PHARMACOKINETIC DERIVATION OF RATES AND ORDERS OF REACTIONS IN MULTI-COMPARTMENT MODEL USING MATLAB

Pharmacokinetic modeling is the representation of the logarithmic mathematical equations in order to measure the physiologic response of the body to the drug. Absorption, distribution, metabolism and excretion follow drug kinetic principles according to specific reaction mechanisms in which concentration of the drug may either be dependent or independent of drug-body interactions. Michaelis-Menten equation exhibits association between drug concentration and its mass transfer through a kinetics transport mechanism, a principle also known as Fick’s Law of Diffusion. Reaction orders are the sum of the powers of drug concentrations being raised to a certain degree that follows a certain pattern of drug kinetics according to rate laws being established. Reactions between the drug and the body usually follows first and second order rate. First order rate of reaction can be described as drug concentration dependent, whereas, zero order reaction rate can be explained as drug concentration independent. This paper aims to describe the derivation of pharmacokinetic principles acting in multi-compartment model as the drug enters and exits the body using partial differential equations. It explains mathematically the mechanism behind clinical pharmacokinetics through mass diffusivity. Hence, drug-body interactions can be understood mathematically using logarithmic derivations by quantitative response between drug concentration and the human body according to laws governed by each order of reaction.