“Ant-Wall” model to study drug release from excipient matrix

We propose a two-dimensional lattice model to study the effects of drug loading, matrix structure, and drug–excipient interactions on the drug release through excipient matrix. Analogy is made with the random walk of ants (drug molecules) in a maze (excipient matrix). Ants can be “blind” (non-aggregating) or “friendly” (aggregating), representing hydrophilic and hydrophobic drugs, respectively. Excipient–drug interactions are accounted as the probability of ants (drug molecules) crossing walls (excipient molecules). Monte Carlo simulations of the model are performed to obtain the amount of drug escape (release) as a function of time for different values of drug loading, excipient–drug interaction, and matrix size. Although a Weibull function is able to fit the drug release in the entire time range for the hydrophilic case, two Weibull functions are required in the hydrophobic case signifying an initial burst release followed by a long-time sustained release. The competition between the drug escape and drug aggregation results in the existence of an optimum drug loading for sustained drug release in the case of hydrophobic drugs. Also, the drug release is best controlled at moderate excipient–drug interactions, since strong excipient–drug interactions results in substantial amount of trapped drugs that are never released. Results of this study may provide design rules of matrix formulations for the delivery of poorly soluble drugs and stimuli-responsive drug delivery formulations.