Three-Dimensional Pulsatile Flow Simulation Before and After Endovascular Coil Embolization of a Terminal Cerebral Aneurysm

Three-Dimensional Pulsatile Flow Simulation Before and AfterEndovascular Coil Embolization of a Terminal

Cerebral Aneurysm

*Christoph Groden, †Jochen Laudan, †Scott Gatchell, and *Herrmann Zeumer

Departments of *Neuroradiology, University Hospital, Eppendorf, and †Hamburgische Schiffbau-Versuchsanstalt GmbH,Hamburg, Germany

Summary: The effect of different percentages of coil mesh ina cerebral aneurysm on the pulsatile flow and pressure in theparent vessel and aneurysm lumen was evaluated. Geometricdata on a basilar tip aneurysm and vertebrobasilar arteries aftersubarachnoid hemorrhage was obtained by computer tomo-graphic angiography. Intraarterial pressure was measured atfour vertebrobasilar points before and after treatment with de-tachable coils. Pulsatile flow was documented by transcranialultrasonography. A three-dimensional computer simulationwas created using a commercial fluid dynamics solver for fouraneurysm conditions: (1) before intervention; (2) with a 20%filling showing a complete cessation of the inflow through theaneurysm neck; (3) with a 12% filling showing an incomplete

deceleration of inflow through the aneurysm neck, with a re-maining flow around the embedded platinum coils; and (4) witha 12% filling and simulation of clotted aneurysm dome, whichdid not inhibit persisting flow phenomena. The relative pres-sure amplitudes neither increased nor decreased under thedifferent simulated aneurysm filling conditions. Insertedplatinum coils can immediately and decisively relieve theinflux of pulsating blood and allow for initial clotting. To reachthis effect, a volume density of 20% platinum coil mesh inthe aneurysm neck is needed. Key words: Cerebral aneu-rysm—Circulation—Computer simulation—Endovascular—Hemodynamics—Thrombosis.

The less invasive character of endovascular methodsfor the management of cerebral aneurysms is a redeem-ing aspect for many patients who are confronted withbrain surgery as the only alternative treatment. Particu-larly since the introduction of Guglielmi detachable coils(GDC), results are comparable with those achieved withsurgery in cases of acute aneurysm rupture (Groden etal., 1998, 2000, 2001). However, factors influencing theachieved results, especially longer-term results, are stillunder discussion. In vitro studies of aneurysm-relatedhemodynamics have focused on wall stress (Steiger etal., 1989), geometric relations (Steiger et al., 1988a),flow rate and pulsatility (Steiger et al., 1988b), and an-eurysmal flow disturbances after partial embolisation(Gobin et al., 1994; Graves et al., 1990). The alteration offlow as a major factor, even evoking spontaneous aneu-rysm regression, has been reported after treatment of

arteriovenous malformation shunts by embolization (Re-dekop et al., 1998). Angiographic follow-up studies at 1year after GDC treatment have reported a 15% coil com-paction (Byrne et al., 1999). To understand the influenceof embedded coils on the flow and pressure conditions inparent vessels and the aneurysm lumen, a three-dimensional computer model based on in vivo data wascreated. The pulsatile flow conditions of a cerebral vesselwith an aneurysm were simulated for different stages ofaneurysm occlusion.

METHODS

The present study was not necessarily focused on a detailedanatomical reconstruction of the parent vessel as reportedFoutrakis et al. (1996), but rather on creating a geometricalmodel that did not greatly vary with vessel narrowing or bend-ing, such as in terms of flow pattern with only minor influenceon the resulting calculations. The constructed model simplyapproximated the form and shape of the actual aneurysm (com-pare aneurysm in Figs. 1A and 1B with the model in Fig. 1C).To our knowledge, such an aneurysm-modeling procedure hasno parallel in the medical literature and, thus, depended oncorroboration from the fields of physics and hydraulics.

Several parameters were used to model the interactive he-modynamic aspects between intracranial vessels and aneu-rysms. The brain of a patient with a subarachnoid hemorrhage

Received May 8, 2001; final revision received August 27, 2001;accepted August 27, 2001.

Supported by a grant from Cordis Neurovascular, Miami, FL, U.S.A.Address correspondence and reprint requests to Christoph Groden,

Department of Neuroradiology, University Hospital Eppendorf, Mar-tinistrasse 52, D-20246 Hamburg, Germany.

Journal of Cerebral Blood Flow & Metabolism21:1464–1471 © 2001 The International Society for Cerebral Blood Flow and MetabolismPublished by Lippincott Williams & Wilkins, Inc., Philadelphia

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of a basilar tip aneurysm was scanned using computed tomog-raphy with 120-mL contrast medium. The simplified geometricsizes of the arteriae vertebrales, arteria basilaris, arteriae pos-teriores, and the diameters of the aneurysm lumen (14 mm) andneck (4 mm) were derived from source-data depiction (Fig.1C). For modeling purposes, the somewhat oblong-appearinganeurysm was reckoned as a sphere. The connecting arterieswere approximated to round forms (Figs. 1B and 1D).

After obtaining informed consent from the patient, intraar-terial pressure was measured at four points in the vertebrobasi-lar arteries with a 0.014-in guidewire-mounted pressure sensor(Pressure Wire Sensor, RADI Medical Systems, Uppsala, Swe-den) (see Table 1) regarding before and after treatment of thebasilar tip aneurysm with GDC. The pulsatile flow in the arteriabasilaris was documented by transcranial ultrasonography witha DWL Multi-Dop X-4 (Elektronische Systeme GmbH, Sip-plingen, Germany).

For calculation of the flow in and near the aneurysm, thesoftware package STAR-CD (Computational Dynamics, Lon-don, UK) was used. This software package solves the time-averaged Navier-Stokes equation and the continuity equation(Reynolds-averaged Navier-Stokes equations) using a finite-volume approach. The grid-generation software ICEM CFDwas used to divide the control volume into a finite number ofnonoverlapping, nonorthogonal, boundary-fitted control vol-umes, or cells (127,856 cells were used). An O-grid method(Ferziger and Peric, 1996), which is most commonly used forpipe systems to ensure good cell quality, was used to create theblock-structured grid. For each cell, the conservation equationsfor the impulse (Navier-Stokes equation) and mass (continuityequation) were set, whereby the convection and diffusion termsof the conservation equation were approximated by a centraldifference scheme. The resulting nonlinear system of equationswas solved iteratively. The coupling of the velocity with thepressure was achieved according to the PISO-method (Issa,1986). The geometry of the aneurysm and the vessels wasderived from computed tomographic data (Figs. 1A and 1B).To solve the equations, the boundary conditions of all compu-tational domains must be formulated. On the vessel walls,which were considered nonelastic, the no-slip and no-penetration conditions were applied (i.e., all velocity compo-nents at the vessel wall must be zero). At the inlet, a periodictime-varying fluid velocity was prescribed (Fig. 2). The timevariation was fitted to the measurements by transcranial ultra-sonography, which amounted to a mean-flow velocity of 0.43m/sec.

For the outlet, two possibilities formulate the boundaryconditions:

FIG. 1. (A) Maximum intensity projection of CT angiography. (B) Geometry of the simulated model. (C) Source date image. (D) The grayarea details the 7 topographic levels of the aneurysm neck, in which the coil mesh is simulated.

TABLE 1. In vivo measured vertebrobasilar blood pressurebefore and after aneurysm treatment

Measuringpoint*

P1/P2segmentof ACP

ProximalP1 segment

Level ofACS

Level ofAICA

Before intervention 100/59 99/59 100/60 102/60After intervention 101/59 100/59 100/57 100/58

Blood pressure values: systolic/diastolic (mm Hg).* Measurement tolerance according to manufacturer at 50 to 300

mm Hg � 3%.ACP, arteria cerebri posterior; ACS, arteria cerebelli superior;

AICA, arteria inferior cerebelli anterior.

COIL-INDUCED HEMODYNAMIC CHANGES IN ANEURYSMS 1465

J Cereb Blood Flow Metab, Vol. 21, No. 12, 2001

1. It is assumed that for each outlet a specified amount of thetotal inflow exits. With two outlets, the inflow is dividedequally between the two outlets only when the outletsare identical.

2. A constant pressure is prescribed to both outlet boundaries.The outflow distribution then resolves itself. All pressures inthe computational domain are referenced relative to the out-let pressure.

For both outlet boundaries, the second method was chosenand a constant pressure was prescribed. In the actual total sys-tem, of which the computational domain represents only asmall part, the pressure pulsates approximately a nonzero pres-sure. For simulation purposes, this measured absolute valuewas subtracted from the pressure definition. To obtain the ab-solute pressure, the measured absolute pressure must be addedto the relative pressure at each time step. Because this processwas transient, time was also discriminated, calculated in timesteps of 0.001 second. Each computer simulation represented areal-time sequence of 2 seconds. The calculation for one con-dition necessitated approximately 72 hours on a Hewlett-Packard (U.S.A.) 9000/782 Workstation.

The simulation was performed with the following materialconstants: blood density (�) � 1060 kg/m3; blood dynamicviscosity (�) � 0.05 Pa·sec; mean Reynolds number in thearteria basilaris (Rn) � 508. Four aneurysm filling conditionswere studied: (A) before intervention, (B) 20% filling, (C) 12%filling (same procedure as with 20% filling, but cells areblocked to produce a filling degree of 12%), and (D) 12%filling and simulation of clotted aneurysm. The procedure forthe fourth condition was the same procedure as with 12% fill-ing, with the additional parameter that cells in the aneurysmbeyond the coil blockage are filled so that only a small amountof fluid may pass (i.e., the region inside the aneurysm wasdefined in terms of porosity such that a 100% porosity repre-sented no blockage, as in the before-intervention simulation,and a 0% porosity represented full blockage, or a solid mass).For this condition we chose a 10% porosity in the entire aneu-rysm dome, beyond the simulated coiled zone at the ostium.This porosity simulated a gelatinous structure similar to theconsistency of a fresh thrombosis.

The filling of the aneurysm neck with platinum coils wassimulated by a distribution of blocked cells, as created using asimple computer routine. In the first seven cell layers of theaneurysm opening (depicted by the shaded layers in Fig. 1 D),a pattern of adjoining cells was blocked. That is, the fluid wasnot allowed to enter these cells, as if occupied by a segment of

a platinum coil. For the second filling condition (B), the num-ber of cells blocked corresponded to 20% of the cells in thisregion occupied by platinum coils, whereas for the third andfourth conditions (C, D) the number of cells blocked corre-sponded to only 12% of the cells in this region.

The pattern of cell blockage was randomly created by acomputer program according to certain guidelines. The pro-gram began by blocking a randomly selected cell within thedesignated region. The program then randomly selected an ad-joining cell, and determined whether this new cell lay withinthe seven-layer region, was not already blocked, and had nomore than two adjoining cells that were blocked. If the selectedcell fulfilled these requirements, it was also blocked and theprogram continued from this newly filled cell to another ran-domly selected adjoining cell. This process continued until thedesired filling level had been reached. To enhance simulationrealism, an element edge length of 0.4 mm in these seven celllayers was imposed, which a 0.385-mm diameter GDC 18-coilsegment could occupy.

RESULTS

Intraarterial pressure measurementThe recorded intraarterial systolic/diastolic pressure

values from the guidewire mounted pressure sensor aredisplayed in Table 1.

Flow velocityThe blood flow as evaluated by transcranial ultraso-

nography showed a mean flow of 0.43 m/sec andsystolic/diastolic values ranging from 0.52 m/sec to 0.36m/sec. The flow simulation pattern for the three-dimensional computer model was based on the adaptedsinusoidal curve as displayed in Fig. 2.

SimulationColor-coded results for the four different conditions of

aneurysm embolization grading, as described previously,were obtained from three-dimensional simulations. In thedepictions (Figs. 3 and 4), a row represents an identicalpoint of simulation corresponding to the four differentconditions of the aneurysm lumen (A–D). Time variescolumnwise, and is adjusted along the pulsatile flow. Thepoint for Figs. 3 and 4 corresponds with the depiction of

FIG. 2. Simulated blood flow velocity v(m/second)* in the basilar artery. The vertical dotted lines represent the four time points of thedifferent aneurysm filling conditions calculated in Figs. 3 and 4. *Sensibility of velocity measurement according to manufacturer = min. 0.1m/second, max. = 2.5 m/second.

C. GRODEN ET AL.1466


the vertical dotted lines in Fig. 2. The pulsatile pressurevalues are shown in Fig. 3, and the simulated pulsatileflow values are plotted in Fig. 4.

In Fig. 3 the color coding represents the simulatedpressure values of the aneurysm lumen with a graduationof 100 N/m2 per step. The chosen figures are coronalmiddle sections expressed in color code, which is shownin the bottom code row. The relative pressure amplitudesshowed no significant difference in the different simu-lated aneurysm filling conditions. Only column D (fillingdegree of 12% and dome clotting) showed an increase ofthe maximum pressure plane at the neck and clotting coilmesh interface.

In Fig. 4 the color coding represents the simulatedflow values of the aneurysm lumen with a graduation of0.005 m/sec per step. The chosen depictions are coronalmiddle sections expressed in color code, as is shown inthe bottom code row. Column B, which simulates a 20%filling degree of the aneurysm neck, depicts a completedeceleration of the inflow, even at the maximum flow inthe parent vessel. Column C, which simulates a 12%

filling degree of the aneurysm neck, depicts an incom-plete cessation of inflow, showing a remaining flowaround the embedded platinum coils. It should bestressed that an additional clotting simulation of the an-eurysm dome (column D) did not inhibit this persistingflow phenomena. In Fig. 5, the color coding representsthe simulated blood flow vectors of every single voxel ofthe native untreated aneurysm in front of the simulatedcoiled zone at the ostium in Figs. 4 B, C and D.

DISCUSSION

The use of models implies a reality reduction on al-legedly substantial constituents. This loss of reality iswell demonstrated by the difference in the appearance ofthe real aneurysm (Fig. 1A) compared with the depictionof the simulated aneurysm (Fig. 1B) based on source data(Fig. 1C). This procedure, however, also includes a riskof the loss of one or several integral reality references.Therefore, restrictions and simplifications for a modelsimulation of the hemodynamic effects during endovas-cular therapy for cerebral aneurysm had to be postulatedunder certain given considerations.

FIG. 4. Color-coded blood flow values in different stages ofocclusion.

FIG. 3. Color-coded pressure values in different stages ofocclusion.



The three critical blood-flow variables—pressure, re-sistance, and speed—had to be determined. A pressuregradient must exist to overcome friction resistance con-sisting of the combination of internal frictional resistanceand wall friction, and to transport a specific amount offluid through a given conduit (vessel) system at a spe-cific speed. This “relative pressure” consists of the cru-cial difference between inlet and outlet pressure. The onedeterminable entity, the specific speed of the incomingfluid (blood), could be determined by ultrasonic mea-surements. The other two variables, friction and resis-tance and relative pressure, could be calculated. In the

present evaluation all given pressures refer to the pres-sure at the outlet boundary for all intervals.

The cycles of individual blood pulsations were brokeninto small separated segments so that a fully implicitsolving scheme could be used (Ferziger and Peric, 1996;Richtmeyer and Morton, 1967). To hold the computa-tional expenditure within limits, neither the elasticity ofthe vessels nor that of the aneurysm, which is weakenedbecause of the pathologically changed wall construction,was considered in the specifications for the hemody-namic effects. With a steady current, the error causedwould be negligible. However, with an intermittent

FIG. 5. Blood flow vectors at the aneurysm neck.



current, occurring pressure peaks are smoothed (bellowprinciple) depending on the elasticity. This simplificationwould lead overestimation of simulated pressure values.

The Reynolds number, which is calculated accordingto the formula Rn � D V � / � (whereby D is the vesseldiameter, V is the midfluid flow velocity, � is the den-sity, and � is the fluid viscosity) was calculated for theentire simulation model by the value of the Arteria basi-laris. The corpuscle blood constituents were only in-cluded in the calculations regarding the viscosity of theliquid with � � 0.05 Pa/sec and the density of the simu-lated liquid (� � 1060 kg/m3 ). The viscosity of blood asa non-Newtonian fluid, however, does not remain con-stant; a reduction of the viscosity values occurs under theeffects of shearing stresses or acceleration. The effects ofvessel branching on viscosity in cases of aneurysms arenot uniformly judged in the literature. Works by Liepschand Moravec (1984) and by Ku and Liepsch (1986)proved the differences in the flow behavior between aNewtonian and a non-Newtonian fluid. However, in anexperimental work by Steiger et. al. (1988b), no signifi-cant difference in behavior was observed between New-tonian and non-Newtonian fluid in a laser-Doppler in-vestigation of experimental aneurysms. For our model, amean Reynolds number of 508 (maximum, 614; mini-mum, 421) was used. For such an order of magnitude, theinertial forces are dominant in relation to the viscousforces; therefore, the behavior of a Newtonian fluid wasjudged as sufficient for the selected simulation condi-tions. Coagulation leading to a pronounced reduction andstasis of the blood flow was simulated in a simplifiedform as a 90% reduction of the blood flow in the aneu-rysm dome. This was only brought into the calculationfor condition D (Figures 3 and 4, column D).

Hemodynamic effects due to embedding ofplatinum coils

Similar to our simulation results for terminal aneu-rysms, an in vitro study by Gobin et al. (1994) showedthat the blood flow pulsatility into side-wall aneurysmscould be clearly and significantly reduced after insertionof a single platinum coil. In line with that finding, therewas also no effect on pressure-gradient changes betweenparent vessels and the aneurysm lumen in the presentstudy. By reducing blood flow into the aneurysm to thezero point, a coagulative cascade can be evoked thatleads to thrombosis formation and eventually to aneu-rysm clotting. Such mechanisms have been described inthe literature on histologic examinations in animals aftercoil occlusion (Tenjin et al., 1995) and in an autopsyduring which a thrombolized clot consisting of fibrin andthrombocytes was found 36 hours after coil insertion(Stiver et al., 1988). It is presumed that such an endo-vascular treatment prevents spontaneous hemorrhages,which often occur in untreated aneurysms. The hemody-

namic pressure imposed on the inserted platinum coilmesh is dissipated over the wall of the aneurysm cavitythat combined with the reaction of the aneurysm wallagainst the foreign body (coil) initiates a cellular orga-nization of the initially unorganized blood clot into a scarformation, resembling a normal wound healing process(Shimizu et al., 1999; Horowitz et al., 1997).

Ideally, endovascular therapy (aneurysm occlusion)seeks to achieve the goal of roentgen intransparency,which can be achieved by a filling of approximately 25%(Castro et al., 1999) of the aneurysm lumen with plati-num coils. In vitro studies (Satoh et al., 1997; Mandai etal., 1998) have shown a maximum filling of 25% to 35%in silicone or glass aneurysm models. A study by Mandaiet al. (Mandai et al., 1998) confirms that results of invitro fillings are higher than in vivo results and corre-sponds with our clinical experience. Therefore, we mini-malized the maximum filling with coils to 20%. Thefilling reduction to 12% was based on the filling calcu-lation of numerous nondensely packed aneurysms ob-served with coil condensation or coil displacement. Thepattern of cell blockage was uniformly distributed acrossthe first seven cell levels of the aneurysm ostium (seeFig. 1D). The reduction of the in vivo embedded coilfilling in the aneurysm lumen to a seven-coil diameterthick area at the aneurysm neck is not a disadvantage forthe force of expression of the model, because even a 20%filling of the aneurysm neck (Fig. 1D) with platinumcoils can decelerate the aneurysm flow to zero. Thissimulation result can only be explained by a significantvariation of the blood column flow in this neck area dueto a resolution of force by the platinum coil mesh. There-fore, we did not simulate the filling of the whole aneu-rysm dome with platinum coil mesh. A further benefit ofthis reduction was the better observation of the residualflow effects due to a reduced neck filling (12% Figs. 3and 4, column D) at the interface of coil simulation andaneurysm dome.

If an adequate density of the platinum spirals in theaneurysm dome and at the portal (neck) has not beenachieved, a constant water-hammer effect (Kwan andHeilman, 1991) can lead to a “settling” or rearrangementof the coil tuft, albeit not enough to cause single-coilsegments to be exposed to the blood flow of the parentvessel, which could enhance lysis of the forming throm-bus. In cases of coil migration, various effects on theareas around or immediately between coil segmentshave been reported, including aneurysm recanalization(Debrun et al., 1998a,b; Gruber et al., 1999; Vinuela etal., 1997; Turjman et al., 1998), nonreactive thrombuscores without macrophage immigration or scar formation(Molyneux et al., 1995), and thrombus developmentfrom the aneurysm periphery (Shimizu et al., 1999).Ideally, thrombosis formation continues until a stable



endothelium has developed as the final healing step(Castro et al., 1999). However, if the spiral coil meshdensity is not high enough (e.g., 12% as in Figs. 4C and4D), spiral segments can extend out of the thrombus andbe exposed to the blood flow at the aneurysm neck (Mac-donald et al., 1998). This nonthrombolized, uncoatedpart of the mesh “pulls” or “pushes” the rest of the meshinside the aneurysm lumen, enhancing coil compactionwithin aneurysm lumen. A partial aneurysm recanaliza-tion can lead to aneurysm growth and relapsed subarach-noidal bleeding (Kuether et al., 1998). The density of themesh may also be important because a higher mesh den-sity reduces the possibility of large viscous inner vol-umes within the spiral “tuft.” At regular 1-year angio-graphic follow-up examinations, coils or coil mesheshave been found to have changed their positions in up to15% of all cases (Byrne et al., 1999).This finding ex-plains the relation between a stable occlusion rate and theratio of the aneurysm neck width to aneurysm diameter,as reported in the literature (Debrun et al., 1998a,b; Gru-ber et al., 1999; Vinuela et al., 1997; Turjman et al.,1998; Satoh et al., 1998)

In conclusion, the three-dimensional simulation of en-dovascular coil treatment of intracranial aneurysmsbased on in vivo measurements shows both cause andeffect on the local hemodynamics. The inserted platinumcoils immediately and decisively relieve the influx ofpulsating blood and allow for initial clotting. The densityof the installed coils in both the aneurysm dome and atthe orifice plays an important role in further develop-ments; only then can the occlusion process develop. Fora permanent occlusion and undisturbed scar formation, azero-point reduction of the blood flow has to be attainedat the interface of the parent vessel and aneurysm neck toavoid thrombolysis of the fresh clotting and subsequentcoil migration. To achieve this effect, a volume densityof approximately 20% platinum coil mesh in the aneu-rysm neck is needed.

The presented simulation of an in vivo aneurysm suf-fers from the inexactness of the modeling procedure,which could be improved through further research. In ourcenter, studies of the influence of asymmetric outflowbranches in cases of terminal aneurysms, different necksizes, and the modeling of side-wall aneurysm manage-ment are currently underway. Special attention could beplaced on perfecting the simulation of aneurysm irregu-larities (e.g., length, width, indentations caused by bonystructures) and the relative effect of the relation betweencoil density and the proportionate size of neck to theaneurysm. Factors effecting partial thrombosis may alsobe discovered through improved modeling procedures.

Acknowledgment: The authors thank Dr. Jarold Knispel forhis advice regarding language.

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Three-Dimensional Pulsatile Flow Simulation Before and After Endovascular Coil Embolization of a Terminal Cerebral Aneurysm

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