Pharmacokinetic predictions of optimum drug delivery rates from prodrugs designed for maximum duration

Abstract

Recent interest in prodrugs as well as other drug delivery systems has included the control of drug release for the purpose of extending the duration of therapeutic blood levels. While zero-order release rates are generally considered ideal, many systems approach apparent first-order kinetics. These cases may successfully prolong duration if the rate constant for drug delivery (k a) is rate-limiting relative to the elimination rate constant (k or β). For a given drug there is only one optimum rate-limiting input constant which will provide the maximum duration of therapeutic activity for a given dose. This was demonstrated using computer simulations to examine the effect of variations in dose and R (R = k a/k or k a/ β) upon the duration, T, of 1- and 2-compartment model drugs administered by rate-determining first-order input. When dose is held constant, an optimum R, R opt, exists at which duration is maximal (T = T max). When k a is fixed, an optimum value for dose, [D 0] opt, provides the greatest duration per unit mass. Equations were derived which enable estimation of R opt, T, T max, and [D 0] opt when input is rate-determining. The accuracy of these estimates was determined as a function of R. The equations provide estimates with less than 5% error when R ⩽ 0.09. The administration of a 1- or 2-compartment model drug at estimates within the limit, 0.09 < R ⩽ 0.34, provides a duration T ⩾ 0.95 T max. A practical approach for maximizing duration by manipulation of dose and k a is described for drugs with known biological half-life, Vd and minimum effective concentration. The results are significant in that they provide a means for both assessing the feasibility of increasing the duration of drug action by prodrug formation and for evaluating the experimental results by comparison with the theoretical optimum.