A meshless point collocation treatment of transient bioheat problems

Area of Science:

• Computational physics
• Biomedical engineering
• Numerical analysis

Background:

• The Pennes bioheat equation is crucial for modeling heat transfer in biological tissues, particularly during thermal therapies like tumor ablation.
• Accurate modeling requires accounting for complex factors such as water evaporation, tissue damage, and temperature-dependent properties.
• Traditional methods face challenges with unclear boundaries between healthy and pathological tissues, necessitating approximations.

Purpose of the Study:

• To propose a meshless numerical method for solving the transient bioheat equation in 2D and 3D.
• To extend the Pennes bioheat equation to include water evaporation, tissue damage, and temperature-dependent properties for tumor ablation.
• To develop a method that handles local tissue property variations without explicit boundary identification.

Main Methods:

• A meshless numerical approach is employed for solving the bioheat equation.
• The Pennes bioheat equation is modified to incorporate advanced physiological and physical phenomena.
• Tissue conductivity is treated as a local function, reflecting variability and avoiding explicit boundary definitions.

Main Results:

• The proposed method's numerical results for bioheat transfer equation test cases are validated against analytical and other numerical predictions.
• 3D simulations demonstrate the modeling of tumor ablation, including metabolic heat generation, blood perfusion, and heat ablation.
• An evaluation of the effective medium approximation for homogenizing conductivity fields is presented.

Conclusions:

• The developed meshless method offers a robust solution for transient bioheat transfer problems, especially in tumor ablation.
• By treating tissue conductivity as a local function, the method simplifies modeling and improves accuracy in heterogeneous tissue environments.
• The approach provides a more practical and less approximate way to simulate complex bioheat transfer scenarios in medical applications.