Drug Absorption in Man, and its Measurement by MaxEnt

Abstract

In many cases the processes by which a drug is handled in the body, once it has reached the bloodstream, are essentially linear at therapeutic doses. If so, then the concentration in blood after an oral dose may be considered as the convolution of the rate at which the drug reaches the bloodstream with the response of the body to an ‘impulse’ of the drug applied directly into the bloodstream. The input rate may be treated as a ‘blurred’ version of a positive additive distribution, where the ‘blurring’ reflects the diffusive processes which the drug must undergo during its transit from the point of dosing to the general circulation. The standard pharmacokinetic compartmental model of the body leads to an impulse response function which is of the form $\sum\nolimits_i {{A_i}{e^{ - {\lambda _i}t}}}$. One can extend this model, and express the function in terms of a continuous distribution of time constants λ, rather than just a small number of discrete values. Thus the input rate and impulse response can both be characterised using positive additive distributions, which should be reconstructed from experimental data by a process of Bayesian inference using Skilling’s generalisation of the Shannon/Jaynes entropy.