Modelling the Mechanical Behaviour of a Pharmaceutical Tablet Using PDEs
Detailed design of pharmaceutical tablets is essential nowadays in order to produce robust tablets with tailor-made properties. Compressibility and compactibility are the main compaction properties involved in the design and development of solid dosage forms. The data obtained from measured forces and displacements of the punch are normally analysed using the Heckel model to assess the mechanical behaviour of pharmaceutical powders. In this paper, we present a technique for shape modelling of pharmaceutical tablets based on the PDE method. We extended the formulation of the PDE method to a higher dimensional space in order to generate a solid tablet and a cuboid mesh is created to represent the tablet’s components. We also modelled the displacement components of a compressed PDE-based representation of a tablet by utilising the solution of the axisymmetric boundary value problem for a finite cylinder subject to a uniform axial load. The experimental data and the results obtained from the developed model are shown in Heckel plots and a good agreement is found between both.
KeywordsRemainder Function Lactose Monohydrate Pharmaceutical Tablet Pharmaceutical Powder Lactose Powder
Unable to display preview. Download preview PDF.
- 1.González Castro, G., Ugail, H., Willis, P., Palmer, I.J.: A survey of partial differential equations in geometric design. Vis. Comput. 24(3), 213–225 (2008)Google Scholar
- 2.Hao-Jiang, D., Xiang-Yu, L., Wei-Qiu, C.: Analytic solutions for a uniformly loaded circular plate with clamped edges. J. Zhejiang University-Science A. 6, 1163–1168 (2005)Google Scholar
- 3.Ilić, I., Kása, P., Dreu, R., Pintye-Hódi, K., Srčič, S.: The compressibility and compactibility of different types of lactose. Drug Dev. Ind. Pharm. 35, 1271–1280 (2009)Google Scholar
- 4.Peiró, J., Formaggia, L., Gazzola, M., Radaelli, A., Rigamonti, V.: Shape reconstruction from medical images and quality mesh generation via implicit surfaces. Int. J. Numer. Meth. Fluid. 53, 1339–1360 (2007)Google Scholar
- 5.Song, C.M., Lim, S.J., Tong, J.C.: Recent advances in computer-aided drug design. Brief Bioinform. 10, 579–591 (2009)Google Scholar
- 6.Timoshenko, S.P., Goodier, J.N.: Theory of elasticity (3rd Ed.). McGraw Hill, New York (1970)Google Scholar
- 7.Ugail, H.: Method of trimming PDE surfaces. Comput. Graph. 30, 225–232 (2006)Google Scholar
- 8.Yap, S.F., Adams, M.J., Seville, J.P.K., Zhang, Z.: Single and bulk compression of pharmaceutical excipients: Evaluation of mechanical properties. Powder Tech. 185, 1–10 (2008)Google Scholar
- 9.Zhang, Y., Law, Y., Chakrabarti, S.: Physical properties and compact analysis of commonly used direct compression binders. AAPS Pharm. Sci. Tech. 4(62), (2003)Google Scholar