Ultrasound longitudinal-wave anisotropy estimation in muscle tissue
2021
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. Quantifying anisotropy is therefore
essential to improve velocity estimates while providing a new metric
that relates to both muscle composition and architecture. This work
presents a method to estimate longitudinal-wave anisotropy in
transversely isotropic tissues. We assume elliptical anisotropy and
consider an experimental setup that includes a flat reflector located
in front of the linear probe. Moreover, we consider transducers
operating multistatically. This setup allows us to measure
first-arrival reflection traveltimes. 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 relationship between traveltimes and anisotropy
parameters, accounting for reflector inclinations. To analyze the
structure of this nonlinear forward problem, we formulate the
inversion statistically using the Bayesian framework. Solutions are
probability density functions useful for quantifying uncertainties in
parameter estimates. Using numerical examples, we demonstrate that
all parameters can be well constrained when traveltimes from
different reflector inclinations are combined. Results from a wide
range of acquisition and medium properties show that uncertainties in
velocity estimates are substantially lower than expected velocity
differences in muscle. Thus, our formulation could provide accurate
muscle anisotropy estimates in future clinical applications.
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