Model Mathematics

\frac{d}{d time} (V) = \frac{- 1}{Cm} (i_Ca_L + i_K + i_K_Ca + i_Ki + i_M + i_NaCa + i_NaK + i_CaP + i_B)

i_Ca_L = g_Ca_L d f (V - E_Ca_L) E_Ca_L = \frac{R T}{2 F} \ln (\frac{Ca_o}{Ca_i})

d_infinity = \frac{1}{1 + ⅇ^{\frac{- (V + 1.878)}{7.5704}}} tau_d = 2.8928 ⅇ^{- ({(\frac{V + 8.6344}{12.3884})}^{2})} + 2.4343 \frac{d}{d time} (d) = \frac{d_infinity - d}{tau_d}

f_infinity = \frac{1}{1 + ⅇ^{\frac{V + 29.3188}{1.5389}}} tau_ff = 295.5937 ⅇ^{- ({(\frac{V - 4.7187}{112.545})}^{2})} + 23.1907 \frac{d}{d time} (ff) = \frac{f_infinity - ff}{tau_ff} f = 0.74 ff + 0.26

i_K_Ca = g_K_Ca P_K_Ca (V - E_K) E_K = \frac{R T}{F} \ln (\frac{K_o}{K_i})

Po_infinity = \frac{1}{1 + ⅇ^{\frac{- (V - V_1_2_K_Ca)}{21.7}}} V_1_2_K_Ca = (- 45) \log_{10} Ca_i - 198.55 Pf_infinity = Ps_infinity - Po_infinity \frac{d}{d time} (Pf) = \frac{Pf_infinity - Pf}{tau_Pf} \frac{d}{d time} (Ps) = \frac{Ps_infinity - Ps}{tau_Ps} P_K_Ca = 0.65 Pf + 0.35 Ps

i_K = g_K {Pk}^{2} (V - E_K)

Pk_infinity = \frac{1}{1 + ⅇ^{\frac{- (V - V_1_2)}{k}}} tau_P1 = 210.9873 ⅇ^{- ({(\frac{V + 214.3355}{195.3502})}^{2})} - 20.5866 tau_P2 = 821.3949 ⅇ^{- ({(\frac{V + 31.5891}{27.4568})}^{2})} - 0.1892 \frac{d}{d time} (P2) = \frac{Pk_infinity - P2}{tau_P2} \frac{d}{d time} (P1) = \frac{Pk_infinity - P1}{tau_P1} Pk = 0.58 P1 + 0.42 P2

i_M = i_M_K + i_M_Na + i_M_Ca i_M_K = \frac{\frac{Am Pm F^{2} V}{R T} P_K (K_o - (K_i ⅇ^{\frac{F V}{R T}}))}{1 - (ⅇ^{\frac{F V}{R T}})} i_M_Na = \frac{\frac{Am Pm F^{2} V}{R T} P_Na (Na_o - (Na_i ⅇ^{\frac{F V}{R T}}))}{1 - (ⅇ^{\frac{F V}{R T}})} i_M_Ca = \frac{\frac{Am Pm F^{2} V}{R T} 2^{2} P_Ca (Ca_o - (Ca_i ⅇ^{\frac{F V}{R T}}))}{1 - (ⅇ^{\frac{F V}{R T}})} Pm = \frac{1}{1 + ⅇ^{\frac{- (sigma - sigma_1_2)}{k_sigma}}}

i_Ki = \frac{g_max_Ki (V - E_K)}{1 + ⅇ^{\frac{- (V - V_1_2_Ki)}{28.89}}} g_max_Ki = G_Ki K_o n_Ki V_1_2_Ki = A \log_{10} K_i + B

i_CaP = \frac{I_Ca_P CaCM}{CaCM + K_CaCM}

i_NaK = \frac{\frac{\frac{I_NaK K_o}{K_o + Km_Ko} {Na_i}^{1.5}}{{Na_i}^{1.5} + {Km_Nai}^{1.5}} (V + 150)}{V + 200}

i_NaCa = \frac{g_NaCa ({Na_i}^{3} Ca_o phi_F - ({Na_o}^{3} Ca_i))}{1 + {Na_o}^{3} Ca_i phi_R + {Na_i}^{3} Ca_o} phi_F = ⅇ^{\frac{gamma V F}{R T}} phi_R = ⅇ^{\frac{(1 - gamma) V F}{R T}}

i_B = i_B_Na + i_B_Ca + i_B_K i_B_Na = g_Nab (V - E_Na) i_B_Ca = g_Cab (V - E_Ca) i_B_K = g_Kb (V - E_K) E_Na = \frac{R T}{F} \ln (\frac{Na_o}{Na_i}) E_Ca = \frac{R T}{2 F} \ln (\frac{Ca_o}{Ca_i})

\frac{d}{d time} (Na_i) = \frac{- (3 i_NaK + 3 i_NaCa + i_B_Na + i_M_Na)}{F Vol_i} \frac{d}{d time} (K_i) = \frac{- (i_K + i_K_Ca + i_Ki + i_B_K + i_M_K - (2 i_NaK))}{F Vol_i} \frac{d}{d time} (Ca_i) = \frac{- (i_Ca_L + i_CaP + i_B_Ca + i_M_Ca + i_up - (2 i_NaCa + i_rel))}{2 F Vol_Ca} + delta_S_CM_cal + delta_B_F_cal \frac{d}{d time} (S_CM_cal) = delta_S_CM_cal delta_S_CM_cal = k_1 CaS_CM - (k1 Ca_i S_CM_cal) CaS_CM = CaCM CaCM = S_CM_Ca - S_CM_cal \frac{d}{d time} (B_F_cal) = delta_B_F_cal delta_B_F_cal = k_d CaB_F - (kd Ca_i B_F_cal) CaB_F = B_F_Ca - B_F_cal

i_up = \frac{I_up Ca_i}{Ca_i + Km_up} i_tr = \frac{(Ca_u - Ca_r) 2 F Vol_u}{tau_tr} i_rel = \frac{{R10}^{2} (Ca_u - Ca_r) 2 F Vol_r}{tau_rel} \frac{d}{d time} (Ca_up) = \frac{i_up - i_tr}{2 F Vol_u} \frac{d}{d time} (Ca_r) = \frac{i_tr - i_rel}{2 F Vol_r}

R00 = Kr1_R10 + Kr2_R01 - ((Kr1 {Ca_i}^{2} + Kr2 Ca_i) R00) R10 = Kr1 {Ca_i}^{2} R00 + Kr2_R11 - ((Kr2 Ca_i + Kr1_) R10) R11 = Kr1 {Ca_i}^{2} R01 + Kr2 Ca_i R10 - ((Kr2_+ Kr1_) R11) R01 = Kr1_R11 + Kr2 Ca_i R00 - ((Kr1 {Ca_i}^{2} + Kr2_) R01)

M = K2 Mp + K7 AM - (K1 M) Mp = K1 M + K4 AMp - ((K2 + K3) Mp) AMp = K6 AM + K3 Mp - ((K5 + K4) AMp) AM = K5 AMp - ((K7 + K6) AM) K1 = K6 K6 = \frac{{CaCM}^{2}}{{CaCM}^{2} + {K_CaCM}^{2}}

Fp = kp (ⅇ^{\frac{alpha_p (lc - l0)}{l0}} - 1)

Fx = (kx1 AMp + kx2 AM) lx ⅇ^{(- beta) {(\frac{la - lopt}{lopt})}^{2}}

Fa = (fAMp AMp (vx + ia) + fAM AM ia) ⅇ^{(- beta) {(\frac{la - lopt}{lopt})}^{2}}

Fs = mu_s delta_ls + ks (ⅇ^{\frac{alpha_s (ls - ls0)}{ls0}} - 1) \frac{d}{d time} (ls) = delta_ls