Extensão tridimensional e paralelização de um modelo para a formação de edemas inflamatórios

Abstract

The inflammatory response is an essential biological defense mechanism that, while combating pathogens, induces edema formation through increased vascular permeability and fluid extravasation into the interstitial space. A detailed analysis of this phenomenon requires mathematical models that systemically integrate the dynamics of immune cell populations and the behavior of interstitial fluid. This work proposes a three-dimensional extension of a mathematical model from the literature aimed at inflammatory edema formation. The original system employs coupled partial differential equations to describe the interaction between bacteria, neutrophils, and fluid pressure in a porous medium. The spatial discretization of the extended model was performed using the Finite Volume Method (FVM), ensuring local conservation of physical quantities, while time integration employed a first-order explicit scheme. To overcome the high computational cost associated with large three-dimensional meshes, parallelization strategies were developed for shared-memory architectures (OpenMP for CPU) and accelerators (CUDA for GPU). Numerical experiments with different mesh resolutions validated the consistency of the solution and the performance of the implementations. The results indicate that CPU parallelization provides speedups of up to approximately 11 times compared to the sequential version, whereas the GPU implementation achieves performance gains of up to 426 times, making large-scale three-dimensional simulations feasible.