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Laminar structure of the heart: a mathematical model
I J Legrice1, P J Hunter, B H Smaill
1Department of Physiology, School of Medicine, University of Auckland, New Zealand.
The American Journal of Physiology
|May 1, 1997
Summary
This study presents a mathematical model for cardiac anatomy using finite element methods. This model accurately describes heart geometry and microstructure for advanced cardiac function simulations.
Area of Science:
- Computational Biology
- Biomedical Engineering
- Cardiovascular Research
Background:
- Finite element models are crucial for simulating cardiac electrical and mechanical functions.
- Accurate geometric and microstructural descriptions of the heart are essential for these models.
Purpose of the Study:
- To develop a mathematical description of cardiac anatomy for finite element modeling.
- To define cardiac microstructure using fiber and sheet orientations.
- To create a model applicable to various heart dimensions and deformation states.
Main Methods:
- Utilized prolate spheroidal coordinates for heart geometry definition within a finite element mesh.
- Employed linear Lagrange and cubic Hermite basis functions for interpolation.
- Defined cardiac microstructure with three orthogonal axes: fiber, sheet, and sheet-normal.
Main Results:
- Successfully fitted the geometry, fiber, and sheet-axis directions of a dog heart using nodal parameters.
- Developed a model adaptable to different heart dimensions.
- Ensured the model's utility across various states of deformation for continuum models.
Conclusions:
- The proposed mathematical framework provides a robust method for describing cardiac anatomy and microstructure.
- This approach facilitates advanced finite element modeling of cardiac electrical and mechanical functions.
- The model's adaptability supports its application in dynamic simulations of cardiac contraction.