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

Revisiting the theory for diffusion-controlled drug release from spherically symmetric systems, we propose a unified description of the solutions of the diffusion equation as well as a new method to extract useful results from data fitting, e.g. using the Weibull function. This method is based on the fact that most fitting functions provide good estimates of the surface area under the curve, τ∗, when the normalized release function M∗(t) is plotted vs time t. We show that one can directly compute a good estimate of the diffusion coefficient D of the drug molecules from the value of τ∗. We then compare the results obtained using both the Weibull function and a recently proposed theory-based Semi-Empirical fitting function. In particular, we test the accuracy of the resulting estimates for D when these two fitting functions are used with noisy synthetic data, and we show that fits can generate counter intuitive estimates of fitting uncertainties.