>
1144    </rdf:RDF>
1145    <math xmlns="http://www.w3.org/1998/Math/MathML"
1146      cmeta:id="dj_dt_eq">
1147      <apply id="dj_dt"><eq />
1148        <apply><diff />
1149          <bvar><ci> time </ci></bvar>
1150          <ci> j </ci>
1151        </apply>
1152        <apply><minus />
1153          <apply><times />
1154            <ci> alpha_j </ci>
1155            <apply><minus />
1156              <cn cellml:units="dimensionless"> 1.0 </cn>
1157              <ci> j </ci>
1158            </apply>
1159          </apply>
1160          <apply><times />
1161            <ci> beta_j </ci>
1162            <ci> j </ci>
1163          </apply>
1164        </apply>
1165      </apply>
1166    </math>
1167  </component>
1168  
1169  
1170  <component name="L_type_Ca_channel" cmeta:id="L_type_Ca_channel">
1171    <rdf:RDF
1172      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
1173      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
1174      <rdf:Description rdf:about="#L_type_Ca_channel">
1175        <cmeta:comment rdf:parseType="Resource">
1176          <rdf:value>
1177            The JWR model creates a new mathematical model to describe the
1178            L-type calcium channel that is based on the experimentally observed
1179            mode-switching behaviour of the channel. Inactivation occurs as
1180            calcium ion binding induces the channel to switch (from mode normal)
1181            to a mode in which transitions to open states are extremely slow
1182            (mode Ca). The channel has one voltage inactivation gate, y. As well
1183            as Ca, the channel is assumed permeable to K ions also.
1184          </rdf:value>
1185        </cmeta:comment>
1186      </rdf:Description>
1187    </rdf:RDF>
1188
1189    <!-- These variables are defined here and used in other components. -->
1190    <variable name="i_Ca_L_Ca" public_interface="out" units="uA_per_mm2" />
1191    <variable name="i_Ca_L_K" public_interface="out" units="uA_per_mm2" />
1192    
1193    <!-- These variables are defined here and only used internally. -->
1194    <variable name="P_Ca" initial_value="33.75e-6" units="mm_per_ms" />
1195    <variable name="P_K" initial_value="1.0e-9" units="mm_per_ms" />
1196    <variable name="p_k" units="mm_per_ms" />
1197    <variable name="i_Ca_L_Ca_half" initial_value="-4.58e-3" units="uA_per_mm2" />
1198    <variable name="i_Ca_L_Ca_max" units="uA_per_mm2" />
1199    <variable name="O" initial_value="9.84546e-21" units="dimensionless" />
1200    <variable name="O_Ca" initial_value="0.0" units="dimensionless" />
1201    <variable name="alpha" units="per_ms" />
1202    <variable name="beta" units="per_ms" />
1203    <variable name="gamma" units="per_ms" />
1204    <variable name="alpha_a" units="per_ms" />
1205    <variable name="beta_b" units="per_ms" />
1206    <variable name="a" initial_value="2.0" units="dimensionless" />
1207    <variable name="b" initial_value="2.0" units="dimensionless" />
1208    <variable name="g" initial_value="2.0" units="per_ms" />
1209    <variable name="f" initial_value="0.3" units="per_ms" />
1210    <variable name="g_" initial_value="0.0" units="per_ms" />
1211    <variable name="f_" initial_value="0.0" units="per_ms" />
1212    <variable name="omega" initial_value="0.01" units="per_ms" />
1213    <variable name="C0" initial_value="0.997208" units="dimensionless" />
1214    <variable name="C1" initial_value="6.38897e-5" units="dimensionless" />
1215    <variable name="C2" initial_value="1.535e-9" units="dimensionless" />
1216    <variable name="C3" initial_value="1.63909e-14" units="dimensionless" />
1217    <variable name="C4" initial_value="6.56337e-20" units="dimensionless" />
1218    <variable name="C_Ca0" initial_value="2.72826e-3" units="dimensionless" />
1219    <variable name="C_Ca1" initial_value="6.99215e-7" units="dimensionless" />
1220    <variable name="C_Ca2" initial_value="6.71989e-11" units="dimensionless" />
1221    <variable name="C_Ca3" initial_value="2.87031e-15" units="dimensionless" />
1222    <variable name="C_Ca4" initial_value="4.59752e-20" units="dimensionless" />
1223    
1224    <!--  These variables are imported from other components. -->          
1225    <variable name="time" public_interface="in" private_interface="out" units="ms" />
1226    <variable name="V" public_interface="in" private_interface="out" units="mV" />
1227    <variable name="Ca_SS" public_interface="in" units="mM" />
1228    <variable name="Cao" public_interface="in" units="mM" />
1229    <variable name="Ko" public_interface="in" units="mM" />
1230    <variable name="Ki" public_interface="in" units="mM" />
1231    <variable name="R" public_interface="in" units="gas_constant_units" />
1232    <variable name="T" public_interface="in" units="kelvin" />
1233    <variable name="F" public_interface="in" units="faradays_constant_units" />
1234    
1235    <!-- These variables are imported from encapsulated components. -->
1236    <variable name="y" private_interface="in" units="dimensionless" />
1237    
1238    <rdf:RDF
1239      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
1240      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
1241      <rdf:Description rdf:about="#i_Ca_L_Ca_calculation_eq">
1242        <cmeta:comment rdf:parseType="Resource">
1243          <rdf:value>
1244            Calculation of the calcium current component of the total channel
1245            current, given as the maximal current multiplied by the
1246            voltage-dependent inactivation gate and the open probability of the
1247            channel based on the mode-switching model.
1248          </rdf:value>
1249        </cmeta:comment>
1250      </rdf:Description>
1251    </rdf:RDF>
1252    <math xmlns="http://www.w3.org/1998/Math/MathML"
1253      cmeta:id="i_Ca_L_Ca_calculation_eq">
1254      <apply id="i_Ca_L_Ca_calculation"><eq />
1255        <ci> i_Ca_L_Ca </ci>
1256        <apply><times />
1257          <ci> i_Ca_L_Ca_max </ci>
1258          <ci> y </ci>
1259          <apply><plus />
1260            <ci> O </ci>
1261            <ci> O_Ca </ci>
1262          </apply>
1263        </apply>
1264      </apply>
1265    </math>
1266      
1267    <rdf:RDF
1268      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
1269      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
1270      <rdf:Description rdf:about="#i_Ca_L_K_calculation_eq">
1271        <cmeta:comment rdf:parseType="Resource">
1272          <rdf:value>
1273            Calculation of the potassium current component of the total channel
1274            current.
1275          </rdf:value>
1276        </cmeta:comment>
1277      </rdf:Description>
1278    </rdf:RDF>
1279    <math xmlns="http://www.w3.org/1998/Math/MathML"
1280      cmeta:id="i_Ca_L_K_calculation_eq">
1281      <apply id="i_Ca_L_K_calculation"><eq />
1282        <ci> i_Ca_L_K </ci>
1283        <apply><times />
1284          <ci> p_k </ci>
1285          <ci> y </ci>
1286          <apply><plus />
1287            <ci> O </ci>
1288            <ci> O_Ca </ci>
1289          </apply>
1290          <apply><divide />
1291            <apply><times />
1292              <ci> V </ci>
1293              <apply><power/>
1294                <ci> F </ci>
1295                <cn cellml:units="dimensionless"> 2.0 </cn>
1296              </apply>
1297            </apply>
1298            <apply><times />
1299              <ci> R </ci>
1300              <ci> T </ci>
1301            </apply>
1302          </apply>
1303          <apply><divide />
1304            <apply><minus />
1305              <apply><times />
1306                <ci> Ki </ci>
1307                <apply><exp />
1308                  <apply><divide />
1309                    <apply><times />
1310                      <ci> V </ci>
1311                      <ci> F </ci>
1312                    </apply>
1313                    <apply><times />
1314                      <ci> R </ci>
1315                      <ci> T </ci>
1316                    </apply>
1317                  </apply>
1318                </apply>
1319              </apply>
1320              <ci> Ko </ci>
1321            </apply> 
1322            <apply><minus />
1323              <apply><exp />
1324                <apply><divide />
1325                  <apply><times />
1326                    <ci> V </ci>
1327                    <ci> F </ci>
1328                  </apply>
1329                  <apply><times />
1330                    <ci> R </ci>
1331                    <ci> T </ci>
1332                  </apply>
1333                </apply>
1334              </apply>
1335              <cn cellml:units="dimensionless"> 1.0 </cn>
1336            </apply>
1337          </apply>
1338        </apply>
1339      </apply>
1340    </math>
1341      
1342    <rdf:RDF
1343      xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
1344      xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
1345      <rdf:Description rdf:about="#p_K_calculation_eq">
1346        <cmeta:comment rdf:parseType="Resource">
1347          <rdf:value>
1348            The potassium permeability of the channel, which depends on the
1349            calcium current component.
1350          </rdf:value>
1351        </cmeta:comment>
1352      </rdf:Description>
1353    </rdf:RDF>
1354    <math xmlns="http://www.w3.org/1998/Math/MathML"
1355      cmeta:id="p_K_calculation_eq">
1356      <apply id="p_k_calculation"><eq />
1357        <ci> p_k </ci>
1358        <apply><divide />
1359          <ci> P_K </ci>
1360          <apply><plus />
1361            <cn cellml:units="dimensionless"> 1.0 </cn>
1362            <apply><divide />
1363              <ci> i_Ca_L_Ca…

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