Dynamic mode decomposition based Doppler monitoring of de novo cavitation induced by pulsed HIFU: an in vivo feasibility study | Scientific Reports

Scientific Reports volume 14, Article number: 22295 (2024) Cite this article

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Pulsed high-intensity focused ultrasound (pHIFU) has the capability to induce de novo cavitation bubbles, offering potential applications for enhancing drug delivery and modulating tissue microenvironments. However, imaging and monitoring these cavitation bubbles during the treatment presents a challenge due to their transient nature immediately following pHIFU pulses. A planewave bubble Doppler technique demonstrated its potential, yet this Doppler technique used conventional clutter filter that was originally designed for blood flow imaging. Our recent study introduced a new approach employing dynamic mode decomposition (DMD) to address this in an ex vivo setting. This study demonstrates the feasibility of the application of DMD for in vivo Doppler monitoring of the cavitation bubbles in porcine liver and identifies the candidate monitoring metrics for pHIFU treatment. We propose a fully automated bubble mode identification method using k-means clustering and an image contrast-based algorithm, leading to the generation of DMD-filtered bubble images and corresponding Doppler power maps after each HIFU pulse. These power Doppler maps are then correlated with the extent of tissue damage determined by histological analysis. The results indicate that DMD-enhanced power Doppler map can effectively visualize the bubble distribution with high contrast, and the Doppler power level correlates with the severity of tissue damage by cavitation. Further, the temporal characteristics of the bubble modes, specifically the decay rates derived from DMD, provide information of the bubble dissolution rate, which are correlated with tissue damage level—slower rates imply more severe tissue damage.

Pulsed high-intensity focused ultrasound (pHIFU) therapy has emerged as a promising non-invasive treatment modality, holding significant potential in various clinical applications. These include enhancing drug delivery into tumors by increasing permeability for passive diffusion1,2,3 and modulating the microenvironment of both malignant and non-malignant tissue, thereby resulting in therapeutic outcomes4,5,6,7. This pHIFU modality employs relatively short ultrasound pulses, ranging from 1 to 100 milliseconds at frequencies near 1 MHz and at a duty cycle under 5% with high spatial-peak pulse-average intensity (ISPPA), to induce de novo inertial cavitation in tissue without administration of exogenous contrast agents1,2,3,4,5,6,7,8,9. This process allows to achieve mechanical disruption of the target area while minimizing thermal effects.

For the pHIFU targeting, ultrasound (US) B-mode imaging, realized with an imaging probe that is incorporated coaxially in the center opening of the HIFU transducer, is currently the most widely used method. While B-mode imaging is quite effective at targeting and qualitative monitoring of cavitation, it faces challenges in quantitative assessment of cavitation and its correlation with tissue damage. This difficulty arises because the rapid dissolution of cavitation bubbles following each pHIFU pulse can degrade the consistency and sensitivity of the B-mode imaging quality8,10. Passive methods such as passive cavitation detection (PCD) and passive acoustic mapping (PAM), which are alternatives to the active pulse-echo techniques like B-mode, quantify the broadband signal from inertial cavitation collapse during each pHIFU pulse. Although these methods demonstrate sensitive detection of cavitation activity, they lack the capability to image cavitation with sufficient resolution8. Specifically, the point-spread function in the axial direction for PAM is limited by the angular aperture of the imaging probe, making it challenging to map cavitation accurately11,12,13.

A variation of Doppler ultrasound imaging (also termed bubble Doppler) has been proposed for mapping pHIFU-induced cavitation bubbles14,15,16,17. This technique employs a series of planewave imaging pulses, emitted immediately following each HIFU pulse. Those imaging pulses interact with residual cavitation bubbles that rapidly dissolve ranging from a millisecond to a few hundred milliseconds depending on several factors such as HIFU pulse amplitude, level of tissue disruption, and in some cases – amplitude of the imaging pulses14,18,19. Doppler processing of the backscattered pulses interprets those changes as motion, and the resulting Doppler power map corresponds to the spatial distribution of bubbles14. As in any Doppler processing, selecting the appropriate wall filter is crucial for isolation of bubbles from clutter motion of tissue and blood flow20.

Traditional frequency-based Doppler wall filters, like the infinite impulse response (IIR) high pass filter, are designed to eliminate low-frequency tissue clutter motion in Doppler acquisition domain. However, the use of those filters in bubble Doppler is challenging because the rapid dissolution of bubbles places a limitation on the number of usable Doppler pulses in the ensemble, which causes initialization issues and degrades the filtering quality16. Similarly, singular value decomposition (SVD) filter, another common choice in vascular imaging21,22 and proposed for cavitation imaging16, encounters the same challenges, greatly reducing decomposition performance. In addition, SVD decomposes a matrix of images into orthogonal modes, and the modes of interest can be selected based on their amplitude of singular values. However, in pHIFU the amplitudes of SVD modes from tissue and from bubbles can be comparable, which reduces the efficiency of filtering14,23,24.

Recently, we introduced dynamic mode decomposition (DMD) as an advanced Doppler clutter filtering technique25. DMD is a fast-growing data-driven approach to provide spatiotemporal decomposition of a dataset matrix with dimensionality reduction, where each mode is characterized by spatial coherence and unique temporal behavior26,27,28. Unlike the SVD that provides spatial coherence in dataset images without considering their temporal relation, DMD provides not only spatial coherence but also temporal characteristics of the modes, like fast Fourier transform (FFT). We had evaluated the performance of DMD as a Doppler clutter filter during pHIFU exposures in silico and ex vivo to map the fast-dissolving bubbles and additionally capture temporal characteristics, most importantly their dissolution rate. This was achieved under linear approximation of the temporal behavior of bubbles (i.e. harmonic oscillation with exponential growth or decay), which is a reasonable approximation of the Doppler signals backscattered from dissolving bubbles14. Each mode and its temporal decay rate, extracted by DMD, are trackable over pHIFU pulses and are physically interpretable as backscatter from stationary scatterers, tissue motion due to acoustic radiation force (ARF), and dissolving residual bubbles.

The goal of this work was to demonstrate the feasibility of DMD for mapping inertial cavitation during pHIFU treatments of in vivo surgically exposed porcine liver, and to identify candidate DMD-provided quantitative metrics by correlating to the resulting areas of tissue damage. Porcine liver is a representative model of heterogeneous, highly vascularized tissue, containing vascular and biliary structures of different scales. Externalization was done for precise localization and characterization of the tissue damage by cavitation.

Illustration of the experimental setup for pHIFU exposures of surgically exposed porcine liver in vivo and the ultrasound imaging sequences for treatment guidance. (a) A HIFU transducer equipped with water-filled coupling cone on the front and a coaxial imaging probe mounted at the center opening were used to deliver pHIFU pulses and acquire imaging data, respectively. A midline abdominal incision was made, allowing the cone tip to be in direct contact with the liver surface. (b) The ultrasound imaging sequence. 13 planewave Doppler pulses were emitted immediately after each pHIFU pulse, followed by conventional ray-line B-mode imaging pulses. The imaging probe was operated in ‘listening mode’ for passive cavitation detection (PCD), capturing radio-frequency (RF) signals during HIFU pulses to monitor inertial cavitation activity.

The US imaging data were obtained during pHIFU exposures targeting the surgically exposed liver of a female domestic swine (100 lbs) as follows. A 1.5 MHz HIFU transducer attached to a degassed water-filled coupling cone was used to consecutively treat 12 different target locations in the liver, with 60 HIFU pulses (1 ms in duration) administered at each location (Fig. 1(a)). An US imaging probe was coaxially installed at the center opening of the HIFU transducer to acquire PCD signals during the HIFU pulse, as well as planewave Doppler images and a ray-line B-mode image following the HIFU pulse, as shown in Fig. 1(b). After the exposures the animal was euthanized, and the targeted areas of tissue, referred to as lesions from here on out, were collected for histology.

Three different HIFU output levels (peak acoustic powers of 170, 260, and 600 W) were selected based on preliminary observations25 to induce various levels of cavitation activity and thus degrees of tissue damage. The focal waveforms corresponding to those output levels are shown in Fig. 2(a). Note that the peak negative pressure level for the HIFU output of 170 W was expected to be just below the cavitation threshold. Representative photographs of the liver surface after pHIFU exposures at the three output levels are presented in Fig. 2(b). A bruise resulting from subsurface inertial cavitation was observed for all treatment locations except those corresponding to the lowest HIFU output level (170 W), but the size of the bruise varied depending on the HIFU output level. The diameter of surface bruises was approximately 1.2 mm for 260 W and 3.5 mm for 600 W treatment locations.

Peak acoustic power in pHIFU exposures correlates with broadband emissions (i.e. inharmonic signal) by cavitation bubbles and with gross tissue disruption. (a) The focal waveform for three different pHIFU peak acoustic power levels used in this study. (b) Representative gross photos of liver tissue treated with varying pHIFU output levels. The treated areas on the tissue surface are marked in white dotted circles, and surface bruises are clearly visible for 260 and 600 W, but not 170 W treatments (c) Two representative examples of PCD radio-frequency (RF) signal before (black) and after (green) filtering to isolate broadband emission signal for the pulses where cavitation was present (top) and absent (bottom). (d) Box graphs presenting the relationship between passive cavitation detection (PCD) metrics—noise level (left) and amplitude ratio (right)—and the pHIFU output level. Each green circle indicates individual data point from a single pHIFU pulse. The box graphs display the median values, 25th and 75th percentiles, and the whiskers extend to 1.5 times the interquartile range. The two-sample t-test between datasets of subsequent output levels was performed and statistical significance is indicated by asterisks (p < 0.0001).

While each HIFU pulse was being delivered, all elements of the imaging probe passively captured the sound emissions from inertial cavitation collapses at a sampling frequency of 20 MHz, commonly referred to as passive cavitation detection (PCD). The broadband signal (i.e. inharmonic signal) was processed, and two PCD metrics were derived from it: noise level (NL), which reflects the temporal average of broadband signal amplitude, and the amplitude ratio (AR), indicating the ratio between the maximum and the cavitation threshold. Here, the cavitation threshold was defined by the maximum background noise multiplied by \(\:\sqrt{5}\) (see “Methods” section). Figure 2(c) shows the two representative examples where substantial cavitation activity was observed throughout the HIFU pulse in the top figure, while in the bottom figure, cavitation was only transiently observed at the beginning of the pulse. The latter case was expected to produce negligible tissue damage. In Fig. 2(d), the PCD metrics NL and AR corresponding to all HIFU pulses across all exposures are presented as box plots for each HIFU output level. As expected for sub-threshold output level, both NL and AR are near zero for the vast majority of pules at 170 W, which is in agreement with the absence of grossly visible damage at the tissue surface. As expected, the values of both NL and AR at the two higher output levels were not only progressively and statistically significantly higher, but also varied from pulse to pulse and depending on location. These variations can be attributed to the structural differences within tissue between treatment points and the stochastic nature of cavitation nucleation, especially at the intermediate output level.

To quantify the tissue damage induced by each of the pHIFU exposures, we first selected a hematoxylin and eosin (H&E)-stained histological section for each lesion that showed the most extensive damage, assuming that it corresponds to the lesion center. Subsequently, the damaged area was manually outlined within this selected histological section, as shown in Fig. 3(a)–(e). Separate outlines were used for damage of different severity, graded in three levels29,30. Grade 3 (Fig. 3(b)) indicated gross tissue damage, with tissue structures broken down to the subcellular level, similar to the lesions induced by mechanical ablation techniques (i.e. histotripsy)31. This grade may also encompass hemorrhagic regions embedded within the completely fractionated damage area. Grade 2 (Fig. 3(c)) was characterized by gross hemorrhage and distinct tissue disruption, with preservation of the overall tissue structure. This grade included widespread hepatic cords disruption. Grade 1 (Fig. 3(d)) indicated the damage with evidence of petechial hemorrhage and localized hepatic cords disruption, with tissue architecture comparable to undamaged tissue. Areas that did not fall into any of these grades were indicative of intact tissue with no visible damage.

Figure 3(f)-(h) shows representative histological images of tissue damage induced by a pHIFU exposure. The highest pHIFU output (600 W) resulted in significant variability in tissue damage. Specifically, Fig. 3(f) illustrates a cohesive damaged area that includes the most severe grade (grade 3), while Fig. 3(g) shows only scattered areas of minor disruption in the superficial layer. Of the four locations treated at this power level, half showed the former type of severe damage, and the other half – the latter. This variation in tissue damage could be attributed to the presence of large scale vascular and biliary structures within the HIFU focal area (yellow arrows in Fig. 3(g)), and preferential nucleation of cavitation within those structures32. Large scale (e.g. hundred microns) connective tissue structures are known to be less susceptible to cavitation damage even in histotripsy33.

At a moderate pHIFU power of 260 W, the extent of tissue damage also varied: two out of five lesions included grade 3 damage, albeit smaller in size compared to those shown in Fig. 3(f); two lesions included grade 2 damage; and one lesion only minor damage akin to that in Fig. 3(g). At the lowest power setting of 170 W, no discernable damage was observed (Fig. 3(h)), consistent with PCD observations indicating little to no cavitation activity at that power.

In order to compare the overall extent of tissue damage to the PCD metrics NL and AR for each pHIFU exposure, scaled damage area (SDA) was calculated (see “Methods” section). Figure 3(i) and (j) show a strong positive correlation between the PCD metrics (NL and AR) and SDA, with coefficients of determination (R2) of 0.91 and 0.97, respectively. Notably, data points marked in red triangles, corresponding to minor tissue damage induced at the highest power in the vicinity of large biliary or vascular structures as shown in Fig. 3(g), were excluded from this correlation analysis. This exclusion highlights a current limitation of PCD: its inability to spatially map cavitation occurrence and differentiate between cavitation within vasculature and tissue parenchyma.

PCD metrics quantitatively correlate to damage severity. (a) Representative example of a wide-view hematoxylin and eosin (H&E)-stained tissue section with 600 W pHIFU output pulses, where the tissue damage is categorized into three distinct grades. The zoom-in versions of each damage grades were presented: (b) grade 3, showing the most severe damage with the destruction in subcellular level, (c) grade 2, indicating moderate damage with visible hemorrhages, (d) grade 1, depicting minor damage with petechial hemorrhages marked as yellow arrows, and (e) an intact area, representing one without noticeable damage. Representative results of tissue damage grading: (f) severe damage with 600 W pHIFU output, (g) an outlier case of minor damage with 600 W due to the presence of large scale vascular and biliary structures within the HIFU focal area (yellow arrows), and (h) no discernible damage with 170 W. The graphs on the right show the correlation between overall damage level from histological image, termed scaled damage area, and PCD metrics, (i) noise level and (j) amplitude ratio. Notably, anomalous cases like (g) are marked with red triangles and excluded from the regression fits.

In our study, DMD was used for two purposes. The first was to isolate cavitation bubble images (or modes) from the planewave image datasets, akin to Doppler clutter filter. The second was to obtain the temporal characteristics of the bubble modes in slow time-oscillation frequency and decay rate, that correspond to the average time of bubble dissolution. The overall processing procedure is shown in Fig. 4. DMD provided the reduced-order eigen-decomposition of the given planewave image dataset where eigenvectors indicate mode shapes and eigenvalues present temporal characteristics. Of the unclassified sets of modes, bubble modes were then identified based on their spatiotemporal characteristics using k-means clustering of eigenvalues and a peak-to-sidelobe ratio (PSR) thresholding method. Then, the bubble images in slow time were generated for each HIFU pulse using only the bubble modes. The last step included conventional power Doppler processing and pixelwise integration of the Doppler power maps over the HIFU pulses (see “Methods” section).

Illustration of the principle of DMD processing of planewave Doppler data. I/Q modulated planewave images underwent DMD processing, yielding a reduced order set of spatiotemporal modes along with modal parameters such as mode frequency and temporal decay rate. From these unclassified modes, bubble modes were identified using k-means clustering and a contrast-based thresholding method. These bubble modes were then reconstructed into bubble images, which were further processed using a conventional Doppler power algorithm. Finally, the Doppler power maps corresponding to each pHIFU pulse were cumulatively summed over all pHIFU pulses, enabling a comparison with histological images.

Figure 5(a)-(e) shows the distribution of DMD eigenvalues on the complex plane for all pulses of five different pHIFU exposures to illustrate the process of bubble mode selection. The eigenvalues are denoted as colored crosses, with each color representing a separate cluster. DMD modes that exhibited high contrast within the region of interest (ROI), surpassing the PSR threshold, are further highlighted with squares atop the crosses. The clusters were designated bubble clusters when half of the modes in the same cluster exceeded the PSR threshold. Areas of the complex plane associated with bubble clusters were marked with gray background for clearer visualization.

DMD enhanced Doppler power maps and correlation to the severity of tissue damage from histological images Bubble modes were identified using discrete time DMD eigenvalues on the complex plane based on the k-means clustering and a peak-to-sidelobe ratio (PSR) thresholding. (a) no discernible damage at a pHIFU output level of 170 W, (b) low and (c) moderate damage at 260 W, (d) severe damage at 600 W, and (e) an anomalous case of minor damage at 600 W. Further investigations of DMD based Doppler power map for the severe damage lesion corresponding to (d) are shown below: (f) representative mode shapes in each cluster, (g) B-mode image captured immediately after 60th HIFU pulse, (h) histological image with damage grading (green arrows show vessels seen in B-modes as well), (i) a cumulative Doppler power map over 60 HIFU pulses, superimposed onto the B-mode captured during 1st HIFU pulse, (j) a contour map of cumulative Doppler power superimposed onto the histological image, and (k) stretched axially by 20% in the contour map to compensate for the pressure applied during the treatment. Other representative examples of cumulative Doppler power map and corresponding histological images of the damage with (l,m) maximum grade 2, (n,o) maximum grade 3. (p) A box plot showing the correlation between spatially averaged cumulative Doppler power level and damage grade, (*p < 0.05, ** p < 0.01).

The absence of bubble clusters was observed in lesions with no damage (Fig. 5(a)) and those with minor damage where cavitation activity within vascular and biliary structures was expected based on B-mode images (Fig. 5(e), Supplementary Fig. A). Clusters in these instances were more compact compared to cases where bubble clusters were present. The cluster distribution in Fig. 5(a) occupied the right side of the plane, which indicated low frequency of the modes. This is consistent with our prior observations in ex vivo tissue pHIFU exposures without cavitation, and corresponds to near-stationary tissue and its acoustic radiation force-induced motion25. Conversely, the bubble clusters in Fig. 5(b)-(d) predominantly occupied the left sector of the eigenvalue circle, indicative of higher mode frequency. They were also more spread out compared to the non-cavitation cases, likely due to the stochastic nature of the cavitation over pHIFU pulses and larger and more variable ARF-induced motion. An increase in the number of bubble modes, marked as squares in bubble clusters, was observed with the severe tissue damage level, reflecting an increase in the complexity of bubble modes behavior (i.e. increase in rank of the bubble mode).

A more detailed investigation of a specific exposure corresponding to Fig. 5 (d) is shown in Fig. 5(f)-(k). The DMD eigenvalues were grouped into 10 clusters, with three of them (clusters 8–10) designated as bubble clusters. Figure 5(f) shows the representative mode shapes for each cluster, arranged in ascending order of their frequencies. These mode shapes are the most dominant patterns within their respective clusters. They are obtained through an additional SVD process, followed by the selection of the first SVD mode that corresponds to the largest singular value. Figure 5(g) and (h) display the corresponding B-mode image, captured at the last (60th) pHIFU pulse, and histological image with damage grading, respectively. The connective tissue structures, observed in the histological image and identified in the B-mode and DMD images, are marked by the green triangles in Fig. 5(f), (g), (h), and (i). In Fig. 5(f), clusters 1 and 2 display tissue speckles throughout the images, which are expected to represent stationary tissue, as indicated by their low frequency nature. Clusters 3 and 4 more prominently highlight connective tissue structures, as denoted by green triangles. Clusters 5–7 show hyperechoic areas with a slight central focus, with background tissue speckles, suggesting mixed modes resulting from residual bubbles and ARF-induced tissue motion. Clusters 8–10, designated as bubble clusters, were much more localized to within the ROI compared to other clusters.

Figure 5(i) presents a cumulative Doppler power map using only bubble modes superimposed onto a B-mode image at the 1st pHIFU pulse. The contour Doppler power map in Fig. 5(j) is superimposed onto the histological image. The overall shape of the power iso-levels corresponds quite closely to that of tissue damage area, whereas the width is slightly larger, and the length is substantially smaller. This may be attributed to the two opposite effects: tissue shrinking during the fixation process (both width and length) and the slight compression applied to the tissue by the coupling cone during pHIFU treatment (length). Because in this exposure vascular landmarks could be identified in both B-mode and histological images (green triangles in Fig. 5(g) and (h)), it was possible to compensate for the compression by axially stretching the Doppler map with the compensation amount associated with the distance between the tissue surface and these landmarks. Figure 5(k) represents such adjustment with 20% axial elongation, thereby providing a better agreement with the tissue damage region. Unfortunately, not all treated regions had the available landmarks for such alignment, and all the analyses presented below were based on Doppler power maps without compression compensation.

Two other representative cases of cumulative Doppler power maps and corresponding histological grading for different tissue damage levels are presented in Fig. 5(l)-(o). Specifically, Fig. 5(l) and (m) represent a lesion with maximum damage level of grade 2, whereas Fig. 5(n) and (o) show a lesion with maximum damage level of grade 3. Overall, the shape of the iso-levels in Doppler power maps are qualitatively consistent with the damaged areas graded histologically.

With the analysis across all exposures where at least a bubble mode was identified, Fig. 5(p) shows the correlation between the damage severity and corresponding Doppler power levels, calculated by spatially averaging within each histologically graded damage region, as described in “Methods” section. This result suggests that more severe damage corresponds to areas of higher Doppler power level.

The analysis of the changes in mode frequency and temporal decay rate of the DMD modes over the course of pHIFU treatment for a representative case is described in Fig. 6(a)-(i). The box plots for the mode frequency, temporal decay rate, and spatially averaged mode power levels for each eigenvalue cluster are presented in Fig. 6(a) through (c). The power of a mode is defined by |ϕ|2, where ϕ represents one column vector of mode shape matrix Φ. The bubble clusters are distinctively characterized by frequencies exceeding 0.7 kHz, marginally high temporal decay rates ranging between 0.5 and 2.5 ms-1, and low average power levels compared to clusters corresponding to stationary tissue and connective tissue structures. While, as mentioned earlier, Cluster 6 represents mixed modes between residual bubbles and ARF-induced tissue motion, this cluster also includes outlier modes, situated centrally in the eigenvalue circle in Fig. 5(d). The modes in this cluster likely represent noise due to motion out of the imaging plane caused by the respiration motion, leading to random fluctuations in pixels over slow time.

Evolution of DMD mode parameters over the course of pHIFU treatment and correlation to the highest grade level of tissue damage. The box graphs show (a) mode frequency, (b) temporal decay rate, and (c) average power of each DMD cluster for 60 HIFU pulses. Changes of (d–f) frequency and (g–i) temporal decay rate for bubble clusters (cluster 8–10) with respect to pHIFU pulse number. (j) Temporal decay rate at the last HIFU pulse, averaged across all bubble clusters from all HIFU exposures, for lesions with highest damage grades 2 and 3 (*p < 0.05).

The progression of mode frequency for each bubble cluster (clusters 8–10) with respect to the pHIFU pulse number is shown in Fig. 6(d) to (f). Early in treatment before the 20th HIFU pulse, the identification of bubble modes across the clusters was inconsistent. Notably, the bubble mode in cluster 10, corresponding to the highest frequency, was initially detected at the 5th pHIFU pulse, whereas clusters 8 and 9 were discernible from the 13th and 17th pulses, respectively. Overall, the frequencies of all clusters remain within the same range over the course of treatment, with substantial variability and no overall trend. The frequencies of clusters 8 and 9 slightly decrease, and that of the cluster 10 increases over the course of treatment. This is consistent with the physical interpretation of frequency in the context of bubble modes25. The frequency likely reflects the velocity of the bubble wall, averaged over multiple bubbles of multiple sizes within a pixel, during their dissolution following each HIFU pulse. The average velocities can be estimated as 15–40 cm/s, which is consistent with the dissolution of approximately hundred-micron sized bubbles within 1–2 ms, as reported previously14.

Figure 6(g) through (i) show the changes in temporal decay rate of the bubble clusters over the course of treatment. In all three bubble clusters the temporal decay rates decrease over the course of treatment and become less variable, although the slopes of these trends differ among the clusters. These trends were observed across all pHIFU exposures, suggesting a gradual slowdown in the dissolution rate of residual bubbles as the treatment progressed, as well as merging of the bubbles, which is aligned with the observation from our prior study and other research group25,34.

The temporal decay rate at the last (60th ) HIFU pulse collected across all exposures, averaged across all bubble clusters for each exposure, and grouped by maximum observed damage grade, is shown in Fig. 6(j). The results indicate that bubble modes from exposures with more severe damage had a lower temporal decay rate at the end of the treatment. This phenomenon could be attributed to the presence of contiguous liquefied area in grade 3 tissue damage, which may provide greater stability to the bubbles, slowing down their dissolution.

In this study, DMD was applied to planewave Doppler-based imaging of residual bubbles during pHIFU treatment in vivo, and to evaluating bubble dissolution rate following each HIFU pulses. A fully automated bubble mode identification method was developed based on two assumptions: that residual bubbles dissolve rapidly, within milliseconds, and that the bubbles are localized to the HIFU focal regions. Accordingly, to identify bubble modes, a combination of k-means clustering of discrete time eigenvalues within the left half of the complex plane and PSR based thresholding of modes for localization to ROI were used. Subsequently, DMD filtered cumulative Doppler power maps were compared to the outlines of tissue damage on H&E-stained histological images. In addition, the evolution of the frequency and decay rate of bubble modes over the course of pHIFU treatments were investigated.

First, unlike PCD, which is limited in its ability to distinguish between cavitation activity within tissue parenchyma and that occurring within vasculature or biliary structures (Fig. 3(i) and (j)), the proposed DMD and bubble modes identification method can effectively differentiate these cases. DMD modes associated with cavitation in vasculature (Fig. 5(e)) are typically tightly clustered and do not exhibit high PSR, because they may occur outside of targeted ROI. Accordingly, the DMD-filtered power Doppler map showed no significant bubble activity in those cases. This method is also effective when cavitation is induced in the intended target tissue: by deselecting clusters 1–7 shown in Fig. 5(f) that correspond to the stationary tissue, vascular flow, and acoustic radiation force-based signals, and those mixed with cavitation.

On top of that, spatial distribution of cumulative Doppler power corresponded well to the distribution of cavitation-caused tissue damage and its severity evaluated from histological sectioning. Contrasting with the IIR highpass Doppler wall filter, which relies on the frequency characteristics of bubbles and tissue, DMD-based filter leverages additional parameters: the temporal decay rates and bubbles’ spatial characteristics (i.e. their confinement to the HIFU focus), as well as their frequencies.

The comparison of DMD-filtered cumulative Doppler power maps with the extent of tissue damage from histological examination suggests a relationship between Doppler power levels and the tissue damage severity. The correlation provides a candidate quantitative indicator—Doppler power within bubble modes—of tissue damage that could be displayed in real-time to inform treatment completion. Note that, although in this work the DMD filtering and bubble mode selection were performed in post-processing, these operations are rapid, taking 0.11 s per Doppler ensemble. Further, because the adequate regions for bubble cluster identification on the complex plane were confirmed in this work, it may be feasible to select bubble modes directly in real-time, without needing to cluster the entire set of eigenvalues from all pHIFU pulses.

Crucially, DMD offers a convenient analytical perspective on the residual bubbles, much like modal analysis does in structural dynamics, by providing DMD modal parameters (e.g. mode frequency and decay rate). Following the termination of a pHIFU pulse, the residual bubbles are expected to reduce in size, at variable rates, which will cause overall amplitude reduction and rapid phase change within each pixel. DMD can efficiently extract these changes as mode decay rates and frequencies, respectively. For instance, the descending trends in decay rate over pHIFU exposure, as shown in Fig. 6(g)–(i) can be interpreted as indicative of increased bubble stability, a consequence of tissue disruption providing more space. This information can be applied to evaluate tissue damage during treatment. The decay rate of 1.5–2 ms[-1 for the current pHIFU pulse suggests an expected tissue damage level of grade 2, while a rate below 1.5 ms-1 indicates a grade 3 tissue damage level, as shown in Fig. 6(j). Furthermore, as shown in Fig. 5(p), cumulative Doppler power level can reinforce this evaluation. Although each individual parameter—decay rate or Doppler power level—displays large variance in correlation with tissue damage level, employing both parameters concurrently could enhance the reliability of the real-time damage level assessment. In practical use, the decay rate of bubble modes would be tracked in real-time and displayed throughout the treatment to estimate the maximum tissue damage level based on the threshold levels identified here. The cumulative Doppler power map can also be updated in real-time in the targeted area to predict the spatial distribution of damage based on the thresholds from Fig. 5(p).

This study is not without limitations. First, the current study was conducted on the liver tissue of only one pig; the number of damage regions was limited. Additionally, the pHIFU exposure was performed on a surgically exposed organ, and the Doppler images were devoid of noise from intervening tissues. Another challenge lies in the high complexity of planewave image datasets, which can contain multi-structural motions, potentially diminishing the decomposition quality of the DMD analysis. Due to the rapid dissolution of residual bubbles, the dataset size for DMD in slow time is necessarily limited; for instance, only 13 planewave images were utilized in this study, which consequently caps the maximum achievable decomposition rank. To mitigate this, the DMD processing window was carefully adjusted to the confined area around HIFU focus, as mentioned in “Methods” section. Further enhancements in decomposition quality could be achieved through the implementation of a high pulse repetition frequency (PRF) acquisition scheme to increase the dataset25 or by compensating for respiration motion35—a primary factor to the dataset’s complexity. Furthermore, the proposed bubble clusters/modes selection algorithm has potential for improvement. The PSR threshold and the bubble cluster selection method used in this study (i.e. 50% of modes above PSR threshold) were empirically determined from our prior study in ex vivo tissue25. The method is yet to be optimized for effectiveness. Additionally, the accuracy of eigenvalue clustering could be enhanced by leveraging advancements in unsupervised clustering techniques, particularly those employing state-of-the-art machine learning algorithms.

HIFU transducer used in this study was a 1.5 MHz, spherically focused 12-element sector array that had 8 cm aperture size, 6 cm nominal focal distance, and 2 cm circular central opening. The size of the focal region of this transducer in linear propagation regime at -6dB was 0.46 mm diameter by 3.8 mm length. A degassed water-filled coupling cone was attached to the front side of the HIFU transducer and sealed with acoustically transparent membrane. The distance from the membrane to the HIFU focus was 2.5 mm, and the diameter of the opening was 13 mm. The transducer was controlled by high power driving electronics – a custom built 12-channel class D amplifier system36,37. The ultrasound imaging probe was a 64-element ATL P7-4 probe coaxially installed at the center opening of the HIFU transducer, controlled by Verasonics V1 system.

All procedures in the animal experiments followed the protocols approved by the Institutional Animal Care and Use Committee at the University of Washington, Seattle, WA, USA, and all experiments were performed in accordance with relevant guidelines and regulations. This study was also conducted in accordance with ARRIVE guidelines. The pig was housed in a facility at the University of Washington, which is fully accredited by the Association for Assessment and Accreditation of Laboratory Animal Care International. Before the experiment, the pig was anesthetized with Telazol premedication and then maintained in surgical plane of anesthesia with isoflurane over the course of the experiment. The approximately 20 cm midline abdominal incision was made, and sterile degassed saline was poured into the abdominal cavity for acoustic contact. The HIFU transducer assembly was mounted to a flexible gooseneck holder, and before each exposure the tip of the coupling cone was brought into direct contact with the surface of the liver, with slight pressure, and the transducer position was locked. The pig’s respiration rate was in the range of 2.3–3.4 s/breath with approximately 1–2 mm lateral displacement at the HIFU cone tip. During the treatment, real-time B-mode and PCD were used to monitor for cavitation within the coupling water in the cone. If such cavitation was detected, the membrane and water were immediately replaced. After the treatment, the position of each target was marked on the liver surface at 5 mm distance by a brief contact with a cautery device cross-wise in four locations and photographed for gross examination of the treated tissue surface. After the exposures the animal was euthanized via anesthetic overdose (intravenous injection of pentobarbital solution, > 87 mg/kg), and the targeted area of tissue, referred to as lesions from here on out, were collected en bloc and fixed in 10% neutral buffered formalin. Following fixation, the lesions were bisected along the line of cautery markers and then paraffin-embedded for histology. Two 5-micron thick histological sections were taken from either side of the bisected lesion, and another two sections – 500 microns below the surface to ensure that the center of the lesion was captured, and stained with H&E. The section that contained the largest lesion was assumed to be most centrally located and was selected for subsequent analysis.

The pHIFU pulsing protocol used in this study was the same as that used in previous studies from our group1,14,37: 1 ms long pulse was delivered at 1 Hz PRF. Each HIFU pulse was immediately followed by 13 planewave Doppler pulses with a 3 kHz PRF and conventional 128 ray-lines B-mode imaging pulses. Each of these Doppler pulses had a center frequency of 5 MHz and a pulse length of 3 cycles. The spatial resolution of the planewave images at the focus, obtained from the full width half maximum of point-spread function from measurement, was 2.17 mm in lateral and 0.46 mm in axial.

The focal waveforms corresponding to the three different HIFU output levels were measured in water using a fiber-optic probe hydrophone (FOPH 2000, RP Acoustics, Leutenbach, Germany). Among the 12 locations treated, three were subjected to the lowest HIFU output level (acoustic power of 170 W, peak positive/negative pressure levels of 67.0/-11.4 MPa), that was expected to be just below the cavitation threshold. Five locations were treated at the intermediate output level (260 W and 87.0/-13.1 MPa), expected to induce low to medium cavitation activity and moderate tissue damage. The other four locations underwent treatment at the highest output level (600 W, 120.2/-16.0 MPa) to generate more severe mechanical tissue damage.

PCD processing consisted of the following steps. First, delay-and-sum beamforming was applied to the radio-frequency (RF) signals captured by the imaging probe to align their phases at the HIFU focal point. Subsequently, the beamformed RF signal underwent a two-step filtering process to eliminate the backscattered HIFU harmonics. First, a bandpass filter with a cut-off frequency range of 2.5–7.5 MHz was applied. Then, a comb notch filter with a 500 Hz stopband at HIFU harmonics was used. The resulting signal corresponded to broadband signal from inertial bubble collapses, and two PCD metrics were derived from it. The first was the noise level (NL), which reflects the temporal average of broadband signal amplitude:

where x represents the filtered RF signal, and N is the total number of sampling points in the signal. The other metric was the amplitude ratio (AR), indicating the ratio between the maximum absolute value of signal and the cavitation threshold, defined as maximum absolute value of background noise multiplied by \(\:\sqrt{5}\), in accordance with Rose criterion38:

where \(\:{x}_{noise}\) denotes the background noise of the filtered RF signal.

The signal processing described in this section was performed offline using MATLAB 2022a (v9.12) (MathWorks). The processing was applied to the 2-dimensional in-phase quadrature (I/Q) modulated planewave image datasets acquired by Verasonics.

To perform DMD, each of the 13 planewave I/Q images, acquired immediately after a HIFU pulse, was reshaped into column vectors, and then arranged into matrices \(\:\varvec{X}\) and \(\:{\varvec{X}}^{\varvec{{\prime\:}}}\), each having 12 columns. These matrices corresponded to the 1st–12nd and 2nd–13rd planewave images, respectively. The number of rows (\(\:n\)) in these matrices was on the order of \(\:{10}^{3}\), corresponding to the total pixel count within the DMD processing window (\(\:\cong\:\)1 cm square). In the linear approximation, the two matrices are related as:

Here, \(\:\varvec{A}\) is an \(\:n\times\:n\) matrix, and its direct calculation can be computationally expensive. Instead, DMD provides a rank- \(\:r\) approximation of eigenvectors (\(\:\varvec{\Phi\:}\)) and eigenvalues (\(\:\varvec{\Lambda\:}\)) of \(\:\varvec{A}\), expressed as

where \(\:\varvec{\Phi\:}\) is an \(\:n\times\:r\) matrix, each of columns is eigenvector of \(\:\varvec{A}\); \(\:\varvec{\Lambda\:}\) is an \(\:r\times\:r\) diagonal matrix, each of diagonal elements is eigenvalue of \(\:\varvec{A}\); and the superscript \(\:-1\) indicates the inverse of the given matrix.

DMD processing aims to find \(\:\varvec{\Phi\:}\) and \(\:\varvec{\Lambda\:}\), and was described in detail in our previous study on pHIFU ex vivo25 and other studies in fluid mechanics27,39,40. Thus, we provide an abbreviated description of the procedure here.

Calculate the truncated singular value decomposition (TSVD) of \(\:\varvec{X}\), with the truncation rank r determined such that the cumulative sum of the top \(\:r\) singular values exceeds 97% of the total sum of them25:

where columns of \(\:{\varvec{U}}_{r}\) and \(\:{\varvec{V}}_{r}\) matrices are the left and right singular vectors truncated to rank \(\:r\), \(\:{\varvec{\Sigma\:}}_{r}\) is a rank \(\:r\) diagonal matrix where each element is a singular value, and the asterisk denotes the conjugate transpose.

Compute the reduced order \(\:r\times\:r\) matrix \(\:{\varvec{A}}_{\varvec{r}}\), which is a similarity transformation matrix of \(\:\varvec{A}\):

Find matrix Λ through the eigen-decomposition of \(\:{\varvec{A}}_{\varvec{r}}\):

where \(\:\varvec{W}\) is the eigenvector matrix of \(\:{\varvec{A}}_{\varvec{r}}\).

Calculate matrix \(\:\varvec{\Phi\:}\):

Each eigenvector (column vectors of \(\:\varvec{\Phi\:}\)) is also referred to as mode shape. These can be transformed into 2D images, with the expectation that they correspond to physically interpretable modes such as bubbles, near-stationary tissue, ARF-induced motion, or blood vessels25. The discrete-time eigenvalues (diagonal elements of \(\:\varvec{\Lambda\:}\)) provide information about how these corresponding DMD mode shapes evolve over slow time with regard to frequency and temporal decay rate.

Identification of the modes associated with bubbles was based on their spatiotemporal characteristics. We hypothesized that, as a temporal characteristic, bubbles would be rapidly dissolving or undergoing size changes. Furthermore, as a spatial characteristic, these bubbles were expected to occur at the confined area around HIFU focus, in contrast to tissue or vasculature. In light of this hypothesis, we used a dual approach for automatic bubble mode identification: k-means clustering of eigenvalues to assess the temporal characteristics and the contrast-based metric thresholding of the DMD mode shapes to evaluate the contrast in the area where bubbles are expected.

In each pHIFU exposure, the discrete-time eigenvalues for all HIFU pulses were plotted on the complex plane. Here, the angle corresponding to a data point represents the frequency, and the distance from the origin indicates growth or decay rate. Subsequently, the eigenvalues were grouped using k-means clustering, an unsupervised learning method that groups the dataset into ‘k’ clusters by minimizing the distance between each data point and the centroid of its corresponding cluster25. The number of input clusters was set as the average number of modes identified by DMD across the HIFU pulses. This process enabled the grouping of modes with similar temporal characteristics into the same cluster, under the assumption that the temporal behavior of the same modes (e.g. bubbles or tissue) had similar dynamics over the course of pHIFU exposure.

Within the set of clusters, the bubble clusters were identified using a peak-to-sidelobe ratio (PSR) thresholding method. PSR stands as a contrast-based metrics, similar to the contrast-to-noise ratio (CNR), designed to quantify the level of contrast within the ROI in comparison to the background. The distinction between PSR and CNR is PSR’s utilization of the maximum value within the ROI, as opposed to the average value. PSR was defined as

where \(\:{S}_{ROI}\) and \(\:{S}_{background}\) represent the mode shape image within ROI and all other regions, respectively, and \(\:{\sigma\:}_{background}\)denotes the standard deviation of the brightness of the pixels in the background region. In this method, the size of ROI was set to be laterally 3.5 mm around HIFU focus and axially 2.5 mm, positioned just below the tissue surface, as bubbles were expected in that area. The clusters were identified as associated with bubbles when over 50% of modes within the same cluster exceeded the PSR threshold. Finally, the bubble images in slow time were generated for each HIFU pulse using only the modes that surpassed the PSR threshold within the identified bubble clusters:

where \(\:{\varvec{x}}_{k,bubble}\) represents kth bubble images in slow time, subscript \(\:B\) denotes bubble modes, and \(\:\varvec{b}\) is the initial mode amplitude vector corresponding to the first planewave image \(\:{x}_{1}\) (i.e. \(\:\varvec{b}={\varvec{\Phi\:}}^{\dag}{x}_{1}\), where \(\:\dag\) denotes pseudo inverse).

Following the generation of 12 bubble mode images in slow time, a conventional zero-lag autocorrelation was applied to them to obtain a Doppler power map. Note that this Doppler image corresponded to a single HIFU pulse. Subsequently, the cumulative Doppler power map was normalized by the spatially averaged power level of the lowest frequency mode shape among the DMD modes corresponding to the first HIFU pulse. This mode shape is representative of the brightness level from near-stationary tissue around the targeted area (i.e. lowest frequency mode), before the tissue damage occurs (i.e. first HIFU pulse). This normalization step was expected to account for natural variability in backscattered signal amplitude between pHIFU exposures. The final processing step involved summing the Doppler power maps over the 60 HIFU pulses. The resulting cumulative Doppler power map was directly compared to the distribution of tissue damage within the corresponding histological section.

The scaled damage area (SDA) was calculated for the graded histological maps as follows:

where \(\:G\) indicates the grade within the range of 1 to 3, and \(\:{A}_{G}\) represents the area assigned to each grade.

Comparison of the spatial distributions of tissue damage to the cumulative Doppler power maps in each pHIFU exposure was performed as follows. The cumulative Doppler power map was superimposed onto the graded histological image by aligning the position of the HIFU focus on both images. In the histological image, the distance from the focus location to the tissue surface was determined using raw RF signals from PCD. Specifically, we measured the distance corresponding to the time between arrival of the reflection from the tissue surface and the time of flight corresponding to the focus, as measured by FOPH. The lateral focus location was defined as the centroid of the area presenting the highest grade of tissue damage. Subsequently, the Doppler power levels falling within each of the three damage grade regions were averaged.

The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

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This work was supported by NIH under Grant R01EB023910, and 2R01CA154451.

Minho Song

Present address: Department of Radiology, Stanford University, Stanford, USA

Department of Mechanical Engineering, University of Washington, Seattle, WA, 98195, USA

Minho Song

Applied Physics Laboratory, Center for Industrial and Medical Ultrasound, University of Washington, Seattle, WA, 98195, USA

Oleg A. Sapozhnikov, Vera A. Khokhlova, Stephanie Totten, Yak-Nam Wang & Tatiana D. Khokhlova

Physics Faculty, Moscow State University, Moscow, 119991, Russia

Oleg A. Sapozhnikov & Vera A. Khokhlova

Division of Gastroenterology, University of Washington School of Medicine, Seattle, WA, 98195, USA

Helena Son & Tatiana D. Khokhlova

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M.S. and T.K. conceived the concept. M.S., H.S., S.T., Y-N.W., and T.K. performed in vivo experiments and data acquisition. H.S., S.T., and Y-N.W. prepared samples for histology, M.S. processed and analyzed the data and wrote the manuscript draft. M.S., O.S., V.K., and T.K. interpreted the results, M.S., O.S., Y-N.W., V.K., and T.K. reviewed and edited the manuscript.

Correspondence to Minho Song.

The authors declare no competing interests.

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Song, M., Sapozhnikov, O.A., Khokhlova, V.A. et al. Dynamic mode decomposition based Doppler monitoring of de novo cavitation induced by pulsed HIFU: an in vivo feasibility study. Sci Rep 14, 22295 (2024). https://doi.org/10.1038/s41598-024-73787-w

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Received: 11 June 2024

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DOI: https://doi.org/10.1038/s41598-024-73787-w

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