How to use fitting functions to estimate the diffusion coefficient of molecules in diffusion-controlled drug release systems

We propose a unified approach to describe the solutions of the diffusion equation for spherically symmetric diffusion-controlled drug release systems. Using this unified description, we investigate how we can extract useful results from data fitting. The method we propose exploits the fact that most fitting functions (even those that appear to give poor results) provide good estimates of the surface area under the curve, τ*, when the normalized release function M*(t) is plotted as a function of time t. In particular, we demonstrate that we can obtain a good estimate of the molecular diffusion coefficient D from the value of τ*. As an example, we compare the results obtained using both the Weibull function and our recent theory-based Semi-Empirical fitting function. Finally, we test the accuracy of the estimated value of D when these fitting functions are used with various types of noisy synthetic data.