Linear, weakly nonlinear and fully nonlinear models for soft tissues: which ones provide the most reliable estimations of the stiffness?

Abstract

Benign and malignant lesions in tissues or organs can be detected by elastographic investigations in which pathological regions are spotted from local alterations of the stiffness. As is known, the shear modulus provides a measure of the stiffness of an elastic material. Based on the classical theory of linear elasticity, an elastogram yields estimations of the linear shear modulus from measurements of the speed of small-amplitude transverse waves propagating in the medium tested. In this paper, we show that the estimation of the shear modulus can be improved significantly by employing the fourth-order weakly nonlinear theory of elasticity (FOE), and indicate how the stiffness can be assessed more precisely with the use of FOE. We discuss also why FOE provides more reliable results than the fully nonlinear theory of elasticity. This article is part of the theme issue ‘The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity’.

The Ogden model of rubber mechanics: 50 years of impact on nonlinear elasticity

“…Saccomandi et al . [30] show that using the fourth-order weakly nonlinear theory of elasticity results in an improved estimate of the material stiffness of healthy and diseases tissues compared with the fully nonlinear theory. The authors discuss in detail some of the shortcomings encountered by some sophisticated models developed within the latter theory when describing the responses of real materials.…”

A constitutive model for transversely isotropic dispersive materials

“…The RRG model can be viewed as the phenomenological version of the discrete theory proposed by Rosenau [8], falls within the theory of simple materials [17], does not require the introduction of additional initial and/or boundary conditions, and can be easily applied to amorphous materials. It has been used also to study the propagation of finite-amplitude bulk waves in isotropic dispersive solids [18,19], and hence to generalize prior studies in crystalline materials [20,21] and amorphous solids [22]. Incidentally, within the RRG theory terms containing higher-order mixed derivatives with respect to spatial and temporal variables have to be added to the classical wave equation producing the nonlinear Love equation.…”

A Force-Matched Approach to Large-Strain Nonlinearity in Elasticity Imaging for Breast Lesion Characterization

“…When subjected to large strains (greater than approximately 5%), soft tissues have a nonlinear elastic response in which the tangential elastic stiffness of the tissue increases with increasing strain. This nonlinear elastic response is known to alter the characterization of tissue elasticity made in elasticity imaging techniques [4] and is often cited as a source of user dependence in clinical applications of elasticity imaging [1,2].More recent developments in elasticity imaging have begun to leverage this nonlinear response to characterize the nonlinear elasticity of various soft tissues [5][6][7][8][9][10][11][12], including in breast lesions [13][14][15][16][17][18][19]. Interest in using nonlinear characterization for breast imaging is driven by the observation in ex vivo compression testing of breast tissue samples which suggests differing nonlinear elastic behavior between malignant and benign breast tissues [20][21][22].…”