Modelling Drug Behaviour in the Body with Maxent

Abstract

Description of the passage of drugs into, around and out of the body is conventionally based on simple compartmental models, often with only one or two compartments. These models are clearly gross simplifications of such a complex biological system. Continuous (‘free-form’) distributions, appropriately used, seem more suitable for summarising the complexities of such systems. The use of distributions for this purpose, and their reconstruction from experimental data, is illustrated. The response (concentration of drug in blood) to a rapid intravenous injection of drug is often taken to vary linearly with the injected dose, which suggests characterising the system by its impulse response function, i.e., the concentration in blood as a function of time after a rapid injection of a unit dose. A distribution closely related to the inverse Laplace transform of this impulse response function forms the starting point for an improved model, but is too empirical to have a physiologically useful interpretation. This model can, however, be re-parameterised in a way which has more physiological meaning, and which immediately suggests an extension to take account of the finite capacity of the enzyme systems which metabolise the drug. The system may become markedly nonlinear when this capacity is approached, and so this type of model has important applications in the design of those dosing regimens where this happens.