1. Mathematical Modeling of Desorption-Diffusion Controlled Drug Release from Polymer Matrices Rami Tzafriri Institute of Computer Science and The Department of Neurobiology, The Hebrew University, Jerusalem, Israel This research was supported by a grant from the Isreali MOS

2. The binding of charged polypeptides onto a hydrogel matrix is modeled as Langmuir adsorption and the release of free drug is assumed to be governed by simple diffusion from a 1D slab. The model of Singh et al. (1994) (1) (2) (3) (4)

3. Qualitative Analysis This problem involves 2 typical time scales: and Accordingly, two limiting cases are of interest: Instantaneous desorption Fast diffusion

4. Instantaneous desorption and linear binding In this limit and with This can be solved analytically and has been used to model the release of polylysine and gentamicine from collagen matrices

5. Analytical solution of the linear binding case For small L (films, microspheres) we are more likely to for which no analytical solution is available in the literature and the experimental results can only be analyzed by solving the equations numerically, which is rather cumbersome. However, it turns out that Eqs. (1)-(4) can be solved analytically in the case linear binding: encounter the case of fast diffusion:

6. In this case: Integrating this yields: and (2`) The system (2`), (3)-(4) can be solved analytically for slabs, spheres, long cylinders and rectangular parallelepipeds, and predicts a bi-phasic release profile. (1`)

7. Example: lysozyme release from a gelatin film Kuijpers et al. (1998) measured the release of lysozyme from cross-linked gelatin films into a PBS solution under perfect sink conditions. They considered the case: and estimated: which implies that 83.3% of the initial drug load is adsorbed onto the gelatin matrix.

8. Fitted values: According to this fit 19.6% of the initial drug load is released in a short diffusive burst at a rate of 3.85/h, whereas 80.4% is adsorbed and released at a rate of 0.06/h. Experimental estimate: