Novel Approach to the Analysis of in Vitro–in Vivo Relationships**Presented in part at the Ninth Annual Meeting and Exposition of the American Association of Pharmaceutical Scientists, San Diego, CA, November 1994.

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Abstract
The objective of this study was to quantify the dependence of degree of in vitro-in vivo correlation on the relative rates of dissolution and intestinal permeation and on the fraction of dose absorbed. The following equation was derived assuming first-order dissolution and permeation after oral drug administration: Fa = fa-1(1 - alpha(alpha - 1)-1 (1 - Fd) + (alpha - 1)-1(1 - Fd)alpha), where Fa is the fraction of the total amount of drug absorbed at time t, fa the fraction of the dose absorbed at t = infinitive, alpha is the ratio of the first-order permeation rate constant to the first-order dissolution rate constant, and Fd is the fraction of dose dissolved in vitro at time t. This equation was examined in order to pursue a theoretical treatment of in vitro-in vivo correlation. The degree of in vitro-in vivo correlation between Fa and Fd was measured by r2. alpha was varied between 1000 and 0.001. fa was varied between 0.1 and 1.0. Points employed in the linear regression were geometrically balanced about the derived equation. r2 values decreased as alpha decreased for all values of fa. r2 values were virtually independent of fa for all values of alpha, except for 0.01 < alpha < 1.0. The slope of the regression was modulated by both alpha and fa; larger alpha and smaller fa each increased slope. Application of the equation to a piroxicam data set demonstrated the equation's utility relative to the USP Level A correlation approach. It is concluded that the degree of in vitro-in vivo correlation depends on the relative rates of dissolution and intestinal permeation and on the fraction of dose absorbed and that the derived model merits further study.

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