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Abstract-Compressibility influences the mechanical bidomain model describing the elastic properties of tissue. Displacements of the intracellular and extracellular spaces are analyzed individually, and differences in these displacements produce membrane forces. Two length constants are associated with the membrane spring constant, one contains the shear moduli and the other contains the bulk moduli. The analytical solutions in these examples indicate that the monodomain part does not contribute to the membrane force. Accounting for compressibility has its largest impact on the intracellular and extracellular pressures. The bidomain contribution to the pressure obeys the Helmholtz equation rather than Laplace's equation. This model predicts membrane forces that might cause tissue remodeling or mechanotransduction.

In the heart, cardiac muscle fibers curve creating zones of membrane forces resulting in regions of mechanotransduction. This study uses the finite difference method to solve the mechanical bidomain equations numerically for a complex fiber geometry. The magnitude of the active tension T is constant but its direction makes an angle with the x-axis that varies with position. Differences between the intracellular and extracellular displacements result from the bidomain behavior of the tissue that gives rise to forces on the integrin proteins in the membrane. The long-term goal is to use the mechanical bidomain model to suggest experiments and make predictions about growth and remodeling in the heart.

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