LAMINAR STRUCTURE OF THE HEART - A MATHEMATICAL-MODEL

A mathematical description of cardiac anatomy is presented for use wit h finite element models of the electrical activation and mechanical fu nction of the heart. The geometry of the heart is given in terms of pr olate spheroidal coordinates defined at the nodes of a finite element mesh and interpolated within elements by a combination of linear Lagra nge and cubic Hermite basis functions. Cardiac microstructure is assum ed to have three axes of symmetry: one aligned with the muscle fiber o rientation (the fiber axis); a second set orthogonal to the fiber dire ction and lying in the newly identified myocardial sheet plane (the sh eet axis); and a third set orthogonal to the first two, in the sheet-n ormal direction. The geometry, fiber-axis direction, and sheet-axis di rection of a dog heart are fitted with parameters defined at the nodes of the finite element mesh. The fiber and sheet orientation parameter s are defined with respect to the ventricular geometry such that 1) th ey can be applied to any heart of known dimensions, and 2) they can be used for the same heart at various states of deformation, as is neede d, for example, in continuum models of ventricular contraction.