Location: A 0D model of the Heart @ b4f1199958a2 / HOD.cellml
- Author:
- rmollero <rochmollero@hotmail.com>
- Date:
- 2016-12-26 21:27:25+01:00
- Desc:
- new README.md from Alan
- Permanent Source URI:
- https://models.cellml.org/workspace/44c/rawfile/b4f1199958a2f35524212312eea6975c99c841b3/HOD.cellml
<?xml version='1.0'?>
<model name="HOD" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#">
<units name="viscosity">
<unit units="pascal"/>
<unit units="second"/>
</units>
<units name="flow">
<unit exponent="3" units="meter"/>
<unit exponent="-1" units="second"/>
</units>
<units name="resistivity">
<unit units="flow"/>
<unit exponent="-1" units="pascal"/>
</units>
<units name="resistance">
<unit exponent="-1" units="resistivity"/>
</units>
<units name="mL">
<unit prefix="milli" units="liter"/>
</units>
<units name="speed">
<unit units="meter"/>
<unit exponent="-1" units="second"/>
</units>
<units name="density">
<unit units="kilogram"/>
<unit exponent="-3" units="meter"/>
</units>
<units name="per_second">
<unit exponent="-1" units="second"/>
</units>
<units name="mL_per_cubicmeter">
<unit prefix="milli" units="mL"/>
<unit exponent="-3" units="meter"/>
</units>
<component name="main">
<!--Sarcomere Stuff-->
<variable initial_value="0" name="t" units="second"/>
<variable initial_value="0.8" name="HeartPeriod" units="second"/>
<variable initial_value="1.5" name="alpha" units="dimensionless"/>
<variable initial_value="1" name="w" units="dimensionless"/>
<variable name="u_p" units="per_second"/>
<variable name="u_m" units="per_second"/>
<variable initial_value="1" name="n_0" units="dimensionless"/>
<variable initial_value="1e5" name="k_0" units="pascal"/>
<variable initial_value="5e4" name="sigma_0" units="pascal"/>
<variable initial_value="30" name="katp" units="per_second"/>
<variable initial_value="30" name="krs" units="per_second"/>
<variable initial_value="0" name="tau_c" units="second"/>
<variable initial_value="0" name="k_c" units="pascal"/>
<variable initial_value="0" name="e_c" units="dimensionless"/>
<variable name="t_HeartPeriod" units="second"/>
<variable initial_value="0.3" name="APD" units="second"/>
<variable initial_value="0.12" name="AV_delay" units="second"/>
<variable initial_value="0.085" name="QRS_duration" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>t_HeartPeriod</ci>
<apply>
<minus/>
<ci>t</ci>
<apply>
<times/>
<ci>HeartPeriod</ci>
<apply>
<floor/>
<apply>
<divide/>
<ci>t</ci>
<ci>HeartPeriod</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>u_p</ci>
<piecewise>
<piece>
<cn cellml:units="per_second">0</cn>
<apply>
<gt/>
<ci>t_HeartPeriod</ci>
<apply>
<plus/>
<ci>AV_delay</ci>
<ci>APD</ci>
<ci>QRS_duration</ci>
</apply>
</apply>
</piece>
<piece>
<apply>
<times/>
<ci>katp</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<minus/>
<ci>t_HeartPeriod</ci>
<apply>
<plus/>
<ci>AV_delay</ci>
<ci>APD</ci>
</apply>
</apply>
<ci>QRS_duration</ci>
</apply>
</apply>
</apply>
<apply>
<gt/>
<ci>t_HeartPeriod</ci>
<apply>
<plus/>
<ci>AV_delay</ci>
<ci>APD</ci>
</apply>
</apply>
</piece>
<piece>
<ci>katp</ci>
<apply>
<gt/>
<ci>t_HeartPeriod</ci>
<apply>
<plus/>
<ci>AV_delay</ci>
<ci>QRS_duration</ci>
</apply>
</apply>
</piece>
<piece>
<apply>
<divide/>
<apply>
<times/>
<ci>katp</ci>
<apply>
<minus/>
<ci>t_HeartPeriod</ci>
<ci>AV_delay</ci>
</apply>
</apply>
<ci>QRS_duration</ci>
</apply>
<apply>
<gt/>
<ci>t_HeartPeriod</ci>
<ci>AV_delay</ci>
</apply>
</piece>
<otherwise>
<cn cellml:units="per_second">0</cn>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>u_m</ci>
<piecewise>
<piece>
<apply>
<minus/>
<ci>krs</ci>
</apply>
<apply>
<gt/>
<ci>t_HeartPeriod</ci>
<apply>
<plus/>
<ci>AV_delay</ci>
<ci>APD</ci>
<ci>QRS_duration</ci>
</apply>
</apply>
</piece>
<piece>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>krs</ci>
</apply>
<apply>
<minus/>
<ci>t_HeartPeriod</ci>
<apply>
<plus/>
<ci>AV_delay</ci>
<ci>APD</ci>
</apply>
</apply>
</apply>
<ci>QRS_duration</ci>
</apply>
<apply>
<gt/>
<ci>t_HeartPeriod</ci>
<apply>
<plus/>
<ci>AV_delay</ci>
<ci>APD</ci>
</apply>
</apply>
</piece>
<piece>
<cn cellml:units="per_second">0</cn>
<apply>
<gt/>
<ci>t_HeartPeriod</ci>
<apply>
<plus/>
<ci>AV_delay</ci>
<ci>QRS_duration</ci>
</apply>
</apply>
</piece>
<piece>
<apply>
<times/>
<apply>
<minus/>
<ci>krs</ci>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<minus/>
<ci>t_HeartPeriod</ci>
<ci>AV_delay</ci>
</apply>
<ci>QRS_duration</ci>
</apply>
</apply>
</apply>
<apply>
<gt/>
<ci>t_HeartPeriod</ci>
<ci>AV_delay</ci>
</apply>
</piece>
<otherwise>
<apply>
<minus/>
<ci>krs</ci>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>k_c</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<abs/>
<ci>u_p</ci>
</apply>
<apply>
<times/>
<ci>w</ci>
<apply>
<abs/>
<ci>u_m</ci>
</apply>
</apply>
<apply>
<times/>
<ci>alpha</ci>
<apply>
<abs/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>e_c</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>k_c</ci>
</apply>
<apply>
<times/>
<ci>n_0</ci>
<ci>k_0</ci>
<apply>
<abs/>
<ci>u_p</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>tau_c</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<abs/>
<ci>u_p</ci>
</apply>
<apply>
<times/>
<ci>w</ci>
<apply>
<abs/>
<ci>u_m</ci>
</apply>
</apply>
<apply>
<times/>
<ci>alpha</ci>
<apply>
<abs/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>e_c</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<ci>tau_c</ci>
</apply>
<apply>
<times/>
<ci>n_0</ci>
<ci>sigma_0</ci>
<apply>
<abs/>
<ci>u_p</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_c</ci>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>e_c</ci>
</apply>
</apply>
</apply>
</apply>
</math>
<variable initial_value="0" name="x" units="speed"/>
<variable initial_value="0" name="y" units="meter"/>
<variable initial_value="0.028" name="R_0" units="meter"/>
<variable initial_value="0.014" name="d_0" units="meter"/>
<variable initial_value="1070" name="rho" units="density"/>
<variable name="SIGMA_sph" units="pascal"/>
<variable name="e_1D" units="dimensionless"/>
<variable name="C" units="dimensionless"/>
<variable name="dC_dT" units="per_second"/>
<variable initial_value="3e7" name="E_s" units="pascal"/>
<variable initial_value="70" name="mu" units="viscosity"/>
<variable name="sigma_1D" units="pascal"/>
<variable initial_value="800" name="c_1" units="pascal"/>
<variable initial_value="800" name="c_2" units="pascal"/>
<variable initial_value="100" name="eta" units="viscosity"/>
<variable name="sigma_visco" units="pascal"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>C</ci>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>y</ci>
<ci>R_0</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>dC_dT</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>x</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>y</ci>
<ci>R_0</ci>
</apply>
</apply>
</apply>
<ci>R_0</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>e_1D</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>C</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<apply>
<eq/>
<ci>sigma_1D</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>E_s</ci>
<apply>
<minus/>
<ci>e_1D</ci>
<ci>e_c</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>e_c</ci>
</apply>
<apply>
<power/>
<ci>e_c</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<!-- Manual Exponential Integration-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>e_c</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<plus/>
<ci>e_1D</ci>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<minus/>
<ci>tau_c</ci>
</apply>
<ci>mu</ci>
</apply>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<ci>E_s</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>e_1D</ci>
</apply>
<apply>
<power/>
<ci>e_1D</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>e_c</ci>
</apply>
<apply>
<power/>
<ci>e_c</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<ci>mu</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>E_s</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>e_1D</ci>
</apply>
<apply>
<power/>
<ci>e_1D</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>e_c</ci>
</apply>
<apply>
<power/>
<ci>e_c</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<ci>mu</ci>
</apply>
<ci>dt</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>e_c</ci>
<apply>
<exp/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci>E_s</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>e_1D</ci>
</apply>
<apply>
<power/>
<ci>e_1D</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<ci>e_c</ci>
</apply>
<apply>
<power/>
<ci>e_c</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<ci>mu</ci>
</apply>
<ci>dt</ci>
</apply>
</apply>
</apply>
</apply>
<ci>e_c</ci>
</apply>
<ci>dt</ci>
</apply>
</apply>
<!--Normal Equation
ode(e_c, t) = E_s*(e_1D-e_c)*(1{dimensionless}+2{dimensionless}*e_1D+sqr(e_1D))/pow(1{dimensionless}+2{dimensionless}*e_c+sqr(e_c), 3{dimensionless})/mu-tau_c/mu;-->
<apply>
<eq/>
<ci>sigma_visco</ci>
<apply>
<times/>
<ci>eta</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<cn cellml:units="dimensionless">2</cn>
<apply>
<power/>
<ci>C</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">6</cn>
</apply>
</apply>
</apply>
</apply>
<ci>dC_dT</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>SIGMA_sph</ci>
<apply>
<plus/>
<ci>sigma_1D</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<power/>
<ci>C</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</apply>
<apply>
<plus/>
<ci>c_1</ci>
<apply>
<times/>
<ci>C</ci>
<ci>c_2</ci>
</apply>
</apply>
</apply>
<ci>sigma_visco</ci>
</apply>
</apply>
</math>
<!--//////////////////////////
Pressure Coupling
//////////////////////////-->
<variable name="P_at" units="pascal"/>
<variable initial_value="1500" name="P_at_Upper" units="pascal"/>
<variable initial_value="1000" name="P_at_Lower" units="pascal"/>
<variable initial_value="0.005" name="P_at_t1" units="second"/>
<variable initial_value="0.100" name="P_at_t2" units="second"/>
<variable name="P_at_t3" units="second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>P_at_t3</ci>
<apply>
<plus/>
<ci>P_at_t1</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>P_at_t2</ci>
<ci>P_at_t1</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</math>
<variable name="P_at_rate1" units="per_second"/>
<variable name="P_at_rate2" units="per_second"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>P_at_rate1</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">7</cn>
<apply>
<minus/>
<ci>P_at_t2</ci>
<ci>P_at_t1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>P_at_rate2</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">7</cn>
<apply>
<minus/>
<ci>P_at_t3</ci>
<ci>P_at_t2</ci>
</apply>
</apply>
</apply>
</math>
<variable initial_value="0.0001" name="K_at" units="resistivity"/>
<variable initial_value="0.000001" name="K_ar" units="resistivity"/>
<variable initial_value="0.0000000000001" name="K_iso" units="resistivity"/>
<variable initial_value="13500" name="P_ar" units="pascal"/>
<variable initial_value="10000" name="P_ar_Lower" units="pascal"/>
<variable initial_value="0.8" name="Tau" units="second"/>
<variable initial_value="2e7" name="R_p" units="resistance"/>
<variable initial_value="8e6" name="Z_c" units="resistance"/>
<variable name="P_v" units="pascal"/>
<variable initial_value="0" name="phase" units="dimensionless"/>
<variable initial_value="0.00001" name="dt" units="second"/>
<variable name="Q" units="flow"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>Q</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">4</cn>
<pi/>
<apply>
<power/>
<ci>R_0</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>y</ci>
<ci>R_0</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>x</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_at</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>P_at_Lower</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<divide/>
<ci>P_at_Upper</ci>
<ci>P_at_Lower</ci>
</apply>
<cn cellml:units="dimensionless">1.0</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci>P_at_rate1</ci>
</apply>
<apply>
<minus/>
<ci>t_HeartPeriod</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>P_at_t2</ci>
<ci>P_at_t1</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<gt/>
<ci>t_HeartPeriod</ci>
<ci>P_at_t1</ci>
</apply>
<apply>
<leq/>
<ci>t_HeartPeriod</ci>
<ci>P_at_t2</ci>
</apply>
</apply>
</piece>
<piece>
<apply>
<times/>
<ci>P_at_Lower</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<divide/>
<ci>P_at_Upper</ci>
<ci>P_at_Lower</ci>
</apply>
<cn cellml:units="dimensionless">1.0</cn>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1.0</cn>
<apply>
<exp/>
<apply>
<times/>
<ci>P_at_rate2</ci>
<apply>
<minus/>
<ci>t_HeartPeriod</ci>
<apply>
<divide/>
<apply>
<plus/>
<ci>P_at_t2</ci>
<ci>P_at_t3</ci>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<and/>
<apply>
<gt/>
<ci>t_HeartPeriod</ci>
<ci>P_at_t2</ci>
</apply>
<apply>
<lt/>
<ci>t_HeartPeriod</ci>
<ci>P_at_t3</ci>
</apply>
</apply>
</piece>
<otherwise>
<ci>P_at_Lower</ci>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>P_ar</ci>
</apply>
<piecewise>
<piece>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>K_ar</ci>
<ci>P_v</ci>
</apply>
<ci>Q</ci>
</apply>
<apply>
<times/>
<ci>K_iso</ci>
<ci>P_at</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>K_ar</ci>
<ci>K_iso</ci>
</apply>
</apply>
<ci>P_ar</ci>
</apply>
<ci>dt</ci>
</apply>
<apply>
<gt/>
<ci>phase</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>Tau</ci>
<ci>P_ar</ci>
</apply>
<apply>
<times/>
<ci>dt</ci>
<ci>P_ar_Lower</ci>
</apply>
</apply>
<apply>
<plus/>
<ci>dt</ci>
<ci>Tau</ci>
</apply>
</apply>
<ci>P_ar</ci>
</apply>
<ci>dt</ci>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
<variable name="dd_0" units="resistance"/>
<variable name="dd_1" units="dimensionless"/>
<variable name="PPP" units="pascal"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>dd_0</ci>
<apply>
<plus/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<divide/>
<ci>Tau</ci>
<ci>dt</ci>
</apply>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<plus/>
<ci>Z_c</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<plus/>
<ci>K_ar</ci>
<ci>K_iso</ci>
</apply>
</apply>
</apply>
</apply>
<ci>R_p</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>dd_1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>K_ar</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Tau</ci>
<ci>dt</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>K_ar</ci>
<ci>K_iso</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>PPP</ci>
<apply>
<plus/>
<ci>P_ar_Lower</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>P_ar</ci>
<ci>Tau</ci>
</apply>
<ci>dt</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci>K_iso</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>Tau</ci>
<ci>dt</ci>
</apply>
</apply>
</apply>
<apply>
<minus/>
<ci>K_ar</ci>
<ci>K_iso</ci>
</apply>
</apply>
<ci>P_at</ci>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci>Tau</ci>
<ci>Z_c</ci>
<ci>Q</ci>
</apply>
<ci>dt</ci>
</apply>
</apply>
</apply>
</math>
<variable name="F_d" units="flow"/>
<variable name="D" units="resistivity"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>F_d</ci>
<piecewise>
<piece>
<apply>
<minus/>
<apply>
<times/>
<ci>K_iso</ci>
<ci>P_at</ci>
</apply>
<ci>Q</ci>
</apply>
<apply>
<lt/>
<ci>phase</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
<piece>
<apply>
<minus/>
<apply>
<divide/>
<ci>PPP</ci>
<ci>dd_0</ci>
</apply>
<ci>Q</ci>
</apply>
<apply>
<gt/>
<ci>phase</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<minus/>
<apply>
<times/>
<ci>K_at</ci>
<ci>P_at</ci>
</apply>
<ci>Q</ci>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>D</ci>
<piecewise>
<piece>
<ci>K_iso</ci>
<apply>
<lt/>
<ci>phase</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
<piece>
<apply>
<divide/>
<ci>dd_1</ci>
<ci>dd_0</ci>
</apply>
<apply>
<gt/>
<ci>phase</ci>
<cn cellml:units="dimensionless">0</cn>
</apply>
</piece>
<otherwise>
<ci>K_at</ci>
</otherwise>
</piecewise>
</apply>
<!--Equation without Windkessel Model Coupling
ode(x, t) = (P_v*sqr(1{dimensionless}+y/R_0)-d_0/R_0*(1{dimensionless}+y/R_0)*SIGMA_sph)/(rho*d_0);-->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>x</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<minus/>
<ci>d_0</ci>
</apply>
<ci>R_0</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>y</ci>
<ci>R_0</ci>
</apply>
</apply>
<ci>SIGMA_sph</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>y</ci>
<ci>R_0</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>D</ci>
</apply>
<ci>F_d</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>rho</ci>
<ci>d_0</ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>y</ci>
<ci>R_0</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>D</ci>
</apply>
<cn cellml:units="dimensionless">4</cn>
<pi/>
<apply>
<power/>
<ci>R_0</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>y</ci>
<ci>R_0</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
<ci>dt</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>P_v</ci>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>rho</ci>
<ci>d_0</ci>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>x</ci>
</apply>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci>d_0</ci>
<ci>R_0</ci>
</apply>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>y</ci>
<ci>R_0</ci>
</apply>
</apply>
<ci>SIGMA_sph</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>y</ci>
<ci>R_0</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>phase</ci>
</apply>
<piecewise>
<piece>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<ci>phase</ci>
<ci>dt</ci>
</apply>
</apply>
<apply>
<gt/>
<ci>P_v</ci>
<ci>P_ar</ci>
</apply>
</piece>
<piece>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
</apply>
<apply>
<divide/>
<ci>phase</ci>
<ci>dt</ci>
</apply>
</apply>
<apply>
<gt/>
<ci>P_v</ci>
<ci>P_at</ci>
</apply>
</piece>
<otherwise>
<apply>
<divide/>
<apply>
<minus/>
<ci>phase</ci>
</apply>
<ci>dt</ci>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>y</ci>
</apply>
<ci>x</ci>
</apply>
</math>
<variable name="V_ml" units="mL"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>V_ml</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="mL_per_cubicmeter">1000000</cn>
<cn cellml:units="dimensionless">4</cn>
<pi/>
<apply>
<power/>
<apply>
<plus/>
<ci>R_0</ci>
<ci>y</ci>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
<cn cellml:units="dimensionless">3</cn>
</apply>
</apply>
</math>
</component>
</model>