Comparing finite elements and finite differences for developing diffusive models of glioma growth

Area of Science:

• Computational biology
• Mathematical oncology
• Biomedical modeling

Background:

• Glioma, an aggressive brain tumor, necessitates accurate mathematical models for understanding its development.
• Diffusion-reaction equations (DREs) are commonly employed to simulate glioma's spatiotemporal cell concentration dynamics.
• Finite difference (FD) and finite element (FE) methods are prevalent numerical techniques for solving DREs in these models.

Purpose of the Study:

• To experimentally compare the performance of finite element (FE) and finite difference (FD) methods in the context of glioma modeling.
• To investigate the influence of different brain mesh configurations on the computational consistency, simulation time, and overall efficiency of DRE-based glioma models.

Main Methods:

• Implementation and comparison of FE and FD numerical methods for solving the diffusion-reaction equation.
• Experimental analysis using a glioma model with a known analytical solution to quantify errors.
• Evaluation of computational consistency, simulation duration, and model efficiency across varying mesh structures.

Main Results:

• The study presents experimental findings comparing the accuracy and efficiency of FE and FD methods for glioma simulation.
• Variations in brain mesh resolution significantly affect the computational performance and consistency of the models.
• Quantifiable error metrics were calculated for both methods using a validated test case.

Conclusions:

• Both FE and FD methods offer viable approaches for simulating glioma progression, with performance influenced by mesh strategy.
• Understanding the trade-offs between mesh complexity, computational cost, and accuracy is crucial for selecting appropriate numerical methods.
• This comparative analysis provides valuable insights for developing more efficient and accurate computational tools for glioma research.