Model Mathematics

\frac{d}{d time} (Cgen_pp) = \frac{Qpp H_Cgen_B Cgen_B - (\frac{Qpp H_Cgen_pp Cgen_pp}{Ppp})}{Vpp} H_Cgen_pp = \{\begin{matrix} 0.0 if Cgen_pp < 0.0 \\ 1.0 otherwise \end{matrix} Qpp = 0.528 Qt

\frac{d}{d time} (Cgen_rp) = \frac{Qrp H_Cgen_B Cgen_B - (\frac{Qrp H_Cgen_rp Cgen_rp}{Prp})}{Vrp} - (kgen_urine H_Cgen_rp Cgen_rp) H_Cgen_rp = \{\begin{matrix} 0.0 if Cgen_rp < 0.0 \\ 1.0 otherwise \end{matrix} Qrp = 0.289 Qt

\frac{d}{d time} (Cgen_l) = \frac{(Ql H_Cgen_B Cgen_B - (\frac{(Ql + QGI) H_Cgen_l Cgen_l}{Pl})) + vinf + \frac{QGI H_Cgen_GI Cgen_GI}{Prp}}{Vl} - (\frac{Vmax H_Cgen_l Cgen_l}{Km + H_Cgen_l Cgen_l}) H_Cgen_l = \{\begin{matrix} 0.0 if Cgen_l < 0.0 \\ 1.0 otherwise \end{matrix} Ql = 0.03 Qt

\frac{d}{d time} (Cgen_GI) = \frac{QGI H_Cgen_B Cgen_B - (\frac{QGI H_Cgen_GI Cgen_GI}{Prp})}{VGI} H_Cgen_GI = \{\begin{matrix} 0.0 if Cgen_GI < 0.0 \\ 1.0 otherwise \end{matrix} QGI = 0.153 Qt

\frac{d}{d time} (Ccon_l) = \frac{Vmax H_Cgen_l Cgen_l}{Km + H_Cgen_l Cgen_l} - (kbile H_Ccon_l Ccon_l + \frac{(Ql + QGI) (H_Ccon_l Ccon_l - (H_Ccon_ROB Ccon_ROB))}{Vl}) H_Ccon_l = \{\begin{matrix} 0.0 if Ccon_l < 0.0 \\ 1.0 otherwise \end{matrix}

\frac{d}{d time} (Ccon_ROB) = \frac{(Ql + QGI) (H_Ccon_l Ccon_l - (H_Ccon_ROB Ccon_ROB))}{VROB} - (kcon_urine H_Ccon_ROB Ccon_ROB) H_Ccon_ROB = \{\begin{matrix} 0.0 if Ccon_ROB < 0.0 \\ 1.0 otherwise \end{matrix}

\frac{d}{d time} (Acon_b) = kbile H_Ccon_l Ccon_l Vl d_t_Cgen_l = tbasal + cgen H_Cgen_l Cgen_l ⅇ^{- (\frac{time}{ct})}

Cgen_B = \frac{\frac{Qrp H_Cgen_rp Cgen_rp}{Prp} + \frac{Qpp H_Cgen_pp Cgen_pp}{Ppp} + \frac{(Ql + QGI) H_Cgen_l Cgen_l}{Pl}}{Qt} H_Cgen_B = \{\begin{matrix} 0.0 if Cgen_B < 0.0 \\ 1.0 otherwise \end{matrix}

vinf = \{\begin{matrix} cv F if time < epsilon \land time \geq 0.0 \\ cv G if time ≦ 1.0 - epsilon \land time \geq epsilon \\ cv H if time ≦ 1.0 \land time > 1.0 - epsilon \\ cv I if time ≦ 1.0 + \frac{5.0}{60.0} \land time > 1.0 \end{matrix} F = \frac{-2.0}{{epsilon}^{3.0}} {time}^{3.0} + \frac{3.0}{{epsilon}^{2.0}} {time}^{2.0} G = 1.0 H = \frac{3.0 {(1.0 - time)}^{2.0}}{{epsilon}^{2.0}} - (\frac{2.0 {(1.0 - time)}^{3.0}}{{epsilon}^{3.0}}) I = 0.0 Qt = 14.1 {m_rat}^{0.75}