Location: Katsnelson, Nikitina, Chemla, Solovyova, Coirault, Lecarpentier, Markhasin, 2004 @ ff37a293c456 / katsnelson_2004b.cellml

Author:
Catherine Lloyd <c.lloyd@auckland.ac.nz>
Date:
2010-06-21 23:23:42+12:00
Desc:
Removed xml:base="" from all 3 model files.
Permanent Source URI:
http://models.cellml.org/workspace/katsnelson_nikitina_chemla_solovyova_coirault_lecarpentier_markhasin_2004/rawfile/ff37a293c456b587f8256e8274c1652f8d5cfe77/katsnelson_2004b.cellml

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COR (0.9.31.1319)
Copyright 2002-2009 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk

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http://www.cellml.org/
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				<title>Influence of viscosity on myocardium mechanical activity: a mathematical model</title>
				<author>
					<firstname>Geoffrey</firstname>
					<surname>Nunns</surname>
					<affiliation>
						<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
					</affiliation>
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			<section id="sec_status">
				<title>Model Status</title>
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        This model has been checked and it runs in both COR and PCEnv to recreate the published results. Units are consistent throughout.  In this particular version of the model, time is expressed in seconds and all calcium variables and parameters are in absolute values.        
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		  <para>
		  With default setting the model produce isometric contraction (parameter isotonic=0). To switch from isomentric mode to isotonic mode isotonic parameter should be set 1. Then set parameter F_afterload to the value less then the maximum force calculated at isometric mode. Make sure that the model is run in isometric mode first and see the value of the maximum of isometric force. If F_afterload is not less than this value, model performs isometric mode instead of isotonic.
          </para>
			</section>
			<sect1 id="sec_structure">
				<title>Model Structure</title>
				<para>
Abstract: We have previously proposed and validated a mathematical model of myocardium contraction-relaxation cycle based on current knowledge of regulatory role of Ca2+ and cross-bridge kinetics in cardiac cell. That model did not include viscous elements. Here we propose a modification of the model, in which two viscous elements are added, one in parallel to the contractile element, and one more in parallel to the series elastic element. The modified model allowed us to simulate and explain some subtle experimental data on relaxation velocity in isotonic twitches and on a mismatch between the time course of sarcomere shortening/lengthening and the time course of active force generation in isometric twitches. Model results were compared with experimental data obtained from 28 rat LV papillary muscles contracting and relaxing against various loads. Additional model analysis suggested contribution of viscosity to main inotropic and lusitropic characteristics of myocardium performance.   
</para>
				<para>
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									<title>model diagram</title>
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						<caption>Schematic diagram of the Katsnelson et al model - an updated rheological scheme of the heart muscle including
contractile element CE, two passive elastic elements PE (parallel one) and SE (series one) and two viscous elements VS1 and VS2. The effect of calcium and the calcium binding ligand (B) in facilitating actin-myosin binding is also highlighted.</caption>
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				</para>
				<para>
The original paper reference is cited below:
</para>
				<para>
					Influence of viscosity on myocardium mechanical activity: a mathematical model, Leonid B. Katsnelson, Larissa V. Nikitina, Denis Chemla, Olga Solovyova, Catherine Coirault, Yves Lecarpentier and Vladimir S. Markhasin, 2004,
						<emphasis>Journal of Theoretical Biology</emphasis>, 230, 385-485.  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=15302547&amp;dopt=Abstract">PubMed ID: 15302547     </ulink>
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      <variable initial_value="0.9" name="m_0" public_interface="out" units="dimensionless"/>
      <variable initial_value="5.6" name="v_max" public_interface="out" units="micrometre_per_second"/>
      <variable initial_value="0.25" name="a" public_interface="out" units="dimensionless"/>
      <variable initial_value="0.5" name="d_h" public_interface="out" units="dimensionless"/>
      <variable initial_value="4" name="alpha_P" public_interface="out" units="dimensionless"/>
   </component>
   <component name="isotonic">
      <variable name="time" public_interface="in" units="second"/>
      <variable name="isotonic" public_interface="in" units="dimensionless"/>
      <variable name="l" public_interface="in" units="micrometre"/>
      <variable name="F_muscle" public_interface="in" units="millinewton"/>
      <variable name="flag" units="dimensionless"/>
      <variable initial_value="2" name="F_afterload" units="millinewton"/>
      <variable name="isotonic_mode" public_interface="out" units="dimensionless"/>
      <variable initial_value="0.527" name="l_0" units="micrometre"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>flag</ci>
            <piecewise>
               <piece>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0</cn>
                  <apply>
                     <and/>
                     <apply>
                        <geq/>
                        <ci>l</ci>
                        <ci>l_0</ci>
                     </apply>
                     <apply>
                        <lt/>
                        <ci>time</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="second">0.15</cn>
                     </apply>
                  </apply>
               </piece>
               <otherwise>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>isotonic_mode</ci>
            <piecewise>
               <piece>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0</cn>
                  <apply>
                     <eq/>
                     <ci>isotonic</ci>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0</cn>
                  </apply>
               </piece>
               <piece>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                  <apply>
                     <and/>
                     <apply>
                        <eq/>
                        <ci>isotonic</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     </apply>
                     <apply>
                        <geq/>
                        <ci>F_muscle</ci>
                        <ci>F_afterload</ci>
                     </apply>
                  </apply>
               </piece>
               <piece>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0</cn>
                  <apply>
                     <and/>
                     <apply>
                        <eq/>
                        <ci>isotonic</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     </apply>
                     <apply>
                        <geq/>
                        <ci>l</ci>
                        <ci>l_0</ci>
                     </apply>
                     <apply>
                        <eq/>
                        <ci>flag</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     </apply>
                  </apply>
               </piece>
            </piecewise>
         </apply>
      </math>
   </component>
   <component name="parameters_izakov_et_al_1991">
      <variable initial_value="1.14" name="S_0" public_interface="out" units="micrometre"/>
      <variable name="q_v" public_interface="out" units="per_second"/>
      <variable initial_value="17.3" name="q_1" units="per_second"/>
      <variable initial_value="259" name="q_2" units="per_second"/>
      <variable initial_value="17.3" name="q_3" units="per_second"/>
      <variable initial_value="15" name="q_4" public_interface="out" units="per_second"/>
      <variable initial_value="5.3035675" name="v_star" public_interface="out" units="micrometre_per_second"/>
      <variable name="v_1" public_interface="out" units="micrometre_per_second"/>
      <variable initial_value="1" name="alpha_G" public_interface="out" units="dimensionless"/>
      <variable initial_value="32.85" name="a_on" public_interface="out" units="per_second_micromole"/>
      <variable initial_value="290" name="a_off" public_interface="out" units="per_second"/>
      <variable initial_value="0.04" name="k_A" public_interface="out" units="per_micromole"/>
      <variable name="v" public_interface="in" units="micrometre_per_second"/>
      <variable name="v_max" public_interface="in" units="micrometre_per_second"/>
      <variable initial_value="10" name="alpha_Q" units="dimensionless"/>
      <variable initial_value="5000" name="beta_Q" units="dimensionless"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>q_v</ci>
            <piecewise>
               <piece>
                  <apply>
                     <minus/>
                     <ci>q_1</ci>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <ci>q_2</ci>
                           <ci>v</ci>
                        </apply>
                        <ci>v_max</ci>
                     </apply>
                  </apply>
                  <apply>
                     <leq/>
                     <ci>v</ci>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micrometre_per_second">0</cn>
                  </apply>
               </piece>
               <piece>
                  <apply>
                     <plus/>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <apply>
                              <minus/>
                              <ci>q_4</ci>
                              <ci>q_3</ci>
                           </apply>
                           <ci>v</ci>
                        </apply>
                        <ci>v_star</ci>
                     </apply>
                     <ci>q_3</ci>
                  </apply>
                  <apply>
                     <and/>
                     <apply>
                        <leq/>
                        <ci>v</ci>
                        <ci>v_star</ci>
                     </apply>
                     <apply>
                        <lt/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micrometre_per_second">0</cn>
                        <ci>v</ci>
                     </apply>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <ci>q_4</ci>
                     <apply>
                        <power/>
                        <apply>
                           <plus/>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <ci>beta_Q</ci>
                                 <apply>
                                    <minus/>
                                    <ci>v</ci>
                                    <ci>v_star</ci>
                                 </apply>
                              </apply>
                              <ci>v_max</ci>
                           </apply>
                        </apply>
                        <ci>alpha_Q</ci>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>v_1</ci>
            <apply>
               <divide/>
               <ci>v_max</ci>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">10</cn>
            </apply>
         </apply>
      </math>
   </component>
   <component name="force">
      <variable cmeta:id="force_F_CE" name="F_CE" units="millinewton"/>
      <variable name="F_muscle" public_interface="out" units="millinewton"/>
      <variable cmeta:id="force_F_XSE" name="F_XSE" units="millinewton"/>
      <variable cmeta:id="force_F_SE" name="F_SE" units="millinewton"/>
      <variable cmeta:id="force_F_PE" name="F_PE" units="millinewton"/>
      <variable name="N" public_interface="in" units="dimensionless"/>
      <variable name="k_P_vis" public_interface="in" units="millinewton_second_per_micrometre"/>
      <variable name="k_S_vis" public_interface="in" units="millinewton_second_per_micrometre"/>
      <variable name="w" public_interface="in" units="micrometre_per_second"/>
      <variable name="v" public_interface="in" units="micrometre_per_second"/>
      <variable name="l_1" public_interface="in" units="micrometre"/>
      <variable name="l_2" public_interface="in" units="micrometre"/>
      <variable name="l_3" public_interface="in" units="micrometre"/>
      <variable name="p_v" public_interface="in" units="dimensionless"/>
      <variable name="alpha_1" public_interface="in" units="per_micrometre"/>
      <variable name="beta_1" public_interface="in" units="millinewton"/>
      <variable name="alpha_2" public_interface="in" units="per_micrometre"/>
      <variable name="beta_2" public_interface="in" units="millinewton"/>
      <variable name="alpha_3" public_interface="in" units="per_micrometre"/>
      <variable name="beta_3" public_interface="in" units="millinewton"/>
      <variable name="lambda" public_interface="in" units="millinewton"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>F_CE</ci>
            <apply>
               <times/>
               <ci>lambda</ci>
               <ci>p_v</ci>
               <ci>N</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>F_muscle</ci>
            <ci>F_XSE</ci>
         </apply>
         <apply>
            <eq/>
            <ci>F_SE</ci>
            <apply>
               <times/>
               <ci>beta_1</ci>
               <apply>
                  <minus/>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <ci>alpha_1</ci>
                        <apply>
                           <minus/>
                           <ci>l_2</ci>
                           <ci>l_1</ci>
                        </apply>
                     </apply>
                  </apply>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>F_PE</ci>
            <apply>
               <times/>
               <ci>beta_2</ci>
               <apply>
                  <minus/>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <ci>alpha_2</ci>
                        <ci>l_2</ci>
                     </apply>
                  </apply>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>F_XSE</ci>
            <apply>
               <times/>
               <ci>beta_3</ci>
               <apply>
                  <minus/>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <ci>alpha_3</ci>
                        <ci>l_3</ci>
                     </apply>
                  </apply>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component name="crossbridge_kinetics">
      <variable initial_value="0.0001" name="N" public_interface="out" units="dimensionless"/>
      <variable name="K_chi" public_interface="out" units="per_second"/>
      <variable name="M_A" units="dimensionless"/>
      <variable name="n_1" units="dimensionless"/>
      <variable name="L_oz" public_interface="out" units="dimensionless"/>
      <variable name="k_p_v" units="per_second"/>
      <variable name="k_m_v" units="per_second"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="A" public_interface="in" units="micromole"/>
      <variable name="l_1" public_interface="in" units="micrometre"/>
      <variable name="A_half" public_interface="in" units="micromole"/>
      <variable name="mu" public_interface="in" units="dimensionless"/>
      <variable name="chi" public_interface="in" units="dimensionless"/>
      <variable name="chi_0" public_interface="in" units="dimensionless"/>
      <variable name="m_0" public_interface="in" units="dimensionless"/>
      <variable name="S_0" public_interface="in" units="micrometre"/>
      <variable name="q_v" public_interface="in" units="per_second"/>
      <variable name="v" public_interface="in" units="micrometre_per_second"/>
      <variable name="v_star" public_interface="in" units="micrometre_per_second"/>
      <variable name="G_star" public_interface="in" units="dimensionless"/>
      <variable name="P_star" public_interface="in" units="dimensionless"/>
      <variable name="q_4" public_interface="in" units="per_second"/>
      <variable initial_value="560" name="v_0" units="micrometre_per_second"/>
      <variable initial_value="1000" name="q_star" units="per_second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>M_A</ci>
            <apply>
               <divide/>
               <apply>
                  <power/>
                  <ci>A</ci>
                  <ci>mu</ci>
               </apply>
               <apply>
                  <plus/>
                  <apply>
                     <power/>
                     <ci>A</ci>
                     <ci>mu</ci>
                  </apply>
                  <apply>
                     <power/>
                     <ci>A_half</ci>
                     <ci>mu</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>n_1</ci>
            <apply>
               <plus/>
               <apply>
                  <times/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_micrometre">0.6</cn>
                  <ci>l_1</ci>
               </apply>
               <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.5</cn>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>L_oz</ci>
            <apply>
               <divide/>
               <apply>
                  <plus/>
                  <ci>l_1</ci>
                  <ci>S_0</ci>
               </apply>
               <apply>
                  <plus/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micrometre">0.46</cn>
                  <ci>S_0</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>k_p_v</ci>
            <apply>
               <times/>
               <ci>chi</ci>
               <ci>chi_0</ci>
               <ci>q_v</ci>
               <ci>m_0</ci>
               <ci>G_star</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>k_m_v</ci>
            <piecewise>
               <piece>
                  <apply>
                     <times/>
                     <ci>chi_0</ci>
                     <ci>q_v</ci>
                     <apply>
                        <minus/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                        <apply>
                           <times/>
                           <ci>chi</ci>
                           <ci>m_0</ci>
                           <ci>G_star</ci>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <leq/>
                     <ci>v</ci>
                     <ci>v_star</ci>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <times/>
                     <ci>chi_0</ci>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <ci>q_4</ci>
                           <apply>
                              <minus/>
                              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                              <apply>
                                 <times/>
                                 <ci>chi</ci>
                                 <ci>m_0</ci>
                                 <ci>G_star</ci>
                              </apply>
                           </apply>
                        </apply>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <ci>q_star</ci>
                              <apply>
                                 <minus/>
                                 <ci>v</ci>
                                 <ci>v_star</ci>
                              </apply>
                           </apply>
                           <apply>
                              <minus/>
                              <ci>v_0</ci>
                              <ci>v_star</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>K_chi</ci>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>k_p_v</ci>
                  <ci>M_A</ci>
                  <ci>n_1</ci>
                  <ci>L_oz</ci>
                  <apply>
                     <minus/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     <ci>N</ci>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>k_m_v</ci>
                  <ci>N</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>N</ci>
            </apply>
            <ci>K_chi</ci>
         </apply>
      </math>
   </component>
   <component name="length">
      <variable name="dl_1_dt" public_interface="out" units="micrometre_per_second"/>
      <variable initial_value="0.437" name="l_1" public_interface="out" units="micrometre"/>
      <variable name="dl_2_dt" public_interface="out" units="micrometre_per_second"/>
      <variable initial_value="0.439" name="l_2" public_interface="out" units="micrometre"/>
      <variable name="dl_3_dt" public_interface="out" units="micrometre_per_second"/>
      <variable initial_value="0.089" name="l_3" public_interface="out" units="micrometre"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="isotonic_mode" public_interface="in" units="dimensionless"/>
      <variable name="v" public_interface="in" units="micrometre_per_second"/>
      <variable name="w" public_interface="in" units="micrometre_per_second"/>
      <variable name="l" public_interface="out" units="micrometre"/>
      <variable name="k_S_vis" public_interface="in" units="millinewton_second_per_micrometre"/>
      <variable name="phi_chi_2" public_interface="in" units="micrometre_per_second"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>l</ci>
            <apply>
               <plus/>
               <ci>l_2</ci>
               <ci>l_3</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>dl_1_dt</ci>
            <ci>v</ci>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>l_1</ci>
            </apply>
            <ci>dl_1_dt</ci>
         </apply>
         <apply>
            <eq/>
            <ci>dl_2_dt</ci>
            <piecewise>
               <piece>
                  <ci>phi_chi_2</ci>
                  <apply>
                     <eq/>
                     <ci>k_S_vis</ci>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millinewton_second_per_micrometre">0</cn>
                  </apply>
               </piece>
               <otherwise>
                  <ci>w</ci>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>l_2</ci>
            </apply>
            <ci>dl_2_dt</ci>
         </apply>
         <apply>
            <eq/>
            <ci>dl_3_dt</ci>
            <piecewise>
               <piece>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micrometre_per_second">0</cn>
                  <apply>
                     <eq/>
                     <ci>isotonic_mode</ci>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                  </apply>
               </piece>
               <piece>
                  <apply>
                     <minus/>
                     <ci>phi_chi_2</ci>
                  </apply>
                  <apply>
                     <and/>
                     <apply>
                        <eq/>
                        <ci>isotonic_mode</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0</cn>
                     </apply>
                     <apply>
                        <eq/>
                        <ci>k_S_vis</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millinewton_second_per_micrometre">0</cn>
                     </apply>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <minus/>
                     <ci>w</ci>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>l_3</ci>
            </apply>
            <ci>dl_3_dt</ci>
         </apply>
      </math>
   </component>
   <component name="CE_velocity">
      <variable initial_value="0" name="v" public_interface="out" units="micrometre_per_second"/>
      <variable name="phi_chi" public_interface="out" units="micrometre_per_second2"/>
      <variable name="phi_chi_2" public_interface="out" units="micrometre_per_second"/>
      <variable name="k_P_vis" public_interface="out" units="millinewton_second_per_micrometre"/>
      <variable name="k_S_vis" public_interface="in" units="millinewton_second_per_micrometre"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="w" public_interface="in" units="micrometre_per_second"/>
      <variable name="K_chi" public_interface="in" units="per_second"/>
      <variable name="N" public_interface="in" units="dimensionless"/>
      <variable name="l_1" public_interface="in" units="micrometre"/>
      <variable name="dl_1_dt" public_interface="in" units="micrometre_per_second"/>
      <variable name="l_2" public_interface="in" units="micrometre"/>
      <variable name="l_3" public_interface="in" units="micrometre"/>
      <variable name="alpha_1" public_interface="in" units="per_micrometre"/>
      <variable name="beta_1" public_interface="in" units="millinewton"/>
      <variable name="alpha_2" public_interface="in" units="per_micrometre"/>
      <variable name="beta_2" public_interface="in" units="millinewton"/>
      <variable name="alpha_3" public_interface="in" units="per_micrometre"/>
      <variable name="beta_3" public_interface="in" units="millinewton"/>
      <variable name="lambda" public_interface="in" units="millinewton"/>
      <variable name="isotonic_mode" public_interface="in" units="dimensionless"/>
      <variable name="p_v" public_interface="in" units="dimensionless"/>
      <variable name="p_prime_v" public_interface="in" units="second_per_micrometre"/>
      <variable initial_value="16" name="alpha_P_lengthening" units="per_micrometre"/>
      <variable initial_value="0.0015" name="beta_P_lengthening" units="millinewton_second_per_micrometre"/>
      <variable initial_value="16" name="alpha_P_shortening" units="per_micrometre"/>
      <variable initial_value="0.0015" name="beta_P_shortening" units="millinewton_second_per_micrometre"/>
      <variable name="alp_p" units="per_micrometre"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alp_p</ci>
            <piecewise>
               <piece>
                  <ci>alpha_P_lengthening</ci>
                  <apply>
                     <leq/>
                     <ci>v</ci>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micrometre_per_second">0</cn>
                  </apply>
               </piece>
               <otherwise>
                  <ci>alpha_P_shortening</ci>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>k_P_vis</ci>
            <piecewise>
               <piece>
                  <apply>
                     <times/>
                     <ci>beta_P_lengthening</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <times/>
                           <ci>alpha_P_lengthening</ci>
                           <ci>l_1</ci>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <leq/>
                     <ci>v</ci>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micrometre_per_second">0</cn>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <times/>
                     <ci>beta_P_shortening</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <times/>
                           <ci>alpha_P_shortening</ci>
                           <ci>l_1</ci>
                        </apply>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>phi_chi</ci>
            <piecewise>
               <piece>
                  <apply>
                     <divide/>
                     <apply>
                        <minus/>
                        <apply>
                           <plus/>
                           <apply>
                              <times/>
                              <ci>lambda</ci>
                              <ci>K_chi</ci>
                              <ci>p_v</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>alp_p</ci>
                              <ci>k_P_vis</ci>
                              <apply>
                                 <power/>
                                 <ci>v</ci>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                              </apply>
                           </apply>
                           <apply>
                              <times/>
                              <ci>alpha_2</ci>
                              <ci>beta_2</ci>
                              <apply>
                                 <exp/>
                                 <apply>
                                    <times/>
                                    <ci>alpha_2</ci>
                                    <ci>l_2</ci>
                                 </apply>
                              </apply>
                              <ci>w</ci>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <ci>lambda</ci>
                           <ci>N</ci>
                           <ci>p_prime_v</ci>
                        </apply>
                        <ci>k_P_vis</ci>
                     </apply>
                  </apply>
                  <apply>
                     <eq/>
                     <ci>isotonic_mode</ci>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <apply>
                        <minus/>
                        <apply>
                           <plus/>
                           <apply>
                              <times/>
                              <ci>lambda</ci>
                              <ci>K_chi</ci>
                              <ci>p_v</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>alp_p</ci>
                              <ci>k_P_vis</ci>
                              <apply>
                                 <power/>
                                 <ci>v</ci>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                              </apply>
                           </apply>
                           <apply>
                              <times/>
                              <apply>
                                 <plus/>
                                 <apply>
                                    <times/>
                                    <ci>alpha_2</ci>
                                    <ci>beta_2</ci>
                                    <apply>
                                       <exp/>
                                       <apply>
                                          <times/>
                                          <ci>alpha_2</ci>
                                          <ci>l_2</ci>
                                       </apply>
                                    </apply>
                                 </apply>
                                 <apply>
                                    <times/>
                                    <ci>alpha_3</ci>
                                    <ci>beta_3</ci>
                                    <apply>
                                       <exp/>
                                       <apply>
                                          <times/>
                                          <ci>alpha_3</ci>
                                          <ci>l_3</ci>
                                       </apply>
                                    </apply>
                                 </apply>
                              </apply>
                              <ci>w</ci>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <ci>lambda</ci>
                           <ci>N</ci>
                           <ci>p_prime_v</ci>
                        </apply>
                        <ci>k_P_vis</ci>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>phi_chi_2</ci>
            <piecewise>
               <piece>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>alpha_1</ci>
                        <ci>beta_1</ci>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <ci>alpha_1</ci>
                              <apply>
                                 <minus/>
                                 <ci>l_2</ci>
                                 <ci>l_1</ci>
                              </apply>
                           </apply>
                        </apply>
                        <ci>v</ci>
                     </apply>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <ci>alpha_1</ci>
                           <ci>beta_1</ci>
                           <apply>
                              <exp/>
                              <apply>
                                 <times/>
                                 <ci>alpha_1</ci>
                                 <apply>
                                    <minus/>
                                    <ci>l_2</ci>
                                    <ci>l_1</ci>
                                 </apply>
                              </apply>
                           </apply>
                        </apply>
                        <apply>
                           <times/>
                           <ci>alpha_2</ci>
                           <ci>beta_2</ci>
                           <apply>
                              <exp/>
                              <apply>
                                 <times/>
                                 <ci>alpha_2</ci>
                                 <ci>l_2</ci>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <eq/>
                     <ci>isotonic_mode</ci>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>alpha_1</ci>
                        <ci>beta_1</ci>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <ci>alpha_1</ci>
                              <apply>
                                 <minus/>
                                 <ci>l_2</ci>
                                 <ci>l_1</ci>
                              </apply>
                           </apply>
                        </apply>
                        <ci>v</ci>
                     </apply>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <ci>alpha_1</ci>
                           <ci>beta_1</ci>
                           <apply>
                              <exp/>
                              <apply>
                                 <times/>
                                 <ci>alpha_1</ci>
                                 <apply>
                                    <minus/>
                                    <ci>l_2</ci>
                                    <ci>l_1</ci>
                                 </apply>
                              </apply>
                           </apply>
                        </apply>
                        <apply>
                           <times/>
                           <ci>alpha_2</ci>
                           <ci>beta_2</ci>
                           <apply>
                              <exp/>
                              <apply>
                                 <times/>
                                 <ci>alpha_2</ci>
                                 <ci>l_2</ci>
                              </apply>
                           </apply>
                        </apply>
                        <apply>
                           <times/>
                           <ci>alpha_3</ci>
                           <ci>beta_3</ci>
                           <apply>
                              <exp/>
                              <apply>
                                 <times/>
                                 <ci>alpha_3</ci>
                                 <ci>l_3</ci>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>v</ci>
            </apply>
            <piecewise>
               <piece>
                  <apply>
                     <divide/>
                     <apply>
                        <minus/>
                        <apply>
                           <times/>
                           <ci>alpha_1</ci>
                           <ci>beta_1</ci>
                           <apply>
                              <exp/>
                              <apply>
                                 <times/>
                                 <ci>alpha_1</ci>
                                 <apply>
                                    <minus/>
                                    <ci>l_2</ci>
                                    <ci>l_1</ci>
                                 </apply>
                              </apply>
                           </apply>
                           <apply>
                              <minus/>
                              <ci>phi_chi_2</ci>
                              <ci>v</ci>
                           </apply>
                        </apply>
                        <apply>
                           <plus/>
                           <apply>
                              <times/>
                              <ci>lambda</ci>
                              <ci>K_chi</ci>
                              <ci>p_v</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>alp_p</ci>
                              <ci>k_P_vis</ci>
                              <apply>
                                 <power/>
                                 <ci>v</ci>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <ci>lambda</ci>
                           <ci>N</ci>
                           <ci>p_prime_v</ci>
                        </apply>
                        <ci>k_P_vis</ci>
                     </apply>
                  </apply>
                  <apply>
                     <eq/>
                     <ci>k_S_vis</ci>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millinewton_second_per_micrometre">0</cn>
                  </apply>
               </piece>
               <otherwise>
                  <ci>phi_chi</ci>
               </otherwise>
            </piecewise>
         </apply>
      </math>
   </component>
   <component name="PE_velocity">
      <variable initial_value="0" name="w" public_interface="out" units="micrometre_per_second"/>
      <variable name="k_S_vis" public_interface="out" units="millinewton_second_per_micrometre"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="v" public_interface="in" units="micrometre_per_second"/>
      <variable name="phi_chi" public_interface="in" units="micrometre_per_second2"/>
      <variable name="l_1" public_interface="in" units="micrometre"/>
      <variable name="dl_1_dt" public_interface="in" units="micrometre_per_second"/>
      <variable name="l_2" public_interface="in" units="micrometre"/>
      <variable name="dl_2_dt" public_interface="in" units="micrometre_per_second"/>
      <variable name="l_3" public_interface="in" units="micrometre"/>
      <variable name="alpha_1" public_interface="in" units="per_micrometre"/>
      <variable name="beta_1" public_interface="in" units="millinewton"/>
      <variable name="alpha_2" public_interface="in" units="per_micrometre"/>
      <variable name="beta_2" public_interface="in" units="millinewton"/>
      <variable name="alpha_3" public_interface="in" units="per_micrometre"/>
      <variable name="beta_3" public_interface="in" units="millinewton"/>
      <variable name="lambda" public_interface="in" units="millinewton"/>
      <variable name="isotonic_mode" public_interface="in" units="dimensionless"/>
      <variable initial_value="39" name="alpha_S_lengthening" units="per_micrometre"/>
      <variable initial_value="0.008" name="beta_S_lengthening" units="millinewton_second_per_micrometre"/>
      <variable initial_value="46" name="alpha_S_shortening" units="per_micrometre"/>
      <variable initial_value="0.006" name="beta_S_shortening" units="millinewton_second_per_micrometre"/>
      <variable name="alp_s" units="per_micrometre"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>alp_s</ci>
            <piecewise>
               <piece>
                  <ci>alpha_S_lengthening</ci>
                  <apply>
                     <leq/>
                     <ci>w</ci>
                     <ci>v</ci>
                  </apply>
               </piece>
               <otherwise>
                  <ci>alpha_S_shortening</ci>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>k_S_vis</ci>
            <piecewise>
               <piece>
                  <apply>
                     <times/>
                     <ci>beta_S_lengthening</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <times/>
                           <ci>alpha_S_lengthening</ci>
                           <apply>
                              <minus/>
                              <ci>l_2</ci>
                              <ci>l_1</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <leq/>
                     <ci>w</ci>
                     <ci>v</ci>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <times/>
                     <ci>beta_S_shortening</ci>
                     <apply>
                        <exp/>
                        <apply>
                           <times/>
                           <ci>alpha_S_shortening</ci>
                           <apply>
                              <minus/>
                              <ci>l_2</ci>
                              <ci>l_1</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>w</ci>
            </apply>
            <piecewise>
               <piece>
                  <apply>
                     <divide/>
                     <apply>
                        <minus/>
                        <apply>
                           <minus/>
                           <apply>
                              <times/>
                              <ci>k_S_vis</ci>
                              <apply>
                                 <minus/>
                                 <ci>phi_chi</ci>
                                 <apply>
                                    <times/>
                                    <ci>alp_s</ci>
                                    <apply>
                                       <power/>
                                       <apply>
                                          <minus/>
                                          <ci>w</ci>
                                          <ci>v</ci>
                                       </apply>
                                       <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                                    </apply>
                                 </apply>
                              </apply>
                           </apply>
                           <apply>
                              <times/>
                              <ci>alpha_1</ci>
                              <ci>beta_1</ci>
                              <apply>
                                 <exp/>
                                 <apply>
                                    <times/>
                                    <ci>alpha_1</ci>
                                    <apply>
                                       <minus/>
                                       <ci>l_2</ci>
                                       <ci>l_1</ci>
                                    </apply>
                                 </apply>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>w</ci>
                                 <ci>v</ci>
                              </apply>
                           </apply>
                        </apply>
                        <apply>
                           <times/>
                           <ci>alpha_2</ci>
                           <ci>beta_2</ci>
                           <apply>
                              <exp/>
                              <apply>
                                 <times/>
                                 <ci>alpha_2</ci>
                                 <ci>l_2</ci>
                              </apply>
                           </apply>
                           <ci>w</ci>
                        </apply>
                     </apply>
                     <ci>k_S_vis</ci>
                  </apply>
                  <apply>
                     <eq/>
                     <ci>isotonic_mode</ci>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <minus/>
                     <apply>
                        <minus/>
                        <ci>phi_chi</ci>
                        <apply>
                           <times/>
                           <ci>alp_s</ci>
                           <apply>
                              <power/>
                              <apply>
                                 <minus/>
                                 <ci>w</ci>
                                 <ci>v</ci>
                              </apply>
                              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <divide/>
                        <apply>
                           <plus/>
                           <apply>
                              <times/>
                              <ci>alpha_1</ci>
                              <ci>beta_1</ci>
                              <apply>
                                 <exp/>
                                 <apply>
                                    <times/>
                                    <ci>alpha_1</ci>
                                    <apply>
                                       <minus/>
                                       <ci>l_2</ci>
                                       <ci>l_1</ci>
                                    </apply>
                                 </apply>
                              </apply>
                              <apply>
                                 <minus/>
                                 <ci>w</ci>
                                 <ci>v</ci>
                              </apply>
                           </apply>
                           <apply>
                              <times/>
                              <apply>
                                 <plus/>
                                 <apply>
                                    <times/>
                                    <ci>alpha_2</ci>
                                    <ci>beta_2</ci>
                                    <apply>
                                       <exp/>
                                       <apply>
                                          <times/>
                                          <ci>alpha_2</ci>
                                          <ci>l_2</ci>
                                       </apply>
                                    </apply>
                                 </apply>
                                 <apply>
                                    <times/>
                                    <ci>alpha_3</ci>
                                    <ci>beta_3</ci>
                                    <apply>
                                       <exp/>
                                       <apply>
                                          <times/>
                                          <ci>alpha_3</ci>
                                          <ci>l_3</ci>
                                       </apply>
                                    </apply>
                                 </apply>
                              </apply>
                              <ci>w</ci>
                           </apply>
                        </apply>
                        <ci>k_S_vis</ci>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
      </math>
   </component>
   <component name="average_crossbridge_force">
      <variable name="p_v" public_interface="out" units="dimensionless"/>
      <variable name="p_prime_v" public_interface="out" units="second_per_micrometre"/>
      <variable name="P_star" public_interface="out" units="dimensionless"/>
      <variable name="G_star" public_interface="out" units="dimensionless"/>
      <variable name="gamma" units="dimensionless"/>
      <variable name="case_1" units="second_per_micrometre"/>
      <variable name="case_2" units="second_per_micrometre"/>
      <variable name="case_3" units="second_per_micrometre"/>
      <variable name="case_4" units="second_per_micrometre"/>
      <variable name="v" public_interface="in" units="micrometre_per_second"/>
      <variable name="phi_chi" public_interface="in" units="micrometre_per_second2"/>
      <variable name="v_1" public_interface="in" units="micrometre_per_second"/>
      <variable name="v_max" public_interface="in" units="micrometre_per_second"/>
      <variable name="a" public_interface="in" units="dimensionless"/>
      <variable name="d_h" public_interface="in" units="dimensionless"/>
      <variable name="alpha_G" public_interface="in" units="dimensionless"/>
      <variable name="alpha_P" public_interface="in" units="dimensionless"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>gamma</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>a</ci>
                  <ci>d_h</ci>
                  <apply>
                     <power/>
                     <apply>
                        <divide/>
                        <ci>v_1</ci>
                        <ci>v_max</ci>
                     </apply>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                  </apply>
               </apply>
               <apply>
                  <minus/>
                  <apply>
                     <times/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn>
                     <ci>a</ci>
                     <ci>d_h</ci>
                  </apply>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <apply>
                           <plus/>
                           <ci>a</ci>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                        </apply>
                        <ci>v_1</ci>
                     </apply>
                     <ci>v_max</ci>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>P_star</ci>
            <piecewise>
               <piece>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>a</ci>
                        <apply>
                           <plus/>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                           <apply>
                              <divide/>
                              <ci>v</ci>
                              <ci>v_max</ci>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <minus/>
                        <ci>a</ci>
                        <apply>
                           <divide/>
                           <ci>v</ci>
                           <ci>v_max</ci>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <leq/>
                     <ci>v</ci>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micrometre_per_second">0</cn>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <minus/>
                     <apply>
                        <plus/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                        <ci>d_h</ci>
                     </apply>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <apply>
                              <power/>
                              <ci>d_h</ci>
                              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                           </apply>
                           <ci>a</ci>
                        </apply>
                        <apply>
                           <plus/>
                           <apply>
                              <times/>
                              <apply>
                                 <divide/>
                                 <apply>
                                    <times/>
                                    <ci>a</ci>
                                    <ci>d_h</ci>
                                 </apply>
                                 <ci>gamma</ci>
                              </apply>
                              <apply>
                                 <power/>
                                 <apply>
                                    <divide/>
                                    <ci>v</ci>
                                    <ci>v_max</ci>
                                 </apply>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                              </apply>
                           </apply>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <apply>
                                    <plus/>
                                    <ci>a</ci>
                                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                                 </apply>
                                 <ci>v</ci>
                              </apply>
                              <ci>v_max</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>a</ci>
                              <ci>d_h</ci>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>G_star</ci>
            <piecewise>
               <piece>
                  <apply>
                     <plus/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.6</cn>
                           <ci>v</ci>
                        </apply>
                        <ci>v_max</ci>
                     </apply>
                  </apply>
                  <apply>
                     <and/>
                     <apply>
                        <leq/>
                        <apply>
                           <minus/>
                           <ci>v_max</ci>
                        </apply>
                        <ci>v</ci>
                     </apply>
                     <apply>
                        <leq/>
                        <ci>v</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micrometre_per_second">0</cn>
                     </apply>
                  </apply>
               </piece>
               <piece>
                  <apply>
                     <divide/>
                     <ci>P_star</ci>
                     <apply>
                        <plus/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <plus/>
                                 <apply>
                                    <times/>
                                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.4</cn>
                                    <ci>a</ci>
                                 </apply>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                              </apply>
                              <ci>v</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>a</ci>
                              <ci>v_max</ci>
                           </apply>
                        </apply>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     </apply>
                  </apply>
                  <apply>
                     <and/>
                     <apply>
                        <lt/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micrometre_per_second">0</cn>
                        <ci>v</ci>
                     </apply>
                     <apply>
                        <leq/>
                        <ci>v</ci>
                        <ci>v_1</ci>
                     </apply>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <divide/>
                     <apply>
                        <times/>
                        <ci>P_star</ci>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <ci>alpha_G</ci>
                              </apply>
                              <apply>
                                 <power/>
                                 <apply>
                                    <divide/>
                                    <apply>
                                       <minus/>
                                       <ci>v</ci>
                                       <ci>v_1</ci>
                                    </apply>
                                    <ci>v_max</ci>
                                 </apply>
                                 <ci>alpha_P</ci>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <plus/>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <plus/>
                                 <apply>
                                    <times/>
                                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.4</cn>
                                    <ci>a</ci>
                                 </apply>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                              </apply>
                              <ci>v</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>a</ci>
                              <ci>v_max</ci>
                           </apply>
                        </apply>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>case_1</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>a</ci>
                  <apply>
                     <plus/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.4</cn>
                     <apply>
                        <times/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.4</cn>
                        <ci>a</ci>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>v_max</ci>
                  <apply>
                     <power/>
                     <apply>
                        <times/>
                        <apply>
                           <plus/>
                           <ci>a</ci>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                        </apply>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.4</cn>
                     </apply>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>case_2</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>a</ci>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                  <apply>
                     <plus/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     <apply>
                        <times/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.4</cn>
                        <ci>a</ci>
                     </apply>
                     <apply>
                        <divide/>
                        <apply>
                           <times/>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.2</cn>
                           <ci>v</ci>
                        </apply>
                        <ci>v_max</ci>
                     </apply>
                     <apply>
                        <times/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.6</cn>
                        <apply>
                           <power/>
                           <apply>
                              <divide/>
                              <ci>v</ci>
                              <ci>v_max</ci>
                           </apply>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <times/>
                  <ci>v_max</ci>
                  <apply>
                     <power/>
                     <apply>
                        <times/>
                        <apply>
                           <minus/>
                           <ci>a</ci>
                           <apply>
                              <divide/>
                              <ci>v</ci>
                              <ci>v_max</ci>
                           </apply>
                        </apply>
                        <apply>
                           <plus/>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                           <apply>
                              <divide/>
                              <apply>
                                 <times/>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.6</cn>
                                 <ci>v</ci>
                              </apply>
                              <ci>v_max</ci>
                           </apply>
                        </apply>
                     </apply>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>case_3</ci>
            <apply>
               <divide/>
               <apply>
                  <plus/>
                  <apply>
                     <times/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.4</cn>
                     <ci>a</ci>
                  </apply>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
               </apply>
               <apply>
                  <times/>
                  <ci>a</ci>
                  <ci>v_max</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>case_4</ci>
            <apply>
               <times/>
               <apply>
                  <divide/>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                  <ci>v_max</ci>
               </apply>
               <apply>
                  <exp/>
                  <apply>
                     <times/>
                     <apply>
                        <minus/>
                        <ci>alpha_G</ci>
                     </apply>
                     <apply>
                        <power/>
                        <apply>
                           <minus/>
                           <apply>
                              <divide/>
                              <ci>v</ci>
                              <ci>v_max</ci>
                           </apply>
                           <apply>
                              <divide/>
                              <ci>v_1</ci>
                              <ci>v_max</ci>
                           </apply>
                        </apply>
                        <ci>alpha_P</ci>
                     </apply>
                  </apply>
               </apply>
               <apply>
                  <plus/>
                  <apply>
                     <divide/>
                     <apply>
                        <plus/>
                        <apply>
                           <times/>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.4</cn>
                           <ci>a</ci>
                        </apply>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                     </apply>
                     <ci>a</ci>
                  </apply>
                  <apply>
                     <times/>
                     <ci>alpha_G</ci>
                     <ci>alpha_P</ci>
                     <apply>
                        <plus/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                        <apply>
                           <divide/>
                           <apply>
                              <times/>
                              <apply>
                                 <plus/>
                                 <apply>
                                    <times/>
                                    <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.4</cn>
                                    <ci>a</ci>
                                 </apply>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                              </apply>
                              <ci>v</ci>
                           </apply>
                           <apply>
                              <times/>
                              <ci>a</ci>
                              <ci>v_max</ci>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <power/>
                        <apply>
                           <minus/>
                           <apply>
                              <divide/>
                              <ci>v</ci>
                              <ci>v_max</ci>
                           </apply>
                           <apply>
                              <divide/>
                              <ci>v_1</ci>
                              <ci>v_max</ci>
                           </apply>
                        </apply>
                        <apply>
                           <minus/>
                           <ci>alpha_P</ci>
                           <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                        </apply>
                     </apply>
                  </apply>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>p_v</ci>
            <apply>
               <divide/>
               <ci>P_star</ci>
               <ci>G_star</ci>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>p_prime_v</ci>
            <piecewise>
               <piece>
                  <ci>case_1</ci>
                  <apply>
                     <leq/>
                     <ci>v</ci>
                     <apply>
                        <minus/>
                        <ci>v_max</ci>
                     </apply>
                  </apply>
               </piece>
               <piece>
                  <ci>case_2</ci>
                  <apply>
                     <and/>
                     <apply>
                        <lt/>
                        <apply>
                           <minus/>
                           <ci>v_max</ci>
                        </apply>
                        <ci>v</ci>
                     </apply>
                     <apply>
                        <leq/>
                        <ci>v</ci>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micrometre_per_second">0</cn>
                     </apply>
                  </apply>
               </piece>
               <piece>
                  <ci>case_3</ci>
                  <apply>
                     <and/>
                     <apply>
                        <lt/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="micrometre_per_second">0</cn>
                        <ci>v</ci>
                     </apply>
                     <apply>
                        <leq/>
                        <ci>v</ci>
                        <ci>v_1</ci>
                     </apply>
                  </apply>
               </piece>
               <otherwise>
                  <ci>case_4</ci>
               </otherwise>
            </piecewise>
         </apply>
      </math>
   </component>
   <component name="calcium_handling">
      <variable initial_value="0.7" name="A" public_interface="out" units="micromole"/>
      <variable name="dA_dt" units="micromole_per_second"/>
      <variable name="N_A" units="dimensionless"/>
      <variable name="pi_N_A" units="dimensionless"/>
      <variable cmeta:id="calcium_handling_B" initial_value="0" name="B" public_interface="out" units="micromole"/>
      <variable name="dB_dt" units="micromole_per_second"/>
      <variable initial_value="0" name="Ca_C" public_interface="out" units="micromole"/>
      <variable name="time" public_interface="in" units="second"/>
      <variable name="N" public_interface="in" units="dimensionless"/>
      <variable name="a_on" public_interface="in" units="per_second_micromole"/>
      <variable name="a_off" public_interface="in" units="per_second"/>
      <variable name="k_A" public_interface="in" units="per_micromole"/>
      <variable name="L_oz" public_interface="in" units="dimensionless"/>
      <variable initial_value="70" name="A_tot" units="micromole"/>
      <variable initial_value="28" name="B_tot" units="micromole"/>
      <variable initial_value="37.143" name="b_on" units="per_second_micromole"/>
      <variable initial_value="182" name="b_off" units="per_second"/>
      <variable initial_value="5200" name="a_c" units="per_second2"/>
      <variable initial_value="650" name="r_Ca" units="per_second"/>
      <variable initial_value="0.714" name="q_Ca" units="per_micromole"/>
      <variable initial_value="0.033" name="t_d" units="second"/>
      <variable initial_value="2.1" name="Ca_m" units="micromole"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>N_A</ci>
            <apply>
               <divide/>
               <apply>
                  <times/>
                  <ci>A_tot</ci>
                  <ci>N</ci>
               </apply>
               <apply>
                  <times/>
                  <ci>L_oz</ci>
                  <ci>A</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <ci>pi_N_A</ci>
            <piecewise>
               <piece>
                  <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                  <apply>
                     <geq/>
                     <ci>N_A</ci>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <power/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.02</cn>
                     <ci>N_A</ci>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
         <apply>
            <eq/>
            <ci>dA_dt</ci>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>a_on</ci>
                  <apply>
                     <minus/>
                     <ci>A_tot</ci>
                     <ci>A</ci>
                  </apply>
                  <ci>Ca_C</ci>
               </apply>
               <apply>
                  <times/>
                  <ci>a_off</ci>
                  <apply>
                     <exp/>
                     <apply>
                        <times/>
                        <apply>
                           <minus/>
                           <ci>k_A</ci>
                        </apply>
                        <ci>A</ci>
                     </apply>
                  </apply>
                  <ci>pi_N_A</ci>
                  <ci>A</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>A</ci>
            </apply>
            <ci>dA_dt</ci>
         </apply>
         <apply>
            <eq/>
            <ci>dB_dt</ci>
            <apply>
               <minus/>
               <apply>
                  <times/>
                  <ci>b_on</ci>
                  <apply>
                     <minus/>
                     <ci>B_tot</ci>
                     <ci>B</ci>
                  </apply>
                  <ci>Ca_C</ci>
               </apply>
               <apply>
                  <times/>
                  <ci>b_off</ci>
                  <ci>B</ci>
               </apply>
            </apply>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>B</ci>
            </apply>
            <ci>dB_dt</ci>
         </apply>
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>Ca_C</ci>
            </apply>
            <piecewise>
               <piece>
                  <apply>
                     <times/>
                     <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn>
                     <ci>a_c</ci>
                     <ci>Ca_m</ci>
                     <ci>time</ci>
                     <apply>
                        <minus/>
                        <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <ci>a_c</ci>
                              </apply>
                              <apply>
                                 <power/>
                                 <ci>time</ci>
                                 <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                              </apply>
                           </apply>
                        </apply>
                     </apply>
                     <apply>
                        <exp/>
                        <apply>
                           <times/>
                           <apply>
                              <minus/>
                              <ci>a_c</ci>
                           </apply>
                           <apply>
                              <power/>
                              <ci>time</ci>
                              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn>
                           </apply>
                        </apply>
                     </apply>
                  </apply>
                  <apply>
                     <lt/>
                     <ci>time</ci>
                     <ci>t_d</ci>
                  </apply>
               </piece>
               <otherwise>
                  <apply>
                     <minus/>
                     <apply>
                        <minus/>
                        <apply>
                           <minus/>
                           <ci>dA_dt</ci>
                        </apply>
                        <ci>dB_dt</ci>
                     </apply>
                     <apply>
                        <times/>
                        <ci>r_Ca</ci>
                        <apply>
                           <exp/>
                           <apply>
                              <times/>
                              <apply>
                                 <minus/>
                                 <ci>q_Ca</ci>
                              </apply>
                              <ci>Ca_C</ci>
                           </apply>
                        </apply>
                        <ci>Ca_C</ci>
                     </apply>
                  </apply>
               </otherwise>
            </piecewise>
         </apply>
      </math>
   </component>
   <connection>
      <map_components component_1="environment" component_2="isotonic"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="parameters" component_2="isotonic"/>
      <map_variables variable_1="isotonic" variable_2="isotonic"/>
   </connection>
   <connection>
      <map_components component_1="force" component_2="isotonic"/>
      <map_variables variable_1="F_muscle" variable_2="F_muscle"/>
   </connection>
   <connection>
      <map_components component_1="length" component_2="isotonic"/>
      <map_variables variable_1="isotonic_mode" variable_2="isotonic_mode"/>
      <map_variables variable_1="l" variable_2="l"/>
   </connection>
   <connection>
      <map_components component_1="PE_velocity" component_2="isotonic"/>
      <map_variables variable_1="isotonic_mode" variable_2="isotonic_mode"/>
   </connection>
   <connection>
      <map_components component_1="CE_velocity" component_2="isotonic"/>
      <map_variables variable_1="isotonic_mode" variable_2="isotonic_mode"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="crossbridge_kinetics"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="length"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="CE_velocity"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="PE_velocity"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="environment" component_2="calcium_handling"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection>
      <map_components component_1="parameters" component_2="parameters_izakov_et_al_1991"/>
      <map_variables variable_1="v_max" variable_2="v_max"/>
   </connection>
   <connection>
      <map_components component_1="force" component_2="parameters"/>
      <map_variables variable_1="alpha_1" variable_2="alpha_1"/>
      <map_variables variable_1="beta_1" variable_2="beta_1"/>
      <map_variables variable_1="alpha_2" variable_2="alpha_2"/>
      <map_variables variable_1="beta_2" variable_2="beta_2"/>
      <map_variables variable_1="alpha_3" variable_2="alpha_3"/>
      <map_variables variable_1="beta_3" variable_2="beta_3"/>
      <map_variables variable_1="lambda" variable_2="lambda"/>
   </connection>
   <connection>
      <map_components component_1="force" component_2="crossbridge_kinetics"/>
      <map_variables variable_1="N" variable_2="N"/>
   </connection>
   <connection>
      <map_components component_1="force" component_2="length"/>
      <map_variables variable_1="l_1" variable_2="l_1"/>
      <map_variables variable_1="l_2" variable_2="l_2"/>
      <map_variables variable_1="l_3" variable_2="l_3"/>
   </connection>
   <connection>
      <map_components component_1="force" component_2="CE_velocity"/>
      <map_variables variable_1="v" variable_2="v"/>
      <map_variables variable_1="k_P_vis" variable_2="k_P_vis"/>
   </connection>
   <connection>
      <map_components component_1="force" component_2="PE_velocity"/>
      <map_variables variable_1="w" variable_2="w"/>
      <map_variables variable_1="k_S_vis" variable_2="k_S_vis"/>
   </connection>
   <connection>
      <map_components component_1="force" component_2="average_crossbridge_force"/>
      <map_variables variable_1="p_v" variable_2="p_v"/>
   </connection>
   <connection>
      <map_components component_1="crossbridge_kinetics" component_2="parameters"/>
      <map_variables variable_1="A_half" variable_2="A_half"/>
      <map_variables variable_1="mu" variable_2="mu"/>
      <map_variables variable_1="chi" variable_2="chi"/>
      <map_variables variable_1="chi_0" variable_2="chi_0"/>
      <map_variables variable_1="m_0" variable_2="m_0"/>
   </connection>
   <connection>
      <map_components component_1="crossbridge_kinetics" component_2="calcium_handling"/>
      <map_variables variable_1="A" variable_2="A"/>
      <map_variables variable_1="N" variable_2="N"/>
      <map_variables variable_1="L_oz" variable_2="L_oz"/>
   </connection>
   <connection>
      <map_components component_1="crossbridge_kinetics" component_2="average_crossbridge_force"/>
      <map_variables variable_1="G_star" variable_2="G_star"/>
      <map_variables variable_1="P_star" variable_2="P_star"/>
   </connection>
   <connection>
      <map_components component_1="crossbridge_kinetics" component_2="length"/>
      <map_variables variable_1="l_1" variable_2="l_1"/>
   </connection>
   <connection>
      <map_components component_1="crossbridge_kinetics" component_2="CE_velocity"/>
      <map_variables variable_1="K_chi" variable_2="K_chi"/>
      <map_variables variable_1="v" variable_2="v"/>
      <map_variables variable_1="N" variable_2="N"/>
   </connection>
   <connection>
      <map_components component_1="crossbridge_kinetics" component_2="parameters_izakov_et_al_1991"/>
      <map_variables variable_1="S_0" variable_2="S_0"/>
      <map_variables variable_1="q_v" variable_2="q_v"/>
      <map_variables variable_1="v_star" variable_2="v_star"/>
      <map_variables variable_1="q_4" variable_2="q_4"/>
   </connection>
   <connection>
      <map_components component_1="length" component_2="CE_velocity"/>
      <map_variables variable_1="v" variable_2="v"/>
      <map_variables variable_1="phi_chi_2" variable_2="phi_chi_2"/>
      <map_variables variable_1="dl_1_dt" variable_2="dl_1_dt"/>
      <map_variables variable_1="l_1" variable_2="l_1"/>
      <map_variables variable_1="l_2" variable_2="l_2"/>
      <map_variables variable_1="l_3" variable_2="l_3"/>
   </connection>
   <connection>
      <map_components component_1="length" component_2="PE_velocity"/>
      <map_variables variable_1="w" variable_2="w"/>
      <map_variables variable_1="k_S_vis" variable_2="k_S_vis"/>
      <map_variables variable_1="dl_1_dt" variable_2="dl_1_dt"/>
      <map_variables variable_1="l_1" variable_2="l_1"/>
      <map_variables variable_1="dl_2_dt" variable_2="dl_2_dt"/>
      <map_variables variable_1="l_2" variable_2="l_2"/>
      <map_variables variable_1="l_3" variable_2="l_3"/>
   </connection>
   <connection>
      <map_components component_1="CE_velocity" component_2="parameters"/>
      <map_variables variable_1="alpha_1" variable_2="alpha_1"/>
      <map_variables variable_1="beta_1" variable_2="beta_1"/>
      <map_variables variable_1="alpha_2" variable_2="alpha_2"/>
      <map_variables variable_1="beta_2" variable_2="beta_2"/>
      <map_variables variable_1="alpha_3" variable_2="alpha_3"/>
      <map_variables variable_1="beta_3" variable_2="beta_3"/>
      <map_variables variable_1="lambda" variable_2="lambda"/>
   </connection>
   <connection>
      <map_components component_1="CE_velocity" component_2="parameters_izakov_et_al_1991"/>
      <map_variables variable_1="v" variable_2="v"/>
   </connection>
   <connection>
      <map_components component_1="CE_velocity" component_2="PE_velocity"/>
      <map_variables variable_1="v" variable_2="v"/>
      <map_variables variable_1="w" variable_2="w"/>
      <map_variables variable_1="k_S_vis" variable_2="k_S_vis"/>
      <map_variables variable_1="phi_chi" variable_2="phi_chi"/>
   </connection>
   <connection>
      <map_components component_1="PE_velocity" component_2="parameters"/>
      <map_variables variable_1="alpha_1" variable_2="alpha_1"/>
      <map_variables variable_1="beta_1" variable_2="beta_1"/>
      <map_variables variable_1="alpha_2" variable_2="alpha_2"/>
      <map_variables variable_1="beta_2" variable_2="beta_2"/>
      <map_variables variable_1="alpha_3" variable_2="alpha_3"/>
      <map_variables variable_1="beta_3" variable_2="beta_3"/>
      <map_variables variable_1="lambda" variable_2="lambda"/>
   </connection>
   <connection>
      <map_components component_1="average_crossbridge_force" component_2="parameters"/>
      <map_variables variable_1="v_max" variable_2="v_max"/>
      <map_variables variable_1="a" variable_2="a"/>
      <map_variables variable_1="d_h" variable_2="d_h"/>
      <map_variables variable_1="alpha_P" variable_2="alpha_P"/>
   </connection>
   <connection>
      <map_components component_1="average_crossbridge_force" component_2="parameters_izakov_et_al_1991"/>
      <map_variables variable_1="v_1" variable_2="v_1"/>
      <map_variables variable_1="alpha_G" variable_2="alpha_G"/>
   </connection>
   <connection>
      <map_components component_1="average_crossbridge_force" component_2="CE_velocity"/>
      <map_variables variable_1="v" variable_2="v"/>
      <map_variables variable_1="phi_chi" variable_2="phi_chi"/>
      <map_variables variable_1="p_v" variable_2="p_v"/>
      <map_variables variable_1="p_prime_v" variable_2="p_prime_v"/>
   </connection>
   <connection>
      <map_components component_1="calcium_handling" component_2="parameters_izakov_et_al_1991"/>
      <map_variables variable_1="a_on" variable_2="a_on"/>
      <map_variables variable_1="a_off" variable_2="a_off"/>
      <map_variables variable_1="k_A" variable_2="k_A"/>
   </connection>
</model>