An Application of Prony’s Sum of Exponentials Method to Pharmacokinetic Data Analysis

We discuss the basic concept of compartmental modelling in pharmacokinetics and demonstrate that all the solutions admitted by multi-compartment models of classical pharmacokinetics are expressed as linear combinations of exponential functions of time. This lends itself to data analysis that depends on fitting exponential functions to finite size sets. A mathematical method developed a long time ago to deal with this type of problem is called Prony’s method. We discuss the usefulness of this method in pharmacokinetic modeling and apply it to a particular data set obtained for the drug mibefradil. In spite of the method’s power in dealing with well-behaved data sets, we indicate the existence of severe limitations since real concentration curves coming from pharmacokinetic data are seldom purely exponential. PACS: 82.39.-k, 05.45.Df, 61.43.Hv, 82.30.-b