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The Ultrasound Journal logoLink to The Ultrasound Journal
. 2026 Mar 4;18(1):18060. doi: 10.5826/tuj.2026.18060

Towards reduced ultrasound localization microscopy acquisition times by uncoupling a bi-disperse microbubble population

Giulia Tuccio 1, Lisa te Winkel 2, Corinne Bruggeman 2, Wim Van Hoeve 2, Libertario Demi 1,✉
PMCID: PMC13320580  PMID: 41926114

Abstract

Background:

Ultrasound Localization Microscopy (ULM) is a milestone in the medical vascular imaging context, enabling the precise characterization of microvascular structures using ultrasound imaging. By accurately localizing contrast microbubbles (MBs) flowing in the circulatory system, ULM generates microresolved vascular images, overcoming the ultrasonic diffraction limit. However, as ULM relies on precise localization and tracking of individual MBs, high MB concentrations yield to increased localization errors and, ultimately, ULM failure. This constraint limits ULM to low MB concentrations, resulting in long acquisition times that pose challenges in clinical settings.

Methods:

Here, we show the feasibility of uncoupling a bi-disperse MB population, composed of two monodisperse MB populations. The uncoupling is performed through a signal processing pipeline that exploits the strong nonlinear response of MBs having resonance frequency tuned with the transmission frequency. After uncoupling, ULM density and velocity flow maps are generated.

Results:

Density and velocity maps are generated after uncoupling, when injecting the bi-disperse population individually and simultaneously in a vascular 3D-printed phantom. Furthermore, density maps generated after uncoupling are compared with the one obtained using standard ULM. Results demonstrate the capability of the proposed uncoupling pipeline to separate the bi-disperse population.

Conclusions:

This work presents a signal processing pipeline to uncouple a bidisperse MB population, formed by two monodisperse MB populations. are validated in a 3D-printed phantom and demonstrate the feasibility of the uncoupling which, in turn, would enable higher concentrations and reduce acquisition times for micro-vascular imaging.

Keywords: ultrasound localization microscopy, ultrasound contrast agents, microbubble uncoupling, monodisperse microbubble population, signal processing

Background

Ultrasound imaging is extensively used in the clinical context owing to low cost, nontoxicity and ease of use (1, 2). Because of these features, it is applied in various medical fields, including maternity, gynaecology, urology, cerebrovascular examinations, and intraoperative procedures (3). Despite its broad range of applications, imaging the micro-vascular bed is challenging for ultrasound imaging. Ultrasound is not able, per se, to resolve vascular structures smaller than the diffraction limit, which is half-awavelength (for instance, a 5 MHz ultrasound wave in tissue has a 300 µm wavelength) (1, 4). Micro-vascular structures reach down to 10 µm (5), thus are indistinguishable to ultrasound (4, 5). In an effort to break the ultrasound resolution limit, Couture et al. (4) and Siepmann et al. (6) proposed to accumulate localizations of injected microbubbles (MBs) to enhance microvascular imaging spatial resolution. These works gave birth to Ultrasound Localization Microscopy (ULM). ULM combines the ultrasound-based medical imaging benefits, enabling the visualization of static and dynamic properties of microvascular structures (4, 6). The spatial resolution of ULM-generated images ranges from a fifth to a tenth of the wavelength (8). ULM exploits the strong acoustic scattering signals produced by gas-filled contrast microbubbles, whose dimension is substantially smaller than the typical ultrasound wavelength (9). While the diffraction limit dictates the resolution of MBs’ ultrasound images, which can be estimated through a Point Spread Function (PSF) (see Figure 1a as an example), individual MB can be localized with precision below the diffraction limit (4, 6, 10). By tracking the localized MBs through a sequence of ultrasound images, ULM generates the micro-resolved density maps. These tracks also provide dynamic information on vascular structures, such as flow velocity and direction, allowing ULM to capture structural and functional information (1, 4, 6, 11, 12). The level of detail provided by ULM’s density and velocity maps has the potential to be a powerful tool in the clinical context. Specifically, ULM preserves the benefits of ultrasound (such as safety, cost-efficiency, and non-toxicity) while offering resolution beyond the diffraction limit at clinically relevant depth. Furthermore, ULM can be implemented as a post-processing step, making it easy to integrate into clinical practice to provide a more comprehensive understanding of the circulatory system and its functioning. ULM could also help understand the correlation between microvascular alterations and diseases like cancer, diabetes, and arteriosclerosis, which is valuable for diagnostic and therapeutic monitoring (1, 4, 3–15). Although the technique has been present for more than a decade, its clinical applications are limited by various factors, including long acquisition times, high temporal resolution and MBs’ inaccurate localization and tracking due to noise and motion (1, 2, 11). This study addresses the ULM’s long acquisition time constraint. MB localization precision is crucial for the quality of the reconstructed images. However, ULM requires isolated MB signals for accurate localization. Failing to ensure MB sparsity would cause overlapping MB PSF in ultrasound images. Because localization errors related to such situations are high, these MBs are usually excluded from the analysis. As a result, ULM often operates with low MB concentrations, leading to long acquisition times to accumulate an adequate number of MBs to cover the microvasculature in the region of interest. These limitations are particularly restrictive in clinical applications where microvascular imaging is of diagnostic relevance (11, 16, 17) and where physiological motion is unavoidable (11, 18, 19). To improve MB localization despite high concentrations, different flavors of deep neural network architectures have been proposed (20–23). Furthermore, in (11), Huang et al. alleviated the localization problem for high-density injections by dividing the MBs into subpopulations based on flow dynamics. Unlike the polydisperse MBs commonly used in ULM, monodisperse MBs exhibit a narrow size distribution. This small size variability enables optimal tuning of the imaging frequency to match the MBs specific characteristics (e.g. MB resonance frequency), thereby enhancing acoustic performance and improving ultrasound contrast imaging. This has been demonstrated by studies showing that monodisperse MBs reduce imaging artifacts and enable the visualization of deeper blood vessels (24–26). In this study, we leverage the advantages of monodisperse MBs to overcome the trade-off between MB concentration and acquisition time. Specifically, we introduce a bi-disperse MB population composed of two distinct monodisperse MB types. We propose an uncoupling pipeline to separate these two populations based on their different frequency response. As a proof of concept, we apply this technique to ultrasound data acquired from a 3D-printed vascular phantom.

Figure 1.

Figure 1.

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Full field Point Spread Function (PSF) and frequency response in dB for p5.5MHz (a) and p3MHz (b). The frequency response is evaluated as the Fourier transform along the fast time at the maximum-intensity line, highlighted by the red dashed line.

Methods

Bi-disperse MB populations

By localizing and tracking the echoes produced by individual MBs flowing in the circulation, ULM generates micro-resolved density maps (1, 4, 7, 27). In this study, we uncouple a bi-disperse MB population. The bi-disperse population is composed of two monodisperse MB populations, each having a different frequency response. In particular, we select one population (p5.5MHz) generating mainly the fundamental response, having the resonance frequency not tuned with the transmission frequency and one population (p3MHz) producing a strong nonlinear signal, having the resonance frequency matching the transmission frequency. Thus, the non-linear signal intensity allows for the uncoupling of the two populations. p5.5MHz and p3MHz diameter and resonance frequency are presented in Table 1. Figure 1 shows the Point S Spread Function (PSF) and frequency response of p5.5MHz (in Figure. 1a) and p3MHz (in Figure. 1b) obtained when acquiring the data at 3 MHz in water. The frequency response is evaluated as the Fourier transform along the fast time at the maximum-intensity line, shown in Figure 1 with the red dashed line. Being p3MHz the population whose resonance frequency matches the transmission frequency, its frequency response is strongly nonlinear (in Figure 1b). Oppositely, p5.5MHz’s frequency response exhibits a linear behaviour.

Table 1.

Populations p5.5MHz and p3MHz dimensions in micro-meter and resonance frequency in MHz.

p 5.5MHz p 3MHz
Diameter 2.5 µm 4.0 µm
Resonance Frequency 5.5 MHz 3 MHz
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The bi-disperse MB population used in this study is produced by Solstice Pharmaceuticals. Each monodisperse MB population is created using a microfluidic chip device (MicroSphere Creator, Solstice Pharmaceuticals, Enschede, the Netherlands) (28). The microfluidic chip allows for control of the dimension, and consequently, the resonance frequency of the MBs, ensuring monodispersity (29). During the production phase, the chip mixes the gas and liquid with a flow rate tailored to the desired MB size. Following production, the MB size distribution and resonance frequency are measured. Figure 2 shows the size distribution of the bi-disperse population when mixed over an hour. The size distribution is measured every 5 minutes using a Coulter Counter (MultiSizer 4e, Beckman Coulter, Brea, CA). Figure 2a demonstrates that the MBs remain bi-disperse in a time window typical of ULM. Figure 2b displays the resonance frequency of p5.5MHz and p3MHz. As in (30), the resonance frequency is estimated through attenuation for individual populations. Briefly, a 7.5 MHz (for p5.5MHz) and 5 MHz (for p3MHz) transducer (V309-SU and V320-SU, Olympus, Waltham, Massachusetts, USA) generate an acoustic beam, which after traversing a bubble screen, is reflected and received by the same transducer. The pulser (DPR300 Ultrasonic Pulser Receiver JSR Ultrasonic NY, USA) synchronises the transmitting and receiving phases (30). In transmission, a broad-bandwidth pulse is sent to the bubble screen. Then, the attenuation is measured as the difference between the received power spectrum crossing the MB screen and a reference spectrum measured without MBs. Finally, the resonance frequency is estimated to be the frequency showing the highest attenuation. The high control of the MB dimensions and their stability over time offers the possibility to select two distinguishable MB populations.

Figure 2.

Figure 2.

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Size distribution (a) and resonance frequency (b) measurements for p5.5MHz (2.5 µm) and p3MHz (4.0 µm), evaluated after MB production.

Data acquisition

Ultrasound data were acquired with MBs flowing through a custom 3D printed flow phantom running at a constant flow rate with MBs varying concentrations (dilution of 10000x-20000x in de-gassed water). The phantom is printed in collaboration with PROM Facility, Rovereto, Italy, using the Selective Sintering Laser technique, which fuses polymer powders material via laser (31). The laser thermal source allows heating of the polymer at a specific location, thus building the 3D solid structure layer-bylayer at a sub-millimetre scale. The material used to print the 3D vascular phantom (Flexa TPU, elastic module 76 MPa, and, density 1.04 g/cm2) permitted ultrasound imaging. The 3D model design is visible in Figure 3. The model has three injection points, and channels with varying dimensions ranging from a diameter of 2 mm to 1.5 mm. The experimental data acquisition is performed with the phantom positioned vertically in a tissue-mimicking gel to avoid any movement during the acquisition process, as shown in Figure 3. In the study, we utilize two injection points, each connected to a syringe pump flowing at a constant rate of 2 ml/min. Each syringe contains a different MB population. MB populations are diluted in de-gassed water and kept in suspension with a steering plate. Injections of 20 ml are performed continuously. Ultrasound data are acquired for each MB population singularly and simultaneously. For individual injections, we inject MBs into the first channel and water in the second channel for p5.5MHz, while for p3MHz, the injections are reversed.

Figure 3.

Figure 3.

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Experimental set up. The phantom has three injection points, two of which are connected through tubes to a pair of syringes, each containing a specific MB population. Continuous injections are performed using a syringe pump. Data acquisitions are performed using the ULAOP and and a linear array.

To acquire the radio-frequency data, we employ a programmable ultrasound platform (ULAOP), and a linear array probe (Esaote LA533, Florence, Italy (32)), placed horizontally to the 3D printed channels, as shown in Figure 3. Line-by-line was implemented acquiring 64 lines for each image. A pulse with a center frequency of 3 MHz and bandwidth of 1 MHz was used in transmission. For each record, 250 frames are acquired with a frame rate of 187 Hz. The sampling frequency is 50 MHz.

ULM data processing

To generate the density and dynamic maps of the MB populations, we implement a common ULM framework, summarized in Figure 4. After data acquisition, filtering is applied to the ultrasound RF data. Specifically, filtering is implemented by a Butterworth band-pass filter, with 2 MHz and 20 MHz as lower and upper cut-off frequencies. A singular value decomposition (SVD) filter is then applied. The SVD filter removes the first k-value of the decomposition, assuming that these represent the coherent spatio-temporal background signal (1, 4). In this study, the k-value is experimentally selected to 5, consistent with the range discussed in other studies (4, 33). Next, the MBs uncoupling is deployed to generate two subsets of ultrasound images, each of which represents one of the uncoupled populations (hp3MHz for population p3MHz and hp5.5MHz for population p5.5MHz). Finally, the ULM framework comprising detection, localization, tracking, and accumulation is applied. The detection step is performed using two different methods (Ipix and ncc):

Figure 4.

Figure 4.

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At the top (a) uncoupling pipeline for the bi-disperse MB population. Uncoupling is performed after data acquisition and filtering. As a result of the uncoupling, a set of images for each population (hp5.5MHz for p5.5MHz and hp3MHz for p3MHz) are obtained. Next, a ULM framework comprising of detection, localization, tracking and accumulation, is applied. At the bottom (b) detail of the uncoupling procedure of p5.5MHz and p3MHz. First, the first and second harmonics are filtered employing a Butterworth filter in the frequency domain. Successively, the envelope detection is used to generate the images of the first (h1) and second harmonics (h2). Images of the two populations hp5.5MHz and hp3MHz are evaluated as h1 −h2 and h2 respectively.

  1. Localization using Pixel Intensity (Ipix). The technique, presented by Couture et. al. (33), assumes that an MB echo is represented by the brightest pixels in the ultrasound image. The technique requires estimating m (the number of MBs) present in each frame. Here, m is optimally selected to 30-50 MBs/frame based on the dilution. Next, the m brightest pixels, isolated at least by the dimensions of a MB PSF are considered MB detections.

  2. Localization through correlation (ncc). Similar to (5, 33), this technique utilizes a mean PSF obtained by acquiring the ultrasound data of p5.5MHz and p3MHz in water. The PSF is specific to each population and is obtained by averaging the PSF of 20 MBs in different acquisitions. The PSF for the two populations can be seen on the right side of Figure 4b. For each frame, a 2D normalized cross-correlation between the filtered images and the MB PSF is evaluated. This results in a crosscorrelation map, where the peaks correspond to MB detections. To further improve the detection performance, a threshold of 0.5 is selected as the minimum correlation to consider the pixels as MB signals. This threshold value was empirically selected based on the data of this study. If the correlation is lower than the threshold value, the pixels are considered background noise and are excluded.

  3. Localization through correlation and pixel intensity (Ipix + ncc). This detection technique consists of merging in cascade the ncc and Ipix methods. In particular, the detections identified by ncc proceed to the localization step only if their intensity, evaluated at its center, is among the k brightest pixels. The correlation threshold and k are optimally selected as 0.4 and 12 respectively.

The comparison between these detection algorithms provides proof of the robustness of the proposed uncoupling pipeline. In this way, we confirm the uncoupling capability when using a standard algorithm (brightest pixel) while demonstrating the possibility of improving performance using a model-based algorithm (normalized-cross-correlation) and a combination of the two. To ensure a fair comparison between the methods, the parameter values are empirically determined through a parameter search optimization. Note that the results using Ipix + ncc detection method are produced only for simultaneous MB injections as this represents the more realistic scenario. After detection, a Gaussian fitting (4, 7, 1) is performed to further refine the localization estimate. For each detection, a Gaussian distribution is fitted by subsampling the pixels by a factor of 10, as described in (1). Next, MB centroids for each population are tracked through a bipartite matching algorithm. The algorithm finds the optimal frame-to-frame pair for all the MB signals, matching them in such a way that the total distances of all the MBs are minimized (1, 32, 34). Repeating the process for all the frames in a record generates MB tracks. To improve tracking precision, MBs with persistence shorter than 7 frames are discarded. Finally, density and dynamic maps are obtained through the accumulation of these tracks.

Microbubble uncoupling

The uncoupling is performed as a pre-processing stage (see Figure 4). First, we apply a Butterworth filter to separate the first and second harmonic components. The filter has a center frequency of 3 MHz and 6 MHz for the first and second harmonic respectively, and 1 MHz of bandwidth. Next, we apply a Hilbert transform to generate the ultrasound images associated with the first (h1) and second (h2) harmonic signal. As shown by Figure 4b, the uncoupling is performed as follows:

  • - p5.5MHz is the population characterized by a resonance frequency (5.5 MHz) not matching the transmission frequency (3 MHz) and, as a consequence, by a linear response. p5.5MHz images (hp5.5MHz) are obtained by subtracting the first (h1) and second (h2) harmonic images:

hp5.5MHz = h1− h2. (1)

An example of PSF for h1, h2 and hp5.5MHz is shown in Figure 5b.

Figure 5.

Figure 5.

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Example of h1 and h2 for populations p3MHz and p5.5MHz (a). Results of applying Equations 1 and 2 to both populations(b).

  • - p3MHz is the population whose resonance frequency matches the transmission frequency (3 MHz) and thus has a strong nonlinear response. p3MHz is isolated by imaging the second harmonic:

hp3MHz = h2. (2)

The first (h1) and second (h2) harmonic PSFs of a MB belonging to population p3MHz are shown in Figure 5b.

Note that, by applying 1 to population p3MHz would cancel out this MB population signal. Similarly, using equation 2 to image p5.5MHz would cancel out its contribution. As such, the equations allow to selectively image each MB population, thus permitting the uncoupling. To verify this, we perform the experiments having only one population injected in one channel, meanwhile flushing water in the other. This choice would allow us to understand the potential cross-talk between the two MB populations. Next, we apply the proposed pipeline when injecting the two MB populations at the same time.

Results

This work demonstrates the feasibility of uncoupling the bi-disperse MB population based on the intensity of each MB’s population nonlinear response. In fact, we are able to reconstruct density and flow dynamics maps in a 3D printed phantom using the proposed uncoupling pipeline (Figure 4). Figures 6a and 6b show respectively the density and flow direction maps for the detection method based on the brightest pixels (Ipix) and normalized cross-correlation method (ncc). Data are acquired after separate injections of each population, and the uncoupling generates images of population p5.5MHz and p3MHz, marked as hp5.5MHz and hp3MHz. Figure 6b shows the flow direction images which are color-coded, with red marking the flow away from the probe, and blue the flow towards the probe. Individual injections serve as an initial validation for the uncoupling pipeline while having a ground truth. During single injections and in case of perfect uncoupling, the residual images obtained by attempting to image the non-injected population should be empty. For instance, in 6a first column, only p3MHz has been injected. After injection, the uncoupling and ULM pipeline produce images of both populations hp3MHz and hp5.5MHz, using Equations 1 and 2, respectively. As such, hp3MHz displays tracks of the MB population, since p3MHz is the population injected. On the other hand, h5.5MHz is empty, as it attempts to image the population which is not present. We mark the residual images with a red background for both the density and flow direction maps (Figure 6). Intensity profiles of two cross-sections for both detection methods (Ipix and ncc) are displayed in Figure 7a and 7b, for p3MHz and p5.5MHz respectively. Additionally, the full width half maximum (FWHM) values further highlight the ability of the proposed pipeline to depict the geometry of the vascular structures (see arrows in Figure 7).

Figure 6.

Figure 6.

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ULM-generated density (a) and flow direction (b) maps for population p3MHz (hp3MHz) and p5.5MHz (hp5.5MHz) after individual injection as indicated by each column subtitle. The first row of (a) and (b) represents the images of p3MHz and p5.5MHz when injecting MBs; the second row shows the images of each when injecting the other. Images are shown for detection methods Ipix and ncc. In (b), flow direction is color-coded: red = flow away from the probe, blue = flow toward the probe.

Figure 7.

Figure 7.

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One-dimensional intensity profiles at different depths as indicated in the top images corresponding to the solid (1) and dashed line (2). The FWHM values are indicated in millimeters and by black arrows. Images are shown for detection methods Ipix and ncc, for population p3MHz (a) and population p5.5MHz (b).

Table 2 shows the quantitative metrics for the density maps generated for the two populations utilizing Ipix and ncc as detection methods. The table presents the results in terms of saturation, evaluated as the number of pixels covered by MBs tracks, mean detections per frame and mean tracks per record. The mean track/record is the average value of the total tracks found after applying the bi-partite tracking algorithm. The mean detections/frame and mean tracks/frame metrics are particularly relevant in discussing the performance of the uncoupling pipeline. In fact, knowing which MB population is present in each channel, the number of residual detections and tracks is a direct evaluation of false positives. Finally, we evaluate the percentage of mean accepted track per record, which represents the percentage of the total number of tracks after filtering out short tracks. This metric reflects tracks quality, since short tracks are likely the results of poor detections and noise, and, as such, are unreliable for micro-vascular reconstruction (8, 35). Figure 8 shows the ncc generated tracks for both populations superimposed with the 3D printed phantom design. Figure 9 and Table 3 show the density maps and the evaluation metrics generated when injecting the two populations simultaneously for the three detection methods. Furthermore, a comparison with density maps generated by using a standard ULM pipeline before uncoupling for Ipix and ncc detection methods is presented in Figure 10. Note that for Ipix detection method the number of MBs present per frame has been increased to account for more MBs in one frame. Regarding the ncc detection method, the same correlation threshold has been applied.

Table 2.

Results for the two detection methods Ipix (brightest pixel) and ncc (normalized cross-correlation).

I pix
Injections of p3MHz Injections of p5.5MHz
hp3MHz hp5.5MHz hp5.5MHz hp3MHz
Saturation (%) 9.1 4.1 10 0.5
Mean detections/frame 6 4.2 15 2
Mean tracks/record 150.3 124.9 358 20
Mean accepted tracks (%) 57 15 27.7 1
ncc
Injections of p3MHz Injections of p5.5MHz
hp3MHz hp5.5MHz hp5.5MHz hp3MHz
Saturation (%) 10.7 1 12 0.4
Mean detections/frame 5 1.5 11.2 1
Mean tracks/record 104.5 14 334 12
Mean accepted tracks (%) 28.2 3.1 16.7 0.1
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Figure 8.

Figure 8.

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Superimposed image of the ULM generated density maps with the phantom design utilizing ncc as detection method.

Figure 9.

Figure 9.

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Density maps generated after uncoupling when injecting the MB populations simultaneously. Maps are generated using Ipix (a), ncc (b) and Ipix+ncc (c).

Table 3.

Results for the three detection methods when injecting the two MB populations simultanously.

I pix ncc Ipix + ncc
hp5.5MHz hp3MHz hp5.5MHz hp3MHz hp5.5MHz hp3MHz
Saturation (%) 14.1 12.4 13.2 18.3 13.1 8.9
Mean detections/frame 10 10 21 17 12 12
Mean tracks/record 168.6 347 822 923 199 84
Mean accepted tracks (%) 74.2 44.7 57.3 62.8 72.2 82.5
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Figure 10.

Figure 10.

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Standard ULM generated density maps (before uncoupling) for the simultaneous injections using two detection methods: Ipix and ncc.

Discussion

In this article, we present an acoustically separable bi-disperse MB population composed of two monodisperse MB populations. Separation is achieved through an uncoupling pipeline that exploits differences in the nonlinear acoustic responses of the two MB populations. This approach potentially enables the use of higher MB concentrations in ULM vascular imaging, resulting in faster vascular filling and shorter data acquisition times. Reducing acquisition times is essential for clinical translation of ULM, as it decreases susceptibility to physiological motion such as respiration, cardiac pulsatility, and organ displacement. Results highlight the performance of the technique when individual (Figure 6) and simultaneous (Figure 9) injections are performed. Figures 6 and 9 show density maps obtained utilizing different detection methods: the brightest pixel (Ipix), a context-unaware detection method, and normalized cross-correlation (ncc), a model-based detection approach and the combination of the two (Ipix + ncc) (only for simultaneous injections). These results confirm the robustness of the proposed uncoupling pipeline in separating the bi-disperse population. Furthermore, the flow direction maps (Figure 6b) demonstrate that the proposed pipeline preserves flow information. Note how the color encoding, with blue representing MB flow towards the probe and red away from it, is consistent with the direction imposed by the experimental setup. The performance of the proposed method is further supported by the quantitative results in Table 2, where saturation, mean detections and mean tracks decrease in the residual column (marked in red in Table 2, reinforcing uncoupling capability). Figure 6 demonstrate that ncc outperforms Ipix. This is visible from the spurious tracks present in the residual images. For instance, observe the tracks present in the lower part of image hp5.5MHz generated using Ipix for injections of p3MHz. In this image, Ipix-generated images show a high number of false positives tracks compared to ncc. The reason for Ipix lower uncoupling performance lies in the way Ipix works. Ipix detections are pushed to find the m brightest pixels. However, these pixels might be the result of uncoupling errors or the filtering results, leading to false positive detections and the appearance of spurious tracks. Ipix detects on average 4.2 MBs/frame for p5.5MHz when injecting p3MHz (see Table 2). For the same case, ncc detects 1.5 MBs/frame, showing better uncoupling performance. The improved separation capability of a model-based detection method (ncc) is confirmed by the mean tracks per record and the mean percentage of accepted tracks in Table 2. On average for p3MHz injections, ncc accepts 3.1 % of the detected tracks for p5.5MHz, whereas Ipix accepts 15 % of the tracks, causing the appearance of false tracks. Despite a similar mean number of tracks/record for p3MHz for acquisitions where only p3MHz is present, the mean tracks/record substantially drops for p5.5MHz (from 124.9 to 14 tracks/record) when using ncc method. The high number of tracks indicates a large number of tracks likely caused by false positive MB detections, reflecting Ipix poorer uncoupling performance. However, these false positive tracks are partially filtered out by the track length threshold. The robustness of ncc’s detection performance is further evident from the density profiles shown in Figure 7. For instance, observe the profile for cross-section 1 in Figure 7b, where ncc allows the visualization of different phantom branches with comparable intensity. Although Ipix produces tracks for both channels, the number of detected MBs flowing in one of the two channels is significantly higher. While ncc shows better separability, the performance improvement comes at the cost of a higher computational demand. Table 3 confirms the superiority of ncc for uncoupling the two populations when injected together across all the metrics. The mean detections per frame (see Table 3) are higher for the ncc method, leading to more tracks and a more saturated final density map, confirming the analysis of single injections. However, the tracks obtained with the ncc method for population p3MHz (Figure 9 b) appear to be more scattered and less smooth, probably due to the higher number of detections, which makes tracking more challenging. Figure 9a and b present a few spurious tracks, which are absent for the results produced by the Ipix + ncc method (Figure 9c). In fact, the number of discarded tracks, observable by the higher number of accepted tracks in Table 3, is lower with respect to the other two methods. This can be explained by the fact that Ipix + ncc method acts as a two layer filter, one based on correlation and the other based on pixel intensity, which selects few and more likely MBs detections. It is worth noting that this method requires fine-tuning of more parameters; k′ the number of brightest pixels and the correlation level. Increasing k′ means more MBs detected, which could be noise. However, if the correlation threshold is set high enough (e.g. > 0), the possibility of these detections being noise is low. Although the approach Ipix +ncc produces similar results to ncc, the need of more data for vascular filling and the need of further parameter tuning, makes it more difficult to translate clinically. Besides the detection method, the number of tracks resulting from the uncoupling allows to discriminate the two populations. To demonstrate the potential advantage of using the proposed technique with respect to standard ULM, we compare the density maps generated before (Figure 10) and after uncoupling (Figure 9). Compared to standard ULM, the reconstructed maps highlight how the proposed pipeline better reconstructs the geometry of the phantom for both methods. The main reason for the improved performance can be explained by the fact that, when both MBs are present, there is a higher concentration of MBs, which make standard ULM more difficult. For Ipix density maps, fewer tracks are present, probably due to the higher number of overlapping MBs detections. On the other hand, ncc appears to reconstruct the vasculature, but more spurious tracks are present. These results strengthen the clinical utility of the proposed uncoupling pipeline, which improves the MB localization efficacy and imaging speed of ULM under high MB concentrations. All of this might alleviate the long acquisition times hindering ULM practical implementation. From a clinical standpoint, reduced acquisition times are especially important in applications in which microvascular characterization yields clinically meaningful biomarkers and motion remains a major challenge. For example, in oncologic imaging, characterization of tumor microvascular density, tortuosity and flow provides clinically meaningful biomarkers, but prolonged acquisition times increase sensitivity to motion artifacts (11, 18). Similarly, in renal imaging where respiratory motion is prominent, the feasibility of ULM is strongly influenced by acquisition duration (19, 20). In these contexts, the ability to operate at higher MB concentrations, while preserving separability may improve robustness to motion and support the translation of ULM into routine clinical practice. Results highlight the advantage of using 3D printed vascular phantoms as physical ground truth for assessing ULM-generated maps. There are few missing branches in the reconstructed density maps, which can be explained by the misalignment between the imaging plane and the phantom positioning. Nevertheless, the reconstructed tracks align with the phantom geometry (Figure 8) and the vascular dimension estimated from ULM images are consistent with those of the phantom. In Figure 7, the channel width is evaluated at the FWHM of the intensity profiles and found to be approximately 2 mm, matching the phantom’s inner diameter. This study presents several limitations. Firstly, the stability and separability studies have been tested on data acquired in a 3D printed phantom. While these in vitro results provide an opportunity to validate the proposed approach, testing it on clinical in vivo data is essential to assess the method’s feasibility in a physiological context, characterized by many challenges, such as tissue attenuation, clutter noise, spectral distortion and motion. Furthermore, a natural extension of the study involves injecting a mixture of the two monodisperse populations, rather than performing injections either individually or simultaneously. This next step is crucial not only for validating the MB response when both populations are present, but also verifying the uncoupling performance of the proposed algorithms and investigating the feasibility of increasing MB concentrations. By mixing the two populations, we can assess the effectiveness of the uncoupling technique in real-world scenarios. Furthermore, given the control on 64 elements, line-by-line imaging has been implemented for this study. While this choice guarantees a wide field of view, it comes at the price of lower frame rates compared to ultrafast imaging normally implemented in standard ULM. In future in vivo studies, we plan to implement plane wave imaging, which would allow to achieve higher frame rates. Finally, a limitation of this study is the variability of the in vitro experiments due to the manual selection of the imaging plane and phantom instability. As a consequence, some vascular branches present in the phantom are not visible in the final density and velocity maps. To solve this, improvements on the replicability of the set up can be performed. In addition, 3D imaging would solve the imaging plane selection issue.

Conclusions

In this study, we demonstrate the feasibility of uncoupling a bi-disperse MB population. Results show the ability of the proposed uncoupling pipeline to generate dynamic and functional maps when singularly and simultaneously injecting distinct MB populations in two separate phantom branches. We tested the proposed uncoupling framework using two detection methods. Ipix performs detection based on the brightest pixels, whereas ncc utilizes cross-correlation for detecting MBs. Both methods allow the uncoupling of the two selected populations. However, results show a better performance of a model-based approach (ncc) with respect to a context-unaware method (Ipix). Furthermore, we compare the reconstructed density maps before and after uncoupling. Results confirm that standard ULM fails to capture the vasculature, possibly due to high MBs concentrations, whereas by utilizing the uncoupling technique, the reconstructed vascular structures appear to better represent the ground truth geometries. Results confirm that standard ULM fails to capture the vasculature, possibly due to high MBs concentrations, whereas by utilizing the uncoupling technique, the reconstructed vascular structures appear to better represent the ground truth geometries. The results demonstrate that the proposed approach can address ULM’s key challenges, including prolonged acquisition times and low MB concentrations, thereby supporting its practical and clinical applicability. As a future work, we plan to simultaneously inject in the same channel the two populations to verify the advantage of using a bi-disperse population over a poly- and/or mono-disperse population. Furthermore, we plan to perform in vivo experiments to verify the separability of the bi-disperse MB population and the performance of the proposed uncoupling pipeline towards advanced ULM. This would ultimately allow for an increase of MBs concentrations, thus alleviating the need for long acquisition time for micro-vascular imaging. In addition, it is worth highlighting that in this study we 3D-printed a vascular phantom compatible with ultrasound imaging. As a next step, we aim at 3D printing structures having dimensions and geometries comparable with the in-vivo vascular bed. The phantoms would provide a fully controllable tool to validate ULM’s results both in terms of geometry depiction and velocity information. Finally, the use of different populations might benefit not only on a practical level (shortening the acquisition time) but also on a more diagnostic and monitoring level. Distinguishable populations might represent a first step towards an advanced and optimized contrast-enhanced ultrasound imaging system. For instance, depending on the MBs’ sizes, different populations might selectively transit in micro-vessels characterized by different properties, expanding ULM capability to characterize the microvascular flow.

Acknowledgements:

Part of this work was supported by the Hub Life ScienceAdvanced Diagnosis (HLS-AD), PNRR PNC-E3-2022-23683266 PNC-HLS-DA, INNOVA – CUP: E63C22003780001, funded by the Italian Ministry of Health under the National Complementary Plan Innovative Health Ecosystem - Unique Investment Code: PNC-E.3. We thank PROM Facility, in Rovereto, Italy for the support in the 3D printing of the vascular phantom. In particular, M. Perini and C. Malacarne for 3D designing, material selection and printing of the vascular phantom.

Appendix. Supplementary files

The manuscript presents a novel bi-disperse MB population, composed by two monodisperse MB populations. One population (p3MHz) is characterized by a strong non linear response, whereas the other MB population (p5.5MHz) mainly presents a fundamental response. To uncouple the bi-disperse MB population, the following equations are applied:

  • - h3MHz = h2, (Eq. 1)

  • - hp5.5MHz = h1 – h2. (Eq. 2)

where h3MHz and hp5.5MHz represent the images of the two uncoupled populations. H1 and h2 represent the images of the first and second harmonic after filtering by means of Fourier in the frequency domain of the MB signal.

In the supplementary files we present the results of individual injections and simultaneous injections. Experiments with individual injections serve as an initial validation for the uncoupling pipeline while having a ground truth. During single injections and in case of perfect uncoupling, the residual images, obtained by attempting to image the non-injected population, should be empty. On the other hand, simultaneous injections serve as a proof-of-concept of the separability when both MB populations are present.

Video 1 presents videos of singular injections of p3MHz. The video presents the results obtained before (a) and after (b) SVD filtering, and after uncoupling (c and d). In particular, (c ) presents the results after applying equation Eq. 1 and (d) Eq. 2. In other words, in (c ), we are imaging the population that is being injected (p3MHz) and in (d) we are imaging the residuals.

Video 2 presents videos of singular injections of p3MHz. The video presents the results obtained before (a) and after (b) SVD filtering, and after uncoupling (c and d). In particular, (c ) presents the results after applying equation Eq. 2 and (d) Eq. 1. In (c ), we are imaging the population that is being injected (p5.5MHz) and in (d) we are imaging the residuals.

Figure S1 shows the intensity projection obtained after simultaneous injections of the bi-disperse population. The colors code the two different MB populations.

Results of individual and simultaneous injections confirm the performance of the proposed uncoupling technique.

See the supplementary files on the website: https://www.mattioli1885journals.com/index.php/theultrasoundjournal/article/view/18060

Supplementary information.

See supplementary material for images and videos pre- and post- uncoupling on the website: https://www.mattioli1885journals.com/index.php/theultrasoundjournal/article/view/18060

Author’s contributions:

GT, LTW, CB, WVH, LD contributed to the study design and development. GT performed data acquisition and analysis. LTW, CB, WVH contributed to microbubble production. GT, WVH, LD contributed to writing the manuscript and revisions of the study. All authors read and approved the final manuscript.

Availability of data and material:

The data that supports the findings of this study are available from the corresponding author upon reasonable request

Ethics approval and consent to participate:

No patient is part of this work.

Competing interests:

The authors have no relevant financial or non-financial interests to disclose. The authors have no conflicts of interest to declare that are relevant to the content of this article.

Declaration on the use of AI:

none.

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