Toward speed-of-sound anisotropy quantification in muscle with
pulse-echo ultrasound
Abstract
The velocity of ultrasound longitudinal waves (speed of sound) is
emerging as a valuable biomarker for a wide range of diseases, including
musculoskeletal disorders. Muscles are fiber-rich tissues that exhibit
anisotropic behavior, meaning that velocities vary with the
wave-propagation direction. Therefore, quantifying anisotropy is
essential to improve velocity estimates while providing a new metric
related to muscle composition and architecture. For the first time, this
work presents a method to estimate speed-of-sound anisotropy in
transversely isotropic tissues using pulse-echo ultrasound. We assume
elliptical anisotropy and consider an experimental setup with a flat
reflector parallel to the linear probe, with the muscle in between. This
setup allows us to measure first-arrival reflection traveltimes using
multistatic operation. Unknown muscle parameters are the orientation
angle of the anisotropy symmetry axis and the velocities along and
across this axis. We derive analytical expressions for the nonlinear
relationship between traveltimes and anisotropy parameters, including
reflector inclinations. These equations are exact for homogeneous media
and are useful to estimate the effective average anisotropy in muscles.
To analyze the structure of this forward problem, we formulate the
inversion statistically using the Bayesian framework. We demonstrate
that anisotropy parameters can be uniquely constrained by combining
traveltimes from different reflector inclinations. Numerical results
from wide-ranging acquisition and anisotropy properties show that
uncertainties in velocity estimates are substantially lower than
expected velocity differences in the muscle. Thus, our approach could
provide meaningful muscle anisotropy estimates in future clinical
applications.