New developments in using stochastic recipe for multi-compartmentmodel: Inter-compartment traveling route, residence time, andexponential convolution expansion - Liang Zhao (Mathematical Biosciences and Engineering)
Drug residence time in ''compartmentalized'' human body system had been studiedfrom both deterministic and Markovian perspectives. However, probability andprobability density functions for a drug molecule to be (1) in anycompartment of study interest, (2) with any defined inter-compartmenttraveling route, and (3) with/without specified residence times in itsvisited compartments, has not been systemically reported. In Markovian viewof compartmental system, mathematical solutions for the probability orprobability density functions, for a drug molecule with any defined inter-compartment traveling routes in the system and/or with specified residencetimes in any visited compartments, are provided. Matrix convolution isdefined and thus employed to facilitate methodology development. Laplacetransformations are used to facilitate convolution operations in linearsystems. This paper shows that the drug time-concentration function can bedecomposed into the summation of a series of component functions, which isnamed as convolution expansion. The studied probability or probabilitydensity functions can be potentially engaged with physiological orpharmacological significances and thus be used to describe a broad range ofdrug exposure-response relationships.