Model Mathematics

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Component: environment

Component: model_parameters

Sms = 2 3.141592 {rc}^{2} + 2 3.14159 rc Lc Vc = 3.14159 {rc}^{2} Lc Vmyo = Vc 0.68 VSRup = Vc 0.055 VSRrel = Vc 0.00316 Vd = Vc 0.68 0.00006 pt = ptcm 2 3.14159 rc Lc Smt = 2 3.14159 rt Lt pt Vt = 3.14159 {rt}^{2} Lt pt Cmt = Smt 1 Cms = Sms 1 Rst = \frac{\frac{Rot Lt}{2}}{3.14159 {rt}^{2} pt}

Component: i_circ

i_circ = 1000 (\frac{Vm_t}{Rst} - (\frac{Vm_s}{Rst}))

Component: membrane_permeabilities

g_Na_s = g_Na (Sms + Smt) (1 - fNat) g_Na_t = g_Na (Sms + Smt) fNat g_Naps_s = g_Naps (Sms + Smt) (1 - fNapst) g_Naps_t = g_Naps (Sms + Smt) fNapst q_Ks_s = q_Ks (Sms + Smt) (1 - fKst) q_Ks_t = q_Ks (Sms + Smt) fKst q_Kr_s = q_Kr (Sms + Smt) (1 - fKrt) q_Kr_t = q_Kr (Sms + Smt) fKrt g_K1_s = g_K1 (Sms + Smt) (1 - fK1t) g_K1_t = g_K1 (Sms + Smt) fK1t g_Kp_s = g_Kp (Sms + Smt) (1 - fKpt) g_Kp_t = g_Kp (Sms + Smt) fKpt g_Kto_s = g_Kto (Sms + Smt) (1 - fKtot) g_Kto_t = g_Kto (Sms + Smt) fKtot g_KNa_s = g_KNa (Sms + Smt) (1 - fKNat) g_KNa_t = g_KNa (Sms + Smt) fKNat g_Nab_s = g_Nab (Sms + Smt) (1 - fNabt) g_Nab_t = g_Nab (Sms + Smt) fNabt g_Cab_s = g_Cab (Sms + Smt) (1 - fCabt) g_Cab_t = g_Cab (Sms + Smt) fCabt g_KATP_s = g_KATP (Sms + Smt) (1 - fKATPt) g_KATP_t = g_KATP (Sms + Smt) fKATPt P_CaL_s = P_CaL (Sms + Smt) (1 - fCaLt) P_CaL_t = P_CaL (Sms + Smt) fCaLt P_KL_s = P_KL (Sms + Smt) (1 - fCaLt) P_KL_t = P_KL (Sms + Smt) fCaLt P_nsNa_s = P_nsNa (Sms + Smt) (1 - fnsNat) P_nsNa_t = P_nsNa (Sms + Smt) fnsNat P_nsK_s = P_nsK (Sms + Smt) (1 - fnsKt) P_nsK_t = P_nsK (Sms + Smt) fnsKt i_NaCa_max_s = i_NaCa_max (Sms + Smt) (1 - fNaCat) i_NaCa_max_t = i_NaCa_max (Sms + Smt) fNaCat i_NaK_max_s = i_NaK_max (Sms + Smt) (1 - fNaKt) i_NaK_max_t = i_NaK_max (Sms + Smt) fNaKt i_pCa_max_s = i_pCa_max (Sms + Smt) (1 - fpCat) i_pCa_max_t = i_pCa_max (Sms + Smt) fpCat

Component: i_Kext

i_Kext = \{\begin{matrix} 45 (Sms + Smt) if time - (⌊ \frac{time}{stim_Period} ⌋ stim_Period) \geq 0 \land time - (⌊ \frac{time}{stim_Period} ⌋ stim_Period) ≦ 0.001 \\ 0 otherwise \end{matrix}

Component: i_Na_s

E_Na_s = \frac{\ln (\frac{Na_e}{Na_i}) R T}{F} i_Na_s = g_Na_s m^{3} h (Vm_s - (\frac{\ln (\frac{Na_e + 0.12 K_e}{Na_i + 0.12 K_i}) R T}{F}))

Component: i_Na_s_m_gate

m_infinity = \frac{1}{1 + ⅇ^{\frac{Vm_s + 52.2 - 9}{- 7.4}}} tau_m = \frac{\frac{0.001}{101.6 ⅇ^{Vm_s 0.1135} + 0.02268 ⅇ^{(- 0.0717) Vm_s}} + 0.0001}{4.83} \frac{d}{d time} (m) = \frac{m_infinity - m}{tau_m}

Component: i_Na_s_h_gate

h_infinity = \frac{1}{1 + ⅇ^{\frac{Vm_s + 85.6 - 9}{5.5}}} tau_h = \frac{\frac{0.001}{(1.1381e-6) ⅇ^{(- 0.1017) Vm_s} + 6.537 ⅇ^{Vm_s 0.08016}} + 0.0005}{4.83} \frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h}

Component: i_Na_t

E_Na_t = \frac{\ln (\frac{Na_t}{Na_i}) R T}{F} i_Na_t = g_Na_t m^{3} h (Vm_t - (\frac{\ln (\frac{Na_t + 0.12 K_t}{Na_i + 0.12 K_i}) R T}{F}))

Component: i_Na_t_m_gate

m_infinity = \frac{1}{1 + ⅇ^{\frac{Vm_t + 52.2 - 9}{- 7.4}}} tau_m = \frac{\frac{0.001}{101.6 ⅇ^{Vm_t 0.1135} + 0.02268 ⅇ^{(- 0.0717) Vm_t}} + 0.0001}{4.83} \frac{d}{d time} (m) = \frac{m_infinity - m}{tau_m}

Component: i_Na_t_h_gate

h_infinity = \frac{1}{1 + ⅇ^{\frac{Vm_t + 85.6 - 9}{5.5}}} tau_h = \frac{\frac{0.001}{(1.1381e-6) ⅇ^{(- 0.1017) Vm_t} + 6.537 ⅇ^{Vm_t 0.08016}} + 0.0005}{4.83} \frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h}

Component: i_Naps_s

i_Naps_s = \frac{g_Naps_s}{1 + ⅇ^{\frac{- 54 - Vm_s}{8}}} (Vm_s - (\frac{\ln (\frac{Na_e + 0.12 K_e}{Na_i + 0.12 K_i}) R T}{F}))

Component: i_Naps_t

i_Naps_t = \frac{g_Naps_t}{1 + ⅇ^{\frac{- 54 - Vm_t}{8}}} (Vm_t - (\frac{\ln (\frac{Na_t + 0.12 K_t}{Na_i + 0.12 K_i}) R T}{F}))

Component: i_CaL_s

i_CaL_s = \frac{\frac{1 P_CaL_s 4 (Co + Ccao) y Vm_s F^{2}}{R T} (0.001 ⅇ^{\frac{2 Vm_s F}{R T}} - (0.341 Ca_e))}{ⅇ^{\frac{2 Vm_s F}{R T}} - 1} i_KL_s = \frac{\frac{\frac{1 P_KL_s}{1 - (\frac{i_CaL_s + i_CaL_t}{0.458 (Sms + Smt)})} (Co + Ccao) y Vm_s F^{2}}{R T} (K_i ⅇ^{\frac{Vm_s F}{R T}} - K_e)}{ⅇ^{\frac{Vm_s F}{R T}} - 1} \frac{d}{d time} (Cst) = betas C1 + omega Ccast - ((4 alfas + gama) Cst) \frac{d}{d time} (C1) = 4 alfas Cst + 2 betas C2 + \frac{omega}{b} Cca1 - ((betas + 3 alfas + gama a) C1) \frac{d}{d time} (C2) = 3 alfas C1 + 3 betas C3 + \frac{omega}{b^{2}} Cca2 - ((2 betas + 2 alfas + gama a^{2}) C2) \frac{d}{d time} (C3) = 2 alfas C2 + 4 betas C4 + \frac{omega}{b^{3}} Cca3 - ((3 betas + alfas + gama a^{3}) C3) \frac{d}{d time} (C4) = alfas C3 + g Co + \frac{omega}{b^{4}} Cca4 - ((4 betas + f + gama a^{4}) C4) \frac{d}{d time} (Co) = f C4 - (g Co) \frac{d}{d time} (Ccast) = beta2s Cca1 + gama Cst - ((4 alfa2s + omega) Ccast) \frac{d}{d time} (Cca1) = 4 alfa2s Ccast + 2 beta2s Cca2 + gama a C1 - ((beta2s + 3 alfa2s + \frac{omega}{b}) Cca1) \frac{d}{d time} (Cca2) = 3 alfa2s Cca1 + 3 beta2s Cca3 + gama a^{2} C2 - ((2 beta2s + 2 alfa2s + \frac{omega}{b^{2}}) Cca2) \frac{d}{d time} (Cca3) = 2 alfa2s Cca2 + 4 beta2s Cca4 + gama a^{3} C3 - ((3 beta2s + alfa2s + \frac{omega}{b^{3}}) Cca3) \frac{d}{d time} (Cca4) = alfa2s Cca3 + g2 Ccao + gama a^{4} C4 - ((4 beta2s + f2 + \frac{omega}{b^{4}}) Cca4) \frac{d}{d time} (Ccao) = f2 Cca4 - (g2 Ccao) alfas = 400 ⅇ^{\frac{Vm_s + 12}{10}} betas = 50 ⅇ^{\frac{- (Vm_s + 12)}{13}} gama = 187.5 Ca_ss alfa2s = alfas a beta2s = \frac{betas}{b}

Component: i_CaL_s_y_gate

y_infinity = \frac{1}{1 + ⅇ^{\frac{Vm_s + 35}{6}}} tau_y = \frac{0.001}{0.02 + 0.0197 ⅇ^{- ({((Vm_s + 10) 0.0337)}^{2})}} + \frac{0.55}{1 + ⅇ^{\frac{Vm_s + 40}{9.5} 4}} \frac{d}{d time} (y) = \frac{y_infinity - y}{tau_y}

Component: i_CaL_t

i_CaL_t = \frac{\frac{1 P_CaL_t 4 (TCo + TCcao) y Vm_t F^{2}}{R T} (0.001 ⅇ^{\frac{2 Vm_t F}{R T}} - (0.341 Ca_t))}{ⅇ^{\frac{2 Vm_t F}{R T}} - 1} i_KL_t = \frac{\frac{\frac{1 P_KL_t}{1 - (\frac{i_CaL_s + i_CaL_t}{0.458 (Sms + Smt)})} (TCo + TCcao) y Vm_t F^{2}}{R T} (K_i ⅇ^{\frac{Vm_t F}{R T}} - K_t)}{ⅇ^{\frac{Vm_t F}{R T}} - 1} \frac{d}{d time} (TCst) = betat TC1 + omega TCcast - ((4 alfat + gama) TCst) \frac{d}{d time} (TC1) = 4 alfat TCst + 2 betat TC2 + \frac{omega}{b} TCca1 - ((betat + 3 alfat + gama a) TC1) \frac{d}{d time} (TC2) = 3 alfat TC1 + 3 betat TC3 + \frac{omega}{b^{2}} TCca2 - ((2 betat + 2 alfat + gama a^{2}) TC2) \frac{d}{d time} (TC3) = 2 alfat TC2 + 4 betat TC4 + \frac{omega}{b^{3}} TCca3 - ((3 betat + alfat + gama a^{3}) TC3) \frac{d}{d time} (TC4) = alfat TC3 + g TCo + \frac{omega}{b^{4}} TCca4 - ((4 betat + f + gama a^{4}) TC4) \frac{d}{d time} (TCo) = f TC4 - (g TCo) \frac{d}{d time} (TCcast) = beta2t TCca1 + gama TCst - ((4 alfa2t + omega) TCcast) \frac{d}{d time} (TCca1) = 4 alfa2t TCcast + 2 beta2t TCca2 + gama a TC1 - ((beta2t + 3 alfa2t + \frac{omega}{b}) TCca1) \frac{d}{d time} (TCca2) = 3 alfa2t TCca1 + 3 beta2t TCca3 + gama a^{2} TC2 - ((2 beta2t + 2 alfa2t + \frac{omega}{b^{2}}) TCca2) \frac{d}{d time} (TCca3) = 2 alfa2t TCca2 + 4 beta2t TCca4 + gama a^{3} TC3 - ((3 beta2t + alfa2t + \frac{omega}{b^{3}}) TCca3) \frac{d}{d time} (TCca4) = alfa2t TCca3 + g2 TCcao + gama a^{4} TC4 - ((4 beta2t + f2 + \frac{omega}{b^{4}}) TCca4) \frac{d}{d time} (TCcao) = f2 TCca4 - (g2 TCcao) gama = 187.5 Ca_ss alfat = 400 ⅇ^{\frac{Vm_t + 12}{10}} betat = 50 ⅇ^{\frac{- (Vm_t + 12)}{13}} alfa2t = alfat a beta2t = \frac{betat}{b}

Component: i_CaL_t_y_gate

y_infinity = \frac{1}{1 + ⅇ^{\frac{Vm_t + 35}{6}}} tau_y = \frac{0.001}{0.02 + 0.0197 ⅇ^{- ({((Vm_t + 10) 0.0337)}^{2})}} + \frac{0.55}{1 + ⅇ^{\frac{Vm_t + 40}{9.5} 4}} \frac{d}{d time} (y) = \frac{y_infinity - y}{tau_y}

Component: i_Kr_s

i_Kr_s = q_Kr_s 0.02614 \sqrt{\frac{K_e}{5.4}} xr xri (Vm_s - E_Kr_s) E_Kr_s = \frac{\ln (\frac{K_e}{K_i}) R T}{F}

Component: i_Kr_s_xr_gate

xr_infinity = \frac{1}{1 + ⅇ^{\frac{- (Vm_s + 21.5)}{7.5}}} tau_xr = \frac{0.001}{\frac{0.00138 (Vm_s + 14.2)}{1 - (ⅇ^{(- 0.123) (Vm_s + 14.2)})} + \frac{0.00061 (Vm_s + 38.9)}{ⅇ^{0.145 (Vm_s + 38.9)} - 1}} \frac{d}{d time} (xr) = \frac{xr_infinity - xr}{tau_xr}

Component: i_Kr_s_xri_gate

xri = \frac{1}{1 + ⅇ^{\frac{Vm_s + 9}{22.4}}}

Component: i_Kr_t

i_Kr_t = q_Kr_t 0.02614 \sqrt{\frac{K_t}{5.4}} xr xri (Vm_t - E_Kr_t) E_Kr_t = \frac{\ln (\frac{K_t}{K_i}) R T}{F}

Component: i_Kr_t_xr_gate

xr_infinity = \frac{1}{1 + ⅇ^{\frac{- (Vm_t + 21.5)}{7.5}}} tau_xr = \frac{0.001}{\frac{0.00138 (Vm_t + 14.2)}{1 - (ⅇ^{(- 0.123) (Vm_t + 14.2)})} + \frac{0.00061 (Vm_t + 38.9)}{ⅇ^{0.145 (Vm_t + 38.9)} - 1}} \frac{d}{d time} (xr) = \frac{xr_infinity - xr}{tau_xr}

Component: i_Kr_t_xri_gate

xri = \frac{1}{1 + ⅇ^{\frac{Vm_t + 9}{22.4}}}

Component: i_Ks_s

i_Ks_s = q_Ks_s (0.2308 + \frac{0.7692}{1 + ⅇ^{\frac{- (\log_{10} (1 Ca_i)) - 4.2}{0.6}}}) {xs}^{2} (Vm_s - E_Ks_s) E_Ks_s = \frac{\ln (\frac{K_e + PRNaK Na_e}{K_i + PRNaK Na_i}) R T}{F}

Component: i_Ks_s_xs_gate

xs_infinity = \frac{1}{1 + ⅇ^{\frac{- (Vm_s - 1.5)}{16.7}}} tau_xs = \frac{0.001}{\frac{(7.19e-5) (Vm_s + 30)}{1 - (ⅇ^{(- 0.148) (Vm_s + 30)})} + \frac{(1.31e-4) (Vm_s + 30)}{ⅇ^{0.0687 (Vm_s + 30)} - 1}} \frac{d}{d time} (xs) = \frac{xs_infinity - xs}{tau_xs}

Component: i_Ks_t

i_Ks_t = q_Ks_t (0.2308 + \frac{0.7692}{1 + ⅇ^{\frac{- (\log_{10} (1 Ca_i)) - 4.2}{0.6}}}) {xs}^{2} (Vm_t - E_Ks_t) E_Ks_t = \frac{\ln (\frac{K_t + PRNaK Na_t}{K_i + PRNaK Na_i}) R T}{F}

Component: i_Ks_t_xs_gate

xs_infinity = \frac{1}{1 + ⅇ^{\frac{- (Vm_t - 1.5)}{16.7}}} tau_xs = \frac{0.001}{\frac{(7.19e-5) (Vm_t + 30)}{1 - (ⅇ^{(- 0.148) (Vm_t + 30)})} + \frac{(1.31e-4) (Vm_t + 30)}{ⅇ^{0.0687 (Vm_t + 30)} - 1}} \frac{d}{d time} (xs) = \frac{xs_infinity - xs}{tau_xs}

Component: i_K1_s

i_K1_s = \frac{g_K1_s \sqrt{\frac{K_e}{5.4}} aK1s}{aK1s + bK1s} (Vm_s - E_K1_s) E_K1_s = E_Kr_s aK1s = \frac{1020}{1 + ⅇ^{0.2385 (Vm_s - E_K1_s - 59.215)}} bK1s = \frac{1000 (0.49124 ⅇ^{0.08032 ((Vm_s - E_K1_s) + 5.476)} + ⅇ^{0.06175 (Vm_s - E_K1_s - 594.31)})}{1 + ⅇ^{(- 0.5143) ((Vm_s - E_K1_s) + 4.753)}}

Component: i_K1_t

i_K1_t = \frac{g_K1_t \sqrt{\frac{K_t}{5.4}} aK1t}{aK1t + bK1t} (Vm_t - E_K1_t) E_K1_t = E_Kr_t aK1t = \frac{1020}{1 + ⅇ^{0.2385 (Vm_t - E_K1_t - 59.215)}} bK1t = \frac{1000 (0.49124 ⅇ^{0.08032 ((Vm_t - E_K1_t) + 5.476)} + ⅇ^{0.06175 (Vm_t - E_K1_t - 594.31)})}{1 + ⅇ^{(- 0.5143) ((Vm_t - E_K1_t) + 4.753)}}

Component: i_Kp_s

i_Kp_s = g_Kp_s kps (Vm_s - E_Kp_s) E_Kp_s = E_Kr_s kps = \frac{1}{1 + ⅇ^{\frac{20 - Vm_s}{5}}}

Component: i_Kp_t

i_Kp_t = g_Kp_t kpt (Vm_t - E_Kp_t) E_Kp_t = E_Kr_t kpt = \frac{1}{1 + ⅇ^{\frac{20 - Vm_t}{5}}}

Component: i_Kto_s

i_Kto_s = \frac{g_Kto_s}{(1 + ⅇ^{\frac{Vm_s + 57.53}{- 5.863}}) (1 + ⅇ^{\frac{Vm_s - 45.8}{25.87}})} (r2 fr2 + r3 (1 - fr2)) (Vm_s - E_Kto_s) E_Kto_s = E_Kr_s

Component: i_Kto_s_r2_gate

r2_infinity = \frac{1.006}{1 + ⅇ^{\frac{Vm_s + 36.69 + 10}{12.43}}} \frac{d}{d time} (r2) = \frac{r2_infinity - r2}{tau_r2}

Component: i_Kto_s_r3_gate

r3_infinity = r2_infinity \frac{d}{d time} (r3) = \frac{r3_infinity - r3}{tau_r3}

Component: i_Kto_t

i_Kto_t = \frac{g_Kto_t}{(1 + ⅇ^{\frac{Vm_t + 57.53}{- 5.863}}) (1 + ⅇ^{\frac{Vm_t - 45.8}{25.87}})} (r2 fr2 + r3 (1 - fr2)) (Vm_t - E_Kto_t) E_Kto_t = E_Kr_t

Component: i_Kto_t_r2_gate

r2_infinity = \frac{1.006}{1 + ⅇ^{\frac{Vm_t + 36.69 + 10}{12.43}}} \frac{d}{d time} (r2) = \frac{r2_infinity - r2}{tau_r2}

Component: i_Kto_t_r3_gate

r3_infinity = r2_infinity \frac{d}{d time} (r3) = \frac{r3_infinity - r3}{tau_r3}

Component: i_KNa_s

i_KNa_s = \frac{g_KNa_s (0.8 - (\frac{0.65}{1 + ⅇ^{\frac{Vm_s + 125}{15}}})) 0.85}{1 + {(\frac{66}{Na_i})}^{2.8}} (Vm_s - E_KNa_s) E_KNa_s = E_Kr_s

Component: i_KNa_t

i_KNa_t = \frac{g_KNa_t (0.8 - (\frac{0.65}{1 + ⅇ^{\frac{Vm_t + 125}{15}}})) 0.85}{1 + {(\frac{66}{Na_i})}^{2.8}} (Vm_t - E_KNa_t) E_KNa_t = E_Kr_t

Component: i_nsNa_s

i_nsNa_s = \frac{\frac{\frac{1 P_nsNa_s Vm_s F^{2}}{R T} (0.75 Na_i ⅇ^{\frac{Vm_s F}{R T}} - (0.75 Na_e))}{ⅇ^{\frac{Vm_s F}{R T}} - 1}}{1 + {(\frac{0.0025}{Ca_i})}^{3}}

Component: i_nsNa_t

i_nsNa_t = \frac{\frac{\frac{1 P_nsNa_t Vm_t F^{2}}{R T} (0.75 Na_i ⅇ^{\frac{Vm_t F}{R T}} - (0.75 Na_t))}{ⅇ^{\frac{Vm_t F}{R T}} - 1}}{1 + {(\frac{0.0025}{Ca_i})}^{3}}

Component: i_nsK_s

i_nsK_s = \frac{\frac{\frac{1 P_nsK_s Vm_s F^{2}}{R T} (0.75 K_i ⅇ^{\frac{Vm_s F}{R T}} - (0.75 K_e))}{ⅇ^{\frac{Vm_s F}{R T}} - 1}}{1 + {(\frac{0.0025}{Ca_i})}^{3}}

Component: i_nsK_t

i_nsK_t = \frac{\frac{\frac{1 P_nsK_t Vm_t F^{2}}{R T} (0.75 K_i ⅇ^{\frac{Vm_t F}{R T}} - (0.75 K_t))}{ⅇ^{\frac{Vm_t F}{R T}} - 1}}{1 + {(\frac{0.0025}{Ca_i})}^{3}}

Component: i_Nab_s

i_Nab_s = g_Nab_s (Vm_s - E_Na_s)

Component: i_Nab_t

i_Nab_t = g_Nab_t (Vm_t - E_Na_t)

Component: i_Cab_s

i_Cab_s = g_Cab_s (Vm_s - E_Ca_s) E_Ca_s = \frac{\ln (\frac{Ca_e}{Ca_i}) R T}{2 F}

Component: i_Cab_t

i_Cab_t = g_Cab_t (Vm_t - E_Ca_t) E_Ca_t = \frac{\ln (\frac{Ca_t}{Ca_i}) R T}{2 F}

Component: i_NaCa_s

i_NaCa_s = \frac{i_NaCa_max_s ⅇ^{\frac{(- 0.85) Vm_s F}{R T}} (ⅇ^{\frac{Vm_s F}{R T}} {Na_i}^{3} Ca_e - ({Na_e}^{3} Ca_i))}{1 + 0.0001 ⅇ^{\frac{(- 0.85) Vm_s F}{R T}} (ⅇ^{\frac{Vm_s F}{R T}} {Na_i}^{3} Ca_e + {Na_e}^{3} Ca_i)}

Component: i_NaCa_t

i_NaCa_t = \frac{i_NaCa_max_t ⅇ^{\frac{(- 0.85) Vm_t F}{R T}} (ⅇ^{\frac{Vm_t F}{R T}} {Na_i}^{3} Ca_t - ({Na_t}^{3} Ca_i))}{1 + 0.0001 ⅇ^{\frac{(- 0.85) Vm_t F}{R T}} (ⅇ^{\frac{Vm_t F}{R T}} {Na_i}^{3} Ca_t + {Na_t}^{3} Ca_i)}

Component: i_NaK_s

i_NaK_s = \frac{\frac{\frac{i_NaK_max_s}{1 + 0.1245 ⅇ^{\frac{(- 0.1) Vm_s F}{R T}} + \frac{0.0365 1}{7} (ⅇ^{\frac{Na_e}{67.3}} - 1) ⅇ^{\frac{(- Vm_s) F}{R T}}} 1}{1 + {(\frac{10}{Na_i})}^{1.5}} K_e}{K_e + 1.5}

Component: i_NaK_t

i_NaK_t = \frac{\frac{\frac{i_NaK_max_t}{1 + 0.1245 ⅇ^{\frac{(- 0.1) Vm_t F}{R T}} + \frac{0.0365 1}{7} (ⅇ^{\frac{Na_t}{67.3}} - 1) ⅇ^{\frac{(- Vm_t) F}{R T}}} 1}{1 + {(\frac{10}{Na_i})}^{1.5}} K_t}{K_t + 1.5}

Component: i_pCa_s

i_pCa_s = \frac{i_pCa_max_s Ca_i}{0.0005 + Ca_i}

Component: i_pCa_t

i_pCa_t = \frac{i_pCa_max_t Ca_i}{0.0005 + Ca_i}

Component: i_KATP_s

i_KATP_s = \frac{g_KATP_s 1}{1 + {(\frac{ATP_i}{0.114})}^{2}} {(\frac{K_e}{4})}^{0.24} (Vm_s - E_KATP_s) E_KATP_s = E_Kr_s

Component: i_KATP_t

i_KATP_t = \frac{g_KATP_t 1}{1 + {(\frac{ATP_i}{0.114})}^{2}} {(\frac{K_t}{4})}^{0.24} (Vm_t - E_KATP_t) E_KATP_t = E_Kr_t

Component: t_tubular_ion_fluxes

JteNa = \frac{1 Vt}{tau_Na} (Na_t - Na_e) JteCa = \frac{1 Vt}{tau_Ca} (Ca_t - Ca_e) JteK = \frac{1 Vt}{tau_K} (K_t - K_e)

Component: JCaSRup

JCaSRup = \frac{1 1000 Vmyo 0.0018 {Ca_i}^{2}}{{Ca_i}^{2} + {0.0005}^{2}}

Component: JCaSRleak

JCaSRleak = 1250 Vmyo 0.000058 (CaSRup - Ca_i)

Component: Jtr

Jtr = \frac{1 VSRrel}{tau_tr} (CaSRup - CaSRrel)

Component: JCaSRrel

JCaSRrel = 1800 VSRrel (F2 + F3) (CaSRrel - Ca_ss) \frac{d}{d time} (F1) = F2 kam - (F1 kap {Ca_ss}^{4}) \frac{d}{d time} (F2) = F1 kap {Ca_ss}^{4} + F3 kbm + F4 kcm - (F2 (kam + kbp {Ca_ss}^{3} + kcp)) \frac{d}{d time} (F3) = F2 kbp {Ca_ss}^{3} - (F3 kbm) \frac{d}{d time} (F4) = F2 kcp - (F4 kcm) kap = 3 12.15e12 kbp = 4.05e9

Component: JCad

JCad = \frac{1 (Ca_ss - Ca_i) Vmyo}{tau_d}

Component: CaSRrel

\frac{d}{d time} (CaSRrel) = \frac{\frac{1}{1 + \frac{15 0.8}{{(0.8 + CaSRrel)}^{2}}} (Jtr - JCaSRrel)}{VSRrel}

Component: CaSRup

\frac{d}{d time} (CaSRup) = \frac{JCaSRup - JCaSRleak - Jtr}{1 VSRup}

Component: ion_concentrations

\frac{d}{d time} (Ca_ss) = \frac{1}{1 + \frac{0.05 0.00238}{{(0.00238 + Ca_ss)}^{2}}} (\frac{- (i_CaL_s + i_CaL_t)}{2 F Vd} + \frac{1 JCaSRrel}{Vd} - (\frac{1 JCad}{Vd})) \frac{d}{d time} (Ca_i) = \frac{1}{1 + \frac{0.05 0.00238}{{(0.00238 + Ca_i)}^{2}}} (\frac{(- 2) (i_NaCa_s + i_NaCa_t) + i_Cab_s + i_Cab_t + i_pCa_s + i_pCa_t}{(- 2) F Vmyo} + \frac{1 (JCad + JCaSRleak - JCaSRup)}{Vmyo} - (dBTRH 0.14) - (dBTRL 0.07)) dBTRH = 20000 Ca_i (1 - BTRH) - (0.07 BTRH) dBTRL = 40000 Ca_i (1 - BTRL) - (BTRL 40) \frac{d}{d time} (BTRH) = dBTRH \frac{d}{d time} (BTRL) = dBTRL \frac{d}{d time} (Na_i) = \frac{- (i_Na_s + i_Na_t + i_Naps_s + i_Naps_t + i_nsNa_s + i_nsNa_t + i_Nab_s + i_Nab_t + 3 i_NaCa_s + 3 i_NaCa_t + 3 i_NaK_s + 3 i_NaK_t)}{F Vmyo} \frac{d}{d time} (K_i) = \frac{- (((- 0) i_Kext + i_Ks_s + i_Ks_t + i_Kr_s + i_Kr_t + i_K1_s + i_K1_t + i_Kp_s + i_Kp_t + i_KL_s + i_KL_t + i_KNa_s + i_KNa_t + i_nsK_s + i_nsK_t - (2 i_NaK_s) - (2 i_NaK_t)) + i_KATP_s + i_KATP_t + i_Kto_s + i_Kto_t)}{F Vmyo} \frac{d}{d time} (Na_t) = \frac{\frac{i_Na_t + i_Naps_t + i_nsNa_t + i_Nab_t + 3 i_NaCa_t + 3 i_NaK_t}{F} - (1 JteNa)}{Vt} \frac{d}{d time} (Ca_t) = \frac{\frac{(- 2) i_NaCa_t + i_CaL_t + i_Cab_t + i_pCa_t}{2 F} - (1 JteCa)}{Vt} \frac{d}{d time} (K_t) = \frac{\frac{(i_Ks_t + i_Kr_t + i_K1_t + i_Kp_t + i_KNa_t + i_KL_t + i_nsK_t - (2 i_NaK_t)) + i_KATP_t + i_Kto_t}{F} - (1 JteK)}{Vt}

Component: Vm_s

\frac{d}{d time} (Vm_s) = \frac{1000 (i_Kext + i_circ - i_Na_s - i_Naps_s - i_CaL_s - i_KL_s - i_Ks_s - i_Kr_s - i_K1_s - i_Kp_s - i_KNa_s - i_KATP_s - i_nsNa_s - i_nsK_s - i_Nab_s - i_Cab_s - i_NaCa_s - i_NaK_s - i_pCa_s - i_Kto_s)}{Cms}

Component: Vm_t

\frac{d}{d time} (Vm_t) = \frac{1000 (- i_circ - i_Na_t - i_Naps_t - i_CaL_t - i_KL_t - i_Ks_t - i_Kr_t - i_K1_t - i_Kp_t - i_KNa_t - i_KATP_t - i_nsNa_t - i_nsK_t - i_Nab_t - i_Cab_t - i_NaCa_t - i_NaK_t - i_pCa_t - i_Kto_t)}{Cmt}