Model Mathematics

\frac{d}{d time} (V_i) = Lie_p (pi_i - pi_e) pi_i = R T (Na_i + K_i + Cl_i + \frac{X_i}{V_i}) pi_e = R T (Na_e + K_e + Cl_e + \frac{X_e}{V_e}) delta_init = delta_i - delta_e \frac{d}{d time} (delta) = \frac{V_i F R T (Na_i + K_i - (Cl_i + \frac{z_i X_i}{V_i}))}{C_m A_s} X_i = \frac{V_i (Na_i + K_i - Cl_i)}{z_i}

\frac{d}{d time} (Na_i) = - (\frac{g_Na}{F} (delta - delta_Na) + 3.0 P) g_Na = g_b_Na + g_Na_max {m_infinity}^{3.0} h_infinity delta_Na = \frac{R T}{F} \ln (\frac{Na_e}{Na_i})

A_m = \frac{0.1 ((25.0 - delta) + delta_eq)}{ⅇ^{0.1 ((25.0 - delta) + delta_eq)} - 1.0} B_m = 4.0 ⅇ^{\frac{(- delta) + delta_eq}{18.0}} m_infinity = \frac{A_m}{A_m + B_m}

A_h = 0.07 ⅇ^{0.05 ((- delta) + delta_eq)} B_h = \frac{1.0}{ⅇ^{0.1 ((30.0 - delta) + delta_eq)} + 1.0} h_infinity = \frac{A_h}{A_h + B_h}

\frac{d}{d time} (K_i) = - (\frac{g_K}{F} (delta - delta_K) - (2.0 P)) g_K = g_b_K + g_K_max {n_infinity}^{4.0} delta_K = \frac{R T}{F} \ln (\frac{K_e}{K_i})

A_n = \frac{0.01 ((10.0 - delta) + delta_eq)}{ⅇ^{0.1 ((10.0 - delta) + delta_eq)} - 1.0} B_n = 0.125 ⅇ^{\frac{(- delta) + delta_eq}{80.0}} n_infinity = \frac{A_n}{A_n + B_n}

\frac{d}{d time} (Cl_i) = \frac{g_Cl}{F} (delta + delta_Cl) delta_Cl = \frac{R T}{(-1.0) F} \ln (\frac{Cl_e}{Cl_i})

\frac{d}{d time} (Na_e) = \frac{g_Na}{F} (delta - delta_Na) + 3.0 P - (Jv_Na + Jh_Na)

\frac{d}{d time} (K_e) = \frac{g_K}{F} (delta - delta_K) - (2.0 P) - (Jv_K + Jh_K)

\frac{d}{d time} (Cl_e) = - (\frac{g_Cl}{F} (delta + delta_Cl)) - (Jv_Cl + Jh_Cl)

\frac{d}{d time} (V_e) = Lie_p (pi_e - pi_i) - (Jv_H2O + Jh_H2O) X_e = \frac{V_e (Na_e + K_e - Cl_e)}{z_e}

Jh_H2O = - (\frac{1.0}{tau_1} (V_infinity_e - V_e) + \frac{1.0}{tau_2} (V_infinity_T - (V_i + V_e)))

Jh_Na = P_h alpha_Na \frac{Na_infinity_e - (Na_e ⅇ^{alpha_Na})}{1.0 - (ⅇ^{alpha_Na})} alpha_Na = \frac{Jh_H2O}{P_h} - (\frac{1.0 F}{R T delta_eh})

Jh_K = P_h alpha_K \frac{K_infinity_e - (K_e ⅇ^{alpha_K})}{1.0 - (ⅇ^{alpha_K})} alpha_K = \frac{Jh_H2O}{P_h} - (\frac{1.0 F}{R T delta_eh})

Jh_Cl = P_h alpha_Cl \frac{Cl_infinity_e - (Cl_e ⅇ^{alpha_Cl})}{1.0 - (ⅇ^{alpha_Cl})} alpha_Cl = \frac{Jh_H2O}{P_h} - (\frac{(-1.0) F}{R T delta_eh})

Na_v = \frac{Qa Na_a + Jv_Na}{Qv} delta_ev_Na = \frac{R T}{F} \ln (\frac{Na_v}{Na_e}) Jv_Na = Qv Na_v - (Qa Na_a)

K_v = \frac{Qa K_a + Jv_K}{Qv} delta_ev_K = \frac{R T}{F} \ln (\frac{K_v}{K_e}) Jv_K = Qv K_v - (Qa K_a)

Cl_v = \frac{Qa Cl_a + Jv_Cl}{Qv} delta_ev_Cl = \frac{R T}{F} \ln (\frac{Cl_v}{Cl_e}) Jv_Cl = Qv Cl_v - (Qa Cl_a)

Qv = Qa + Jv_H2O Jv_H2O = Qv - Qa pi_v = Na_v + K_v + Cl_v + Pr_v Pr_v = \frac{Na_v + K_v + (- Cl_v)}{z_v}

Qa = \frac{Qv Pr_v}{Pr_a}

P = a_t P_max f_NaK \frac{1.0}{1.0 + {(\frac{Km_Na_i}{Na_i})}^{1.5}} \frac{K_e}{Km_K_e + K_e} f_NaK = \frac{1.0}{1.0 + 0.1245 ⅇ^{\frac{(-0.1) delta F}{R T}} + (0.0365 7.0 ⅇ^{\frac{(-0.1) delta F}{R T}} ⅇ^{\frac{Na_e}{67.3}} - 1.0)} a_t = {0.35}^{\frac{time}{15.0}}