Generalized Anisotropic Inverse Mechanics for Soft Tissues

Abstract

Elastography, which is the imaging of soft tissues on the basis of elastic modulus (or, more generally, stiffness) has become increasingly popular in the last decades and holds promise for application in many medical areas. Most of the attention has focused on inhomogeneous materials that are locally isotropic, the intent being to detect a (stiff) tumor within a (compliant) tissue. Many tissues of mechanical interest, however, are anisotropic, so a method capable of determining material anisotropy would be attractive. We present here an approach to determine the mechanical anisotropy of inhomogeneous, anisotropic tissues, by directly solving the finite element representation of the Cauchy stress balance in the tissue. The method divides the sample domain into subdomains assumed to have uniform properties and solves for the material constants in each subdomain. Two-dimensional simulated experiments on linear anisotropic inhomogeneous systems demonstrate the ability of the method, and simulated experiments on a nonlinear model demonstrate the ability of the method to capture anisotropy qualitatively even though only a linear model is used in the inverse problem. As with any inverse problem, ill-posedness is a serious concern, and multiple tests may need to be done on the same sample to determine the properties with confidence.

Collagen Structure and Mechanical Properties of the Human Sclera: Analysis for the Effects of Age

“…By doing so, we did not have to approximate or fit the stiffness of the LC or assume boundary conditions and geometry of the sclera at the holder, which was not in the field of view of the DIC measurements. The idea of restricting the domain of the finite element model in inverse methods was originally presented by Seshaiyer and Humphrey [53] and recently revisited by Raghupathy and Barocas [54]. This method can be applied to calculate material properties of biological tissues with complex geometry or boundary conditions such as the posterior segment of the eye.…”

Anisotropic behaviour of human gallbladder walls

“…In many elastography studies one estimates either the elastic moduli (Guo et al 2010), or a general linear elasticity tensor (Raghupathy and Barocas 2010) directly by solving the equilibrium equations iteratively. Normally this requires solving direct linear problems repeatedly with successively updated material parameters.…”

“…Young's modulus (Guo et al 2010) or a general linear elasticity tensor (Raghupathy and Barocas 2010), can be determined directly from the force equilibrium equation iteratively (Moulton et al 1995;Govindjee and Mihalic 1998;Kauer et al 2002;Seshaiyer and Humphrey 2003;Bosisio et al 2007;Lei and Szeri 2007;Samani and Plewes 2007;Gokhale et al 2008;Karimi et al 2008;Li et al 2009;Balocco et al 2010;Kroon 2010). …”

A model of human skin under large amplitude oscillatory shear

“…In addition, we were able to capture the nonlinear response resulting from large shear deformations up to γ 0 = 0.2. Compared to Lamers et al (2013) improvements in image acquisition and especially the determination of local skin displacements have been made by increasing the frame rate of the camera and the use of novel DIC software (Raghupathy and Barocas, 2010). This enabled stable local displacement analysis at large strain amplitudes and associated strain rates.…”

“…These movies were converted into an image sequence using FIJI software (ImageJ, La Jolla, USA). Determination of local displacement was performed via DIC in Matlab 2014b (Mathworks, Natick, MA, USA) using a strain tracking code kindly provided by Victor Barocas' group from the University of Minnesota (Raghupathy and Barocas, 2010). A region of interest was defined by specifying a rectangular grid of 21 × 11 tracking points in xand y-direction, respectively (see Fig.…”