Finite element modelling and analyses of nonlinearly elastic, orthotropic, vascular tissue in distension

Cardiovascular disease remains the leading cause of death in the Western world. It is hypothesized that the elastic moduli of cardiovascular tissue are altered in disease. The scope of this research was to develop a method to determine these moduli for healthy and diseased tissue. A rigorous constitutive law was developed and validated specifically for this purpose. Application of the "material identification" method to vascular tissue is presented.

Previous attempts to model the stress-strain behavior of cardiovascular tissue are compromised by numerous assumptions that are usually invalidated by experimental evidence. With these shortcomings in mind, a constitutive law was developed from principles of continuum mechanics that describes the nonlinear, three-dimensional behavior of an orthotropic, slightly-compressible, hyperelastic material. A nonlinear finite element (FE) program was developed for the purposes of solving the resulting equilibrium equations. The program predicts, for a given loading (boundary conditions) and assumed set of elastic moduli, the stress and strain fields within a discretized domain.

Experimental data was obtained from ex-vivo measurements made on a freshly excised rabbit infrarenal aorta and a canine carotid artery. The measured loads served as boundary conditions to the FE program. A robust nonlinear least-squares regression algorithm yielded a set of elastic moduli for which the sum-of-squares difference between the experimentally measured and FE (model) predicted displacements was minimized. These moduli were estimated for the rabbit aorta and canine carotid artery and were considered to best describe the constitutive behavior of the specimens within the framework of the present model.

The model-fit to the data was reasonable in all cases (coefficient of variation ranging from 8% to 21%). Disparity was evident between the elastic moduli for each specimen. This suggests first that the elastic response of canine arteries differs from that of rabbit aorta, and second that hypertension manifests itself by altering the elastic properties of blood vessels.

Further data collection and refinement of the developed techniques will facilitate new understanding of the biomechanical implications of cardiovascular disease. The present work sets the stage for similar analyses of the biomechanical behavior of the intact heart.