# Model Mathematics

### Component: membrane

$RTONF=R⁢TFddtimeV=-i_f+i_K+i_K1+i_Na_b+i_Ca_b+i_p+i_NaCa+i_Na+i_siC$

### Component: hyperpolarising_activated_current

$E_Na=RTONF⁢ln⁡NaoNaiE_K=RTONF⁢ln⁡KcKii_fNa=y⁢KcKc+Km_f⁢g_f_Na⁢V-E_Nai_fK=y⁢KcKc+Km_f⁢g_f_K⁢V-E_Ki_f=i_fNa+i_fK$

### Component: hyperpolarising_activated_current_y_gate

$E0_y=V+52alpha_y=0.05⁢ⅇ-0.067⁢E0_ybeta_y=2.5if|E0_y|

### Component: time_dependent_potassium_current

$I_K=i_K_max⁢Ki-Kc⁢ⅇ-VRTONF140i_K=x⁢I_K$

### Component: time_dependent_potassium_current_x_gate

$E0_x=V+22alpha_x=2.5if|E0_x|

### Component: time_independent_potassium_current

$i_K1=g_K1⁢KcKc+Km_K1⁢V-E_K1+ⅇV+10-E_K⁢2RTONF$

### Component: sodium_background_current

$i_Na_b=g_Nab⁢V-E_Na$

### Component: calcium_background_current

$E_Ca=0.5⁢RTONF⁢ln⁡CaoCaii_Ca_b=g_Cab⁢V-E_Ca$

### Component: sodium_potassium_pump

$i_p=I_p⁢KcK_mK+Kc⁢NaiK_mNa+Nai$

### Component: Na_Ca_exchanger

$i_NaCa=K_NaCa⁢ⅇgamma⁢n_NaCa-2⁢VRTONF⁢Nain_NaCa⁢Cao-ⅇgamma-1⁢n_NaCa-2⁢VRTONF⁢Naon_NaCa⁢Cai1+d_NaCa⁢Cai⁢Naon_NaCa+Cao⁢Nain_NaCa⁢1+Cai0.0069$

### Component: fast_sodium_current

$E_mh=RTONF⁢ln⁡Nao+0.12⁢KcNai+0.12⁢Kii_Na=g_Na⁢m3⁢h⁢V-E_mh$

### Component: fast_sodium_current_m_gate

$E0_m=V+41alpha_m=2000if|E0_m|

### Component: fast_sodium_current_h_gate

$alpha_h=20⁢ⅇ-0.125⁢V+75beta_h=2000320⁢ⅇ-0.1⁢V+75+1ddtimeh=alpha_h⁢1-h-beta_h⁢h$

### Component: second_inward_current

$i_siCa=4⁢P_si⁢V-50RTONF⁢1-ⅇ-1⁢V-50⁢2RTONF⁢Cai⁢ⅇ100RTONF-Cao⁢ⅇ-2⁢V-50RTONF⁢d⁢f⁢f2i_siK=0.01⁢P_si⁢V-50RTONF⁢1-ⅇ-1⁢V-50RTONF⁢Ki⁢ⅇ50RTONF-Kc⁢ⅇ-1⁢V-50RTONF⁢d⁢f⁢f2i_siNa=0.01⁢P_si⁢V-50RTONF⁢1-ⅇ-1⁢V-50RTONF⁢Nai⁢ⅇ50RTONF-Nao⁢ⅇ-1⁢V-50RTONF⁢d⁢f⁢f2i_si=i_siCa+i_siK+i_siNa$

### Component: second_inward_current_d_gate

$E0_d=V+24-5alpha_d=120if|E0_d|

### Component: second_inward_current_f_gate

$E0_f=V+34alpha_f=25if|E0_f|

### Component: second_inward_current_f2_gate

$beta_f2=Cai⁢alpha_f2K_mf2ddtimef2=alpha_f2-f2⁢alpha_f2+beta_f2$

### Component: intracellular_sodium_concentration

$V_Cell=3.141592654⁢radius2⁢lengthVi=V_Cell⁢1-V_e_ratioddtimeNai=-1⁢i_Na+i_Na_b+i_fNa+i_siNa+i_p⁢3+i_NaCa⁢n_NaCan_NaCa-21⁢Vi⁢F$

### Component: intracellular_calcium_concentration

$i_up=2⁢1⁢Vi⁢F1⁢tau_up⁢Ca_up_max⁢Cai⁢Ca_up_max-Ca_upi_tr=2⁢1⁢V_rel⁢F1⁢tau_rep⁢p⁢Ca_up-Ca_relE0_p=V+34--30alpha_p=0.625⁢E0_pⅇE0_p4-1beta_p=51+ⅇ-1⁢E0_p4i_rel=2⁢1⁢V_rel⁢F1⁢tau_rel⁢Ca_rel⁢CairCaCairCa+K_mCarCaddtimep=alpha_p⁢1-p-beta_p⁢pddtimeCa_up=1⁢i_up-i_tr2⁢1⁢V_up⁢FV_up=Vi⁢0.05ddtimeCa_rel=1⁢i_tr-i_rel2⁢1⁢V_rel⁢FV_rel=Vi⁢0.02ddtimeCai=-1⁢i_siCa+i_Ca_b-2⁢i_NaCan_NaCa-2-i_rel+i_up2⁢1⁢Vi⁢F$

### Component: extracellular_potassium_concentration

$i_mK=i_K1+i_K+i_fK+i_siK-2⁢i_pddtimeKc=-pf⁢Kc-Kb+1⁢i_mK1⁢V_e⁢F$

### Component: intracellular_potassium_concentration

$ddtimeKi=-1⁢i_mK1⁢Vi⁢F$
Source
Derived from workspace Noble, Noble, 1984 at changeset ecd89b532183.
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