A mathematical description of the convectional reaction-diffusion of metabolites in a biological system

The process of reaction-diffusion combined with advection plays a crucial role in biological systems. It establishes concentration gradients inside the cells, which in turn facilitates the regulation of signaling and metabolic activities. Theoretical descriptions of these processes make use of boundary problems linked to parabolic partial differential equations. This review focuses on the key biological characteristics that contribute to the formulation of the governing equation. The explanation of biochemical processes and transport mechanisms confirms the validity of both the terms in the equations and the established boundary conditions. In the context of real biological objects, a meticulous description of the modeled area is a fundamental requirement. Therefore, special care is taken in the formulation of algorithms that facilitate the creation of three-dimensional digital phantoms. The concept of phantom creation was illustrated through the application of 3D Voronoi diagrams. Indeed, in biological systems, fluid dynamics also play a crucial role, enabling the characterization of advection via the solution of boundary problems associated with the Navier-Stokes equation or through the application of the Darcy law in porous media. Furthermore, the convection velocity field is incorporated into the reaction-diffusion equation, and efforts are made to determine the solutions through numerical methods. The results acquired can serve to illustrate multiple biological phenomena. The capabilities of COMSOL Multiphysics software in relation to the biological aspects of reaction-diffusion are also discussed.