Dynamic coronary blood flow velocity and wall shear stress estimation using ultrasound in an ex vivo porcine heart

Abstract

Purpose

Wall shear stress (WSS) is a critically important physical factor contributing to atherosclerosis. Mapping the spatial distribution of local, oscillatory WSS can identify important mechanisms underlying the progression of coronary artery disease.

Methods

In this study, blood flow velocity and time-varying WSS were estimated in the left anterior descending (LAD) coronary artery of an ex vivo beating porcine heart using ultrasound with an 18 MHz linear array transducer aligned with the LAD in a forward-viewing orientation. A pulsatile heart loop with physiologically-accurate flow was created using a pulsatile pump. The coronary artery wall motion was compensated using a local block matching technique. Next, 2D and 3D velocity magnitude and WSS maps in the LAD coronary artery were estimated at different time points in the cardiac cycle using an ultrafast Doppler approach. The blood flow velocity estimated using the presented approach was compared with a commercially-available, calibrated single element blood flow velocity measurement system.

Results

The resulting root mean square error (RMSE) of 2D velocity magnitude acquired from a high frequency, linear array transducer was less than 8% of the maximum velocity estimated by the commercial system.

Conclusion

When implemented in a forward-viewing intravascular ultrasound device, the presented approach will enable dynamic estimation of WSS, an indicator of plaque vulnerability in coronary arteries.

Introduction

Atherosclerotic plaque rupture and erosion are the most important mechanisms resulting in acute coronary syndromes, which is one of the leading causes of death in the United States [1]. Wall shear stress (WSS) has been recognized as one of the critical physical factors contributing to atherosclerosis. Low wall shear stress is believed to be associated with plaque formation and remodeling, while high wall shear stress is associated with likelihood of plaque rupture [2, 3]. Because the spatial distribution of wall shear stress varies with flow conditions and with vascular anatomy, accurate estimation of local hemodynamics and local WSS distribution in coronary arteries could be used for identifying vulnerable plaques [4]. Furthermore, coronary artery motion during the cardiac cycle and oscillatory shear stress may affect mass transport patterns of oxygen and low-density lipoproteins and contribute to the spatial distribution of atherosclerosis [5–8].

The spatial distribution of WSS can be estimated in coronary arteries using computational fluid dynamics (CFD) based on geometries reconstructed from non-invasive imaging modalities such as X-ray angiography or computed tomography angiography in combination with high resolution intravascular imaging, i.e. optical coherence tomography (IV-OCT) or intravascular ultrasound (IVUS) [9–12]. However, CFD models can be sensitive to patient-specific physiological conditions, which can be challenging or impossible to acquire, and can also be computationally expensive [13]. Phase contrast magnetic resonance imaging (PC-MRI) can directly estimate the WSS spatial distribution in vivo, however, PC-MRI has primarily been restricted to larger arteries such as the abdominal aorta or carotid artery due to a spatial resolution ranging from 0.5 × 0.5 to 4.0 × 4.0 mm², and a temporal resolution of approximately 50 ms to 5 min [14–16]. WSS has been most accurately estimated when utilizing velocity profiles fitted using 10–15 data points [17]. Therefore, in order to estimate WSS across coronary arteries, at least 10 points per mm are required, i.e. spatial resolution of 0.3 mm or less for a 3 mm diameter artery.

Ultrasound has been used to estimate blood flow velocity and WSS in larger arteries, and has higher temporal resolution relative to PC-MRI, potentially improving estimation of temporal variations in blood flow over the cardiac cycle. This could be useful given that highly pulsatile flow has been identified as one of the important physical factors in the atherosclerotic process [18]. Transverse oscillation and multi-angle least squares vector flow imaging techniques have been developed for estimation of 2D and 3D velocity vectors with improved accuracy [19–23]. Ultrafast techniques have increased the maximum detectable velocity to enable more accurate estimation of velocity and WSS in physiological flow conditions [24–26]. WSS has previously been estimated in vivo with ultrasound in larger arteries such as the carotid bifurcation, femoral artery, or brachial artery using ultrafast plane-wave multi-angle Doppler velocimetry [27, 28]. Recently, Chee et al. presented WASHI, a noninvasive wall shear rate (WSR) mapping technique using high-frame-rate ultrasound and demonstrated its performance in healthy and diseased carotid bifurcation models [22]. WSS has also been estimated with ultrasound in the femoral artery and abdominal aorta using echo-PIV [29, 30]. Thus ultrasound-based techniques for estimating velocity and WSS in larger arteries have been established.

Although these non-invasive, ultrasound-based approaches have been successful in estimating WSS in larger, superficial arteries, they lack sufficient spatial resolution at depth needed for non-invasive imaging of WSS in coronary arteries. To address this issue, Correia et al. have demonstrated in vivo blood flow velocity in an open-chest swine model [31]. Other researchers have demonstrated 3D blood volume flow estimation as an objective, angle-independent measurement [32–34]. Separately, several groups have estimated blood flow velocity using minimally-invasive intravascular ultrasound (IVUS) devices [35–38]. Also, velocity and WSS estimation using forward-viewing ultrasound-based approaches in tissue-mimicking phantoms with coronary geometries have been investigated [39, 40]. Despite these advances, estimating coronary WSS remains a challenge. Recently, our lab has demonstrated a real-time 3D velocity fields estimation in peripheral arteries with a catheter-based, forward-viewing matrix array transducer [41], although this 4 mm device is still too large for coronary arteries. Following completion of a forward-viewing intravascular array transducer, which is currently in development, velocity and WSS distributions in coronary arteries can be estimated to guide intervention in the cardiac catheterization lab [42].

When using a catheter-based, forward-viewing IVUS transducer in a coronary artery in vivo, the transducer will be subjected to the motion of the coronary artery located on the surface of the beating heart. The bulk motion of the coronary artery can lead to misalignment of regions-of-interest when the RF signals are compounded, and this can lead to inaccurate measurement of velocity and WSS [43, 44]. For this reason, bulk cardiac motion has previously been tracked and compensated in IVUS palpography [43–45], and in vivo in a beating rat heart [46]. Implementation of motion compensation techniques in coronary blood flow velocity and WSS estimation will result in more accurate estimates of both quantities, improving assessment of vulnerable plaques with forward-viewing IVUS for patients in the cardiac catheterization lab.

In this work, blood flow velocity and wall shear stress were estimated in the coronary artery of an ex vivo pig heart with cardiac motion using an ultrasound array in a forward-viewing position. To our knowledge, this is the first dynamic estimation of coronary WSS with cardiac motion. Dynamic estimation of WSS is important because time-varying artery motion and oscillatory shear stress are believed to influence the location and progression of atherosclerosis in coronary arteries [5, 7]. Separately, in carotid arteries, locations with high WSS and low relative residence times have demonstrated significantly higher likelihood of ulceration within the plaque [47]. In the present study, time-varying WSS in coronary arteries was captured by using local block matching algorithms to track physiological displacements of heart tissue in multiple planes, then the motion was compensated prior to estimation of blood flow velocity in the coronary artery. Motion-compensated velocity estimates acquired using a linear array transducer in a forward-viewing arrangement were compared with Doppler velocity estimates acquired with a commercial blood flow velocity measurement system. While building on our previous work, the forward-viewing array used in previous studies was 4 mm in diameter and operated at 5 MHz, making it both too large and lacking sufficient spatial resolution for intracoronary imaging. Thus an external linear array transducer was used in this work while an intravascular ultrasound transducer with a small diameter for coronary velocity and WSS estimation is in development. Following the development of this coronary artery-sized forward-viewing array, the motion-compensated 2D and 3D velocity and WSS estimation techniques described in this manuscript could enable direct estimation of WSS in coronary arteries. Both temporal and spatial variations in blood flow velocity and WSS are analyzed in 2D and 3D based on maps acquired at different times in the cardiac cycle. To our knowledge, this is the first investigation of time-varying coronary artery WSS in laboratory experiments which is important because time-varying WSS affects mass transport patterns of oxygen and low-density lipoproteins, leading advancement of atherosclerosis [5–8].

Material and Methods

Ex vivo pulsatile flow loop

A porcine heart obtained from a healthy adult pig was purchased from Lampire Biological Laboratories (Pipersville, PA, USA). The left ventricle was cannulated at the apex using a custom 3D-printed apex tube [48, 49]. An ex vivo pulsatile flow loop using the porcine heart was adapted from previous studies designed to simulate the left heart [48, 49]. The heart was submerged in 0.9% saline solution for ultrasound imaging at a depth of 15 mm from the top surface of the water to the LAD coronary artery (Fig. 1 (a) and Fig. 1 (b)). A pulmonary reservoir was placed 140 mm above the left atrium and was connected to a pair of pulmonary veins (Fig. 1 (d)). Another tube was connected from the aorta to an aortic reservoir located 180 mm above the apex of the heart. To create a closed loop, the aortic reservoir could overflow to the pulmonary reservoir, and the pulmonary reservoir could overflow to the pump reservoir, which was located 350 mm below the heart. The outlet of the pulsatile pump (1423 Pulsatile blood pump, Harvard Apparatus, MA, USA) was connected to the 3D apex tube in the left ventricle. The pump was set to create physiological flow conditions of 4.9 liters per minute at 60 beats per min, mimicking the healthy resting heart rate of an adult human and a systole/diastole duration ratio of 40/60 [50]. A 0.9% saline solution with microbubbles was used as the working fluid in this study. These microbubbles are synthesized in-house and have properties similar to the FDA-approved microbubble contrast agent, Definity^® (Lantheus Medical Imaging, North Billerica, MA), as described previously [51–53]. Microbubbles were diluted 2000 times in degassed saline, yielding a concentration of 5 × 10⁶ microbubbles per mL.

Fig. 1.

Ex vivo pulsatile flow loop setup using porcine heart. (a) Picture of the setup. 1. Tube connected to aorta, 2. Tube connected to left atrium, 3. LAD coronary artery, 4. MS400 linear array transducer, 5. Tube connected to 3D printed structure at apex of the heart. (b) Picture of the porcine heart. The blue dotted line indicates the imaging region-of-interest of LAD coronary artery. The ultrasound transducer was placed in a forward-viewing direction so that the ultrasound beam was aligned with the long-axis of the LAD coronary artery using the red clamp. (c) Diagram of ultrasound transducer placement and its scan plane relative to the LAD coronary artery. (d) Schematic representation of the setup. Black arrows indicate the direction of the flow. Pulsatile flow was introduced to 3D printed structure at apex of the heart using a pulsatile piston pump.

Ultrasound measurements

A high-frequency linear array transducer (MS400, FUJIFILM VisualSonics, Inc., Toronto, Canada) with a center frequency of 30 MHz and bandwidth of 18–38 MHz was connected to a high frame rate ultrasound imaging system (Verasonics Vantage 256, Kirkland, WA, USA). The transducer was positioned 2 mm above the top surface of the LAD artery to avoid compressing the tissue and was oriented in a forward-viewing direction. The array pitch is 0.06 mm or 0.7 × λ. According to simulations (Field II), when imaging at a depth of 7 mm and steering the beam to 15°, this results in the first grating lobe occurring at 7.6 mm in the lateral direction, which is outside of the field of view of ±3 mm used in this work. The transducer was positioned 2 mm above the top surface of the LAD artery to avoid compressing the tissue and was oriented in a forward-viewing direction. Imaging was performed with unfocused plane wave transmit events of 4-cycle, 18 MHz pulses (rectangular window). These pulses were transmitted with 3 compounding angles (−15°, 0°, +15°) at a frame rate of 10,000 frames/s for estimation of velocity and WSS. 1250 frames of RF data after compounding were saved to obtain the in-phase and quadrature (IQ) data offline using Matlab (MATLAB, Version 9.8.0 R2020a). An ensemble size of 200 was used; frames at the end of the acquisition were excluded to maintain a constant ensemble length. To estimate 3D velocity and WSS maps, the ultrasound transducer was linearly translated in the elevation direction from −1.5 mm to 1.5 mm with an increment of 0.25 mm using a computer-controlled motion stage (XPS-Q8, Newport, Irvine, CA, USA). For each location in the elevation direction, acquisitions were repeated 3 times.

To validate the accuracy of velocity measurements estimated using a high-frequency linear array transducer, a commercial system consisting of a single element, 2-mm diameter, 20 MHz Doppler probe and a commercial Doppler Signal Processing Workstation (Model DSPW, Indus Instruments, Houston, TX, USA) was used to acquire spectral Doppler velocity estimates in the same experimental setup. A pulse repetition frequency of 125 kHz was used, and the probe was focused at the same location as the center of the ultrasound beam from the linear array transducer, similar to a Doppler wire measurement. To quantitatively compare the velocity estimated using the linear array transducer and the velocity estimated from the commercial system, the root mean square error (RMSE) was calculated as

$$\begin{array}{c}RMSE=\sqrt{\frac{1}{N}\sum {\left(V_{single}-V_{linear}\right)}^2}\end{array}$$ #(1)

where $N$ is number of velocity data points, $V_{single}$ is velocity estimated from a single element probe with the commercial system and $V_{linear}$ is velocity estimated from the linear array transducer.

In addition, to assess the cardiac motion of the top surface of the LAD coronary artery over multiple cardiac cycles, a separate acquisition with a longer acquisition time (2.48 seconds) using a lower frame rate (500 frame/s) was performed.

Motion-compensated velocity and wall shear stress estimation

The processing chain from ultrasound acquisition to velocity and WSS maps is shown in Fig. 2. First, 1250 frames of beamformed RF data were low pass filtered with the cutoff frequency of 500 Hz to keep only the tissue signal. This was done because the flow in the coronary artery was not readily visible in all frames of the cardiac cycle, thus myocardial tissue and fat surrounding the coronaries were used as a surrogate for tracking coronary motion [54]. In-plane motion of the surrounding tissue was tracked using a local block matching technique [55]. Out-of-plane motion was not considered because minimal out-of-plane motion present during diastole [56], and coronary resistance is most stable and minimized during diastole. For this reason, two techniques developed for assessing the severity of coronary artery stenoses – instantaneous wave-free ratio and intravascular palpography – are used during diastole [56, 57].

Fig. 2.

Processing chain from ultrasound acquisition to velocity and wall shear stress estimation. LPF: low pass filter. SVD: Singular Value Decomposition

The dimensions of the block were 132 μm × 82.5 μm to remain similar to the spatial resolution of the image [58]. The search window was (264 μm × 165 μm) so that the margin corresponds to the maximum possible 2D displacement between two consecutive frames. Sum-of-absolute differences (SAD) was used as the similarity criteria for local block matching [59, 60]. A block identified from an image is used as a template to search for a match within a larger search region in a subsequent frame of image. This block is compared to all possible translations within the search region (i.e., exhaustive search), and the best match is identified by finding the minimum SAD. Block matching using SAD has similar performance to normalized cross correlation, but SAD is more computationally efficient [59, 60]. Both lateral and axial displacements were estimated. Motion of the LAD coronary artery underneath the top surface was assumed to be the mean displacement in the top surface of the LAD coronary artery. This assumption was based on previous reports that LAD coronary artery bulk motion during mid-diastole is primarily in-plane [61]. Next, based on the pixel-wise displacement values, beamformed RF data was shifted in both lateral and axial directions. Singular Value Decomposition (SVD) filtering was then performed to remove stationary echoes by discarding the first, largest singular value from beamformed RF data [62]. Transverse oscillation was introduced to the filtered data to estimate velocity in the lateral direction [63, 64]. The lateral velocity component was estimated using a fourth-order autocorrelation estimation [65], while the axial velocity component was estimated using a standard cross-correlation estimator.

Using 2D velocity vectors estimated from the Doppler approach, WSS was estimated at both walls of the LAD coronary artery adopting a novel approach [66]. The boundary of the coronary artery was identified using semi-automatic segmentation from 2D ultrasound images with a sparse field method [67]. This approach assumes a Newtonian fluid, and as such the WSS derives from the deviatoric stress tensor σ:

$$\sigma =-\mu \left(\nabla u+{\nabla }^{T}u\right)$$ #(2)

where u is the velocity and μ is the (positive) constant kinetic viscosity. The viscosity value of 1.02 mPa·s was used to match the dynamic viscosity of 0.9% saline solution. WSS on a portion of the boundary Γ⊂∂Ω is defined as the part of the normal component of the deviatoric tensor σ ⋅n tangential to the boundary (here n is the outward normal unit vector), and can be defined as

$$\begin{array}{c}\tau \equiv \sigma \cdot n-\left(n\cdot \sigma \cdot n\right)n.\end{array}$$ #(3)

To compute the deviatoric stress tensor σ using equation (2), one needs to calculate the velocity gradient $\mathit{\nabla }\mathit{u}$, which in this particular case has four components instead of nine, as 2D ultrasound imaging employed in this work provides only in-plane velocities. The $\mathit{\nabla }\mathit{u}$ components involve partial derivatives with respect to two directions: radial and axial. Among these, the radial direction has a more significant impact, hence we used a more sophisticated approximation for it. Specifically, we used a truncated Sine Fourier series to represent pixelated velocity data at each section, allowing for the estimation of radial derivatives. On the other hand, axial derivatives are computed numerically over velocity data that has been previously smoothed using a 3% data span moving average. This pseudo-spectral method was chosen over the current state of the art after the evidence presented in [66]. The conventional approach typically involves fitting polynomials of degree two or three to data points near the vessel wall, where the velocity gradient $\mathit{\nabla }\mathit{u}$ must be obtained, and hence its notably sensitive to noise. In contrast, our pseudo-spectral method is a more robust and effective tool for filtering the noise present in the ultrasound imaging data, enabling more accurate estimation of WSS.

Results

Motion analysis of LAD coronary artery

The lateral and axial displacements of the top surface of the LAD coronary artery over a duration of 2.48 seconds are shown in Fig. 3. When subsequent images are compared to the first frame (Fig. 3 (a)), cyclical cardiac pulsing can be identified, with greater motion in the lateral direction (Fig. 3 (b)). The maximum absolute lateral displacement of the top surface of the LAD artery was 156 ± 24 μm, while the maximum absolute axial displacement was 102 ± 21 μm. The duration of the cycle was 0.75 ± 0.4 sec.

Fig. 3.

Displacement of the top surface of LAD coronary artery over time with respect to the first frame. (a) The first frame of B-mode images that was used for tracking motion of the top surface of LAD. The top surface of the LAD coronary artery is located between myocardial surfaces. The yellow box indicates the region-of-interest used for motion tracking in the subsequent frames. (b) Displacement of the top surface of LAD coronary artery (yellow box) over multiple cycles with respect to the first frame. The blue line indicates displacement in the lateral direction while the red line indicates displacement in the axial direction.

2D velocity magnitude and wall shear stress maps

Spatial and temporal variations of 2D velocity magnitude and WSS maps are shown in Fig. 4. Velocities as a function of time in three different spatial locations (magenta, red, and cyan colored markers in Fig. 4 (b)) were investigated (Fig. 4 (a)). At four points in time (I: 0.47 s, II: 0.50 s, III: 0.53 s, and IV: 0.56 s), 2D velocity magnitude maps are shown (Fig. 4 (b)). The time at 0.47s was selected relative to the cardiac cycle such that it was when the systole ended, and thus the ultrasound acquisition was performed during diastole. The direction of the flow is from bottom to top, and the transducer was located at the top in a forward-viewing direction. The maximum velocity magnitude across all four times was present at time II (15.30 ± 2.24 cm/s). At time II, velocity magnitudes greater than the mean velocity magnitude of 12.13 ± 2.80 cm/s were located primarily on the right side of the artery between 8 to 10.5 mm in depth. At time III, velocity magnitudes greater than the mean velocity magnitude of 8.64 ± 2.20 cm/s were located on the right side of the artery up to 12 mm in depth, while noticeably lower velocity magnitudes were present on the left side of the artery.

Fig. 4.

2D velocity magnitude and wall shear stress maps. (a) Velocity at three spatial locations (magenta, red, and cyan colored dots in Fig. 4 (b)) over time. The dash-dotted line indicates velocity over time at magenta colored marker location (7 mm in depth from the transducer and 0.5 mm in lateral direction). The solid line indicates velocity over time at the red colored marker (10.3 mm in depth from the transducer and 0.6 mm in the lateral direction). The dotted line indicates velocity over time at the cyan colored marker location (7.8 mm in depth from the transducer and −0.55 mm in lateral direction). (b) Velocity magnitude maps corresponding to four time points indicated on Fig. 4 (a). I is at 0.47 s, II is at 0.50 s, III is at 0.53 s, and IV is at 0.56 s. The vertical axis indicates the depth from the transducer. The coronary flow is introduced from the bottom of the image, and the transducer is located at the top and the ultrasound beam is facing towards the flow in a forward-viewing direction. (c) Wall shear stress maps at four time points indicated on Fig. 4 (a).

Spatial variation in wall shear stress is shown in the maps corresponding to these four times (Fig. 4 (c)). For all four times, the maximum WSS value at each time were located on the right side of the artery. The maximum WSS value across all four times was 0.26 ± 0.05 Pa, and it was present at time II. The maximum WSS decreased over time reaching 0.14 ± 0.08 Pa at time IV.

3D velocity and wall shear stress maps

3D velocity vector and wall shear stress maps acquired from translating the linear array transducer are shown in Fig. 5. In Fig. 5 (a), velocity was plotted as a function of time at the spatial location indicated by the red colored marker in Fig. 5 (c). 3D velocity vectors at three points in time (I: 0.49 s, II: 0.52 s, III: 0.54 s) are shown in Fig. 5 (c). Time I was at the maximum velocity in diastole. The flow was primarily in the axial direction, and the magnitude of the lateral flow vector was an order of magnitude smaller than that of the axial flow vector. Also, WSS maps corresponding to these time points are shown in Fig. 5 (d). Compared to other times, at time I, there was greater variation in WSS in the elevation direction and higher WSS values on both sides of the wall.

Fig. 5.

3D velocity and wall shear stress maps. (a) Velocity at one fixed spatial location (indicated by the red marker in Fig. 5 (c)) with respect to time. The red marker is located 10.3 mm in depth from the transducer and 0.6 mm in the lateral direction. Temporal variation at one fixed location in the coronary artery vessel is shown. (b) Axial (left) and lateral (right) components of velocity for the central plane at time I. (c) 3D vector maps corresponding to three time points indicated on Fig. 5 (a). Time I corresponds to 0.49 s which was relative to the cardiac cycle such that it was at the maximum velocity during diastole. Time II corresponds to 0.52 s and time III corresponds to 0.54 s. Spatial variation across the coronary artery at three time points are shown. (d) Wall shear stress maps corresponding to three time points indicated on Fig. 5 (a). Variations in the luminal diameter and shape are due to compliance of the LAD coronary artery and changes in local arterial pressure.

Spectral Doppler estimates comparison

Spectral Doppler results from a single element probe at the center of the LAD coronary artery over one cardiac cycle were displayed using the Doppler Signal Processing Workstation of the commercial system (Fig. 6 (a)). Fig. 6 (b) shows spectral Doppler estimates acquired using the linear array transducer and the single element probe during 0.46 to 0.54 s at the same location in the LAD artery. Mean velocity vector magnitude from the linear array transducer over the duration from 0.46 to 0.54 s were overlaid on mean velocity results from the commercial single element probe over a cardiac cycle (Fig. 6 (c)). The velocity corresponding to the maximum power based on the velocity estimated using the linear array transducer was 14.09 ± 1.28 cm/s, while for the single element ultrasound probe, it was 14.12 ± 1.30 cm/s. During the period of ultrasound acquisition, RMSE of velocity estimated using the linear array transducer compared to velocity estimated from the commercial system was 1.13 ± 0.12 cm/s.

Fig. 6.

Comparison of spectral Doppler estimates using the proposed approach with a linear array transducer (Visualsonics MS400) with a calibrated commercial system (Indus Instrument). (a) Spectral Doppler results of one cardiac cycle estimated using single element ultrasound probe and displayed on Doppler Signal Processing Workstation. (b) Spectral Doppler results estimated using linear array transducer over 1250 frames and at 10000 frames/s (left). Spectral Doppler estimates measured using the commercial system during the same time period (right). (c) Spectral Doppler estimates from the data acquired with the linear array transducer overlaid on spectral Doppler estimates from the commercial system with a single element probe over one cardiac cycle.

Discussion

2D and 3D flow velocity and wall shear stress distributions were estimated in the LAD coronary artery of an ex vivo beating pig heart for the first time using a high frequency, linear array transducer in a forward-viewing orientation. Myocardial tissue motion as shown in Fig. 3 has been compensated for estimation of motion-compensated flow velocity and wall shear stress in LAD coronary artery.

By estimating dynamic flow velocity and WSS in the moving LAD artery, it was observed that depending on the spatial locations within the LAD coronary artery, velocity profiles over time were different (Fig. 4 (a)). 2D velocity magnitude and WSS maps at four time points in the cardiac cycle are shown (Fig. 4 (b) and (c)). The outlines of the wall identified for WSS maps are different for different points in time because the pulsation of the coronary artery introduced changes in the luminal diameter [68, 69]. At time I, higher velocity magnitudes were present near the center of the artery, and mostly parabolic cross-sectional velocity magnitude profiles were present. This was reflected in the WSS map where RMSE of WSS between left and right side of the wall were less than 0.03 ± 0.01 Pa. However, at time II, high velocity flow was skewed to the right side of the artery, which is likely due to the flow, accelerating and this change in the flow velocity could have contributed to the flow disturbance. This was reflected in WSS map at II, where the maximum WSS values (0.27 ± 0.10 Pa) were present at 1.76 mm in the lateral direction. Next, at time III, the high velocity flow was still skewed to the right side of the artery, but the skewness was lower. Therefore, in the WSS map, the WSS on the right side of the wall was 0.09 ± 0.03 Pa greater than the left wall, and the maximum WSS at this time was 44% smaller than the maximum WSS at time II. This is likely due to the flow momentum dissipating after time II, resulting in decrease of velocity and WSS. Lastly, at time IV, velocity magnitudes were relatively uniform across the artery, demonstrating that most of the flow momentum has dissipated. The maximum WSS value was 37% lower than the maximum WSS at time III. The decrease in WSS with a decrease in velocity magnitude after the peak in the cardiac cycle observed experimentally is consistent with what has been reported in literature using CFD [70].

In addition, similar flow characteristics were found in 3D velocity and WSS maps (Fig. 5 (c) and (d)). At time I, the maximum velocity magnitudes were located at the middle of the artery, and higher values of WSS and greater spatial variation were observed. However, after time I, both velocity magnitudes and WSS decreased. At time II, elevated wall shear stress values were concentrated on the right side of the wall, which could be explained by higher velocity profile more concentrated on the right side while at time III, WSS values were more uniform across the entire artery, which could be explained by the decrease in the flow momentum. Also, the luminal diameter changed over time. For each time point, the outlines of the wall identified for creating WSS maps were different shapes because during the cardiac cycle, the coronary artery experiences changes in luminal diameter driven by the pulsation of the human coronary artery [68, 69]. The luminal diameter decreased from a luminal diameter of 3.01 ± 0.24 mm at time I to 2.78 ± 0.15 mm at time III, which was within the luminal diameter change measured using intravascular ultrasound [69].

Spatial variation in flow velocity and WSS demonstrate the value in measuring 2D and 3D spatial distributions of velocity and WSS rather than one spatial location, which is the current method for acquiring spectral estimates of velocity in the coronary artery using an intravascular Doppler guide wire [71]. Estimation of time-varying WSS due to wall motion and temporal variations in flow is important because time-varying WSS alters mass transport patterns of oxygen and low-density lipoproteins which leads to progression of atherosclerosis [5–8]. In this study, time-varying coronary WSS has been estimated in an ex vivo beating heart porcine model using accurate estimation of coronary flow velocity with wall motion compensation. Also, although flow patterns demonstrated in this study were in a healthy coronary artery, because complex and pulsatile flow patterns in an atherosclerosis-prone coronary artery region contribute to a progression of atherosclerosis, temporal variation in velocity and WSS acquired using ultrasound could be valuable for identifying vulnerable plaques [18].

Fig. 6 shows the spectral Doppler estimate from a high frequency linear array transducer overlapped with the estimate from the commercial single-element ultrasound probe system (similar to a Doppler wire). The waveform acquired with the single element ultrasound probe during a cardiac cycle illustrates typical flow characteristics of the human left coronary artery, in which inflow occurs predominantly during diastole [72].

In conclusion, the estimated velocity at the artery center was in agreement with the velocity estimated by a commercial single-element Doppler system. By using an ultrasound array, 2D and 3D velocity and WSS were mapped. Physiological motion represents a significant challenge for coronary WSS estimation, however, realistic cardiac motion was overcome to allow estimation even in the beating heart. These studies demonstrate that ultrasound imaging can resolve time-varying WSS in space and time, with high frame rate ultrasound providing sufficient temporal resolution to perform motion compensation and allow accurate estimation of coronary flow velocity.

Limitations

While the motion-compensated velocity and WSS estimation technique developed in this work can be applied to ultrasound images without contrast agents, the SNR without contrast agents will be lower, which may result in decreased accuracy in the velocity and WSS estimation. More studies are needed to optimize the proposed approach for flow estimation without contrast agents. Furthermore, only in-plane motion is compensated for velocity and WSS estimation using ultrasound imaging acquired during diastole, when minimal out-of-plane motion is present. However, to estimate velocity and WSS throughout the entire cardiac cycle, it would be important to also compensate out-of-plane motion. Moreover, in this study, saline solution with microbubbles was used as the flow medium, but because blood is a non-Newtonian fluid, in vivo flow conditions will be different from this setup. In future work, blood-mimicking fluids will be used to recreate blood mechanical properties more accurately.

In addition, although spectral Doppler estimates from a commercial single element ultrasound probe were compared to the velocity estimated from the linear array transducer as the first validation attempt in an ex vivo beating porcine model, validation using 2D or 3D velocity and WSS maps estimated by other imaging modalities or CFD would be necessary in future works. Another limitation is that even though velocity estimated in real-time by the commercial transducer was used to guide the placement of the commercial transducer at the same location as the linear array transducer, there could have been misalignment. However, this is likely to be minimal, as the RMSE of the maximum velocity magnitudes estimated from linear array transducer was 8% less than that of the commercial transducer. In addition, although flow patterns demonstrated in this study were in a healthy coronary artery, because complex and pulsatile flow patterns in an atherosclerosis-prone coronary artery region contribute to a progression of atherosclerosis, temporal variation in velocity and WSS acquired using ultrasound could be useful for identifying vulnerable plaques [18].

In this work, dynamic 2D and 3D velocity and WSS in the LAD coronary artery were estimated in an ex vivo beating heart for the first time. Both temporal and spatial variations of 2D and 3D velocity and WSS in the LAD coronary artery during diastole were shown. Estimation of time-varying WSS in space and time has been demonstrated using motion compensation techniques to accurately estimate coronary flow velocity, which could be useful for identifying vulnerable plaques given the effect of time-varying or oscillatory WSS on the progression of atherosclerosis. When this technique is implemented in a forward-viewing, intravascular ultrasound transducer that is currently under development, direct 3D estimation of WSS in coronary arteries could be used to guide intervention in the cardiac catheterization lab.