Calibration of hyperelastic constitutive models: the role of boundary conditions, search algorithms, and experimental variability

An experimental study of the heterogeneity and anisotropy of porcine meniscal ultimate tensile strength

Characterizing the ultimate tensile strength (UTS) of the meniscus is critical in studying knee damage and pathology. This study aims to determine the UTS of the meniscus with an emphasis on its heterogeneity and anisotropy. We performed tensile tests to failure on the menisci of six month old Yorkshire pigs at a low strain rate. Specimens from the anterior, middle and posterior regions of the meniscus were tested in the radial and circumferential directions. Then the UTS was obtained for each specimen and the data were analyzed statistically, leading to a comprehensive view of the variations in porcine meniscal strength. The middle region has the highest average strength in the circumferential (43.3 ± 4.7 MPa) and radial (12.6 ± 2.2 MPa) directions. This is followed by the anterior and posterior regions, which present similar average values (about 34.0MPa) in circumferential direction. The average strength of each region in the radial direction is approximately one-fourth to one-third of the value in the circumferential direction. This study is novel as it is the first work to focus on the experimental methods to investigate the heterogeneity and anisotropy only for porcine meniscus.

Experiments and hyperelastic modeling of porcine meniscus show heterogeneity at high strains

Constitutive modeling of the meniscus is critical in areas like knee surgery and tissue engineering. At low strain rates, the meniscus can be described using a hyperelastic model. Calibration of hyperelastic material models of the meniscus is challenging on many fronts due to material variability and friction. In this study, we present a framework to determine the hyperelastic material parameters of porcine meniscus (and similar soft tissues) using no-slip uniaxial compression experiments. Because of the nonhomogeneous deformation in the specimens, a finite element solution is required at each step of the iterative calibration process. We employ a Bayesian calibration approach to account for the inherent material variability and a Bayesian optimization approach to minimize the resulting cost function in the material parameter space. Cylindrical specimens of porcine meniscus from the anterior, middle and posterior regions are tested up to 30% compressive strain and the Yeoh form of hyperelastic strain energy density function is used to describe the material response. The results show that the Yeoh form is able to accurately describe the compressive response of porcine meniscus and that the Bayesian calibration and optimization approaches are able to calibrate the model in a computationally efficient manner while taking into account the inherent material variability. The results also show that the shear modulus or the initial stiffness is roughly uniform across the different areas of the meniscus, but there is significant spatial heterogeneity in the response at high strains. In particular, the middle region is considerably stiffer at high strains. This heterogeneity is important to consider in modeling the response of the meniscus for clinical applications.