A closed-form expression for the relationship between shear modulus from shear wave elastography and tangent modulus from tensile test

Abstract

Although shear wave elastography has been increasingly employed for in-vivo studies of the mechanical properties of human tendons, critical questions have emerged regarding the correlation between acoustic measurements and the shear modulus determined from mechanical testing. This study proposes a closed-form expression for estimating the tangent modulus of tendons under tension. This expression is formulated as a function of the shear modulus and is obtained by combining identifications on both tensile testing and elastography measurements. A one-dimensional nonlinear model is employed for tensile test data, accounting for the strain behavior of tendon fiber bundles as a function of stress and four identifiable parameters. This model describes the entire physiological range, including the tendon in its crimped state. A new model based on empirical observations defines the shear modulus response obtained from elastography in terms of tensile stress. By combining these models, the closed-form expression was derived. Stress-strain data obtained from tensile tests and shear modulus measurements from shear wave elastography of eleven in vitro samples of fresh-frozen human Achilles tendons, experimentally obtained, were reanalyzed. The proposed methodology reduces high-frequency noise in the stress-strain data, producing tangent-modulus estimates less sensitive to numerical differentiation. This approach is also practical in scenarios where tendons are crimped, or fibers are fully extended, providing estimations of material properties that combine potentially in-vivo SSI elastography with a tendon material constitutive model.