Fitting Drug Dissolution Measurements of Immediate Release Solid Dosage Forms by Numerical Solution of Differential Equations

H. Loth, Th. Schreiner, M. Wolf, K. Schittkowski, U. Schaefer: Report, Department of Mathematics, University of Bayreuth  (2001)
Abstract: Dissolution profiles of ketoprofen are measured from immediate release powder mixtures, granules, and tablets with different compositions. Fast data sampling is performed by means of a paddle dissolution tester connected to an optimized pumping system including a photometer- PC combination quantifying the drug concentration with time. The observed data are fitted by means of a computer program for parameter estimation in systems of ordinary differential equations. 

The mathematical model is derived from the Noyes-Whitney equation into which distribution functions reflecting the alterations of the 'effective' surface in dependence on time are inserted. The combination with the lognormal distribution corresponds best with the dissolution data and shows to be best adaptable to different curve shapes. Dissolution rate factors are calculated from the estimated parameters. The maximum rate and time values are used to characterize the drug liberation. Comparing these values by t-tests indicates the influences of excipients and manufacturing processes. Therefore the maximum rate factor can be an effective aid for optimizing formulations and controlling manufacturing.

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