Method to optimize the placement of a single-element transducer for transcranial focused ultrasound

Abstract

Background and Objective Transcranial focused ultrasound (tFUS) is a promising neuromodulation technique because of its non-invasiveness and high spatial resolution (within millimeter scale). However, the presence of the skull can lead to disrupting and shifting the acoustic focus in the brain. In this study, we propose a computationally efficient way to determine the optimal position of a single-element focused ultrasound transducer which can effectively deliver acoustic energy to the brain target. We hypothesized that the placement of a single element transducer with the lowest average reflection coefficient would be the optimal position.

Methods The reflection coefficient is defined by the ratio of the amplitude of the reflected wave to the incident wave. To calculate the reflection coefficient, we assumed ultrasound waves as straight lines (beam lines). At each beam line, the reflection coefficient was calculated from the incidence angle at the skull interface (outer/inner skull surfaces). The average reflection coefficient (ARC) was calculated at each possible placement of the transducer using a custom-built software. For comparison purposes, acoustic simulations (k-Wave MATLAB toolbox) which numerically solved the linear wave equation were performed with the same transducer positions used in the ARC calculation. In addition, the experimental validation of our proposed method was also performed by measuring acoustic wave propagation through the calvaria skull phantom in water. The accuracy of our method was defined as the distance between the two optimal transducer placements which were determined from the acoustic simulations and from the ARC method.

Result Simulated acoustic pressure distribution corresponding to each ARC showed an inverse relationship with peak acoustic pressures produced in the brain. In comparison to the acoustic simulations, the accuracy of our method was 5.07 ± 4.27&#8239

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