Analytical Solution for Controlled Drug Release with Time-Dependent Diffusion Parameter

• DOI: 10.3390/math10213951
• Publication Date: 2022-10-24T15:53:55Z
• Authors: Shalela Mohd Mahali; Amanina Setapa; Fatimah Noor Harun; Song Wang
• Keywords: controlled drug release; swelling drug device; time-dependent diffusion parameter; controlled drug release; time-dependent diffusion parameter; QA1-939; swelling drug device; 01 natural sciences; Mathematics; 0104 chemical sciences

Drugs seem to diffuse in different manners in a delivery device due to the increment of the device pore size during swelling. However, the diffusion parameter, D, is often assumed constant. In this work, a new developed controlled drug release model with a time-dependent diffusion parameter is compared to one- and two-phase models. The new model was obtained as an improvement of the previous constant and piece-wise constants models. The models are developed by solving an advection–diffusion equation using the Landau transformation method and the separation of variables method. To test these models, we fit experimental data by the developed models using the least squares fitting technique. The curve-fitting result shows that the least squares error of the two-phase and the time-dependent models are 10 times smaller than the single-phase model. The CPU time for the time-dependent model is the lowest, showing that a time-dependent model is the best option among all three tested models considering both factors of the determined least squares error and the time consumption.