A FUS transducer (WS100-0.5-P38, Ultran Group, State College, PA, USA) was actuated by a sinusoidal electrical waveform (function generator, 33500B, Keysight, Santa Rosa, CA, USA) that was amplified by a linear power amplifier (240L, Electronics and Innovations, Rochester, NY, USA) with impedance matching. The acoustic pressure profiles across the three different fundamental frequencies (400, 500, and 600 kHz) were mapped with a needle hydrophone (HNC-200, Onda Corp., Sunnyvale, CA, USA) mounted to a 3-axis robotic linear stage (Bi-Slides, Velmex Inc., Bloomfield, NY, USA), in a water tank degassed to <2 ppm oxygen (K-7512 ChemMets kit, Chemetrics, Midland, VA, USA), using an established method [38]. The pressure profile longitudinal to the center of the sonication path was mapped over a 7×3 cm area in 1-mm steps, with a 5-mm gap from the exit plane of the transducer (the colormap represents the range of acoustic pressure corresponding to the two acoustic intensities used in the present study) (Fig. 1). The gap was introduced to avoid potential contact of the hydrophone tip with the transducer surface. The location of the maximum pressure was identified as the focal coordinate, and the area perpendicular to the sonication axis was also mapped covering 3×3 cm. The focal dimension (i.e., length and diameter of the focus defined in the area bound by full width at half-maximum of the pressure) and the focal distance across different frequencies are listed in Table 1. To depict the area proximal to a focal center, the spatial profile encompassing the full width at 90% maximum of the pressure was delineated with dotted lines across the frequencies (Fig. 1). The magnitude of acoustic pressure at the acoustic focus with respect to input voltage was also measured at each frequency using a hydrophone that was separately calibrated across the frequencies (HNR-0500, 2.5-mm probe diameter, Onda Corp.). The frequency calibration was needed to circumvent the need for estimating the frequency response function and sensitivity for the transducer and electronic system. To provide equivalent pressure amplitude across three fundamental frequencies at the focus, the tip of a calibrated hydrophone was placed at the focal center, and the input voltage to the transducer was adjusted until the desired level of voltage value from the hydrophone was recorded at each frequency.

Three types of media having different porosities were used. Melamine foam blocks (IEXL21, Sponge Outlet, Kenmore, NY, USA), having a pore size ranging between ~150-200 µm (Fig. 2A), were cut to 50×45×35 mm (width×height×thickness) dimensions and hydrated in phosphate-buffered saline (PBS; Thermo Fisher, Waltham, MA, USA). A dehydrated PVA foam (AION Co. Ltd., Osaka, Japan), with a smaller porosity than the melamine foam (~80-100 µm) (Fig. 2B), was cut thinner (48×48×6 mm) than the melamine foams (to promote hydration in PBS using a vacuum chamber). The hydration increased the thickness of the PVA blocks to ~7 mm. To make agar hydrogel blocks, low gelling-temperature agar (A4018, Millipore Sigma, Burlington, MA, USA) was dissolved in PBS at 2.5% weight concentration (50°C) and poured into a 30×30×10 mm mold to gel in room temperature, mimicking the porosity of neuropil [37,39]. After preparation, the various media blocks were individually inserted into a 3D-printed chamber (Form3, Formlabs, Somerville, MA, USA) containing the TbO dye solution (T3269, Millipore Sigma, prepared in a 25 µg/mL concentration in PBS). The chambers were designed with slots to accommodate the different focal distances to position the acoustic focus on the front surface of the media blocks (Fig. 2C). The wall of the chamber was lined with a 2.5-mm-thick rubber pad to absorb acoustic energy.

FUS was applied in a pulsed manner (with a PD of 100 ms) every second for 10 minutes across the frequencies of 400 kHz, 500 kHz, and 600 kHz. The initial values for PD and repetition frequency (1 Hz) were chosen based on the previous study that examined the acoustic streaming effects on TbO dye infiltration in melamine foam at 200 kHz [29]. Two sets of data were collected using an I_SPPA of 3 W/cm² and 4 W/cm² (corresponding to 597.8 and 684.8 kPa peak-to-peak pressure, respectively). Thus, the maximum mechanical index used in this part of experiment was 0.54 (in the case of 400 kHz given at 4 W/cm² I_SPPA). Factoring in a 10% duty cycle operation, the spatial-peak temporal-averaged intensities (I_SPTA) were 0.3 W/cm² and 0.4 W/cm², respectively. Ten measurements were taken for each parameter in a randomized and balanced fashion, with 30% volume of fresh dye solution replaced in-between. The temperature in the PBS-dye bath was recorded (4425 Traceable Workhorse Thermometer, Traceable Products, Webster, TX, USA) at the beginning and end of sonication. The process was repeated for trials involving agar hydrogel blocks.

Based on the frequency that yielded the highest dye infiltration to the melamine foam (400 kHz at 4 W/cm² I_SPPA; see Frequency-dependent degree of dye infiltration to melamine foam in "Results"), the effect of variable PDs on dye infiltration was assessed by sonicating melamine and PVA foam blocks. Agar gel was not used in this part of the experiment because the agar gel did not allow any detectable dye infiltration, being dominated by a passive diffusional process (see Dye infiltration to agar hydrogel blocks in "Results"). Five PDs were used (50, 75, 100, 125, and 150 ms) with a repetition frequency of 1 Hz. An I_SPTA of 0.4 W/cm² was maintained across the measurement, and accordingly, the I_SPPA was varied to 8, 5.3, 4, 3.2, and 2 W/cm², respectively (corresponding o pressure levels of 972.8, 792.1, 684.8, 615.3, and 489.1 kPa peak-to-peak) whereby the maximum mechanical index was 0.77 (in the case 50 ms PD at 8 W/cm² I_SPPA). To allow visible dye infiltration, accounting for the smaller pores in the PVA foam, the overall sonication duration was extended to 15 minutes, and the process was repeated across the five different PD conditions (n=10 for each condition).

Upon completion of sonication, the foam/agar blocks were imaged with the sonicated surface down over a high-resolution flatbed photo scanner (Epson Perfection V600 Photo, Epson, Suwa, Japan) to measure the diameter of dye infiltration at the focal location. The blocks were then cut along the center of the acoustic focus and re-imaged on the inner sectional surfaces to measure the depth of infiltration (example shown in Fig. 3). Measurement analysis was conducted through ImageJ software (version 1.53i, https://imagej.nih.gov/ij/). The color image was split into red-green-blue channels and an 8-bit red-channel grayscale image (bit depth ranging from 0 to 255, inverted range) having a value ≥40 was used to visualize the area of dye infiltration. Kruskal-Wallis one-way analysis of variance (ANOVA) was performed to compare dye infiltration (in terms of depth and diameter) across the frequencies and PDs, followed by the Tukey honest significant difference (HSD) post-hoc test for multiple comparisons (MATLAB R2021b, MathWorks, Natick, MA, USA). In addition, a paired-sample permutation test was conducted to evaluate changes in bath temperature observed across experimental conditions (MATLAB R2021b; number of permutations=10,000).

Despite the use of an extremely low acoustic intensity in the current experimental setting, the PBS-dye solution was not degassed and thus may have been susceptible to the possibility of cavitation. Therefore, acoustic emission detection (AED) was employed to detect the presence of cavitation that might have affected the dye infiltration during the application of FUS. To do so, a broadband ultrasound transducer (0.5 MHz, V318-SU, Olympus NDT, Waltham, MA, USA) was placed in the PBS bath (~10 ppm oxygen content, not degassed), 10 mm away toward the site of target focus, and continuous sonication (400 kHz) was applied at 4 and 5 W/cm² I_SPPA for ~3 s. The transducer served as an emission detector and the signals were recorded in a frequency spectrum (0-2 MHz range, with 1-kHz steps) and averaged (n=10 measurement). To induce cavitation at these low intensities, ultrasound microbubbles were added to the bath (0.1 µL/mL volume concentration; Definity, Lantheus, Billerica, MA, USA), and the emission spectra were separately recorded at 5 W/cm² I_SPPA.

In the analysis of the dye infiltration diameter from sonication using an I_SPPA of 3 W/cm² (Fig. 4A), Kruskal-Wallis one-way analysis of variance (ANOVA) revealed a frequency-dependent difference (F(2,27)=47.6, P<0.001). The use of 400 kHz frequency condition induced a wider diameter of infiltration (17.4±1.0 mm; average±standard deviation, n=10) than 500 kHz and 600 kHz (12.2±4.9 mm and 2.6±3.2 mm, respectively; post-hoc Tukey HSD, all P<0.05) (Fig. 4A). The use of 500 kHz yielded a greater diameter than 600 kHz (post-hoc Tukey HSD, P<0.05) (Fig. 4A). A frequency-dependent difference was also found in terms of dye infiltration depth (F(2,27)=34.4, P<0.001) (Fig. 4B). Post-hoc comparisons showed that the depths of infiltration using frequencies of 400 and 500 kHz (8.5±0.5 mm and 6.4±2.8 mm, respectively) were significantly greater those when 600 kHz was used (2.1±1.0 mm; post-hoc Tukey HSD, P<0.03 following ANOVA), with the greatest depth observed with the 400 kHz condition.

The trials utilizing an I_SPPA of 4 W/cm² also resulted in a frequency-dependent difference in the dye infiltration diameter (ANOVA, F(2,27)=77.0, P<0.001) (Fig. 4C). Specifically, 400 kHz generated a wider diameter of infiltration (17.2±2.4 mm), than 500 kHz and 600 kHz (post-hoc Tukey HSD, all *P<0.05 (Fig. 4); 11.7±2.4 mm and 3.7±2.6 mm, respectively). The infiltration diameter from sonication using 500 kHz was significantly wider than that obtained using 600 kHz (post-hoc Tukey HSD, *P<0.05). There was also a frequency-dependent difference in the depth of dye infiltration (ANOVA; F(2,27)=108.6, P<0.001) (Fig. 4D). Pair-wise comparison after ANOVA revealed that the use of 400 kHz showed a significantly greater depth of infiltration (9.4±0.9 mm) than the use of 500 or 600 kHz (6.2±1.3 mm and 2.1±1.1 mm; post-hoc Tukey HSD, all P<0.001). When the infiltration depths and diameter were compared between the two intensities at each frequency, a greater infiltration depth was observed only at 400 kHz (two-tailed t-test, P<0.001; noted as *** in Fig. 4B and D).

Lack of visible dye infiltration on the sonicated surfaces of the agar hydrogel blocks prevented any diameter measurements (an example shown in Fig. 3B). The infiltration depths in agar hydrogel blocks, resulting from intensities of 3 and 4 W/cm², were much lower (all <1.5 mm) than those measured in melamine foam across the frequency range. ANOVA did not reveal a frequency-dependent difference in dye infiltration depth among any of the frequencies at both intensities (P>0.05; F-value, P-value) (Fig. 5).

ANOVA revealed a PD-dependent difference upon analysis of the diameter of dye infiltration to melamine foam (F(4,45)=34.81, P<0.001) (Fig. 6A). A pair-wise comparison determined that a PD of 75 ms resulted in a significantly greater diameter (20.1±1.1 mm) than all other PDs except for the 100 ms condition, while a PD of 100 ms produced a greater infiltration diameter (17.8±1.4 mm) than 150 ms (11.5±2.5 mm, all P<0.05). In addition, PD-dependent differences were found in terms of the dye infiltration depth in the melamine foam (ANOVA, F(4,45)=38.93, P<0.001) (Fig. 6B). A pair-wise comparison among the PD conditions showed that PDs of 75 ms, 100 ms, and 125 ms (9.4±0.8 mm, 8.9±0.9 mm, and 7.9±0.7 mm, respectively) resulted in a greater infiltration depth than a PD of 50 ms (3.3±1.3 mm, post-hoc Tukey HSD, all P<0.05). The PD of 75 ms resulted in the greatest dye infiltration, with values greater than those observed with 150 ms (post-hoc Tukey HSD, P=0.001) (Fig. 6B).

When the experiment was repeated with PVA foam blocks, a PD-dependent difference in the diameter of dye infiltration was also observed (ANOVA, F(4,45)=24.40, P<0.001) (Fig. 6C). The 75 ms PD condition resulted in the highest infiltration diameter (10.9±0.2 mm) than all other PDs (post-hoc Tukey HSD, all P<0.05). Similarly, a PD-dependent difference was found in the infiltration depth (ANOVA; F(4,45)=10.20, P<0.001) (Fig. 6D). Pair-wise comparisons showed that a PD of 75 ms yielded greater infiltration depth (1.1±0.1 mm) with respect to 150 ms (0.9±0.1 mm; post-hoc Tukey HSD, P=0.040).

The temperature of the TbO dye bath measured before and after the sonication sessions ranged from 23.0°C to 23.4°C throughout the experiment. No significant change in temperature was observed across the conditions (all P>0.05; n=10 for each group).

The amplitude of frequency spectra across the harmonics of fundamental frequency (multiples of 400 kHz) did not show differences in the tested acoustic intensities, suggesting the absence of cavitation (Fig. 7). The acoustic emission spectral power visibly increased in the 200-1,000 kHz range (marked with arrows) only after the microbubbles were added to intentionally increase the susceptibility for cavitation at 5 W/cm² (red line, Fig. 7). This broadband emission spectra indicated the presence of inertial cavitation [40-42]. These results suggest that cavitation was not likely to have contributed to our observations.