Model Mathematics

\frac{d}{d time} (Ca_i) = Ca_o + (Ca_max - Ca_o) \frac{time}{tau_Ca} ⅇ^{\frac{1.0 - time}{tau_Ca}}

\frac{d}{d time} (Ca_b) = rho_0 Ca_i (Ca_b_max - Ca_b) - (rho_1 Ca_b (1.0 - (\frac{T}{lambda To})))

\frac{d}{d time} (z) = alpha_0 ({(\frac{Ca_b}{C_50})}^{n} (1.0 - z) - z) To = T_ref (1.0 + beta_0 (lambda - 1.0)) z n = n_ref (1.0 + beta_1 (lambda - 1.0)) pC_50 = pC_50_ref (1.0 + beta_2 (lambda - 1.0))

dlambda_dt = \frac{alpha_1}{A1} \frac{\frac{T}{To} - 1.0}{\frac{T}{To} + a} T = To \frac{1.0 + a Q}{1.0 - Q} Q = A1 ⅇ^{(- alpha_1) (time - tau)} dlambda_dt tau + A2 ⅇ^{(- alpha_2) (time - tau)} dlambda_dt tau + A3 ⅇ^{(- alpha_3) (time - tau)} dlambda_dt tau