Matlab vr2012b

A six compartment model was used to estimate the distribution of human albumin produced by the liver model. The albumin production rate was estimated for each interaction period by assuming a constant production rate calculated to yield the measured concentration at the 17 hr time point. The production rate was assumed constant for the remaining 31 hr interaction period and then re-estimated during the new interaction period. The initial concentration was assumed zero everywhere. The equations are shown below and were simulated in Matlab v. R2012b (Mathworks, Natick, MA).
$$\begin{array}{l}\frac{{dC}_{Mi}}{dt}=\frac{1}{V_{Mi}}\left[(Q_{L1}+Q_{\mathit{hpv}})C_{Li}+Q_{L2}{C}_{L2}+Q_{L3}{C}_{L3}-Q_{Mi}{C}_{Mi}\right]\\ \frac{{dC}_{L1}}{dt}=\frac{Q_{L1}}{V_{L1}}\left[C_{Mi}-C_{L1}\right]\\ \frac{{dC}_{Li}}{dt}=\frac{1}{V_{Li}}\left[Q_{\mathit{hpv}}{C}_{Mi}+Q_{L1}{C}_{L1}-(Q_{L1}+Q_{\mathit{hpv}})C_{Li}+K_p\right]\\ \frac{{dC}_{L2}}{dt}=\frac{Q_{L2}}{V_{L2}}\left[C_{Mi}-C_{L2}\right]\\ \frac{{dC}_{L3}}{dt}=\frac{Q_{L3}}{V_{L3}}\left[C_{Mi}-C_{L3}\right]\\ \frac{{dC}_{L4}}{dt}=0\end{array}$$ where C_Mi = Drug concentration in mixer [mol/L], C_Ln= Drug concentration in Airway #n compartment [mol/L](n=1 to 4), C_Li= Drug concentration in liver compartment [mol/L], V_Mi = Volume in Mixer [L], V_Ln = Volume in Airway#n compartment [L] (n=1 to 4), V_Li= Volume in Liver [L], Q_Mi = Flow Thru Mixer [L/min], Q_Ln= Flow Thru Airway#n compartment [L/min] (n=1 to 3), Q_Li= Flow Thru HPV (Mixer to Liver) [L/min].