Computational modeling and minimization of unintended neuronal excitation in a LIFU stimulation

Abstract

The neuromodulation effect of low-intensity focused ultrasound (LIFU) is highly target-specific. Unintended off-target neuronal excitation can be elicited when the beam focusing accuracy and resolution are limited, whereas the resulted side effect has not been evaluated quantitatively. There is also a lack of methods addressing the minimization of such side effects. Therefore, this work introduces a computational model of unintended neuronal excitation during LIFU neuromodulation, which evaluates the off-target activation area (OTAA) by integrating an ultrasound field model with the neuronal spiking model. In addition, a phased array beam focusing scheme called constrained optimal resolution beamforming (CORB) is proposed to minimize the off-target neuronal excitation area while ensuring effective stimulation in the target brain region. A lower bound of the OTAA is analytically approximated in a simplified homogeneous medium, which could guide the selection of transducer parameters such as aperture size and operating frequency. Simulations in a human head model using three transducer setups show that CORB markedly reduces the OTAA compared with two benchmark beam focusing methods. The high neuromodulation resolution demonstrates the capability of LIFU to effectively limit the side effects during neuromodulation, allowing future clinical applications such as treatment of neuropsychiatric disorders.

Figure 1

The computational modeling method of unintended neuronal excitation during LIFU stimulation. (a) A 2-D human head model with a target point denoted by the red circle and ultrasound transducer elements denoted by white triangles. (b) An illustrative figure of the input signals for phased array transducer elements to focus the beam. (c) The ultrasound intensity distribution in the human head model generated by the transducer beam, simulated with the k-Wave toolbox. (d) The elicited neuronal spiking patterns of on-target and off-target brain regions, simulated with SONIC model given the ultrasound waveform (500 kHz continuous wave), intensity (0.078 and 0.175 W/cm${}^2$ for on-target and off-target regions), and the stimulation duration (100 ms), etc., of that region. (e) The map that demonstrates the number of neuronal spikes elicited in different brain regions. The highlighted region except the target point is defined as OTAA, showing the influence of unintended neuronal excitation.

Figure 2

The number of neuronal spikes elicited by continuous-wave (duration: 100 ms) and pulsed-wave (duration: 100 ms; pulse repetition frequency (PRF): 1000 Hz; duty cycle: $36\%$) stimulation simulated with the SONIC model. The dependence of neuronal spike counts on LIFU intensities during continuous-wave and pulsed-wave stimulations is demonstrated.

Figure 3

The beam patterns and neuronal spike patterns of transcranial stimulation with single transducer array, demonstrating the minimized OTAA of CORB compared with two benchmarks. The distance between the target point and array is approximately 7.33 cm. (a–c): Approximate beam patterns for continuous-wave stimulation generated by the conjugate benchmark, the off-target suppression benchmark, and CORB, respectively. The color maps demonstrate the spatial distribution of mean ultrasound intensity normalized by the target signal intensity (0.078 W/cm${}^2$). (d–f): Neuronal spike count map of conjugate benchmark, the off-target suppression benchmark, and CORB, respectively, in a continuous-wave LIFU stimulation (target intensity: 0.078 W/cm${}^2$; duration: 100 ms). Ultrasound pressures at all other points are scaled proportionally to the target based on the mean intensity distributions in (a)–(c). (g): The OTAA in log-scale with different stimulation intensities (duration: 100 ms). (textbfh) The OTAA in log-scale with different stimulation durations (target intensity: 0.078 W/cm${}^2$).

Figure 4

The beam patterns and neuronal spike patterns of intracranial stimulation with single transducer array, demonstrating the minimized OTAA of CORB compared with two benchmarks. The location of the target is the same as in Fig. 3, whereas the distance between the target point and array is approximately 5.71 cm. (a–c) Approximate beam patterns for continuous-wave stimulation generated by the conjugate benchmark, the off-target suppression benchmark, and CORB, respectively. The color maps demonstrate the spatial distribution of mean ultrasound intensity normalized by the target signal intensity (0.078 W/cm${}^2$). (d–f) Neuronal spike count map of conjugate benchmark, the off-target suppression benchmark, and CORB, respectively, in a continuous-wave LIFU stimulation (target intensity: 0.078 W/cm${}^2$; duration: 100 ms). Ultrasound pressures at all other points are scaled proportionally to the target based on the mean intensity distributions in (a–c). (g) The OTAA with different stimulation intensities (duration: 100 ms). (h) The OTAA with different stimulation durations (target intensity: 0.078 W/cm${}^2$).

Figure 5

The beam patterns and neuronal spike patterns of intracranial stimulation with double transducer arrays, demonstrating the minimized OTAA of CORB compared with two benchmarks. The location of the target is the same as in Fig. 4. The distance between the target point and the left array is approximately 7.35 cm. (a–c) Approximate beam patterns during a pulse of $T=0.36$ ms generated by the conjugate benchmark, the off-target suppression benchmark, and CORB, respectively. The color maps demonstrate the spatial distribution of mean ultrasound intensity normalized by the target signal intensity in the pulse (0.90 W/cm${}^2$). (d–f) Neuronal spike count map of conjugate benchmark, the off-target suppression benchmark, and CORB, respectively, in a pulsed-wave LIFU stimulation (target intensity: 0.90 W/cm${}^2$; duration: 100 ms; duty cycle: $36\%$; PRF: 1 kHz). Ultrasound pressures at all other points are scaled proportionally to the target based on the mean intensity distributions in (a–c). (g) The OTAA with different stimulation intensities (duration: 100 ms; duty cycle: $36\%$; PRF: 1 kHz). (h) The OTAA with different stimulation durations (target intensity: 0.61 W/cm${}^2$; duty cycle: $36\%$; PRF: 1 kHz). (i) The OTAA with different duty cycles given the fixed pulse duration (target intensity: 0.61 W/cm${}^2$; duration: 100 ms).

Figure 6

The beam patterns and neuronal spike patterns of intracranial stimulation using double transducer arrays, demonstrating the minimized OTAA of CORB compared with two benchmarks. The distance from the target point to the bottom array is approximately 8.18 cm, and the distance to the left array is approximately 13.73 cm. (a–c) Approximate beam patterns during a pulse of $T=0.36$ ms generated by the conjugate benchmark, the off-target suppression benchmark, and CORB, respectively. The color maps demonstrate the spatial distribution of mean ultrasound intensity normalized by the target signal intensity in the pulse (0.70 W/cm${}^2$). (d–(f)) Neuronal spike count map of conjugate benchmark, the off-target suppression benchmark, and CORB, respectively, in a pulsed-wave LIFU stimulation (target intensity: 0.70 W/cm${}^2$; duration: 100 ms; duty cycle: $36\%$; PRF: 1 kHz). Ultrasound pressures at all other points are scaled proportionally to the target based on the mean intensity distributions in (a–c). (g) The OTAA with different stimulation intensities (duration: 100 ms; duty cycle: $36\%$; PRF: 1 kHz). (h) The OTAA with different stimulation durations (target intensity: 0.61 W/cm${}^2$; duty cycle: $36\%$; PRF: 1 kHz). (i) The OTAA with different duty cycles given the fixed pulse duration (target intensity: 0.61 W/cm${}^2$; duration: 100 ms).

Figure 7

Approximated OTAA and lower bound plotted in log-scale for a single-array system with analytical approximations in homogeneous white matter/CSF. Solid black curves denote the actual $S(\mathit{w})$ of the conjugate benchmark. The optimum of formulation (5) is denoted by dashed black curves. The red curves denote the intermediate far-field approximation (S-7) of the conjugate benchmark. The blue curve denotes the lower bound $S_{\mathit{LB}}$.