- Email: [email protected]
Computational Fluid Dynamics Modeling of Intracranial Aneurysms:
Computational Fluid Dynamics Modeling of Intracranial Aneurysms: Qualitative Comparison with Cerebral Angiography1 Juan R. Cebral, PhD, Richard S. Pergolizzi, Jr., MD, Christopher M. Putman, MD
Rationale and Objective. The purpose of this study is to determine whether computational fluid dynamics modeling can correctly predict the location of the major intra-aneurysmal flow structures that can be identified by conventional angiography. Materials and Methods. Patient-specific models of three cerebral aneurysms were constructed from three-dimensional rotational angiography images and computational fluid dynamic simulations performed. Using these velocity fields, contrast transport was simulated and visualizations constructed to provide a “virtual” angiogram. These models were then compared to images from high frame rate conventional angiography to compare flow structures. Results. Computational fluid dynamics simulations showed three distinct flow types ranging from simple to complex. Virtual angiographic images showed good agreement with images from conventional angiography for all three aneurysms with analogous size and orientation of the inflow jet, regions of impaction, and flow type. Large intra-aneurysmal vortices and regions of outflow also corresponded between the images. Conclusions. Patient-specific image-based computational models of cerebral aneurysms can realistically reproduce the major intra-aneurysmal flow structures observed with conventional angiography. The agreement between computational models and angiographic structures is less for slower zones of recirculation later in the cardiac cycle. Key Words. Cerebral aneurysms; rotational angiography; computational fluid dynamics; cerebral angiography. ©
AUR, 2007
Cerebral aneurysms are widely believed to form and grow on the basis of hemodynamic interactions with the wall biology. Researchers have used a variety of tools to study these complex biological phenomena including animal, in vitro models, and computational models (1– 8). The goal of these experiments has been to approximate the in vivo
Acad Radiol 2007; 14:804 – 813 1
From the School of Computational Sciences, George Mason University, Fairfax, VA 22030 (J.R.C.); Interventional Neuroradiology, Inova Fairfax Hospital, 3300 Gallows Road, Fairfax Radiological Consultants, Falls Church, VA 22042 (R.S.P. Jr., C.M.P.); and the Department of Neurosurgery, George Washington University School of Medicine (C.M.P., R.S.P. Jr.). Received Oct 16, 2006; accepted Mar 9, 2007. The authors thank Philips Medical Systems for financial support. Address correspondence to: C.M.P. e-mail: [email protected]
© AUR, 2007 doi:10.1016/j.acra.2007.03.008
804
environment so that theories can be developed and further tested in more realistic systems. Ultimately, a link between the research and the clinical outcomes (i.e., aneurysmal growth and rupture) is necessary to reach an understanding of the relative importance of the forces or mechanisms that are discovered. Previously used methods fall short of this goal because they cannot reproduce the in vivo state of a particular patient. Until recently, computational studies have been only performed on idealized aneurysm geometries or approximations of a specific patient geometry. As computational techniques have improved, more refined models have been constructed, leading to a transition from idealized geometries to “realistic” models based on typical patient anatomies. Most recently, studies have tried to replicate the exact anatomy of specific patients to connect specific hemodynamic factors to
MODELING OF INTRACRANIAL ANEURYSMS
Academic Radiology, Vol 14, No 7, July 2007
clinical events, allowing statistical analysis in a patient population (9, 10). Despite these more sophisticated methods, one question still remains: Are these models accurately reproducing what is occurring in a specific patient? Without accurate in vivo measurements for comparison, a complete validation of computational methods is not possible. But, there is growing evidence that computational methods are reliably reproducing the in vivo intravascular environment. Comparisons with a variety of simplified experimental biological systems have shown good correlation with computational models (11–16). In addition to this direct validation, sensitivity analysis has been performed to obtain an understanding of the influence of a variable within a physiologic range are on the results of a specific model (17, 18). These analyses have been done to test a variety of assumptions used in modeling including flow rates, flow asymmetries, inflow boundary conditions, Newtonian properties of fluids, reconstruction/grid generation techniques, and small branch segmentation (17, 19). Even without knowing the exact value of the input variable, this analysis can measure the influence of changes (or errors) in the variable would have on the results of a simulation. Previous work has shown that inaccuracies in geometry have the largest potential for adversely influencing intra-aneurysmal hemodynamics (17). Other variables appear to have only minor effects on the models and are considered higher order variables. Although there currently are no proved methods for doing noninvasive in vivo measurements of flow, pressure, or wall shear stress in cerebral aneurysms, there are some techniques that can give some qualitative flow information. Conventional cerebral angiography has long been used for defining the anatomy and flow patterns of the intracranial vessels. Using high frame rates and/or judicious use of masking techniques, intra-arterial DSA can image inflow jets and some zones of recirculation in many aneurysms (20, 21). MR angiography can provide similar information with appropriate postprocessing of the time of flight data acquisitions (8). These methods are not sufficient to give accurate quantitative measures of intraaneurysmal hemodynamics but do give a direct representation of the intra-aneurysmal flow structure and therefore make possible a qualitative comparison. For this study, we use images from conventional angiograms in selected aneurysms to determine the major intra-aneurysmal flow structures and conventional 3D rotational angiography to define the patient-specific 3D geometries. Our purpose is to determine whether our computational fluid dynamic (CFD) method can correctly predict and explain the ob-
Table 1 Cases selected for study Patient
Location
Size (mm)
Rupture
Flow type
1 2 3
LICA LICA RMCA
25 11 5
Yes No Yes
IV III I
served flow structures as a means of providing evidence to support the validity of the CFD method.
METHODS Patients and Images Three patients with cerebral aneurysms were selected from our database in order to study whether CFD could predict the major intra-aneurysmal flow structures found on conventional angiography. The aneurysms that were selected had different flow types and had high frame rate conventional angiography images with definable major flow structures. These angiographic images were obtained using a short injection (10 ml/sec for total volume of 3 ml) and biplane angiography at 7.5 frames/sec using DSA. Characteristics of these aneurysms are summarized in Table 1. Patient-specific geometries were obtained by rotational acquisition during conventional cerebral angiography using a Philips Integris system. (Philips Medical Systems, Best, The Netherlands). The images used for the 3D reconstruction were obtained during a 180-degree rotation and imaging at 15 frames/sec for a total of 8 seconds. The corresponding 120 projection images were reconstructed into a 3D dataset of 256 ⫻ 256 ⫻ 256 voxels covering a field of view of 54.02 mm on a dedicated Phillips workstation. The voxel data was exported into a PC for mathematical vascular modeling using a recently developed methodology (17, 22, 23). Vascular Models Vascular models were constructed from the 3D rotational angiography (3DRA) images using geometric deformable models (24). High-quality volumetric finite element grids composed of tetrahedral elements were then generated using an advancing front technique to fill the space inside these geometrical models (25–27). The mesh minimum resolution was approximately 0.16 mm. The meshes contained roughly 2.2 million (M), 2.5 M, and 2.2 M elements for patients 1 through 3, respectively. In all these
805
CEBRAL ET AL
Figure 1. Patient 1. Top row, Volume rendering of 3DRA image from three orthogonal views. Second row from top, Geometrical model from same views. Third row from top, Streamlines at three time points during the cardiac cycle. Bottom row, Wall shear stress magnitude at same instants of time.
models, the entire proximal portions of the parent arteries visible in the 3DRA images were reconstructed. The 3DRA images and the vascular models for each patient are shown in Figures 1 through 3, respectively. Note that patient 2 had a clip from a previous surgery proximal to the aneurysm neck. This clip was manually removed from the anatomical model by interactive editing of the surface triangulation. Blood Flow Models Blood flow was modeled as an incompressible Newtonian fluid described by the unsteady Navier-Stokes equations in 3D (28). The blood density was ⫽ 1.0 g/cm3, and the viscosity was ⫽ 0.04 Poise. Vessel walls were assumed rigid, and no slip boundary conditions were applied at the walls. Assuming that all the distal vascular beds have similar total resistance to flow, traction-free boundary conditions with the same pressure level were applied to all the model outlets. At the inflows, pulsatile velocity profiles were prescribed using the Womersley
806
Academic Radiology, Vol 14, No 7, July 2007
Figure 2. Patient 2. Top row, Volume rendering of 3DRA image from three orthogonal views. Second row from top, Geometrical model from same views. Third row from top, Streamlines at three time points during the cardiac cycle. Bottom row, Wall shear stress magnitude at same instants of time.
solution for the fully developed pulsatile flow in a rigid straight pipe (29). These velocity profiles were computed from the Fourier decomposition of the prescribed flow rate curves (30). Flow measurements were not available for these patients; therefore, the flow conditions were derived from phase-contrast magnetic resonance measurements performed on normal subjects in the same arteries (31). Numerical solutions of the Navier-Stokes equations were obtained using a fully implicit finite element formulation that allows arbitrary timestep sizes (17). Two cardiac cycles were computed using 100 timesteps per cycle, and all the results presented correspond to the second cardiac cycle.
Contrast Transport Models Virtual or synthetic angiograms were produced for each patient. For this purpose, the entire flow field computed by the finite element solver was stored at each time
Academic Radiology, Vol 14, No 7, July 2007
MODELING OF INTRACRANIAL ANEURYSMS
ing streamlines were produced for each patient. The origins of the streamlines were interactively placed in the neck of the original models of each patient. The streamlines were then computed from these origins in both directions (upstream and downstream). The virtual angiogram was visualized on a 3D workstation and projections chosen that approximated the projection from the corresponding conventional angiograms. Frame-by-frame inspection of both image sets was done and images selected for corresponding moments in the passage of contrast through the aneurysms. In addition, both image sets were reviewed as cine loops in order to assess the dynamic movements of the contrast. Assessments were made for the size and orientation of the inflow jet, size and location of the impaction zone, location any major intra-aneurysmal vortices, location of the outflow stream, and the flow type (9) for each aneurysm.
RESULTS
Figure 3. Patient 3. Top row, Volume rendering of 3DRA image from three orthogonal views. Second row from top, Geometrical model from same views. Third row from top, Streamlines at three time points during the cardiac cycle. Bottom row, Wall shear stress magnitude at same instants of time.
step of the second cardiac cycle. Using this time-dependent velocity field a simulation of the transport of a virtual dye was performed by solving the transport (convection-diffusion) equation using a stabilized finite element method (32). At the inlet of the models, a time-dependent concentration was prescribed mimicking the contrast injection used in the actual angiograms. At the model outlets and walls, natural (Neumann) boundary conditions were prescribed. The solution of the transport equation is a time-dependent scalar field representing the time-variation of the concentration of the simulated contrast agent at each grid point. This concentration field was used to produce visualizations of the flow structures analogous to the actual angiograms. To this end, volume renderings of the concentration field were performed by plotting all grid points in a gray scale and with transparencies modulated by the local concentration. Postprocessing and Visualization Animations or cine loops of the wall shear stress (WSS) magnitude and intra-aneurysmal flow patterns us-
Patient 1 Results of the CFD simulations are presented in Figure 1. A single inflow jet is seen that affects the dome of the aneurysm in line with the efferent parent artery and divides into two major vortices with several small vortical structures consistent with a type IV flow pattern. A region of elevated WSS is seen corresponding to the zone of impaction. Outflow is along the distal wall for the superior vortex and along the inferior wall for the inferior vortex. Virtual and conventional angiography images are shown in Figure 4 (lateral view) and Figure 5 (anteroposterior view). Images are displayed to show corresponding phases in the passage of the contrast. Both the virtual and conventional angiograms show a large single inflow in the same orientation and zone of impaction. The virtual angiogram images appear to represent an inflow jet and impaction zone slightly more diffuse compared with the conventional angiogram. Two major vortical structures are identified in both sets of images with corresponding zones of outflow. Some differences in the smaller secondary vortices are seen in the later phases with the virtual angiogram predicting more complex pattern than is discernable on the conventional angiogram, but these are largely obscured as the aneurysm fills with contrast. Both virtual and conventional angiograms show flow structures that would place this aneurysm in flow type IV. Overall, there is an excellent agreement between the two represen-
807
CEBRAL ET AL
Academic Radiology, Vol 14, No 7, July 2007
Figure 4. Comparison of dynamic DSA images (left column and third column from the left) and virtual angiograms obtained from CFD simulations (second and fourth columns from the left) for patient 1, side view projection. The DSA corresponds to the filling phase obtained with a long injection of contrast.
tations, and several of the detail features observed in the conventional angiogram can also be clearly observed in the virtual angiogram. Figure 5 shows two frames corresponding to the aneurysm filling phase in the anteriorposterior view for both the conventional and virtual angiograms. Although there are more overlapping vessels, this figure shows that the location of the inflow jet and overall characteristics of the major vortex structures of the intra-aneurysmal flow pattern are also in good agreement in this second projection view. Patient 2 The results of the CFD analysis are shown in Figure 2. A single inflow jet is seen entering from the downstream portion of a well-defined neck. The jet impacts directly into the dome and splits into two well-defined vortices. A small secondary vortex is formed in the medial portion of the dome during the cardiac cycle, making this a flow type III aneurysm. Outflow is through the upstream por-
808
tion of the neck from both major vortices. A region of elevated WSS corresponds with the impaction zone on the aneurysm dome. Virtual and conventional angiography images are shown side by side for both the lateral and a right anterior oblique projection (RAO) in Figure 6. The RAO view shows the well defined inflow jet with good agreement between the two series. The inflow jet from the virtual angiogram is somewhat larger than the conventional angiographic view and with a slightly larger impaction zone. However, the location of the region of impaction is the same. The two major vortical structures are well seen on both sequences with only minor differences. Both sequences show the filling of the small medial lobulation later in the angiogram, consistent with predictions by the CFD representations. This confirms the type III flow type. The differences in the two sequences are more apparent on the lateral projection. Once again, the flow jets have similar orientation and location with only a small differ-
Academic Radiology, Vol 14, No 7, July 2007
MODELING OF INTRACRANIAL ANEURYSMS
and a type I flow pattern. Location and impaction of the inflow jet show excellent agreement. There are some minor differences in the shape and pattern of the single vortex. However, both sequences show the delayed filling of the medial and superior branch, which is receiving flow as a continuation from the outflow zone of the aneurysm. This effect is best seen in the anteroposterior projection.
DISCUSSION
Figure 5. Comparison of dynamic DSA images (left column) and virtual angiograms obtained from CFD simulations (right column) for patient 1, anteroposterior projection. The DSA corresponds to the filling phase obtained with a long injection of contrast.
ence in thickness. Both show a clockwise rotation of the internal vortices, but in the later phases, the conventional angiogram show significant “pooling” of the contrast in the dependent portion of the aneurysm. The virtual angiogram predicts this in a much smaller amount with the pooling occurring preferentially in the inferoposterior portion of the aneurysm. As with patient 1, the differences between the two sequences become more prominent in the later phases, i.e., during aneurysm washout. Patient 3 The result of the CFD analysis is shown in Figure 3. The simulation predicts a simple single vortical flow structure consistent with flow type I. The single inflow jet enters the neck inferiorly and nearly tangentially strikes the neck and continues to impact the body. The single vortex rotates in a counterclockwise fashion with the major portion of the outflow going to the superior and medial branch. A focal region of elevated WSS is seen in the inferior neck extending into a portion of the body, consistent with the impaction of the inflow jet. Virtual and conventional angiography images are provided for both anteroposterior and lateral projections in Figure 7. Both confirm the single inflow jet and the single counterclockwise vortex consistent with the CFD result
CFD is an attractive tool for the study of cerebral aneurysms and other cerebrovascular diseases and has been used in numerous studies. However, the CFD methodology has not been completely validated in aneurysmal systems, largely because of a lack of available data for comparison. Strict validation of this method would require point-by-point comparison with a number of “gold standards” to understand the variability and accuracy of the method. For intra-aneurysmal hemodynamics, this is simply not possible because no proved in vivo method for measuring intra-aneurysmal hemodynamic quantities is available. Also, because the mechanisms responsible for the pathogenesis of cerebral aneurysm are not well understood, we do not know which variables are important and what level of accuracy is needed for clinical purposes. Cerebral aneurysms are widely believed to form and grow on the basis of hemodynamic interactions with the wall biology (1– 8). On the basis of in vitro, animal, and computational studies, oscillatory stress, wall shear stress, and pressure have been suggested as potentially responsible for the wall injury that leads to rupture. Most recently, a population-based study using CFD found a correlation between impingement region (the region of collision between the inflow jet and the aneurysmal wall) and the clinical history of rupture with an additional trend of more complex intra-aneurysmal flow patterns with rupture (9). These studies point to the major flow structures as likely major determinants of clinical outcome (i.e., rupture). Therefore, determining whether the CFD method can correctly predict these major flow structures becomes an important question when evaluating the usefulness of those conclusions. Cerebral angiography remains the gold standard for the evaluation of cerebral aneurysms. Both conventional 2D imaging and now 3DRA are widely used in medical practice for understanding the geometry of aneurysms for both conventional and endovascular surgeons. With the use of high frame rate angiography and the judicious use of
809
CEBRAL ET AL
Academic Radiology, Vol 14, No 7, July 2007
Figure 6. Comparison of two different DSA image sequences (left column and third column from the left) obtained with different injections with corresponding numerical simulations (second and fourth columns from the left), for patient 2.
masking techniques, Lanzieri et al. (21) have shown that cerebral angiography can better define the neck of an aneurysm by clearer visualization of the inflow stream. We take advantage of this by using high frame rate angiography to register the phases of filling of three aneurysms to use in comparison with our CFD models. Qualitative comparisons of flow visualizations produced from these conventional angiograms and CFDbased virtual angiograms show excellent agreement of the major intra-aneurysmal flow structures for three patients with cerebral aneurysms. In particular, these visualizations show that the CFD simulations correctly predict the location and size of the inflow jet, flow impaction zone, the major vortex structures, and the outflow regions. The
810
CFD simulations are in best agreement with the images from conventional angiography in the early filling phase of the aneurysm. In the later phases, the CFD simulations show greater complexity than the conventional angiography accounting for the divergence. The fine details of the conventional and virtual angiograms also exhibit some differences. For instance, the computational models tend to produce inflow jets and impaction zones slightly more diffuse than those observed in the conventional angiograms. The differences in the flow structures are more pronounced during the washout phases. In particular, one of the aneurysms (patient 2) presented a significant “pooling” effect at the end of the washout phase, which was not entirely reproduced by the corresponding computational model.
Academic Radiology, Vol 14, No 7, July 2007
MODELING OF INTRACRANIAL ANEURYSMS
Figure 7. Comparison of biplane DSA image sequences (left column and third column from the left) with corresponding numerical simulations (second and fourth columns from the left), for patient 3.
Interestingly, with careful inspection of the conventional angiograms or virtual angiograms in these three patients, we were able to correctly assign a flow type (9) to each of the three aneurysms. So, potentially, refinement in high frame rate “dynamic” conventional angiography techniques may be useful for the characterization of aneurysms if the preliminary results of Cebral are born out. With the newer flat panel detectors (not used in this study), frame rates in excess of 30 Hz will be possible. Thus, information of this type may allow clinicians to classify aneurysms “hemodynamically” without resorting to laborious calculations required by the CFD method and use this as one predictor of aneurysm outcome. However, further work will be necessary in validation and study of the aneurysmal hemodynamics before this could be recommended. Some of the differences between our virtual angiogram and conventional angiography may be explained by our choices in modeling the contrast transport. In these experiments, we did not try to exactly reproduce the dynamic behavior of the injected contrast dye. We simply used
virtual angiograms to visualize the flow structures and qualitatively compare them with corresponding flow structures observed in the conventional angiograms. There are a number of effects that can influence the results of the transport simulation and therefore the comparison between the simulated and conventional angiograms. The transport model neglects the alterations in the inflow waveform introduced by the injection of contrast agent and assumes an input concentration profile that does not exactly reproduce shape and duration of the actual injection used in the conventional angiograms. These factors have been shown to have an effect on the time-density curves obtained from simulated angiograms (33). For more quantitative comparisons, it would be necessary to measure the patient-specific flow rates, for instance, with phase-contrast magnetic resonance or intravascular Doppler ultrasound, and to obtain angiograms at a high enough frame rate to measure the input concentration profile in the parent vessel. When constructing the virtual angiograms, a simple volume-rendering technique was used to visualize the dye concentration fields. This technique does
811
CEBRAL ET AL
not exactly simulate the attenuation of the x-rays traveling through the computational model filled with contrast material. The conventional angiographic views are limited by overlapping vessels that can obscure the view and confound the details of the aneurysmal flow structures. Therefore, the angiographic view may include density not modeled by the CFD method. Finally, accurate modeling of the pooling effect observed in one of the patients requires modeling multiphase flows with gravity and accounting for the different densities of blood and the contrast agent (34). These effects would have their greatest influence on the zones of slower flows as typically seen in the later phase of the cardiac cycle. This is where we identified the largest divergence between our virtual angiograms and the conventional angiograms. Some of the differences between the virtual and conventional angiograms may be related to our flow modeling assumptions. The flow model assumes a) rigid walls, b) Newtonian viscosity, and c) inflow waveforms measured in other subjects. Our previous sensitivity analysis indicated that these factors do not change the fundamental character of intra-aneurysmal flow patterns, which are primarily determined by the geometry of the aneurysm and the parent vessel (17). However, our analysis has shown some subtle differences in the flow structures that may contribute to the differences we observed. The inflow conditions (mean flow rate, flow waveform shape, and heart rate) may be important for quantitative comparison of virtual and conventional angiograms because they determine the speed at which the contrast material is transported along the vessel and enters the aneurysm. They may also affect the “intensity” of the flow patterns, which may lead to larger (or thinner) inflow jets and impaction zones. Despite these numerous limiting assumptions and approximations, the computational models yielded visualizations of the major intra-aneurysmal flow structures that are qualitatively in very good agreement with corresponding conventional angiograms. Furthermore, the results presented indicate that the CFD results are consistent with angiographic observations for aneurysms with flow structures ranging from simple stable to complex unstable flow patterns. This work does not intend to be a rigorous validation of the computational models but rather to show that patient-specific CFD models can realistically reproduce the in vivo flow structures observed during conventional angiographic examinations.
812
Academic Radiology, Vol 14, No 7, July 2007
CONCLUSIONS CFD modeling of selected aneurysms shows a good qualitative agreement with imaging of intra-aneurysmal flow structures by conventional angiography. As methods are developed for better and quantitative in vivo measurements, further studies should be performed to validate and refine the CFD method. REFERENCES 1. Nakatani H, Hashimoto N, Kang S. Cerebral blood flow patterns at major vessel bifurcations and aneurysms in rats. J Neurosurg 1991; 74: 258 –262. 2. Gonzalez CF, Choi YI, Ortega V. Intracranial aneurysms: Flow analysis of their origin and progression. AJNR Am J Neuroradiol 1992; 13:181– 188. 3. Gobin YP, Counard JL, Flaud P. In vitro study of haemodynamics in a giant saccular aneurysm model: Influence of flow dynamics in the parent vessel and effects of coil embolization. Neuroradiology 1994; 36(7): 530 –536. 4. Burleson AC, Strother CM, Turitto VT. Computer modeling of intracranial saccular and lateral aneurysms for the study of their hemodynamics. Neurosurgery 1995; 37:774 –784. 5. Tenjin H, Asakura F, Nakahara Y. Evaluation of intraaneurysmal blood velocity by time-density curve analysis and digital subtraction angiography. AJNR Am J Neuroradiol 1998; 19:1303–1307. 6. Ujiie H, Tachibana H, Hiramtsu O. Effects of size and shape (aspect ratio) on the hemodynamics of saccular aneurysms: A possible index for the surgical treatment of intracranial aneurysms. Neurosurgery 1999; 45:119 –130. 7. Tateshima S, Murayama Y, Villablanca J. Intraaneurysmal flow dynamics study featuring an acrylic aneurysm model manufactured using computerized tomography angiogram as a mold. J Neurosurg 2001; 95(6):1020 –1027. 8. Satoh T, Onoda K, Tsuchimoto S. Visualization of intraaneurysmal flow patterns with transluminal flow images of 3D MR angiograms in conjunction with aneurysmal configurations. AJNR Am J Neuroradiol 2003; 24:1436 –1445. 9. Cebral JR, Castro MA, Burgess JE, et al. Characterization of cerebral aneurysm for assessing risk of rupture using patient-specific computational hemodynamics models. AJNR Am J Neuroradiol 2005; 26:2550 – 2559. 10. Cebral JR, Castro MA, Millan D, et al. Pilot clinical investigation of aneurysm rupture using image-based computational fluid dynamics models. SPIE Medical Imaging Conference, San Diego, February 12⫺17, 2005. 11. Cebral JR, Yim PJ, Löhner R, et al. Blood flow modeling in carotid arteries using computational fluid dynamics and magnetic resonance imaging. Acad Radiol 2002; 9:1286 –1299. 12. Yim PJ, Cebral JR, Weaver A, et al. Estimation of the differential pressure at renal artery stenoses. Magn Reson Med 2004; 51:969 –977. 13. Lieber BB, Livescu V, Hopkins LN, et al. Particle image velocimetry assessment of stent design influence on intra-aneurysmal flow. Ann Biomed Eng 2002; 30:768 –777. 14. Ionita CN, Hoi Y, Meng H, Rudin S. Particle image velocimetry (PIV) evaluation of flow modification in aneurysm phantoms using asymmetric stents. SPIE Medical Imaging Conference, San Diego, February 14⫺19, 2004. 15. Moore JA, Steinman DA, Holdworth DW, et al. Accuracy of computational hemodynamics in complex arterial geometries reconstructed from magnetic resonance imaging. Ann Biomed Eng 1999; 27:32– 41. 16. Taylor CA, Draney MT. Experimental and computational methods in cardiovascular fluid mechanics. Annu Rev Fluid Mechan 2004; 36:197– 231.
Academic Radiology, Vol 14, No 7, July 2007
17. Cebral JR, Castro MA, Appanaboyina S, et al. Efficient pipeline for image-based patient-specific analysis of cerebral aneurysm hemodynamics: Technique and sensitivity. IEEE Trans Med Imaging 2005; 24(1):457– 467. 18. Venugopal P, Chen H, Duckwiler G, et al. Correlating aneurysm growth to hemodynamic parameters: The case of a patient-specific anterior communicating arterial aneurysm. SPIE Medical Imaging Conference, San Diego, February 12⫺17, 2005. 19. Oshima M, Sakai H, Torii R. Modeling of inflow boundary conditions for image-base simulation of cerebrovascular flow. Int J Numerical Methods Fluids 2005; 47:603– 617. 20. Sato O, Kamitani H. Giant aneurysm of the middle cerebral artery: Angiographic analysis of blood flow. Surg Neurol 1975; 4:27–31. 21. Lanzieri CF, Tarr RW, Selman WR, et al. Use of the delayed mask for improved demonstration of aneurysms on intraarterial DSA. AJNR Am J Neuroradiol 1992; 13:1589 –1593. 22. Castro MA, Putman CP, Cebral JR. Computational modeling of cerebral aneurysms in arterial networks reconstructed from multiple 3D rotational angiography images. SPIE Med Imaging 2005; 5746:233–244. 23. Castro MA, Putman CM, Cebral JR. Patient-specific computational modeling of cerebral aneurysms with multiple avenues of flow from 3D rotational angiography images. Acad Radiol 2006; 13(7):811– 821. 24. Yim PJ, Vasbinder B, Ho VH, et al. A deformable isosurface and vascular applications. SPIE Med Imaging 2002; 4684:1390 –1397.
MODELING OF INTRACRANIAL ANEURYSMS
25. Löhner R. Automatic unstructured grid generators. Finite Elements Anal Design 1997; 25:111–134. 26. Löhner R. Extensions and improvements of the advancing front grid generation technique. Comput Methods Appl Mechanics Eng 1996; 5:119 –132. 27. Löhner R. Regridding surface triangulations. J Comput Phys 1996; 126: 1–10. 28. Mazumdar J. Biofluid Mechanics. Singapore: World Scientific, 1992. 29. Womersley JR. Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J Physiol 1955; 127:553–563. 30. Taylor CA, Hughes TJR, Zarins CK. Finite element modeling of blood flow in arteries. Comput Methods Appl Mechanics Eng 1998; 158:155– 196. 31. Cebral JR, Castro MA, Soto O, et al. Blood flow models of the circle of Willis from magnetic resonance data. J Eng Math 2003; 47(3– 4):369 – 386. 32. Calamante F, Yim PJ, Cebral JR. Estimation of bolus dispersion effects in perfusion MRI using image-based computational fluid dynamics. NeuroImage 2003; 19:342–352. 33. Ford MD, Stuhne GR, Nikolov HN, et al. Virtual angiography for visualization and validation of computational models of aneurysm hemodynamics. IEEE Trans Med Imaging 2005; 24(12):1586 –1592. 34. Wang ZJ, Hoffmann KR, Wang Z, et al. Contrast setting in cerebral aneurysm angiography. Phys Med Biol 2005; 50:3171–3181.
813
Rationale and Objective. The purpose of this study is to determine whether computational fluid dynamics modeling can correctly predict the location of the major intra-aneurysmal flow structures that can be identified by conventional angiography. Materials and Methods. Patient-specific models of three cerebral aneurysms were constructed from three-dimensional rotational angiography images and computational fluid dynamic simulations performed. Using these velocity fields, contrast transport was simulated and visualizations constructed to provide a “virtual” angiogram. These models were then compared to images from high frame rate conventional angiography to compare flow structures. Results. Computational fluid dynamics simulations showed three distinct flow types ranging from simple to complex. Virtual angiographic images showed good agreement with images from conventional angiography for all three aneurysms with analogous size and orientation of the inflow jet, regions of impaction, and flow type. Large intra-aneurysmal vortices and regions of outflow also corresponded between the images. Conclusions. Patient-specific image-based computational models of cerebral aneurysms can realistically reproduce the major intra-aneurysmal flow structures observed with conventional angiography. The agreement between computational models and angiographic structures is less for slower zones of recirculation later in the cardiac cycle. Key Words. Cerebral aneurysms; rotational angiography; computational fluid dynamics; cerebral angiography. ©
AUR, 2007
Cerebral aneurysms are widely believed to form and grow on the basis of hemodynamic interactions with the wall biology. Researchers have used a variety of tools to study these complex biological phenomena including animal, in vitro models, and computational models (1– 8). The goal of these experiments has been to approximate the in vivo
Acad Radiol 2007; 14:804 – 813 1
From the School of Computational Sciences, George Mason University, Fairfax, VA 22030 (J.R.C.); Interventional Neuroradiology, Inova Fairfax Hospital, 3300 Gallows Road, Fairfax Radiological Consultants, Falls Church, VA 22042 (R.S.P. Jr., C.M.P.); and the Department of Neurosurgery, George Washington University School of Medicine (C.M.P., R.S.P. Jr.). Received Oct 16, 2006; accepted Mar 9, 2007. The authors thank Philips Medical Systems for financial support. Address correspondence to: C.M.P. e-mail: [email protected]
© AUR, 2007 doi:10.1016/j.acra.2007.03.008
804
environment so that theories can be developed and further tested in more realistic systems. Ultimately, a link between the research and the clinical outcomes (i.e., aneurysmal growth and rupture) is necessary to reach an understanding of the relative importance of the forces or mechanisms that are discovered. Previously used methods fall short of this goal because they cannot reproduce the in vivo state of a particular patient. Until recently, computational studies have been only performed on idealized aneurysm geometries or approximations of a specific patient geometry. As computational techniques have improved, more refined models have been constructed, leading to a transition from idealized geometries to “realistic” models based on typical patient anatomies. Most recently, studies have tried to replicate the exact anatomy of specific patients to connect specific hemodynamic factors to
MODELING OF INTRACRANIAL ANEURYSMS
Academic Radiology, Vol 14, No 7, July 2007
clinical events, allowing statistical analysis in a patient population (9, 10). Despite these more sophisticated methods, one question still remains: Are these models accurately reproducing what is occurring in a specific patient? Without accurate in vivo measurements for comparison, a complete validation of computational methods is not possible. But, there is growing evidence that computational methods are reliably reproducing the in vivo intravascular environment. Comparisons with a variety of simplified experimental biological systems have shown good correlation with computational models (11–16). In addition to this direct validation, sensitivity analysis has been performed to obtain an understanding of the influence of a variable within a physiologic range are on the results of a specific model (17, 18). These analyses have been done to test a variety of assumptions used in modeling including flow rates, flow asymmetries, inflow boundary conditions, Newtonian properties of fluids, reconstruction/grid generation techniques, and small branch segmentation (17, 19). Even without knowing the exact value of the input variable, this analysis can measure the influence of changes (or errors) in the variable would have on the results of a simulation. Previous work has shown that inaccuracies in geometry have the largest potential for adversely influencing intra-aneurysmal hemodynamics (17). Other variables appear to have only minor effects on the models and are considered higher order variables. Although there currently are no proved methods for doing noninvasive in vivo measurements of flow, pressure, or wall shear stress in cerebral aneurysms, there are some techniques that can give some qualitative flow information. Conventional cerebral angiography has long been used for defining the anatomy and flow patterns of the intracranial vessels. Using high frame rates and/or judicious use of masking techniques, intra-arterial DSA can image inflow jets and some zones of recirculation in many aneurysms (20, 21). MR angiography can provide similar information with appropriate postprocessing of the time of flight data acquisitions (8). These methods are not sufficient to give accurate quantitative measures of intraaneurysmal hemodynamics but do give a direct representation of the intra-aneurysmal flow structure and therefore make possible a qualitative comparison. For this study, we use images from conventional angiograms in selected aneurysms to determine the major intra-aneurysmal flow structures and conventional 3D rotational angiography to define the patient-specific 3D geometries. Our purpose is to determine whether our computational fluid dynamic (CFD) method can correctly predict and explain the ob-
Table 1 Cases selected for study Patient
Location
Size (mm)
Rupture
Flow type
1 2 3
LICA LICA RMCA
25 11 5
Yes No Yes
IV III I
served flow structures as a means of providing evidence to support the validity of the CFD method.
METHODS Patients and Images Three patients with cerebral aneurysms were selected from our database in order to study whether CFD could predict the major intra-aneurysmal flow structures found on conventional angiography. The aneurysms that were selected had different flow types and had high frame rate conventional angiography images with definable major flow structures. These angiographic images were obtained using a short injection (10 ml/sec for total volume of 3 ml) and biplane angiography at 7.5 frames/sec using DSA. Characteristics of these aneurysms are summarized in Table 1. Patient-specific geometries were obtained by rotational acquisition during conventional cerebral angiography using a Philips Integris system. (Philips Medical Systems, Best, The Netherlands). The images used for the 3D reconstruction were obtained during a 180-degree rotation and imaging at 15 frames/sec for a total of 8 seconds. The corresponding 120 projection images were reconstructed into a 3D dataset of 256 ⫻ 256 ⫻ 256 voxels covering a field of view of 54.02 mm on a dedicated Phillips workstation. The voxel data was exported into a PC for mathematical vascular modeling using a recently developed methodology (17, 22, 23). Vascular Models Vascular models were constructed from the 3D rotational angiography (3DRA) images using geometric deformable models (24). High-quality volumetric finite element grids composed of tetrahedral elements were then generated using an advancing front technique to fill the space inside these geometrical models (25–27). The mesh minimum resolution was approximately 0.16 mm. The meshes contained roughly 2.2 million (M), 2.5 M, and 2.2 M elements for patients 1 through 3, respectively. In all these
805
CEBRAL ET AL
Figure 1. Patient 1. Top row, Volume rendering of 3DRA image from three orthogonal views. Second row from top, Geometrical model from same views. Third row from top, Streamlines at three time points during the cardiac cycle. Bottom row, Wall shear stress magnitude at same instants of time.
models, the entire proximal portions of the parent arteries visible in the 3DRA images were reconstructed. The 3DRA images and the vascular models for each patient are shown in Figures 1 through 3, respectively. Note that patient 2 had a clip from a previous surgery proximal to the aneurysm neck. This clip was manually removed from the anatomical model by interactive editing of the surface triangulation. Blood Flow Models Blood flow was modeled as an incompressible Newtonian fluid described by the unsteady Navier-Stokes equations in 3D (28). The blood density was ⫽ 1.0 g/cm3, and the viscosity was ⫽ 0.04 Poise. Vessel walls were assumed rigid, and no slip boundary conditions were applied at the walls. Assuming that all the distal vascular beds have similar total resistance to flow, traction-free boundary conditions with the same pressure level were applied to all the model outlets. At the inflows, pulsatile velocity profiles were prescribed using the Womersley
806
Academic Radiology, Vol 14, No 7, July 2007
Figure 2. Patient 2. Top row, Volume rendering of 3DRA image from three orthogonal views. Second row from top, Geometrical model from same views. Third row from top, Streamlines at three time points during the cardiac cycle. Bottom row, Wall shear stress magnitude at same instants of time.
solution for the fully developed pulsatile flow in a rigid straight pipe (29). These velocity profiles were computed from the Fourier decomposition of the prescribed flow rate curves (30). Flow measurements were not available for these patients; therefore, the flow conditions were derived from phase-contrast magnetic resonance measurements performed on normal subjects in the same arteries (31). Numerical solutions of the Navier-Stokes equations were obtained using a fully implicit finite element formulation that allows arbitrary timestep sizes (17). Two cardiac cycles were computed using 100 timesteps per cycle, and all the results presented correspond to the second cardiac cycle.
Contrast Transport Models Virtual or synthetic angiograms were produced for each patient. For this purpose, the entire flow field computed by the finite element solver was stored at each time
Academic Radiology, Vol 14, No 7, July 2007
MODELING OF INTRACRANIAL ANEURYSMS
ing streamlines were produced for each patient. The origins of the streamlines were interactively placed in the neck of the original models of each patient. The streamlines were then computed from these origins in both directions (upstream and downstream). The virtual angiogram was visualized on a 3D workstation and projections chosen that approximated the projection from the corresponding conventional angiograms. Frame-by-frame inspection of both image sets was done and images selected for corresponding moments in the passage of contrast through the aneurysms. In addition, both image sets were reviewed as cine loops in order to assess the dynamic movements of the contrast. Assessments were made for the size and orientation of the inflow jet, size and location of the impaction zone, location any major intra-aneurysmal vortices, location of the outflow stream, and the flow type (9) for each aneurysm.
RESULTS
Figure 3. Patient 3. Top row, Volume rendering of 3DRA image from three orthogonal views. Second row from top, Geometrical model from same views. Third row from top, Streamlines at three time points during the cardiac cycle. Bottom row, Wall shear stress magnitude at same instants of time.
step of the second cardiac cycle. Using this time-dependent velocity field a simulation of the transport of a virtual dye was performed by solving the transport (convection-diffusion) equation using a stabilized finite element method (32). At the inlet of the models, a time-dependent concentration was prescribed mimicking the contrast injection used in the actual angiograms. At the model outlets and walls, natural (Neumann) boundary conditions were prescribed. The solution of the transport equation is a time-dependent scalar field representing the time-variation of the concentration of the simulated contrast agent at each grid point. This concentration field was used to produce visualizations of the flow structures analogous to the actual angiograms. To this end, volume renderings of the concentration field were performed by plotting all grid points in a gray scale and with transparencies modulated by the local concentration. Postprocessing and Visualization Animations or cine loops of the wall shear stress (WSS) magnitude and intra-aneurysmal flow patterns us-
Patient 1 Results of the CFD simulations are presented in Figure 1. A single inflow jet is seen that affects the dome of the aneurysm in line with the efferent parent artery and divides into two major vortices with several small vortical structures consistent with a type IV flow pattern. A region of elevated WSS is seen corresponding to the zone of impaction. Outflow is along the distal wall for the superior vortex and along the inferior wall for the inferior vortex. Virtual and conventional angiography images are shown in Figure 4 (lateral view) and Figure 5 (anteroposterior view). Images are displayed to show corresponding phases in the passage of the contrast. Both the virtual and conventional angiograms show a large single inflow in the same orientation and zone of impaction. The virtual angiogram images appear to represent an inflow jet and impaction zone slightly more diffuse compared with the conventional angiogram. Two major vortical structures are identified in both sets of images with corresponding zones of outflow. Some differences in the smaller secondary vortices are seen in the later phases with the virtual angiogram predicting more complex pattern than is discernable on the conventional angiogram, but these are largely obscured as the aneurysm fills with contrast. Both virtual and conventional angiograms show flow structures that would place this aneurysm in flow type IV. Overall, there is an excellent agreement between the two represen-
807
CEBRAL ET AL
Academic Radiology, Vol 14, No 7, July 2007
Figure 4. Comparison of dynamic DSA images (left column and third column from the left) and virtual angiograms obtained from CFD simulations (second and fourth columns from the left) for patient 1, side view projection. The DSA corresponds to the filling phase obtained with a long injection of contrast.
tations, and several of the detail features observed in the conventional angiogram can also be clearly observed in the virtual angiogram. Figure 5 shows two frames corresponding to the aneurysm filling phase in the anteriorposterior view for both the conventional and virtual angiograms. Although there are more overlapping vessels, this figure shows that the location of the inflow jet and overall characteristics of the major vortex structures of the intra-aneurysmal flow pattern are also in good agreement in this second projection view. Patient 2 The results of the CFD analysis are shown in Figure 2. A single inflow jet is seen entering from the downstream portion of a well-defined neck. The jet impacts directly into the dome and splits into two well-defined vortices. A small secondary vortex is formed in the medial portion of the dome during the cardiac cycle, making this a flow type III aneurysm. Outflow is through the upstream por-
808
tion of the neck from both major vortices. A region of elevated WSS corresponds with the impaction zone on the aneurysm dome. Virtual and conventional angiography images are shown side by side for both the lateral and a right anterior oblique projection (RAO) in Figure 6. The RAO view shows the well defined inflow jet with good agreement between the two series. The inflow jet from the virtual angiogram is somewhat larger than the conventional angiographic view and with a slightly larger impaction zone. However, the location of the region of impaction is the same. The two major vortical structures are well seen on both sequences with only minor differences. Both sequences show the filling of the small medial lobulation later in the angiogram, consistent with predictions by the CFD representations. This confirms the type III flow type. The differences in the two sequences are more apparent on the lateral projection. Once again, the flow jets have similar orientation and location with only a small differ-
Academic Radiology, Vol 14, No 7, July 2007
MODELING OF INTRACRANIAL ANEURYSMS
and a type I flow pattern. Location and impaction of the inflow jet show excellent agreement. There are some minor differences in the shape and pattern of the single vortex. However, both sequences show the delayed filling of the medial and superior branch, which is receiving flow as a continuation from the outflow zone of the aneurysm. This effect is best seen in the anteroposterior projection.
DISCUSSION
Figure 5. Comparison of dynamic DSA images (left column) and virtual angiograms obtained from CFD simulations (right column) for patient 1, anteroposterior projection. The DSA corresponds to the filling phase obtained with a long injection of contrast.
ence in thickness. Both show a clockwise rotation of the internal vortices, but in the later phases, the conventional angiogram show significant “pooling” of the contrast in the dependent portion of the aneurysm. The virtual angiogram predicts this in a much smaller amount with the pooling occurring preferentially in the inferoposterior portion of the aneurysm. As with patient 1, the differences between the two sequences become more prominent in the later phases, i.e., during aneurysm washout. Patient 3 The result of the CFD analysis is shown in Figure 3. The simulation predicts a simple single vortical flow structure consistent with flow type I. The single inflow jet enters the neck inferiorly and nearly tangentially strikes the neck and continues to impact the body. The single vortex rotates in a counterclockwise fashion with the major portion of the outflow going to the superior and medial branch. A focal region of elevated WSS is seen in the inferior neck extending into a portion of the body, consistent with the impaction of the inflow jet. Virtual and conventional angiography images are provided for both anteroposterior and lateral projections in Figure 7. Both confirm the single inflow jet and the single counterclockwise vortex consistent with the CFD result
CFD is an attractive tool for the study of cerebral aneurysms and other cerebrovascular diseases and has been used in numerous studies. However, the CFD methodology has not been completely validated in aneurysmal systems, largely because of a lack of available data for comparison. Strict validation of this method would require point-by-point comparison with a number of “gold standards” to understand the variability and accuracy of the method. For intra-aneurysmal hemodynamics, this is simply not possible because no proved in vivo method for measuring intra-aneurysmal hemodynamic quantities is available. Also, because the mechanisms responsible for the pathogenesis of cerebral aneurysm are not well understood, we do not know which variables are important and what level of accuracy is needed for clinical purposes. Cerebral aneurysms are widely believed to form and grow on the basis of hemodynamic interactions with the wall biology (1– 8). On the basis of in vitro, animal, and computational studies, oscillatory stress, wall shear stress, and pressure have been suggested as potentially responsible for the wall injury that leads to rupture. Most recently, a population-based study using CFD found a correlation between impingement region (the region of collision between the inflow jet and the aneurysmal wall) and the clinical history of rupture with an additional trend of more complex intra-aneurysmal flow patterns with rupture (9). These studies point to the major flow structures as likely major determinants of clinical outcome (i.e., rupture). Therefore, determining whether the CFD method can correctly predict these major flow structures becomes an important question when evaluating the usefulness of those conclusions. Cerebral angiography remains the gold standard for the evaluation of cerebral aneurysms. Both conventional 2D imaging and now 3DRA are widely used in medical practice for understanding the geometry of aneurysms for both conventional and endovascular surgeons. With the use of high frame rate angiography and the judicious use of
809
CEBRAL ET AL
Academic Radiology, Vol 14, No 7, July 2007
Figure 6. Comparison of two different DSA image sequences (left column and third column from the left) obtained with different injections with corresponding numerical simulations (second and fourth columns from the left), for patient 2.
masking techniques, Lanzieri et al. (21) have shown that cerebral angiography can better define the neck of an aneurysm by clearer visualization of the inflow stream. We take advantage of this by using high frame rate angiography to register the phases of filling of three aneurysms to use in comparison with our CFD models. Qualitative comparisons of flow visualizations produced from these conventional angiograms and CFDbased virtual angiograms show excellent agreement of the major intra-aneurysmal flow structures for three patients with cerebral aneurysms. In particular, these visualizations show that the CFD simulations correctly predict the location and size of the inflow jet, flow impaction zone, the major vortex structures, and the outflow regions. The
810
CFD simulations are in best agreement with the images from conventional angiography in the early filling phase of the aneurysm. In the later phases, the CFD simulations show greater complexity than the conventional angiography accounting for the divergence. The fine details of the conventional and virtual angiograms also exhibit some differences. For instance, the computational models tend to produce inflow jets and impaction zones slightly more diffuse than those observed in the conventional angiograms. The differences in the flow structures are more pronounced during the washout phases. In particular, one of the aneurysms (patient 2) presented a significant “pooling” effect at the end of the washout phase, which was not entirely reproduced by the corresponding computational model.
Academic Radiology, Vol 14, No 7, July 2007
MODELING OF INTRACRANIAL ANEURYSMS
Figure 7. Comparison of biplane DSA image sequences (left column and third column from the left) with corresponding numerical simulations (second and fourth columns from the left), for patient 3.
Interestingly, with careful inspection of the conventional angiograms or virtual angiograms in these three patients, we were able to correctly assign a flow type (9) to each of the three aneurysms. So, potentially, refinement in high frame rate “dynamic” conventional angiography techniques may be useful for the characterization of aneurysms if the preliminary results of Cebral are born out. With the newer flat panel detectors (not used in this study), frame rates in excess of 30 Hz will be possible. Thus, information of this type may allow clinicians to classify aneurysms “hemodynamically” without resorting to laborious calculations required by the CFD method and use this as one predictor of aneurysm outcome. However, further work will be necessary in validation and study of the aneurysmal hemodynamics before this could be recommended. Some of the differences between our virtual angiogram and conventional angiography may be explained by our choices in modeling the contrast transport. In these experiments, we did not try to exactly reproduce the dynamic behavior of the injected contrast dye. We simply used
virtual angiograms to visualize the flow structures and qualitatively compare them with corresponding flow structures observed in the conventional angiograms. There are a number of effects that can influence the results of the transport simulation and therefore the comparison between the simulated and conventional angiograms. The transport model neglects the alterations in the inflow waveform introduced by the injection of contrast agent and assumes an input concentration profile that does not exactly reproduce shape and duration of the actual injection used in the conventional angiograms. These factors have been shown to have an effect on the time-density curves obtained from simulated angiograms (33). For more quantitative comparisons, it would be necessary to measure the patient-specific flow rates, for instance, with phase-contrast magnetic resonance or intravascular Doppler ultrasound, and to obtain angiograms at a high enough frame rate to measure the input concentration profile in the parent vessel. When constructing the virtual angiograms, a simple volume-rendering technique was used to visualize the dye concentration fields. This technique does
811
CEBRAL ET AL
not exactly simulate the attenuation of the x-rays traveling through the computational model filled with contrast material. The conventional angiographic views are limited by overlapping vessels that can obscure the view and confound the details of the aneurysmal flow structures. Therefore, the angiographic view may include density not modeled by the CFD method. Finally, accurate modeling of the pooling effect observed in one of the patients requires modeling multiphase flows with gravity and accounting for the different densities of blood and the contrast agent (34). These effects would have their greatest influence on the zones of slower flows as typically seen in the later phase of the cardiac cycle. This is where we identified the largest divergence between our virtual angiograms and the conventional angiograms. Some of the differences between the virtual and conventional angiograms may be related to our flow modeling assumptions. The flow model assumes a) rigid walls, b) Newtonian viscosity, and c) inflow waveforms measured in other subjects. Our previous sensitivity analysis indicated that these factors do not change the fundamental character of intra-aneurysmal flow patterns, which are primarily determined by the geometry of the aneurysm and the parent vessel (17). However, our analysis has shown some subtle differences in the flow structures that may contribute to the differences we observed. The inflow conditions (mean flow rate, flow waveform shape, and heart rate) may be important for quantitative comparison of virtual and conventional angiograms because they determine the speed at which the contrast material is transported along the vessel and enters the aneurysm. They may also affect the “intensity” of the flow patterns, which may lead to larger (or thinner) inflow jets and impaction zones. Despite these numerous limiting assumptions and approximations, the computational models yielded visualizations of the major intra-aneurysmal flow structures that are qualitatively in very good agreement with corresponding conventional angiograms. Furthermore, the results presented indicate that the CFD results are consistent with angiographic observations for aneurysms with flow structures ranging from simple stable to complex unstable flow patterns. This work does not intend to be a rigorous validation of the computational models but rather to show that patient-specific CFD models can realistically reproduce the in vivo flow structures observed during conventional angiographic examinations.
812
Academic Radiology, Vol 14, No 7, July 2007
CONCLUSIONS CFD modeling of selected aneurysms shows a good qualitative agreement with imaging of intra-aneurysmal flow structures by conventional angiography. As methods are developed for better and quantitative in vivo measurements, further studies should be performed to validate and refine the CFD method. REFERENCES 1. Nakatani H, Hashimoto N, Kang S. Cerebral blood flow patterns at major vessel bifurcations and aneurysms in rats. J Neurosurg 1991; 74: 258 –262. 2. Gonzalez CF, Choi YI, Ortega V. Intracranial aneurysms: Flow analysis of their origin and progression. AJNR Am J Neuroradiol 1992; 13:181– 188. 3. Gobin YP, Counard JL, Flaud P. In vitro study of haemodynamics in a giant saccular aneurysm model: Influence of flow dynamics in the parent vessel and effects of coil embolization. Neuroradiology 1994; 36(7): 530 –536. 4. Burleson AC, Strother CM, Turitto VT. Computer modeling of intracranial saccular and lateral aneurysms for the study of their hemodynamics. Neurosurgery 1995; 37:774 –784. 5. Tenjin H, Asakura F, Nakahara Y. Evaluation of intraaneurysmal blood velocity by time-density curve analysis and digital subtraction angiography. AJNR Am J Neuroradiol 1998; 19:1303–1307. 6. Ujiie H, Tachibana H, Hiramtsu O. Effects of size and shape (aspect ratio) on the hemodynamics of saccular aneurysms: A possible index for the surgical treatment of intracranial aneurysms. Neurosurgery 1999; 45:119 –130. 7. Tateshima S, Murayama Y, Villablanca J. Intraaneurysmal flow dynamics study featuring an acrylic aneurysm model manufactured using computerized tomography angiogram as a mold. J Neurosurg 2001; 95(6):1020 –1027. 8. Satoh T, Onoda K, Tsuchimoto S. Visualization of intraaneurysmal flow patterns with transluminal flow images of 3D MR angiograms in conjunction with aneurysmal configurations. AJNR Am J Neuroradiol 2003; 24:1436 –1445. 9. Cebral JR, Castro MA, Burgess JE, et al. Characterization of cerebral aneurysm for assessing risk of rupture using patient-specific computational hemodynamics models. AJNR Am J Neuroradiol 2005; 26:2550 – 2559. 10. Cebral JR, Castro MA, Millan D, et al. Pilot clinical investigation of aneurysm rupture using image-based computational fluid dynamics models. SPIE Medical Imaging Conference, San Diego, February 12⫺17, 2005. 11. Cebral JR, Yim PJ, Löhner R, et al. Blood flow modeling in carotid arteries using computational fluid dynamics and magnetic resonance imaging. Acad Radiol 2002; 9:1286 –1299. 12. Yim PJ, Cebral JR, Weaver A, et al. Estimation of the differential pressure at renal artery stenoses. Magn Reson Med 2004; 51:969 –977. 13. Lieber BB, Livescu V, Hopkins LN, et al. Particle image velocimetry assessment of stent design influence on intra-aneurysmal flow. Ann Biomed Eng 2002; 30:768 –777. 14. Ionita CN, Hoi Y, Meng H, Rudin S. Particle image velocimetry (PIV) evaluation of flow modification in aneurysm phantoms using asymmetric stents. SPIE Medical Imaging Conference, San Diego, February 14⫺19, 2004. 15. Moore JA, Steinman DA, Holdworth DW, et al. Accuracy of computational hemodynamics in complex arterial geometries reconstructed from magnetic resonance imaging. Ann Biomed Eng 1999; 27:32– 41. 16. Taylor CA, Draney MT. Experimental and computational methods in cardiovascular fluid mechanics. Annu Rev Fluid Mechan 2004; 36:197– 231.
Academic Radiology, Vol 14, No 7, July 2007
17. Cebral JR, Castro MA, Appanaboyina S, et al. Efficient pipeline for image-based patient-specific analysis of cerebral aneurysm hemodynamics: Technique and sensitivity. IEEE Trans Med Imaging 2005; 24(1):457– 467. 18. Venugopal P, Chen H, Duckwiler G, et al. Correlating aneurysm growth to hemodynamic parameters: The case of a patient-specific anterior communicating arterial aneurysm. SPIE Medical Imaging Conference, San Diego, February 12⫺17, 2005. 19. Oshima M, Sakai H, Torii R. Modeling of inflow boundary conditions for image-base simulation of cerebrovascular flow. Int J Numerical Methods Fluids 2005; 47:603– 617. 20. Sato O, Kamitani H. Giant aneurysm of the middle cerebral artery: Angiographic analysis of blood flow. Surg Neurol 1975; 4:27–31. 21. Lanzieri CF, Tarr RW, Selman WR, et al. Use of the delayed mask for improved demonstration of aneurysms on intraarterial DSA. AJNR Am J Neuroradiol 1992; 13:1589 –1593. 22. Castro MA, Putman CP, Cebral JR. Computational modeling of cerebral aneurysms in arterial networks reconstructed from multiple 3D rotational angiography images. SPIE Med Imaging 2005; 5746:233–244. 23. Castro MA, Putman CM, Cebral JR. Patient-specific computational modeling of cerebral aneurysms with multiple avenues of flow from 3D rotational angiography images. Acad Radiol 2006; 13(7):811– 821. 24. Yim PJ, Vasbinder B, Ho VH, et al. A deformable isosurface and vascular applications. SPIE Med Imaging 2002; 4684:1390 –1397.
MODELING OF INTRACRANIAL ANEURYSMS
25. Löhner R. Automatic unstructured grid generators. Finite Elements Anal Design 1997; 25:111–134. 26. Löhner R. Extensions and improvements of the advancing front grid generation technique. Comput Methods Appl Mechanics Eng 1996; 5:119 –132. 27. Löhner R. Regridding surface triangulations. J Comput Phys 1996; 126: 1–10. 28. Mazumdar J. Biofluid Mechanics. Singapore: World Scientific, 1992. 29. Womersley JR. Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J Physiol 1955; 127:553–563. 30. Taylor CA, Hughes TJR, Zarins CK. Finite element modeling of blood flow in arteries. Comput Methods Appl Mechanics Eng 1998; 158:155– 196. 31. Cebral JR, Castro MA, Soto O, et al. Blood flow models of the circle of Willis from magnetic resonance data. J Eng Math 2003; 47(3– 4):369 – 386. 32. Calamante F, Yim PJ, Cebral JR. Estimation of bolus dispersion effects in perfusion MRI using image-based computational fluid dynamics. NeuroImage 2003; 19:342–352. 33. Ford MD, Stuhne GR, Nikolov HN, et al. Virtual angiography for visualization and validation of computational models of aneurysm hemodynamics. IEEE Trans Med Imaging 2005; 24(12):1586 –1592. 34. Wang ZJ, Hoffmann KR, Wang Z, et al. Contrast setting in cerebral aneurysm angiography. Phys Med Biol 2005; 50:3171–3181.
813