Simulated pathline visualization of computed periodic blood #ow patterns

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1 Journal of Biomechanics 33 (2000) 623}628 Technical note Simulated pathline visualization of computed periodic blood #ow patterns David A. Steinman * Imaging Research Labs, John P. Robarts Research Institute, P.O. Box 5015, 100 Perth Drive, London, Ont, Canada N6A 5K8 Department of Medical Biophysics, University of Western Ontario, London, Ont, Canada N6A 5C1 Accepted 8 October 1999 Abstract Improvements in computer hardware and software have made it possible to model pulsatile blood #ow in realistic arterial geometries. Such studies produce enormous amounts of velocity data, which are often di$cult to interpret and communicate using traditional contour and/or vector "eld plots. Inspired by in vitro #ow visualization techniques such as particle image velocimetry (PIV), we describe a simple and e!ective method for visualizing periodic three-dimensional velocity data, based on the subdivision and sequential display of computed particle trajectories. Analogous to a PIV experiment, the length and spacing of such simulated particle pathlines are controlled by user-speci"ed shutter-speed and frame rate variables. Strategies for color-coding pathlines to highlight important hemodynamic features such as recirculation zones and branch #ow division are presented Elsevier Science Ltd. All rights reserved. Keywords: Flow visualization; Particle tracking; Hemodynamics; Computer modeling 1. Introduction In the last few years, advances in computer hardware and modeling software have made it possible to routinely carry out computational #uid dynamic (CFD) studies of pulsatile hemodynamics in realistic, three-dimensional models derived from imaged or cast arteries (Chandran et al., 1996; Milner et al., 1998; Perktold et al., 1998; Moore et al., 1999). Unlike traditional idealized models * where contour or vector plots are typically displayed on planes of symmetry * realistic models rarely provide such convenient planes for display. The unsteady nature of these #ow "elds can make it di$cult to comprehend the dynamic relationships between primary and secondary #ow or to identify the locations of increased blood residence time * important factors in the study of hemodynamics and vascular disease * using conventional streamline or vector "eld plots alone. Experimental #ow studies based on the introduction of tracer particles into the #ow "eld can provide readily * Tel.: # x34113; fax: # address: steinman@irus.rri.on.ca (D.A. Steinman) comprehensible visualizations of complex #ow patterns. For example, in particle image velocimetry (PIV) studies, re#ective particles are seeded into a #ow "eld and illuminated as they are passively advected through a sheet (or sheets) of laser light. Analog or digital cameras acquire sequential images of the #ow "eld at a speci"ed frame rate and shutter speed. The shutter speed determines the length of individual pathlines, such that long exposures produce longer pathlines. The frame rate controls, for each particle, the spacing between pathlines in successive frames. (This information is then often used to estimate the local velocity "eld.) Experimental #ow visualization studies are, however, di$cult to carry out for pulsatile #ows in realistic arterial geometries. In this paper, we present a simulated pathline animation technique for visualizing CFD-computed pulsatile 3-D blood #ow patterns. This technique relies on extracting and animating pathlines from computed particle trajectories based on intuitive user-speci"ed frame rate and shutter speed criteria. Using a model of a normal human carotid bifurcation, we demonstrate how color-coding of the pathlines can also be used to enhance important hemodynamic features such as #ow recirculation and branch #ow division /00/$- see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S ( 9 9 )

2 624 D.A. Steinman / Journal of Biomechanics 33 (2000) 623} Methods 2.1. Particle tracking Given a continuous representation of a time-varying vector velocity "eld u(x, t), the trajectory of a mass-less, neutrally buoyant and non-di!using particle can be computed by integrating the time-varying velocity "eld according to the following equation: dx dt "u(x, t), x(t )"x, (1) where x de"nes the initial coordinates of a particle `seededa at time t. Any number of numerical techniques may be used to integrate this equation; for our studies we use a fourth-order Runge}Kutta integration with adaptive time-stepping, and an e$cient algorithm for identifying the location of the particle in the "nite element mesh (Kunov et al., 1996) Pathline extraction In general, for the ith frame, F, the pathline of the jth particle represents the portion of the particle trajectory between x (t ) and x (t # t ), where t is the shutterspeed and t is de"ned as t " i!1, (2) f where f is the acquisition frame rate, and we have arbitrarily assigned t"0 as the start time of the "rst frame (F ). For periodic pulsatile #ow, it is su$cient to consider frames for a single cardiac cycle, and repeat them in a loop. However, because particles may reside within the model for more than one cardiac cycle, it is necessary to display multiple pathlines of the same particle in a given frame in order to preserve the appearance of continuity in the animation loop, i.e.: t ¹ "n#i!1 NF, n"0, 1, 2, 2, (3) where NF is the integer number of frames per cardiac cycle (i.e. NF "f * ¹). For convenience, we also de"ne a dimensionless shutter speed, SS, normalized to the period of the cardiac cycle (i.e. SS" t /¹). These steps are illustrated in Fig Particle seeding Fig. 1. Identi"cation of discrete pathlines from two continuous particle trajectories, using NF"4 and SS". Changes in grayscale along the trajectories distinguish the pathlines associated with even and odd frames, and the inset #ow waveform identi"es the respective time intervals corresponding to each frame. Since the particle exiting the ICA branch remains in the model for more than one cardiac cycle, two separate pathlines (corresponding to the pathlines of the "rst and second cycle) would be displayed in Frame 1. Note that the apparent discontinuity of the ICA pathline in frame 2 is actually a #ow-reversal hidden by the adjacent frame 3 pathline. Note also the orientation axis in the top-right corner. (ICA"internal carotid artery; ECA"external carotid artery; CCA"common carotid artery.) To simulate the uniform concentration of tracer particles in the #uid, it would be necessary to seed particles according to a scheme that accounts for both the spatial and temporal variations in the number of particles entering the model throughout the cardiac cycle. Although there are ways to mimic this computationally (Kunov et al., 1996), for the purposes of #ow visualization we have found it su$cient to seed NP particles at NF times equally spaced throughout the cardiac cycle. The NP particles are distributed randomly across the model inlet, and this random distribution is updated for each seeding time, t /¹, corresponding to the start time of each frame. This results in a total of NP*NF particle trajectories, each of which is computed independently until it has left the model domain (or the desired "eld-of-view). The coordinates, velocities, and time along the trajectory are written to disk for subsequent extraction of pathlines Animation An individual frame, F, is constructed by displaying, for each particle, only those entries in the disk "le whose times fall between t /¹ and t /¹#SS. The pathline coordinates provide the spatial locations for screen display,

3 D.A. Steinman / Journal of Biomechanics 33 (2000) 623} while the corresponding velocities may be used to colorcode the pathlines in a variety of ways (see Results and Discussion). Tecplot software (Amtec Engineering, Inc.; Bellevue, WA) is used to display and color-code the pathlines, and each frame is saved as a bitmap image. The resulting series of bitmap images is then converted into a MPEG animation using software supplied with the Indigo/2 workstation (Silicon Graphics Inc.; Mountain View, CA) on which all calculations were carried out. Further details of the animation procedure are omitted, as they are highly speci"c to the display software and hardware used. We note, however, that these animation techniques can be implemented with any graphical display software that can plot (and, ideally, color-code) three-dimensional line segments. 3. Results In this section we present frames from visualizations of physiologically pulsatile #ow computed in a model of a normal human carotid bifurcation reconstructed from magnetic resonance imaging (Milner et al., 1998). The complete visualizations over the cardiac cycle (which can be found on the Webpage of the Journal of Biomechanics: 2/1/) were constructed from the time-varying computed velocity "eld using the steps outlined in the Methods. The frame rate used was NF"60, to adequately resolve the rapid temporal accelerations near peak systole. The number of particles used was NP"40, which was found to provide a su$cient number of pathlines to discern * but not obscure *#ow structures of interest. The images presented in Figs. 2}4 represent individual frames from the complete visualizations. Fig. 2 illustrates the e!ect of shutter speed on the display of peak systolic and late diastolic #ow patterns. At peak systole, pathlines in the branches largely overlap when using the slower shutter speed, making it di$cult to discern the relative magnitudes of the branch velocities (Fig. 2a). The faster shutter speed, however, clearly shows the presence of higher velocities in the ECA compared to the ICA (Fig. 2b). Conversely, pathlines imaged using SS" more clearly show the complex recirculating #ow patterns proximal to the bifurcation than do those from the SS" pathlines. This is particularly evident in late diastole, where the secondary #ow patterns (i.e. horizontal pathlines) are much more clearly visualized with SS" (Fig. 2c) than with SS" (Fig. 2d). Although information about #uid velocity and direction is contained in the length and orientation of the pathlines, the projected nature of the pathline animations can, as Fig. 2 demonstrates, makes it di$cult to distinguish individual pathlines without the aid of stereoscopic displays. This can be alleviated in part through the use of color-coding to further distinguish velocity magnitudes and identify overlapping pathlines. Fig. 2. The e!ect of normalized shutter speed (SS) on the display of pathlines from frames at peak systole and late diastole. (a) Peak systole, SS". (b) Peak systole, SS". (c) Late diastole, SS". (d) Late diastole, SS". In all cases NF"60, NP"40.

4 626 D.A. Steinman / Journal of Biomechanics 33 (2000) 623}628 Fig. 3. Regions of blood recirculation are highlighted by applying a pseudo-doppler ultrasound color map (Vera et al., 1992) to the axial (Z) velocity component to distinguish forward from reverse #ow. Shown are frames 6,8,10, and 12 from an animation with NF"60, SS", and NP"40. Note the contour legends in each frame, indicating velocities in cm/s. Fig. 4. The complex mixing of #ow to the ICA and ECA branches is highlighted by applying a red/blue color map based on branch exit criteria and velocity magnitude. Apart from color map, frames are identical to those in Fig. 3.

5 D.A. Steinman / Journal of Biomechanics 33 (2000) 623} In Fig. 3, for example, pathlines are color-coded according to the axial (Z) velocity component using a pseudo-doppler color map (Vera et al., 1992) to highlight axial velocity magnitude and direction. From this sequence of frames it is much easier to identify the presence of the dynamic recirculation zones at both hips of the bifurcation. The horizontal blue pathlines superimposed on the vertical yellow and red pathlines during #ow deceleration indicate that these recirculation zones e!ectively communicate via the secondary #ows around the periphery of the lumen. In the ICA, pathlines at peak systole (Fig. 3a) mostly follow the curve of the lumen, indicating uniform #ow. As the #ow decelerates (Fig. 3b}d), however, the progression of helical #ow down the ICA branch is clearly evident. Adi!erent view of the same #ow "eld is provided in Fig. 4, in which a red/blue color-map has been used to distinguish blood exiting the ICA and ECA branches. Inspection of the #ow "eld in the CCA proximal to the bifurcation reveals that blood entering the ECA arises largely from a high-speed core o!set from the CCA centerline. In contrast, #ow in the ICA branch is fed largely by the slower, secondary #ows around the periphery of the CCA. Also evident is the somewhat surprising presence of retrograde #ow mixing in the ECA, as evidenced by the presence of ICA #ow (i.e. red pathlines) in the ECA downstream of the bifurcation apex during #ow deceleration (Fig. 4b}d). 4. Discussion and conclusions In the absence of a corresponding experimental #ow visualization, it is admittedly di$cult to prove the `trutha of the #ow features portrayed in such animations of a complex #ow "eld. However, simulated pathline visualization of pulsatile #ow in an idealized stenosed carotid bifurcation model was able to accurately reproduce key #ow structures observed in a corresponding DPIV visualization (Steinman et al., 2000). Furthermore, the unanticipated presence of retrograde #ow mixing observed in Fig. 3 has been hypothesized as a cause of toxic neurological reactions to local anaesthetic agents injected into the external carotid artery branches (Aldrete et al., 1977). We therefore conclude that, within the stated assumptions, our simulated pathline visualization technique provides a faithful representation of the computed #ow "eld. Our experience has been that this dynamic, Lagrangian visualization technique has made it easier for us to comprehend computed pulsatile blood #ow patterns, but perhaps more importantly to communicate their intricacies to lay audiences and clinical collaborators. Because they represent the `historya of a given particle, pathlines may also be color-coded according to such variables as time-since-release or accumulated shear exposure, thus allowing the observer to more easily visualize the dynamics of hemolysis or platelet activation. Ultimately, when coupled with parallel computing architectures and highperformance graphic displays, it should be also possible to compute and display pathlines on-the-#y (Kenwright and Lane, 1996), to allow more interactive control over the user-speci"ed variables, model orientation, colormapping, etc. Finally, Lagrangian visualization techniques such as the one described here are not in principle limited to operating on computed velocity data. Medical imaging technologies such as 3-D Doppler ultrasound and magnetic resonance (MR) imaging can also provide measurements of the entire velocity "eld, albeit typically at lower resolutions than CFD studies. Some attempts have been made to track streamlines (Napel et al., 1992; Buonocore, 1998) and pathlines (Wigstrom et al., 1999) from MR phase contrast velocity measurements, and we are investigating the use of these simulated pathline techniques to animate such non-invasively imaged pulsatile #ow "elds. Acknowledgements This work was supported by the Medical Research Council of Canada (Group Grant GR-14973), and the author is supported by a Research Scholarship from the Heart & Stroke Foundation of Canada. The author also thanks Je!ery Kay, Jaques Milner, and Mauro Tambasco for helping to implement and optimize the various steps of the #ow visualization process. References Aldrete, J.A., Narang, R., Sada, T., Tan, L.S., Miller, G.P., Reverse carotid blood #ow * a possible explanation for some reactions to local anesthetics. Journal of the American Dental Association 94, 1142}1145. Buonocore, M.H., Visualizing blood #ow patterns using streamlines, arrows, and particle paths. Magnetic Resonance Medicine 40, 210}226. Chandran, K.B., Vonesh, M.J., Roy, A., Green"eld, S., Kane, B., Greene, R., McPherson, D.D., Computation of vascular #ow dynamics from intravascular ultrasound images. Medicine and Engineering Physics 18, 295}304. Kenwright, D.N., Lane, D.A., Interactive time-dependent particle tracing using tetrahedral decomposition. IEEE Transaction Visualization and Computer Graphics 2, 120}129. Kunov, M.J., Steinman, D.A., Ethier, C.R., Particle volumetric residence time calculations in arterial geometries. Journal of the Biomechanical Engineering 118, 158}164. Milner, J.S., Moore, J.A., Ethier, C.R., Rutt, B.K., Steinman, D.A., Computed hemodynamics of normal human carotid artery bifurcations derived from magnetic resonance imaging. Journal of the Vascular Surgery 28, 143}156. Moore, J.A., Steinman, D.A., Prakash S., Johnston, K.W., Ethier, C.R., A numerical study of blood #ow patterns in anatomically realistic and simpli"ed end-to-side anastomoses. 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6 628 D.A. Steinman / Journal of Biomechanics 33 (2000) 623}628 Napel, S., Lee, D.H., Frayne, R., Rutt, B.K., Visualizing threedimensional #ow with simulated streamlines and three-dimensional phase-contrast MR imaging. Journal of Magnetic Resonance Imaging 2, 143}153. Perktold, K., Hofer, M., Rappitsch, G., Loew, M., Kuban, B.D., Friedman, M.H., Validated computation of physiologic #ow in a realistic coronary artery branch. Journal of Biomechanics 31, 217}228. Steinman, D.A., Poepping, T.L., Tambasco, M., Rankin, R.N., Holdsworth, D.W., Flow patterns at the stenosed carotid bifurcation: e!ect of concentric vs. eccentric stenosis. Annales of Biomedical Engineering, Submitted for publication. Vera, N., Steinman, D.A., Ethier, C.R., Johnston, K.W., Cobbold, R.S., Visualization of complex #ow "elds, with application to the interpretation of colour #ow Doppler images. Ultrasound in Medical Biology 18, 1}9. WigstroK m, L., Ebbers, T., Fyrenius, A., Karlsson, M., Engvall, J., Wranne, B., Bolger, A.F., Particle trace visualization of intracardiac #ow using time-resolved 3D phase contrast MRI. Magnetic Resonance Medicine 41, 793}799.