Quantification of nonlinear elastic constants using polynomials in quasi-incompressible soft solids

Early detection of pathological processes is crucial for the prognosis and treatment of patients, which can be facilitated through studying tissue biomechanical properties. Shear wave elastography is a technique to estimate the shear modulus of tissue. Such measurements quantify elasticity linearized around an immediate state of local stress condition, under applied nature of excitation. Stress-strain is known to be nonlinearly related in tissues, and the quantification of such nonlinearity may be utilized to facilitate diagnostic and image analytic approaches. In this work, we compare different methods for quantifying such nonlinear relationships, in particular the estimation of elasticity parameters, including third (A) and fourth (D) order nonlinear elastic constants, from measurements. We study the fitness and robustness in approximating these parameters, and compare those in terms of tissue differentiation, applied to ex-vivo liver and muscle tissues.