A Differential Equations Approach to In Vitro – In Vivo Correlation Modelling in NONMEM
Clare Gaynor (1), Adrian Dunne (1) and John Davis (2)
(1) UCD School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4
Background: The main applications of In Vitro – In Vivo Correlation (IVIVC) models are to reduce the number of human studies required in drug development, to act as a surrogate for human bioequivalence studies and in setting dissolution specifications. As a result, considerable effort goes into their development and “the ability to predict, accurately and precicely, expected bioavailability characteristics for an ER [extended release] product from dissolution profile characteristics is a long sought after goal” .
Many methods of developing IVIVC models have been proposed. Previous research has highlighted a number of statistical concerns with a group of methods based on deconvolution  and has shown that a convolution method based on that of O’Hara et al  produces superior results . Implementation of this convolution-based method involves the production of a user-written subroutine for the NONMEM  software package, a task that can be time consuming and complex. As a result, this methodology, despite its advantages over the deconvolution-based approach, is not in widespread use.
Methods: An approach based on systems of differential equations, has been proposed  It has been shown  that the convolution based and differential equation based models can be mathematically equivalent. Software which implements a differential equation based approach has been developed. This method utilises existing NONMEM libraries and is an accurate method of modelling which is far more straightforward for users to implement.
Results and Conclusions: This research shows that, when the system being modelled is linear, the use of differential equations will produce results that are practically identical to those obtained from the convolution method.
Both the convolution and deconvolution based methods assume that the system being modelled is linear but, in practice, this is not always the case. Our work to date has shown that the convolution-based method is superior, but when presented with nonlinear data even this approach will fail. The use of a differential equation based model could also allow for the possibility of accurately modelling non-linear systems and further investigation is being carried out into the case where the drug is eliminated by a nonlinear, saturable process.
 Food and Drug Administration (1997) Guidance for Industry: Extended Release Oral Dosage Forms: Development, Evaluation, and Application of In vitro/In vivo Correlations.
 Dunne A., Gaynor C. and Davis J. (2005) Deconvolution Based Approach for Level A In vivo-In Vitro Correlation Modelling: Statistical Considerations. Clinical Research and Regulatory Affairs, 22, 1-14.
 O’Hara T., Hayes S., Davis J., Devane J., Smart T. and Dunne A. (2001) In vivo-In Vitro Correlation (IVIVC) Modeling Incorporating a Convolution Step. Journal of Pharmacokinetics and Pharmacodynamics, 28, 277-298.
 Gaynor, C., Dunne, A. and Davis, J. A Comparison of the Prediction Accuracy of Two IVIVC Modelling Techniques. Journal of Pharmaceutical Sciences, Published Online: 7 Nov 2007
 S.L. Beal and L. B. Sheiner. NONMEM User’s Guides, NONMEM Project Group, University of California, San Francisco, 1992.
 Buchwald, P. (2003) Direct, differential-equation-based in-vitro-in-vivo correlation (IVIVC) method. Journal of Pharmacy and Pharmacology, 55: 495-504.
 Dunne, A. (2007) Approaches to developing IVIVC models, Ch 5. In Chilukuri, Sunkara and Young (Eds), Pharmaceutical Product Development: In Vitro – In vivo Correlation. Taylor and Francis, New York