Shear wave propagation in complex sub wavelength tissue geometries: Theoretical and experimental implications in the framework of cornea and skin shear wave imaging

Abstract

Quantitative measurements of cornea and skin biomechanical properties have many applications in medicine. In ophthalmology, it could lead to a better diagnosis of pathologies or monitoring of treatments. In dermatology, it could help the skin lesions removal monitoring. In the framework of Supersonic Shear Imaging (SSI), these organs are characterized by their complex sub wavelength geometry (thin plate and thin capsule) that strongly influences the shear wave propagation. In this work, a theoretical framework is proposed and validated in experiments for the quantification of elastic modulus in these layered tissues. Shear wave dispersion induced by the guided propagation in such thin layers is estimated and fitted to the analytical dispersion curve derived from the “leaky” Lamb Wave theory. SSI is refined and used in order to map in real time the tissues elasticity. This technique consists in generating a shear wave by ultrasonic radiation force and imaging its propagation through the medium at a high frame rate (20 kHz). For infinite media the shear wave velocity is then linked to the Young's modulus. In cornea and skin layers, the high-frequency shear wave (from 500 to 2000 Hz) is guided similarly to a Lamb wave, with plate thickness (<1 mm) close to its wavelength. Experimental dispersion curves have been confronted to numerical studies. First, finite differences simulations were performed to obtain numerical dispersion curves in plates with exactly known thickness and elasticity. Besides, theoretical dispersion equations were derived by solving numerically the propagation equation. Dispersion curves obtained in vitro on phantoms are found consistent with analytical calculations. Least mean squares fitting of curves enables to recover a quantitative assessment of elasticity (standard deviation < 10%).