On the Variability of Dissolution Data

Abstract

Purpose. To investigate dissolution data variability and its origins.

Methods. The Weibull function with four parameters, t₀ (dissolution lag-time), K (the rate parameter), β (the shape parameter) and D (the fraction dissolved as t →∞), is used to describe the dissolution curve. The variance of the dissolution data is expressed in terms of these parameters and their individual variances σ² _t0, σ² _K;, σ² _β, and σ² _D. These four variances originate from variable physical properties of the dosage units and from a variable dissolution environment. Therefore, dissolution data variability depends on both, the functional form of the curve and on the variance of the physical conditions. The use of this method enables the elucidation of the sources of dissolution data variability.

Results. In the case of a sigmoidal dissolution curve (β > 1), data variance is zero as dissolution begins (following dissolution lag-time). This initial variance diverges when the dissolution curve is non-sigmoidal (with β < 1) but assumes a finite value, proportional to the dissolution lag-time variance (σ² _t0) when the data fits a regular first order rate curve (β = 1). Following a long dissolution time, data variance attains a constant value equal to the dissolution extent variance, σ² _D. When the dissolution curve is sigmoidal and the variability related to the dissolution extent is sufficiently small (σ_D/D << 1), a maximum in the variance is expected at some intermediate time point (corresponding to the curve inflection point, when the main source of variability is dissolution lag-time t₀, or around t = 1/K + t₀, when the main sources of variability are the rate parameter K or the shape parameter β). When the curve is sigmoidal (β > 1) and the main source of variability relates to the dissolution extent, the overall variance grows with time all the way to the plateau of the dissolution curve. With a non-sigmoidal dissolution curve (β ≤ 1), data variability decreases with time soon after dissolution begins. In that case, if the main source of variability is the dissolution lag-time (t₀), the variance decreases all the way to the plateau of the dissolution curve. If the dissolution extent, D, is the main source of variability, a minimum in the variance is expected at some intermediate time point. The dissolution relative variance, on the other hand, diverges as dissolution begins and decreases with time at least until 63% of the drug is released, irrespective to the Weibull parameter values. Later, it may decrease or increase, attaining a fixed value (σ² _D/D²) at the plateau of the dissolution curve.

Conclusions. The particular time dependence of dissolution data variance is well defined in terms of the Weibull shape parameters and their individual variances. Dissolution data variability may decrease or increase with time along the curve. It may attain a maximum or a minimum value at some intermediate time point. It may converge or diverge as dissolution begins. When the dissolution data is well fitted to the Weibull function, the sources of data variability (in terms of the Weibull parameters) may be elucidated. The variability of dissolution data originates from physical sources but is also dependent on the functional form of the curve.