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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