Hyperelastic Material Parameters Research Articles

Nonlinear finite element analysis of anular lesions in the L4/5 intervertebral disc

Degenerate intervertebral discs exhibit both material and structural changes. Structural defects (lesions) develop in the anulus fibrosus with age. While degeneration has been simulated in numerous previous studies, the effects of structural lesions on disc mechanics are not well known. In this study, a finite element model (FEM) of the L4/5 intervertebral disc was developed in order to study the effects of anular lesions and loss of hydrostatic pressure in the nucleus pulposus on the disc mechanics. Models were developed to simulate both healthy and degenerate discs. Degeneration was simulated with either rim, radial or circumferential anular lesions and by equating nucleus pressure to zero. The anulus fibrosus ground substance was represented as a nonlinear incompressible material using a second-order polynomial, hyperelastic strain energy equation. Hyperelastic material parameters were derived from experimentation on sheep discs. Endplates were assumed to be rigid, and annulus lamellae were assumed to be vertical in the unloaded state. Loading conditions corresponding to physiological ranges of rotational motion were applied to the models and peak rotation moments compared between models. Loss of nucleus pulposus pressure had a much greater effect on the disc mechanics than the presence of anular lesions. This indicated that the development of anular lesions alone (prior to degeneration of the nucleus) has minimal effect on disc mechanics, but that disc stiffness is significantly reduced by the loss of hydrostatic pressure in the nucleus. With the degeneration of the nucleus, the outer innervated anulus or surrounding osseo-ligamentous anatomy may therefore experience increased strains.

Correlations between tissue-level stresses and strains and cellular damage within the guinea pig spinal cord white matter

Strain magnitude, strain rate, axon location, axon size, and the local tissue stress state have been proposed as the mechanisms governing primary cellular damage within the spinal cord parenchyma during slow compression injury. However, the mechanism of axon injury has yet to be fully elucidated. The objective of this study was to correlate cellular damage within the guinea pig spinal cord white matter, quantified by a horseradish peroxidase (HRP) exclusion test, with tissue-level stresses and strains using a combined experimental and computational approach. Force–deformation curves were acquired by transversely compressing strips of guinea pig spinal cord white matter at a quasi-static rate. Hyperelastic material parameters, derived from a Mooney–Rivlin constitutive law, were varied within a nonlinear, plane strain finite element model of the white matter strips until the computational force–deformation curve converged to the experimental results. In addition, white matter strips were subjected to nominal compression levels of 25%, 50%, 70%, and 90% to assess axonal damage by quantifying HRP uptake. HRP uptake density increased with tissue depth and with increased nominal compression. Using linear and nonlinear regression analyses, the strongest correlations with HRP uptake density were found for groups of tissue-level stresses and groups of log-transformed tissue-level strains.

Characterization of the Biomechanical Properties of the Lower Esophagus for Surgical Simulation

In this work a method to characterize soft tissue properties for mechanical modeling is presented. Attention is especially focused on developing a model of the lower esophagus to be used in a surgical simulation, which shows a promise as a training method for medical personnel. The viscoelastic properties of the lower esophageal junction are characterized using data from animal experiments and an inverse FE parameter estimation algorithm. Utilizing the assumptions of quasilinear- viscoelastic theory, the viscoelastic and hyperelastic material parameters are estimated to provide a physically based simulation of tissue deformations in real time. To calibrate the parameters to the experimental results, a three dimensional FE model that simulates the forces at the indenter and an optimization program that updates new parameters and runs the simulation iteratively are developed. It was possible to reduce the time and computation resources by decoupling the viscoelastic part and elastic part in a tissue model. The comparison of the simulation and the experimental behavior of pig esophagus are presented to provide validity to the tissue model using the proposed approach.

Determination of the compressive material properties of the supraspinatus tendon.

A methodology was developed for determining the compressive properties of the supraspinatus tendon, based on finite element principles. Simplified three-dimensional models ure re reated based on anatomical thickness measurements of unloaded supraspinatus tendons over 15 points. The tendon material was characterized as a composite structure of' longitudinally arranged collagen fibers within an extrafibrillar matrix. The matrix was formulated as a hyperelastic material described by the Ogden form of the strain energy potential. The hyperelastic material parameters were parametrically manipulated until the analytical load-displacement results were similar to the results obtaizned from indentation testinrg. In the geometrically averaged tendon, the average ratio of experimental to theoretical maximum indentation displacement was 1.00 (SD: 0.01). The average normalization of residuals was 2.1 g (SD: 0.9 g). Therefjore, the compressive material properties of the supraspinatus tendo'n extrafibrillar matrix were adequately derived with a first-order hyperelastic formulation. The initial comnpressive elastic modulus ranged from 0.024 to 0.090 MPa over the tendon surface and increased nonlinearly with additional compression. Using these material properties, the stresses induced during acromional impingement can be analyzed.