Model Mathematics

Component: main

Component: TT04

phi_Cai=T_o-1.2K_Cai pC_50=pC_50_ref1.0+beta_2lambda-1.0 C_50=1.0e-3106-pC_50 n=n_ref1.0+beta_1lambda-1.0 T_o=T_ref1.0+beta_0lambda-1.0z ddtimeCa_b=rho_0Ca_iCa_b_max-Ca_b-rho_1Ca_b ddtimez=alpha_0Ca_bC_50n1.0-z-z

Component: cvs

u_lv_max=phiE_lv_maxq_lv-q_lv_u+1-phiu_lv_0k_lv_Eq_lv-1 u_rv_max=phiE_rv_maxq_rv-q_rv_u+1-phiu_rv_0k_rv_Eq_rv-1 ddtq_ra=v_sv-v_TV ddtq_rv=v_TV-v_PV ddtq_pa=v_PV-v_pa ddtq_pc=v_pa-v_pv ddtq_pv=v_pv-v_la ddtq_la=v_la-v_MV ddtq_lv=v_MV-v_AV ddtq_sa=v_AV-v_sa ddtq_sc=v_sa-v_sc q_sv=q_tot-q_tot_u-q_ra+q_rv+q_pa+q_pc+q_pv+q_la+q_lv+q_sa+q_sc u_ra=q_raC_ra u_rv=u_rv_max-R_PVv_PV u_pa=q_paC_pa u_pc=q_pcC_pc u_pv=q_pvC_pv u_la=q_laC_la u_lv=u_lv_max-R_AVv_AV u_sa=q_saC_sa u_sc=q_scC_sc u_sv=q_svC_sv du_sa=v_AV-v_saC_sa v_TV=0ifu_ra<u_rvu_ra-u_rvR_TVotherwise v_PV=0ifu_rv_max<u_pau_rv_max-u_paR_PVotherwise R_PV=k_PV_Ru_rv_max ddtv_pa=u_pa-u_pc-R_pav_paL_pa v_pv=u_pc-u_pvR_pv v_la=u_pv-u_laR_la v_MV=0ifu_la<u_lvu_la-u_lvR_MVotherwise v_AV=0ifu_lv_max<u_sau_lv_max-u_saR_AVotherwise R_AV=k_AV_Ru_lv_max ddtv_sa=u_sa-u_sc-R_sav_saL_sa v_sc=u_sc-u_svR_sc v_sv=u_sv-u_raR_sv

Component: environment

Component: membrane

stim_period=rest_periodiftime<rest_durationrest_period+1rest_periodact_periodiftimerest_durationrest_period+1rest_periodtime<rest_duration+act_durationact_periodact_periodrest_periodotherwise i_Stim=stim_amplitudeiftime-timestim_periodstim_periodstim_starttime-timestim_periodstim_periodstim_start+stim_duration0otherwise ddtimeV=-i_K1+i_to+i_Kr+i_Ks+i_CaL+i_NaK+i_Na+i_b_Na+i_NaCa+i_b_Ca+i_p_K+i_p_Ca+i_Stim

Component: activation

u=tT_0-tT_0 T=t-T_0tT_0 T_sys=T_sys_0-k_sysTifT>0T_sys_0-k_sysT_0otherwise phi=sinπuTT_sys_02ifu0uT_sys_0T0otherwise

Component: fast_sodium_current

i_Na=g_Nam3hjV-E_Na

Component: L_type_Ca_current

i_CaL=g_CaLdffCa4VF2RTCa_i2VFRT-0.341Ca_o2VFRT-1

Component: rapid_time_dependent_potassium_current

i_Kr=g_KrK_o5.4Xr1Xr2V-E_K

Component: slow_time_dependent_potassium_current

i_Ks=g_KsXs2V-E_Ks

Component: sodium_background_current

i_b_Na=g_bnaV-E_Na

Component: calcium_background_current

i_b_Ca=g_bcaV-E_Ca

Component: transient_outward_current

i_to=g_torsV-E_K

Component: sodium_potassium_pump_current

i_NaK=P_NaKK_oK_o+K_mkNa_iNa_i+K_mNa1+0.1245-0.1VFRT+0.0353-VFRT

Component: sodium_calcium_exchanger_current

i_NaCa=K_NaCagammaVFRTNa_i3Ca_o-gamma-1VFRTNa_o3Ca_ialphaKm_Nai3+Na_o3Km_Ca+Ca_o1+K_satgamma-1VFRT

Component: calcium_pump_current

i_p_Ca=g_pCaCa_iCa_i+K_pCa

Component: potassium_pump_current

i_p_K=g_pKV-E_K1+25-V5.98

Component: calcium_dynamics

i_rel=a_relCa_SR2b_rel2+Ca_SR2+c_reldg i_up=Vmax_up1+K_up2Ca_i2 i_leak=V_leakCa_SR-Ca_i g_inf=11+Ca_i0.000356ifCa_i<0.0003511+Ca_i0.0003516otherwise d_g=g_inf-gtau_g ddtimeg=0ifg_inf>gV>-60d_gotherwise ddt_Ca_i_total=-i_CaL+i_b_Ca+i_p_Ca-2i_NaCa2V_cFCm+i_leak-i_up+i_rel ddt_Ca_sr_total=V_cV_sri_up-i_rel+i_leak f_JCa_i_free=11+Buf_cK_buf_cCa_i+K_buf_c2 f_JCa_sr_free=11+Buf_srK_buf_srCa_SR+K_buf_sr2 ddtimeCa_i=ddt_Ca_i_totalf_JCa_i_free ddtimeCa_SR=ddt_Ca_sr_totalf_JCa_sr_free

Component: sodium_dynamics

ddtimeNa_i=-i_Na+i_b_Na+3i_NaK+3i_NaCaCmV_cF

Component: potassium_dynamics

ddtimeK_i=-i_K1+i_to+i_Kr+i_Ks+i_p_K+i_Stim-2i_NaKCmV_cF

Component: reversal_potentials

E_Na=RTFlnNa_oNa_i E_K=RTFlnK_oK_i E_Ks=RTFlnK_o+P_knaNa_oK_i+P_knaNa_i E_Ca=0.5RTFlnCa_oCa_i

Component: inward_rectifier_potassium_current

alpha_K1=0.11+0.06V-E_K-200 beta_K1=30.0002V-E_K+100+10.1V-E_K-101+-0.5V-E_K xK1_inf=alpha_K1alpha_K1+beta_K1 i_K1=g_K1xK1_infK_o5.4V-E_K

Component: fast_sodium_current_m_gate

m_inf=11+-56.86-V9.032 alpha_m=11+-60-V5 beta_m=0.11+V+355+0.11+V-50200 tau_m=1alpha_mbeta_m ddtimem=m_inf-mtau_m

Component: fast_sodium_current_h_gate

h_inf=11+V+71.557.432 alpha_h=0.057-V+806.8ifV<-400otherwise beta_h=2.70.079V+3100000.3485VifV<-400.770.131+V+10.66-11.1otherwise tau_h=1alpha_h+beta_h ddtimeh=h_inf-htau_h

Component: fast_sodium_current_j_gate

j_inf=11+V+71.557.432 alpha_j=-254280.2444V-6.948e-6-0.04391VV+37.7811+0.311V+79.23ifV<-400otherwise beta_j=0.02424-0.01052V1+-0.1378V+40.14ifV<-400.60.057V1+-0.1V+32otherwise tau_j=1alpha_j+beta_j ddtimej=j_inf-jtau_j

Component: L_type_Ca_current_d_gate

d_inf=11+-5-V7.5 alpha_d=1.41+-35-V13+0.25 beta_d=1.41+V+55 gamma_d=11+50-V20 tau_d=1alpha_dbeta_d+gamma_d ddtimed=d_inf-dtau_d

Component: L_type_Ca_current_f_gate

f_inf=11+V+207 tau_f=1125-V+272240+80+1651+25-V10 ddtimef=f_inf-ftau_f

Component: L_type_Ca_current_fCa_gate

alpha_fCa=11+Ca_i0.0003258 beta_fCa=0.11+Ca_i-0.00050.0001 gama_fCa=0.21+Ca_i-0.000750.0008 fCa_inf=alpha_fCa+beta_fCa+gama_fCa+0.231.46 tau_fCa=2 d_fCa=fCa_inf-fCatau_fCa ddtimefCa=0iffCa_inf>fCaV>-60d_fCaotherwise

Component: rapid_time_dependent_potassium_current_Xr1_gate

xr1_inf=11+-26-V7 alpha_xr1=4501+-45-V10 beta_xr1=61+V+3011.5 tau_xr1=1alpha_xr1beta_xr1 ddtimeXr1=xr1_inf-Xr1tau_xr1

Component: rapid_time_dependent_potassium_current_Xr2_gate

xr2_inf=11+V+8824 alpha_xr2=31+-60-V20 beta_xr2=1.121+V-6020 tau_xr2=1alpha_xr2beta_xr2 ddtimeXr2=xr2_inf-Xr2tau_xr2

Component: slow_time_dependent_potassium_current_Xs_gate

xs_inf=11+-5-V14 alpha_xs=11001+-10-V6 beta_xs=11+V-6020 tau_xs=1alpha_xsbeta_xs ddtimeXs=xs_inf-Xstau_xs

Component: transient_outward_current_s_gate

s_inf=11+V+205 tau_s=85-V+452320+51+V-205+3 ddtimes=s_inf-stau_s

Component: transient_outward_current_r_gate

r_inf=11+20-V6 tau_r=9.5-V+4021800+0.8 ddtimer=r_inf-rtau_r