- Author:
- chthompson <chthompson@BBC-J2P11R1.phys.mcw.edu>
- Date:
- 2012-08-01 14:58:27-05:00
- Desc:
- CBF Model 8/1/2012
- Permanent Source URI:
- http://models.cellml.org/w/thompsct/Spronck_Martens_2012/rawfile/5a6dbf11dcc0eefb96221447e5a82ad6da58daf7/CerebralBloodFlow.cellml
<?xml version="1.0"?>
<model xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="hnFjlz6syjR" name="Spronck_Cerebral_Blood"><component name="Environment"><variable initial_value="0" name="time" public_interface="out" units="second"/></component><component name="Parameters"><variable initial_value="3E-5" name="Eta_b" public_interface="out" units="mmHg_sec"/><variable initial_value="1.05E6" name="Rho_b" public_interface="out" units="gram_per_cubic_meter"/><variable initial_value="1.2E4" name="E_p" public_interface="out" units="mmHg"/><variable initial_value="1.05E-3" name="r_p" public_interface="out" units="meter"/><variable initial_value="8.6E-2" name="l_p" public_interface="out" units="meter"/><variable initial_value="2.6E-4" name="h_p" public_interface="out" units="meter"/><variable initial_value="7.5E-5" name="r_a0" public_interface="out" units="meter"/><variable initial_value="2.5E-5" name="h_a0" public_interface="out" units="meter"/><variable initial_value="11.19" name="sigma_ae0" public_interface="out" units="mmHg"/><variable initial_value="4.5" name="K_a_sigma" public_interface="out" units="dimensionless"/><variable initial_value="41.32" name="sigma_ac" public_interface="out" units="mmHg"/><variable initial_value="1.5E-2" name="T_a_max0" public_interface="out" units="mmHg_m"/><variable initial_value="1.28E-4" name="r_am" public_interface="out" units="meter"/><variable initial_value="1.74E-4" name="r_at" public_interface="out" units="meter"/><variable initial_value="1.75" name="n_am" public_interface="out" units="dimensionless"/><variable initial_value="47.8" name="Eta_a" public_interface="out" units="mmHg_sec"/><variable initial_value="8.83E-7" name="Q_bl" public_interface="out" units="cubic_m_per_sec"/><variable initial_value="10" name="P_ic" public_interface="out" units="mmHg"/><variable initial_value="1.6E7" name="R_v" public_interface="out" units="mmHg_sec_per_cubic_m"/><variable initial_value="2.5E-8" name="C_v" public_interface="out" units="cubic_m_per_mmHg"/><variable initial_value="96.0" name="P_ai" public_interface="out" units="mmHg"/><variable initial_value="3.58E-3" name="T_myo0" public_interface="out" units="mmHg_m"/><variable initial_value="3E-3" name="T_myo_s" public_interface="out" units="mmHg_m"/><variable initial_value="7" name="Tau_myo" public_interface="out" units="second"/><variable initial_value="60" name="Tau_shear" public_interface="out" units="second"/><variable initial_value="4" name="G_myo" public_interface="out" units="dimensionless"/><variable initial_value="0" name="G_shear" public_interface="out" units="dimensionless"/><variable initial_value="-0.7" name="G_neuro" public_interface="out" units="dimensionless"/><variable initial_value="0" name="G_meta" public_interface="out" units="dimensionless"/><variable initial_value="0" name="x_ini" public_interface="out" units="dimensionless"/><variable initial_value="5" name="Tau_neuro" public_interface="out" units="second"/><variable initial_value="15" name="Tau_meta" public_interface="out" units="second"/><variable initial_value="20.65" name="conc_CO2_a" public_interface="out" units="Molar"/><variable initial_value="1.3479E-7" name="M_CO2_0" public_interface="out" units="mol_per_sec"/><variable initial_value="0.9571" name="alpha_tv" public_interface="out" units="dimensionless"/><variable initial_value="8.9295" name="Beta_tv" public_interface="out" units="Molar"/><variable initial_value="5.99E-6" name="vol_PVC" public_interface="out" units="cubic_m"/><variable initial_value="5.2E-7" name="K_shear" public_interface="out" units="second"/><variable initial_value="2.54E-9" name="K_Ra" public_interface="out" units="mmHg_sec_m"/><variable initial_value="12.4057" name="conc_CO2_t_sp" public_interface="out" units="Molar"/><variable initial_value="1.2453" name="f_Q" public_interface="out" units="dimensionless"/><variable initial_value="2.2" name="n_QM" public_interface="out" units="dimensionless"/><variable initial_value="120.0764" name="K_Va" public_interface="out" units="meter"/><variable initial_value="14" name="P_vo" public_interface="out" units="mmHg"/></component><units name="mmHg_sec"><unit units="mmHg"/><unit units="second"/></units><units base_units="yes" name="mmHg"/><units name="gram_per_cubic_meter"><unit units="gram"/><unit exponent="-3" units="meter"/></units><units name="mmHg_m"><unit units="mmHg"/><unit units="meter"/></units><units name="cubic_m_per_sec"><unit exponent="3" units="meter"/><unit exponent="-1" units="second"/></units><component name="PCA"><variable initial_value="8.83E-7" name="Q_Lp" units="cubic_m_per_sec"/><variable initial_value="91.2" name="P_p" public_interface="out" units="mmHg"/><variable name="C_p" public_interface="in" units="cubic_m_per_mmHg"/><variable name="L_p" public_interface="in" units="mmHg_sec2_per_m3"/><variable name="R_p" public_interface="in" units="mmHg_sec_per_cubic_m"/><variable name="P_ic" public_interface="in" units="mmHg"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><apply><diff/><bvar><ci>time</ci></bvar><ci>P_p</ci></apply><apply><divide/><apply><times/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn><apply><plus/><apply><minus/><apply><times/><ci>Q_Lp</ci><ci>R_a</ci></apply><apply><times/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn><ci>P_p</ci></apply></apply><apply><times/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn><ci>P_a</ci></apply></apply></apply><apply><times/><ci>R_a</ci><ci>C_p</ci></apply></apply></apply><apply><eq/><apply><diff/><bvar><ci>time</ci></bvar><ci>Q_Lp</ci></apply><apply><divide/><apply><minus/><apply><minus/><ci>P_ai</ci><ci>P_p</ci></apply><apply><times/><ci>Q_Lp</ci><ci>R_p</ci></apply></apply><ci>L_p</ci></apply></apply></math><variable name="time" public_interface="in" units="second"/><variable name="P_ai" public_interface="in" units="mmHg"/><variable name="R_a" public_interface="in" units="mmHg_sec_per_cubic_m"/><variable name="P_a" public_interface="in" units="mmHg"/></component><component name="PCA_Components"><variable name="C_p" public_interface="out" units="cubic_m_per_mmHg"/><variable name="L_p" public_interface="out" units="mmHg_sec2_per_m3"/><variable name="R_p" public_interface="out" units="mmHg_sec_per_cubic_m"/><variable name="r_p" public_interface="in" units="meter"/><variable name="h_p" public_interface="in" units="meter"/><variable name="E_p" public_interface="in" units="mmHg"/><variable name="l_p" public_interface="in" units="meter"/><variable name="Rho_b" public_interface="in" units="gram_per_cubic_meter"/><variable name="Eta_b" public_interface="in" units="mmHg_sec"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><ci>C_p</ci><apply><times/><apply><divide/><apply><times/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">3</cn><pi/><apply><power/><ci>r_p</ci><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn></apply><apply><power/><apply><plus/><apply><divide/><ci>r_p</ci><ci>h_p</ci></apply><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn></apply><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn></apply></apply><apply><times/><ci>E_p</ci><apply><plus/><apply><divide/><apply><times/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn><ci>r_p</ci></apply><ci>h_p</ci></apply><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn></apply></apply></apply><ci>l_p</ci></apply></apply><apply><eq/><ci>L_p</ci><apply><times/><apply><divide/><ci>Rho_b</ci><apply><times/><pi/><apply><power/><ci>r_p</ci><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn></apply></apply></apply><ci>l_p</ci><apply><power/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">0.001</cn><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn></apply></apply></apply><apply><eq/><ci>R_p</ci><apply><times/><apply><divide/><apply><times/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">8</cn><ci>Eta_b</ci></apply><apply><times/><pi/><apply><power/><ci>r_p</ci><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">4</cn></apply></apply></apply><ci>l_p</ci></apply></apply></math></component><units name="cubic_m_per_mmHg"><unit exponent="3" units="meter"/><unit exponent="-1" units="mmHg"/></units><units name="mmHg_sec_per_cubic_m"><unit units="second"/><unit units="mmHg"/><unit exponent="-3" units="meter"/></units><units name="mmHg_sec2_per_m3"><unit units="mmHg"/><unit exponent="2" units="second"/><unit exponent="-3" units="meter"/></units><connection><map_components component_1="Parameters" component_2="PCA_Components"/><map_variables variable_1="Eta_b" variable_2="Eta_b"/><map_variables variable_1="Rho_b" variable_2="Rho_b"/><map_variables variable_1="E_p" variable_2="E_p"/><map_variables variable_1="r_p" variable_2="r_p"/><map_variables variable_1="l_p" variable_2="l_p"/><map_variables variable_1="h_p" variable_2="h_p"/></connection><component name="Arteriolar_Circulation"><variable name="P_a" public_interface="out" units="mmHg"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><apply><diff/><bvar><ci>time</ci></bvar><ci>r_a</ci></apply><apply><divide/><apply><times/><ci>r_a0</ci><apply><minus/><apply><plus/><apply><times/><ci>P_p</ci><apply><plus/><ci>R_a</ci><ci>R_v</ci></apply><ci>r_a</ci></apply><apply><times/><ci>P_v</ci><ci>R_a</ci><ci>r_a</ci></apply></apply><apply><times/><apply><plus/><ci>T_ae</ci><ci>T_am</ci><apply><times/><ci>P_ic</ci><apply><plus/><ci>r_a</ci><ci>h_a</ci></apply></apply></apply><apply><plus/><apply><times/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn><ci>R_a</ci></apply><ci>R_v</ci></apply></apply></apply></apply><apply><plus/><apply><times/><ci>r_a0</ci><apply><power/><ci>r_a</ci><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn></apply><ci>K_Va</ci><ci>R_a</ci><apply><plus/><ci>R_a</ci><ci>R_v</ci></apply></apply><apply><times/><ci>Eta_a</ci><ci>h_a</ci><apply><plus/><apply><times/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn><ci>R_a</ci></apply><ci>R_v</ci></apply></apply></apply></apply></apply><apply><eq/><ci>P_a</ci><apply><divide/><apply><plus/><ci>T_a</ci><apply><times/><ci>P_ic</ci><apply><plus/><ci>r_a</ci><ci>h_a</ci></apply></apply></apply><ci>r_a</ci></apply></apply></math><variable name="C_a" public_interface="in" units="cubic_m_per_mmHg"/><variable name="R_a" public_interface="in" units="mmHg_sec_per_cubic_m"/><variable name="Q_a" public_interface="in" units="cubic_m_per_sec"/><variable name="time" public_interface="in" units="second"/><variable name="P_v" public_interface="in" units="mmHg"/><variable initial_value="7.7157E-5" name="r_a" public_interface="out" units="meter"/><variable name="r_a0" public_interface="in" units="meter"/><variable name="P_p" public_interface="in" units="mmHg"/><variable name="T_ae" public_interface="in" units="mmHg_m"/><variable name="T_am" public_interface="in" units="mmHg_m"/><variable name="T_av" public_interface="in" units="mmHg_m"/><variable name="K_Va" public_interface="in" units="meter"/><variable name="Eta_a" public_interface="in" units="mmHg_sec"/><variable name="T_a" public_interface="in" units="mmHg_m"/><variable name="P_ic" public_interface="in" units="mmHg"/><variable name="R_v" public_interface="in" units="mmHg_sec_per_cubic_m"/><variable name="h_a" public_interface="in" units="meter"/></component><component name="AC_Components"><variable name="C_a" public_interface="out" units="cubic_m_per_mmHg"/><variable name="R_a" public_interface="out" units="mmHg_sec_per_cubic_m"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><ci>R_a</ci><apply><divide/><ci>K_Ra</ci><apply><power/><ci>r_a</ci><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">4</cn></apply></apply></apply><apply><eq/><ci>C_a</ci><apply><divide/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="second">1.0312</cn><ci>R_a</ci></apply></apply></math><variable name="K_Ra" public_interface="in" units="mmHg_sec_m"/><variable name="r_a" public_interface="in" units="meter"/></component><component name="AC_Flow"><variable name="Q_a" public_interface="out" units="cubic_m_per_sec"/><variable name="P_a" public_interface="in" units="mmHg"/><variable name="P_v" public_interface="in" units="mmHg"/><variable name="R_a" public_interface="in" units="mmHg_sec_per_cubic_m"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><ci>Q_a</ci><apply><divide/><apply><times/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn><apply><minus/><ci>P_a</ci><ci>P_v</ci></apply></apply><apply><plus/><ci>R_a</ci><ci>R_v</ci></apply></apply></apply></math><variable name="R_v" public_interface="in" units="mmHg_sec_per_cubic_m"/></component><component name="Venous_Circulation"><variable initial_value="21" name="P_v" public_interface="out" units="mmHg"/><variable name="Q_a" public_interface="in" units="cubic_m_per_sec"/><variable name="R_v" public_interface="in" units="mmHg_sec_per_cubic_m"/><variable name="C_v" public_interface="in" units="cubic_m_per_mmHg"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><apply><diff/><bvar><ci>time</ci></bvar><ci>P_v</ci></apply><apply><times/><apply><divide/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn><ci>C_v</ci></apply><apply><minus/><apply><divide/><apply><minus/><ci>P_a</ci><ci>P_v</ci></apply><apply><plus/><ci>R_a</ci><ci>R_v</ci></apply></apply><apply><divide/><apply><minus/><ci>P_v</ci><ci>P_vo</ci></apply><ci>R_v</ci></apply></apply></apply></apply></math><variable name="time" public_interface="in" units="second"/><variable name="R_a" public_interface="in" units="mmHg_sec_per_cubic_m"/><variable name="P_a" public_interface="in" units="mmHg"/><variable name="P_vo" public_interface="in" units="mmHg"/></component><connection><map_components component_1="Environment" component_2="PCA"/><map_variables variable_1="time" variable_2="time"/></connection><connection><map_components component_1="Parameters" component_2="PCA"/><map_variables variable_1="P_ic" variable_2="P_ic"/><map_variables variable_1="P_ai" variable_2="P_ai"/></connection><connection><map_components component_1="PCA_Components" component_2="PCA"/><map_variables variable_1="C_p" variable_2="C_p"/><map_variables variable_1="L_p" variable_2="L_p"/><map_variables variable_1="R_p" variable_2="R_p"/></connection><connection><map_components component_1="AC_Components" component_2="Arteriolar_Circulation"/><map_variables variable_1="C_a" variable_2="C_a"/><map_variables variable_1="R_a" variable_2="R_a"/><map_variables variable_1="r_a" variable_2="r_a"/></connection><connection><map_components component_1="AC_Flow" component_2="Arteriolar_Circulation"/><map_variables variable_1="Q_a" variable_2="Q_a"/><map_variables variable_1="P_a" variable_2="P_a"/></connection><connection><map_components component_1="Environment" component_2="Arteriolar_Circulation"/><map_variables variable_1="time" variable_2="time"/></connection><connection><map_components component_1="AC_Flow" component_2="Venous_Circulation"/><map_variables variable_1="Q_a" variable_2="Q_a"/><map_variables variable_1="P_v" variable_2="P_v"/></connection><connection><map_components component_1="AC_Components" component_2="AC_Flow"/><map_variables variable_1="R_a" variable_2="R_a"/></connection><connection><map_components component_1="Parameters" component_2="Venous_Circulation"/><map_variables variable_1="R_v" variable_2="R_v"/><map_variables variable_1="C_v" variable_2="C_v"/><map_variables variable_1="P_vo" variable_2="P_vo"/></connection><connection><map_components component_1="Environment" component_2="Venous_Circulation"/><map_variables variable_1="time" variable_2="time"/></connection><connection><map_components component_1="PCA" component_2="Arteriolar_Circulation"/><map_variables variable_1="P_p" variable_2="P_p"/><map_variables variable_1="P_a" variable_2="P_a"/></connection><connection><map_components component_1="Parameters" component_2="AC_Flow"/><map_variables variable_1="R_v" variable_2="R_v"/></connection><component name="AC_Tension"><variable name="T_a" public_interface="out" units="mmHg_m"/><variable name="T_ae" public_interface="out" units="mmHg_m"/><variable name="T_am" public_interface="out" units="mmHg_m"/><variable name="T_av" public_interface="out" units="mmHg_m"/><variable name="sigma_ae0" public_interface="in" units="mmHg"/><variable name="h_a" public_interface="in" units="meter"/><variable name="r_a" public_interface="in" units="meter"/><variable name="r_a0" public_interface="in" units="meter"/><variable name="K_a_sigma" public_interface="in" units="dimensionless"/><variable name="sigma_ac" public_interface="in" units="mmHg"/><variable name="T_a_max" public_interface="in" units="mmHg_m"/><variable name="r_am" public_interface="in" units="meter"/><variable name="r_at" public_interface="in" units="meter"/><variable name="n_am" public_interface="in" units="dimensionless"/><variable name="Eta_a" public_interface="in" units="mmHg_sec"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><ci>T_a</ci><apply><plus/><ci>T_ae</ci><ci>T_am</ci><ci>T_av</ci></apply></apply><apply><eq/><ci>T_ae</ci><apply><times/><ci>h_a</ci><apply><minus/><apply><times/><ci>sigma_ae0</ci><apply><minus/><apply><exp/><apply><divide/><apply><times/><ci>K_a_sigma</ci><apply><minus/><ci>r_a</ci><ci>r_a0</ci></apply></apply><ci>r_a0</ci></apply></apply><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn></apply></apply><ci>sigma_ac</ci></apply></apply></apply><apply><eq/><ci>T_am</ci><apply><times/><ci>T_a_max</ci><apply><exp/><apply><minus/><apply><power/><apply><abs/><apply><divide/><apply><minus/><ci>r_a</ci><ci>r_am</ci></apply><apply><minus/><ci>r_at</ci><ci>r_am</ci></apply></apply></apply><ci>n_am</ci></apply></apply></apply></apply></apply><apply><eq/><ci>T_av</ci><apply><times/><apply><divide/><ci>Eta_a</ci><ci>r_a0</ci></apply><apply><diff/><bvar><ci>time</ci></bvar><ci>r_a</ci></apply><ci>h_a</ci></apply></apply></math><variable name="time" public_interface="in" units="second"/><variable name="P_a" public_interface="in" units="mmHg"/><variable name="P_ic" public_interface="in" units="mmHg"/></component><connection><map_components component_1="Environment" component_2="AC_Tension"/><map_variables variable_1="time" variable_2="time"/></connection><connection><map_components component_1="Parameters" component_2="AC_Tension"/><map_variables variable_1="r_a0" variable_2="r_a0"/><map_variables variable_1="sigma_ae0" variable_2="sigma_ae0"/><map_variables variable_1="K_a_sigma" variable_2="K_a_sigma"/><map_variables variable_1="sigma_ac" variable_2="sigma_ac"/><map_variables variable_1="r_am" variable_2="r_am"/><map_variables variable_1="r_at" variable_2="r_at"/><map_variables variable_1="n_am" variable_2="n_am"/><map_variables variable_1="Eta_a" variable_2="Eta_a"/><map_variables variable_1="P_ic" variable_2="P_ic"/></connection><component name="AC_Tension_Variables"><variable name="h_a" public_interface="out" units="meter"/><variable name="T_a_max" public_interface="out" units="mmHg_m"/><variable name="r_a" public_interface="in" units="meter"/><variable name="h_a0" public_interface="in" units="meter"/><variable name="r_a0" public_interface="in" units="meter"/><variable name="M_s" public_interface="in" units="dimensionless"/><variable name="T_a_max0" public_interface="in" units="mmHg_m"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><ci>h_a</ci><apply><minus/><apply><root/><apply><plus/><apply><power/><ci>r_a</ci><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn></apply><apply><times/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn><ci>r_a0</ci><ci>h_a0</ci></apply><apply><power/><ci>h_a0</ci><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn></apply></apply></apply><ci>r_a</ci></apply></apply><apply><eq/><ci>T_a_max</ci><apply><times/><ci>T_a_max0</ci><apply><plus/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn><ci>M_s</ci></apply></apply></apply></math></component><connection><map_components component_1="Parameters" component_2="AC_Tension_Variables"/><map_variables variable_1="r_a0" variable_2="r_a0"/><map_variables variable_1="h_a0" variable_2="h_a0"/><map_variables variable_1="T_a_max0" variable_2="T_a_max0"/></connection><connection><map_components component_1="AC_Tension" component_2="AC_Tension_Variables"/><map_variables variable_1="h_a" variable_2="h_a"/><map_variables variable_1="T_a_max" variable_2="T_a_max"/></connection><component name="CBF_Regulation"><variable name="M_s" public_interface="out" units="dimensionless"/><variable name="M_s1" units="dimensionless"/><variable name="G_myo" public_interface="in" units="dimensionless"/><variable name="G_shear" public_interface="in" units="dimensionless"/><variable name="G_neuro" public_interface="in" units="dimensionless"/><variable name="G_meta" public_interface="in" units="dimensionless"/><variable name="x_myo" public_interface="in" units="dimensionless"/><variable name="x_shear" public_interface="in" units="dimensionless"/><variable name="x_neuro" public_interface="in" units="dimensionless"/><variable name="x_meta" public_interface="in" units="dimensionless"/><variable name="x_ini" public_interface="in" units="dimensionless"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><ci>M_s</ci><apply><divide/><apply><minus/><apply><exp/><apply><times/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn><ci>M_s1</ci></apply></apply><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn></apply><apply><plus/><apply><exp/><apply><times/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">2</cn><ci>M_s1</ci></apply></apply><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn></apply></apply></apply><apply><eq/><ci>M_s1</ci><apply><plus/><apply><times/><ci>G_myo</ci><ci>x_myo</ci></apply><apply><times/><ci>G_shear</ci><ci>x_shear</ci></apply><apply><times/><ci>G_neuro</ci><ci>x_neuro</ci></apply><apply><times/><ci>G_meta</ci><ci>x_meta</ci></apply><ci>x_ini</ci></apply></apply></math></component><connection><map_components component_1="AC_Tension_Variables" component_2="CBF_Regulation"/><map_variables variable_1="M_s" variable_2="M_s"/></connection><units name="cubic_m"><unit exponent="3" units="meter"/></units><component name="Myo_Regulation"><variable name="A_myo" units="dimensionless"/><variable initial_value="-1.3504E-11" name="x_myo" public_interface="out" units="dimensionless"/><variable name="T_a" public_interface="in" units="mmHg_m"/><variable name="T_myo0" public_interface="in" units="mmHg_m"/><variable name="T_myo_s" public_interface="in" units="mmHg_m"/><variable name="Tau_myo" public_interface="in" units="second"/><variable name="time" public_interface="in" units="second"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><ci>A_myo</ci><apply><divide/><apply><minus/><ci>T_a</ci><ci>T_myo0</ci></apply><ci>T_myo_s</ci></apply></apply><apply><eq/><apply><diff/><bvar><ci>time</ci></bvar><ci>x_myo</ci></apply><apply><divide/><apply><minus/><ci>A_myo</ci><ci>x_myo</ci></apply><ci>Tau_myo</ci></apply></apply></math></component><component name="Shear_Regulation"><variable name="A_shear" units="dimensionless"/><variable initial_value="1.0385E-12" name="x_shear" public_interface="out" units="dimensionless"/><variable name="K_shear" public_interface="in" units="second"/><variable name="Q_a" public_interface="in" units="cubic_m_per_sec"/><variable name="r_a" public_interface="in" units="meter"/><variable name="Tau_shear" public_interface="in" units="second"/><variable name="time" public_interface="in" units="second"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><ci>A_shear</ci><apply><minus/><apply><divide/><apply><times/><ci>K_shear</ci><ci>Q_a</ci></apply><apply><power/><ci>r_a</ci><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">3</cn></apply></apply><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn></apply></apply><apply><eq/><apply><diff/><bvar><ci>time</ci></bvar><ci>x_shear</ci></apply><apply><divide/><apply><minus/><ci>A_shear</ci><ci>x_shear</ci></apply><ci>Tau_shear</ci></apply></apply></math></component><component name="Neuro_Regulation"><variable name="A_neuro" public_interface="out" units="dimensionless"/><variable initial_value="0" name="x_neuro" public_interface="out" units="dimensionless"/><variable name="Tau_neuro" public_interface="in" units="second"/><variable name="time" public_interface="in" units="second"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><apply><diff/><bvar><ci>time</ci></bvar><ci>x_neuro</ci></apply><apply><divide/><apply><minus/><ci>A_neuro</ci><ci>x_neuro</ci></apply><ci>Tau_neuro</ci></apply></apply><apply><eq/><ci>A_neuro</ci><piecewise><piece><cn>1</cn><apply><geq/><ci>time</ci><cn>1</cn></apply></piece><otherwise><cn>0</cn></otherwise></piecewise></apply></math></component><component name="Meta_Regulation"><variable name="A_Meta" units="dimensionless"/><variable initial_value="-3.5969E-12" name="x_meta" public_interface="out" units="dimensionless"/><variable initial_value="0.5917" name="G_a_Meta" units="per_Molar"/><variable name="conc_CO2_t" public_interface="in" units="Molar"/><variable name="conc_CO2_t_sp" public_interface="in" units="Molar"/><variable name="Tau_Meta" public_interface="in" units="second"/><variable name="time" public_interface="in" units="second"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><ci>A_Meta</ci><apply><times/><ci>G_a_Meta</ci><apply><minus/><ci>conc_CO2_t</ci><ci>conc_CO2_t_sp</ci></apply></apply></apply><apply><eq/><apply><diff/><bvar><ci>time</ci></bvar><ci>x_meta</ci></apply><apply><divide/><apply><minus/><ci>A_Meta</ci><ci>x_meta</ci></apply><ci>Tau_Meta</ci></apply></apply></math></component><units name="Molar"><unit units="mole"/><unit exponent="-1" units="cubic_m"/></units><units name="per_Molar"><unit exponent="-1" units="Molar"/></units><component name="Meta_CO2_Kinetics"><variable initial_value="12.4057" name="conc_CO2_t" public_interface="out" units="Molar"/><variable name="conc_CO2_v" units="Molar"/><variable name="conc_CO2_a" public_interface="in" units="Molar"/><variable name="alpha_tv" public_interface="in" units="dimensionless"/><variable name="Beta_tv" public_interface="in" units="Molar"/><variable name="time" public_interface="in" units="second"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><apply><diff/><bvar><ci>time</ci></bvar><ci>conc_CO2_t</ci></apply><apply><times/><apply><divide/><cn xmlns:cellml="http://www.cellml.org/cellml/1.1#" cellml:units="dimensionless">1</cn><ci>vol_PVC</ci></apply><apply><minus/><ci>M_CO2</ci><apply><times/><ci>Q_a</ci><apply><minus/><ci>conc_CO2_v</ci><ci>conc_CO2_a</ci></apply></apply></apply></apply></apply><apply><eq/><ci>conc_CO2_v</ci><apply><plus/><apply><times/><ci>alpha_tv</ci><ci>conc_CO2_t</ci></apply><ci>Beta_tv</ci></apply></apply></math><variable name="vol_PVC" public_interface="in" units="cubic_m"/><variable name="Q_a" public_interface="in" units="cubic_m_per_sec"/><variable name="M_CO2" public_interface="in" units="mol_per_sec"/></component><units name="mol_per_sec"><unit units="mole"/><unit exponent="-1" units="second"/></units><component name="VC_Meta_Stim"><variable name="M_CO2" public_interface="out" units="mol_per_sec"/><variable name="M_CO2_0" public_interface="in" units="mol_per_sec"/><variable name="A_neuro" public_interface="in" units="dimensionless"/><variable name="f_Q" public_interface="in" units="dimensionless"/><variable name="n_QM" public_interface="in" units="dimensionless"/><variable initial_value="1" name="unity" units="dimensionless"/><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><eq/><ci>M_CO2</ci><apply><times/><ci>M_CO2_0</ci><apply><plus/><ci>unity</ci><apply><times/><ci>A_neuro</ci><apply><divide/><apply><minus/><ci>f_Q</ci><ci>unity</ci></apply><ci>n_QM</ci></apply></apply></apply></apply></apply></math></component><connection><map_components component_1="Parameters" component_2="CBF_Regulation"/><map_variables variable_1="G_myo" variable_2="G_myo"/><map_variables variable_1="G_shear" variable_2="G_shear"/><map_variables variable_1="G_neuro" variable_2="G_neuro"/><map_variables variable_1="G_meta" variable_2="G_meta"/><map_variables variable_1="x_ini" variable_2="x_ini"/></connection><connection><map_components component_1="Parameters" component_2="Myo_Regulation"/><map_variables variable_1="T_myo0" variable_2="T_myo0"/><map_variables variable_1="T_myo_s" variable_2="T_myo_s"/><map_variables variable_1="Tau_myo" variable_2="Tau_myo"/></connection><connection><map_components component_1="Environment" component_2="Myo_Regulation"/><map_variables variable_1="time" variable_2="time"/></connection><connection><map_components component_1="CBF_Regulation" component_2="Myo_Regulation"/><map_variables variable_1="x_myo" variable_2="x_myo"/></connection><connection><map_components component_1="Environment" component_2="Shear_Regulation"/><map_variables variable_1="time" variable_2="time"/></connection><connection><map_components component_1="Parameters" component_2="Shear_Regulation"/><map_variables variable_1="Tau_shear" variable_2="Tau_shear"/><map_variables variable_1="K_shear" variable_2="K_shear"/></connection><connection><map_components component_1="Environment" component_2="Neuro_Regulation"/><map_variables variable_1="time" variable_2="time"/></connection><connection><map_components component_1="Parameters" component_2="Neuro_Regulation"/><map_variables variable_1="Tau_neuro" variable_2="Tau_neuro"/></connection><connection><map_components component_1="CBF_Regulation" component_2="Neuro_Regulation"/><map_variables variable_1="x_neuro" variable_2="x_neuro"/></connection><connection><map_components component_1="Environment" component_2="Meta_Regulation"/><map_variables variable_1="time" variable_2="time"/></connection><connection><map_components component_1="CBF_Regulation" component_2="Meta_Regulation"/><map_variables variable_1="x_meta" variable_2="x_meta"/></connection><connection><map_components component_1="Parameters" component_2="Meta_CO2_Kinetics"/><map_variables variable_1="conc_CO2_a" variable_2="conc_CO2_a"/><map_variables variable_1="alpha_tv" variable_2="alpha_tv"/><map_variables variable_1="Beta_tv" variable_2="Beta_tv"/><map_variables variable_1="vol_PVC" variable_2="vol_PVC"/></connection><connection><map_components component_1="Environment" component_2="Meta_CO2_Kinetics"/><map_variables variable_1="time" variable_2="time"/></connection><connection><map_components component_1="AC_Flow" component_2="Meta_CO2_Kinetics"/><map_variables variable_1="Q_a" variable_2="Q_a"/></connection><connection><map_components component_1="Parameters" component_2="VC_Meta_Stim"/><map_variables variable_1="M_CO2_0" variable_2="M_CO2_0"/><map_variables variable_1="f_Q" variable_2="f_Q"/><map_variables variable_1="n_QM" variable_2="n_QM"/></connection><connection><map_components component_1="VC_Meta_Stim" component_2="Neuro_Regulation"/><map_variables variable_1="A_neuro" variable_2="A_neuro"/></connection><connection><map_components component_1="Meta_CO2_Kinetics" component_2="VC_Meta_Stim"/><map_variables variable_1="M_CO2" variable_2="M_CO2"/></connection><connection><map_components component_1="AC_Tension" component_2="Myo_Regulation"/><map_variables variable_1="T_a" variable_2="T_a"/></connection><connection><map_components component_1="Meta_Regulation" component_2="Meta_CO2_Kinetics"/><map_variables variable_1="conc_CO2_t" variable_2="conc_CO2_t"/></connection><connection><map_components component_1="CBF_Regulation" component_2="Shear_Regulation"/><map_variables variable_1="x_shear" variable_2="x_shear"/></connection><connection><map_components component_1="AC_Flow" component_2="Shear_Regulation"/><map_variables variable_1="Q_a" variable_2="Q_a"/></connection><connection><map_components component_1="Parameters" component_2="Meta_Regulation"/><map_variables variable_1="Tau_meta" variable_2="Tau_Meta"/><map_variables variable_1="conc_CO2_t_sp" variable_2="conc_CO2_t_sp"/></connection><connection><map_components component_1="Arteriolar_Circulation" component_2="AC_Tension"/><map_variables variable_1="P_a" variable_2="P_a"/><map_variables variable_1="T_a" variable_2="T_a"/><map_variables variable_1="T_ae" variable_2="T_ae"/><map_variables variable_1="T_am" variable_2="T_am"/><map_variables variable_1="T_av" variable_2="T_av"/><map_variables variable_1="r_a" variable_2="r_a"/></connection><connection><map_components component_1="Parameters" component_2="AC_Components"/><map_variables variable_1="K_Ra" variable_2="K_Ra"/></connection><units name="mmHg_sec_m"><unit units="mmHg"/><unit units="second"/><unit units="meter"/></units><connection><map_components component_1="Arteriolar_Circulation" component_2="Shear_Regulation"/><map_variables variable_1="r_a" variable_2="r_a"/></connection><connection><map_components component_1="Parameters" component_2="Arteriolar_Circulation"/><map_variables variable_1="r_a0" variable_2="r_a0"/><map_variables variable_1="Eta_a" variable_2="Eta_a"/><map_variables variable_1="P_ic" variable_2="P_ic"/><map_variables variable_1="K_Va" variable_2="K_Va"/><map_variables variable_1="R_v" variable_2="R_v"/></connection><connection><map_components component_1="Venous_Circulation" component_2="Arteriolar_Circulation"/><map_variables variable_1="P_v" variable_2="P_v"/><map_variables variable_1="P_a" variable_2="P_a"/></connection><connection><map_components component_1="AC_Components" component_2="Venous_Circulation"/><map_variables variable_1="R_a" variable_2="R_a"/></connection><connection><map_components component_1="Arteriolar_Circulation" component_2="AC_Tension_Variables"/><map_variables variable_1="r_a" variable_2="r_a"/><map_variables variable_1="h_a" variable_2="h_a"/></connection><connection><map_components component_1="AC_Components" component_2="PCA"/><map_variables variable_1="R_a" variable_2="R_a"/></connection><units name="mmHg_sec2_per_m3_g"><unit units="mmHg"/><unit exponent="2" units="second"/><unit exponent="-3" units="meter"/><unit exponent="-1" units="gram"/></units><rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"><rdf:Description rdf:nodeID="n1"><maximumStepSize xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">0.1</maximumStepSize><endingValue xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">30</endingValue><algorithm xmlns="http://www.cellml.org/metadata/simulation/1.0#nonstandard-" xml:lang="en">bdf15</algorithm></rdf:Description><rdf:Description rdf:nodeID="n2"><rdf:first><rdf:Description rdf:nodeID="n1"/></rdf:first><rdf:rest><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/></rdf:rest></rdf:Description><rdf:Description rdf:about="#hnFjlz6syjR"><simulation xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n3"/></simulation></rdf:Description><rdf:Description rdf:nodeID="n3"><boundIntervals xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n2"/></boundIntervals></rdf:Description></rdf:RDF></model>
