Abstract

In complex biological settings, coupled reaction-diffusion models are essential for determine the transport, diffusion, absorption, and controlled release of drugs. The model balances the diffusion of drugs, kinetic and reaction processes, and the interaction of drugs with cell membranes, the extracellular matrix and heterogeneous tissues. The research model uses non-linear partial differential equations to mathematically describe the concentration of drugs in time and space in the various compartments of biological systems. The model allows for varying diffusion coefficients, reaction kinetics, anisotropic spaces, and time-varying reaction kinetics to describe the complexity of biological systems. Concentration control, drug release kinetic control, and control over how deeply the drug penetrates tissues are some of the goals of the modeled systems. Using finite difference and finite element techniques, various controlled release systems were modeled to assess the effects of varying controlled release systems on drug bioavailability, retention, and therapeutic efficacy. Results show that a release system with a high diffusion coefficient generally increased the speed of transport, but may have resulted in less retention, when the release system had improved reaction kinetics, the retention improved within diseased tissues. Compared to conventional delivery systems, controlled release systems had a prolonged therapeutic effect and reduced systemic toxicity. Sensitivity analysis identifies tissue permeability, reaction constants, and release rates as among the most significant factors affecting treatment performance. From a pharmaceutical engineering perspective, this approach will support a predictive analysis of drug dispersal and dynamic control of drug release in complex biological systems, offering improvements in drug delivery optimization in biomedical research and personalized medicine.