Model Mathematics

Component: environment

Component: membrane

RTONF=RTF ddtimeV=-i_f+i_K+i_K1+i_Na_b+i_Ca_b+i_p+i_NaCa+i_Na+i_siC

Component: hyperpolarising_activated_current

E_Na=RTONFlnNaoNai E_K=RTONFlnKcKi i_fNa=yKcKc+Km_fg_f_NaV-E_Na i_fK=yKcKc+Km_fg_f_KV-E_K i_f=i_fNa+i_fK

Component: hyperpolarising_activated_current_y_gate

E0_y=V+52 alpha_y=0.05-0.067E0_y beta_y=2.5if|E0_y|<delta_yE0_y1-1-0.2E0_yotherwise ddtimey=speed_yalpha_y1-y-beta_yy

Component: time_dependent_potassium_current

I_K=i_K_maxKi-Kc-VRTONF140 i_K=xI_K

Component: time_dependent_potassium_current_x_gate

E0_x=V+22 alpha_x=2.5if|E0_x|<delta_x0.5E0_x1--E0_x5otherwise beta_x=2.5if|E0_x|<delta_x0.178E0_xE0_x15-1otherwise ddtimex=alpha_x1-x-beta_xx

Component: time_independent_potassium_current

i_K1=g_K1KcKc+Km_K1V-E_K1+V+10-E_K2RTONF

Component: sodium_background_current

i_Na_b=g_NabV-E_Na

Component: calcium_background_current

E_Ca=0.5RTONFlnCaoCai i_Ca_b=g_CabV-E_Ca

Component: sodium_potassium_pump

i_p=I_pKcK_mK+KcNaiK_mNa+Nai

Component: Na_Ca_exchanger

i_NaCa=K_NaCagamman_NaCa-2VRTONFNain_NaCaCao-gamma-1n_NaCa-2VRTONFNaon_NaCaCai1+d_NaCaCaiNaon_NaCa+CaoNain_NaCa1+Cai0.0069

Component: fast_sodium_current

E_mh=RTONFlnNao+0.12KcNai+0.12Ki i_Na=g_Nam3hV-E_mh

Component: fast_sodium_current_m_gate

E0_m=V+41 alpha_m=2000if|E0_m|<delta_m200E0_m1--0.1E0_motherwise beta_m=8000-0.056V+66 ddtimem=alpha_m1-m-beta_mm

Component: fast_sodium_current_h_gate

alpha_h=20-0.125V+75 beta_h=2000320-0.1V+75+1 ddtimeh=alpha_h1-h-beta_hh

Component: second_inward_current

i_siCa=4P_siV-50RTONF1--1V-502RTONFCai100RTONF-Cao-2V-50RTONFdff2 i_siK=0.01P_siV-50RTONF1--1V-50RTONFKi50RTONF-Kc-1V-50RTONFdff2 i_siNa=0.01P_siV-50RTONF1--1V-50RTONFNai50RTONF-Nao-1V-50RTONFdff2 i_si=i_siCa+i_siK+i_siNa

Component: second_inward_current_d_gate

E0_d=V+24-5 alpha_d=120if|E0_d|<delta_d30E0_d1--1E0_d4otherwise beta_d=120if|E0_d|<delta_d12E0_dE0_d10-1otherwise ddtimed=alpha_d1-d-beta_dd

Component: second_inward_current_f_gate

E0_f=V+34 alpha_f=25if|E0_f|<delta_f6.25E0_fE0_f4-1otherwise beta_f=501+-1V+344 ddtimef=alpha_f1-f-beta_ff

Component: second_inward_current_f2_gate

beta_f2=Caialpha_f2K_mf2 ddtimef2=alpha_f2-f2alpha_f2+beta_f2

Component: extracellular_sodium_concentration

Component: intracellular_sodium_concentration

V_Cell=3.141592654radius2length Vi=V_Cell1-V_e_ratio ddtimeNai=-1i_Na+i_Na_b+i_fNa+i_siNa+i_p3+i_NaCan_NaCan_NaCa-21ViF

Component: extracellular_calcium_concentration

Component: intracellular_calcium_concentration

i_up=21ViF1tau_upCa_up_maxCaiCa_up_max-Ca_up i_tr=21V_relF1tau_reppCa_up-Ca_rel E0_p=V+34--30 alpha_p=0.625E0_pE0_p4-1 beta_p=51+-1E0_p4 i_rel=21V_relF1tau_relCa_relCairCaCairCa+K_mCarCa ddtimep=alpha_p1-p-beta_pp ddtimeCa_up=1i_up-i_tr21V_upF V_up=Vi0.05 ddtimeCa_rel=1i_tr-i_rel21V_relF V_rel=Vi0.02 ddtimeCai=-1i_siCa+i_Ca_b-2i_NaCan_NaCa-2-i_rel+i_up21ViF

Component: extracellular_potassium_concentration

i_mK=i_K1+i_K+i_fK+i_siK-2i_p ddtimeKc=-pfKc-Kb+1i_mK1V_eF

Component: intracellular_potassium_concentration

ddtimeKi=-1i_mK1ViF