Wave Propagation in a Fractional Viscoelastic Tissue Model: Application to Transluminal Procedures
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Transluminal elastographyShear waveFractional viscoelasticityKelvin voigt fractional derivativeFinite difference
Gomez, A.; Rus, G.; Saffari, N. Wave Propagation in a Fractional Viscoelastic Tissue Model: Application to Transluminal Procedures. Sensors 2021, 21, 2778. https://doi.org/10.3390/s21082778
SponsorshipUniversity College London, United Kingdom; Talentia scholarship (grant C2012H-75146405T-1) from the regional government of Andalusia, Spain; the Ministry of Education and Science, Spain, grants DPI2017-83859-R, EQC2018-004508-P and UNGR15-CE3664; Andalusia, Spain, grants SOMM17/6109/UGR, B-TEP-026-UGR18, IE2017-5537 and P18-RT-1653
In this article, a wave propagation model is presented as the first step in the development of a new type of transluminal procedure for performing elastography. Elastography is a medical imaging modality for mapping the elastic properties of soft tissue. The wave propagation model is based on a Kelvin Voigt Fractional Derivative (KVFD) viscoelastic wave equation, and is numerically solved using a Finite Difference Time Domain (FDTD) method. Fractional rheological models, such as the KVFD, are particularly well suited to model the viscoelastic response of soft tissue in elastography. The transluminal procedure is based on the transmission and detection of shear waves through the luminal wall. Shear waves travelling through the tissue are perturbed after encountering areas of altered elasticity. These perturbations carry information of medical interest that can be extracted by solving the inverse problem. Scattering from prostate tumours is used as an example application to test the model. In silico results demonstrate that shear waves are satisfactorily transmitted through the luminal wall and that echoes, coming from reflected energy at the edges of an area of altered elasticity, which are feasibly detectable by using the transluminal approach. The model here presented provides a useful tool to establish the feasibility of transluminal procedures based on wave propagation and its interaction with the mechanical properties of the tissue outside the lumen.