Numerical and experimental evaluation of low-intensity transcranial focused ultrasound wave propagation using human skulls for brain neuromodulation

Abstract

Background

Low-intensity transcranial focused ultrasound (tFUS) has gained considerable attention as a promising noninvasive neuromodulatory technique for human brains. However, the complex morphology of the skull hinders scholars from precisely predicting the acoustic energy transmitted and the region of the brain impacted during the sonication. This is due to the fact that different ultrasound frequencies and skull morphology variations greatly affect wave propagation through the skull.

Purpose

Although the acoustic properties of human skull have been studied for tFUS applications, such as tumor ablation using a multielement phased array, there is no consensus about how to choose a single-element focused ultrasound (FUS) transducer with a suitable frequency for neuromodulation. There are interests in exploring the magnitude and dimension of tFUS beam through human parietal bone for modulating specific brain lobes. Herein, we aim to investigate the wave propagation of tFUS on human skulls to understand and address the concerns above.

Methods

Both experimental measurements and numerical modeling were conducted to investigate the transmission efficiency and beam pattern of tFUS on five human skulls (C3 and C4 regions) using single-element FUS transducers with six different frequencies (150–1500 kHz). The degassed skull was placed in a water tank, and a calibrated hydrophone was utilized to measure acoustic pressure past it. The cranial computed tomography scan data of each skull were obtained to derive a high-resolution acoustic model (grid point spacing: 0.25 mm) in simulations. Meanwhile, we modified the power-law exponent of acoustic attenuation coefficient to validate numerical modeling and enabled it to be served as a prediction tool, based on the experimental measurements.

Results

The transmission efficiency and −6 dB beamwidth were evaluated and compared for various frequencies. An exponential decrease in transmission efficiency and a logarithmic decrease of −6 dB beamwidth with an increase in ultrasound frequency were observed. It is found that a >750 kHz ultrasound leads to a relatively lower tFUS transmission efficiency (<5%), whereas a <350 kHz ultrasound contributes to a relatively broader beamwidth (>5 mm). Based on these observations, we further analyzed the dependence of tFUS wave propagation on FUS transducer aperture size.

Conclusions

We successfully studied tFUS wave propagation through human skulls at different frequencies experimentally and numerically. The findings have important implications to predict tFUS wave propagation for ultrasound neuromodulation in clinical applications, and guide researchers to develop advanced ultrasound transducers as neural interfaces.

1 INTRODUCTION

Due to the mechanical and thermal bioeffects,¹ ultrasound has manifested its applicability and effectiveness not only as a diagnostic tool but also as a therapeutic approach for numerous biomedical applications,^{2, 3} including drug and gene delivery, tumor treatment, and neural modulation.^4-8 In the early 1920s, Harvey and Loomis found that ultrasound was capable of stimulating muscle or nerve tissue under certain conditions.⁹ Inspired by this study, researchers started to explore the application of ultrasound in nerve tissue.¹⁰ Employing ultrasound to stimulate and modulate neural activity has raised the possibility of using ultrasound as a new investigative and therapeutic tool in brain research.¹¹ The past decade has witnessed an explosion of research interest in using low-intensity transcranial focused ultrasound (LI-tFUS) as a potential noninvasive brain neuromodulation tool. In comparison with other noninvasive brain stimulation methods, such as transcranial magnetic stimulation and transcranial direct/alternating current stimulation,^{12, 13} LI-tFUS is promising due to its excellent spatial resolution (<5 mm at 500 kHz) and superior penetration depth (>50 mm at 500 kHz). LI-tFUS has been successfully demonstrated for modulating the human motor cortex,¹⁴ somatosensory cortex, visual cortex, and thalamus.^14-17 However, challenges exist in precisely predicting ultrasound wave propagation through skulls at different frequencies during LI-tFUS neuromodulation,^{18, 19} which is critically important to further study the interaction of ultrasound through the skull, as well as the interaction of ultrasound with the brain for clinical translations.²⁰

The human skull has been considered a virtually impassable barrier for transcranial ultrasound applications for over 50 years.²¹ The acoustic reflection and attenuation caused by the acoustic impedance mismatch between the skull and the water (or the scalp), and the distortion of the ultrasound beam due to the porous structure of the skull makes it impracticable to transmit the required ultrasonic energy to a target region of the brain.²¹ Craniotomy, that is, opening a skull window by removing a section of bone surgically, was needed for ultrasound treatment before the 2000s.²² Over the past two decades, low-frequency (<1 MHz) ultrasound has been found to have a decreased attenuation of the transcranial ultrasound beam.²³ Efforts showed the potential of transmitting high-intensity ultrasound through the skull at relatively low frequencies for therapeutic applications, including tissue ablation (I_SPTA [spatial peak temporal average intensity] > 100 W/cm²) or histotripsy (I_SPTA > 1 W/cm²).²⁴ However, for neuromodulation, low-intensity ultrasound (I_SPTA < 1 W/cm²) is sufficient, and thus, the single-element ultrasound transducer is usually utilized for LI-tFUS neuromodulation, especially considering its ease of use and low cost.²⁵ In this case, being capable of predicting the transcranial ultrasound beam from a single-element ultrasound transducer would be key to achieving successful brain neuromodulation. Given the complex morphology of the human skull, cranial computerized tomography (CT) or magnetic resonance imaging scans of a patient's head are needed before therapeutic applications.²⁶

On the other hand, the exact mechanism of LI-tFUS neuromodulation is still unclear to date. Which ultrasound bioeffects are involved and how they modulate the neural activity remains to be explored. One of the theories is the acoustic radiation force that stems from ultrasound wave propagation can deform the neuronal cell membrane, and alter the permeability of mechano-sensitive ion channels, to eventually modulate the nervous system activity.^27-29 Besides, other underlying mechanisms include intramembrane cavitation, that is, membrane-localized cavitation within two lipid bilayers of the neurons,^{28, 30} and the thermal effect of ultrasound, which may perturb the synaptic junction for neurotransmission.^{29, 31} The lack of clarity on the mechanism of actions not only hinders scholars from ensuring the safe use of LI-tFUS, but also from selecting optimal sonication parameters for brain neuromodulation. Taking an example of neuromodulation for the human primary motor cortex, it is reported that low-frequency (<1 MHz) focused ultrasound (FUS) can inhibit cortical excitability,¹⁴ whereas high-frequency (>1 MHz) unfocused ultrasound can induce cortical excitability.³² It is speculated that the beam size and the transmitted energy of transcranial ultrasound at different frequencies are crucial to the excitation or inhibition of nerve tissue.^33-35

To address the above issues, it is necessary and important to understand the LI-tFUS wave propagation through the human skull at different frequencies to pave the way for the subsequent translational study. Fry et al.^{36, 37} investigated the acoustic properties of the human skull and conducted pioneering studies of trans-skull transmission of FUS beam. Hynynen et al.^{38, 39} further studied the longitudinal and shear ultrasound propagation in human skull bone, especially regarding acoustic characteristics of the human skull for longitudinal sound transmission at multifrequencies (0.27–2.5 MHz). Meanwhile, Aubry et al.^{40, 41} turned their eyes on predicting tFUS wave propagation using numerical computation. By virtue of the detailed information of the skull provided by CT scan images, they found a way to simulate the heterogeneities inside the skull. Based on that, Mueller et al.^{42, 43} further developed detailed numerical modeling to simulate tFUS for human brain neuromodulation, where linear, nonlinear, and elastic wave propagation are simulated. In addition, other reported studies include wave propagation modeling of single-element ultrasound transducer based on finite element method or finite difference method,^{44, 45} exploring the impact of CT image parameters on the accuracy of tFUS simulations,⁴⁶ and the computation efficiency improvement for tFUS wave propagation simulation,^{47, 48} as well as the optimization study of the placement of the single-element ultrasound transducer.⁴⁹

However, the above studies did not fully illuminate the impacts of ultrasound frequency on tFUS transmission efficiency and beam pattern for human skulls using a single-element ultrasound transducer. Major limitations include (1) involving animal (e.g., sheep) skulls instead of human skulls⁴⁵; (2) considering a very limited number of ultrasound frequencies⁴³; (3) neglecting the normal configuration for ultrasound neuromodulation in clinical applications, for example, placing the hydrophone outside the skull and fixing the transducer inside the skull³⁹; (4) lacking experimental measurements or poor agreement between experimental and numerical results.^{43, 15} Those limitations hinder the current numerical model to become a dependable prediction tool for various ultrasound frequencies. We compare both experimental measurement and numerical modeling to investigate the tFUS wave propagation for human brain neuromodulation. Based on the experimental measurement using real human skull samples, transmission efficiency and beam pattern of tFUS were evaluated and quantified to give insight into a dependable prediction tool for LI-tFUS neuromodulation by modifying the empirical formula of power-law exponent of acoustic attenuation coefficient. In addition, the dependence of tFUS wave propagation on FUS transducer aperture size was studied in order to develop appropriate ultrasound transducers in the future.

2 MATERIALS AND METHODS

2.1 Ultrasound parameters

Typical ultrasound sequences for neuromodulation are illustrated in Figure 1. Note that it only includes one single sonication duration without involving interstimulus interval (ISI).²⁵ Usually, ISI needs to be set between each sonication duration for clinical application. To achieve steady-state conditions for acoustic evaluation, each pulse duration includes 10-cycle pulses so that the ultrasound transducers can stabilize their output in the experiment. Although for the simulations, the ultrasound transducers generated pulses continuously. The spatial peak pulse average intensity (I_SPPA) is defined as²⁸

$$$$\begin{equation}{I_{SPPA}} = {\rm{\;max}}\left( {\frac{1}{{PD}}\mathop \int \limits_0^{PD} \frac{{P{{\left( t \right)}^2}}}{Z}dt} \right) \approx {\rm{\;}}\frac{{{P^2}}}{{2Z}} = \frac{{{P^2}}}{{2\rho c}}\end{equation}$$$$(1)

where Z is the acoustic impedance, P is the peak acoustic pressure, ρ is the density of the medium, and c is the sound speed of the medium. To quantify the acoustic transmission efficiency through the skull, we define transmission efficiency as the ratio of transcranial acoustic pressure (or intensity) to acoustic pressure (or intensity) in free water.

FIGURE 1

Typical schematic and key parameters of pulsed ultrasound sequences for neuromodulation. Here, FF represents the fundamental frequency; PD represents the pulse duration; PRP is the pulse repetition period, which equals the inverse of pulse repetition frequency (PRF); SD is the sonication duration.

2.2 Skull samples

The human skull is an assemblage of bones, including frontal bone, parietal, occipital, and temporal bone.⁴³ The temporal bone is usually chosen for transcranial ultrasound applications because it is the thinnest part of the skull and has the lowest transcranial acoustic energy loss. However, in order to modulate the neural activity of some specific parts of cerebral cortex (e.g., parietal lobe and frontal lobe), it is necessary to transmit ultrasound beams through the parietal bone rather than the temporal bone in some applications. For example, Legon et al.¹⁵ transmitted ultrasound waves through the parietal bone to stimulate the somatosensory cortex in the parietal lobe. In this study, five pieces of real human skulls (Figure S1) were provided by Duke Human Anatomy Lab. After cleaning and preserving, each skull was kept sealed and stored in dry and cool places before tests. To understand the tFUS wave propagation for neuromodulation on the human primary motor cortex, the ultrasound beam was transmitted through the corresponding area on the parietal bone (i.e., C3 and C4 regions, Figure S1). The thickness of these target areas of each skull varied from 7 to 9 mm.

2.3 Ultrasound transducers

To generate the required ultrasound waveform, six single-element FUS transducers (Blatek Industries, PA, USA, Figure S2) with different frequencies were used for the tests. These frequencies include 150, 350, 500, 750, 1000, and 1500 kHz. Detailed specifications of each ultrasound transducer, including aperture size, focal length, −6 dB beamwidth, and transmitting sensitivity, are summarized in Table 1. The input voltage was set as 100 Vpp (peak-to-peak voltage) for all the experiments, and the corresponding acoustic pressure output ranges from 0.17 to 1.72 MPa (zero-to-peak pressure) in free water. After the skull attenuation, the transcranial ultrasound pressure was less than 0.3 MPa (zero-to-peak pressure), which is far less than the FDA limits for diagnostic ultrasound (i.e., mechanical index <1.9; derated I_SPPA < 190 W/cm²).⁵⁰ It is believed that such a range of acoustic pressure is suitable for ultrasound neuromodulation applications.^{20, 29} Additionally, it should be noted that the 500 kHz FUS transducer has a relatively larger focal length and −6 dB beamwidth compared to other transducers. We speculated that this was due to the fabrication materials and dimensions being different. Given that the position of the human primary motor cortex is about 20 mm beneath the human skull, the focal length of each single-element ultrasound transducer was chosen close to 30 mm.

TABLE 1. Specification of the focused ultrasound (FUS) transducers

Item	Center frequency (kHz)	Aperture size (mm)	Focal length (mm)	−6 dB beamwidth (mm)	Transmitting sensitivity (kPa/V)
I	150	50	22.9	12.04	1.7
II	350	50	24.9	5.22	5.3
III	500	30	36.0	5.70	3.4
IV	750	30	24.9	2.93	6.2
V	1000	30	27.9	2.63	9.2
VI	1500	30	27.5	1.64	17.2

2.4 Experimental setup

Figure 2 shows the schematic of the overall experimental setup. Before the experiments, the human skulls were degassed using a vacuum pump for 12 h in order to remove the air trapped inside the bones. A water tank was filled with degassed water to avoid interference from the air. The electrical waveform, generated first by a function generator (33250A, Agilent Technologies, CA, USA) and then amplified by a radio frequency power amplifier (75A250A, Amplifier Research Corporation, PA, USA), was used to drive the FUS transducers.²⁵ The skull bone was placed at a distance of 2–4 mm from the transducer and guaranteed a focal spot of ultrasound beam 20–25 mm behind the outside surface of the skull, corresponding to the location of the human primary motor cortex. The ultrasound transducer was aimed at the C3 or C4 region of parietal bone, and its surface was positioned parallel to the outside surface of the skull to reduce the effect of acoustic wave refraction (Figure S3). A needle hydrophone (HNA-0400, Onda Corporation, CA, USA) was placed at the actual focal area behind the skull with a 3-axis positioning system. The information of acoustic pressure was acquired and recorded with a digital oscilloscope (DSO7104B, Agilent Technologies, CA, USA). Then, the acoustic intensity, pressure ratio, and intensity ratio were calculated.

FIGURE 2

Experiment setup: (a) a schematic diagram for all apparatuses; (b) side view of focused ultrasound (FUS) transducer, human skull, and hydrophone

2.5 Simulation model

tFUS wave propagation simulations were performed using k-wave to compare the results from the experiments.^{51, 52} As a numerical model that utilizes k-space corrected pseudo-spectral time-domain schemes, k-wave requires fewer spatial and temporal grid points to guarantee the accuracy of the simulation compared to finite-difference time-domain schemes-based numerical model.^{51, 52} Given this, it has been used widely for acoustic simulation of highly heterogeneous media and has proved its accuracy for transcranial ultrasound simulation.^{43, 53}

To develop a reliable acoustic simulation model, the 2D morphology of each skull (Figure S4A) was obtained using a CT scanner (SOMATOM Definition Flash, Siemens Healthineers, Erlangen, Germany) with an X-ray tube voltage of 120 kVp (peak kilovoltage). The 2D cranial CT image was taken in the sagittal plane of the skull at a 5 mm slice thickness. To simulate the highly heterogeneous media, the data of cranial CT images were loaded into MATLAB (R2020a, MathWorks, MA, USA), and the acoustic parameters (speed of sound and density) were calculated based on CT Hounsfield units (H) and porosity (ψ).⁴³ Figure S4B shows the calculated acoustic impedance (Z) distribution, and the corresponding calculation equations are listed below:

$$$$\begin{equation}\psi {\rm{\;}} = {\rm{\;}}1 - \frac{H}{{{\rm{max}}\left( H \right)}}\end{equation}$$$$(2)

$$$$\begin{equation}{c_{skull}} = {c_{water}}{\rm{\;}} \times \psi + {c_{bone}} \times \left( {1 - \psi } \right)\end{equation}$$$$(3)

$$$$\begin{equation}{\rho _{skull}} = {\rho _{water}}{\rm{\;}} \times \psi + {\rho _{bone}} \times \left( {1 - \psi } \right)\end{equation}$$$$(4)

$$$$\begin{equation}{Z_{skull}} = {\rho _{skull}}{\rm{\;}} \times {c_{skull}}\end{equation}$$$$(5)

$$$$\fontsize{9}{11} \begin{equation}{\alpha _{skull}} = {\rm{\;}}\left[ {{\alpha _{0\_{\rm{min}},{\rm{\;}}skull}} + \left( {{\alpha _{0\_{\rm{max}},skull}} - {\alpha _{0\_{\rm{min}},skull}}} \right) \times {\psi ^{0.5}}} \right] \times {f^y}\end{equation}$$$$(6)

where ψ is the porosity, H is the Hounsfield unit value, and max(H) means the maximum Hounsfield unit value in the CT image. c is the sound speed of the medium, ρ represents the density of the medium, and α is the attenuation coefficient of media in Np/m, whereas α₀ is the power-law prefactor in Np/(MHz m). Moreover, f indicates the ultrasound frequency, and y is the power-law exponent of acoustic attenuation coefficient. Corresponding values of the above acoustic parameters are summarized in Table 2.⁴³ It should be noted that there are currently no reliable references for the power-law exponent of acoustic attenuation coefficient on human parietal bone. We derived the value of power-law exponent based on experimental measurements under various ultrasound frequencies. The power-law exponent values can be found in Section 3.3.

TABLE 2. Acoustic parameters of media

Sound speed (m/s)	Density (kg/m^3)	Power-law prefactor (Np/(MHz/m))
$${C_{water}} = 1482$$	$${\rho _{water}} = 1000$$	$${\alpha _{0\_min,\;skull}} = 21.5$$
$${C_{bone}} = 3100$$	$${\rho _{bone}} = 2200$$	$${\alpha _{0\_max,skull}} = 208.9$$

In order to precisely quantify the dimension of tFUS beam, we developed a high-resolution acoustic model with a grid point spacing of 0.25 mm. The computational domain was 1023 × 625 grid points, covering an area of 255.75 × 156.25 mm². Courant–Friedrichs–Lewy stability criterion (CFL number) was selected as 0.05, and spatial discretization was chosen as seven points per wavelength to obtain stable solutions for all simulations.⁴³ Considering that increasing the ultrasound frequency would increase the computation time and there were 60 cases of simulation need to be carried out, we did not perform the numerical modeling in 3D domain this time. We utilized a regular commercial computer (Intel Core i5-8500B, 6 cores, 3.0 GHz, 8 GB RAM) to run the 2D simulation, and it typically takes 1 h to complete the simulation process for 350 kHz case and 4 h for 1500 kHz case. Furthermore, the elastic wave was not considered in simulations as the incident angles of tFUS beam are far less than 20°. It is believed that the role of shear waves was not important in such conditions.^{38, 43} We confirmed this phenomenon by comparing the nonelastic simulation and elastic simulation for skull #3, C4 region at a frequency of 350 kHz (Figure S5).

3 RESULTS

3.1 tFUS transmission efficiency

The FUS transmission efficiency determines how much acoustic energy can be transmitted through a human skull. In this section, experiments were first conducted, followed by simulation validation. Figure 3 illustrates the relationship between ultrasound frequency and acoustic transmission efficiency through the skull (n = 10), including acoustic intensity (i.e., I_SPPA) ratio and pressure (i.e., max pressure) ratio. Transmission efficiencies on both the C3 and C4 regions of each skull were then summarized. The results illustrated that lower ultrasound frequency generally contributes to higher transmission efficiency, which is in agreement with previous studies.^{38, 39} In terms of intensity ratio, the frequency of 150 kHz could reach acoustic intensity transmission efficiency as high as 20%–30%, whereas the frequency of 1000 kHz could only achieve an acoustic intensity transmission efficiency of less than 5%. For the pressure ratio, frequencies less than 500 kHz could provide an acoustic pressure transmission efficiency larger than 30%, whereas a frequency of 1500 kHz could merely provide 5%. Besides, it was found that the transmission efficiency at 500 kHz frequency was higher than at 350 kHz frequency. As the aperture size of the 500 kHz ultrasound transducer is 30 mm but the 350 kHz ultrasound transducer has an aperture size of 50 mm, we speculated the acoustic refraction difference induced by disparate transducer aperture size might be the reason behind this effect.⁵⁴ Detailed study and discussion are presented in Sections 3.3 and 4.

FIGURE 3

Experimental results of the dependence of the transcranial focused ultrasound (tFUS) transmission efficiency on various ultrasound frequencies, including (a) intensity ratio and (b) pressure ratio (n = 10)

Based on the experimental results, simulation studies were further conducted and validated. To exclude the impact of ultrasound transducer aperture size variation, we fixed it as 30 mm for the following numerical studies in Sections 3.1 and 3.2. Figure 4 illustrates the comparison between experimental and simulation results in terms of tFUS transmission efficiency (n = 10). A good match between experimental measurements and numerical modeling can be observed, validating the reliability of the simulation. Overall, both experimental and simulation results suggested that ultrasound at a frequency larger than 750 kHz leads to a relatively low tFUS transmission efficiency, corresponding to an intensity ratio of less than 5% and a pressure ratio of less than 20%.

FIGURE 4

Comparison between experiment and simulation results in terms of the transcranial focused ultrasound (tFUS) transmission efficiency for various ultrasound frequencies, including (a) intensity ratio and (b) pressure ratio. The standard deviation refers to the different skulls. The p-values (*) of one-sample t-test are larger than 0.05. (n = 10)

3.2 tFUS beam pattern

Besides the tFUS transmission efficiency, another critical factor is the tFUS beam pattern. The tFUS beam pattern determines the impact region in the brain. In this section, we first compared the tFUS beamwidth of experimental measurements and numerical modeling at 350 kHz frequency. After validating the simulations in terms of beamwidth, the tFUS beam patterns at different frequencies, including 150, 350, 500, 750, 1000, and 1500 kHz, were simulated and analyzed. Figure S6 illustrates the 350 kHz tFUS beamwidth at focal depth for experimental measurement and numerical modeling. Besides the side lobes, the simulated beamwidth was generally in-line with our experimental measurement, validating the reliability of transcranial ultrasound wave propagation simulation.

To investigate the ultrasound frequency effect on transcranial tFUS beam pattern, the ultrasound frequency was varied, whereas other parameters were kept constant, for example, the aperture size of the FUS transducer, the curvature of the FUS transducer surface, and the position and angle of the FUS transducer. The tFUS beam patterns for six different frequencies were analyzed and shown in Figure 5. It shows that a higher ultrasound frequency would generate a narrower −6 dB beamwidth. To evaluate such variations, all the −6 dB beamwidths of six frequencies, five skulls, and two regions (C3 and C4 regions) were calculated and are shown in Figure 6. The value of −6 dB beamwidth decreased logarithmically with the increase of ultrasound frequency. It should be noted that the 1500 kHz ultrasound case only involved skull #2 and skull #4, with other beam patterns of the skulls non-distinguishable under this frequency. In addition, the −6 dB beamwidth of FUS in free water was simulated and summarized in Figure 6 for comparison.

FIGURE 5

Simulation results of transcranial focused ultrasound (tFUS) pressure distribution over human skull #3, C4 region, for (a) 150 kHz, (b) 350 kHz, (c) 500 kHz, (d)750 kHz, (e) 1000 kHz, and (f) 1500 kHz

FIGURE 6

Simulation results of the −6 dB beamwidth (i.e., full width at half maximum, FWHM) of transcranial focused ultrasound (tFUS) beam pattern and free water focused ultrasound (FUS) beam pattern for various ultrasound frequencies (n = 10)

3.3 Impact of tFUS modeling

In this work, we also investigated the effect of the aperture size of the FUS transducer and the acoustic attenuation coefficients of skull bone. The experimental studies presented in Section 3.1 indicated that the 500 kHz FUS transducer with a 30 mm aperture size provided a higher transmission efficiency than the 350 kHz FUS transducer with a 50 mm aperture size. To explain such unexpected results, we simulated the tFUS wave propagation at 350 kHz for various aperture sizes of the transducer, including 30, 35, 40, and 45 mm on skull #3, C4 region (n = 1). The curvature of the FUS transducer surface and the positioning and steering of the FUS transducer were fixed in this simulation study. Figure S7 shows the tFUS beam pattern profile for four different aperture sizes. To evaluate and quantify the transmission efficiency changes for different aperture sizes of the FUS transducer, the acoustic pressure ratio was analyzed as a function of aperture size, shown in Figure 7.

FIGURE 7

The dependence of acoustic pressure ratio on aperture size of the 350 kHz focused ultrasound (FUS) transducer (n = 1)

In addition to parameters related to the FUS transducer, acoustic parameters of the medium are also crucial to reliable tFUS modeling. Regarding the acoustic attenuation of the medium, scholars believed that it obeys the frequency power law,^{55, 56} which was expressed as

$$$$\begin{equation}\alpha {\rm{\;}} = {\alpha _0}{\rm{\;}} \times {f^y}\end{equation}$$$$(7)

The power-law exponent of acoustic attenuation coefficient y is dependent on the acoustic loss characterization of the medium, and it varies with the ultrasound frequency range. Bamber summarized the values of y for various ultrasound frequencies and biological tissues.⁵⁷ For the skull bone, the value of y ranges from 0.5 to 2.1. However, this data originated from a paper published 70 years ago.⁵⁸ It was not clear what parts of skull bone were tested for sonication. Thus, we further evaluated the relationship between the value of y and ultrasound frequency for human parietal bone. Based on several initial simulations, we found that the acoustic absorption of the skull was too weak if the y equals 0.5, whereas it was too strong if the y was close to 1. After analyzing the two regions (C3 and C4 regions) for each of the five skulls, we narrowed down the range of the y using a binary search algorithm, and eventually estimated it as a function of ultrasound frequency. As illustrated in Figure 8, the empirical formula of this function obeyed the power law. With the increment of ultrasound frequency, the value of y infinitely approached 1. A possible explanation for this is the stronger acoustic dispersion caused by higher ultrasound frequency.^{55, 56} Moreover, the reason why the power-law exponent of acoustic attenuation coefficient y cannot be equal to 1 is due to the singularity issue of Kramers–Kronig relations.⁵⁶ This modified empirical formula of acoustic attenuation power-law exponent might help develop a dependable prediction tool for LI-tFUS neuromodulation.

FIGURE 8

The dependence of acoustic attenuation power-law exponent of human skulls on ultrasound frequency (n = 10)

4 DISCUSSIONS

To verify these experimental results in terms of transmission efficiency, we compared them with published data by Lee et al.^{16, 59, 60} and Legon et al.^{15, 61, 62} Lee et al. conducted three tFUS neuromodulation studies on human subjects using three ultrasound frequencies at 210, 250, and 270 kHz. They indicated the intensity ratios were 22.50% ± 1.25%,⁵⁹ 24% ± 8%,⁶⁰ and 18% ± 5%,¹⁶ respectively. Their results closely match our experimental results. Furthermore, Legon et al. only used the ultrasound frequency of 500 kHz in their experiment. Intensity ratios of 24.69%,¹⁵ 24.72%,⁶¹ and 29% ± 4%⁶² were reported, which manifested a higher tFUS transmission efficiency than our data. This is likely due to the varying dimensions of human skulls and the different locations of the target area. Legon et al. utilized a 6-mm-thick fragment of human cortical bone for the experiment, and the ultrasound transducer was aimed at the CP3 region.¹⁵ In general, thicker bone induces more acoustic attenuation, and various regions of parietal bone may have different levels of porosity. Besides, different skull locations may induce various degrees of ultrasound refraction due to the curvature of bone surface.

Although the transmission efficiency for the high-frequency ultrasound (>750 kHz) is relatively low, it still can be useful for tFUS human applications. This is due to the fact that a higher frequency contributes to a narrower −6 dB beamwidth and a higher transmit sensitivity, thus generating a larger I_SPPA. For example, with a 1000 kHz FUS transducer, a maximum pressure of 0.92 MPa and an I_SPPA of 28.6 W/cm² in free water could be reached, for an input voltage of 100 Vpp. Accordingly, the transcranial acoustic pressure (i.e., max pressure) and intensity (i.e., I_SPPA) were about 111.6 kPa and 0.43 W/cm², respectively. Such a level of transcranial acoustic energy could be applied to modulate the brain according to a previous study.⁶³

According to tFUS beam patterns in Figure 5, it was found that a portion of the acoustic energy was reflected by the surface of skull bone due to the acoustic mismatch. This kind of reflection may enhance the possibility of overheating of the ultrasound transducer. Besides, in the acoustic pressure field, the maximum pressure was located within the skull bone. The anisotropic heterogeneous porous microstructure of skull bone confined and attenuated the transmitted acoustic energy due to reflection and scattering.^{64, 65} Similar phenomena were reported by simulation studies of Mueller et al. and Phipps et al.^{43, 66} This may induce concerns about the heating of human skulls during the process of tFUS brain neuromodulation. Furthermore, it was observed that the beam pattern of 150 kHz ultrasound lost its focal profile to some extent. This might be attributed to the wavelength of 150 kHz ultrasound (∼10 mm) is larger than the size of bone microstructure (∼5 mm).⁶⁴ In addition, as the attenuation of 1500 kHz ultrasound is high, it was hard to distinguish its beam pattern, especially the focal area. It indicated that such high-frequency ultrasound cannot form an effective focal area of beam pattern for targeting a desired area of the brain.

Although lower frequency could easily cover a larger region of interest, it demonstrated a poor spatial resolution. Thus, it is applicable for modulating the whole or major part of a human cortex. On the other hand, the higher spatial resolution obtained at a higher frequency makes it possible to modulate a specific area of the human cortex without affecting the surrounding area. Therefore, the selection of ultrasound frequency should depend on the purpose and target of neuromodulation. It is expected that, by taking advantage of the collaboration of various ultrasound frequencies and acoustic energy, desired ultrasound signals might be transmitted into the human brain for neuromodulation, to induce excitatory or inhibitory influence on neuron activity of specific brain structure, to develop the potential of the neural interface, and to further transfer complex information and instructions.⁶⁷

By studying the influence of aperture size on tFUS beam pattern (Figures S7 and 7), it was apparent that the larger aperture size led to a more defined focal area. Moreover, given that the curvature of the FUS transducer surface is larger than that of the bone surface of skull #3, C4 region, the refraction of the ultrasound beam was stronger for the larger aperture size. That was because both ends of the transducer surface were not positioned parallel to the bone surface compared to the smaller aperture size. Such stronger ultrasound refraction inhibited a higher efficiency tFUS transmission. It was observed that the transcranial acoustic pressure decreased linearly with an increase of aperture size. This is because the larger aperture size of transducer contributes to higher refraction of ultrasound waves. Considering the complex morphology of the human skull, it is not recommended to increase the tFUS transmission efficiency by changing the aperture size of the FUS transducer. Nevertheless, these results inspired us to further develop a flexible ultrasound transducer that can be attached to the surface of skull bone perfectly, to enhance the tFUS transmission efficiency as an advanced neural interface.^{68, 69}

5 CONCLUSIONS

In this paper, by combining experimental measurements and numerical modeling, we investigated the tFUS transmission efficiency and beam pattern at six ultrasound frequencies on five human skulls. The results suggested an exponential decrease in transmission efficiency and a logarithmic decrease of −6 dB beamwidth with the increase of ultrasound frequency. Such findings can help scholars address questions regarding the amounts of acoustic energy transmitted into the brain, and the size of brain tissue volume impacted for human neuromodulation. Moreover, the impacts of FUS transducer aperture size and acoustic attenuation were analyzed, which paves the way to develop a reliable tFUS numerical modeling for fabricating advanced neural interfaces as well as predicting transcranial ultrasound propagation.

To best mimic the physical environment of tFUS brain neuromodulations, future works should be focused on the tFUS wave propagation experiment using a human cadaver brain and validate the associated simulation. It is postulated that a confined space (i.e., an intact skull with a cadaver brain) has different acoustic boundaries and frequency-dependent characteristics as compared to the free space (i.e., a calvaria immersed in degassed water). Furthermore, a practical concern for computational costs centers on calculation time and computer memory for tFUS numerical modeling. A rapid 3D modeling method that can run on an ordinary commercial computer would be essential for the translational investigation of ultrasound neuromodulation. We hope this work can be useful for scholars to predict the tFUS wave propagation in future human translational ultrasonic stimulation research, and additionally, it may advance ultrasound transducer development.

ACKNOWLEDGMENTS

The authors would like to acknowledge the funding support from the American Heart Association/American Stroke Association (innovative project award to WF 20IPA35360039). The authors also thank the equipment support from Dr. Yun Jing at Pennsylvania State University and the acoustic simulation inspiration from Dr. Gianmarco Pinton at University of North Carolina at Chapel Hill.

CONFLICT OF INTEREST

The authors have no conflicts of interest to disclose.

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DATA AVAILABILITY STATEMENT

The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials. Raw data that support the findings of this work are available from the corresponding author, upon reasonable request.