Identification of local nonlinear shear-wave dynamics using Volterra kernels: application to prostate cancer detection

Cancer remains a major health concern worldwide. Shear-wave elastography (SWE) holds promise for cancer detection by quantifying linear elastic changes in tissue through shear-wave (SW) velocity estimation. However, shear viscosity and nonlinearity are often over-looked, despite their potential as additional biomarkers. This study evaluates the visco-hyperelastic properties of soft tissue, including linear shear modulus, shear viscosity, and shear nonlinearity. We propose using Volterra kernels to characterize local nonlinear SW dynamics, with kernel identification based on SW particle velocity measurements at adjacent locations. The method was validated using in-silico simulations and in-vitro gelatin phantoms. To evaluate its clinical relevance, we applied the method for prostate cancer (PCa) detection. To our knowledge, this is the first in-vivo assessment of voxel-based visco-hyperelastic properties of the prostate. In 90 patients, our results indicated that the linear kernel correlated with the linear shear modulus, while the quadratic kernel reflected both viscosity and nonlinearity. A convolutional neural network trained on these parameters with registered histopathology as ground truth achieved area under the receiver operating characteristic curve (AUC) values of 0.60 (95% confidence interval [CI]: 0.57, 0.62) and 0.66 (95% CI: 0.64, 0.68) for PCa detection, respectively-both significantly outperforming the linear shear modulus (AUC of 0.54; 95% CI, 0.52 to 0.56). Our findings suggest that Volterra kernels reflect information related to the visco-hyperelastic properties of prostate tissue, highlighting the potential of viscosity and nonlinearity as additional biomarkers for PCa detection.