 Drug release kinetics

Drug release kinetics describes how the amount leaving a formulation changes with time. Let $M_0$ be the initially releasable amount and $M_{\mathrm{rel}}(t)$ the cumulative amount released. The released fraction and instantaneous drug release rate areA fraction has no units; a rate has units of amount per time. These definitions also require stating the releasable amount used for normalization, rather than silently identifying it with every molecule initially loaded.

Several simple models give distinct curve shapes. Constant-rate release gives $M_{\mathrm{rel}}=r_{0}t$ until the available amount is exhausted. First-order depletion of a reservoir gives $F=1-e^{-kt}$, with an amount released per time that declines as the reservoir empties. In a suitable early-time diffusion-controlled drug release regime, a model may instead give $F=a\sqrt{t}$. Thenso equal increments of released fraction do not occur in equal time intervals. The square-root expression is a limited-time model, not a law that applies from arbitrarily small times through complete release.

For an illustrative curve $F(t)=0.10\sqrt{t/\mathrm{h}}$, the fractions at one, four and nine hours are $0.10$, $0.20$ and $0.30$. The mean fraction released per hour in the intervals $0$–$1$, $1$–$4$ and $4$–$9$ hours is respectively $0.10$, $0.0333$ and $0.020$. A plot with equally spaced vertical increments can therefore conceal a strongly changing release rate.

The mechanism must be tested, not inferred solely from a convenient curve fit. Diffusion, material erosion, changing geometry and the measurement apparatus can produce overlapping features. The historical polymer sustained-release work and the modern FDA assay account illustrate the separate tasks of designing a carrier and measuring what it releases.^[ref][ref] A defensible comparison states the time range, normalization, sampling correction and physical assumptions, then checks whether the proposed mechanism is consistent with additional observations.