Characterization of velocity patterns produced by pulsatile and constant flows using 1000 fps high-speed angiography (HSA)

Abstract

In order to accurately quantify rapidly changing blood flow velocities, as typically seen in the neurovasculature, high temporal resolution is necessary. Current methods to extract velocity data from angiographic image sequences are generally limited to 30 fps or less. High-speed angiography (HSA) with a maximal frame rate of 1000 fps can be used to evaluate time-dependent flow details normally averaged out with lower frame rates. For new HSA image sequences, two different quantitative methods were utilized to extract high-temporal resolution velocity changes: X-Ray Particle Image Velocimetry (X-PIV) and optical flow (OF). A variety of flow conditions were examined in a range of patient-specific 3D-printed phantoms. Both pulsatile and constant flow settings were investigated. X-PIV was performed using radiopaque sub-millimeter microspheres, which were tracked throughout the image sequence to provide accurate, but limited sampling of the velocity field within the 3D-printed models. Also, an open source optical flow algorithm, OpenOpticalFlow, was used to perform velocity estimation based on the spatio-temporal intensity changes of iodinated contrast wavefronts. Periodic changes in velocity within each phantom ROI can be illustrated throughout the pulsatile cycle capture by the high-speed detector. In the constant flow sequences, changes in velocity across the phantom geometry can be seen. The ability to accurately measure detailed velocity distributions and velocity changes throughout various flow conditions at high temporal resolution enables further insight into the evaluation and treatment of neurovascular disease states.

1. INTRODUCTION

In the United States, neurovascular disease is a leading cause of serious long-term disability. Generally speaking, Digital Subtraction Angiography (DSA) is utilized to evaluate structural aspects of vascular disease, rather than physiological flow. Perfusion CT, MRI, and transcranial doppler ultrasound are all used to assess the severity of many abnormal neurovascular conditions, such as stroke and vascular stenosis. However, all patients undergo treatment for these conditions in angiography suites using x-ray image guidance, and angiography is still considered the gold standard for treatment and post-treatment evaluation of vascular disease. The options for evaluating the severity of abnormal hemodynamics as well as the effectiveness of a particular vascular intervention in real-time are limited. The application of high-speed x-ray imaging during an interventional procedure holds much potential in this area.

Additionally, evaluation of neurovascular detail is currently limited in the clinical setting due to the inadequate temporal resolution of flat panel detectors. With increased frame rate capabilities, there is the possibility of deriving quantitative flow information from angiographic sequences on a real-time basis. The ability to accurately quantify abnormal flows, which is currently not available to clinicians, may be significant in the assessment of neurovascular disease. In-vitro computational fluid dynamics (CFD) is considered the most comprehensive option for evaluation of blood flow, but it is based on a number of assumptions and requires a considerable amount of time and computer power for the calculations. One alternative method includes discrete tracking of particles embedded in the fluid. Particle Image Velocimetry (PIV) is discussed here in the context of x-ray imaging, where discrete radio-opaque particles can be tracked throughout the image sequence. Previously, other research groups have used CO₂ microbubbles as flow tracers, where our research group has created a novel method for performing 2D-PIV in patient-specific 3D-printed phantoms using iodine-soaked microspheres, or XPIV (X-Ray Particle Image Velocimetry).^1,2 An additional flow quantification method utilizes optical flow (OF) principles, where the motion of iodinated contrast media can be estimated on a frame-to-frame basis to obtain a two-dimensional velocity distribution at a resolution of one vector per pixel. The velocity distributions obtained through XPIV are a useful tool for comparison of velocity distributions calculated through OF in 3D-printed phantoms, as these microspheres would not be suitable for in-vivo use at this time. The two methods discussed here can be applied to HSA sequences to derive accurate velocity distributions, which can then be used to further quantify important hemodynamic parameters such as wall shear stress and vorticity. Various flow conditions must be investigated to evaluate the efficacy of both XPIV and OF in determining a range of blood velocities, as applied to HSA images.

2. MATERIALS AND METHODS

2.1. Flow Loop and 3D-Printed Phantoms

To create a wide range of flow conditions, two different pumps with both pulsatile and constant flow conditions were applied to flow loops having a variety of 3D-printed patient-specific phantoms, with variations in anatomical location and geometry as shown in figure 1; 1A: idealized internal carotid artery saccular aneurysm, 1B: wide-necked internal carotid artery saccular aneurysm, 1C: basilar tip aneurysm. Each model was evaluated for different ROI’s placed over the inflow vessel, the aneurysm sac, and the outflow vessel. The red arrows in figure 1 indicate inflow direction, yellow arrows indicate outflow direction for each model. The blue boxes indicate the detector FOV (approx. 1”x1”).

Figure 1:

3D-Printed Models

As shown in figure 2, each phantom was adhered to a platform with inflow, outflow, and collateral tubing, which were connected to either a pulsatile cardiac pump (Harvard Apparatus, Model #1423, Holliston, Massachusetts), or programmable pump (CompuFlow 1000, Shelley Medical Imaging Technologies) which provided both constant flows and programmable flow waveforms. Flow settings were chosen to provide a range of blood flow velocities, typical of those seen in both normal and abnormal physiologic conditions. The phantoms were positioned on a unistrut platform underneath the Actaeon photon-counting detector (Direct Conversion, Sweden), which has a 1”x1” FOV, 256x256 pixel readout, and 100-μm pixel size. Imaging was performed at 1000 fps using the Canon-Toshiba Surginix SXT 2000A Mobile C-Arm x-ray system. The C-Arm parameters were set to 70 kVp and 100 mA. A 3-second continuous-output exposure was used to provide velocity sampling at multiple phases of each pulsatile cycle, as the detector and source are presently not synchronized to the pumps.

Figure 2:

Flow Loop

For the iodinated contrast media injections, a 3-French microcatheter was placed proximal to each phantom model, and injection rates were chosen such that the injection would not interfere with any flow visualizations. The radiopaque microspheres were prepared by soaking embolic beads in iodinated contrast for a minimum of three days, and then manually injected in the same manner as the contrast media. The ROI’s within each model (as indicated in figure 1) were evaluated for both pulsatile and constant flow conditions.

2.2. HSA Flow Quantification Methods

Tracking of the microspheres was performed using TrackPy, an open source algorithm implemented in Python (Python Software Foundation, Wilmington, DE).⁴ TrackPy is based on the widely used Crocker-Grier algorithm, which can be summarized in 5 stages; pre-processing of images, locating candidate particle positions, refinement of these positions, discrimination of “false” particles, and then linking of the time-resolved particle locations into trajectories.⁵ As shown in figure 3, the algorithm looks for either bright or dark blob-like features, depending on the user input.

Figure 3:

Automatic Particle Centroid Localization.

A) Single 1-ms frame XPIV B) TrackPy centroid locations (red circles)

Peak intensities can be further refined via the use of size and intensity thresholds. Once the particle centroids are located in one frame, they are then tracked to the next frame, and so on. To filter out spurious trajectories due to the interference of noise, the user can specify a maximum displacement per frame. In the case where a particle is “lost” for several frames and then reappears, the unique ID associated with that particle may be stored for a user-specified number of frames. The location of each particle per frame is stored in a data table, along with the particle ID, intensity, etc. The change in centroid location frame-to-frame is then used to calculate the particle velocity, given the acquisition frame rate, magnification factor, and detector pixel size.

Initially, particles were manually tracked throughout the HSA sequence by calculating the position of each particle centroid within a user-defined 9x9 bounding box (9x9 pixels) around each particle. When using such high frame rates, the total number of photons per pixel decreases, leading to an increase in image noise and possible degradation in automatic centroid location accuracy. To test the accuracy of TrackPy under such conditions, synthetic particle images were simulated and compared against the manual centroid method.

To evaluate velocity changes using an OF approach, the open source algorithm OpenOpticalFlow was implemented in Matlab (Mathworks, Natick, MA) and utilized to derive 2D velocity fields from pairs of images in the HSA sequence.³ OF can broadly be described as the distribution of apparent velocities of brightness patterns between two images. This original OF assumption has been further developed for fluid flow measurements within the OpenOpticalFlow algorithm. Essentially, the injection of iodinated contrast material and subsequent mixing/ modulation of the contrast throughout the vessel provides the basis for the optical flow signal. The OF algorithm can be summarized as follows (figure 4): a full HSA sequence is converted to individual frames, which are then evaluated on a pair-by-pair basis. Pre-processing measures can be taken to enhance the intensity gradient in the image and reduce noise, thus improving the accuracy of the OF computation. Generally, a gaussian smoothing or median spatial filter is used to improve the contrast correlation between frames by reducing the effect of image noise. The user then defines a region of interest for OF computation, which is accomplished by applying a binary mask as shown in step 3 of the workflow resulting in zero velocity outside the vessel boundary. User-drawn line profiles can be placed across the vessels to evaluate the velocity profiles on a pixel-row basis. Example line profiles are shown (orange, blue green) in different locations within the phantom ROI. The first step in the OF estimation process includes a coarse-to-fine iteration scheme, where each image in the pair is downsampled and a coarse velocity estimation between the two images is made. This allows for improved accuracy in velocity estimation when large displacements are encountered in the image sequence. For example, a downsampling factor of 0.5 produces an image with half the original resolution. The resulting coarse-grained velocity field is then used to generate a synthetic shifted image with the original (full) spatial resolution. The velocity difference field between the synthetically shifted image and the second image in the pair is determined using the OF estimator, which is added on the initial velocity field for improvement. Refinements are then made with each iteration; generally 1–2 iterations are sufficient.³ The outputs of the algorithm are the x- and y-velocity components in the image plane at a resolution of one velocity vector per pixel per millisecond, represented in the last step of the workflow as a color-coded velocity distribution. The high velocities are indicated by the red vectors, middle white, and lowest blue.

Figure 4:

OF Algorithm Workflow

3. RESULTS

3.1. TrackPy Accuracy

To create simulated XPIV images, the contrast between the synthetic particles and background were modeled after actual HSA data within a custom Matlab script. To create an individual “particle”, an integer location within the image matrix was selected as the centroid location. The actual microsphere size used for HSA acquisitions were 700 – 900 μm, so synthetic particles were given a diameter of 9 pixels. To simulate varying levels of exposure, each 8-bit image was multiplied by a decimal value ranging from 0.9 – 0.3 to uniformly decrease the intensity of each pixel, or the mean number of “photons” per pixel, while still maintaining the same contrast between the particle and background. For each resulting floating-point image, every pixel was individually fed into a random number generator based on the Poisson distribution. A lower pixel value, corresponding to a lower number of “counts”, results in a greater level of Poisson noise. Figure 5 illustrates the resulting increase in image noise and decrease in mean counts per pixel. The maximum (5A) and minimum (5B) count images are shown. Both images have the same contrast, but are windowed and leveled to better illustrate the increase in noise.

Figure 5:

Simulated Particle Images (Windowed and Leveled for Display)

To ensure that a linear relationship existed between the simulated image mean and detector exposure, actual exposure data from the XCounter Actaeon was utilized (figure 6). The technique parameters were set at 70 kVp and the tube current was varied from 1– 400 mA. An RQA5 attenuator was placed in the beam, and the measured exposure to the detector ranged from 13 μR/frame to 520 μR/frame. Exposure was measured and plotted against the mean counts per image, as well as the image variance. The equation for the line of best fit was used to extrapolate the simulated image mean to exposure, as shown in figure 7. When the simulated image mean and variance were plotted against the derived exposure, both plots had correlation values >0.9999 indicating a linear relationship.

Figure 6:

Linearity of XCounter Actaeon PCD. Exposure was measured while varying the tube current from 1 – 400 mA.

Figure 7:

Simulated image mean and variance were plotted against the derived exposure, which was obtained using the equation of best fit from figure 6.

First, each image was fed into both the automatic and manual tracking algorithms, to determine the effect of image noise on centroid location accuracy. For the manual centroid calculation, the user places a rectangular ROI of fixed dimensions over each particle in the image (figure 8A), which creates a binary mask (figure 8B). Within each masked ROI the weighted centroid is calculated, as indicated by the blue ‘*’ in 8C, which is zoomed in on the particle. Figure 8(DEFG) illustrates the effect of noise on centroid location accuracy for both TrackPy and the manual method.

Figure 8:

TrackPy Centroid Location vs. Manual Centroid Location Accuracy for Varying Image Mean (Exposure). Note that several of the centroids are overlapping in 8F/G.

8D/E give two examples of how TrackPy performed when locating particles 1 and 4, and 8F/G shows the same particles located by the manual method. Note the coordinate scale for each set of images; although at first glance the particle locations appear to be vastly different, they tend to remain within the boundary of 1 pixel. The black ‘X’ represents the true particle location, and each colored ‘O’ represents the estimated particle location for varying levels of exposure in the synthetic image.

The subpixel accuracy of TrackPy is clearly susceptible to noise, as further illustrated in figure 9. The green ‘X’ on particle 4 illustrates the centroid coordinate estimated by TrackPy from the least noisy (A) and the noisiest image (B). Spatial filtering can be used to suppress noise and improve automatic subpixel estimation accuracy; 9C/D utilizes a gaussian filter (sigma = 3), 9E/F utilizes a median filter (sigma = 3). The red ‘*’ indicates the actual centroid location.

Figure 9:

TrackPy Centroid Estimation Error (Particle 4). 9C/D show the same centroid estimation after gaussian filtering (sigma = 3), and 9E/F after median filtering (sigma = 3).

3.2. X-Ray Particle Image Velocimetry Results

Using the cardiac pump to produce pulsatile flows, individual sub-millimeter iodinated microspheres were tracked on a frame-to-frame (1-ms) basis throughout both systole and diastole as captured by the detector. The cardiac pump settings for all XPIV runs were 30 mL/stroke, 50 rpm, and 40/60 systolic/diastolic output. Variations in velocity between models are due to the model geometry, and the portion of the cardiac cycle captured by the detector over the 3-s interval. The three videos below show XPIV in three different aneurysm models, including an idealized internal carotid artery saccular aneurysm (video 1), a wide-necked internal carotid artery saccular aneurysm (video 2), and a basilar apex aneurysm (video 3).

Example trajectories are shown in the idealized internal carotid artery saccular aneurysm model, corresponding to figure 1A/ video 1. From these displacement measurements, we can evaluate the 1-ms velocity changes of individual particles throughout the XPIV sequence to get a better idea of the spatial variations in velocity. Figure 10A shows the trajectory of a single particle entering the diastolic phase, moving around the aneurysm sac and then entering the outflow vessel. The frame-to-frame velocities show a decreasing trend in 10B. Conversely, 10C shows the trajectory of a single particle entering the systolic phase, moving from the aneurysm sac into the outflow vessel. The particle gradually gains speed as it moves out of the aneurysm sac in synchrony with the changing pump phase, shown in 10D.

Figure 10:

Individual particle trajectories shown in idealized internal carotid artery saccular aneurysm model. 10A/B correspond to a single particle track during the initial diastolic phase of the pump cycle, 10C/D correspond to a different particle entering the systolic phase of the pump cycle.

The colorbar to the right of 10A/C indicates the velocity of the particle. Both particle tracks are fairly smooth, with some minor breaks in the trajectory where TrackPy may have lost the particle and then began tracking it again. Each graph in figure 10 shows both the raw velocity estimation data per frame (data points), as well as a 5-frame moving trendline (solid curve). It was shown that image noise affects the performance of the algorithm, which may help to explain the variations in frame-to-frame velocity. Within 1 millisecond, most particles are moving at most a few pixels per frame. During the diastolic phase in particular, many particles move quite slowly within the aneurysm sac and undergo sub-pixel displacements.

Figure 11 illustrates the systolic (11A) and diastolic (11B) change of velocity in the wide-necked internal carotid artery saccular aneurysm, corresponding to Figure 1B/ video 2. Velocity measurements are averaged per frame, per ROI. Example plots are shown for the first part of the inflow vessel (11C), and the outflow vessel (11D). Some fluctuations in the frame-to-frame velocity data may be present due to spatial averaging over the entire ROI, as well as particle movement out of the plane of the detector which cannot be accounted for without 3D acquisition capability.

Figure 11:

All particle trajectories shown in the wide-necked internal carotid artery saccular aneurysm model. 11A/C correspond to the inflow vessel ROI, 11B/D correspond to the outflow vessel ROI.

Figure 12 illustrates all particle trajectories within a basilar apex aneurysm, corresponding to figure 1C/ video 3. Figure 12A represents the systolic portion of the cardiac cycle, and figure 12B the diastolic. The velocity changes are shown for the entire phantom (all regions shown in A/B), averaged per frame over the total 2.4-s sequence in 12C. Fewer vectors indicate that there were fewer particles in the phantom during that phase of the pump cycle.

Figure 12:

Systolic and diastolic particle trajectories, shown in the basilar apex aneurysm model. 12A shows all particle tracks recorded during one of the systolic phases of the pump cycle, and 12B shows all particle tracks recorded during one of the diastolic phases of the pump cycle. 12C illustrates the 1-ms changes in velocity throughout the whole model, over the entire sequence captured by the detector.

Figure 13A follows a single particle trajectory over 93 frames throughout the same basilar apex model, corresponding to video 4. The particle can be seen colliding with the aneurysm wall, as well as undergoing many velocity changes throughout its time in the aneurysm sac. The particle appears to be gaining speed when it passes by the inflow vessel, and gradually loses speed as it moves towards the center of the aneurysm sac. Average per-frame velocity changes are shown in 13B.

Figure 13:

Single particle trajectory, basilar apex aneurysm.

3.3. Optical Flow Results

Using both the cardiac pump and programmable pump, the displacement of iodinated contrast media was evaluated on a frame-by-frame (1-ms) basis. The HSA sequence illustrating flow throughout the systolic and diastolic portions of the cardiac cycle within the idealized internal carotid artery saccular aneurysm model (corresponding to figure 1A) are shown in video 2. The pump was set to a stroke volume of 20 mL/stroke, 50 rpm, and 40/60 systolic output (slightly lower than that used for XPIV sequences). Plots illustrating instantaneous 1-ms changes in velocity during peak systole are shown in figure 14. The inflow vessel (A – D) and aneurysm sac (E – H) are evaluated separately. Velocity distributions are normalized to the maximum velocity, corresponding to the colorbar to the right of each image. Within the inflow vessel, velocity distributions are shown as contrast moves through the vessel, each image is temporally separated by 25 milliseconds. We can see how the velocity tends to be higher nearest the first curvature, and then moves toward the vessel centerline as the contrast approaches the aneurysm sac. The same systolic interval within the aneurysm sac illustrates the development of vortex flow, with the flow velocity increasing from the center of the aneurysm out to the wall. Each frame is temporally separated by 50 milliseconds. Figure 15 illustrates the average and maximum velocity changes within the aneurysm sac ROI.

Figure 14:

Instantaneous velocity distributions in idealized internal carotid artery saccular aneurysm model in inflow vessel ROI 14(A – D), and aneurysm sac ROI 14(E – H).

Figure 15:

Average and maximum velocity data per 1-ms frame, idealized internal carotid artery saccular aneurysm model.

Figure 16 illustrates the velocity changes within the same saccular aneurysm using the programmable carotid waveform shown at the top corner of the plot. Velocity distributions are evaluated in the aneurysm sac on a 1-ms basis with OF. Peak pump flow rates reached 25 mL/s, with an average flow rate of 8 mL/s. A single period was approximately 830 milliseconds.

Figure 16:

Average velocity changes, carotid waveform, idealized internal carotid artery saccular aneurysm model.

The same saccular aneurysm model was then evaluated under constant flow conditions, for the inflow, outflow, and aneurysm sac ROI (figure 17A). The average flow rate was measured as 4.2 mL/s. Plots for the aneurysm inflow vessel, sac, and outflow vessel are shown in figure 17B. Given the smaller diameter of the inflow vessel versus the outflow vessel, we would expect the inflow vessel to have a slightly higher velocity. The aneurysm sac has the lowest velocity. Fluctuations in velocity data are due to the effect of quantum mottle in the optical flow calculation, which becomes a significant factor when dealing with sub-pixel movements of the iodine contrast.

Figure 17:

Average velocity changes, constant flow, idealized internal carotid artery saccular aneurysm model.

4. DISCUSSION

For XPIV, the comparison of the manual centroid calculation and automatic methods illustrated the magnitude of localization error depending on the quantum mottle present in the HSA sequence. Although each iodinated microsphere is only 900 μm in diameter, subpixel errors in centroid location can impact the overall velocity calculation when particle displacements are only a few pixels per frame. Window and leveling of the input images can be performed to enhance the signal from the particles, as well as spatial filtering to aid in the suppression of noise. Additional penalties associated with increasing quantum mottle include the occasional misidentification of background noise as a particle, or a particle may be lost for several frames and therefore it’s entire trajectory won’t be recorded. This manifests as breaks in the vector field, as shown in figure 10A. If two particles come too close, the program may make an error in tracking each particle’s movement, again affecting the overall particle trajectory recorded by TrackPy. Combined with preprocessing techniques, the previously mentioned size and maximum displacement thresholds can help to alleviate these errors.

While the method of velocity determination used in OF is substantially different from that of particle tracking, the OF method is susceptible to many of the same factors. Like the XPIV data, plots of average velocity measurements per frame per phantom ROI show fluctuations in velocity data, again due to the effect of quantum mottle in the OF calculation, which becomes a significant factor when dealing with sub-pixel movements of the iodine contrast. Larger intensity gradients will provide a stronger signal for the OF algorithm, which is dependent on the contrast injection. Binning of the 100-μm pixels may be another method to reduce the effect of quantum mottle on the OF output, although the effect of this change on the overall accuracy of the algorithm has not yet been evaluated.

For both methods, the averaging of velocities from vessel centerlines to the vessel wall, the entire aneurysm sac, etc. may also contribute to the variation in per frame velocity. It is clearly shown in figure 13 the velocities in the center of the aneurysm sac differ substantially from those at the outer wall, which is also dependent on the phase of the cardiac cycle. The general trend of systole to diastole can be appreciated, and binning of multiple systolic/ diastolic phases may help to reduce errors in the velocity measurement. Future use of biplane capability, should allow the out-of-plane velocity component to be accounted for.

5. CONCLUSIONS

Two different quantitative methods were utilized to extract high-temporal resolution velocity changes throughout HSA image sequences, based on movements of discrete radiopaque microspheres and iodinated contrast injections. The chosen pump settings encompassed a wide range of flow situations, which all produced unique velocity measurements over the flow duration as captured by the detector. Variations in velocity are illustrated due to both the cyclic action of the pump and phantom morphology. Additional fluctuations in the calculated velocity can be attributed to the influence of quantum mottle, spatial averaging of velocities over the entire phantom ROI, and out-of-plane velocities that are currently undetectable with single plane methods. The methods discussed here can be applied to HSA to derive a wide range of velocity distributions, which may then be used to further quantify important hemodynamic parameters in a clinical setting as guidance during the course of an actual clinical intervention.

Supplementary Material

Shield2-video

Video 2: XPIV in Wide-Necked Internal Carotid Artery Saccular Aneurysm (Fig. 1B)

Video1

Video 1: XPIV in Idealized Internal Carotid Artery Saccular Aneurysm (Fig. 1A)

Video2

Video 2: Cardiac pump contrast injection, idealized internal carotid artery saccular aneurysm model.

Video3

Video 3: XPIV in Basilar Apex Aneurysm (Fig. 1C)

Video4

Video 4: HSA sequence corresponding to figure 12.