P1B-11 A 2D-Array for Transcranial Ultrasound Focusing Using Shear-Mode Conversion: A Numerical Study

An incident ultrasonic acoustic wave with a frequency around 1 MHz creates longitudinal and shear waves inside the skull. Both waves propagate independently through the skull and create two longitudinal waves after the skull: a purely longitudinal wave and a longitudinal-shear-longitudinal wave. The process of the last wave is identified here as the shear-mode conversion (S
_c
). The interest of developing ultrasound techniques based on S
_c
resides in the fact that the transmitted wave due to Sc has less phase-shift. The present study shows the feasibility of focusing ultrasound after the skull using a 2D-array (S
_c
TX) conceived to take advantage of the Sc and with dimensions comparable to near-flat skull regions such as the anterior part of the frontal bone. The S
_c
TX array is composed of two columns of 44 times 7 elements each one separated of 3 cm following its length. The configuration in column is aimed to produce an entering wavefront favorable to the shear-mode conversion. Each element is independently driven at 1 MHz and square-shaped with a length of 1.5 mm. The space between elements is 0.4 mm. The length and width of the device are, respectively, 9.7 and 5.9 cm. The new device was compared to a conventional 2D-array (C
_n
TX) which has the same specifications of the S
_c
TX device, with the exception of the inter-column space. The degree of focus steering of both devices was compared for depths of 1, 2, 4 and 6 cm from the inner face of the skull (d
_fs
). For each depth, and assuming X and Y perpendicular to the sound propagation axis Z, four focal spots were tested at (x,y)=(0, 0), (2 cm, 0), (0, 2 cm) and (2 cm, 2 cm). A prismatic volume of 10.7 times 6.5 times 0.9 cm, located 1 cm from the device, was used to simulate the skull bone. The required phase of elements was calculated using a back-propagation (BP) method. Tests were done with the corrected phase calculated with only shear-mode BP (S
_c
BP), only longitudinal BP (L
_n
BP) and sum of both back-propagated waves (S
_c
BP+L
_n
BP). The resulting acoustic field for each focal point considered the forward-propagation due to the longitudinal and shear-mode transmissions. S
_c
TX with S
_c
BP produced the most focused fields for targets found close to the face of the skull (d
_fs
= 1 cm) and steered following the X direction. For deeper targets (d/s= 2 cm, 4 cm, 6 cm), the correction S
_c
BP+L
_n
BP was more effective to focus ultrasound. For the same targets, the correction S
_c
BP produced focal zones located closer to the device than expected. Calculation of surface area at -3 dB on XZ and YZ planes indicated that the S
_c
TX device created more focused fields for most of tested cases, excepting a few cases involving steering following the Y direction. In conclusion, Focusing using shear mode conversion is feasible using a simple device that is compatible with the geometry of the frontal human bone. Using the proposed device, this focusing is limited to tissues located about 1 cm from the inner face of the skull.