Constitutive equations and model validation

Of the four basic biomechanics modeling steps outlined in the Introduction, determining the constitutive equations for cardiovascular tissue is often the most difficult step, especially when the tissue properties vary with time and sarcomere length history, as is the case with contracting myocardium. Using a cylindrical model to study transmural variations in stress and strain rather than a finite element model of the entire left ventricle allows for the implementation of a time-and sarcomere length history-dependent constitutive equation. The cylindrical model simulations can then be repeated with progressively simpler constitutive equations and the resulting transmural stress and strain distributions compared to determine under what conditions the most computationally efficient constitutive equations are valid. This chapter is primarily concerned with an instructive review of the constitutive equations we have implemented in cylindrical and finite element models of the passive and beating left ventricle, including that of diseased and surgically treated hearts. The last section of this chapter is concerned with experimental measurements that we have used to validate these models.