Interframe Echo Intensity Variation of Subregions and Whole Plaque in Two‐Dimensional Carotid Ultrasonography

The risk of cardiovascular disease is associated with the echo intensity of carotid plaques in ultrasound images and their cardiac cycle‐induced intensity variations. In this study, we aimed to 1) explore the underlying origin of echo intensity variations by using simulations and 2) evaluate the association between the two‐dimensional (2D) spatial distribution of these echo intensity variations and plaque vulnerability.

Clinically, ultrasound imaging is the first-line method to mainly assess the degree of stenosis in symptomatic patients suffering from a transient ischemic attack or stroke to determine if blood flow needs to be surgically restored (endarterectomy or stent). 2 In addition, carotid tissue abnormalities observed during clinical examination are commonly accompanied by the prescription of risk-reducing pharmacological drugs.
The identification of plaques in the arteries has been shown to add predictive value for risk assessment. However, the plaques may be stable or vulnerable. Stroke is often caused by a rupture of a vulnerable plaque's cap. Ultrasound imaging followed by quantitative texture analysis can be used to stratify the risk of rupture of a plaque. 1,3 In these methods, the image features, so-called risk markers, are typically computed from a segmented plaque in a single Bmode image of an ultrasound sequence. The grayscale median (GSM) is a risk marker that quantifies the echo intensity of the plaque and has been shown to assess the risk of plaque rupture. [4][5][6][7][8][9] Recent findings show that GSM (and other risk markers) is timevariant in ultrasound images sequence during the cardiac cycle, [10][11][12][13] causing reduced reproducibility 10 and risk re-classification. 12,14 Interestingly, this variation is higher in vulnerable plaques compared to stable plaques. 10,12,14 There is some experimental evidence that these variations are caused by out-of-plane motion and compression of the whole or parts of the plaque 10,11 due to the periodic pulse pressure changes over the cardiac cycle. However, studies that explicitly investigate the influence of these mechanisms on echo intensity are lacking.
We hypothesize that these mechanisms may cause non-uniform echo intensity variation within the plaque since plaques are composed of different tissues. To the best of our knowledge, no study has explored the spatial distribution of such echo intensity variations within the plaque and their potential association with plaque vulnerability.
This work aims to 1) investigate how the echo intensity is affected by the mechanisms of out-of-plane motion and compression by using simulations and 2) propose a method to segment and analyze subregions with high echo intensity variations within carotid plaques. In addition, 3) we compare echo intensity variations in whole plaque with subregions and their association with a plaque vulnerability marker in experimental ultrasound plaque image sequences.

Materials and Methods
A methodological overview is presented in Figure 1, illustrating the data and processing steps used to target the different aims of this study. Figure 1. Methodological overview. For the first aim, we simulated ultrasound images of scattering spheres for different out-of-plane motion and compressions and evaluated how these mechanisms influence the echo intensity. For the second aim, we proposed a processing pipeline to analyze echo intensity variation of whole-plaque and intra-plaque subregions of experimental image sequences of carotid plaques. Finally, the third aim was assessed by comparing echo intensity variations in stable and vulnerable plaques.

Ultrasound Tissue Modeling
Ultrasound wave propagation in tissue was modeled using the k-space pseudo-spectral method, which was based on the coupled first-order partial differential equations 15 : where c 0 denote the equilibrium sound speed, ρ 0 the equilibrium density, p the acoustic pressure, ρ medium density, u the acoustic particle velocity, and d the acoustic particle displacement. The operator L is a linear integro-differential operator that accounts for acoustic absorption and dispersion that follows a frequency power law.
To simulate the plaque acoustic echoes, we used the k-Wave toolbox, 16 which is designed to be applicable for tissue-realistic medium. The toolbox provides optimized parallel C++/CUDA GPU simulation codes to run large three-dimensional simulations. The simulations were conducted by running the k-Wave C++ codes on the Kebnekaise supercomputer at HPC2N, Umeå, Sweden.

Simulation Setup and Settings
The transducer was modeled as a 128-element ultrasound probe with a 5-14 MHz frequency band. The pitch was modeled as 0.3 mm and the elevation height as 4 mm. We selected the central frequency of the transmitted pulse to be 7.5 MHz. A total of 32 elements were used in transmitter and receiver focus beamforming. We used rectangular windows for both the transmitter and the receiver apodizations, where the transmit and receive was focused at 20 mm depth.
We used two media components as a model: a background tissue with a speckle pattern and one spherical scatterer placed at a depth of 20 mm. We set the background tissue parameters as in 16 : where ρ 0 ¼ 1000 kg/m 3 , c 0 ¼ 1540 m/second, and ω 1 were a Gaussian random variable with mean 1 and standard deviation (SD) 0.008. For the spherical scattering object, the model was 16 : where ω 2 was a Gaussian random variable with mean 25 m/second and SD 75 m/second. The simulations of out-of-plane and tissue compression of the spherical scattering object were performed using the following definitions.
Definition 1: (Out-of-plane motion): The scattering object moves away from the ultrasound probe beam center along the y direction, out of the image plane xz.
Definition 2: (Compression): The scattering object's volume changes when compressed, and the density and acoustic impedance increase. The out-of-plane motion and tissue compression are illustrated in Figure 2. We simulated up to 2 mm out-of-plane motion based on the assumption that the motion is of the same magnitude as in-plane motions (1 mm in a previous study 17 ).
For the compressions, we assume that the tissue mass m is constant when the tissue is compressed. Thus, we have: Then, where ρ 0 is the initial density, r 0 the initial spherical radius, ρ t ð Þ the density at time t, and r t ð Þ the radius at time t. Also, since the shear waves can be neglected in soft tissues, the compressional wave propagation speed can be approximated 18 as: where K is the bulk modulus, and K ≈ 2:2 GPa in soft tissues. 18 Strain up to 10% was simulated based on empirical studies showing that the axial strain in plaques is 5%. 19 Time gain compensation was applied with 0.4 dB/(MHz cm).

Subjects
Fifty-seven ultrasound image sequences with plaques from 28 subjects (men and women, ages 50 and 60 years) were retrospectively included from the baseline of the population-based cohort study VIPVIZA (visualization of asymptomatic atherosclerotic disease for optimum cardiovascular prevention-a randomized controlled study within Västerbotten Intervention Program). 20 Selection criteria included those referred for an expanded ultrasound examination during 2013-2016 who were found to have subclinical atherosclerosis and plaques visible on ultrasound images. The subjects gave informed consent verbally and in written form. VIPVIZA conformed to the Declaration of Helsinki and was approved by the Regional Ethical Review Board at Umeå University (reference 2011-445-31M, 2012-463-32M, and 2013-373-32M). VIPVIZA is registered with ClinicalTrials.gov, number NCT01849575.
Note on included subjects: The main VIPVIZA study included 3532 subjects in their 40, 50, and 60 years at baseline, where the study protocol included measurement of clinical risk factors (eg, blood pressure, smoking habits, body mass index [BMI], etc.), questionnaires, for example, psychological profiling, blood analyses, and an ultrasound scan of the carotids' intima-media thickness and plaques. For the main VIPVIZA study, the CardioHealth Station system (Panasonic Healthcare Corporation of North America, Newark, NJ, USA) was used, which is optimized for carotid intima-media thickness measurement but not specifically for plaques. The subjects referred to an expanded ultrasound were scanned using the Phillips iU22 system (Andover, MA, USA), which allows higher quality imaging of the plaques included, that is, harmonic imaging. This increased image quality of the plaques was prioritized in this study, and therefore the expanded ultrasound subjects were included.

Ultrasound Acquisition and Plaque Detection
As a standard clinical carotid ultrasound examination, experienced sonographers (biomedical scientists specifically trained in carotid ultrasound techniques) acquired ultrasound image sequences at the Department of Clinical Physiology at Umeå University Hospital, Sweden. Subjects were scanned using a Philips iU22 system (Philips Medical Systems, Andover, MA, USA) and a 9 MHz linear transducer (L9-3) with 3-9 MHz bandwidth, 160 elements, 38 mm aperture, and transmit center frequency of 7 MHz. Acquired image sequences had approximately a 33 Hz frame rate.
Carotid plaques were identified using the Mannheim consensus as a focal structure that encroached into the lumen by at least 0.5 mm or >50% of the surrounding intima-media thickness or demonstrated a thickness of >1.5 mm as measured from the mediaadventitia interface to the intima-lumen interface. 21 In practice, the operator first scanned the arteries using B-mode imaging in a cross-sectional projection to locate potential plaques. When a plaque was detected, the probe was rotated to allow a longitudinal projection at its thickest portion, and an image sequence of three consecutive cardiac cycles was acquired. The B-mode image sequences were exported for postprocessing in the DICOM format in 8-bit representation. Image analyses were carried out in MATLAB (2021a, MathWorks, Natick, MA, USA) and Python (Python 3, Python Software Foundation).

Real Data Echo Intensity Variation Analysis
The echo intensity variation analysis consisted of the following processing steps: 1) intensity normalization, 2) motion stabilization, 3) whole plaque segmentation and analysis, and 4) plaque subregion segmentation and analysis. Finally, 5) we assessed the associations of the echo variations in the whole plaque with its subregions, respectively, with plaque vulnerability.

Intensity Normalization
Prior to all processing described below, the images of each sequence were normalized to be able to compare the echo intensities between subjects. First, the mean intensity of the lumen's region of interest (ROI) was subtracted. Then pixel intensities were multiplied by 190 and divided by the maximal intensity of an ROI over the adventitia. 1 The ROI reference values were measured in the first image and applied for normalization of all subsequent images of the sequence. The ROIs for the lumen and adventitia were manually segmented by the operator. This normalization procedure has been applied in the previous studies. 1,12,14 Motion Stabilization The B-mode image sequences (I 0 x, y, t ð Þ) were preprocessed by stabilizing the in-plane motion such that every pixel of the plaque image corresponded to the same plaque tissue segment in all frames of the sequence. The rationale for motion stabilization is that the plaque and vascular tissue may move (axial and longitudinal) on the order of millimeters in the image plane 22 due to the periodic pulse pressure changes over the cardiac cycle. The following procedure achieved motion stabilization: 1) The displacement of pixels in all image sequences was estimated with respect to the initial image using an optical flow algorithm. Gunner Farneback's algorithm 23 in Ope-nCV 24 was used, and the parameters were optimized by the differential evolution global optimization algorithm 25 and implemented in SciPy. 26 2) Motion stabilization was achieved using the OpenCV 24 geometric transformation method for all the images based on the corresponding estimated velocity fields. The resulting stabilized image sequences I x, y, t ð Þ were then used in all subsequent processing. The performance of the motion stabilization method has not been evaluated before for this application. While many methods have been proposed in the literature to estimate motion in vascular tissues, [27][28][29][30] no methods have been evaluated for motion stabilization application. To assess the chosen method's validity, we qualitatively compared the image pattern of the motion stabilized plaques with the plaques in the original B-mode images throughout their sequences (online supplemental Figure 1). Motion stabilization was classified as successful when plaque morphology was stable across the frames without apparent distortion of its texture.

Whole Plaque Segmentation and Analysis
Next, the plaques were manually segmented and cropped from the initial frame of I x, y, 0 ð Þ. The plaque area was quantified based on the cropped mask. Echo intensity was quantified using the GSM descriptor, that is, the median of intensities in the cropped plaque region of each frame, GSM(t). The mean and coefficient of variation (CV) were used to quantify the GSM signal's interframe variability. An echo intensity variation map (SD map [SD-map]) was quantified using SD in the time domain of I x, y, t ð Þaccording to SD x, y ð Þ¼σ I x,y,t

ð Þ
In addition, the correlation coefficient (CC) between each pixel's echo intensity signals and the whole plaque GSM signal was computed (CC-map) to assess plaque tissue connectivity as: where Cov is the covariance, and σ Á ð Þ denotes the SD.
A B-mode map (B-map) was defined as I x, y, 0 ð Þ and samples the echo structure of the plaque at a given point in time. The similarity between the maps (B, SD, and CC) was assessed using the CC. The heterogeneity of the B and SD map textures was quantified using the coarseness variable computed from the neighborhood gray-tone matrix. 31 High coarseness corresponds to a heterogeneous texture and lows to a homogeneous texture.

Subregion Segmentation and Analysis
Subregions within a plaque with high echo intensity variation were automatically segmented, and their characteristics quantified. The subregions were segmented from the SD-maps by thresholding at 50% maximal intensity. The number of identified subregions was calculated and normalized to the plaque area. The subregions' equivalent diameter was calculated based on , where A Á ð Þ is the region area, and the CV GSM of the individual subregions was calculated as SD GSM subregion where GSM t ð Þ is the mean of GSM(t). As a comparison, the number of regions per plaque area with amplitude >50% of max in the B-maps was also calculated.

Association with Plaque Vulnerability
The plaque image sequences were divided into two groups based on their corresponding plaque GSM values. A hypoechoic plaque group with GSM < 32 and a hyperechoic plaque group with GSM ≥ 32. GSM values below this threshold have been associated with vulnerable plaques. 28 Wilcoxon's univariate non-parametric statistic was used to test differences in the features between the two groups with Bonferroni correction of the P-value for multiple testing (P = .05/11 = .0045). The effect size of the between-group-differences was quantified using the area-under-curve (AUC) statistic, where 0.5 means no difference and 1.0 means completely nonoverlapping distributions.

Results
Simulations: Echo Intensity Versus Out-of-Plane Motion Figure 3 depicts an example of a simulated B-mode image sequence with out-of-plane motions for two scattering spheres with radii r ¼ 1 mm and r ¼ 2 mm. When the scattering sphere moves along the y-axis, that is, away from the image plane (out-of-plane movement), the echo intensity drops, and the reflecting cross-section of the scatterer decreases dramatically.
Intensity changes for out-of-plane motions were computed based on simulations of three different spherical scattering spheres with radii: r ¼ 1, 2, 4 f g mm. For larger scattering spheres, that is, r ¼ 4 mm, when Δy ¼ 2 mm, the sphere's center moves to the end of the y-aperture, and the echo intensity only dropped around 9%, as there is still a large echo reflecting surface. However, for smaller scattering spheres, that is, r ¼ 1 mm, the intensity decreased by almost 68% (Figure 5A). The intensity change was mathematically defined as the percent change between the mean intensity inside the scattering sphere at a different motion position Δy and that of no motion (Δy ¼ 0). The scattering object regions are shown as the red-dotted circles in Figure 3. Figure 4 depicts an example of a B-mode image sequence with various compressions, represented by strain defined as r 0 À r ð Þ=r 0 , for two scattering spheres with radii r 0 ¼ 1 mm and r 0 ¼ 2 mm. The echo intensity inside the sphere decreased with increasing strain, and the echo intensity increased on the boundary. Figure 5B shows the echo intensity changes with varying strains. The intensity change was also computed as the percent change between the mean intensity inside the scattering sphere and that of no compression (strain equals 0). Thus, both mechanisms show a similar relative intensity decrease at typical out-of-plane motion and compression (1 mm versus 5%). We want to stress that these are relative intensity changes. The absolute echo intensity changes will depend on the scattering object's acoustic impedance (eg, lower for lipids and higher for fibrotic tissues).

Real Data Echo Intensity Variation
Eight out of 57 plaque image sequences were excluded due to visually distorted images after manual inspection of the motion stabilization step. Subsequently, 49 plaques were included from 28 subjects (57% female), 11% (50 years), and 89% (60 years). The subjects' systolic/diastolic blood pressures were  (10), and the low-density lipoprotein cholesterol level was 3.2 (1.0). A total of 75% were overweight (BMI > 25.0), 18% were smokers, 7% had diabetes, and 39% had a family history of cardiovascular disease. Figure 6 shows an example of a plaque B-mode image sequence over one cardiac cycle after motion stabilization, where the overall echo intensity of the plaque increased until the middle of the sequence and then decreased. A small region of about 2 mm in diameter in the lower right corner was visible only in the middle of the sequence and not at the sequence's start and end. Visual inspection of the results of the motion stabilization showed that the plaques were not moving, and the two-dimensional (2D) intra-plaque echo intensity pattern was maintained between the original and motion stabilized images (online supplemental Figure 1).  . Example of two-dimensional B-mode echo intensity variations over one cardiac cycle for a plaque of a 60-year-old individual with atherosclerosis. Motion stabilization was applied, and image intensities were normalized with respect to the initial frame. The overall whole plaque echo intensity can be seen to modulate (maximal echo intensity at frame 12 and minimal at frames 0 and 22). In addition, echo intensity variation was also present in a local subregion of about 1 mm diameter (red dashed circle). Figure 7 shows an illustration of the analysis and results from two plaques-one hyperechoic stable plaque and one hypoechoic vulnerable plaque. The echo intensity features for whole-plaque and subregions are summarized in Table 1.

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The overall plaque intensity variation (CV GSM) was 4% (range 1%-15%). The similarity between the B-map images and the SD maps was, in general, low for all plaques (0.25 CC) and close to zero between B or SD maps with CC-maps. The coarseness of the B and SD maps was similar (15.5 versus 18.5). The number of subregions in SD-maps was 0.12 per mm 2 , and the SD-map subregions' diameter was, on average, 0.94 mm (range 0.6-2.3 mm). In addition, the CV GSM of subregions was higher than the CV GSM of the whole plaque, 0.41 (0.32) versus 0.04 (0.03).
Comparison between features of hypoechoic plaques (GSM < 32) and hyperechoic plaques (GSM ≥ 32) showed that CV GSM, coarseness B-map, CC B versus SD, CC B versus CC, and CV GSM subregions were different (P < .05). However, using Bonferroni correction for multiple tests (n = 12), only CV GSM for the whole plaque and CV GSM for subregions remained significant. Moreover, they also had the highest AUC (0.81 and 0.94, respectively). In addition, a leave-10-out crossvalidation analysis showed an AUC SD of 4% and 2%, respectively, indicating stable estimates.
A second observer also performed the manual segmentation of the whole plaques. The interrater variability between the two observers was calculated using the CV and was less than 10% for all the mean estimates in Table 1.

Discussion
In this work, we analyzed echo intensity and its variations in 2D carotid plaque ultrasound image sequences. First, simulations showed that the echo intensity of scattering spheres decreases with both out-of-plane motion and compression. Second, experimental data analysis of the 2D spatial distribution of echo intensities in the plaque demonstrated intensity variations in the whole plaque and local subregions.
The results indicate that 2D intensity variation analysis may provide a new venue for plaque vulnerability assessment.

Influence of Out-of-Plane Motion and Compression
Many previous studies have hypothesized that out-ofplane motion and compression may cause echo intensity change in the B-mode image. [10][11][12] However, none have explicitly studied this effect. In this study, the echo intensity decreased with out-of-plane motions of spherical objects with different radii, which was expected. In particular, the smaller the sphere radius, the more the echo intensity decreased. Thus, small intra-plaque structures may be subject to large intensity changes during a cardiac pulse. Also, the echo intensity decreased with compression of the scattering spheres. The spheres' size had little influence on the intensity change.
Previous research indicates 4%-5% whole-plaque strain values 19 and intra-plaque component strains of 5%. 32 Given the results of our simulations, these values would correspond to about a 30% decrease in echo intensity ( Figure 5B). Unfortunately, we could not find any values in the literature for typical out-ofplane motions over the cardiac cycle. Suppose we assume a similar amplitude to typical in-plane motions (about 1 mm axial and lateral motions of the carotid wall 17 ). In that case, this will correspond to an echo intensity decrease of up to 40% ( Figure 5A) for 1-mm-radius scatterer. Thus, for small scattering structures, the out-of-plane motion should be the main maker of cardiac cycle-induced intensity changes in the 2D B-mode image sequence of arterial plaques. In a related study by Li et al, 33  .0000* 0.94

the authors
The entries are described by mean AE SD (min; max). GSM, grayscale median; CC, correlation coefficient; SD-map, standard deviation map; CC-map, correlation coefficient map; CV, coefficient of variation; AUC, area under the curve. *Bold indicates significant differences. Bonferroni correction was applied to adjust significance level to P = .05/12 = .0042.
evaluated the influence of out-of-plane motion on elastography using a tissue-mimicking phantom. They found that out-of-plane motions up to 2 mm did not influence strain estimations. However, we would like to stress that elastography is based on measuring the deformation of the tissue and is inherently different from the echogenicity of the tissue. Carotid plaques comprise different tissue components, for example, lipids, fibrous tissue, hemorrhage, and calcification. These tissues have different acoustic impedances (densities), for example, lipids appear with low echo intensity, and calcified tissues appear with high echo intensity. 1 While our results ( Figure 5) showed that the relative intensity decrease was similar, for example, 1-mm displacement and 5% compression, this needs to be related to the actual tissue. For example, a lipid-rich region has low echo intensity, so the absolute echo intensity decrease caused by out-of-plane motion will be small. In contrast, a calcified tissue has high echo intensity which means that the absolute decrease in echo intensity is also high. In addition, the model we used to simulate compression is only valid for soft tissues rather than calcified tissues. Thus, high echoic scatterers with large intensity variations are most likely caused by out-of-plane motion.
We chose a simplified tissue model (with a homogeneous background and a spherical scatterer) with a simulation model. Such modeling provides the basis for investigating echo intensity changes' core mechanisms concerning out-of-plane motions and compressions. Since we investigated the relative intensity changes, a more complicated tissue model should not have significantly impacted our results. These mechanisms could also have been studied using experimental tissue phantoms, commonly used in ultrasound studies. However, by using the simulation model, we argue that we have better control over the parameters to explicitly study the mechanisms' impact on echo intensity.

Intensity Variations in the Whole Plaque
The echo intensity variation of the whole plaque, GSM CV, was in the range 1%-15%, similar to previous studies. 10,12,14 In addition, we found that the GSM CV of vulnerable plaques (low GSM) was significantly larger as compared to stable plaques (high GSM), which also is in line with previous studies. 10,12,14 In addition, B-mode texture heterogeneity (coarseness) also showed lower values for hypoechoic (high GSM) compared to hyperechoic (low GSM) plaques, similar to other studies. 12,28 The SD-maps and CC-maps have not been previously demonstrated in the literature. There was only a low correlation (0.24) between the B and SD-maps, and this correlation was slightly higher in hypoechoic plaques (0.34 versus 0.2, P = .017). Thus, this indicates that the textures of the B and SD-maps are different and contain complementary information on plaque tissue composition and vulnerability.
The CC-maps had a weak correlation to the SDmaps (0.24) and without any differences between the hypo-and hyperechoic plaques. There was no correlation between CC-and B-maps (0.01). Thus, this indicates that the CC-map contains complementary information to the B-maps but without significant association with vulnerability (P = .009). Therefore, the B-map, SD-and CC-maps contained complementary information but only weak associations (P < .05) with plaque vulnerability.

Intensity Variations in Subregions of the Plaque
Subregions with the highest echo intensity variations were automatically segmented for each plaque. There were 0.12 regions per mm 2 with an equivalent diameter of 0.94 mm (range 0.55-2.27 mm). Neither showed any significant difference between hyper-and hypoechoic plaques. The GSM CV of the subregions was 10 times higher than GSM CV for whole plaque (0.41 versus 0.04) and significantly differed between hypo-and hyperechoic plaques. In addition, the AUC showed that it was the best overall variable to differentiate between the two groups. Based on the discussion of the simulations above, these subregions with high echo intensity and small size are most likely caused by out-of-plane motion.
Since the echo intensity and its variations of the subregions are included when computing the whole plaque GSM and GSM CV, we analyzed if the subregions were the makers of the whole plaque GSM and GSM CV. The influence of the subregions on the whole plaque GSM and GSM CV, respectively, was assessed using paired t test. The results showed non-significant differences for GSM 2.1 (3.2), P = .5, and GSM CV 0.010 (0.015), P = .2. Therefore, the GSM CV of subregions may serve as a new potential risk marker for plaque vulnerability, which may be stronger than previously described plaque risk markers according to the AUC.
A few previous studies have also studied intraplaque composition heterogeneity. For example, Huang et al 34 used texture analysis of strain (rate) images of plaques. They found that local regions ($5 mm diameter) with large deformation were more frequent in vulnerable plaques as compared to stable plaques. In contrast, in the present work, we found that local regions ($1 mm diameter) with high echo intensity variation were more frequent in vulnerable plaques compared to stable ones. These two findings indicate that tissue characterization based on elastography and echogenicity (providing information on different aspects of the tissue constituents) may be beneficial for differentiation between vulnerable and stable plaques. In future studies, their combination should be evaluated for improved classification.
In previous studies on static images of plaques, local regions with high echo intensity (static images) have been observed. These so-called discrete white areas (DWAs) are defined as focal areas that appear white but do not produce a shadow and therefore are not due to calcifications. 1 Studies of histological examination have shown that DWAs are associated with hemosiderin and inflammatory cell infiltration. 35 In our study, the local regions with high echo variations did not produce shadow and may be related to the DWA marker.

Limitations
Segmentation of the whole plaque ROI was done manually. Previous research has shown that automatic segmentation methods of whole plaques result in lower interframe variability in, for example, GSM than manual segmentation. 10 However, in this work, the manual segmentation was only carried out on the first image of the image sequence and thus should not contribute to the interframe variations. Segmentation of the subregions was done automatically based on the thresholding of the SD-maps. While some of the smallest subregions could be caused by some noise source, since the size of the subregions of 0.5-2.27 mm (average 0.94 mm) is based on connected pixel regions, we believe that these are not artifacts.
Motion estimation is a difficult task, and a number of different methods have been suggested for arterial tissues. [27][28][29][30] In this work, we used an optical flow technique, and a similar method has shown good performance on motion estimation in arterial tissues. 30 The similarity between the original B-mode plaque images and the motion stabilized frames of a sequence showed that the essence of the plaque morphology and intensity pattern was preserved and provided validity to the quantified intensity variations in Figure 7 and online supplemental Figure 1. Eight image sequences were excluded due to distorted images after the stabilization. Therefore, before doing any large-scale study on clinical ultrasound data, optimization and full evaluation of the motion stabilization method should be carried out for arterial tissues.
The normalization of the echo intensity in the image sequences was carried out based on the reference values of the first image in the sequence. Commonly, each image is normalized based on its intensities in the lumen and adventitia. We chose this approach because changes in the lumen and adventitia may also change and induce variation. However, the echo intensity of the plaque does not change.
We included 49 plaques from a subclinical atherosclerosis population, and only 14 were characterized as hypoechoic (GSM < 32). Due to the small sample, our results need to be verified in a larger cohort. Moreover, the image sequences were only about 2 seconds long in this work. Longer sequences might be preferred in future studies to allow better and more robust estimation of cyclic variations.
While the proposed method's main impact is assessing plaque vulnerability and cardiovascular risk, the potential role of the method in a clinical setting remains to be determined. First, the method should be verified in a retrospective study on a much larger material and with data on major adversarial cardiovascular events. Limitations for potential clinical implementation include the proposed pipeline's manual steps (segmentation) and the offline processing requirement, among others.

Conclusions
In this work, we studied 2D ultrasound echo intensity variations in carotid plaque tissue using simulations and clinical B-mode image sequences. We showed, using simulations, that the relative echo intensity variation was similar for out-of-plane motion and compression of soft scattering spheres, but for small scatterers (<1 mm radius), the influence of out-ofplane dominated. In addition, we studied clinical plaque image sequences and showed a complex 2D distribution of echo intensity variation within the plaques. Subregions ($1 mm diameter) of high echo intensity variations were detected, and the amplitude of their echo intensity variations differed between vulnerable and stable plaques. Our results show that the 2D spatial distribution of echo intensity variations in the plaque provides complementary information to the standard single frame B-mode image and indicates a new opportunity to assess plaque vulnerability. Further studies are needed to verify this method's role in identifying vulnerable plaques and predicting cardiovascular disease risk.