Model Mathematics

Component: environment

Component: intracellular_space

dd time V_i = Lie_p pi_i - pi_e pi_i = R T Na_i + K_i + Cl_i + X_i V_i pi_e = R T Na_e + K_e + Cl_e + X_e V_e delta_init = delta_i - delta_e dd time delta = V_i F R T Na_i + K_i - Cl_i + z_i X_i V_i C_m A_s X_i = V_i Na_i + K_i - Cl_i z_i

Component: intracellular_sodium

dd time Na_i =- 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 = R T F ln Na_e Na_i

Component: intracellular_sodium_m_gate

A_m = 0.1 25.0 - delta + delta_eq 0.1 25.0 - delta + delta_eq - 1.0 B_m = 4.0 - delta + delta_eq 18.0 m_infinity = A_m A_m + B_m

Component: intracellular_sodium_h_gate

A_h = 0.07 0.05 - delta + delta_eq B_h = 1.0 0.1 30.0 - delta + delta_eq + 1.0 h_infinity = A_h A_h + B_h

Component: intracellular_potassium

dd time K_i =- g_K F delta - delta_K - 2.0 P g_K = g_b_K + g_K_max n_infinity 4.0 delta_K = R T F ln K_e K_i

Component: intracellular_potassium_n_gate

A_n = 0.01 10.0 - delta + delta_eq 0.1 10.0 - delta + delta_eq - 1.0 B_n = 0.125 - delta + delta_eq 80.0 n_infinity = A_n A_n + B_n

Component: intracellular_chloride

dd time Cl_i = g_Cl F delta + delta_Cl delta_Cl = R T -1.0 F ln Cl_e Cl_i

Component: extracellular_sodium

dd time Na_e = g_Na F delta - delta_Na + 3.0 P - Jv_Na + Jh_Na

Component: extracellular_potassium

dd time K_e = g_K F delta - delta_K - 2.0 P - Jv_K + Jh_K

Component: extracellular_chloride

dd time Cl_e =- g_Cl F delta + delta_Cl - Jv_Cl + Jh_Cl

Component: extracellular_space

dd time V_e = Lie_p pi_e - pi_i - Jv_H2O + Jh_H2O X_e = V_e Na_e + K_e - Cl_e z_e

Component: water_flux

Jh_H2O =- 1.0 tau_1 V_infinity_e - V_e + 1.0 tau_2 V_infinity_T - V_i + V_e

Component: sodium_flux

Jh_Na = P_h alpha_Na Na_infinity_e - Na_e alpha_Na 1.0 - alpha_Na alpha_Na = Jh_H2O P_h - 1.0 F R T delta_eh

Component: potassium_flux

Jh_K = P_h alpha_K K_infinity_e - K_e alpha_K 1.0 - alpha_K alpha_K = Jh_H2O P_h - 1.0 F R T delta_eh

Component: chloride_flux

Jh_Cl = P_h alpha_Cl Cl_infinity_e - Cl_e alpha_Cl 1.0 - alpha_Cl alpha_Cl = Jh_H2O P_h - -1.0 F R T delta_eh

Component: capillary_compartment_sodium

Na_v = Qa Na_a + Jv_Na Qv delta_ev_Na = R T F ln Na_v Na_e Jv_Na = Qv Na_v - Qa Na_a

Component: capillary_compartment_potassium

K_v = Qa K_a + Jv_K Qv delta_ev_K = R T F ln K_v K_e Jv_K = Qv K_v - Qa K_a

Component: capillary_compartment_chloride

Cl_v = Qa Cl_a + Jv_Cl Qv delta_ev_Cl = R T F ln Cl_v Cl_e Jv_Cl = Qv Cl_v - Qa Cl_a

Component: capillary_space

Qv = Qa + Jv_H2O Jv_H2O = Qv - Qa pi_v = Na_v + K_v + Cl_v + Pr_v Pr_v = Na_v + K_v +- Cl_v z_v

Component: arterial_space

Qa = Qv Pr_v Pr_a

Component: pump_rate

P = a_t P_max f_NaK 1.0 1.0 + Km_Na_i Na_i 1.5 K_e Km_K_e + K_e f_NaK = 1.0 1.0 + 0.1245 -0.1 delta F R T + 0.0365 7.0 -0.1 delta F R T Na_e 67.3 - 1.0 a_t = 0.35 time 15.0