Model Mathematics

t

t = time

delta_t = 1.0

{R_A}_{t + delta_t} = {epsilon}_{t} ⅇ^{gamma H_A}

{P_G}_{t + delta_t} = \frac{P_V + P_A \frac{{R_E}_{t}}{{R_A}_{t}} \frac{{C_A}_{t}}{{C_E}_{t}}}{(1.0 + \frac{{R_E}_{t}}{{R_A}_{t}}) \frac{{C_A}_{t}}{{C_E}_{t}}}

{phi}_{t + delta_t} = epsilon_max - (\frac{psi}{1.0 + ⅇ^{kappa {Na_M}_{t - D_TGF} - Na_half}})

{epsilon}_{t + delta_t} = \frac{{phi}_{t} + {epsilon}_{t} (\frac{2.0 zeta}{omega delta} + \frac{2.0}{{(omega delta)}^{2.0}}) - (\frac{{epsilon}_{t - delta}}{{(omega delta)}^{2.0}})}{1.0 + \frac{2.0 zeta}{omega delta} + \frac{1.0}{{(omega delta)}^{2.0}}}

pi_G = pi \frac{C_A + C_E}{2.0}

{pi}_{C} = a C + b C^{2.0}

SNGFR = Kf (P_G - (P_BC + pi_G))

{Na_I}_{t} = \frac{{Na_R}_{t}}{0.67}

{H2O_I}_{t} = \frac{{H2O_R}_{t}}{0.67}

{H2O_D_M}_{t} = {H2O_D_M}_{t + delta_t}

{Na_D_M}_{t} = {Na_D_M}_{t + delta_t}

{Na_D}_{t} = \frac{{Na_M}_{t}}{{H2O_M}_{t + delta_t}} {H2O_D}_{t + delta_t}

{Na_M}_{t + delta_t} = {H2O_M}_{t} (\frac{{Na_A}_{t + delta_t}}{{H2O_A}_{t}} + Na_G)

{H2O_D}_{t + delta_t} = \frac{{Na_D}_{t}}{{Na_D_M}_{t}} {H2O_D_M}_{t}

{H2O_M}_{t + delta_t} = \frac{{Na_M}_{t}}{{Na_D_M}_{t}} {H2O_D_M}_{t}

{Na_A}_{t + delta_t} = \frac{{H2O_A}_{t}}{{H2O_M_A}_{t + delta_t}} ({Na_M_A}_{t} - ({Na_G}_{t} {H2O_M}_{t}))

Na_G = Na_M - Na_A

Na_M_A = Na_M + Na_A

H2O_M_A = H2O_M + H2O_A

R_ADH = \frac{\log_{10} (ADH_I 1e12)}{2.0}

R_ALD = \frac{\log_{10} (ALD_I 1e11)}{3.0}

H2O_R = R_ADH (H2O_I - (Na_I \frac{H2O_I_IF}{Na_I_IF}))

Na_R = R_ALD Na_max Na_I