Quantitative estimation of complex shear modulus of liver and hydrogels through shear-wave imaging.

Abstract

A Doppler-based shear-wave imaging technique is described for estimating the complex shear modulus (μ+iωη) at shear-wave frequencies between 50 and 450 Hz. The developed technique involves a mechanical actuator that harmonically drives a stainless steel biopsy needle placed in the medium. Narrowband cylindrical shear waves are imaged using pulsed Doppler techniques. Shear moduli were computed from Doppler detected velocity. A phase gradient technique is applied to measure shear-wave speed. Spatially averaged speeds were numerically fit to a mathematical model relating dispersion and complex modulus. The proposed method was used to estimate complex shear modulus of the homogeneous three dimensional collagen hydrogels and of fresh and thermally-damaged porcine liver. The elastic shear modulus of 4% collagen hydrogel was measured, μ=640±14 Pa, using a commercial rheometer as a standard. The phase gradient approach yielded frequency-independent moduli μ=570±67 Pa and η=0.16±0.09 Pa s. For fresh liver shear-wave imaging between 50–300 Hz yielded frequency-independent moduli μ=1757±733 Pa and η=1.72±0.48 Pa s and μ=3851±3233 Pa and η=8.9±2.9 Pa s for thermally-damaged liver. Good agreement between the rheometer measurements and the shear-wave imaging approach shows that we can quantitatively estimate viscoelastic properties of the hydrogels and liver.