Location: Respiratory System @ d2572ee15ff2 / tissue_gas_exchange.cellml
- Author:
- Soroush Safaei <ssaf006@aucklanduni.ac.nz>
- Date:
- 2018-08-15 17:46:49+12:00
- Desc:
- modify pulmonary
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/3a4/rawfile/d2572ee15ff273d02c4e07ad95a7234afe2b9ba5/tissue_gas_exchange.cellml
<?xml version='1.0'?>
<model name="tissue_gas_exchange" 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.cellml">
<units name="m3" units_ref="m3"/>
<units name="mM" units_ref="mM"/>
<units name="m3_per_s" units_ref="m3_per_s"/>
<units name="m6_per_J" units_ref="m6_per_J"/>
<units name="m3_per_J" units_ref="m3_per_J"/>
<units name="per_m" units_ref="per_m"/>
<units name="J_per_m3" units_ref="J_per_m3"/>
<units name="J_s_per_m6" units_ref="J_s_per_m6"/>
<units name="J_s2_per_m6" units_ref="J_s2_per_m6"/>
<units name="J_s2_per_m5" units_ref="J_s2_per_m5"/>
<units name="J_per_s" units_ref="J_per_s"/>
<units name="J_per_m6" units_ref="J_per_m6"/>
<units name="J_s_per_m3" units_ref="J_s_per_m3"/>
</import>
<component name="environment">
<variable name="time" public_interface="out" units="second"/>
</component>
<component name="tissue_gas_exchange">
<variable name="t" public_interface="in" units="second"/>
<!-- Blood Volume in Tissue Compartment-->
<variable initial_value="284e-6" name="V_T_hp" units="m3"/>
<variable initial_value="1300e-6" name="V_T_bp" units="m3"/>
<variable initial_value="31200e-6" name="V_T_mp" units="m3"/>
<variable initial_value="262e-6" name="V_T_ep" units="m3"/>
<variable initial_value="2673e-6" name="V_T_sp" units="m3"/>
<!-- Blood Volume in Systemic Peripheral Compartment-->
<variable initial_value="1.0" name="V_hp" public_interface="in" units="m3"/>
<variable initial_value="1.0" name="V_bp" public_interface="in" units="m3"/>
<variable initial_value="1.0" name="V_mp" public_interface="in" units="m3"/>
<variable initial_value="1.0" name="V_ep" public_interface="in" units="m3"/>
<variable initial_value="1.0" name="V_sp" public_interface="in" units="m3"/>
<!-- Blood Volume in Systemic Venous Compartment-->
<variable initial_value="1.0" name="V_hv" public_interface="in" units="m3"/>
<variable initial_value="1.0" name="V_bv" public_interface="in" units="m3"/>
<variable initial_value="1.0" name="V_mv" public_interface="in" units="m3"/>
<variable initial_value="1.0" name="V_ev" public_interface="in" units="m3"/>
<variable initial_value="1.0" name="V_sv" public_interface="in" units="m3"/>
<!-- Blood Volume in Thoracic Veins-->
<variable initial_value="1.0" name="V_tv" public_interface="in" units="m3"/>
<!-- Blood Flow at the Entrance of Systemic Peripheral Compartment-->
<variable initial_value="0.0" name="Q_hp_in" public_interface="in" units="m3_per_s"/>
<variable initial_value="0.0" name="Q_bp_in" public_interface="in" units="m3_per_s"/>
<variable initial_value="0.0" name="Q_mp_in" public_interface="in" units="m3_per_s"/>
<variable initial_value="0.0" name="Q_ep_in" public_interface="in" units="m3_per_s"/>
<variable initial_value="0.0" name="Q_sp_in" public_interface="in" units="m3_per_s"/>
<!-- Blood Flow at the Exit of Systemic Peripheral Compartment-->
<variable initial_value="0.0" name="Q_hp" public_interface="in" units="m3_per_s"/>
<variable initial_value="0.0" name="Q_bp" public_interface="in" units="m3_per_s"/>
<variable initial_value="0.0" name="Q_mp" public_interface="in" units="m3_per_s"/>
<variable initial_value="0.0" name="Q_ep" public_interface="in" units="m3_per_s"/>
<variable initial_value="0.0" name="Q_sp" public_interface="in" units="m3_per_s"/>
<!-- Blood Flow at the Exit of Systemic Venous Compartment-->
<variable initial_value="0.0" name="Q_hv" public_interface="in" units="m3_per_s"/>
<variable initial_value="0.0" name="Q_bv" public_interface="in" units="m3_per_s"/>
<variable initial_value="0.0" name="Q_mv" public_interface="in" units="m3_per_s"/>
<variable initial_value="0.0" name="Q_ev" public_interface="in" units="m3_per_s"/>
<variable initial_value="0.0" name="Q_sv" public_interface="in" units="m3_per_s"/>
<!-- Blood Flow at the Exit of Thoracic Veins-->
<variable initial_value="0.0" name="Q_tv" public_interface="in" units="m3_per_s"/>
<!-- Gas Concentration in Blood-Tissue Compartment-->
<variable initial_value="0.0" name="C_hp_O2" units="mM"/>
<variable initial_value="0.0" name="C_hp_CO2" units="mM"/>
<variable initial_value="0.0" name="C_bp_O2" units="mM"/>
<variable initial_value="0.0" name="C_bp_CO2" units="mM"/>
<variable initial_value="0.0" name="C_mp_O2" units="mM"/>
<variable initial_value="0.0" name="C_mp_CO2" units="mM"/>
<variable initial_value="0.0" name="C_ep_O2" units="mM"/>
<variable initial_value="0.0" name="C_ep_CO2" units="mM"/>
<variable initial_value="0.0" name="C_sp_O2" units="mM"/>
<variable initial_value="0.0" name="C_sp_CO2" units="mM"/>
<!-- Gas Concentration in Systemic Venous Compartment-->
<variable initial_value="0.0" name="C_hv_O2" units="mM"/>
<variable initial_value="0.0" name="C_hv_CO2" units="mM"/>
<variable initial_value="0.0" name="C_bv_O2" units="mM"/>
<variable initial_value="0.0" name="C_bv_CO2" units="mM"/>
<variable initial_value="0.0" name="C_mv_O2" units="mM"/>
<variable initial_value="0.0" name="C_mv_CO2" units="mM"/>
<variable initial_value="0.0" name="C_ev_O2" units="mM"/>
<variable initial_value="0.0" name="C_ev_CO2" units="mM"/>
<variable initial_value="0.0" name="C_sv_O2" units="mM"/>
<variable initial_value="0.0" name="C_sv_CO2" units="mM"/>
<!-- Gas Concentration in Systemic Arteries and Veins-->
<variable initial_value="0.0" name="C_a_O2" public_interface="in" units="mM"/>
<variable initial_value="0.0" name="C_a_CO2" public_interface="in" units="mM"/>
<variable initial_value="0.0" name="C_v_O2" public_interface="out" units="mM"/>
<variable initial_value="0.0" name="C_v_CO2" public_interface="out" units="mM"/>
<!-- O2 Consumption Rate in Blood-Tissue Compartment-->
<variable initial_value="0.4e-6" name="M_hp_O2" units="m3_per_s"/>
<variable initial_value="0.7917e-6" name="M_bp_O2" units="m3_per_s"/>
<variable initial_value="0.86e-6" name="M_mp_O2" units="m3_per_s"/>
<variable initial_value="0.2447e-6" name="M_ep_O2" units="m3_per_s"/>
<variable initial_value="1.807e-6" name="M_sp_O2" units="m3_per_s"/>
<!-- CO2 Production Rate in Blood-Tissue Compartment-->
<variable initial_value="0.336e-6" name="M_hp_CO2" units="m3_per_s"/>
<variable initial_value="0.665e-6" name="M_bp_CO2" units="m3_per_s"/>
<variable initial_value="0.7224e-6" name="M_mp_CO2" units="m3_per_s"/>
<variable initial_value="0.2055e-6" name="M_ep_CO2" units="m3_per_s"/>
<variable initial_value="1.5178e-6" name="M_sp_CO2" units="m3_per_s"/>
<!-- System of ODEs-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_hp_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_hp_in</ci>
<apply>
<minus/>
<ci>C_a_CO2</ci>
<ci>C_hp_CO2</ci>
</apply>
</apply>
<ci>M_hp_CO2</ci>
</apply>
<apply>
<plus/>
<ci>V_T_hp</ci>
<ci>V_hp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_bp_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_bp_in</ci>
<apply>
<minus/>
<ci>C_a_CO2</ci>
<ci>C_bp_CO2</ci>
</apply>
</apply>
<ci>M_bp_CO2</ci>
</apply>
<apply>
<plus/>
<ci>V_T_bp</ci>
<ci>V_bp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_mp_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_mp_in</ci>
<apply>
<minus/>
<ci>C_a_CO2</ci>
<ci>C_mp_CO2</ci>
</apply>
</apply>
<ci>M_mp_CO2</ci>
</apply>
<apply>
<plus/>
<ci>V_T_mp</ci>
<ci>V_mp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_ep_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_ep_in</ci>
<apply>
<minus/>
<ci>C_a_CO2</ci>
<ci>C_ep_CO2</ci>
</apply>
</apply>
<ci>M_ep_CO2</ci>
</apply>
<apply>
<plus/>
<ci>V_T_ep</ci>
<ci>V_ep</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_sp_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_sp_in</ci>
<apply>
<minus/>
<ci>C_a_CO2</ci>
<ci>C_sp_CO2</ci>
</apply>
</apply>
<ci>M_sp_CO2</ci>
</apply>
<apply>
<plus/>
<ci>V_T_sp</ci>
<ci>V_sp</ci>
</apply>
</apply>
</apply>
<!-- -->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_hv_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_hp</ci>
<apply>
<minus/>
<ci>C_hp_CO2</ci>
<ci>C_hv_CO2</ci>
</apply>
</apply>
<ci>M_hp_CO2</ci>
</apply>
<ci>V_hv</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_bv_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_bp</ci>
<apply>
<minus/>
<ci>C_bp_CO2</ci>
<ci>C_bv_CO2</ci>
</apply>
</apply>
<ci>M_bp_CO2</ci>
</apply>
<ci>V_bv</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_mv_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_mp</ci>
<apply>
<minus/>
<ci>C_mp_CO2</ci>
<ci>C_mv_CO2</ci>
</apply>
</apply>
<ci>M_mp_CO2</ci>
</apply>
<ci>V_mv</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_ev_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_ep</ci>
<apply>
<minus/>
<ci>C_ep_CO2</ci>
<ci>C_ev_CO2</ci>
</apply>
</apply>
<ci>M_ep_CO2</ci>
</apply>
<ci>V_ev</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_sv_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_sp</ci>
<apply>
<minus/>
<ci>C_sp_CO2</ci>
<ci>C_sv_CO2</ci>
</apply>
</apply>
<ci>M_sp_CO2</ci>
</apply>
<ci>V_sv</ci>
</apply>
</apply>
<!-- -->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_hp_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_hp_in</ci>
<apply>
<minus/>
<ci>C_a_O2</ci>
<ci>C_hp_O2</ci>
</apply>
</apply>
<ci>M_hp_O2</ci>
</apply>
<apply>
<plus/>
<ci>V_T_hp</ci>
<ci>V_hp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_bp_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_bp_in</ci>
<apply>
<minus/>
<ci>C_a_O2</ci>
<ci>C_bp_O2</ci>
</apply>
</apply>
<ci>M_bp_O2</ci>
</apply>
<apply>
<plus/>
<ci>V_T_bp</ci>
<ci>V_bp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_mp_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_mp_in</ci>
<apply>
<minus/>
<ci>C_a_O2</ci>
<ci>C_mp_O2</ci>
</apply>
</apply>
<ci>M_mp_O2</ci>
</apply>
<apply>
<plus/>
<ci>V_T_mp</ci>
<ci>V_mp</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_ep_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_ep_in</ci>
<apply>
<minus/>
<ci>C_a_O2</ci>
<ci>C_ep_O2</ci>
</apply>
</apply>
<ci>M_ep_O2</ci>
</apply>
<apply>
<plus/>
<ci>V_T_ep</ci>
<ci>V_ep</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_sp_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_sp_in</ci>
<apply>
<minus/>
<ci>C_a_O2</ci>
<ci>C_sp_O2</ci>
</apply>
</apply>
<ci>M_sp_O2</ci>
</apply>
<apply>
<plus/>
<ci>V_T_sp</ci>
<ci>V_sp</ci>
</apply>
</apply>
</apply>
<!-- -->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_hv_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_hp</ci>
<apply>
<minus/>
<ci>C_hp_O2</ci>
<ci>C_hv_O2</ci>
</apply>
</apply>
<ci>M_hp_O2</ci>
</apply>
<ci>V_hv</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_bv_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_bp</ci>
<apply>
<minus/>
<ci>C_bp_O2</ci>
<ci>C_bv_O2</ci>
</apply>
</apply>
<ci>M_bp_O2</ci>
</apply>
<ci>V_bv</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_mv_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_mp</ci>
<apply>
<minus/>
<ci>C_mp_O2</ci>
<ci>C_mv_O2</ci>
</apply>
</apply>
<ci>M_mp_O2</ci>
</apply>
<ci>V_mv</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_ev_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_ep</ci>
<apply>
<minus/>
<ci>C_ep_O2</ci>
<ci>C_ev_O2</ci>
</apply>
</apply>
<ci>M_ep_O2</ci>
</apply>
<ci>V_ev</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_sv_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci>Q_sp</ci>
<apply>
<minus/>
<ci>C_sp_O2</ci>
<ci>C_sv_O2</ci>
</apply>
</apply>
<ci>M_sp_O2</ci>
</apply>
<ci>V_sv</ci>
</apply>
</apply>
<!-- -->
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_v_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>Q_hv</ci>
<apply>
<minus/>
<ci>C_hv_O2</ci>
<ci>C_v_O2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Q_bv</ci>
<apply>
<minus/>
<ci>C_bv_O2</ci>
<ci>C_v_O2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Q_mv</ci>
<apply>
<minus/>
<ci>C_mv_O2</ci>
<ci>C_v_O2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Q_ev</ci>
<apply>
<minus/>
<ci>C_ev_O2</ci>
<ci>C_v_O2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Q_sv</ci>
<apply>
<minus/>
<ci>C_sv_O2</ci>
<ci>C_v_O2</ci>
</apply>
</apply>
</apply>
<ci>V_tv</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>C_v_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<times/>
<ci>Q_hv</ci>
<apply>
<minus/>
<ci>C_hv_CO2</ci>
<ci>C_v_CO2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Q_bv</ci>
<apply>
<minus/>
<ci>C_bv_CO2</ci>
<ci>C_v_CO2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Q_mv</ci>
<apply>
<minus/>
<ci>C_mv_CO2</ci>
<ci>C_v_CO2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Q_ev</ci>
<apply>
<minus/>
<ci>C_ev_CO2</ci>
<ci>C_v_CO2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>Q_sv</ci>
<apply>
<minus/>
<ci>C_sv_CO2</ci>
<ci>C_v_CO2</ci>
</apply>
</apply>
</apply>
<ci>V_tv</ci>
</apply>
</apply>
</math>
</component>
<connection>
<map_components component_1="environment" component_2="tissue_gas_exchange"/>
<map_variables variable_1="time" variable_2="t"/>
</connection>
</model>