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Homogenization of syncytial tissues
1Department of Mathematics, University of California at Berkeley.
Critical Reviews in Biomedical Engineering
|January 1, 1993
Summary
This study presents a new continuum model for multicellular tissues derived from microstructure. This homogenized syncytium model includes the bidomain model and provides effective tissue conductivities.
Area of Science:
- Biophysics
- Continuum Mechanics
- Computational Biology
Background:
- Multicellular tissues exhibit complex electrical properties.
- Existing models like the bidomain model simplify tissue behavior.
- A direct derivation from microstructure is needed for a more fundamental understanding.
Purpose of the Study:
- To derive a continuum representation of multicellular, syncytial tissue directly from its microstructure.
- To develop a homogenized syncytium model that encompasses the bidomain model.
- To establish formulas for effective tissue conductivities based on microstructural properties.
Main Methods:
- Utilizing an idealized, periodic representation of tissue microstructure.
- Applying Laplace's equation for intracellular and extracellular potentials.
- Employing boundary conditions for membrane electrical properties.
- Implementing a two-scale asymptotic expansion homogenization process.
Main Results:
- Derived two reaction-diffusion equations for the averaged continuum representation.
- Obtained formulas for effective conductivities based on microstructure and constituent conductivities.
- The final equations generalize the bidomain model.
Conclusions:
- The derived homogenized syncytium model offers a fundamental approach to tissue electrophysiology.
- The model is valid for autonomous processes deep within the tissue under specific field conditions.
- Limitations exist at tissue surfaces and under strong or rapidly changing electrical fields.