Experimental evidence of shear waves in fractional viscoelastic rheological models

Open Access

Abstract

The authors want to acknowledge the Fluids Mechanics Research Group from University of Jaen for the use of their facilities and support, Miguel Riveiro for his assistance in the signal generation, and Lydia Fernandez for her collaboration in the phantom fabrication. The first author was supported by a Talentia scholarship (Grant C2012H-75146405T-1) from the regional government of Andalusia, Spain, for the two first years of his PhD programme at University College London, United Kingdom. The other 2 years of his PhD programme he was supported by the Mechanical Engineering Department of University College London, United Kingdom. Other minor financial support was provided by the Ministry of Education and Science, Spain, Grants DPI2017-83859-R, EQC2018-004508-P, UNGR15-CE3664, PID2020-115372RB-I00 and PDC2021-120945-I00, and by the regional government of Andalusia, Spain, grants SOMM17/6109/UGR, B-TEP-026-UGR18, IE2017-5537 and P18-RT-1653. ; Fractional viscoelastic rheological models, such as the Kelvin Voigt Fractional Derivative model, have been proposed in the literature for modelling shear wave propagation in soft tissue. In this article, our previously developed wave propagation model for transluminal propagation based on a Kelvin Voigt Fractional Derivative wave equation is experimentally validated. The transluminal procedure uses the transmission and detection of shear waves through the luminal wall. The model was compared against high-speed camera observations in translucent elastography phantoms with similar viscoelastic properties to prostate tissue. An ad hoc cross-correlation procedure was used to reconstruct the angular displacement from the high-speed camera observations. Rheometry and shear wave elastography were used for characterising the shear wave velocity dispersion curve for the phantoms. Fractional viscoelastic properties were derived after fitting the dispersion curve to its analytical expression. Propagation features and amplitude spectra from simulations and high-speed camera observations ...