## Abstract

As frequency of endovascular treatments for intracranial aneurysms increases, there is a growing need to understand the mechanisms for coil embolization failure. Computational fluid dynamics (CFD) modeling often simplifies modeling the endovascular coils as a homogeneous porous medium (PM), and focuses on the vascular wall endothelium, not considering the biomechanical environment of platelets. These assumptions limit the accuracy of computations for treatment predictions. We present a rigorous analysis using X-ray microtomographic imaging of the coils and a combination of Lagrangian (platelet) and Eulerian (endothelium) metrics. Four patient-specific, anatomically accurate in vitro flow phantoms of aneurysms are treated with the same patient-specific endovascular coils. Synchrotron tomography scans of the coil mass morphology are obtained. Aneurysmal hemodynamics are computationally simulated before and after coiling, using patient-specific velocity/pressure measurements. For each patient, we analyze the trajectories of thousands of platelets during several cardiac cycles, and calculate residence times (RTs) and shear exposure, relevant to thrombus formation. We quantify the inconsistencies of the PM approach, comparing them with coil-resolved (CR) simulations, showing the under- or overestimation of key hemodynamic metrics used to predict treatment outcomes. We fully characterize aneurysmal hemodynamics with converged statistics of platelet RT and shear stress history (SH), to augment the traditional wall shear stress (WSS) on the vascular endothelium. Incorporating microtomographic scans of coil morphology into hemodynamic analysis of coiled intracranial aneurysms, and augmenting traditional analysis with Lagrangian platelet metrics improves CFD predictions, and raises the potential for understanding and clinical translation of computational hemodynamics for intracranial aneurysm treatment outcomes.

## 1 Introduction

Intracranial aneurysm rupture accounts for nearly 5% of all strokes in the U.S., and a majority of ruptured aneurysms result in death or disability [1]. Hemodynamic stresses on the aneurysmal region are closely linked to initiation, growth, and rupture of intracranial aneurysms. Thus, treatment of aneurysms involves isolating the aneurysmal sac from blood flow to eliminate or reduce hemodynamic stresses [24]. Endovascular treatment is quickly becoming the preferred approach to treating intracranial aneurysms, owing to its minimally invasive nature [5,6]. Despite its benefits, endovascular treatment currently carries a risk of failure of up to 40% [7], and retreatment is associated with procedure-related risks in addition to increased healthcare costs [8]. Improving the efficacy of endovascular treatment and predicting treatment outcomes better are unmet needs that would lead to better stroke prevention and improved clinical care.

Endovascular coiling of intracranial aneurysms aims to fill the aneurysmal sac with metal coils deployed via a catheter, to impede and reduce the flow of blood into the aneurysm [9,10]. Increasing blood residence time (RT) within the aneurysmal sac, coupled with the thrombogenic nature of metal coils, is thought to activate platelets and lead to a stable thrombus that results in aneurysmal occlusion and prevents rupture [6,11]. Treatment failure occurs when there is persistent blood flow in the aneurysm, increasing the risk of rupture and often requiring retreatment [12,13]. Understanding how endovascular coils modify the flow of blood in and around the aneurysmal sac is essential in understanding treatment strategies and predicting treatment outcome.

Since measurement of flow inside intracranial aneurysms after endovascular treatment is not possible in vivo, computational fluid dynamics (CFD) is a useful tool to study aneurysmal hemodynamics [1416]. However, CFD modeling of aneurysmal blood flow after treatment requires a number of simplifying assumptions. Simplification of boundary conditions can be overcome through patient-specific measurements of blood pressure and flow velocity, which have been shown to improve CFD simulation accuracy [12,16,17]. Most CFD simulations of coiled aneurysms idealize the endovascular coil mass as a homogeneous and isotropic porous medium (PM) that fills the entire aneurysmal sac. This is due to the difficulty in obtaining coil morphology images in vivo, since available imaging modalities cannot resolve the coils as deployed in the sac [15,1820]. Recent advancements in computational methods have led to the development of virtual coiling techniques [2124]. However, the accuracy of virtual coil morphologies compared to coil configurations in vivo or in vitro is yet to be established.

Eulerian hemodynamic metrics have traditionally been used to quantify the change in blood flow patterns and stresses on the aneurysm and surrounding vessels. Metrics such as wall shear stress (WSS), wall shear stress gradient (WSSG), oscillatory shear index (OSI), flow into the aneurysm (QAneurysm), and relative residence time (RRT) have been used to try to understand how aneurysm coiling correlate to treatment outcomes. The influence of platelets on thrombus formation, however, has not been taken into account. Lagrangian platelet metrics have been introduced in cardiovascular disease investigations to quantify thrombogenicity of left ventricular dysfunction, artificial valves, and left ventricular assist devices [2528]. This method provides a statistical description of platelet trajectories, yielding a distribution of probability of platelet activation. Applying this technique to intracranial aneurysms has not been previously explored, and may augment the potential of CFD analysis to predict if coil embolization promotes stable thrombus formation in the aneurysmal sac [2931].

We present high-resolution, coil-resolved (CR) models of endovascularly treated aneurysmal flow models, obtained from synchrotron X-ray microtomography. For the first time, we couple in vitro synchrotron imaging of endovascular coil morphology, overcoming the simplifications of traditional CFD methods, with Lagrangian analysis, individually tracking thousands of platelets in the aneurysmal region and augmenting traditional Eulerian CFD metrics. The impact of this novel methodology is investigated by comparing hemodynamics inside aneurysms modeled with PM or CR representations, quantifying the influence of accurate representation of the coil morphology. Similarly, platelet residence times and platelet shear exposure are evaluated by comparing Eulerian versus Lagrangian metrics on the coil-resolved hemodynamics model.

## 2 Methods

### 2.1 Patient Data.

Four patients with unruptured cerebral aneurysms who had undergone endovascular coil embolization treatment at the University of Washington's Harborview Medical Center were enrolled after obtaining informed consent, in a protocol approved by the University of Washington's institutional review board. Three-dimensional (3D) rotational angiography was obtained immediately before and after treatment for patient-specific model creation. Endovascular measurements of blood pressure and velocity were obtained immediately before and after treatment using a dual-sensor pressure and Doppler velocity guidewire and analysis workstation (ComboWire and ComboMap, Volcano Philips, San Diego, CA), every 5 ms in at least four peri-aneurysmal locations. These measurements were incorporated as patient-specific boundary conditions for CFD, and used for validation of the results, as described previously [32].

Patient and aneurysm characteristics are shown in Table 1. All patients were treated with Target endovascular coils (Stryker Endovascular, Kalamazoo, MI). Coiling in patient 2 was assisted with an Enterprise stent (Codman Neuro/DuPuy Synthes, Raynham, MA). Doppler guidewire measurements were successful in all patients.

Table 1

Patient and aneurysm characteristics

Patient no.Aneurysm locationAneurysm volume (mm3)No. of coilsTotal coil length (cm)Aneurysm packing density (%)
1Right posterior communicating internal carotid artery44.1032728.22
2Basilar trunk86.4033519.21
3Left supraclinoid internal carotid artery66.5032417.71
4Basilar trunk92.4064624.43
Patient no.Aneurysm locationAneurysm volume (mm3)No. of coilsTotal coil length (cm)Aneurysm packing density (%)
1Right posterior communicating internal carotid artery44.1032728.22
2Basilar trunk86.4033519.21
3Left supraclinoid internal carotid artery66.5032417.71
4Basilar trunk92.4064624.43

### 2.2 Patient-Specific Aneurysm Model Creation

#### 2.2.1 In Silico Segmentation of Aneurysm and Surrounding Vasculature.

Three-dimensional reconstructions of the lumen including the aneurysm and surrounding vessels were created by image segmentation of the 3D angiographic data with the Vascular Modeling Toolkit2 software. The segmentations underwent smoothing, while maintaining high fidelity at regions of interest such as bifurcations and vessel constrictions. Vasculature of the aneurysmal sac and surrounding vessels were isolated and converted to stereolithography format for further in silico and in vitro processing.

#### 2.2.2 In Vitro Aneurysm Phantom Creation.

A detailed description of in vitro phantom creation has been published [33,34]. Briefly, each aneurysm lumen was 3D printed on Flash Forge Creator Pro (Flashforge, Rowland Heights, CA) printers at true anatomical scale, with a resolution of 100 μm. The prints were smoothed and coated (XTC-3D, Smooth-on, Macungie, PA) for casting. Optically clear silicone phantoms were created using a multistep “lost wax casting technique.” An intermediate mold was created by casting the smooth 3D printed models in translucent silicone (Sorta-Clear 12, Smooth-on) and then slicing the negative molds along the model centerlines to remove the 3D printed positive. A water-soluble wax positive (Freeman Optical Soluble Wax, Freeman Manufacturing and Supply Company, Avon, OH) was created using the intermediate mold. The wax positive was then casted in a silicone elastomer (Sylgard 184, Dow Corning Corp., Midland, MI), which was allowed to cure at room temperature for up to 48 h. Finally, the wax model was dissolved in water resulting in the final silicone flow phantom.

#### 2.2.3 Model Treatment and X-Ray Microtomography of Endovascular Coils.

Each silicone flow phantom was treated by experienced neurosurgeons with clinically available endovascular coils, replicating each patient's actual treatment. All treated phantoms were then imaged by a monochromatic X-ray beam at the European Synchrotron Radiation Facility3 in Grenoble, France [34]. Each phantom was rotated 360 deg with respect to an axis perpendicular to the beam and the scan data was deconvoluted into a 3D volume distribution with different attenuation coefficients attributed to different materials (silicone/air/coil). The resulting spatial resolution was between 12 μm and 13 μm in all three directions. Segmentation was performed on the 3D imaging data using ImageJ4 to reconstruct the 3D coil microstructure. Endovascular coil segmentation was verified by comparing the volume of the resulting coil geometry with the known volume of the physical coils placed in each patient model based on manufacturer specifications. Segmented coils for all four patients are shown in Fig. 1.

Fig. 1
Fig. 1
Close modal

### 2.3 Modeling Endovascular Coil Treatment as a Homogeneous Isotropic Porous Medium.

To determine the effect of idealizing the coil mass as a homogeneous isotropic PM, CFD simulations of the flow with the coils represented using this method were also performed in each patient.

As is standard in the porous medium approach, the endovascular coils were assumed to occupy the entire aneurysmal sac volume as a homogeneous isotropic medium. The slowdown of blood flow due to the PM representation of the coils was incorporated via inertial and viscous pressure loss terms in the fluid momentum equations. Coil permeability and form factor, two crucial parameters contributing to the pressure loss terms, were modeled using the Kozeny capillary theory and empirically obtained parameters, respectively [34].

The complete geometry including the parent vessel and aneurysmal sac was meshed in StarCCM+ (Siemens PLM software, Plano, TX) using tetrahedral meshes. As an example, the mesh for patient 1's porous medium simulations consisted of 1.6 × 106 mesh elements. Details of the computational models for patients 2–4 are available in the Supplemental Materials on the ASME Digital Collection.

### 2.4 Modeling Endovascular Coil Treatment Using Coil-Resolved Microtomography.

The coil mass recreated from microtomography (from Sec. 2.2.3) was meshed for the CFD simulations. Using MeshMixer,5 each patient's coils were located inside the aneurysm of each CFD simulation from Sec. 2.2.1. Due to the close proximity of the various coils, some surfaces of the individual coils merged with the neighboring ones. Such surfaces were converted into volumes and the coil mass was separately discretized using grid sizes as small as 20 μm. As an example, the mesh for patient 1's coil-resolved model consists of 10.5 × 106 elements. Data for the patients 2–4 is available in the Supplemental Materials on the ASME Digital Collection.

### 2.5 Computational Fluid Dynamics Simulations

#### 2.5.1 Patient Boundary Conditions.

For all patients, inlet boundary conditions were specified as a time-dependent Womersley velocity profile based on the in vivo patient-specific Doppler guidewire measurements as described in the methods [32]. Briefly, ComboWire in vivo velocity measurements are averaged for ten cardiac cycles and used as the waveform for inlet velocity as a Womersley profile. Patient vasculatures with a single outlet used a zero-pressure outlet condition. Models with multiple outlets used two-element Windkessel models to prescribe the patient-specific flow splits, as described previously [35]. The systolic and time-averaged inlet flow rates into the parent vessel are provided in Table 2.

Table 2

Systolic and time-averaged flow rates into the parent vessel

Patient no.Inlet flow rate systolic (mL/min)Inlet flow rate time-averaged (mL/min)
1416.01226.47
291.3254
3235.53132.6
4183.295.66
Patient no.Inlet flow rate systolic (mL/min)Inlet flow rate time-averaged (mL/min)
1416.01226.47
291.3254
3235.53132.6
4183.295.66

#### 2.5.2 Simulating Blood Flow.

Aneurysmal hemodynamics were simulated with the unsteady Navier–Stokes equations, modeling blood as a homogeneous, Newtonian fluid with a density of 1050 kg/m3 and a viscosity of 0.0035 Pa·s. A second-order spatial discretization using the PISO scheme and a second-order implicit scheme for temporal calculations were used. The temporal resolution of the CFD simulations varied from O (0.001 s) for the Eulerian, porous medium simulations to O (0.0001 s) for the coil-resolved simulations. As mentioned earlier, CFD mesh sizes varied from 1.6 × 106 elements for the porous medium simulations to 10.5 × 106 elements for the coil-resolved simulations, with individual mesh sizes as small as 20 μm. To avoid the influence of transients, the first two cardiac cycles were discarded and the next eight cardiac cycles were considered for analysis in each case. For each patient, three simulations were performed using the finite volume solver (FLUENT V17, ANSYS, Inc., Canonsburg, PA): (i) before endovascular treatment, (ii) after endovascular treatment using PM to represent the coil mass, and (iii) after endovascular treatment with a CR representation of the coil microstructure.

#### 2.5.3 Lagrangian Platelet Tracking.

Platelets were simulated as inertialess particles, initially seeded throughout the vascular domain uniformly, and then injected at the inlet of the parent vessel every 1/10th of a second for eight consecutive cardiac cycles. Platelets were individually tracked until they exited the vascular domain or until the end of the eighth cardiac cycle. To analyze intra-aneurysmal thrombus formation, thrombogenic indices based on the RT and shear stress history (SH) of all the platelets were evaluated.

The particle RT was calculated by tracking the time each particle remained in the aneurysmal sac
$RTi=Tientrance−Tiexit$
where $i$ represents each platelet,$Tientrance$ represents the time the platelet crosses the aneurysm neck surface (or the beginning of the first cardiac cycle if it is platelet seeded initially), and $Tiexit$ represents the time the platelet trajectory exits the sac (or the end of the eighth cardiac cycle). SH was determined as the accumulated shear stress on each platelet along its trajectory
$SH= ∫t0tτ(X(t′),t′)dt′$

where $τ$ is the instantaneous shear stress magnitude at time $t′$ and $X(t′)$ is the platelet's location at that time. Platelet density was such that every platelet was representative of one million platelets in the human circulation. Randomly sampled platelet densities were analyzed to determine statistical independence (i.e., increasing platelet densities does not alter the results presented in this work). More details of the Lagrangian platelet hemodynamic metrics are available in our published work [25,36].

#### 2.5.4 Hemodynamic Metrics.

For each patient, Eulerian metrics (WSS, WSSG, time-averaged WSS (TAWSS), OSI, RRT, QAneurysm) were evaluated before and after endovascular treatment. RRT is an estimate of near-wall transport and residence time determined from the inverse of the TAWSS. QAneurysm is determined by calculating flow across the aneurysm neck as defined by a three-dimensional, surface that wraps around the parent vessel, that is also used to delineate the border of aneurysmal sac from the parent vessel for Lagrangian analyses of intra-aneurysmal RT. Additionally, neck plane shear stress was also evaluated by quantifying the WSS at the neck surface. All parameters were calculated at peak systole and also averaged over the entire cardiac cycle. Comparisons were performed between pre- and posttreatment simulations for both the PM and CR approaches using both platelet-based (Lagrangian) and endothelium-based (Eulerian) hemodynamic metrics. Detailed statistical analysis of the platelet RT and SH distributions, including median and outlier behavior, are presented and discussed in order to elucidate the hemodynamic differences between PM and CR approaches in the presence of individually tracked platelets.

## 3 Results

Results for each treatment modality are described in detail for patient 1, including both the Eulerian and Lagrangian hemodynamics. The results for patients 2–4 are briefly summarized as they relate to those in patient 1, with detailed analysis available in the Supplemental Materials on the ASME Digital Collection.

### 3.1 Pretreatment.

The aneurysm in patient 1 was located on the right internal carotid artery (ICA) proximal to the posterior communicating artery bifurcation. Given its location and orientation, blood flow in and around the aneurysm changed widely and possibly chaotically, through the cardiac cycle, including jet impingement on the distal aneurysmal neck and part of the dome, and a complex recirculating pattern in the sac, as seen in the left panel of Fig. 2. A propagating vortex ring, a hallmark of jet impingement on the aneurysmal wall, can be seen in the aneurysm sac. This created a region of high WSS and WSSG on the medial aneurysmal wall, as can be seen in the left panel of Figs. 3 and 4.

Fig. 2
Fig. 2
Close modal
Fig. 3
Fig. 3
Close modal
Fig. 4
Fig. 4
Close modal

Lagrangian analysis of hemodynamics that characterized the platelet environment within the aneurysm indicated that platelets entering the aneurysm did not recirculate within the aneurysmal volume for long periods of time, with a median RT of 0.04 s (Fig. 5, left panel). More than 85% of platelets that entered the aneurysm exited within the first second (Figs. 6 and 7), demonstrating constant motion of blood within the aneurysmal sac.

Fig. 5
Fig. 5
Close modal
Fig. 6
Fig. 6
Close modal
Fig. 7
Fig. 7
Close modal

### 3.2 Post-treatment.

Blood flow patterns differed significantly between the PM and CR simulations of the posttreatment hemodynamics, with smoother, more averaged intra-aneurysmal flow in the PM simulations. In the PM case, the coil mass distributed throughout the entire aneurysmal volume reduced flow into the aneurysmal sac by 51%, summed over the entire cardiac cycle. This had a significant effect on the time-averaged WSS and WSSG, which were reduced by 80 and 70%, respectively, compared to the untreated case (Figs. 3 and 4). Consequently, the OSI, an endothelial metric quantifying shear stress directional change derived from the WSS vector, showed a 97% reduction, and the RRT on the aneurysmal wall (derived from the magnitude of TAWSS), increased commensurately by a disproportionate 750% (Table 3). The platelet hemodynamic environment also indicated a significant change, with a wide spread of long residence time platelets. Specifically, the PM case resulted in a 224% increase in platelets spending more than a threshold of 3 s (arbitrarily chosen but robust), compared to the pretreatment case (Fig. 5 left panel, middle plot). As expected, this slow-moving blood flow subjects the platelets to very low shear stresses—there was a 35% reduction in the median SH compared to the untreated case (Fig. 5).

Table 3

Eulerian hemodynamic metrics before and after treatment for both porous medium and coil-resolved methods of representing the aneurysm coil mass in patient 1

MetricPrePorous mediaCoil resolved
Wss (Pa)Systolic6.811.252.24
TA2.390.470.81
WSSG (Pa/m)Systolic1.74 × 1044.87 × 1031.27 × 104
TA6140.221844.994466.64
Neck Shear (Pa)Systolic9.1414.939316.35
TA4.1462.1276.634
OSI0.03710.0007910.011
RRT (s)1.2810.95710333.2
Qaneurysm (mL/min)Systolic74.9444.5161.13
TA39.4919.3228.37
MetricPrePorous mediaCoil resolved
Wss (Pa)Systolic6.811.252.24
TA2.390.470.81
WSSG (Pa/m)Systolic1.74 × 1044.87 × 1031.27 × 104
TA6140.221844.994466.64
Neck Shear (Pa)Systolic9.1414.939316.35
TA4.1462.1276.634
OSI0.03710.0007910.011
RRT (s)1.2810.95710333.2
Qaneurysm (mL/min)Systolic74.9444.5161.13
TA39.4919.3228.37

In contrast to the PM case, the CR simulations demonstrated complex blood flow patterns in and around the coil mass within the aneurysmal volume. Since the coil mass is not homogeneously distributed in the aneurysm, there are regions of relatively high velocity flow especially at the aneurysmal neck, leading to a realistic reduction of 28% in time-averaged QAneurysm (compared to 51% reduction for the PM case). Figure 8 shows a close-up of streamlines in the CR simulation; visual inspection suggests that the flow entering the aneurysm is redirected through the small gaps between the individual coils. This leads to a highly heterogeneous distribution of blood velocities in the neck, sac interior and near the aneurysmal walls, determined by the local coil morphology.

Fig. 8
Fig. 8
Close modal

In the CR simulations, endothelial metrics such as WSS and WSSG indicate the effect of heterogeneity in Figs. 3 and 4. There are smaller reductions in WSS and WSSG (67% and 27%, respectively), compared to the PM simulations. This more realistic reduction in QAneurysm is further characterized by Lagrangian analysis: Median platelet RT and median SH decrease by 25% and 12.5%, respectively, for the CR case. As shown in Figs. 6 and 9, platelets in the CR simulation have much more diverse trajectories, with a wide range of intra-aneurysmal RTs (and SH) in the statistical distribution of platelets as different platelets that enter the aneurysmal sac flow at widely different velocities and for widely different times and separations from the walls. This is in contrast with the PM simulation, where the distributions are much more tightly packed, consistent with the homogeneous and isotropic filling of the aneurysmal sac creating uniform flow patterns. Platelets traverse only the space available to them in between the coils, as shown in the right panel of Fig. 6. Consequently, once trapped between the coils, platelets spend far longer within the aneurysm in the CR simulation. The percentage of platelets that spend longer than a threshold of 3 s in the aneurysmal sac increases by over 3000% (a result robust to changes in this arbitrarily chosen RT threshold), compared to an increase of only 224% for the PM simulation (Figs. 5 and 9, Table 4).

Fig. 9
Fig. 9
Close modal
Table 4

Changes in Eulerian and Lagrangian hemodynamic metrics posttreatment for both porous media and coil-resolved simulations for patients 1–4 (P1–4)

% change P1% change P2% change P3% change P4
MetricPorous mediaCoil resolvedPorous mediaCoil resolvedPorous mediaCoil resolvedPorous mediaCoil resolved
Eulerian (endothelium-based) metricsWSS (Pa)Systolic−81.51−67.07−80.48−84.28−56.48−1.60195.46253.01
TA−80.43−66.46−82.87−83.10279.73781.471717.392377.87
WSSG (Pa/m)Systolic−71.93−26.53−77.68−53.4823.75257.69389.37804.16
TA−69.9527.26−79.63−51.471000.192651.573123.906373.48
Neck shear (Pa)Systolic−45.9778.86−68.13−29.32−1.58209.02−15.2564.35
TA−48.6959.99−73.16−38.38−13.82174.57−30.5054.16
OSI−97.87−70.35−6.30123.17−1.50 × 1017−1.48 × 10182.40 × 1017−1.89 × 1017
RRT (s)755.7455.51 × 106202.94318.77−50.73509.40−60.16−54.41
QAneurysm (mL/min)Systolic−40.61−18.42−83.20−85.33−35.732.84−14.92−6.48
TA−51.07−28.15−87.57−87.80−51.52−10.51−35.71−18.80
Lagrangian (platelet-based) metricsMedian RT (s)−75.00−25.00760.06145.45200−72.737860.00−40.00
RT outliers (>3 s)224.003383.08526.82171.56936.9521.672014.58112.30
Median SH (Pa·s)−35.42−12.50−15.7952.63−24.07−22.22−52.389.52
SH outliers (>3 Pa·s)−39.68−8.09−34.6765.68−59.50−52.696138.10−7.14
% change P1% change P2% change P3% change P4
MetricPorous mediaCoil resolvedPorous mediaCoil resolvedPorous mediaCoil resolvedPorous mediaCoil resolved
Eulerian (endothelium-based) metricsWSS (Pa)Systolic−81.51−67.07−80.48−84.28−56.48−1.60195.46253.01
TA−80.43−66.46−82.87−83.10279.73781.471717.392377.87
WSSG (Pa/m)Systolic−71.93−26.53−77.68−53.4823.75257.69389.37804.16
TA−69.9527.26−79.63−51.471000.192651.573123.906373.48
Neck shear (Pa)Systolic−45.9778.86−68.13−29.32−1.58209.02−15.2564.35
TA−48.6959.99−73.16−38.38−13.82174.57−30.5054.16
OSI−97.87−70.35−6.30123.17−1.50 × 1017−1.48 × 10182.40 × 1017−1.89 × 1017
RRT (s)755.7455.51 × 106202.94318.77−50.73509.40−60.16−54.41
QAneurysm (mL/min)Systolic−40.61−18.42−83.20−85.33−35.732.84−14.92−6.48
TA−51.07−28.15−87.57−87.80−51.52−10.51−35.71−18.80
Lagrangian (platelet-based) metricsMedian RT (s)−75.00−25.00760.06145.45200−72.737860.00−40.00
RT outliers (>3 s)224.003383.08526.82171.56936.9521.672014.58112.30
Median SH (Pa·s)−35.42−12.50−15.7952.63−24.07−22.22−52.389.52
SH outliers (>3 Pa·s)−39.68−8.09−34.6765.68−59.50−52.696138.10−7.14

Patients 2–4 show similar trends, with the PM simulations overestimating the reduction in flow into the aneurysm (Table 4). Additionally, shear stress at the aneurysmal neck plane was also underestimated using the PM method for all four patients. This exaggerated effect of treatment on hemodynamics was also found in the platelet RT. Moreover, the combination of platelet-based analysis and CR simulations diverged from the PM simulations for patients 3 and 4. For example, for patient 3, the PM approach predicts a 200% increase in median residence times, while the CR approach predicts a 72% reduction. However, both the PM and CR approaches predict an increase in outlier platelets (those circulating beyond the 3 s threshold), which are the focus of our analysis. In addition, the percentage of platelets with prolonged (>3 s) RT was overestimated for patients 2–4 using the PM approach (Table 4). Statistical analysis of platelets reveals the lack of relevance of median RT for both PM and CR simulations—the long tails of the distribution of platelets spending long times within the aneurysmal sac are the most promising predictors of thrombogenicity. For all four patients, CR simulations reveal the likelihood of platelets spending more than the arbitrarily chosen threshold of 3 s, which is significantly different than those predicted by the PM approach (see implications in Discussion section). More details of Lagrangian results for patients 2–4 are available in the Supplemental Materials on the ASME Digital Collection.

## 4 Discussion

As endovascular therapy for intracranial aneurysm treatment becomes increasingly prevalent, accurate methods to characterize the effect of treatment are needed to predict the risk of failure, in an effort to reduce failure rates and improve outcomes [1,5,12]. Hemodynamics play a critical role in the success of endovascular therapy. The presence of endovascular devices such as coils serves not only to reduce flow into the aneurysmal sac but also to encourage flow stasis within the dome, leading to platelet activation, aggregation, and formation of a stable thrombus, excluding the aneurysm from the circulation and resulting in treatment success [2,37]. Current CFD modeling techniques have been used to quantify important Eulerian hemodynamic parameters such as WSS and QAneurysm, which have been implicated in aneurysm treatment outcome [2,14,15,38]. However, because these Eulerian hemodynamic variables focus predominantly on the effects on the endothelium and ignore the contribution of platelets, they do not directly account for the role of platelet activation and aggregation, and thus remain imperfect predictors of treatment outcome.

Treatment-induced aneurysmal embolization is believed to be initiated by platelet activation and prolonged platelet residence time [6,11,39,40]. Existing CFD models of aneurysm hemodynamics neglect the platelets' exposure to shear and to high residence time regions, which have been associated with platelet activation and triggering of the intrinsic clotting pathway [27,41,42]. Instead, previous models have focused on RRT, an endothelial metric that is derived from the TAWSS and is correlated to blood flow and transport at the vascular wall [30,31]. Thus, this metric becomes increasingly uncorrelated with hemodynamics away from the aneurysm wall, particularly in situations of complex flow such as in patient-specific intracranial aneurysmal sacs. In addition, RRT only determines the residence time of an area of interest relative to the entire domain, and is thus not an actual measure of true residence time. Thus, the combination of the PM idealization and the Eulerian quantification of metrics such as RRT severely reduces the accuracy of current metrics for intra-aneurysmal thrombus formation, which may impede their use for predicting endovascular treatment outcome.

In this study, we employ a coil-resolved approach for endovascularly treated intracranial aneurysm hemodynamics, based on high-resolution synchrotron X-ray microtomography of flow phantoms treated with coils in a patient-specific manner, and a novel platelet-based approach to study the changes in hemodynamics. Given that treatment success requires the formation of a stable thrombus, activation and agglomeration of platelets is an important process that is best studied using Lagrangian analyses. The effect of treatment evaluated with different coil representation strategies (PM versus CR) showed widely different hemodynamic flow patterns in the parent vessel and aneurysm. Due to the reduced flow rate and more homogeneous flow in the aneurysmal volume in the PM model, the fluid shear in the aneurysmal neck plane was reduced by a larger degree using the PM approach than in the CR model in all four patients. This indicates that the presence of the homogeneous porous medium representing the coil mass inside the aneurysm artificially and excessively diverted flow away from the aneurysm. This can be visually observed in the flow streamlines in the right panel of Figs. 2 and 8: accurate representation of the coil mass reduces the flow into the aneurysm by presenting a tangible obstruction to the flow, which is first presented to the flow in the neck region. Thus, aneurysmal neck flow is chaotic and often characterized by large velocity gradients when the flow first encounters the endovascular coils.

This phenomenon is not captured by the PM approach (Fig. 2, middle panel), which smoothly redirects flow away from the aneurysmal neck in an artificial manner [34,43]. As seen in Fig. 6, the distribution of platelets inside the aneurysm is unrealistic for the PM approach since platelets can only occupy the volume between the coils (second and third panel in Fig. 6). That the platelets in the PM approach can occupy the volume which in the CR simulations is occupied by the coils leads to wrongly estimating the RT and SH of platelets inside the aneurysm. The overestimation of reduction in QAneurysm is quantifiable in the platelet-based analysis: median platelet RT and median SH decreases by 25% and 12.5%, respectively, for the CR simulations versus 75% and 35% for the PM simulations. However, the most striking difference is in the statistics of RT and SH for platelets that enter the aneurysm, especially for the extremes of these distributions. As shown in Figs. 5 and 9, platelets in the CR simulations circulate for a wide distribution of intra-aneurysmal RTs and, in the process, accumulate a significant range of SH, with both distributions being much wider than in the PM simulations. Specifically, based on a threshold of 3 s for long residence times within the aneurysmal sac, there was more than a 3000% increase for the CR case compared to 224% increase for the PM simulations for the outlier platelets for patient 1 (Table 4). Considering that activation and aggregation of platelets is statistically an extreme event [41,42], the spread of the tails of those quantities represents the best estimation of the probability that treatment will trigger platelet activation, the clotting response, and stable thrombus formation.

Given the higher blood flow velocities in the untreated aneurysm, platelets experience relatively high values of shear stress in a short span of time, compared to the posttreatment analysis. Considering the posttreatment cases, as the coil mass is applied homogeneously within the aneurysmal dome in the PM simulations, there are markedly different intra-aneurysmal flow patterns compared to the CR simulations [44,45]. Since the orientation of the individual coils is not uniformly distributed, platelets traverse different spatial regions of the dome for varying periods of time for the CR simulations. This is reflected in the wide distribution of shear stress histories of platelets in Figs. 6 and 7 for patient 1, indicating that platelets experience regions of relatively high and low shear as they traverse open space in between a dense packing of coils. Thus, it is not surprising that the accumulated shear on many platelets in the CR simulations approaches the untreated configuration, with increased spatiotemporal variations. This is not observed for the platelet shear exposure in the PM approach, indicating the oversimplification of flow patterns by this method. It should be noted that the differences between distributions of platelet RT and SH were statistically significant (p < 0.05) between the pretreatment, PM and CR cases, as determined by the rank-sum test for non-normal distributions. The inconsistency in over- or underpredicting flow metrics is a critical drawback of the homogeneous PM model, limiting its potential for predictions of treatment success in clinical situations [34].

While the main focus of our study is to characterize the platelet environment using Lagrangian tracking, we also analyze the traditional Eulerian metrics: WSS, WSSG, OSI, etc. As seen in Table 4, there are large differences between patients in the change in these variables posttreatment. For instance, patients 3 and 4 present a very large increase in WSS posttreatment, which is counterintuitive. However, as mentioned earlier, the presence of endovascular coils dramatically changes the flow patterns as blood flows in and around the coil mass. The unexpected WSS behavior for patients 3 and 4 can be partially explained by the location of the aneurysm, aneurysm shape, and the coil morphology within the aneurysmal sac. The flow through the aneurysm for patient 3 increases by 2.8% for the coil-resolved approach, while the porous media approach predicts a reduction of 35%. For patient 4, flow through the aneurysm decreased by 6% for the coil-resolved case, while the porous medium predicts a flow reduction of nearly 15%. The deployed coils could create regions that act as “nozzles” within the aneurysmal sac, increasing the flow velocities (and hence WSS) locally. These trends emphasize the complexity of predicting hemodynamics in cerebral aneurysms postendovascular coil treatment, and the need for combining Eulerian and Lagrangian, platelet-based metrics that incorporate the deployed coil mass, such as this study.

Obtaining accurate representations of coil morphologies after deployment in the aneurysmal dome is impossible with clinical imaging such as angiography, computed tomography, and magnetic resonance imaging, which lack spatial resolution due to beam-hardening artifacts that preclude the identification of the individual coils. Recently, computational models of endovascular coiling (virtual coiling) have been employed to understand the deployment of coils within the aneurysmal sac [21]. However, such models are yet to be conclusively validated for their predictability of aneurysmal coil morphologies once deployed, especially in the clinically relevant scenario of multiple coils of various sizes. In this study, we successfully demonstrate the use of synchrotron X-ray microtomography to eliminate these hurdles and obtain a high-resolution scan of individual coils deployed in a patient-specific in vitro intracranial aneurysm models. This method also considers the issue of relative packing density of coils toward the walls or the interior of the dome, which the PM approach does not consider. With recent advancements in supercomputing technology and accessibility, it has become more feasible to conduct such rigorous investigations of coil-resolved geometry in a relatively short timeframe: for instance, for patient 2, the computational simulation time for one cardiac cycle was 2.5 and 4.25 h for the PM and the CR simulations, respectively. These computational times can be further reduced by more computational resources and faster solution algorithms, thereby enabling the applicability of CFD treatment predictions in a clinically relevant scenario. Such representations could be used to estimate and improve the efficacy of endovascular treatments on a large scale, since the in vitro models are relatively easy to produce within a short time span and are cost-effective. Moreover, an added advantage of in vitro synchrotron models is that coil deployment configuration differences between different placements of each individual coil can be characterized and used to parameterize the coil mass in homogenized models that account for inhomogeneous and anisotropic distribution of the coils [46,47]. This strategy, which is under active investigation, will further strengthen the impact of these patient-specific CFD simulations in clinical practice.

There are some limitations to this study. First, the relatively small number of patient-specific aneurysms evaluated in this study (four) does not account for all the anatomical complexity observed in patients and, as such, we do not intend to predict trends from four patients. However, the four cases presented here are indeed representative of real-world scenarios observed at a high-volume tertiary referral center and demonstrate the variability of aneurysmal hemodynamics, even after endovascular treatment. Second, the small number of cases also does not allow us to perform statistical analysis to determine the degree of improvement enabled by the addition of Lagrangian metrics compared to the Eulerian metrics. Third, high-resolution synchrotron X-ray microtomography in vitro imaging is not routinely available for patient-specific CFD analysis and would be a barrier to direct translation of this methodology. However, by providing the highest resolution imaging of endovascular coils, this coil-resolved study could spur the development of homogenized coil modeling approaches that enable CFD simulations to capture the inhomogeneous and anisotropic nature of coils deployed inside aneurysms, with parametrizations from a database of coil-resolved images [48]. This parametrization would also reduce the computational simulation cost while achieving accurate results. Our group is actively developing a homogenization technique for the coil-resolved images that yields an inhomogeneous anisotropic but continuum porous medium model that produces a three-dimensional spatial variation of porosity equivalent to the endovascular coils deployed in the aneurysm, without the need to resolve the coil surfaces in the imaging or reproduce it in the model. While this study incorporated both Eulerian and platelet-based Lagrangian approaches for both PM and CR methods, further investigation is needed to compare Eulerian and Lagrangian residence times of platelets and determine which method is most accurate in predicting in vivo thrombosis. Recent work by Reza and Arzani [49], for example, uses these methods to compute residence times and attempts to relate them to thrombus formation. Such advancements in computational methodology could also expedite computational time, thereby further bridging the translation to clinical practice. This study was performed using a Newtonian assumption for blood, which was justified considering the high shear rates encountered in the flow domains considered. Moreover, the Newtonian assumption would not overestimate shear stress, and is consistent for all patients and for the two treatment approaches (coil-resolved and porous medium). Future study will also investigate the impact of non-Newtonian blood rheology and platelet aggregation models that build upon the modular approach presented in this work.

## 5 Conclusions

We have conducted a rigorous analysis of the effect of intracranial aneurysms endovascular coil embolization on perianeurysmal hemodynamics using two coil representations: homogeneous porous medium and high-resolution synchrotron X-ray microtomography. Using patient-specific anatomies and in vivo measurements of boundary conditions for four patients with unruptured aneurysms before and after coil treatment, we calculate Eulerian and Lagrangian metrics to quantify the changes in hemodynamics due to treatment and their effect on the formation of a stable thrombus, which is thought to lead to treatment success. We demonstrate that the PM approach largely overestimates, and in some cases underestimates, the effect of endovascular coil embolization of aneurysms on reductions of flow velocity and shear, leading to large inaccuracies when compared to the CR simulations. Platelet-based analysis reveals that the hemodynamics in the aneurysm dome and neck region are markedly different for the PM approximation, which leads to highly inaccurate calculations of RT and SH. The Lagrangian metrics can be linked to platelet activation and thrombus formation. This work demonstrates that the incorporation of high-resolution synchrotron X-ray microtomography and platelet-based hemodynamic analysis can augment CFD-based predictions of cerebral aneurysm treatment outcomes.

## Acknowledgment

This work was supported by the National Institutes of Health/National Institute of Neurological Disorders and Stroke Grant Nos. R01NS088072 and R01NS105692, American Heart Association Grant No. 18CDA34110295, National Science Foundation Grant No. CBET-0748133, and unrestricted educational equipment grants to our academic institution from Volcano Philips and Stryker, which had no role in the experimental design, data analysis, or scholarship of this work.

## Funding Data

• National Institutes of Health/National Institute of Neurological Disorders and Stroke (Grant Nos. R01NS088072 and R01NS105692; Funder ID: 10.13039/100000002).

• American Heart Association (Grant No. 18CDA34110295; Funder ID: 10.13039/100000968).

• National Science Foundation (Grant No. CBET-0748133; Funder ID: 10.13039/100000001).

## Conflict of Interest

The authors declare they have no conflicts of interest.

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