Establishing density-dependent longitudinal sound speed in the vertebral lamina

Focused ultrasound treatments of the spinal cord may be facilitated using a phased array transducer and beamforming to correct spine-induced focal aberrations. Simulations can non-invasively calculate aberration corrections using x-ray computed tomography (CT) data that are correlated to density (rho) and longitudinal sound speed (c(L)). We aimed to optimize vertebral lamina-specific c(L) (rho) functions at a physiological temperature (37 degrees C) to maximize time domain simulation accuracy. Odd-numbered ex vivo human thoracic vertebrae were imaged with a clinical CT-scanner (0.511 x 0.511 x 0.5 mm), then sonicated with a transducer (514 kHz) focused on the canal via the vertebral lamina. Vertebra-induced signal time shifts were extracted from pressure waveforms recorded within the canals. Measurements were repeated 5x per vertebra, with 2.5mm vertical vertebra shifts between measurements. Linear functions relating c(L) with CT-derived density were optimized. The optimized function was c(L) (rho) = 0.35 (rho - rho(w)) + c(L); w m/s, where w denotes water, giving the tested laminae a mean bulk density of 1600 +/- 30 kg/m(3) and a mean bulk c(L) of 1670 +/- 60 m/s. The optimized lamina c(L) (rho) function was accurate to k=16 when implemented in a multilayered ray acoustics model. This modelling accuracy will improve trans-spine ultrasound beamforming. (C) 2022 Acoustical Society of America.