Location: BG_crossbridge_TRPN @ 959277c48267 / BG_crossbridge_TRPN.cellml

Author:
Shelley Fong <sfon036@UoA.auckland.ac.nz>
Date:
2023-07-07 10:37:32+12:00
Desc:
Removing unused equations
Permanent Source URI:
https://models.physiomeproject.org/workspace/7fb/rawfile/959277c48267669dfd0cfd3d2051f1803d8330fc/BG_crossbridge_TRPN.cellml

<?xml version='1.0' encoding='UTF-8'?>
<!-- mass action kinetics for BUWS transitions (state of crossbridge stroke) combined with CaTRPN binding and unbinding (all Land model)-->
<!-- 2-damper system for zeta (distortion)
 assume dLambda/dt = 0 (as per Land)  ..  meaning no extension-->
<model name="individual_crossbridge_TRPN" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#" xmlns:xlink="http://www.w3.org/1999/xlink">
    <import xlink:href="units_and_constants/units_BG.cellml">
        <units name="mM" units_ref="mM"/>
        <units name="fmol" units_ref="fmol"/>
        <units name="per_fmol" units_ref="per_fmol"/>
        <units name="J_per_mol" units_ref="J_per_mol"/>
        <units name="fmol_per_sec" units_ref="fmol_per_sec"/>
        <units name="C_per_mol" units_ref="C_per_mol"/>
        <units name="J_per_C" units_ref="J_per_C"/>
        <units name="microm3" units_ref="microm3"/>
        <units name="fF" units_ref="fF"/>
        <units name="fC" units_ref="fC"/>
        <units name="fA" units_ref="fA"/>
        <units name="per_second" units_ref="per_second"/>
        <units name="millivolt" units_ref="millivolt"/>
        <units name="per_sec" units_ref="per_sec"/>
        <units name="J_per_K_per_mol" units_ref="J_per_K_per_mol"/>
        <units name="fmol_per_L" units_ref="fmol_per_L"/>
        <units name="fmol_per_L_per_sec" units_ref="fmol_per_L_per_sec"/>
        <units name="per_sec_per_fmol_per_L" units_ref="per_sec_per_fmol_per_L"/>
        <units name="uM" units_ref="uM"/>
        <units name="mM_per_sec" units_ref="mM_per_sec"/>
        <units name="uM_per_sec" units_ref="uM_per_sec"/>
        <units name="pL" units_ref="pL"/>
        <units name="m_to_u" units_ref="m_to_u"/>
    </import>
    <import xlink:href="units_and_constants/constants_BG.cellml">
        <component component_ref="constants" name="constants"/>
    </import>
    <units name="mm">
        <unit prefix="milli" units="metre"/>
    </units>
    <units name="mm2">
        <unit exponent="2" units="mm"/>
    </units>
    <units name="N_per_mm2">
        <unit units="newton"/>
        <unit exponent="-1" units="mm2"/>
    </units>
    <units name="mm2_per_N">
        <unit exponent="-1" units="N_per_mm2"/>
    </units>
    <units name="J_per_m">
        <unit units="joule"/>
        <unit exponent="-1" units="metre"/>
    </units>
    <units name="m_per_s">
        <unit units="metre"/>
        <unit exponent="-1" units="second"/>
    </units>
    <units name="Js_per_m2">
        <unit units="joule"/>
        <unit units="second"/>
        <unit exponent="-2" units="metre"/>
    </units>
    <units name="kPa">
        <unit prefix="kilo" units="pascal"/>
    </units>
    <units name="J_per_m_per_kPa">
        <unit units="joule"/>
        <unit exponent="-1" units="metre"/>
        <unit exponent="-1" units="kPa"/>
    </units>
    <units name="k_to_M">
        <unit prefix="mega" units="metre"/>
        <unit exponent="-1" prefix="kilo" units="metre"/>
    </units>
    <component name="environment">
        <variable name="time" public_interface="out" units="second"/>
        <variable name="n_CaTRPN" public_interface="in" units="dimensionless"/>
        <!-- initial values-->
        <variable initial_value="2.57" name="q_TRPN" public_interface="out" units="fmol"/>
        <variable initial_value="6.82e-1" name="q_Ca_i" public_interface="out" units="fmol"/>
        <variable initial_value="1e-6" name="q_Ca_TRPN" public_interface="out" units="fmol"/>
        <variable initial_value="1" name="q_B_XB" public_interface="out" units="fmol"/>
        <variable initial_value="0" name="q_U_XB" public_interface="out" units="fmol"/>
        <variable initial_value="0" name="q_W_XB" public_interface="out" units="fmol"/>
        <variable initial_value="0" name="q_S_XB" public_interface="out" units="fmol"/>
        <!-- From submodule-->
        <variable name="v_R_TRPNCa" public_interface="in" units="fmol_per_sec"/>
        <variable name="v_R_BU" public_interface="in" units="fmol_per_sec"/>
        <variable name="v_R_UW" public_interface="in" units="fmol_per_sec"/>
        <variable name="v_R_WS" public_interface="in" units="fmol_per_sec"/>
        <variable name="v_R_SU" public_interface="in" units="fmol_per_sec"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>q_Ca_i</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <times/>
                        <apply>
                            <minus/>
                            <ci>v_R_TRPNCa</ci>
                        </apply>
                        <ci>n_CaTRPN</ci>
                    </apply>
                    <ci>v_Ca_stim</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>q_TRPN</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_R_TRPNCa</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>q_Ca_TRPN</ci>
                </apply>
                <ci>v_R_TRPNCa</ci>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>q_B_XB</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_R_BU</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>q_U_XB</ci>
                </apply>
                <apply>
                    <plus/>
                    <apply>
                        <minus/>
                        <ci>v_R_BU</ci>
                        <ci>v_R_UW</ci>
                    </apply>
                    <ci>v_R_SU</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>q_W_XB</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_R_UW</ci>
                    <ci>v_R_WS</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>q_S_XB</ci>
                </apply>
                <apply>
                    <minus/>
                    <ci>v_R_WS</ci>
                    <ci>v_R_SU</ci>
                </apply>
            </apply>
        </math>
        <!-- tension-->
        <variable name="T_total" public_interface="in" units="kPa"/>
        <variable name="SL" public_interface="in" units="metre"/>
        <!-- Ca_stim-->
        <variable name="v_Ca_stim" units="fmol_per_sec"/>
        <variable initial_value="1" name="stimPeriod" units="second"/>
        <variable initial_value="0.001" name="stimDuration" units="second"/>
        <variable name="tPeriod" units="second"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>tPeriod</ci>
                <apply>
                    <minus/>
                    <ci>time</ci>
                    <apply>
                        <times/>
                        <apply>
                            <floor/>
                            <apply>
                                <divide/>
                                <ci>time</ci>
                                <ci>stimPeriod</ci>
                            </apply>
                        </apply>
                        <ci>stimPeriod</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_Ca_stim</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">1</cn>
                            <cn cellml:units="fmol_per_sec">80</cn>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <geq/>
                                <ci>tPeriod</ci>
                                <cn cellml:units="second">0.3</cn>
                            </apply>
                            <apply>
                                <leq/>
                                <ci>tPeriod</ci>
                                <apply>
                                    <plus/>
                                    <cn cellml:units="second">0.3</cn>
                                    <ci>stimDuration</ci>
                                </apply>
                            </apply>
                        </apply>
                    </piece>
                    <otherwise>
                        <cn cellml:units="fmol_per_sec">0.0</cn>
                    </otherwise>
                </piecewise>
            </apply>
        </math>
        <!-- changing sarcomere length-->
        <variable name="dSL" public_interface="out" units="m_per_s"/>
        <variable initial_value="19e-6" name="V_max" units="m_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>dSL</ci>
                <piecewise>
                    <piece>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">1</cn>
                            <ci>V_max</ci>
                        </apply>
                        <apply>
                            <lt/>
                            <ci>time</ci>
                            <cn cellml:units="second">0.06</cn>
                        </apply>
                    </piece>
                    <piece>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                            </apply>
                            <ci>V_max</ci>
                        </apply>
                        <apply>
                            <and/>
                            <apply>
                                <gt/>
                                <ci>time</ci>
                                <cn cellml:units="second">0.5</cn>
                            </apply>
                            <apply>
                                <lt/>
                                <ci>time</ci>
                                <cn cellml:units="second">0.56</cn>
                            </apply>
                        </apply>
                    </piece>
                    <otherwise>
                        <apply>
                            <times/>
                            <cn cellml:units="dimensionless">0</cn>
                            <ci>V_max</ci>
                        </apply>
                    </otherwise>
                </piecewise>
            </apply>
        </math>
    </component>
    <component name="crossbridge_TRPN_parameters">
        <variable initial_value="22.8658" name="kappa_R_TRPNCa" public_interface="out" units="fmol_per_sec"/>
        <variable initial_value="2.56831" name="kappa_R_BU" public_interface="out" units="fmol_per_sec"/>
        <variable initial_value="0.338467" name="kappa_R_UW" public_interface="out" units="fmol_per_sec"/>
        <variable initial_value="0.00796392" name="kappa_R_WS" public_interface="out" units="fmol_per_sec"/>
        <variable initial_value="143351" name="kappa_R_SU" public_interface="out" units="fmol_per_sec"/>
        <variable initial_value="0.428971" name="K_TRPN" public_interface="out" units="per_fmol"/>
        <variable initial_value="6.33016" name="K_Ca_i" public_interface="out" units="per_fmol"/>
        <variable initial_value="0.127132" name="K_Ca_TRPN" public_interface="out" units="per_fmol"/>
        <variable initial_value="5.95481" name="K_B_XB" public_interface="out" units="per_fmol"/>
        <variable initial_value="2.23305" name="K_U_XB" public_interface="out" units="per_fmol"/>
        <variable initial_value="14.6007" name="K_W_XB" public_interface="out" units="per_fmol"/>
        <variable initial_value="3.65018e-06" name="K_S_XB" public_interface="out" units="per_fmol"/>
        <variable initial_value="1.1" name="n_Tm" units="dimensionless"/>
        <variable initial_value="2" name="n_CaTRPN" units="dimensionless"/>
    </component>
    <component name="crossbridge_TRPN">
        <variable name="time" public_interface="in" units="second"/>
        <variable name="R" public_interface="in" units="J_per_K_per_mol"/>
        <variable name="T" public_interface="in" units="kelvin"/>
        <!-- parameters-->
        <variable name="kappa_R_TRPNCa" public_interface="in" units="fmol_per_sec"/>
        <variable name="kappa_R_BU" public_interface="in" units="fmol_per_sec"/>
        <variable name="kappa_R_UW" public_interface="in" units="fmol_per_sec"/>
        <variable name="kappa_R_WS" public_interface="in" units="fmol_per_sec"/>
        <variable name="kappa_R_SU" public_interface="in" units="fmol_per_sec"/>
        <variable name="K_TRPN" public_interface="in" units="per_fmol"/>
        <variable name="K_Ca_i" public_interface="in" units="per_fmol"/>
        <variable name="K_Ca_TRPN" public_interface="in" units="per_fmol"/>
        <variable name="K_B_XB" public_interface="in" units="per_fmol"/>
        <variable name="K_U_XB" public_interface="in" units="per_fmol"/>
        <variable name="K_W_XB" public_interface="in" units="per_fmol"/>
        <variable name="K_S_XB" public_interface="in" units="per_fmol"/>
        <variable name="n_Tm" public_interface="in" units="dimensionless"/>
        <variable name="n_CaTRPN" public_interface="in" units="dimensionless"/>
        <!-- Input from global environment-->
        <variable name="q_TRPN" public_interface="in" units="fmol"/>
        <variable name="q_Ca_i" public_interface="in" units="fmol"/>
        <variable name="q_Ca_TRPN" public_interface="in" units="fmol"/>
        <variable name="q_B_XB" public_interface="in" units="fmol"/>
        <variable name="q_U_XB" public_interface="in" units="fmol"/>
        <variable name="q_W_XB" public_interface="in" units="fmol"/>
        <variable name="q_S_XB" public_interface="in" units="fmol"/>
        <!-- Constitutive parameters-->
        <variable name="mu_TRPN" units="J_per_mol"/>
        <variable name="mu_Ca_i" units="J_per_mol"/>
        <variable name="mu_Ca_TRPN" units="J_per_mol"/>
        <variable name="mu_B_XB" units="J_per_mol"/>
        <variable name="mu_U_XB" units="J_per_mol"/>
        <variable name="mu_W_XB" units="J_per_mol"/>
        <variable name="mu_S_XB" units="J_per_mol"/>
        <variable name="v_R_TRPNCa" public_interface="out" units="fmol_per_sec"/>
        <variable name="v_R_BU" public_interface="out" units="fmol_per_sec"/>
        <variable name="v_R_UW" public_interface="out" units="fmol_per_sec"/>
        <variable name="v_R_WS" public_interface="out" units="fmol_per_sec"/>
        <variable name="v_R_SU" public_interface="out" units="fmol_per_sec"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>mu_TRPN</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_TRPN</ci>
                            <ci>q_TRPN</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_Ca_i</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_Ca_i</ci>
                            <ci>q_Ca_i</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_Ca_TRPN</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_Ca_TRPN</ci>
                            <ci>q_Ca_TRPN</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_B_XB</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_B_XB</ci>
                            <ci>q_B_XB</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_U_XB</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_U_XB</ci>
                            <ci>q_U_XB</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_W_XB</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_W_XB</ci>
                            <ci>q_W_XB</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>mu_S_XB</ci>
                <apply>
                    <times/>
                    <ci>R</ci>
                    <ci>T</ci>
                    <apply>
                        <ln/>
                        <apply>
                            <times/>
                            <ci>K_S_XB</ci>
                            <ci>q_S_XB</ci>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_R_TRPNCa</ci>
                <apply>
                    <times/>
                    <ci>kappa_R_TRPNCa</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <plus/>
                                    <apply>
                                        <times/>
                                        <ci>n_CaTRPN</ci>
                                        <ci>mu_Ca_i</ci>
                                    </apply>
                                    <ci>mu_TRPN</ci>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>mu_Ca_TRPN</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_R_BU</ci>
                <apply>
                    <times/>
                    <ci>kappa_R_BU</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <plus/>
                                    <ci>mu_B_XB</ci>
                                    <apply>
                                        <times/>
                                        <ci>n_Tm</ci>
                                        <ci>mu_Ca_TRPN</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <plus/>
                                    <ci>mu_U_XB</ci>
                                    <apply>
                                        <times/>
                                        <ci>n_Tm</ci>
                                        <ci>mu_Ca_TRPN</ci>
                                    </apply>
                                </apply>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_R_UW</ci>
                <apply>
                    <times/>
                    <ci>kappa_R_UW</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>mu_U_XB</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>mu_W_XB</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_R_WS</ci>
                <apply>
                    <times/>
                    <ci>kappa_R_WS</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>mu_W_XB</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>mu_S_XB</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_R_SU</ci>
                <apply>
                    <times/>
                    <ci>kappa_R_SU</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>mu_S_XB</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <ci>mu_U_XB</ci>
                                <apply>
                                    <times/>
                                    <ci>R</ci>
                                    <ci>T</ci>
                                </apply>
                            </apply>
                        </apply>
                    </apply>
                </apply>
            </apply>
        </math>
        <!-- &#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;
 damper system for zeta (distortion) and lambda (extension) variables
 using dimensionalised variables: 
 G = zeta * SL_0
 SL = lambda / SL_0-->
        <variable initial_value="2e-6" name="SL_0" units="metre"/>
        <variable initial_value="1e-6" name="q_MS" units="fmol"/>
        <variable initial_value="0.25" name="r_s" units="dimensionless"/>
        <variable initial_value="0.5" name="r_w" units="dimensionless"/>
        <variable initial_value="25" name="A_eff" units="dimensionless"/>
        <variable initial_value="2.23" name="phi" units="dimensionless"/>
        <variable initial_value="26" name="k_uw" units="per_sec"/>
        <variable initial_value="4" name="k_ws" units="per_sec"/>
        <!-- -->
        <variable initial_value="1e-6" name="G_w" units="metre"/>
        <variable initial_value="1e-6" name="G_s" units="metre"/>
        <variable initial_value="2e-6" name="SL" public_interface="out" units="metre"/>
        <variable name="c_w" units="per_sec"/>
        <variable name="c_s" units="per_sec"/>
        <variable name="A_w" units="dimensionless"/>
        <variable name="A_s" units="dimensionless"/>
        <variable name="nu_1" units="m_per_s"/>
        <variable name="nu_2" units="m_per_s"/>
        <variable name="nu_3" units="m_per_s"/>
        <variable name="nu_4" units="m_per_s"/>
        <variable name="nu_5" units="m_per_s"/>
        <variable name="nu_6" units="m_per_s"/>
        <variable name="v_1" units="m_per_s"/>
        <variable name="v_2" units="m_per_s"/>
        <variable name="v_4" units="m_per_s"/>
        <variable initial_value="1" name="v_to_mu" units="Js_per_m2"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>A_w</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>A_eff</ci>
                        <ci>r_s</ci>
                    </apply>
                    <apply>
                        <plus/>
                        <apply>
                            <times/>
                            <apply>
                                <minus/>
                                <cn cellml:units="dimensionless">1</cn>
                                <ci>r_s</ci>
                            </apply>
                            <ci>r_w</ci>
                        </apply>
                        <ci>r_s</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>A_s</ci>
                <ci>A_w</ci>
            </apply>
            <apply>
                <eq/>
                <ci>c_w</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>phi</ci>
                        <ci>k_uw</ci>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <ci>r_w</ci>
                        </apply>
                    </apply>
                    <ci>r_w</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>c_s</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>phi</ci>
                        <ci>k_ws</ci>
                        <apply>
                            <minus/>
                            <cn cellml:units="dimensionless">1</cn>
                            <ci>r_s</ci>
                        </apply>
                        <ci>r_w</ci>
                    </apply>
                    <ci>r_s</ci>
                </apply>
            </apply>
        </math>
        <!-- -->
        <!-- vary the sarcomere length in a periodic way
        v_2 = 1{dimensionless}*V_max*sin(2{dimensionless}*pi*time);-->
        <variable name="dSL" public_interface="in" units="m_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>v_2</ci>
                <ci>dSL</ci>
            </apply>
            <apply>
                <eq/>
                <ci>v_1</ci>
                <ci>nu_1</ci>
            </apply>
            <apply>
                <eq/>
                <ci>nu_2</ci>
                <apply>
                    <times/>
                    <apply>
                        <minus/>
                        <ci>A_w</ci>
                    </apply>
                    <ci>v_2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>nu_3</ci>
                <apply>
                    <times/>
                    <ci>c_w</ci>
                    <ci>G_w</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>v_4</ci>
                <ci>nu_4</ci>
            </apply>
            <apply>
                <eq/>
                <ci>nu_5</ci>
                <apply>
                    <times/>
                    <apply>
                        <minus/>
                        <ci>A_s</ci>
                    </apply>
                    <ci>v_2</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>nu_6</ci>
                <apply>
                    <times/>
                    <ci>c_s</ci>
                    <ci>G_s</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>G_w</ci>
                </apply>
                <ci>v_1</ci>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>SL</ci>
                </apply>
                <ci>v_2</ci>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>G_s</ci>
                </apply>
                <ci>v_4</ci>
            </apply>
            <!-- constitutive relations-->
            <apply>
                <eq/>
                <ci>nu_1</ci>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <ci>nu_2</ci>
                    </apply>
                    <ci>nu_3</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>nu_4</ci>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <ci>nu_5</ci>
                    </apply>
                    <ci>nu_6</ci>
                </apply>
            </apply>
        </math>
        <!-- &#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;
 Active tension 
 all terms of Eqn 53 are set as potentials
 kPa is a unit of potential ( kPa = kJ/m3 )-->
        <variable name="T_active" units="kPa"/>
        <variable initial_value="40.5" name="T_ref" units="kPa"/>
        <variable name="F_T_S" units="kPa"/>
        <variable name="F_T_W" units="kPa"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>F_T_S</ci>
                <apply>
                    <times/>
                    <apply>
                        <divide/>
                        <ci>T_ref</ci>
                        <apply>
                            <times/>
                            <ci>SL_0</ci>
                            <ci>q_MS</ci>
                            <ci>r_s</ci>
                        </apply>
                    </apply>
                    <ci>q_S_XB</ci>
                    <apply>
                        <plus/>
                        <ci>G_s</ci>
                        <ci>SL_0</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>F_T_W</ci>
                <apply>
                    <times/>
                    <apply>
                        <divide/>
                        <ci>T_ref</ci>
                        <apply>
                            <times/>
                            <ci>SL_0</ci>
                            <ci>q_MS</ci>
                            <ci>r_s</ci>
                        </apply>
                    </apply>
                    <ci>q_W_XB</ci>
                    <ci>G_w</ci>
                </apply>
            </apply>
            <!-- constitutive relation-->
            <apply>
                <eq/>
                <ci>T_active</ci>
                <apply>
                    <plus/>
                    <ci>F_T_S</ci>
                    <ci>F_T_W</ci>
                </apply>
            </apply>
        </math>
        <!-- &#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;
 Passive viscoelastic tension
 C_s and C_d are presented in dimensional forms (multiplied by SL_0)-->
        <variable name="C_s" units="metre"/>
        <variable initial_value="0" name="C_d" units="metre"/>
        <variable name="eta" units="second"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>C_s</ci>
                <apply>
                    <minus/>
                    <apply>
                        <minus/>
                        <ci>SL</ci>
                        <ci>SL_0</ci>
                    </apply>
                    <ci>C_d</ci>
                </apply>
            </apply>
        </math>
        <!--        var eta_l: per_sec {init: 200e3};
        var eta_s: per_sec {init: 20e3};-->
        <variable initial_value="200e3" name="eta_l" units="second"/>
        <variable initial_value="20e3" name="eta_s" units="second"/>
        <variable initial_value="7" name="k" units="dimensionless"/>
        <variable initial_value="2.1" name="alpha" units="kPa"/>
        <variable name="v_Cdd" units="m_per_s"/>
        <variable name="nu_d" units="m_per_s"/>
        <variable name="nu_k" units="m_per_s"/>
        <variable name="nu_f" units="m_per_s"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>eta</ci>
                <piecewise>
                    <piece>
                        <ci>eta_l</ci>
                        <apply>
                            <gt/>
                            <ci>C_s</ci>
                            <cn cellml:units="metre">0</cn>
                        </apply>
                    </piece>
                    <otherwise>
                        <ci>eta_s</ci>
                    </otherwise>
                </piecewise>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>time</ci>
                    </bvar>
                    <ci>C_d</ci>
                </apply>
                <ci>v_Cdd</ci>
            </apply>
            <!--        v_Cdd = nu_d;-->
            <apply>
                <eq/>
                <ci>v_Cdd</ci>
                <apply>
                    <divide/>
                    <apply>
                        <times/>
                        <ci>k</ci>
                        <ci>C_s</ci>
                    </apply>
                    <ci>eta</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>nu_k</ci>
                <apply>
                    <times/>
                    <apply>
                        <divide/>
                        <ci>k</ci>
                        <ci>eta</ci>
                    </apply>
                    <ci>C_d</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>nu_f</ci>
                <apply>
                    <times/>
                    <apply>
                        <divide/>
                        <ci>k</ci>
                        <ci>eta</ci>
                    </apply>
                    <apply>
                        <minus/>
                        <ci>SL</ci>
                        <ci>SL_0</ci>
                    </apply>
                </apply>
            </apply>
            <!-- constitutive relation-->
            <apply>
                <eq/>
                <ci>nu_d</ci>
                <apply>
                    <plus/>
                    <apply>
                        <minus/>
                        <ci>nu_k</ci>
                    </apply>
                    <ci>nu_f</ci>
                </apply>
            </apply>
        </math>
        <!-- passive tension calculation-->
        <variable name="F_d" units="kPa"/>
        <variable name="F_1" units="kPa"/>
        <variable name="T_passive" units="kPa"/>
        <variable initial_value="9.1" name="b" units="dimensionless"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>F_1</ci>
                <apply>
                    <times/>
                    <ci>alpha</ci>
                    <apply>
                        <minus/>
                        <apply>
                            <exp/>
                            <apply>
                                <divide/>
                                <apply>
                                    <times/>
                                    <ci>b</ci>
                                    <ci>SL</ci>
                                </apply>
                                <ci>SL_0</ci>
                            </apply>
                        </apply>
                        <cn cellml:units="dimensionless">1</cn>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>F_d</ci>
                <apply>
                    <times/>
                    <apply>
                        <divide/>
                        <apply>
                            <times/>
                            <ci>alpha</ci>
                            <ci>eta</ci>
                        </apply>
                        <ci>SL_0</ci>
                    </apply>
                    <ci>v_Cdd</ci>
                </apply>
            </apply>
            <!-- F_d = a*k*Cs;-->
            <apply>
                <eq/>
                <ci>T_passive</ci>
                <apply>
                    <plus/>
                    <ci>F_1</ci>
                    <ci>F_d</ci>
                </apply>
            </apply>
        </math>
        <!-- &#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;&#45;
 Total tension-->
        <variable name="T_total" public_interface="out" units="kPa"/>
        <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
                <eq/>
                <ci>T_total</ci>
                <apply>
                    <plus/>
                    <ci>T_active</ci>
                    <ci>T_passive</ci>
                </apply>
            </apply>
        </math>
    </component>
    <connection>
        <map_components component_1="environment" component_2="crossbridge_TRPN"/>
        <map_variables variable_1="time" variable_2="time"/>
        <map_variables variable_1="q_TRPN" variable_2="q_TRPN"/>
        <map_variables variable_1="q_Ca_i" variable_2="q_Ca_i"/>
        <map_variables variable_1="q_Ca_TRPN" variable_2="q_Ca_TRPN"/>
        <map_variables variable_1="q_B_XB" variable_2="q_B_XB"/>
        <map_variables variable_1="q_U_XB" variable_2="q_U_XB"/>
        <map_variables variable_1="q_W_XB" variable_2="q_W_XB"/>
        <map_variables variable_1="q_S_XB" variable_2="q_S_XB"/>
        <map_variables variable_1="v_R_TRPNCa" variable_2="v_R_TRPNCa"/>
        <map_variables variable_1="v_R_BU" variable_2="v_R_BU"/>
        <map_variables variable_1="v_R_UW" variable_2="v_R_UW"/>
        <map_variables variable_1="v_R_WS" variable_2="v_R_WS"/>
        <map_variables variable_1="v_R_SU" variable_2="v_R_SU"/>
        <map_variables variable_1="T_total" variable_2="T_total"/>
        <map_variables variable_1="SL" variable_2="SL"/>
        <map_variables variable_1="dSL" variable_2="dSL"/>
    </connection>
    <connection>
        <map_components component_1="environment" component_2="crossbridge_TRPN_parameters"/>
        <map_variables variable_1="n_CaTRPN" variable_2="n_CaTRPN"/>
    </connection>
    <connection>
        <map_components component_1="crossbridge_TRPN" component_2="crossbridge_TRPN_parameters"/>
        <map_variables variable_1="kappa_R_TRPNCa" variable_2="kappa_R_TRPNCa"/>
        <map_variables variable_1="kappa_R_BU" variable_2="kappa_R_BU"/>
        <map_variables variable_1="kappa_R_UW" variable_2="kappa_R_UW"/>
        <map_variables variable_1="kappa_R_WS" variable_2="kappa_R_WS"/>
        <map_variables variable_1="kappa_R_SU" variable_2="kappa_R_SU"/>
        <map_variables variable_1="K_TRPN" variable_2="K_TRPN"/>
        <map_variables variable_1="K_Ca_i" variable_2="K_Ca_i"/>
        <map_variables variable_1="K_Ca_TRPN" variable_2="K_Ca_TRPN"/>
        <map_variables variable_1="K_B_XB" variable_2="K_B_XB"/>
        <map_variables variable_1="K_U_XB" variable_2="K_U_XB"/>
        <map_variables variable_1="K_W_XB" variable_2="K_W_XB"/>
        <map_variables variable_1="K_S_XB" variable_2="K_S_XB"/>
        <map_variables variable_1="n_Tm" variable_2="n_Tm"/>
        <map_variables variable_1="n_CaTRPN" variable_2="n_CaTRPN"/>
    </connection>
    <connection>
        <map_components component_1="constants" component_2="crossbridge_TRPN"/>
        <map_variables variable_1="R" variable_2="R"/>
        <map_variables variable_1="T" variable_2="T"/>
    </connection>
</model>