Quantifying the effect of acoustic parameters on temporal and spatial cavitation activity: Gauging cavitation dose

Abstract

Objective

Cavitation-enhanced delivery of therapeutic agents is under development for the treatment of cancer, neurodegenerative and cardiovascular diseases, including sonothrombolysis for deep vein thrombosis. The objective of this study was to quantify the spatial and temporal distribution of cavitation activity nucleated by DEFINITY^® infused through the EKOS^™ catheter over a range of acoustic parameters controlled by the EKOS^™ Endovascular system.

Methods

Three insonation protocols were compared in an in vitro phantom mimicking venous flow to measure the effect of peak rarefactional pressure, pulse duration, and pulse repetition frequency on cavitation activity energy, location, and duration. Inertial and stable cavitation activity were quantified using passive cavitation imaging and a metric of cavitation dose based on energy density was defined.

Results

For all three insonation protocols, cavitation was sustained for the entire 30 min DEFINITY^® infusion. The evolution of cavitation energy during each pulse duration was similar for all three protocols. For insonation protocols with higher peak rarefactional acoustic pressures, inertial and stable cavitation dose also increased. A complex relationship between the temporal behavior of cavitation energy within each pulse, and the pulse repetition frequency impacted the cavitation dose for the three insonation protocols. The relative predominance of stable or inertial cavitation dose varied according to insonation schemes. Passive cavitation images demonstrated the spatial distribution of cavitation activity.

Conclusion

Our cavitation dose metric based on energy density enabled the impact of different acoustic parameters on cavitation activity to be measured. Depending on the type of cavitation to be promoted or suppressed, particular pulsing schemes could be employed in future studies, such as to correlate cavitation dose with sonothrombolytic efficacy.

Introduction

The use of therapeutic ultrasound (TUS) to promote cavitation activity from infused nucleation agents is currently being developed to enhance drug delivery,^1-4 sonoporation,^5,6 or therapeutic effects, such as sonothrombolysis.^7-9 DEFINITY^® (Lantheus Medical Imaging, Inc., Billerica, MA, USA) is an injectable contrast agent consisting of lipid-shelled echogenic microbubbles filled with octafluoropropane gas, has a low retention fraction and no adverse hemodynamic effects at the microvascular rheology scale.¹⁰ The sonicated microbubbles act as cavitation nuclei that oscillate, grow, coalesce or collapse,^11-13 potentially causing desirable or deleterious mechanical and thermal effects. The different TUS acoustic parameters such as electrical drive pulse power or acoustic peak pressure amplitude, pulse repetition frequency (PRF), and pulse duration might be specifically tuned in order to control and potentialize the expected therapeutic bioeffect with minimal side effects.

The EKOS^™ Endovascular System (Boston Scientific, Marlborough, MA, USA) is an FDA-cleared catheter for ultrasound-mediated infusion of physician-directed therapeutics into the peripheral vasculature and pulmonary arteries.^14-16 DEFINITY^® infused through the EKOS^™ catheter has been shown to sustain cavitation over 3 min.¹⁷ Both inertial and stable cavitation energy was quantified over a range of electrical drive pulse powers, or peak rarefactional pressures, within a 288-μs window covering the cavitation energy peak of the 15-ms long pulse.¹⁸

Metrics for quantifying cavitation activity within a treatment time, or cavitation doses, that correlate with bioeffects have been widely discussed in the literature.^2,19-24 Different computation methodologies have been introduced and linked to particular bioeffects,^2,19,20-23 but to date there is no standard metric allowing the cavitation dose to be computed from calibrated cavitation acquisitions, which would enable comparison across setups. A detector-independent cavitation dose calculation methodology would enable the amount of stable or inertial cavitation within a treatment to be compared across different in vitro, preclinical, or clinical settings.¹⁹ A quantification methodology for cavitation dose would facilitate safety and efficacy studies with clear strategies for efficiency with respect to treatment time.^21-25

In this study, passive cavitation imaging (PCI) was performed throughout 30 min infusions of DEFINITY^® through the EKOS^™ catheter using three different insonation protocols. The protocols were selected to reveal the impact of peak rarefactional pressure, PRF and pulse duration on cavitation activity. Both stable and inertial cavitation activities were quantified using a calibrated setup and a metric for cavitation dose was defined based on cavitation energy, acoustic parameters, and cavitation spatial distribution. Furthermore, the temporal behavior of both inertial and stable cavitation was measured over the entire duration of each acoustic pulse. The objectives of this study were first to determine if cavitation could be sustained for 30 minutes for each of three acoustic protocols, and second to quantify and compare cavitation activity using a detector-independent cavitation dose metric. A secondary objective was to establish a tool permitting the determination of a strategy to maximize cavitation activity to test in future sonothrombolysis studies.

Materials and Methods

Physiologic Flow Model Setup

A physiological in vitro model mimicking flow in the common femoral vein was developed for the project (Fig. 1). A total volume of 0.5 L of 0.9% saline held in a 37 ± 0.5 °C reservoir (BW-20B, Lab Companion, Yuseong-gu, Daejeon, Republic of Korea) was circulated with a peristaltic pump (MasterFlex^® L/S^® model 7555-00, Cole-Parmer, Vernon Hills, IL, USA) at a volumetric flow rate of 360 mL/min through a flow phantom mimicking the common femoral vein made of latex tubing (9.5 mm-inner diameter with a 1.6-mm wall thickness). A second channel of tubing was used to mimic a collateral vein. Half the total volumetric flow rate through the system went through the collateral vein mimic. An in-line oxygen sensor (FSO2-C2, PyroScience, Aachen, Germany) enabled measurement of the total dissolved gas level. An in-line membrane oxygenating chamber (Radnoti, Covina, CA, USA) was used to maintain the total dissolved gas pressure at 93% ± 5% relative to air-saturation, corresponding to the mixed venous total dissolved gas level²⁶ (Fig. 1). A flow sensor (ME6PXN, Transonic, Ithaca, NY, USA) connected to a flow module (TS410, Transonic) enabled confirmation of a 180 mL/min ± 10 mL/min flow rate through the test section of the tubing. The EKOS^™ catheter was primed with 0.9% room-temperature saline solution and positioned in the flow model using a hemostasis valve.

Figure 1.

Schematic of flow phantom setup for passive cavitation acquisitions. Saline at 37°C was circulated from the reservoir, over the catheter, and back to the reservoir. The L11-5v array imaging plane included the first proximal active therapeutic ultrasound (TUS) transducer.

An L11-5v array (Verasonics, Kirkland, WA, USA) was connected to a Vantage 256 scanner (Verasonics) to obtain both B-mode images and passive cavitation data.²⁷ Data acquisition and analysis were performed using MATLAB (R2018b, The MathWorks Inc., Natick, MA, USA). Using B-mode image guidance with a cross-sectional view of the tubing, the array was positioned so that the tube lumen center was 4 mm beyond the natural focus of the array (18 mm) as in Lafond et al.¹⁷ Using micropositioners (MTS25-Z8, Thorlabs, Newton, NJ, USA), the L11-5v linear array was aligned over the first active transducer pair of the EKOS^™ catheter (Fig. 1) by maximizing the amplitude of the passively received acoustic signal while maintaining the EKOS^™ catheter in the same cross-sectional view.

EKOS^™ Catheter Technical Specifications

The EKOS^™ catheters used in this study had a 5.4 F (1.80 mm) diameter and a 12 cm treatment zone with 12 pairs of 2-mm long TUS transducers located in the core. The TUS transducer pairs were spaced 10 mm apart, and 38- to 46-μm diameter drug delivery ports were located 5 mm distal to each transducer pair (Fig. 2). The first six ultrasound transducer pairs were quiescent and the distal six were active, allowing infusion of DEFINITY^® into the lumen of the vessel phantom tubing proximal to TUS exposure.

Figure 2.

Schematic of EKOS^™ catheter with 12 pairs of 2-mm long, 2.25 MHz therapeutic ultrasound (TUS) transducers. Along the 12 cm treatment zone of the catheter, the first six ultrasound transducer pairs were quiescent while the distal six transducer pairs were active and sonicated the DEFINITY^®. The first drug delivery hole was located 0.5 cm after the first of six quiescent transducer pairs (adapted from Lafond et al. ¹⁷).

A programmable unit provided by Boston Scientific was used to drive the active 2.25 MHz transducers using three different insonation protocols. The first protocol employed a pulse duration of 3 ms and a PRF of 50 Hz at an electrical drive pulse power of 18 W (0.95 MPa peak rarefactional pressure at the surface of the catheter). The second protocol had the same duty cycle and peak pressure amplitude as the first, but the pulse duration was 15 ms and the PRF 10 Hz (Table 1). The third protocol sequenced four different pulsing schemes of acoustic parameters every 5 seconds (Table 1), which approximated the insonation protocol of the FDA-cleared EKOS^™ system. Note that the predicted peak rarefactional pressure at the surface of the catheter for each electrical drive pulse power was reported in a previous study¹⁸ and is summarized in Table 1.

Table 1.

Acoustic parameters for the three insonation protocols. The peak negative pressure is reported as the maximum value at the external surface of the EKOS^™ catheter. The order of schemes for protocol 3 was 1, 2, 3, 4, 3, 2.

Protocol#	Scheme#	Electrical drive pulse power (W)	Peak negative pressure (MPa)	Pulse duration (ms)	PRF (Hz)	Duty cycle (%)
1	-	18	0.95	3	50	15
2	-	18	0.95	15	10	15
3	1	9	0.67	8.0	21	16.93
	2	15	0.87	5.0	27	13.50
	3	30	1.20	6.9	21	14.41
	4	47	1.47	4.0	27	10.80

DEFINITY^® Preparation

Each DEFINITY^® vial was removed from the storage refrigerator (4 °C) and placed on a countertop at room temperature (22 ± 1 °C) for 1 hour, then activated using a VIALMIX^® (Lantheus Medical Imaging, Inc., Billerica, MA, USA). A 1.3 mL aliquot of DEFINITY^® was immediately withdrawn using an 18 G needle attached to a 3 mL syringe (Becton Dickinson, Franklin Lakes, NJ, USA) and transferred into a 15 mL syringe (Becton Dickinson, Franklin Lakes, NJ, USA) containing 13.7 mL of room-temperature 0.9% saline at 100% gas saturation relative to air.

Catheter infusion protocol

Each EKOS^™ catheter was primed with 0.9% room-temperature saline solution at 100% gas saturation. The DEFINITY^® dilution was infused through the drug port of the EKOS^™ catheter using a Legato 180 syringe pump (KD Scientific, Holliston, MA, USA) at 28.6 mL/h. Room-temperature 0.9% saline was infused into the coolant port of the EKOS^™ catheter using a Legato 180 syringe pump (KD Scientific, Holliston, MA, USA) at 35 mL/h. An in-line pressure sensor (Pendotech, Princeton, NJ, USA) was used to monitor the pressure in the drug delivery port during infusions, to assess whether the delivery ports remained unclogged during infusion¹⁸. After use, the catheters were flushed with deionized water and the output of each transducer pair was assessed based on the RF passive acquisitions by the L11-5v linear array. Each catheter was reused for two additional DEFINITY^® infusions after thorough flushing. A total of 5 catheters were used in the entire study.

L11-5v transducer array calibration protocol

The L11-5v transducer array was calibrated in degassed and deionized water based on a substitution technique.²⁸ A 76.2 ⎧m wire (McMaster-Carr, Aurora, OH, USA) was positioned at a single position at a 22 mm depth from the L11-5v, corresponding to the location of the center of the tube lumen, and sonicated with a focused transducer centered at 7.5 MHz ( V320, Olympus NDT, Waltham, MA, USA) driven by an ultrasound pulser-receiver (Panametrics 5077 PR, Olympus NDT, Waltham, MA, USA), see Gray and Coussios²⁸, Fig. 1. First, the L11-5v array was used to receive the emissions scattered from the wire target. Second, the array was substituted with a 0.2-mm needle hydrophone (Precision acoustics, Dorchester, U.K.) mounted on a computer-controlled three-axis positioner (Velmex, NF-90 series, Bloomfield, NY, USA), and the pressure field measured along the previous location of the L11-5v array aperture. The received hydrophone signals were digitized (LT372, LeCroy, Chestnut Ridge, NY, USA), averaged (100 traces per acquisition), and transferred to a Dell precision 5820 desktop computer with an Intel Core i9-10920X, 3.50GHz processor (Dell Technologies, Round Rock, TX, USA) for processing. Next, a 20% Tukey window was applied to the signals recorded by the hydrophone and the array. The calibration factor was computed at each frequency for each array element by taking the ratio of the magnitudes of the Fourier transform of the voltage received by the L11-5v array and the pressure acquired by the hydrophone. Finally, the sensitivity calibration factor was averaged both over the 128 elements of the L11-5v array and the beamformed frequencies. The sensitivity was included as a scalar in the delay, sum and integrate PCI beamforming algorithm.²⁷

Cavitation Quantification and Analysis

Passive cavitation data was acquired approximately every 6 s throughout four 30 min DEFINITY^® infusions through the EKOS^™ catheter for each insonation protocol (on average, 293 ± 69 pulses were acquired for each experiment). The Vantage 256 scanner acquisitions were triggered by the driving unit of the EKOS^® catheter at the beginning of each TUS pulse.¹⁷ Passive cavitation data was acquired throughout the entire TUS pulse duration at a sampling frequency of 31.25 MHz. For each acquired TUS pulse, a passive cavitation image was formed, composite images were created by overlaying a passive cavitation image over a B-Mode image and total cavitation energy calculations were performed using the data processing pipelines shown in Fig. 3.¹⁷

Figure 3.

Algorithm for the computation of spatially filtered passive cavitation images, total cavitation energy, and cavitation dose.

The passively received data was windowed into the maximal integer number of wavelengths covering the pulse duration, to minimize spectral leakage.²⁹ The window began at the start of the pulse. Depending on the pulsing scheme, no more than 0.006% of the pulse occurred past the end of the window. The data was Fourier transformed and inharmonic and ultraharmonic 40-kHz large frequency bands of interest were defined between 0.5 and 11 MHz, representing inertial and stable cavitation, respectively. The ultraharmonic bands were centered at odd multiples of 1.1250 MHz and the ultraharmonic energy was computed in excess of the surrounding inharmonic energy. Inharmonic frequency bands were centered at odd multiples of 0.5625 MHz. The inharmonic energy was scaled to be representative of the total broadband energy over the whole band of interest.¹⁸ For each frequency, delay, sum, and integrate beamforming was performed^17,30 with the “DC offset” or “frequency dependent bias”²⁷ removed from the signal at each frequency of interest immediately after beamforming.

For composite image formation (left hand side of Fig. 3), the beamformed data was integrated over the frequency bands of interest to obtain separate inertial and stable cavitation images. Pixels with non-physical negative energy were set to zero.²⁷ Note that frequency compounding before zeroing the negative energy takes advantage of frequency compounding speckle reduction³¹. Data adaptive spatial filtering using a normalized threshold of 0.643, based on the method of Haworth et al.³², was subsequently applied to the cavitation images where the mask for spatial filtering was obtained from the delay, sum, and integrate beamforming algorithm. The threshold effectively reduces spatial artifacts in energy mapping associated with the point spread function (PSF) of the PCI beamforming algorithm. Based on a precision-recall curve analysis of simulated cavitation sources and cavitation images, the value of 0.643 was found by Haworth et al.³² to maximize the true positive rate and positive predictive value. Composite cavitation images were displayed using the method of Lafond et al.¹⁷ The maximum cavitation energy level in the composite cavitation images was set to the maximum inertial cavitation emissions, with the dynamic range set to 20 dB re 1 μJ to cover both stable and inertial cavitation acquisitions. To compare the cavitation spatial distribution for the three different insonation protocols, all of the individual PCI composite images that were created over 30 min were averaged pixel-wise. Corresponding non-averaged composite videos were also created over the 30 min runs (Supplementary video 1 and Supplementary video 2, 19 frames per second). As in Lafond et al.¹⁷ and Kennedy et al.,¹⁸ inertial cavitation was mapped as red, stable cavitation as green, and the combination of the two appear as yellow.

For total cavitation energy computation throughout the pulse duration (right hand side of Fig. 3), a PSF energy deconvolution was implemented according to previous studies.¹⁷ The resulting data was integrated over the frequency bands of interest. Negative values representing non-physical energy were set to zero, and finally the resulting inertial and stable cavitation data was integrated over all space. In addition to calculating the total cavitation energy over a single pulse, the process was repeated with the temporal selection set to 288-μs windows (an integer number of wavelengths to minimize spectral leakage²⁹) to calculate the evolution of total cavitation energy over the duration of the pulse. The total cavitation energy, whether for the whole pulse or the 288 μs windows, was averaged over four 30 min runs for each insonation protocol. Baseline inertial and stable total cavitation energy was acquired for each run from 10 min 0.9% saline infusions, averaged and then subtracted from the DEFINITY^® runs.

The cavitation dose $CRx$ was computed for each run as an average cavitation energy density scaled over the exposure time:

$$CRx=T_{Treatment}\times PRF\times \frac{\langle E_{cavitation∕pulse}\rangle }{V_{Cav}}$$ (1)

where $T_{Treatment}$ is the exposure time (30 minutes in this study), $PRF$ is the pulse repetition frequency, $\langle E_{cavitation∕pulse}\rangle$ is the total cavitation energy per pulse averaged over the entire acquisition and $V_{Cav}$ corresponds to the cavitation area of each spatially filtered passive cavitation image averaged over the acquisition and converted into volume by multiplying by the 1 mm elevational plane of the L11-5v transducer array. The stable and inertial cavitation doses were computed for each insonation protocol. Statistical significance was determined using Brown-Forsythe and Welch ANOVA tests with Dunnett T3 multiple comparison correction for p ≤ 0.05.

Results

Cavitation was sustained for the entire 30 min infusion using the three insonation protocols, and the pressure in the drug delivery port was constant during the infusions. The average total inertial and stable cavitation energy is shown as a function of time over the two pulse durations for the first and second protocols in Fig. 4. The total inertial and stable cavitation energy for each of the four pulsing schemes employed in the third protocol is plotted as a function of time in Fig. 5a and b, respectively. For all protocols, the peak inertial cavitation energy occurred at the beginning of the pulse and subsequently decreased at least an order of magnitude. The stable cavitation energy initially increased and reached a maximum after ~0.9 ms and subsequently decreased to a level higher than the sustained inertial cavitation energy. This behavior was similar for all the pulsing schemes, independent of the pulse duration, PRF, or electrical drive pulse power.

Figure 4.

Average inertial (red) and stable (green) total cavitation energy during the insonation pulse for protocol 1 (dashed lines) and protocol 2 (solid line), the error bars represent standard deviation, n = 4.

Figure 5.

Average a) inertial (red) and b) stable (green) total cavitation energy over the insonation pulse for protocol 3, scheme 1 (triangle), scheme 2 (dashed lines), scheme 3 (circle) and scheme 4 (solid line), n = 4. Only one error bar is represented for each scheme for visibility.

In Fig. 4, the total inertial and stable cavitation energy for both protocols 1 and 2 were indistinguishable in amplitude for the first 3 ms. Note that protocols 1 and 2 share the same duty cycle and electrical drive pulse power, but the pulse duration and PRF differed. In Fig. 5, the total inertial and stable cavitation energy of each scheme of protocol 3 follow the same overall trend, but the peak cavitation energy increased with electrical drive pulse power. Moreover, the drop in stable cavitation energy over the pulse duration (approximately 1 order of magnitude) is smaller than the drop in inertial cavitation energy over the pulse duration (approximatively 1.5 orders of magnitude). Examples of both inertial and stable cavitation energy plotted over the 30 min run for each protocol are presented in Supplementary Fig. 1 online.

The resulting total cavitation energy per pulse averaged over the entire acquisition, $V_{Cav}$, is presented for each protocol in Table 2. The total inertial and stable cavitation energies per pulse were similar in protocols 1 and 3, but the stable cavitation energy was higher than the inertial cavitation energy in protocol 2. The average spatially filtered PCI cavitation volumes were similar for the three protocols, 56.9 ± 2.6 mm³ and 72.1 ± 3.9 mm³ for inertial and stable cavitation, respectively.

Table 2.

Total stable and inertial cavitation energy per pulse averaged over the entire acquisitions (average ± standard deviation, n = 4), for the three insonation protocols.

Protocol#	Average total inertial cavitation energy (μJ)	Average total stable cavitation energy (μJ)
1	12.0 ± 1.94	11.7 ± 0.87
2	16.4 ± 2.32	26.3 ± 1.96
3	14.6 ± 1.35	13.6 ± 0.52

The cavitation dose $CRx$, based on Equation (1), for the three insonation protocols are shown in Fig. 6a and for the four separate schemes employed by the insonation protocol 3 in Fig. 6b. The inertial and stable cavitation doses are significantly different (p<0.05) for all three insonation protocols (Fig. 6a). Note that the inertial cavitation dose of protocol 1 (Fig. 6a) is roughly a factor of 4 larger than the inertial cavitation dose of protocol 2 (10.7 ± 1.7 vs. 2.7 ± 0.4 μJ / mm³, p<0.05) even though duty cycle and electrical drive pulse power are the same. Similarly, the stable cavitation dose is about a factor of 2 larger for protocol 1 than for protocol 2 (8.1 ± 0.6 vs. 3.5 ± 0.3 μJ / mm³, p<0.05). Concerning protocol 3, as the electrical drive pulse power employed by schemes 1 through 4 increased, both the inertial and stable cavitation doses increased significantly (p<0.05, Fig. 6b). Interestingly, when comparing protocol 1 and scheme 3 of protocol 3, both inertial cavitation doses (10.7 ± 1.7 vs. 9.4 ± 1.5 μJ / mm³, respectively) and stable cavitation doses (8.1 ± 0.6 vs. 7.4 ± 0.5 μJ / mm³, respectively) were similar despite the lower electrical drive pulse power of protocol 1 (18 W vs 30 W, respectively). Overall, the predominance of either stable cavitation or inertial cavitation varied according to the specific insonation schemes.

Figure 6.

a) Inertial and stable cavitation dose, $CRx$, for the three insonation protocols, n = 4. b) Inertial and stable cavitation dose over the pulse duration for the four schemes of the insonation protocol 3, *p<0.05, n = 4.

Fig. 7 includes example composite B-mode and passive cavitation images without and with adaptive spatial filtering.³² Corresponding videos of the individual composite B-mode and spatially filtered passive cavitation images acquired every ~6 s throughout the 30 min DEFINITY^® infusions are available online (Supplementary video 1). Note that the location of the cavitation activity strongly depends on the position of the catheter and acoustic field generated by the transducer pairs within the lumen.

Figure 7.

Examples of composite passive cavitation and B-Mode images mapping stable (green) and inertial (red) cavitation activity averaged over 30 min for protocol 1 (left), protocol 2 (middle) and protocol 3 (right), without (upper row) and with (lower row) adaptive spatial filtering.³² Yellow represents a combination of stable (green) and inertial (red) cavitation activity at a location. To obtain the composite images, infused DEFINITY^® was sonicated by the most proximal active transducer of the EKOS^™ catheter. The entire pulse duration of acquired data was processed to form individual passive cavitation images. Individual images were averaged pixel-wise to obtain a 30 min average passive cavitation image that was overlaid on a B-mode image. The maximum energy level in the colormap was set to the maximum measured energy, with the dynamic range set to 20 dB re 1 μJ which spanned all the acquisitions. Note that the passive cavitation image of protocol 3 represents the average over the 30 min trial, which included 4 different schemes.

In Fig. 8, an example of 30 min averaged inertial and stable cavitation activity for the four schemes of protocol 3 are presented in composite B-mode and passive cavitation images. Corresponding videos of the non-averaged composite PCI and B-mode acquisitions for each scheme throughout the 30 min treatment times are available online (Supplementary video 2). Note that Supplementary video 2 contains the same data as protocol 3 in Supplementary video 1 but is separated by scheme for easier comparison. An increase in the lateral dimension of the cavitation cloud is visualized as the electrical drive pulse power increases from schemes 1 through 4, as well as an increase of inertial cavitation activity.

Figure 8.

Examples of composite passive cavitation and B-Mode images of 30 min averaged stable (green) and inertial (red) cavitation activity for each scheme in protocol 3. Infused DEFINITY^® was sonicated by the most proximal active transducer of the EKOS^™ catheter. The whole acquired pulse was processed and the resulting 30 min average passive cavitation image overlaid on a B-mode image according to the composite cavitation energy color map, where yellow represents both stable and inertial cavitation activity. The maximum energy level in the colormap was set to the maximum measured energy, with the dynamic range set to 20 dB re 1 μJ to cover all the acquisitions.

Discussion

Both ultraharmonic and inharmonic cavitation emissions can be selectively beamformed with frequency-domain PCI.¹⁷ In practice, the ultraharmonic peaks rise above the broadband inertial cavitation signature (see received cavitation spectra in Fig 2). The PCI algorithm used herein attributed inharmonic components to inertial cavitation and ultraharmonic peaks in excess of the neighboring broadband signals to stable cavitation. Note that only the ultraharmonic energy rising above the neighboring inharmonic energy is considered, which may represent an underestimation of ultraharmonic energy. For the PCI display algorithm, a short window of the acquired pulses was previously used to create composite PCI and B-mode images in Lafond et al.¹⁸ and Kennedy et al.¹⁷ for computationally cost-effective display. However, the average cavitation energy over the entire pulse will likely be needed to correlate with a particular bioeffect, such as blood brain barrier disruption.²³

Passive cavitation analysis was used to quantify and compare inertial and stable cavitation activity promoted by three insonation protocols employed with DEFINITY^® infused through an active EKOS^™ Endovascular System. Specific bubble dynamics were studied by processing the received signal over the entire pulse duration. In this study, we only recorded passive cavitation data above one transducer pair. However, it was previously demonstrated that the acoustic output from all four drive electrical powers of the EKOS^™ catheter were sufficient to sustain cavitation from infusions of DEFINITY^® along all the distal six transducer pairs of the catheter.¹⁸ Thus, in this study similar cavitation activity likely occurred over each of the six transducer pairs over the entire 30 min treatment period.

Inertial and stable total cavitation energy evolution over the duration of the TUS pulses was consistent for all three protocols. We hypothesize that lipid shell buckling,¹² lipid shedding,³³ and microbubble rupturing,^12,34,35 contributed to gas release within the first hundred microseconds when inertial cavitation was at a maximum. Free gas bubbles then interacted with each other and coalesced¹² over time to attain the subharmonic resonant size (~8 μm diameter) for stable cavitation activity at the TUS center frequency, 2.25 MHz (see Bader and Holland, Fig. 6³⁶), which was sustained for the remaining duration of the pulse. Other phenomena such as rectified gas diffusion might also take place as gas interacts with the surrounding saline.^37-39 High-speed videography would be complementary to visualize and confirm such behavior^33-35 triggered by insonation with the EKOS^™ Endovascular System.

Insonation protocols 1 and 2, which had the same electrical drive pulse power (18 W) and duty cycle (15%), promoted the same total inertial and stable cavitation energy values over the pulse duration for the first 3 ms (Fig. 4), despite the intrinsic variability that occurs in cavitation nucleation.^3,6,22 Though the PRFs (50 vs. 10 Hz) and pulse durations (3 vs. 15 ms) were different for protocols 1 and 2, the inertial and stable total cavitation energy values were similar over the pulse (Fig. 4). As the pulses are longer for protocol 2 (15 ms) than for protocol 1 (3 ms), the total average stable and inertial cavitation energies per pulse were expected to be larger for protocol 2 (Table 2). However, the cavitation dose was higher for protocol 1 than 2 (Fig. 6) because $CRx$ was proportional to the PRF, which was higher in protocol 1 than 2 (50 Hz vs. 10 Hz).

Protocol 3 presented similar stable and inertial cavitation trends for all four schemes over the pulse duration, and the total cavitation energy values increased with TUS power (peak rarefactional pressure) as shown in Fig. 5. As the pulse drive power increased from 9 W to 47 W, both stable and inertial total cavitation energy and dose increased (Fig 5 and Fig 6b). At the two lowest electrical pulse drive powers (schemes 1 and 2, with 9 and 18 W, respectively) the stable cavitation dose exceeded the inertial cavitation dose. However, for scheme 4 with a 47 W electrical pulse drive power, inertial cavitation dominated.

In Fig. 8 and Supplementary video 2, as the drive power increased in protocol 3, a widening of the cavitation area and an increase in inertial cavitation can be appreciated as the color yellow blooms. Note that the acoustic pressure amplitude decays as a function of distance from the transducers.¹⁷ Furthermore, as the catheter is at the same location for the four pulsing schemes, the widening of cavitation activity as power increases using this strategy of alternating schemes can be appreciated. This observation agrees with Kennedy et al.,¹⁸ who detected cavitation emissions over a larger percentage of tube lumen as the electrical drive power increased. The correlation of the spatial distribution and quantification of the total cavitation energy with bioeffects should be investigated in preclinical models of disease. In general, it was also observed that the PCI cavitation activity varied depending on the catheter position and orientation within the lumen.

A definition of cavitation dose, $CRx$ was proposed to link the insonation parameters to a metric to gauge specific types of bubble activity, taking into account both the amplitude and spatial extent. Specifically, $CRx$ takes into consideration the average cavitation energy (stable or inertial) that an insonation scheme would sustain per pulse, as well as the cavitation spatial distribution based on spatially-filtered passive cavitation images.³² PRF is included in the definition of cavitation dose to obtain the average cavitation energy per second, and we include the treatment time to obtain the average cavitation energy that would be sustained over the whole treatment. As the cavitation energy is not constant over the pulse duration, the choice of pulse duration and PRF are essential parameters affecting the cavitation dose.

Though cavitation nucleation thresholds have been tied to the acoustic pressure amplitude,^40,41 the interaction of acoustically activated bubbles, blood clots, and rt-PA is complex.^42,43 To enable the correlation of the cause (inertial or stable cavitation) to a particular bioeffect, energy density (energy per unit volume) has the same physical units as pressure, but is tied to bubble activity, not cavitation nucleation. The concept of energy density (i.e., cavitation energy divided by the cavitation volume) also allows the inclusion of the spatial extent of cavitation activity within the sonicated medium.¹⁹

Some insonation schemes exhibited a maximum in the inertial cavitation dose and other schemes exhibited a maximum in the stable cavitation dose. Therefore, depending on the type of cavitation desired to promote or suppress a particular bioeffect, a titrated pulsing scheme could be employed, as also discussed previously by Hitchcock et al.⁴⁴ and Goertz et al.⁴⁵ In particular in this study, for the same electrical drive pulse power, shorter pulse durations and higher PRFs maximized the cavitation dose (protocol 1 vs protocol 2). This data is consistent with extracorporeal sonothrombolysis observations of an increase of lytic efficacy using shorter pulse durations and increased PRFs.^46,47 It should be noted that titrating the pulsing scheme may be restricted based on hardware, computer memory, or other limitations.

Different metrics for cavitation activity quantification have been extensively discussed in the literature.^2,9,19-23 A metric for inertial cavitation activity, defined as the root-mean square of a frequency band of interest within the broadband noise of the recorded signal, was correlated with endothelial cell damage²² and hemolysis.²¹ Other effects, such as enhanced drug uptake for therapeutic benefit, have been linked to similar definitions of cavitation dose.² The use of the term “dose” is consistent with the concept of “radiation dose,” prescribed for a particular tumor treatment.⁴⁸

More recently, cavitation activity has been quantified by integrating the beamformed passive cavitation images over space and/or time.^19,20 Smith and Coussios¹⁹ computed cavitation dose based on the energy density, as we defined $CRx$ in Equation (1). A key difference however is the calculation of the volume used to convert from “energy” to “energy density”. Smith and Coussios¹⁹ defined that volume based on the size of the container holding the in vitro sample. This definition provides a fixed volume, which presumably contributed to the excellent correlation observed between their bioeffect, hemolysis, and cavitation dose. A limitation of this choice is that it may not translate easily for in vivo applications. The cavitation dose, $CRx$, used in our study derived the spatial extent of cavitation activity directly from the passive cavitation image data. This choice necessitated defining a pixel amplitude threshold for determining the boundaries over which cavitation activity occurs. We selected 0.643 based on an optimal precision-recall analysis.³² Other choices, such as −6 dB could be selected. Experiments correlating cavitation dose with a bioeffect would help support the choice, which may vary for different applications.¹⁹

A potential limitation of our study is lack of demonstration that cavitation energy correlates with a particular beneficial or deleterious bioeffect. An alternative definition of $CRx$ could rely on a well-defined cavitation threshold. The alternative cavitation dose could be adapted by replacing the cavitation energy per pulse by the cavitation time above the cavitation threshold during the acoustic pulse. This alternative approach, however, would require knowledge of the specific cavitation-based bioeffect threshold a priori.

Furthermore, the passive cavitation data was acquired at a frame rate lower than the PRF for each of the three EKOS^™ protocols. Though the average amplitude of the cavitation energy did not vary over each 30-min experiment, the energy changed within the pulse duration (Figs. 4 and 5). Jones et al.²³ demonstrated that acquiring only part of a cavitation emission pulse can reduce the accuracy of predictions regarding bioeffects based on cavitation emissions. This finding is consistent with our observations that the cavitation emissions varied over the duration of a single pulse (Figs. 4 and 5).

Another limitation of this study is that the sensitivity of the L11-5v arrays was corrected using a single calibration point, which ignored directivity and diffraction patterns that could be rectified using multiple calibration points over the whole sonicated field.²⁸ Though the order of magnitude of the cavitation energy values agreed with previous published data,¹⁹ it was reported that calibration inaccuracies can lead to errors up to 28% in the total energy computations.⁴⁹ Finally, cavitation volumetric information was retrieved from the spatially filtered passive cavitation image. Other advanced processing techniques such as spatial deconvolution,^50,51 robust capon beamforming, or a more complex setup acquisition for 3D acquisitions⁵² could be used, increasing computational or setup complexity.

Conclusion

The EKOS^™ catheter described in this work was cleared by the FDA for the delivery of physician specified fluids, including thrombolytics, into the peripheral vasculature. Both inertial and stable cavitation activity nucleated by infused DEFINITY^® could be sustained for 30 minutes in a physiological model of porcine venous flow. A comparison between three different TUS insonation protocols was performed using a specific definition of cavitation dose. Our data supports an emerging application of cavitation-enhanced sonothrombolysis,^7,8 which has the potential to restore flow in a thrombus occluded vein with minimal lytic use and risks. Future studies aim to correlate inertial and stable cavitation dose with sonothrombolytic efficacy in a model of human deep vein thrombosis.