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Journal of Pharmacokinetics and Biopharmaceutics

, Volume 16, Issue 6, pp 657–666 | Cite as

The sojourn time and its prospective use in pharmacology

  • Giorgio Segre
Article

Abstract

Sojourn time in a given compartment i when the material has been injected in compartment j (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\((\bar t_{ji} )\), which is the average age of the particles leaving the system. If\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{K} \) denotes the transfer matrix of the compartmental system, then\( - \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{K} ^{ - 1} \) provides the sojourn times in each compartment given initial arrival in each of the other compartments. It can be shown that\(S_{ji} = x_i (s)/x_{j,0} \left| {_{s = 0} } \right.\) that is the transfer function between compartment j and i, where xi(s) is the Laplace transform of the function xi(t) and xj,0 indicates the dose introduced in compartment j at time 0. It can be observed that xi¦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,i 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\( - \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{K} ^{ - 1} \) From the height of the rectangle whose area is equal to AUC one should subtract the threshold θ for a given effect; the resulting should indicate the intrinsic efficacy of the drug. These considerations could be applied in pharmacology, toxicology, and chemotherapy.

Key words

sojourn time mean residence time compartments 

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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • Giorgio Segre
    • 1
  1. 1.Institute of Pharmacology, Faculty of MedicineUniversity of SienaSienaItaly

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