Application of Acoustoelasticity to Evaluate Nonlinear Modulus in <italic>Ex Vivo</italic> Kidneys

Abstract

Currently, dynamic elastography techniques estimate the linear elastic shear modulus of different body tissues. New methods that investigate other properties of soft tissues such as anisotropy, viscosity, and shear nonlinearity would provide more information about the structure and function of the tissue and might provide a better contrast than tissue stiffness and hence provide more effective diagnostic tools for some diseases. It has previously been shown that shear wave velocity in a medium changes due to an applied stress, a phenomenon called acoustoelasticity (AE). Applying a stress to compress a medium while measuring the shear wave velocity versus strain provides data with which the third-order nonlinear shear modulus can be estimated. To evaluate the feasibility of estimating , we evaluated ten ex vivo porcine kidneys embedded in 10% porcine gelatin to mimic the case of a transplanted kidney. Under assumptions of an elastic incompressible medium for AE measurements, the shear modulus was quantified at each compression level and the applied strain was assessed by measuring the change in the thickness of the kidney cortex. Finally, was calculated by applying the AE theory. Our results demonstrated that it is possible to estimate a nonlinear shear modulus by monitoring the changes in strain and due to kidney deformation. The magnitudes of are higher when the compression is performed progressively and when using a plate attached to the transducer. Nevertheless, the values obtained for are similar to those previously reported in the literature for breast tissue.

Why Are Viscosity and Nonlinearity Bound to Make an Impact in Clinical Elastographic Diagnosis?

“…[93]. To reduce false-negative and false-positive results and to better understand pathological changes in soft tissues, extended dynamic mechanical parameters such as viscosity need to be investigated [94] and eventually be used as new diagnostic biomarkers. Ex vivo studies evidence the predictive relationship between viscosity and pathology; for instance, the marked Ex vivo neuronal demyelination with development of apparent vacuoles associated with a loss of interneuronal connections and thus with a reduction of matrix dimensionality, causing an observed alteration of viscosity [72,[95][96][97].…”

“…Several experimental studies, including the recent study of Aristizabal et al [94], estimated the nonlinear shear modulus in Ex vivo samples. Particularly, that paper was about Ex vivo kidneys diagnosing end-stage renal disease, for which a better contrast in the diagnosis was shown.…”

“…It is also possible to deduce the nonlinear coefficients in the modified Burgers model using the numerical simulation from the quadratic wave equation rewritten in its nondimensional form [63]. It has been introduced to calculate nonlinear parameters of hydrogels and in Ex vivo porcine kidneys [94], but the cubic orders are valid under a relation that should be verified in some cases depending on acoustic nonlinearity [140].…”

A comparison of hyperelastic constitutive models applicable to shear wave elastography (SWE) data in tissue-mimicking materials

“…Continued developments of SWE techniques are ongoing. Among them, estimation of tissue hyperelastic parameters using the concept of acoustoelastic effect (AE) (Ogden, 2007) in conjunction with SWE data is particularly intriguing (Gennisson et al, 2007, Jiang et al, 2015a, Bernal et al, 2016, Aristizabal et al, 2018. If successful, this approach could offer a viable option to estimate mechanical properties of many in vivo biological tissues.…”

“…traumatic brain injury owing to shocks or blast waves in sports) and virtual surgery require precise knowledge of the detailed mechanical parameters of tissues involved. Among those reports (Gennisson et al, 2007, Jiang et al, 2015a, Bernal et al, 2016, Aristizabal et al, 2018, two AE formulations have been used to establish the relationship between the SWS and elastic constants. In the formulation in (Gennisson et al, 2007) is restricted to a strain energy function(SEF) that is a series expansion of the Green strain tensor and has been linearized in order to establish the relationship between SWS and elastic constants as a function of load (i.e.…”