Anisotropy, inhomogeneity, and tension–compression nonlinearity of human glenohumeral cartilage in finite deformation

Abstract

The tensile and compressive properties of human glenohumeral cartilage were determined by testing 120 rectangular strips in uniaxial tension and 70 cylindrical plugs in confined compression, obtained from five human glenohumeral joints. Specimens were harvested from five regions across the articular surface of the humeral head and two regions on the glenoid. Tensile strips were obtained along two orientations, parallel and perpendicular to the split-line directions. Two serial slices through the thickness, corresponding to the superficial and middle zones of the cartilage layers, were prepared from each tensile strip and each compressive plug. The equilibrium tensile modulus and compressive aggregate modulus of cartilage were determined from the uniaxial tensile and confined compression tests, respectively. Significant differences in the tensile moduli were found with depth and orientation relative to the local split line direction. Articular cartilage of the humeral head was significantly stiffer in tension than that of the glenoid. There were significant differences in the aggregate compressive moduli of articular cartilage between superficial and middle zones in the humeral head. Furthermore, tensile and compressive stressstrain responses exhibited nonlinearity under finite strain while the tensile modulus differed by up to two orders of magnitude from the compressive aggregate modulus at 0% strain, demonstrating a high degree of tension-compression nonlinearity. The complexity of the mechanical properties of human glenohumeral cartilage was exposed in this study, showing anisotropy, inhomogeneity, and tension-compression nonlinearity within the same joint. The observed differences in the tensile properties of human glenohumeral cartilage suggest that the glenoid may be more susceptible to cartilage degeneration than the humeral head.

A Bimodular Theory for Finite Deformations: Comparison of Orthotropic Second-order and Exponential Stress Constitutive Equations for Articular Cartilage

“…For example, in Huang et al (1999) the Poisson's ratios measured at 16% strain for UT in the 1 and 2 directions were 1.31 and 1.33, respectively, whereas the 6-parameter second-order model here resulted in constant Poisson's ratios of 0.499. In contrast to earlier studies with exponential strain energy functions (Klisch and Lotz 1999;Wagner and Lotz 2004), in this study an exact solution to UT can be obtained for the second-order models.…”

“…To develop the UT datasets, a 2-parameter exponential func tion was used to generate data from 0 to 20% strain in 2% increments. For UT in the 1 and 2 directions, the parameters were adopted from Huang et al (1999Huang et al ( , 2005. For UT in the 3 direction, the parameters from the UT in the 1-direction were scaled down using a ratio of the infinitesimal Young's moduli reported in Chahine et al (2004) for bovine cartilage.…”

“…The Poisson's ratio at 0% UT strain was assumed to correspond to the Poisson's ratio for infinitesimal defor mations in unconfined compression since the stress-strain equation is continuous through the origin, and was chosen using theoretical predictions with bovine tissue (Wang et al 2003). The Poisson's ratio at 16% strain was specified using the data reported in Huang et al (1999). To develop the CC datasets, a 2-parameter exponential function (Ateshian et al 1997) was used to generate data from 0 to 20% strain in 2% increments; the parameters were based on results of Huang et al (1999Huang et al ( , 2005.…”

“…The Poisson's ratio at 16% strain was specified using the data reported in Huang et al (1999). To develop the CC datasets, a 2-parameter exponential function (Ateshian et al 1997) was used to generate data from 0 to 20% strain in 2% increments; the parameters were based on results of Huang et al (1999Huang et al ( , 2005. It was assumed that the CC response was the same in the 1 and 2 directions.…”

“…Although MRI mea surements of in situ and in vivo joints have predicted that cartilage is subject to average strains of less than 10% under physiologic loading conditions (Eckstein et al 2000;Herberhold et al 1999), local strains may be much higher due to nonhomogeneous mechanical properties that depend on both anatomic location and depth from the articular surface (Schinagl et al 1997;Wang et al 2001). For physiologic loading conditions, FEM contact analyses (Donzelli et al 1999;Krishnan et al 2003) suggest that in situ cartilage may experience local strains up to 26%, suggest ing that the tissue is in the nonlinear range of its stress-strain relationship (Huang et al 1999). …”