Adaptive wall shear stress imaging in phantoms, simulations and in vivo

A. Ultrasound acquisition setup

A Verasonics Vantage 256 research platform (Verasonics, Bothell, WA, USA) was used to drive an L7–4 Linear array transducer with 128 elements, center frequency 5 MHz and 50% Bandwidth (L7–4, ATL Ultrasound, Bothell, WA, USA). A 5-plane wave and a 3-plane wave compounding acquisition imaging sequences at transmit angles of (−2°,−1°,0°,1°,2°) and (−10°,0°,10°) were implemented for the phantom scans and in-vivo scans, respectively. The pulse repetition frequency was set at 8333–10000 Hz, depending on the depth of the imaged vessel in each case, resulting in an effective frame rate of 1900–2000 frames per second (fps) in the case of the phantom study, and 2770–3333 fps in the human study. A higher number of plane waves was employed in the phantom study to obtain improved quality of RF frames at the cost of temporal resolution, due to the limited flow velocity magnitude generated by the pump. Parameters involving the ultrasound acquisition setup are summarized in TABLE-I.

B. Wall displacement and vector flow imaging

Pulse Wave Imaging (PWI) combined with Vector Flow Imaging (VFI) was carried out, in order to obtain simultaneous maps of arterial wall displacements and vector flow field, as described in [42]. In the case of PWI post-processing, the received channel data for each transmission angle were beamformed using the Delay-and-Sum algorithm and were coherently summed, producing compounded RF frames. The axial and lateral resolutions of the resulting frames were 0.01848 mm and 0.298 mm, respectively. Estimation of axial wall displacements was performed using a 1-D cross-correlation sum-table method [43][44]. VFI was carried out similarly as in [42], where speckle tracking was used to track the 2-D motion of blood scatterers. The compounded RF signals were filtered using a singular value decomposition approach aiming to eliminate the slow motion of the arterial wall. The normalized cross correlation technique described in [45][42] was applied on the filtered RF frames, to estimate the 2-D vector of blood flow velocities. An axial kernel was shifted across the axial and lateral directions among consecutive filtered RF frames, using a kernel overlap of 1 axial sample (0.01848 mm), in order to estimate the 2-D inter-frame displacements of blood scatterers. The size of the kernel was set at 40 (0.7392 mm) axial samples in the case of the phantom study and 80 (1.4784 mm) for the in vivo study. To improve the precision of displacements, a 10:1 linear interpolation was performed between adjacent RF lines across the lateral direction [42]. The resulting inter-frame displacements were then normalized by the frame rate in order to obtain the axial $\left(v_x(z,x,t)\right)$ and lateral $\left(v_y(z,x,t)\right)$ flow velocity components. The resulting flow velocity components were averaged in temporal ensembles of 40 frames with 90% overlap. Finally, $v_x(z,x,t)$ and $v_y(z,x,t)$ estimates were spatially filtered using a 2-D median kernel of size 7×7.

C. Adaptive wall shear stress imaging methodology

The proposed methodology for Wall Shear Stress (WSS) calculation is depicted in Figure 1. Figure 1-A) illustrates a time frame of combined vector flow and pulse wave imaging (PWI) along the longitudinal axis of a vessel phantom. The flow velocity magnitude and axial wall velocities are color-coded with different colormaps and overlaid onto the B-mode, while the white arrows depict the direction of vector flow field at each point location. Figure 1-B) illustrates a magnified version of the region marked in orange rectangle in Figure 1-A), where $\overrightarrow{v}$ is the flow velocity vector, $\overrightarrow{r}$ and $\overrightarrow{t}$ the unit vectors normal and tangent to the wall, respectively. Both $\overrightarrow{r}$ and $\overrightarrow{t}$ are calculated using the segmentation lines, which are obtained through manual wall segmentation on the ultrasound B-mode image. The position of the segmentation lines, as well as the unit vectors $\overrightarrow{r}$ and $\overrightarrow{t}$ are adjusted to the temporally varying position and orientation of the arterial walls throughout the cardiac cycle by using the PWI derived axial wall velocities. WSS can be estimated using the following formula:

Where $\mu$ is the fluid viscosity, ${\gamma }_{wall}$ stands for the shear rate at a distance close to the wall $\text{(}{\text{r}}_{\text{wall}})$, r denotes the spatial position in the direction defined by the normal vector to the wall ($\overrightarrow{r}$) and $v_t$ is the flow velocity component tangent to the wall, which can be derived as follows:

Several VFI-based approaches derive ${\gamma }_{wall}$ by simplifying equation (2) as follows [37][38][46]:

where ${\text{r}}_{\text{wall}}$ is a fixed distance close to the wall. This method is valid under the assumption of zero flow velocity condition at the wall, and linear profile within the selected distance ${\text{r}}_{\text{wall}}$. Other techniques derive ${\gamma }_{wall}$ as the mean, or the max gradient of $v_t$ in a predefined window [36][39]. However, using a window of fixed size may lead to biased ${\gamma }_{wall}$ estimation, given that the flow velocity profile changes with respect to vessel’s geometry and the phase of the cardiac cycle, while also filtering the arterial wall motion may not be ideal, leading to non-zero flow velocity values at the arterial wall. Instead of using a fixed distance, the proposed method analyzes the flow velocity patterns and determines ${\gamma }_{wall}$ in a region close to the wall with most uniform gradient. The aim of this approach is to provide robust WSS estimates by rejecting residual velocity signals at the wall, as well as abrupt variations in shear rate due to noisy or highly non-linear flow velocity measurements.

Figure 1-C) illustrates the tangential velocity signal (along the $\overrightarrow{t}$ direction) with respect to distance, r, at a given lateral position, x. Figure 3-D) demonstrates the velocity signal in a region $r\in (-0.75mm,0.75mm)$ corresponding to 80 samples, centered around the segmentation line of the top wall. A value of 0.75 mm was chosen to account for the maximum expected physiological arterial distension, which has been reported to be approximately 9.33% of the carotid artery diameter [47] which typically ranges from 4.3 to 7.7 mm [48]. It can be observed that a weak residual velocity signal is present at the wall region, due to non-idealized clutter filtering of the RF signals. As shown in Figure 1-D) the interface between the arterial wall and the lumen corresponds to the transition from weak residual velocities to the stronger flow velocity signal. This transition corresponds to the point of maximum curvature of the velocity signal curve shown in Figure 1-D). To identify this point, the velocity signal is filtered by using a 3-rd order Savitzky-Golay filter with a kernel size of 25, and then differentiated with respect to r. The point of maximum curvature is determined as the maximum of the absolute value of the second order derivative proximal to the segmentation line. The determined point is denoted in the solid red line in Figure 1-D). Based on this point, the residual signal corresponding to the wall is rejected.

The resulting flow velocity profile, $v_t$, corresponding to the lumen is illustrated in the scatter-plot of Figure 1-E), which is in turn differentiated with respect to r, in order to obtain the fluid shear rate ($\gamma$). Both the shear rate and distance are normalized within a range of [0 1], as shown in Figure 1-F). The aim is to determine the region where the data points in Figure 3-F) yield more uniform shear rate. To solve this optimization problem, k-means clustering is carried out, in order to partition the shear rate data points of figure 1-F), into k clusters that yield minimum variance ($\sigma$) based on the following criterion:

where k is the total number of clusters, ${\gamma }_j$ stands for the shear rate datapoints, $C_i$ denotes each cluster of datapoints ${\gamma }_j$, and $m_{\gamma ,i}$, is the mean value of datapoints ${\gamma }_j$, in cluster i. The number of clusters, k, is determined by iteratively running the k-means algorithm [49] for $\text{k}\in [2,6]$ and selecting the first k for which ${\sigma }_{min}^2<0.01$. In case this criterion is not satisfied, then the cluster with lowest ${\sigma }_{min}^2$ is selected.

The wall shear rate is defined as the mean value $m_{\gamma ,i}$ of the cluster $C_i$ that satisfies the following criterion:

where $r_j$ denotes the normalized distance of the centroid of the cluster $C_i$ from the wall. This criterion penalizes clusters that are not close to the wall, as well as clusters with low shear rate, that may be the result of non-idealized wall clutter filtering and wall segmentation. Substitution of ${\gamma }_{\text{wall}}$ in (1) provides a WSS estimate. A viscosity, μ, of 4 mPa s was used for the phantom experiments[50], while in the in-vivo studies $\mu$ was assumed to be equal to 3.45 mPa s.

The described algorithm is carried out for each lateral position (x) and time frame (t), in order to obtain a spatiotemporal map, $\text{WSS}(\text{x},\text{t})$, across the artery. A smoothing stage is finally applied on $\text{WSS}(\text{x},\text{t})$, by using moving average filtering of 6 samples across the x direction, and a 6-th order Butterworth low pass filter with a cut-off frequency of 30 Hz across the temporal direction, to suppress high frequency components that do not correspond to pulse wave-induced motion [51][52]. The resulting temporal sampling rate of the WSS sequence was approximately 480–490 Hz for the phantom study (5-angle compounding) and 820–850 Hz for the in-vivo study (3-angle compounding), depending on the depth of the imaged vessel in each case. The time duration of each acquired WSS sequence was 1 second (480–490 temporal frames) and 1.2 seconds (984–1020 temporal frames) for the phantom and in vivo case, respectively.

A. Phantom study

A straight vessel phantom (Figure 1-A)), and a phantom mimicking an atherosclerotic vessel with approximately 50% stenosis were constructed (Figure 1-B)). Both phantoms were attached to separate containers through plastic fittings, and were embedded into gelatin surrounding medium. A programmable physiological flow pump (Compuflow 1000, Shelley Medical Imaging technologies, Ontario, Canada) was connected to the fittings of the phantoms and was programmed to apply a pulsatile flow waveform, as shown in Figure 1. Due to technical limitations entailed by the pump and the limited strength of the phantom material, the flow rate was set at a lower amplitude than the physiological range, which was equal to 10 mL/s. A long time interval equal to 1.9 s was set between pulses, in order for pulse wave reflections from previous cycles to dissipate before the beginning of a new cycle. The blood mimicking fluid described in [50], with a viscosity of 4 mPa s was used. In the case of the straight phantom, six ($\text{N}=6$) longitudinal ultrasound acquisitions were performed proximal to the inlet, while in the atherosclerotic phantoms, four ($\text{N}=4$) acquisitions were carried out at the stenotic segment, with the plaque centered in the field of view (FOV). The temporal waveform of the pressure at the outlet of the phantom was measured using a pressure catheter (MPR-500, Millar, Houston, TX, USA) which was inserted inside the lumen phantom via a cross connector.

FSI simulations were carried out with the same geometry and material properties as the phantoms using software suite FEBio [53][54] (Figure 1-C, D), similarly as in [42][55]. The same flow waveform as the one generated by the programmable pump was prescribed at the inlet of the simulated phantom, while the measured pressure waveform was employed as the outlet boundary condition. The simulated fluid shear stress at the central 2-D slice of each phantom was exported and post-processed in MATLAB 2017b (MathWorks Inc, Natick, MA, USA). Additional information on the phantom fabrication and FSI simulations can be found in supplementary material 1,2).

B. Atherosclerotic swine study

All procedures in this study were approved by the Institutional Animal Care and Use Committee (IACUC) of Columbia University (protocol AC-AAAU6460). Six 3-month-old female Wisconsin Mini Swine-Familial Hypercholesterolemic (WMS-FH^™) were acquired from the University of Wisconsin Swine Research Farm (Madison, WI, USA), and were fed a high fat atherogenic diet [56]. In order to accelerate plaque formation, the left common carotid artery of each animal was ligated in order to disturb flow velocity patterns and accelerate atherosclerotic plaque formation.

In four ($\text{N}=4$) carotids, the ligation induced high degree of vessel stenosis (>80% stenosis), while in $\text{N}=2$ carotids, a low stenotic ligation was performed (<40% stenosis), imposing thus different flow and WSS conditions. The right common carotid arteries ($\text{N}=6$) were left intact, to serve as controls. Ultrasound scans were performed using the WSS imaging sequence at baseline, immediately before and after performing ligation. Biweekly scans were carried out during the first month of the study, and once a month afterwards. Figure 2-A) demonstrates a CT scan of an animal in the supine position, while Figure 2-B) shows a magnified and thresholded area of the CT scan that highlights the carotid arteries. The black marker illustrates the approximate location of the ligation, while the red rectangles illustrate the arterial segments where the WSS maps were obtained. The segment preceding the ligation (pre-ligation segment) was chosen for analysis, because it provided consistent and robust WSS measurements throughout the study. All animals were euthanized at ~ 9 months after baseline scans. After euthanasia, the common carotids were extracted and underwent histological examination. The ligated carotid arteries were cut in a series of 5 mm segments, using the site of initial ligation as a reference, while in the case of non-ligated carotid arteries, three 5 mm segments were obtained for analysis. In each 5-mm segment, cross-sectional histology slices were obtained using hematoxylin-eosin (H&E) and Masson’s trichrome staining. To spatially register the histology slices with their approximate location in the ultrasound images at baseline ultrasound scans, a correction factor was applied, accounting for the in-vivo stretch of common carotid arteries in pigs as reported in [57] and the growth of the animals during the study. By using the correction factor, it was determined that the 5 mm regions corresponded to segments of approximately 5.4 mm in the ultrasound field of view, by using the ligation as reference. Additional information on the atherosclerotic swine study design can be found in the supplementary material 3).

C. Human study

All procedures pertinent to the human study were approved by the Human Research Protection Office (HRPO) and Institutional Review Boards (IRBs) of Columbia University (protocol AAAR0022). The common carotid arteries of $\text{N}=15$ carotid artery disease patients presenting non-stenosing atherosclerosis (9 Male, 6 Female; 68.3 ± 6.9 y.o.; <40% stenosis), and $\text{N}=15$ age matched controls (9 Male, 6 Female; 69.1 ± 7.5 y.o.) without known history of carotid artery disease were scanned in vivo. In addition, the carotid artery of a patient presenting high degree of stenosis (Female; 77 y.o.; >70% stenosis) was imaged with the plaque in the field of view. The subject was scanned using the ultrasound equipment immediately prior to admission for carotid endarterectomy. Upon completion of surgical operation, the excised plaque sample was obtained and underwent histological examination. Signed consent form was obtained from all subjects before performing ultrasound scans. All ultrasound scans were performed by an expert sonographer technician, with the subjects being in the supine position.

D. WSS Performance assessment

In the case of the straight vessel phantom, for each ultrasound scan ($\text{N}=6$), the peak systolic $\left({\text{WSS}}_{\text{PS}}(\text{x})\right)$ and end-diastolic $\left({\text{WSS}}_{\text{ED}}(\text{x})\right)$ WSS values were calculated at each lateral position, x, separately for the top and bottom walls. Therefore, a total of $\text{N}=12$ measurements of ${\text{WSS}}_{\text{PS}}(\text{x})$ and ${\text{WSS}}_{\text{ED}}(\text{x})$ were obtained for each lateral position. The corresponding simulated values ($WS{S}_{PS}^{sim}(x)$, $WS{S}_{ED}^{sim}(x)$) were spatially registered and interpolated into the same grid as the ultrasound FOV. The repeatability and accuracy of the technique were evaluated by calculating the average relative standard error of the means, ${\widehat{\text{SEM}}}_r(\text{\%})$, and relative error, ${\text{E}}_{\text{r}}(\text{\%})$, as follows:

where $AVG{\left\{\right\}}_x$ denotes the averaging operator across the lateral direction and $<{>}_N$ stands for averaging among multiple measurements. The brackets, $\{PS,ED\}$, stand for of the metric calculation either at peak systole, or end diastole.

For the stenotic phantom study, the similarity between measured and simulated WSS spatial distributions across the stenotic wall was evaluated by performing the Pearson test of correlation. The average relative error was calculated separately in the pre-stenotic, stenotic and post-stenotic segments of the acquired ultrasound image as follows:

where ${WSS(x)|}_{x=x_{max}}$ denotes the WSS at the lateral position corresponding to its maximum value. The repeatability was assessed by estimating the ${\widehat{\text{SEM}}}_r(\text{\%})$, similarly as in the case of the straight vessel phantom.

E. In vivo analysis

Two markers were computed based on the WSS measurements: 1) Peak systolic $\text{WSS}\left({\text{WSS}}_{\text{PS}}\right)$ and 2) Harmonic index (HI). HI has been suggested as a metric to quantify the presence of high frequency oscillations in the WSS temporal waveform [58][59]. In this study, the presence of harmonics higher than the frequency of the heart beat was quantified as follows:

where $\text{F}\left\{\right\}\left[\text{n}{\omega }_0\right]$, denotes the Fourier transform of the WSS signal with respect to the n-th harmonic of the fundamental frequency $\left({\omega }_0\right)$. Only harmonics corresponding to frequencies lower than 30 Hz were considered, which is equal to the cutoff frequency of the low-pass filter applied on the WSS temporal waveforms.

In the case of the atherosclerotic swine study global markers, ${\text{WSS}}_{\text{PS},\text{g}}$ and ${\text{HI}}_{\text{g}}$, were obtained by averaging the peak systolic WSS and HI across the imaged arterial segment in the top and bottom walls for each acquisition. The global estimates were compared among different scanning time points using repeated measures ANOVA with Tukey window correction for multiple pair comparisons. In addition, to demonstrate the feasibility of the proposed technique to predict the severity of localized atherosclerotic plaque development, piecewise baseline estimates, ${\text{WSS}}_{\text{PS},\text{pw}}$ and ${\text{HI}}_{\text{pw}}$, were derived in ligated arteries by averaging within arterial segments of 5.4 mm, which correspond to the approximate location of histological slices obtained at the end-point. One-way ANOVA with Tukey window correction was carried out to compare the regional ${\text{WSS}}_{\text{PS}}$ and HI values at baseline ultrasound scans among segments that developed moderate plaques (<80% stenosis), severe plaques (>80% stenosis), and plaque-free segments. In the case of the human study, the global ${\text{WSS}}_{\text{PS},\text{g}}$ and ${\text{HI}}_{\text{g}}$ were calculated for each subject. Comparison was carried out between atherosclerotic carotid arteries with low degree of stenosis and controls carotid arteries using unpaired t-test.

A. Phantom and simulation study

Figure 4-A) shows a time frame of the WSS image sequence in the imaged segment of the straight vessel phantom, with the WSS color-coded and overlaid onto the B-mode image. It is noted that the segmented mask is used only for visualization purposes and does not contribute to the WSS imaging methodology. The red marker indicates a point on the bottom phantom wall where the WSS time waveform was plotted in figure 4-B). Figures 4-C) and D) illustrate a time frame of the WSS imaging sequence in the phantom with 50% stenosis, and an example WSS temporal waveform corresponding to the top stenotic wall, respectively. Videos depicting simultaneous propagation of distension pulse wave and WSS maps in the straight and stenotic vessel phantoms, have been included in supplementary multimedia 1 and 2 respectively.

The solid black lines in figure 4-E, F) demonstrate the average value of ${\text{WSS}}_{\text{PS}}(\text{x})$ and ${\text{WSS}}_{\text{ED}}(\text{x})$, respectively, in the straight phantom, with respect to the lateral position, while the error bars denote the standard error of the means among different measurements. The red solid lines show the corresponding values, ${\text{WSS}}_{PS}^{sim}(\text{x})$ and ${\text{WSS}}_{ED}^{sim}(\text{x})$, as obtained through simulations. The standard error of he means, ${\widehat{\text{SEM}}}_r(\text{\%})$, and relative error, $\widehat{{\text{E}}_r}(\text{\%})$, were equal to 6.9 %, 6.7 %, respectively, in the case of WSS_PS, and 10.9 %, 19.8 %, respectively, in the case of WSS_ED.

Figures 4-G), H) demonstrate the average ${\text{WSS}}_{\text{PS}}(\text{x})$ and ${\text{WSS}}_{\text{ED}}(\text{x})$ distributions of the top stenotic wall, respectively, as obtained through measurements and simulations. The correlation coefficient, R, between measured and simulated WSS spatial distributions was equal to 0.89 and 0.85 for ${\text{WSS}}_{\text{PS}}$ and ${\text{WSS}}_{\text{ED}}$, respectively. An ${\widehat{\text{SEM}}}_r(\text{\%})$ of 11.1% and 18.1% was provided in the case of ${\text{WSS}}_{\text{PS}}$ and ${\text{WSS}}_{\text{ED}}$, respectively. The $\widehat{{\text{E}}_r}(\text{\%})$, in the pre-stenotic, stenotic and post-stenotic segments was equal to 11.0%, 12.3 % and 22.6 %, respectively, in the case of ${\text{WSS}}_{\text{PS}}$, and 12.5%, 16.8% and 10.86%, respectively, in the case of ${\text{WSS}}_{\text{ED}}$.

Additional analysis involving comparison of the proposed adaptive WSS imaging methodology with a conventional WSS calculation approach has been included in supplementary material 4).

B. Atherosclerotic swine study

Figures 5-A), B) show a time frame of the WSS imaging sequence in a highly ligated, and a non-ligated artery, respectively. The red solid lines indicate the regions of the imaged arterial segments, where global estimates, ${\text{WSS}}_{\text{PS},\text{g}}$ and ${\text{HI}}_{\text{g}}$ were obtained. Videos depicting simultaneous propagation of distension pulse wave and WSS maps in the highly ligated, and non-ligated artery, have been included in supplementary multimedia 3 and 4 respectively.

Figures 5-C, D) demonstrate the temporal evolution of ${\text{WSS}}_{\text{PS},\text{g}}$ and ${\text{HI}}_{\text{g}}$ in the ligated carotid arteries, for the first 2 months of the study, which corresponds to the pre-clinical stage of atherosclerosis. The “Day 0” and “Day 0*” labels in the case of the ligated carotid artery stand for the baseline measurements, carried out on the same day before and after performing ligation. In the case of highly ligated arteries, repeated measures ANOVA with Tukey window correction for multiple pairs comparisons demonstrated a significant decrease in ${\text{WSS}}_{\text{PS}}$ before (Day 0*) and after (Day 0*) performing ligation (Day 0:4.49 ± 0.42, Day 0*: 0.77 ± 0.47, p<0.05), followed by an increase 14 days later (Day 0*: 0.77 ± 0.47, Day 14: 3.97 ± 0.29, p<0.01). A significant increase was observed in HI_g after performing ligation (Day 0: 0.62 ± 0.07, Day 0*: 0.89 ± 0.02, p<0.05), indicating that the presence of ligation altered the oscillatory properties of $\text{WSS}.{\text{HI}}_{\text{g}}$ decreased 14 days afterwards (Day 0*: 0.89 ± 0.002, Day 14: 0.58 ± 0.07, p<0.05), restoring thus its baseline value. On the contrary, in the case of low ligated (<40% stenosis) and non-ligated arteries, ${\text{WSS}}_{\text{PS},\text{g}}$ and ${\text{HI}}_{\text{g}}$ presented uniform values, with no significant differences among different time points. Histological examination at end-line of the experiment revealed the presence of either moderately (<80%), or highly (>80%) stenotic atherosclerotic plaques, in carotid arteries with high ligation. On the contrary, no plaques were present in the low ligated, or non-ligated arteries.

Examples of spatial registration between baseline WSS images immediately after performing ligation (Day 0*) and histological slices obtained upon completion of the experiment in two highly ligated carotid arteries, are illustrated in Figures 6-A),B). The red rectangles in the B-mode images demonstrate the regions in which piecewise estimates were derived. The bottom Figures illustrate the respective H&E histological slices. Figures 6-C),D) demonstrate the piecewise ${\text{WSS}}_{\text{PS},\text{pw}}$ and ${\text{HI}}_{\text{pw}}$ values at Day 0*, with respect to atherosclerotic plaque severity. One way ANOVA with Tukey window correction indicated that ${\text{WSS}}_{\text{PS},\text{pw}}$ was significantly higher in plaque free arterial segments, as compared to segments that developed moderate, or severe atherosclerotic plaques (No plaques: 3.47 ± 0.79, moderate plaques: 1.22 ± 0.09, severe plaques: 0.35±0.20 p<0.0001). In addition, higher ${\text{WSS}}_{\text{PS},\text{pw}}$ was observed in segments with moderate, as compared to segments with severe plaques (p<0.05). Finally, ${\text{HI}}_{\text{pw}}$ was lower in regions with no plaques, as compared to moderate, or severe atherosclerotic plaques (No plaques: 0.65 ± 0.07, moderate plaques: 0.91±0.01, severe plaques:0.86±0.05 p<0.0001).

C. Human study

Figures 7-A),B),C) illustrate a time frame of the WSS imaging sequence corresponding to peak systole in the case of a control, a low stenotic and a highly stenotic atherosclerotic carotid artery, respectively. Figure 7-D), E) show the ${\text{WSS}}_{\text{PS}}$ and HI values in control versus pathological carotid arteries. The unpaired Student’s t-test indicated that ${\text{WSS}}_{\text{PS}}$ was significantly higher in age matched controls, as compared pathological arteries with non-stenosing atherosclerosis (controls: 1.98 ± 0.37 Pa; pathological: 1.47 ± 0.55 Pa; p<0.01). HI was on average lower in the control, as compared to the pathological group, however, the difference was not significant. (controls: 0.76 ± 0.04; pathological: 0.79 ± 0.07; p>0.05). Videos depicting simultaneous propagation of distension pulse wave and WSS maps corresponding to the subjects shown in Figures 7-A),B),C) have been included in supplementary multimedia 5, 6 and 7 respectively.

Figure 7-F) demonstrates the excised plaque sample of the patient shown in Figure 7-C), and a histological slice of Masson’s trichrome staining, corresponding to the approximate location of the scanning site. Histological examination revealed a highly vulnerable plaque, with a necrotic core and a thrombus. The presence of a thrombus at the plaque shoulder, upstream to the flow, indicates a potential site of plaque rupture. The approximate location of the rupture site is marked with the red rectangle in Figure 7-C). A high WSS value was observed in this region, indicating that elevated WSS can potentially be the cause of rupture, when a vulnerable atherosclerotic plaque is present.