FITTING OF HYPERELASTIC CONSTITUTIVE MODELS IN DIFFERENT SHEEP HEART REGIONS BASED ON BIAXIAL MECHANICAL PROPERTIES

Heart failure remains one of the leading causes of death especially among people over the age of 60 years worldwide. To develop effective therapy and suitable replacement materials for the heart muscle it is necessary to understand its biomechanical behaviour under load. This paper investigates the passive mechanical response of the sheep myocardia excised from three different regions of the heart. Due to the relatively higher cost and huge ethical demands in acquisition and testing of real animal heart models, this paper evaluates the fitting performances of five different constitutive models on the myocardial tissue responses. Ten sheep were sacrificed, and their hearts excised and transported within 3h to the testing biomechanical laboratory. The upper sections of the hearts above the short axes were carefully dissected out. Tissues were dissected from the mid-sections of the left ventricle, mid-wall and right ventricle for each heart. The epicardia and endocardia were then carefully sliced off each tissue to leave the myocardia. Stress-strain curves were calculated, filtered and resampled. The results show that Choi-Vito model was found to provide the best fit to the LV, the polynomial (Anisotropic) model to RV, the Four-Fiber Family model to RV, Holzapfel (2000) to RV, Holzapfel (2005) to RV and the Fung model to LV.

A Mechanical Characterization of the Porcine Atria at the Healthy Stage and After Ventricular Tachypacing

Atrial fibrillation (AF) is a cardiac arrhythmia that highly increases the risk of stroke and is associated with significant but still unexplored changes in the mechanical behavior of the tissue. Planar biaxial tests were performed on tissue specimens from pigs at the healthy stage and after ventricular tachypacing (VTP), a procedure applied to reproduce the relevant features of AF. The local arrangement of the fiber bundles in the tissue was investigated on specimens from rabbit atria by means of circularly polarized light. Based on this, mechanical data were fitted to two anisotropic constitutive relationships, including a four-parameter Fung-type model and a microstructurally-motivated model. Accounting for the fiber-induced anisotropy brought average R2 = 0.807 for the microstructurally-motivated model and average R2 = 0.949 for the Fung model. Validation of the fitted constitutive relationships was performed by means of FEM simulations coupled to FORTRAN routines. The performances of the two material models in predicting the second Piola-Kirchhoff stress were comparable, with average errors <3.1%. However, the Fung model outperformed the other in the prediction of the Green-Lagrange strain, with 9.2% maximum average error. To increase model generality, a proper averaging procedure accounting for nonlinearities was used to obtain average material parameters. In general, a stiffer behavior after VTP was noted.

Biaxial Mechanical Response of Bioprosthetic Heart Valve Biomaterials to High In-plane Shear

Utilization of novel biologically-derived biomaterials in bioprosthetic heart valves (BHV) requires robust constitutive models to predict the mechanical behavior under generalized loading states. Thus, it is necessary to perform rigorous experimentation involving all functional deformations to obtain both the form and material constants of a strain-energy density function. In this study, we generated a comprehensive experimental biaxial mechanical dataset that included high in-plane shear stresses using glutaraldehyde treated bovine pericardium (GLBP) as the representative BHV biomaterial. Compared to our previous study (Sacks, JBME, v.121, pp. 551–555, 1999), GLBP demonstrated a substantially different response under high shear strains. This finding was underscored by the inability of the standard Fung model, applied successfully in our previous GLBP study, to fit the high-shear data. To develop an appropriate constitutive model, we utilized an interpolation technique for the pseudo-elastic response to guide modification of the final model form. An eight parameter modified Fung model utilizing additional quartic terms was developed, which fitted the complete dataset well. Model parameters were also constrained to satisfy physical plausibility of the strain energy function. The results of this study underscore the limited predictive ability of current soft tissue models, and the need to collect experimental data for soft tissue simulations over the complete functional range.

The Convexity Properties of the Fung Model for Soft Tissues

During the last three decades, the theory of nonlinear elasticity has been used extensively to model biological soft tissues. The now widely accepted belief that an understanding of the mechanical properties of these tissues is critical in order to understand the advent, progression, and treatment of disease has driven this research. More recently, those interested in how soft tissues grow and remodel themselves in response to both normal and pathological conditions have used nonlinear continuum mechanics as a basic tool.