**An Interpretation of Transit Compartment Pharmacodynamic Models As Lifespan Based Indirect Response Models.**

W. Krzyzanski

Department of Pharmaceutical Sciences, University at Buffalo, Buffalo, New York, USA.

**Objectives:** Transit compartments (TC) models are used to describe pharmacodynamic responses that involve drug action on cells undergoing differentiation and maturation [1-3]. Such PD systems can also be described by lifespan based indirect response (LIDR) models [4]. Our objectives were to determine the lifespan distribution for which the LIDR model coincides with the TC model, to show that if the number of transit compartments n increases to infinity, then the TC model approaches the basic LIDR model with the point lifespan distribution centered at the mean lifespan T_{R}, and to propose a new class of LIDR models for agents acting on the cell lifespan distribution.

**Methods:** An integral representation of a solution to the TC model has been used to determine the lifespan distribution for cell population described by this model. This distribution served as a basis for definition of new LIDR models that are mathematically identical to the TC models. Time courses of responses for both types of models were simulated for the monoexponential PK function. The limit response was calculated as n approached infinity. The difference between the limit response and TC responses were evaluated by computer simulations using MATLAB 7.7.

**Results:** The TC model is a special case of the LIDR model with the lifespan distribution described by the gamma function. If drug affects only the production of cells, then the cell lifespan distribution is time invariant. If the drug inhibits or stimulates cell aging, the cell lifespan distribution becomes time dependent revealing a new mechanism for drug effect on the gamma p.d.f. The TC model with a large number of transit compartments converges to a LIDR model. The TC model curves were simulated for n =1 to 100. The difference between TC and LIDR curves was highest for the peak times and ranged between models 14.1%-47.8% for n =10, 9.4%-43.7%, for n =20, and 4.6%-35.5% for n = 100. The new LIDR models are described by a functional operator acting on invariant lifespan distributions and resulting in a time variant distributions due to the changes caused by a time dependent drug effect.

**Conclusions:** The TC models can be considered as LIDR models with the gamma lifespan distribution. If the number of compartments increases and the mean lifespan is constant, then the TC models approach a basic LIDR model with a point lifespan distribution. TC models with the number of TCs between 5 and 20 provide a good approximation of the basic LIDR model.

**References:**

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[4] Krzyzanski W, Woo S, Jusko WJ, Pharmacodynamic models for agents that alter production of natural cells with various distributions of lifespans. J. Pharmacokin. Pharmacodyn. 33:125-165 (2006).