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Drug delivery concerns how a therapeutic substance is presented to a biological system: where it becomes available, over what time and in what form. Formulation, a carrier material and the route of administration can change the resulting transport. Drug release kinetics describes escape from a formulation or reservoir; pharmacokinetics additionally concerns what happens as the substance moves through and is removed from the body. These are related stages rather than interchangeable measurements.

A motivating historical development was the use of polymers for sustained release of proteins and other macromolecules, reported by Robert S. Langer and Judah Folkman in 1976.^[ref] The engineering question includes whether a carrier can retain a substance initially and then make it available over time while preserving the intended activity.

An elementary reservoir model separates remaining material from cumulative release. If the remaining amount $M(t)$ obeysthen $M(t)=M_0{e}^{-kt}$ and the released fraction is $1-e^{-kt}$. For an illustrative reservoir-release half-time of six hours, $k=\ln 2/(6\mathrm{h})$. Half has been released at six hours and three quarters at twelve hours. The second six-hour interval releases one quarter of the initial amount, even though the first interval released one half. These are model fractions, not a drug regimen; the reservoir-release half-time is not an elimination half-life measured in a person.

An in vitro drug release test can place a formulation in a controlled medium, separate released material from retained material and measure amount against time. The apparatus can influence the answer. The FDA’s technical account explains that passive transport through a dialysis membrane can limit the measured response; its adaptive-perfusion prototype instead uses pressure-driven separation to investigate release from complex formulations.^[ref]

A useful experimental record therefore states the medium, temperature, separation method, sampling schedule and material balance. A slowly changing measured concentration could reflect slow carrier release, slow transport through the apparatus or both. Comparing apparatus conditions and accounting for material remaining in the carrier helps distinguish these mechanisms. Evidence about release under those conditions must then be related to the biological environment before making claims about tissue exposure or therapeutic effect.

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.

An in vitro drug release test measures the amount or rate at which a substance leaves a formulation under specified laboratory conditions. The medium, temperature, agitation or flow, separation method and sampling schedule define the experiment. A measured release curve is therefore a property of a formulation–apparatus system under those conditions, rather than a direct measurement of the concentration in a person.

A typical design places the formulation in contact with a receiving medium, separates released material from the carrier and measures concentration at several times. The primary FDA technical account describes pressure-driven separation as an alternative to passive dialysis-membrane transport for complex formulations. It emphasizes that the separation step can itself limit the observed rate.^[ref]

Repeated sampling requires a material balance. Suppose a well-mixed receiver has constant volume $V$. At each observation a volume $v$ is removed and replaced with blank medium. If $C_j$ is the concentration immediately before the $j$th withdrawal, the cumulative amount transferred into the receiver by time $t_n$ isThe first term is material still in the receiver; the sum is material removed at earlier observations. This sampling correction in drug release testing assumes matched replacement, a well-mixed receiver and no unmeasured loss or chemical transformation.

For illustrative $V=100\mathrm{mL}$, $v=5\mathrm{mL}$, $C_1=0.10\mathrm{mg}\mathrm{m}{\mathrm{L}}^{-1}$ and $C_2=0.18\mathrm{mg}\mathrm{m}{\mathrm{L}}^{-1}$, the amount at the second observation is $18+0.5=18.5\mathrm{mg}$, not just $18\mathrm{mg}$. These chosen values demonstrate accounting; they are not a formulation specification or dosing instruction.

An informative experiment also accounts for material retained in the formulation and material lost to the apparatus. Adsorption, incomplete separation or degradation can change a measured concentration without the same change in carrier release. A control without the carrier and a recovery check address different parts of this problem. Comparing the measured curve under several justified apparatus conditions helps distinguish drug release kinetics from transport and analytical limitations.