Model of Chemotaxis for Nanomedicine Applications Utilizing Nonlinear Reaction-Diffusion Systems: Application to Drug Delivery Control and Optimization - Saad, Ali S.; Almijalli, Mohammed; Ibrahim, Moustafa; Saad, Mazen (Mathematics and Computer Science: Contemporary Developments Vol. 9, 2024)
Background: Chemotaxis is a fundamental guidance mechanism of cells and organisms, responsible for attracting microbes to food, embryonic cells into developing tissues, immune cells to infection sites, animals towards potential mates, and mathematicians into biology. Methods: This work focuses on the investigation of the chemotaxis model for drug delivery applications. The investigation focuses on pattern development in a volume-filling system with nonlinear diffusive terms. The proposed mathematical model is regulated by a reaction-diffusion system that simulates the interplay between cell density and chemoattractant concentration. The pattern development of the model was examined through Turing's principle and linear stability analysis. An asymptotic expansion is employed to linearize the nonlinear diffusive components. Subsequently, an implicit finite volume technique was offered and implemented on a triangular mesh that adheres to the orthogonality constraint. Results: Numerical results demonstrating the emergence of the spatial pattern in the chemotaxis model are provided and examined. Conclusion: The results indicate significant advancement in comprehending the mechanisms of targeted drug delivery control and optimization.