Basic Fluid Dynamics and Tribia Related to Flow Diverter

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1 Journal of Neuroendovascular Therapy 2017; 11: Online June 22, 2016 DOI: /jnet.ra-diverter Basic Fluid Dynamics and Tribia Related to Flow Diverter Masaaki Shojima To enrich our understanding of endovascular treatment of cerebral aneurysm in the era of flow diverters (FD), related literature dealing with fluid dynamic engineering is reviewed and elaborated on here. The intra-aneurysmal flow patterns could be classified into shear-driven flow and inertia-driven flow. The flow reduction effects of FD are better anticipated among aneurysms with a shear-driven flow pattern. The FDs with lower porosity reduce more blood flow into aneurysms. Under certain porosity, FDs with thinner filaments reduce more blood flow. The flow reductions of side-branches after FD are estimated as less than 20% by computer simulation. Thus, other factors such as anti-platelet drugs and neo-intimal hyperplasia may also be involved in the ischemic complications in the territory of side-branch after FD placement. Pulsatility of blood flow, which is considerably decreased in the parent artery downstream to large aneurysms, recovers shortly after FD deployment and the peak systolic velocity becomes higher after FD. The peripheral brain circulation might be changed after FD deployment in cases of large aneurysms. Blood flow simulation for FD is not easy but it would provide useful information for selecting the proper cases for FD as well as selecting the proper devices for a certain case. Keywords flow diverter, flow dynamics, computer simulation, cerebral aneurysm Endovascular Treatment for Cerebral Aneurysms and Flow Dynamics Dr. Guglielmi developed the Guglielmi detachable coil to induce electrothrombosis in cerebral aneurysms. 1) The amount of thrombi formed by the application of electricity was smaller than expected; however, a dense placement of coils in aneurysms became easier thanks to the coil that could be manipulated until intentionally detached. The coils placed in aneurysms are obstacles to blood flow. In an animal experiment using rabbits, the blood flow in a cerebral aneurysm was reduced by 30% even when only one coil was placed, and by 90% when the aneurysm was sufficiently. 2) In this way, the coils may also be regarded as a kind of Neurosurgery, The University of Tokyo Hospital, Tokyo, Japan Received: January 18, 2016; Accepted: May 6, 2016 Corresponding author: Masaaki Shojima. Neurosurgery, The University of Tokyo Hospital, Hongo, Bunkyo-ku, Tokyo , Japan mshoji-tky@umin.ac.jp 2017 The Editorial Committee of Journal of Neuroendovascular Therapy. All rights reserved. intraaneurysmal flow diverters since in coil embolization, thrombosis of an aneurysm is induced by changing and reducing the blood flow by coils. Thus, basic knowledge about flow dynamics is useful for understanding not only the flow diverter (FD) but also the general endovascular treatment for cerebral aneurysms. Flow dynamics is one of the most difficult fields even for students of the engineering department, but the experience of endovascular interventionists in flow dynamics is never inferior to that of engineering researchers, because angiography is nothing other than the visualization of the flow by dye injection, which is the most basic experiment of flow dynamics. Here, basic flow dynamics useful for understanding flow diverters 3) and up-to-date knowledge acquired by flow dynamic experiments are discussed. Shear-Driven and Inertia-Driven Flows The flow in a cerebral aneurysm is often discussed by dividing lesions into side-wall aneurysms, such as internal carotid 109

2 Shojima M Changes in the Intraaneurysmal Blood Flow Dynamics by FD Placement Fig. 1 Shear-driven and inertia-driven flows. When the aneurysmal orifice and parent vessel are parallel, the intraaneurysmal blood flow is shear-driven (A). The flow in the aneurysm develops as if it is dragged by the flow of the parent vessel. It enters in the aneurysm through the distal lip of the aneurysm, flows slowly along the aneurysm wall, and exits through the proximal lip of the aneurysm. As the angle between the aneurysmal orifice and parent vessel sharpens, the intraaneurysmal blood flow becomes increasingly inertia-driven (B). The blood flow of the parent vessel rushes into the aneurysm due to inertia. artery aneurysms, and terminal aneurysms located at the vessel branching points. It is widely imagined that only a small part of the blood flow of the parent artery enters the aneurysm in side-wall type aneurysms and that in terminal type aneurysms, most of the blood flow of the parent vessel enters the aneurysm without losing momentum. However, it appears misleading to classify the intraaneurysm flow dynamics into side-wall and terminal types, because the direct influx from the parent vessel is sometimes observed in the cases of sidewall type aneurysms. The blood flow dynamics is easier to understand when the flow is classified into the shear-driven and inertia-driven types. 4) The shear-driven flow occurs in the aneurysm when the plane of the aneurysmal orifice is parallel to the direction of the flow. The flow in the aneurysm develops as if it is dragged by the main flow of the parent vessel (Fig. 1A). On the other hand, when the plane of the aneurysmal orifice is located perpendicularly to the direction of the flow, the blood flow of the parent vessel vigorously rushes into the aneurysm by inertia, causing an inertia-driven flow (Fig. 1B). It is appropriate to generally consider that the flow is shear-driven in side-wall type aneurysms and inertiadriven in terminal type aneurysms, but some side-wall type aneurysms show a vigorous influx from the parent vessel by inertia depending on the relationship between the vascular curvature and the location of the aneurysmal orifice. Since the blood flow of each aneurysm has characteristics of both shear-driven and inertia-driven flows, it is often impossible to classify it as either of the flow types in an all-or-nothing manner. However, as mentioned below, since the effects of FD placement on the intraaneurysmal flow differs considerably between the shear-driven and inertia-driven types, understanding these concepts and evaluating the flow type of each aneurysm is closer to helps with prediction of the effects of the FD (Table 1). The experiments to thrombose cerebral aneurysms by stenting of the parent vessel alone without placing a device, such as a coil, in the aneurysm were already reported in ) In these pioneer experiments, aneurysms about 10 mm in diameter were prepared using venous grafts and stents were placed in the parent vessels, and the blood flow dynamics around the aneurysms were observed by DSA or Doppler ultrasonography. The blood flow dynamics of the side-wall type aneurysms used in these experiments were simple. Blood flowed into the aneurysm via the inflow zone located downstream of the aneurysmal orifice, circulated along the aneurysmal wall (vortex formation), and flowed out via the outflow zone located upstream of the orifice (Fig. 2A). Inherently, the blood flow volume in a side-wall type aneurysm was not large. When a stent was placed in the parent vessel of such an aneurysm, the momentum of the vortex in the aneurysm was seen to be markedly reduced (Fig. 2B). This finding indicates a further decrease in blood flow through the aneurysm. Also, the position of the inflow zone shifted upstream, and the inflow jet ceased to be observed, suggesting that the FD can change the velocity and position of the inflow without manipulation in the aneurysm. These changes (1) change in the position of inflow; (2) decrease in the velocity of inflow; and (3) decrease in the aneurysmal blood flow were also shown to induce complete thrombosis of the aneurysm without placement of coils in the aneurysm, indicating a greater potential of the stent as a flow diverter. Differences in the FD Effect Between Shear-Driven and Inertia-Driven Flows The effect of FD placement differs widely between aneurysms with shear-driven and inertia-driven flows. Differences in the effect of FD placement were studied experimentally using aneurysms with the same diameter (10 mm) prepared on straight and curved vessels with the same diameter (4 mm). 4) The blood flow in the aneurysm decreased by 85% after FD placement in the aneurysm with a shear-driven flow prepared on a straight segment of the parent vessel, but by only 54% in the aneurysm with an inertia-driven flow prepared on a curved part. As a result, the residual blood flow in the aneurysms after FD placement showed an 8-fold difference (Table 2). These were important experimental results 110

3 Basic Fluid Dynamics and Tribia Related to Flow Diver ter Table 1 Comparison between shear-driven and inertia-driven flow Shear-driven flow Inertia-driven flow Anatomical characteristics Side-wall aneurysm, usually Terminal aneurysm, usually Positional relationship with parent vessel curvature Inner side of the curve Outer side of the curve Inflow volume Low High Flow velocity in aneurysm Slow Fast Flow structure in the aneurysm Simple Complex Fig. 2 Changes in the blood flow dynamics between before (A) and after (B) flow diverter placement observed in a sidewall aneurysm. When a flow diverter was placed in a sidewall aneurysm, characteristic changes, i.e., (1) positional change in the inflow zone, (2) attenuation of inflow jet, and (3) reduced blood flow activity in the aneurysm (weakening of the rotational flow along the aneurysmal wall and stagnation of blood), were observed. suggesting that the intraaneurysmal blood flow is markedly reduced in aneurysms of both blood flow types but that the effect of FD placement can vary widely depending on the blood flow type of the aneurysm. The intraaneurysmal blood flow is shear-driven if the angle of the plane of the aneurysmal orifice relative to the parent vessel is nearly 0, but it tends to become increasingly inertia-driven as the angle increases and approaches 90. Similarly, as the tortuosity of the parent vessel increases, the angle between the plane of the aneurysmal orifice and parent vessel increases, and the intraaneurysmal blood flow dynamics becomes progressively inertia-driven. Therefore, is it readily expected that the tortuosity of the vessel markedly affects the effect of the FD. The tortuosity of a blood vessel is expressed as the curvature. The curvature of a circle with a radius of r is defined as 1/r. An arc is straighter with decreases in the curvature and more curved with increases in the curvature. For example, in the case shown in Fig. 3, the curvature of the anterior cerebral artery was about 0.11 mm 1, and that of the carotid siphon was 0.22 mm 1. The effects of FD placement were evaluated in aneurysms prepared on curved parts mm 1 in curvature. 8) While the blood flow into the aneurysm decreased by 95% in an aneurysm prepared in a parent vessel with a curvature of 0.04 mm 1 (curvature similar to that of M1) after FD placement, the decreases were 74% when the curvature was 0.08 mm 1 and only 20% when it was 0.1 mm 1 (similar to that of the carotid siphon) (Table 3). Actually, such differences in the effect of FD placement due to differences in the vascular curvature can be readily estimated even without complicated flow dynamic experiments or simulation. Figure 4 shows stent struts from the viewpoint of blood flow. When the angle between the parent vessel and aneurysmal orifice approaches 90, causing an inertia-driven flow, the strut interval of the FD widens, and the effect of FD placement is reduced. On the other hand, when a shear-driven flow is occurring due to a narrow angle between the parent vessel and aneurysmal orifice, i.e., the stent and the direction of blood flow is nearly parallel, the stent strut intervals appear narrower than reality if seen from the blood flow side, and blood is less likely to flow into the aneurysm across the struts. As observed above, the angle between the parent vessel and the plane of the aneurysmal orifice markedly affects the effect of flow diversion. In aneurysms with a small parent vessel-aneurysmal orifice angle, the intraaneurysmal blood flow dynamics are shear-driven, and a strong FD effect is expected to appear in areas with a moderate intraaneurysmal blood flow, resulting in a marked decrease in the intraaneurysmal blood flow after FD placement. In contrast, in aneurysms with a large parent vessel-aneurysmal orifice angle (close to 90 ), the intraaneurysmal blood flow are inertiadriven, and the FD does not produce a marked effect. The degree of tortuosity of the parent vessel and positional relationship of the plane of the aneurysmal orifice vary among individual patients. Computer simulation based on clinical 3D images is useful for patient-specific approaches. Design and Effect of FD The blood flow blocking effect is greater, but the risk of occlusion of branches of the parent vessel or penetrating branches increases, as the porosity of the FD is lower. Also, since low porosity means a large amount of metal used, the flexibility of the stent decreases with the porosity. Therefore, FDs are designed to maximize the porosity while sufficiently reducing the aneurysmal blood flow. The porosity and filament diameter are particularly important among the many parameters related to the stent (Table 4). 111

4 Shojima M Table 2 Changes in the intraaneurysmal blood flow dynamics after FD placement 4) Intraaneurysmal blood flow type Flow volume of parent vessel Intraaneurysmal flow volume before FD placement Shear-driven flow 300 ml/min 13.3 ml/min Inertia-driven flow 300 ml/min 34.6 ml/min FD: flow diverter Intraaneurysmal flow volume after FD placement (percent decrease) 2.0 ml/min (85% ) 16.0 ml/min (54% ) Fig. 3 Curvature. The curvature is explained by presenting a frontal (A) and lateral (B) image of the right internal carotid artery (a patient with right middle cerebral aneurysm). In A, the curve of the A1 segment of the anterior cerebral artery is nearly identical with the arc of a circle 8.9 mm in radius. Therefore, the curvature of A1 in this patient is about 0.11 mm 1. In B, the curve of the carotid siphon is nearly equal to the arc of a circle 4.6 mm in radius, and its curvature is about 0.22 mm 1. Table 3 Curve of the parent vessel and effect of FD placement 8) Curvature Percent decrease in intraaneurysmal blood flow FD: flow diverter 0.04 mm 1 Corresponding to a circle 50 mm in radius 0.08 mm 1 Corresponding to a circle 25 mm in radius 0.1 mm 1 Corresponding to a circle 20 mm in radius 95% 74% 20% Fig. 4 Differences in the appearance of struts viewed from different angles. Struts deployed at the same interval appear wide or narrow depending on the point of view. 112

5 Basic Fluid Dynamics and Tribia Related to Flow Diver ter Table 4 Various parameters related to the stent design Pore size Cell size Mesh size Pore density Cell density Mesh density Cell angle Porosity Metal coverage ratio Filament diameter Biocompatibility Radial force Surface charge FD: flow diverter Various parameters related to the stent design The small spaces in a mesh made of stent filaments are called pores or cells. These are terms referring to their size. Terms referring to the number of pores per unit area. The angle of woven filaments constituting an FD is called the cell angle. It reflects the shape of the pores (cells) after FD placement. The percentage of the area of stent deployment not covered by metal is called the porosity. The porosity of a neck bridging stent for coil embolization is about 90%, and that of an FD is about 70%. The porosity of a covered stent is 0%. The percentage of the area covered by metal, i.e., the stent struts, is called the metal coverage ratio. The relationship between the porosity and metal coverage ratio is expressed as [Porosity (%) + Metal coverage ratio (%) = 100 (%)]. Current FDs are prepared by weaving metal filaments into a mesh. The thickness of the metal filaments is the filament diameter. Biocompatibility may affect inflammation due to foreign-body reaction, stent stenosis, in-stent thrombosis, etc. The term referring to the force that supports the blood vessel from inside toward the outside or the force of stent expansion. It may affect the prevention of restenosis or wall apposition of the stent. Since the surface of erythrocytes is negatively charged, the charge state of the stent surface may affect in-stent thrombosis. As the porosity is lower, the FD more effectively reduces the intraaneurysmal blood flow volume and velocity. 4) An experiment evaluating the relationship between the porosity of the FD and intraaneurysmal blood flow velocity using a silicone channel confirmed progressive decreases in the intraaneurysmal blood flow velocity with decreases in the porosity. The porosity of the FDs commercially available today is about 70%, but this experiment also showed a very interesting result that the blood flow velocity dropped markedly when the porosity was about 70% (Table 5). The filament diameter is the thickness of the stent strut. Interestingly, the FD is reported to reduce the intraaneurysmal blood flow more potently as its filament diameter is smaller if the porosity is the same. 9) For example, if stents are prepared without changing the porosity, i.e., the amount of metal used, stents can be prepared with a larger number of filaments, and the mesh size can be reduced, as the filament diameter is smaller. Therefore, a stent with a smaller filament diameter is estimated to have exhibited a stronger effect as an FD. In this experiment, however, the flow diversion effect decreased when the filament diameter was excessively reduced. The FDs used in this experiment were not prepared by weaving filaments of multiple sizes but by spirally shaping each of the filaments without fixing them in the device. For this reason, if the filament diameter was excessively reduced, the stiffness of the filaments is considered to have become insufficient, and the filaments, succumbing to the force of the flow, to have been shaken. Presently, the stiffness of FDs is increased by weaving multiple filaments and fixing them at points of crossing. This is considered to allow FDs to resist the blood flow despite the small filament diameter. In designing FDs, a greater intraaneurysmal blood-flow-reducing effect is considered to be obtained by reducing the filament diameter and cell size and increasing the mesh density if the porosity is the same. Blood Flow Dynamics in Side Branches after FD Placement Perforating branch infarction occurs in about 3% of patients after FD placement, and one of its causes is suggested to be interference of the blood flow of side branches by the struts of the FD. 10) According to a previous report based on blood flow analysis, the effect of the FD strut itself on the blood flow dynamics of side branches appears to be small. Simulation by computational fluid dynamics (CFD) of changes in the blood flow of the AICA after FD placement based on 3DCT images of the basilar artery in 31 patients 11) showed that the change between before and after FD placement was only 3.6%. Also, in vivo and CFD analyses of changes in the blood flow dynamics of the lumbar artery after the placement of an FD in the rabbit aorta 12) showed that the decrease in blood flow volume of the 113

6 Shojima M Table 5 Porosity and intraaneurysmal blood flow velocity Porosity 100% (No FD) 87% 74% 63% 45% Mean intraaneurysmal flow velocity (percent decrease) 34.6 cm/sec 22.1 cm/sec 36% 21.1 cm/sec 39% 7.06 cm/sec 80% 2.00 cm/sec 94% The mean flow velocity in an inertia-driven flow type aneurysm (10 mm in diameter) on a curved blood vessel (diameter: 4 mm, curvature: 0.05 mm 1 ) was measured by placing various flow diverters (flow rate in the channel: 300 ml/min). lumbar artery after FD placement was only 9% 20%, and the decrease in maximum flow velocity was only 15% 36%. However, it must be noted that the outflow vascular resistance poses a problem in the evaluation of the results of CFD analysis of the blood flow of side branches. Since the blood flow of a limited region is analyzed by CFD, the analyzed region invariably has inflow and outflow vessels, and the calculation is impossible without inputting appropriate simulation conditions for each vessel. For example, if A1 and M1 are the outflow vessels, it appears reasonable to input the same simulation conditions by assuming that the vascular resistance of the two vessels does not differ markedly. However, is it valid to perform simulation by assuming that the vascular resistance is the same between M1 and anterior choroidal artery? Actually, the peripheral vascular resistance may vary among vessels, but the method to quantify it is still sought for, and nobody, in fact, knows how the outflow resistance should be set as a simulation condition. Thus, as CFD analysis of side branch arteries contain an unsolved problem, i.e., the outflow vascular resistance. However, researchers are in agreement that the degree of interference of blood flow by the strut is not large. From the results of CFD analysis obtained to the present, thrombus formation due to the newly formed intima and stent is suspected to play a greater role than the direct blood-flow-blocking effect of the strut in penetrating branch infarction after FD placement. Blood Flow Dynamics of the Parent/ Distal Vessels after FD Placement Hemorrhagic complications in the brain parenchyma distant from the aneurysm are known to occur in the perioperative period of FD placement at a frequency of about 3%. 10) In addition of hemorrhagic changes associated with cerebral embolism/infarction occurring intraoperatively and excessive effects of dual antiplatelet therapy, changes in the blood flow dynamics that occur in the vessels distal to the aneurysm after FD placement are also suspected to be part of the mechanism of such complications. Interesting findings have been obtained by in vivo blood flow measurements using MRI. 13) The blood flow velocity and waveform of parent vessels was recorded and compared between upstream and downstream of aneurysms located at internal carotid arteries. In cases of large aneurysms exceeding 20 mm in diameter, the blood flow velocity at the downstream of aneurysms was decreased in the systolic phase and it was increased in the diastolic phase, i.e., the pulsatility was decreased. No such changes in the flow velocity and waveform were noted in small aneurysms about 10 mm in diameter. FD placement changed the blood flow velocity and waveform significantly in large aneurysms; the systolic blood flow velocity increased and the diastolic blood velocity decreased immediately after FD placement resulting in the recovery of the pulsatility, while no change was observed in the blood flow volume. Such changes in the hemodynamics between before and after FD placement particularly in large aneurysms deserves attention, because they may be involved in hemorrhage after FD placement in the brain parenchyma at distant sites. CFD Analysis There are various methods to analyze blood flow in cerebral aneurysms. It can be measured by phase contrast MRI (in vivo). Also, particle image velocimetry (PIV), by which a fluid is circulated in a glass or silicone circuit mimicking an aneurysm, and the behavior of the fluid observed with a high-performance optical device such as a high-speed camera, are the mainstreams of fluid dynamic research methods (in vitro). Now, CFD, a technique of computer-assisted simulation of the blood flow in cerebral aneurysms, is increasingly accepted (in silico). CFD would be particularly useful in treating cerebral aneurysms using FDs, not only because the blood flow dynamics of individual aneurysms can be evaluated at reasonable cost using 3D images obtained in regular clinical practice, but also because changes after the deployment of a therapeutic device can be simulated. However, CFD have some unique limitations. Attention to the following points is necessary for clinicians to interpret the results of CFD. Flow velocity and pressure By CFD, the blood flow velocity and pressure in a limited area are calculated, and it does nothing more or less. The 114

7 Basic Fluid Dynamics and Tribia Related to Flow Diver ter results of CFD analysis are presented after quantification or coloring according to various parameters including the wall shear stress (WSS), oscillatory shear index (OSI), and energy loss, but these parameters are part of the infinite secondary parameters calculated by combining the blood flow velocity and pressure values. Boundary condition dependence and morphology dependence For CFD analysis, it is necessary to input boundary conditions calculated by quantification and mathematization of the in vivo environment as well as the vascular morphology. Boundary conditions include the amount of the blood flow that enters via the vascular orifice (inflow boundary condition), resistance present at the outflow orifice (outflow boundary condition), viscosity of blood, and elasticity of the vascular wall. The results of calculation are influenced by these boundary conditions. If the blood flow at the inflow orifice is high, the flow volume in the aneurysm increases inevitably. Also, if the outflow vascular resistance is set relatively low in a particular branch, its blood flow volume is indicated higher than in the other branches. Thus, it must be noted that the results of CFD analysis are dependent on boundary conditions. Also, the results of CFD analysis are affected most strongly by the vascular morphology (morphology dependence). In interpreting the results of CFD, it is necessary to understand the shape of the aneurysm and the rules for the determination of the inflow volume applied to the simulation. Outflow boundary conditions remain an unresolved issue in CFD analysis, which is presently performed often by hypothesizing that all outflows have the same resistance. For example, the anterior cerebral and middle cerebral arteries are often used as the outflow plane in blood flow analysis of internal carotid aneurysms, but smaller vessels such as the ophthalmic artery and anterior choroidal artery, the resistance of which is expected to differ from the above vessels, are often trimmed and excluded from the analysis. Also, simulation of the blood flow of the penetrating branches is difficult, because the differences in the vascular resistance between the penetrating branches and major arteries have not been quantified or mathematized. Mesh dependence In CFD analysis, once the vascular morphology (Dicom data, etc.) has been input into a computer, the lumen must be divided into small computational grids (mesh grids). While the precision of calculation is improved basically as the grids are finer, it may also be deteriorated if the grids are made excessively fine, because truncation errors due to rounding of the values at about the 15th decimal place may occur in computerized calculations. An excessive number of grids may also cause demerits such as prolongation of the time needed for simulation and loss of smoothness in the motion of computer graphics visualized on the monitor. In addition, the values obtained by calculation with the same vascular shape and boundary conditions are markedly affected by differences in grid fineness. Such a phenomenon is called mesh dependence or grid sensitivity. In interpreting the results of CFD analysis different in mesh fineness such as comparisons among patients and between before and after FD placement, attention to the effect of mesh dependence is necessary. Characteristics of CFD Analysis of FD CFD analysis of FD has the following characteristics in addition to the problems with usual CFD analysis of aneurysms. Virtual stenting The porosity and cell shape of the FD may change depending on its nominal diameter, and vascular diameter at the site of its deployment, and the method of its deployment. However, as the FD consists of fine filaments about 30 µm in diameter, it is impossible to image the cell shape or local porosity after its deployment using clinical imaging modalities. The technology to more realistically simulate the stent shape after endovascular deployment of the FD is called virtual stenting. This technology, which requires an extremely sophisticated simulation technique, is currently being developed by front-line researchers. 14) In many of the reports of CFD analysis of FDs, calculations are still made by setting a simple mesh-like structure mimicking an FD only at the inflow orifice of the cerebral aneurysm without adopting the technique of virtual stenting. Mesh size The filaments constituting an FD are only about 30 µm in diameter. For analyzing blood flow around such fine structures, spatial resolution of less than half the diameter of the filaments, i.e., at least 15 µm is required. If the region of CFD analysis including the blood vessels proximal and distal to the aneurysm is assumed to be a cube about 45 mm in each side, and if calculation grids are set for spatial resolution of 15 µm, a vast amount of data from = 27 billion grids are generated. 115

8 Shojima M This corresponds to about 200 times the data for 3D images processed on diagnostic workstations ( ). If the number of calculation grids is excessively large, problems including the following may arise: A long time is needed for the calculation, the calculation may not converge (errors occur), and observation of the analytical results is difficult. Front-line researchers are performing CFD analysis of FDs by modifying the grid shape and reducing the number of grids to about billion, but the time and trouble needed for the calculation and analysis are still immense, and analysis of a large number of cases is difficult. Therefore, CFD analysis by regarding the FD as a porous medium is also performed ) In CFD analysis by assuming the FD as a porous medium, individual filaments constituting the FD are ignored, the FD is regarded as a plane, and the fluid resistance in the plane is expressed as simple values. While this can markedly reduce the number of grids and save the trouble of CFD, whether or not the assumption of the FD as a porous medium is valid remains questionable. Conclusion How the FD changes the blood flow in aneurysms and basic fluid dynamic knowledge considered useful for understanding this mechanism were explained. In the near future, simulation of fluid diversion will be carried out on a workstation using 3D images obtained in clinical practice. Based on such a simulation, whether each patient has an indication for fluid diversion and which FD should be deployed will be evaluated by CFD analysis, and decisions will be made accordingly. Disclosure Statement The author has no conflicts of interest regarding this article. References 1) Guglielmi G, Viñuela F, Sepetka I, et al: Electrothrombosis of saccular aneurysms via endovascular approach. Part 1: Electrochemical basis, technique, and experimental results. J Neurosurg 1991; 75: ) Sorteberg A, Sorteberg W, Rappe A, et al: Effect of Guglielmi detachable coils on intraaneurysmal flow: experimental study in canines. AJNR Am J Neuroradiol 2002; 23: ) Shojima M: The advancement of computational fluid dynamic analysis of cerebral aneurysms. In: Sakai N, Ezura M, Matsumaru Y, Miyaji S, Yoshimura S, editors. Progresses in Endovascular Treatment of the Brain Tokyo: SHIN- DAN TO CHIRYO SHA; pp ) Augsburger L, Farhat M, Reymond P, et al: Effect of flow diverter porosity on intraaneurysmal blood flow. Klin Neuroradiol 2009; 19: ) Turjman F, Acevedo G, Moll T, et al: Treatment of experimental carotid aneurysms by endoprosthesis implantation: preliminary report. Neurol Res 1993; 15: ) Geremia G, Haklin M, Brennecke L: Embolization of experimentally created aneurysms with intravascular stent devices. AJNR Am J Neuroradiol 1994; 15: ) Wakhloo AK, Schellhammer F, de Vries J, et al: Self-expanding and balloon-expandable stents in the treatment of carotid aneurysms: an experimental study in a canine model. AJNR Am J Neuroradiol 1994; 15: ) Meng H, Wang Z, Kim M, et al: Saccular aneurysms on straight and curved vessels are subject to different hemodynamics: implications of intravascular stenting. AJNR Am J Neuroradiol 2006; 27: ) 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: ) Brinjikji W, Murad MH, Lanzino G, et al: Endovascular treatment of intracranial aneurysms with flow diverters: a meta-analysis. Stroke 2013; 44: ) Hu P, Qian Y, Zhang Y, et al: Blood flow reduction of covered small side branches after flow diverter treatment: a computational fluid hemodynamic quantitative analysis. J Biomech 2015; 48: ) Cebral JR, Raschi M, Mut F, et al: Analysis of flow changes in side branches jailed by flow diverters in rabbit models. Int J Numer Method Biomed Eng 2014; 30: ) Eker OF, Boudjeltia KZ, Jerez RA, et al: MR derived volumetric flow rate waveforms of internal carotid artery in patients treated for unruptured intracranial aneurysms by flow diversion technique. J Cereb Blood Flow Metab 2015; 35: ) Cebral JR, Mut F, Raschi M, et al: Strategy for analysis of flow diverting devices based on multi-modality image-based modeling. Int J Numer Method Biomed Eng 2014; 30: ) Kulcsár Z, Augsburger L, Reymond P, et al: Flow diversion treatment: intra-aneurismal blood flow velocity and WSS reduction are parameters to predict aneurysm thrombosis. Acta Neurochir (Wien) 2012; 154: ) Chong W, Zhang Y, Qian Y, et al: Computational hemodynamics analysis of intracranial aneurysms treated with flow diverters: correlation with clinical outcomes. AJNR Am J Neuroradiol 2014; 35: ) Augsburger L, Reymond P, Rufenacht DA, et al: Intracranial stents being modeled as a porous medium: flow simulation in stented cerebral aneurysms. Ann Biomed Eng 2011; 39: