Applications of the finite-element method to ventricular mechanics

The finite-element method of structural analysis is ideally suited for the analysis of complex structures. Applications of this method to analysis of the heart will be discussed in light of the insights that have been obtained as well as the limitations of each analysis. In analyzing the heart, one of the aspects that is particularly difficult to handle is the presumed anisotropy as well as the nonlinearity of the material properties of the wall. Currently, use of finite-element methods for stress analysis requires that one first assumes a reasonable constitutive relation and then use incremental methods to predict the stresses. Studies using this approach will be reviewed. In theory, one could invert this approach by measuring the loading and resulting deformation in an intact heart and using the finite-element method to predict the constitutive relations. In order for this to succeed requires accurate measurement of the loading and the deformations. As we gain increasing expertise in these measurement areas, the feasibility of achieving this seems more realistic. While this alternative approach should be useful, there has been only minimal attention paid to this area. I will discuss this approach from a theoretical viewpoint and review the state-of-the-art.