Release Kinetics Modelling

The mathematical modelling of drug release data serves to identify the underlying physical mechanism governing release from a given dosage form, information...

The mathematical modelling of drug release data serves to identify the underlying physical mechanism governing release from a given dosage form, information that is of substantial value both for rational formulation optimisation and for regulatory characterisation of modified-release products. Several established kinetic models are routinely applied to release data, each associated with a characteristic underlying mechanism and a corresponding linearisation approach used to identify the best-fitting model for a given dataset.

The zero-order model, expressed as the cumulative amount released equal to an initial quantity plus the product of a zero-order rate constant and time, describes constant, concentration-independent release and is identified by linearity when cumulative percentage released is plotted directly against time; this pattern is characteristic of well-designed controlled-release systems, such as certain osmotic pump devices and reservoir-type transdermal patches, in which the release rate is governed by a constant driving force rather than by the declining concentration gradient typical of simple diffusional systems. The first-order model, in which the logarithm of cumulative amount released varies linearly with time, describes concentration-dependent release and is identified by linearity when the logarithm of the percentage of drug remaining is plotted against time; this pattern is frequently observed for porous matrix systems and for many conventional immediate-release products.

The Higuchi model, expressed as the cumulative amount released proportional to the square root of time, describes diffusion-controlled release from an insoluble matrix following Fickian diffusion principles, and is identified by linearity when percentage released is plotted against the square root of time; this model underlies the analysis of both matrix-type controlled-release tablets and the Franz diffusion cell data discussed in the preceding section. The Korsmeyer-Peppas model, a more general power-law expression relating the fraction of drug released to a rate constant and time raised to an exponent n, is particularly valuable because the value of the release exponent n, obtained from the slope of a plot of the logarithm of fraction released against the logarithm of time, provides direct mechanistic insight: values of n at or below 0.45 indicate Fickian diffusion-controlled release, values between 0.45 and 0.89 indicate anomalous, non-Fickian transport reflecting a combination of diffusion and polymer relaxation, and a value of n at or above 0.89 indicates Case II transport, in which release is governed principally by polymer chain relaxation or erosion rather than by diffusion.

The Hixson-Crowell cube root model, describing the relationship between the cube roots of the initial and remaining drug quantities as a linear function of time, is specifically applicable to systems in which drug release is governed by a diminishing surface area as spherical or near-spherical particles progressively dissolve or erode, and is identified by linearity when the cube root of the fraction remaining is plotted against time. In practice, formulation scientists routinely fit release data to each of these models and select the model providing the best statistical fit, most commonly assessed through the coefficient of determination, as the most probable descriptor of the dominant release mechanism operating within a given formulation.