1. Investigations into tablet dissolution in a paddle type apparatus Introduction - What are we doing? Mr. Niall McMahon, School of Computing, Dublin City University Dr. Martin Crane, School of Computing, Dublin City University Prof. Heather Ruskin, School of Computing, Dublin City University Prof. Lawrence Crane, School of Mathematics, Trinity College Dublin We are modelling a tablet dissolving in a well-defined in-vitro environment (specifically, we are estimating the mass transfer rate). Tablet Simple compressed system consisting of alternating layers of drug (salicylic acid) and excipient* (benzoic acid). Environment Nominally a USP 24 type 2 paddle dissolution apparatus, with the tablet positioned 3mm above the bottom. Fig. 1: Multi-layered tablet Why are we doing this? We want to explore the mathematics of drug dissolution and build effective simulations! The potential benefits of mathematical simulation are as unlimited as imagination allows. An ideal simulation could reduce the need for experiment in the design of drug delivery systems, cutting associated costs. Why this type of tablet? 3.It was used in associated studies. This allows us to compare their results with ours. 2.Previous studies indicate that accurately predicting the surface area change (with time) for this type of system may ultimately lead to better models for multi-component systems [1]. 1.Although relatively simple compared with "real" drug delivery systems, a successful model of this tablet would demonstrate the possibility of accurately simulating drug dissolution. It would give us reason to believe that we can potentially model more complex systems. Approach - How are we doing this? To simulate mass transfer, the time dependent diffusion-advection equation is used with simplifying assumptions. Fig. 3: Simplified diffusion-advection equation For example, the diffusion is considered to be two- dimensional, steady state and from a flat plate rather than a cylinder. The equation is ‘discretised’ using an explicit Forward Time Central Space (FTCS) finite difference scheme with initial values provided by the exact Lévêque solution (cited by Schlichting [2]). The important results are the drug mass fluxes and transfer rates. Results - Where are we now? We are currently considering the multi-layered configuration as well as our recent results for the trivial case of a single layered tablet (that is a tablet consisting purely of drug). Single layered tablet results For a given set of input parameters, the finite difference mass flux value, calculated as outlined above, and the exact Lévêque estimate agree to within 0.1 %. This close match is demonstrated by the concentration profiles shown in figure 4. Fig. 4: A comparison of drug concentration profiles at the trailing edge of the tablet Our estimate has a relative error of 0.9 % with respect to a semi-analytical (Pohlhausen type) solution proposed by Crane et al. [1] Mass fluxes computed by Crane et al. agree well with experimental data for both single layered (that is a tablet consisting purely of drug) and multi­layered tablets. Conclusions The good agreement between this finite difference scheme and the other methods for the trivial case indicates that the scheme is behaving as expected. This is encouraging and we are currently extending the model to describe dissolution from a multi-layered tablet. Future Work - Where to next? In the short term we hope to build a simple multi- layered model and compare the results with previous work. In the medium to long term we will consider more realistic systems. Real dissolution systems (those in therapeutic use) have moving boundaries (as the drugs and excipients dissolve) and often the drug is dispersed through a matrix of excipient. Some real systems also use new polymer technologies to protect and deliver the drug. Simulating these systems will almost certainly require the use of alternative mathematical techniques. Acknowledgements The authors would like to thank the Irish National Institute for Cellular Biotechnology (NICB) for supporting this work and Anne-Marie Healy in the School of Pharmacy at Trinity College Dublin who produced the experimental data mentioned in this poster. *excipients are inert substances that together with the drug form a tablet 2. Schlichting, H. 1979. Boundary-Layer Theory 7th Edition. New York ; London [etc.] : McGraw-Hill. Chap. XII p285 eqn. (12.51c). and p291 eqn. (12.60). Note: it seems there is a square root missing in the denominator of equation (12.60) in this edition. References www. google. com + “Niall McMahon” + Search 1. Crane, M. Crane, L. Healy, A. M. Corrigan, O.I. Gallagher, K.M. McCarthy L.G. 2003. A Pohlhausen Solution for the Mass Flux From a Multi-layered Compact in the USP Drug Dissolution Apparatus. Submitted to Simulation Modelling Practice and Theory, Elsevier, 2003. We look forward to these challenges. email: nmcmahon@computing.dcu.ie Fig. 2: Paddle dissolution apparatus