Mathematical formulation for nonuniform multiple dosing

A pharmacokinetic formalism explicitly integrating the patient drug compliance

The adherence phenomenon is now well recognized to seriously compromise drug efficacy. In this paper, we analyze the role of compliance through drug intake history as an integral part of the pharmacokinetic process. Being concerned with what is accessible in medical practice, we develop a stochastic approach to model the drug intake behavior that we combine with a conventional pharmacokinetic model in order to investigate the effect of drug intake history on the pharmacokinetic time-course. For this purpose, we explicitly formalize the plasma concentration variations for the most common administration routes. This analytical approach allows to characterize drug concentration variations directly inherited from patient compliance.

Accumulation profiles during quasi-uniform multiple dosing regimens

An extension of the plasma area method of Chiou to the evaluation of accumulation profiles during quasi-uniform multiple dosing regimens (i.e., regimens with varying doses and/or dosing intervals within a certain time period which are repeated in the successive periods throughout the administration course) is presented. The derivations show, that the equations for the accumulation and steady state curves during quasi-uniform multiple dosing are similar or identical to these for the uniform multiple dosing case, if the constant time interval in the latter is replaced by the constant time period in the former. The equations derived can be used for rapid estimation of the time, required to reach a prespecified fraction of quasi steady state plasma level during quasi-uniform multiple dosing.

Efficient pharmacokinetic modeling of complex clinical dosing regimens: the universal elementary dosing regimen and computer algorithm EDFAST

Dosing regimens used in clinical practice are often complex, involving several different routes of administration, dose sizes, dosing rates, and dosing intervals and durations. A novel universal elementary dosing regimen (uedr), that allows general pharmacokinetic modeling of these clinical regimens, is presented and developed mathematically. The uedr concept is computationally efficient, mathematically exact, and logically simple, and can replace the disparate standard concepts and equations of elementary infusion, "bolus" injection, multiple injection, oral dosing, zero-order-release dosing, etc. An optimized computer algorithm (EDFAST) based on the uedr approach, that readily permits the creation of a single fast and versatile microcomputer program for the analysis of all complex dosing regimens in any set of linear compartmental models, is presented. This is of particular relevance to three areas of application in clinical pharmacokinetics: compartmental drug concentration or amount versus time course prediction (simulation) with known model parameter values; parameter estimation (curve-fitting) from measured concentration versus time data; and individualized complex dosing regimen calculation (optimization) for target sets of concentration-time points. Application examples that show the versatility of the uedr approach are presented in detail.

Nonlinear regression on multiple-dose data

The examples are given to show how Metzler's nonlinear regression program can be used to estimate parameters in a model with multiple dosing. The model of one example is a set of equations involving sums of exponentials, whereas the other model is a set of differential equations reflecting first order absorption and Michaelis-Menten excretion. In both cases no data were given in one of the dosing intervals.