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Dimensionality in cardiac modelling.

Alan Garny¹, Denis Noble, Peter Kohl

¹Department of Physiology, University of Oxford, Parks Road, Oxford OX1 3PT, UK. alan.garny@physiol.ox.ac.uk

Progress in Biophysics and Molecular Biology

|October 9, 2004

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Mathematical models of cardiac rhythm disturbances are crucial for understanding heart function. This study evaluates 0D, 1D, 2D, and 3D models, finding 2D models offer a practical balance for research.

Area of Science:

Computational biology
Biophysics
Cardiac electrophysiology

Background:

Mathematical modeling of the heart has evolved from single-cell (0D) to multicellular (1D, 2D, 3D) representations.
Cardiac rhythm disturbances are fundamentally multicellular phenomena requiring models beyond single-cell descriptions.

Purpose of the Study:

To discuss the merits of different dimensionalities (0D, 1D, 2D, 3D) for simulating cardiac excitation and rhythm.
To evaluate models for simulating the origin and spread of cardiac excitation and the effects of stretch-activated channels.

Main Methods:

Review and discussion of cardiac models across dimensions (0D, 1D, 2D, 3D).
Analysis of model applicability for simulating normal and disturbed cardiac rhythm, including excitation spread and re-entry phenomena.

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Main Results:

1D models have limitations in capturing neighboring tissue effects but are useful for basic excitation spread and re-entry simulation.
2D models overcome limitations of lower dimensions, enabling study of complex re-entry and fibrillation.
3D models offer the highest realism for investigating scroll waves.

Conclusions:

2D models provide a favorable balance of computational resources, complexity, and research applicability.
Models should be chosen based on the specific research question, with 2D models serving as a key step towards detailed simulations.