Model Mathematics

Component: environment

Component: imported_variables

Component: solute_concentrations

dd time C_m_Na =- J_mc_Na + J_ms_Na dd time C_s_Na = J_ms_Na - J_sc_Na dd time C_c_Na = J_mc_Na + J_sc_Na dd time C_m_K =- J_mc_K + J_ms_K dd time C_s_K = J_ms_K - J_sc_K dd time C_c_K = J_mc_K + J_sc_K dd time C_m_Cl =- J_mc_Cl + J_ms_Cl dd time C_s_Cl = J_ms_Cl - J_sc_Cl dd time C_c_Cl = J_mc_Cl + J_sc_Cl

Component: constants

Component: mc_sodium_flux

J_mc_Na = J_mc_NaCl + G_mc_Na G_mc_Na = P_mc_Na F psi_m - psi_c RT C_m_Na - C_c_Na - F RT psi_m - psi_c 1.0 -- F RT psi_m - psi_c J_mc_NaCl = J_mc_NaCl_max C_m_Na K_mc_Na_NaCl C_m_Cl K_mc_Cl_NaCl - C_c_Na K_mc_Na_NaCl C_c_Cl K_mc_Cl_NaCl 1.0 + C_m_Na K_mc_Na_NaCl C_m_Cl K_mc_Cl_NaCl 1.0 + C_c_Na K_mc_Na_NaCl 1.0 + C_c_Cl K_mc_Cl_NaCl + 1.0 + C_c_Na K_mc_Na_NaCl C_c_Cl K_mc_Cl_NaCl 1.0 + C_m_Na K_mc_Na_NaCl 1.0 + C_m_Cl K_mc_Cl_NaCl

Component: mc_potassium_flux

J_mc_K = J_mc_KCl + G_mc_K G_mc_K = P_mc_K F psi_m - psi_c RT C_m_K - C_c_K - F RT psi_m - psi_c 1.0 -- F RT psi_m - psi_c J_mc_KCl = J_mc_KCl_max C_m_K K_mc_K_KCl C_m_Cl K_mc_Cl_KCl - C_c_K K_mc_K_KCl C_c_Cl K_mc_Cl_KCl 1.0 + C_m_K K_mc_K_KCl C_m_Cl K_mc_Cl_KCl 1.0 + C_c_K K_mc_K_KCl 1.0 + C_c_Cl K_mc_Cl_KCl + 1.0 + C_c_K K_mc_K_KCl C_c_Cl K_mc_Cl_KCl 1.0 + C_m_K K_mc_K_KCl 1.0 + C_m_Cl K_mc_Cl_KCl

Component: mc_chloride_flux

J_mc_Cl = J_mc_NaCl + J_mc_KCl + G_mc_Cl G_mc_Cl = P_mc_Cl -1.0 F psi_m - psi_c RT C_m_Cl - C_c_Cl - -1.0 F RT psi_m - psi_c 1.0 -- -1.0 F RT psi_m - psi_c

Component: sc_sodium_flux

J_sc_Na = -3.0 J_a J_a = J_a_max 1.0 1.0 + K_Na_ATPase C_c_Na 3.0

Component: sc_potassium_flux

J_sc_K = 2.0 J_a + G_sc_K G_sc_K = P_sc_K F psi_s - psi_c RT C_s_K - C_c_K - F RT psi_s - psi_c 1.0 -- F RT psi_s - psi_c

Component: sc_chloride_flux

J_sc_Cl = G_sc_Cl G_sc_Cl = P_sc_Cl -1.0 F psi_s - psi_c RT C_s_Cl - C_c_Cl - -1.0 F RT psi_s - psi_c 1.0 -- -1.0 F RT psi_s - psi_c

Component: ms_sodium_flux

J_ms_Na = G_ms_Na G_ms_Na = P_ms_Na F psi_m - psi_s RT C_m_Na - C_s_Na - F RT psi_m - psi_s 1.0 -- F RT psi_m - psi_s

Component: ms_potassium_flux

J_ms_K = G_ms_K G_ms_K = P_ms_K F psi_m - psi_s RT C_m_K - C_s_K - F RT psi_m - psi_s 1.0 -- F RT psi_m - psi_s

Component: ms_chloride_flux

J_ms_Cl = G_ms_Cl G_ms_Cl = P_ms_Cl -1.0 F psi_m - psi_s RT C_m_Cl - C_s_Cl - -1.0 F RT psi_m - psi_s 1.0 -- -1.0 F RT psi_m - psi_s

Component: total_transepithelial_sodium_flux

J_Na = J_mc_Na + J_ms_Na

Component: total_transepithelial_potassium_flux

J_K = J_mc_K + J_ms_K

Component: total_transepithelial_chloride_flux

J_Cl = J_mc_Cl + J_ms_Cl

Component: osmolarities

Osm_m = C_m_Na + C_m_K + C_m_Cl + C_m_Imp Osm_c = C_c_Na + C_c_K + C_c_Cl + C_c_Imp Osm_s = C_s_Na + C_s_K + C_s_Cl + C_s_Imp

Component: mc_transepithelial_volume_flux

J_mc_v = L_mc_v RT Osm_m - Osm_c

Component: ms_transepithelial_volume_flux

J_ms_v = L_ms_v RT Osm_m - Osm_s

Component: sc_transepithelial_volume_flux

J_sc_v = L_sc_v RT Osm_s - Osm_c

Component: total_transepithelial_volume_flux

J_v = J_mc_v + J_ms_v