MacDope: A simulation of drug disposition in the human body. Mathematical considerations

A mathematical analysis is proposed for simulation of drug absorption, distribution and elimination in the human body. Eight interacting compartments are described: stomach, intestine, liver, lipid, interstitial, intracellular and parenteral depot. Disintegration of tablets, ionisation of drug in solution, binding to transport proteins, metabolism within the liver with enterohepatic circulation of metabolite if required, and excretion by the kidneys are described. The interaction of drugs and macromolecules is developed on the basis of the Law of Mass Action and is exemplified in Michaelis-Menten enzyme kinetics and the binding of drug to transport proteins. These descriptions are generalized to permit handling of a number of drugs which may compete for binding sites and thus exhibit kinetic interaction.The administration, absorption and distribution of drug are described by linear equations. These are represented as current generators and admittances in an electrical circuit analogue of the system. The equations describing metabolism and excretion are linearised over short intervals of time. The binding to plasma proteins is considered constant over these iteration intervals and the whole system of differential equations integrated using a standard numerical integration algorithm with variable step length. Drug properties and patient pathophysiology are separately defined in terms of independent and adjustable model parameters. The resulting simulation is of general application in the study and teaching of pharmacokinetics. Specifically pharamacological issues are dealt with in a companion paper.