The sojourn time and its prospective use in pharmacology

Sojourn time in a given compartment i when the material has been injected in compartment i (Sji) corresponds to the average time spent by the particles of the material in i before their definitive exit from that compartment. Sojourn time is different from the mean residence time (tji), which is the average age of the particles leaving the system. If K denotes the transfer matrix of the compartmental system, then -K-1 provides the sojourn times in each compartment given initial arrival in each of the other compartments. It can be shown that Sji = xi(s)/xj. 0/s = 0, corresponds to the value of AUC in compartment i. Since AUCi/xj,0 = Fji.AUC/xi,0 (Fji = fraction of the dose in j reaching i), one has Sji = FjiSii.AUCi corresponds to a rectangle of height equal to xj,0 and base equal to Sii. Therefore in a compartment i a drug acts on the average for a time equal to Sii and the number of molecules in it depends on the dose and on Fji. In compartments which are not sampled the value of AUC can be calculated by a simulated curve or by -K-1. From the height of the rectangle whose area is equal to AUC one should subtract the threshold theta for a given effect; the resulting rectangle should indicate the intrinsic efficacy of the drug. These considerations could be applied in pharmacology, toxicology, and chemotherapy.