- Author:
- Shelley Fong <sfon036@UoA.auckland.ac.nz>
- Date:
- 2022-07-11 10:21:07+12:00
- Desc:
- Fixing equations against original paper
- Permanent Source URI:
- https://models.cellml.org/workspace/7fb/rawfile/604952bc88bf59ed431f755e616d95ccb18abc03/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>
<!-- ----------------------------------------------------------------
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>
<!-- ----------------------------------------------------------------
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>
<!-- ----------------------------------------------------------------
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>
<!-- ----------------------------------------------------------------
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>
