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A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment

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Published on: December 1, 2023

Numerical solution of the bidomain equations.

S Linge¹, J Sundnes, M Hanslien

¹Simula Research Laboratory, PO Box 134, 1325 Lysaker, Norway.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|April 22, 2009

Summary

Mathematical models of cardiac electrophysiology, like the bidomain model, are complex. Recent advances in computational methods and parallel computing have enabled more efficient simulations, but full potential remains untapped.

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Area of Science:

Computational science
Biophysics
Cardiac electrophysiology

Background:

Mathematical models are crucial for understanding cardiac electrophysiology.
The bidomain model, used for analyzing electrical activity, is mathematically complex.
Solving complex models computationally presents significant challenges.

Purpose of the Study:

To review the development of numerical methods for solving the bidomain model.
To focus on advancements in numerical methods since the year 2000.
To highlight progress in computational approaches for cardiac electrophysiology.

Main Methods:

Review of numerical methods for solving the bidomain model.
Focus on advancements since 2000.
Integration of computational science achievements in solving linear systems.

Main Results:

Optimal methods for solving linear systems have been developed, enabling linear CPU effort increase with nodes.
These methods, coupled with parallel computing, allow bidomain model solutions on human heart geometries.
Significant progress has been made in simulating cardiac electrophysiology.

Conclusions:

Modern computational methods have greatly improved the simulation of the bidomain model.
The full potential of these computational advancements is yet to be realized.
Continued development in numerical methods is essential for advancing cardiac electrophysiology research.