Computational sensitivity evaluation of ultrasound neuromodulation resolution to brain tissue sound speed with robust beamforming

Abstract

Low-intensity focused ultrasound (LIFU) neuromodulation requires precise targeting and high resolution enabled by phased array transducers and beamforming. However, focusing optimization usually relies on phantom measurements or simulations with inaccurate acoustic properties to degrade neuromodulation resolution. Therefore, this work analyzes the sensitivity of neuromodulation resolution, measured by off-target activation area (OTAA), to brain tissue sound speed. A Robust Optimal Resolution (ROR) beamforming method is proposed to minimize the worst-case OTAA with restricted sound speed inaccuracy and propagation information estimated with deviated sound speed. The propagation estimation model utilizes equivalent source method (ESM) to map sound field between different acoustic parameter sets. Simulation in a human head model validates the effectiveness of the proposed propagation estimation model, and shows that ROR beamforming method can significantly reduce the worst-case OTAA compared to benchmark methods by [Formula: see text] on average and up to [Formula: see text], improving the robustness of stimulation and addressing the sensitivity issue. This allows reliable high-resolution neuromodulation in potential clinical applications with reduced invasive acquisition of propagation measurements for focusing optimization.

Fig. 1

The framework of sensitivity analysis for LIFU neuromodulation resolution. (a) A 2-D cross section of the human head model built from the imaging data, in which the target region is denoted by the white cross and transducer elements on the surface of brain tissues are denoted by red triangles. (b) Illustration of driving signals for ultrasound transducer beam. (c) Ultrasound beam maps simulated with k-Wave toolbox at different sound speed values from to (usually sampled in a potential range of feasible values). Each represents a set of sound speed values for different brain tissues in nth k-Wave simulation. (d) The neuron spike count map at different sound speed values from to .

Fig. 2

Illustration of SONIC simulation results for continuous wave at kHz. (a) An example spike pattern of a single neuron stimulated since simulated with SONIC model. (b) The firing rate of a single neuron during 100 ms stimulation with respect to the intensity.

Fig. 3

The proposed ROR beam optimization framework for sensitivity mitigation. First, the ultrasound propagation from the phased array transducer to any brain region in the given human head model can be simulated with a limited set of reference sound speed values using the k-Wave toolbox. Next, an Equivalent Source Method (ESM) can be used to infer propagation properties with any arbitrary sound speed values from the propagation simulation results. Finally, ROR beamforming algorithm can optimize the beam profile as well as driving signals by comprehensively considering the propagation properties with any potential sound speed values c inferred with ESM.

Fig. 4

(a) The comparison between the simulated amplitude change in propagation using k-wave and the estimation using ESM. (b) The comparison between the simulated phase shift in propagation using k-wave and the estimation using ESM. (c) The average propagation estimation error using ESM with respect to the k-wave propagation simulation.

Fig. 5

The pressure-based intensity beam pattern (top) and the off-target activation area (bottom) of all beamforming methods. The maximal OTAA of each method is achieved with the corresponding value selected. (a) and (e): Conjugate beamforming; (b) and (f): COR; (c) and (g): ROR-1; (d) and (h): ROR-3.

Fig. 6

The pressure-based intensity beam pattern (top) and the off-target activation area (bottom) of all beamforming methods. The minimal OTAA of each method is achieved with the corresponding value selected. (a) and (e): Conjugate beamforming; (b) and (f): COR; (c) and (g): ROR-1; (d) and (h): ROR-3.

Fig. 7

Sensitivity of OTAA to brain tissue sound speed inaccuracy with different beamforming algorithms.

Fig. 8

Worst-case OTAA of different beamforming algorithms with respect to target locations. The feasibility of ROR for most target points near the brain center is validated. The oscillation of OTAA curves shows the evidence that the mechanism of the sensitivity is related to standing waves.