Two-domain mechanics of a spherical, single chamber heart with applications to specific cardiac pathologies

Continuum approximations of tissue consider responses averaged over many cells in a region. This simplified approach allows consideration of macroscopic effects, such as deformation or action potential propagation. A bidomain (sometimes known as biphasic) approach retains the macroscopic character of a continuum approximation while allowing one to consider microscopic effects; novel behavior arising from interactions between the intracellular and extracellular spaces can also be noted. I consider a spherical, single chamber heart with the new mechanical bidomain model in four separate pathologies: hypertension, hypovolemic hypotension, and hypertrophic and dilational cardiomyopathies. Analytic solutions of intracellular and extracellular displacements and hydrostatic pressures are presented; the distributions describe elastic deformation and hydrostatic fluid pressure buildup of the extracellular collagen matrix and the intracellular muscle under simplified spherical geometry. Potential applications, such as stretch activated membrane channels, are also noted.