Evidence and Mechanisms for Embolic Stroke in Contralateral Hemispheres From Carotid Artery Sources

Abstract

Background

Disambiguation of embolus pathogenesis in embolic strokes is often a clinical challenge. One common source of embolic stroke is the carotid arteries, with emboli originating due to plaque buildup or perioperatively during revascularization procedures. Although it is commonly thought that thromboemboli from carotid sources travel to cerebral arteries ipsilaterally, there are existing reports of contralateral embolic events that complicate embolus source destination relationship for carotid sources. Here, we hypothesize that emboli from carotid sources can travel to contralateral hemispheres and that embolus interactions with collateral hemodynamics in the circle of Willis influence this process.

Methods and Results

We use a patient‐specific computational embolus‐hemodynamics interaction model developed in prior works to conduct an in silico experiment spanning 4 patient vascular models, 6 circle of Willis anastomosis variants, and 3 different thromboembolus sizes released from left and right carotid artery sites. This led to a total of 144 different experiments, estimating trajectories and distribution of approximately 1.728 million embolus samples. Across all cases considered, emboli from left and right carotid sources showed nonzero contralateral transport (P value <−0.05). Contralateral movement revealed a size dependence, with smaller emboli traveling more contralaterally. Detailed analysis of embolus dynamics revealed that collateral flow routes in the circle of Willis played a role in routing emboli, and transhemispheric movement occurred through the anterior and posterior communicating arteries in the circle of Willis.

Conclusions

We generated quantitative data demonstrating the complex dynamics of finite size thromboembolus particles as they interact with pulsatile arterial hemodynamics and traverse the vascular network of the circle of Willis. This leads to a nonintuitive source‐destination relationship for emboli originating from carotid artery sites, and emboli from carotid sources can potentially travel to cerebral arteries on contralateral hemispheres.

Nonstandard Abbreviations and Acronyms

ACA

anterior cerebral artery

AcoA

anterior communicating artery

CoW

circle of Willis

ESUS

embolic stroke of undetermined source

MCA

middle cerebral artery

PCA

posterior cerebral artery

Clinical Perspective.

What Is New?

• We present quantitative high‐resolution embolus transport data across patient‐specific human vascular models for varying embolus sizes driven by pulsatile hemodynamics—data that are otherwise challenging to obtain using imaging or in vivo approaches.

• We show that emboli from the left and right carotid sources can move to contralateral hemispheres (right and left cerebral arteries, respectively), and this contralateral movement is size dependent: that is, smaller emboli may have more contralateral movement.

• We conduct a detailed analysis of proximal collateral flow in the circle of Willis for varying circle anastomoses, showing that proximal collateral flow patterns in the circle of Willis can entrain and route emboli contralaterally in a nonintuitive manner.

What Are the Clinical Implications?

• Understanding stroke risks and embolism sites in the brain from carotid artery sources has major implications on treatment planning and outcomes assessment for carotid revascularization therapy such as endarterectomy or stenting.

• Contralateral embolus distribution from carotid artery sites can be a key contributor to the difficulty in disambiguating stroke pathogenesis in patients with suspected carotid artery embolus sources.

• Embolus routing via the circle of Willis proximal collateral pathways can be a significant underlying factor in adverse events such as microembolic showers, lacunar and watershed infarcts, and microstrokes leading to progressive vascular damage and dementia.

Stroke remains a leading a cause of death and disability worldwide, with a significant fraction of cases being acute ischemic strokes of embolic origin. However, these embolus sources are not always known. Embolic strokes of undetermined sources (ESUS) have received increasing attention in recent years. ¹ , ² ESUS cases refer to an occlusion in the cerebral artery by an embolus that could have originated from multiple potential cooccurring sources, and thereby their pathogenesis is challenging to disambiguate. Although it is believed that approximately 25% to 30% of ischemic strokes can be categorized as ESUS, ³ some studies have reported that up to 60% of ischemic strokes in some cohorts, especially young adults, can be categorized as ESUS. ⁴ This motivates the need to improve clinical identification of the embolus source. Improved methods of identifying embolus source and source–destination relationship would allow for increased treatment efficacy and reduced recurrent events with treatment based on the pathogenesis. ² This source–destination relationship for emboli is determined by an interplay of embolus properties, patient vascular anatomy for the heart–brain pathway, and patient hemodynamics. Specifically, the carotid arteries are a critical source of stroke due to their susceptibility to the buildup of atherosclerotic plaques. ⁵ , ⁶ It is widely regarded that the most relevant cause of strokes from carotid artery diseases are thromboemboli. ⁶ Rupture of unstable plaques, and associated thromboembolic events, can lead to embolic debris to travel into the circle of Willis (CoW) and cause an embolic stroke. This can also occur perioperatively during carotid revascularization therapies such as carotid artery stenting or carotid endarterectomy. ⁷ , ⁸ The common notion about carotid embolus source–destination relationship is that emboli from the carotid arteries travel ipsilaterally to the cerebral arteries or to the same hemisphere relative to the carotid side. Although this is true for a large proportion of cases, there have been many reported instances of emboli traveling contralaterally, or transhemispheric passage of emboli, from the carotid arteries where the embolus intermixes or crosses between the brain hemispheres relative to the source carotid. ⁹ , ¹⁰ , ¹¹ , ¹² Specifically, despite contralateral stroke events being less common, they can be a key contributor to the difficulty in disambiguating stroke pathogenesis as these cases can be the nondecipherable occurrences comprising ESUS patients. It remains challenging to study how emboli released from left/right carotid arteries pass transhemispherically using traditional imaging and animal model studies, and modern in silico techniques can prove to be a viable alternative. In a series of prior works, we have established a patient‐specific in silico flow‐embolus interaction model that enables us to quantitatively study the source–destination relationship for the transport of emboli to the brain. ¹³ , ¹⁴ , ¹⁵ , ¹⁶ We have used this model to demonstrate the transport and distribution of cardiogenic emboli and emboli from aortic arch and illustrate the dependency of embolus distribution on embolus properties, local flow features, and arterial network anatomy. Here, we use our model to conduct a parametric in silico study to understand how emboli from carotid artery sites travel to the 6 cerebral vessels of the CoW as a function of size, CoW anatomy, and laterality of carotid release sites.

Methods

Data, Materials, and Code Disclosure Statement

All quantitative embolus distribution data for this study have been shared through the Open Science Framework as part of project titled, “Dataset: Transport and Distribution of Embolic Particles in Human Vasculature,” which can be accessed at: https://doi.org/10.17605/OSF.IO/CQKZT. All image‐based modeling and computational hemodynamics simulations were conducted using the open source software package SimVascular. The image‐based models (segmentations, pathlines) and computational hemodynamics data will be made available through the Vascular Model Repository associated with the SimVascular project and can be accessed at https://simvascular.github.io/. The sharing process with Vascular Model Repository is ongoing, and we expect sharing to be completed and data ready for access no later than 6 months from the publication of this article. For any data access issues, or for additional access to scripts and tools, please contact the corresponding author directly via email, or via the contact page on the research team's official website: https://www.flowphysicslab.com/.

Image‐Based Modeling of Vascular Anatomy

The CoW anatomy has significant variations in topology and anastomosis across subjects, commonly with 1 or more communicating vessels missing or hypoplastic. ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ Using a meta‐analysis of literature on reported CoW anatomical variations, and a ranking statistics approach outlined in our prior work, ¹⁶ 5 most frequent variations of the CoW anatomy were considered for this study. These variations involved an absent anterior communicating artery (AcoA), absent left and right P1 connectors, and absent left and right communicating arteries. Together with the complete CoW, this led to a total of 6 CoW anatomical variants considered in this study. Figure 1 shows the differences between these CoW anatomies with reference to corresponding missing vessels along with labels for various cerebral arteries. These labels and identifiers are used throughout the article. Four patient anatomical geometries, used in our previous works, ¹⁴ , ¹⁶ were selected from a set of computed tomography images from an institutional review board approved STOP‐Stroke (Screening Technology and Outcome Project in Stroke) database. ²⁰ The STOP‐Stroke database comprised 675 patients who were diagnosed with a stroke or a transient ischemic attack, categorized into large vessel occlusion and non‐large vessel occlusion cases, with 46% of the stroke cases identified as large vessel occlusion. For this study, we used the noncontrast and contrast‐enhanced computed tomography images for retrospective, secondary, computational analysis purposes; and the rest of the data from the database were not used. Consequently, no additional institutional review board approval was required for this study. These patients were selected from the overall database to ensure that (1) they had a complete CoW anatomy; and (2) the branching vessels at the aortic branch were segregated such that there was no fused vessels or bovine arch anatomy. For each patient, artery lumen segmentations were generated from the contrast‐enhanced computed tomography images using a 2‐dimensional planar segmentation approach implemented in the open‐source cardiovascular modeling package SimVascular. ²¹ For each patient segmentation, the cerebral arteries up until the M1, A1, and P1 segments of the middle cerebral artery (MCA), anterior cerebral artery (ACA), and posterior cerebral artery (PCA), respectively, were included. These artery segmentations were then lofted to generate a 3‐dimensional solid model of the complete arterial pathway from the aorta to the CoW. Subsequently, the CoW variation models were created by removing the respective absent CoW artery paths and segments from the complete patient CoW anatomy segmentation and subsequently relofting the new geometry to produce the 3‐dimensional model of the corresponding incomplete CoW anastomosis. Details of this workflow are outlined in prior work. ¹⁶ By removing the arteries from a single patient with a complete CoW anatomy instead of introducing another patient with that specific CoW variation, we eliminate the multiple possible interpatient variabilities in our in silico investigation. Using 4 patients each with 6 CoW anastomoses, 24 total patient CoW vascular models were generated. Figure 1 shows each patient heart‐to‐brain pathway along with diagrams that correspond to the CoW anastomosis variation.

Figure 1. Complete heart‐to‐brain pathway was modeled for 4 patients combining 6 circle of Willis anatomical variations (A, top).

Emboli were released from both carotid arteries for all 4 patients (A, bottom). The 6 variations of the CoW as described in "Methods" are shown in (B), with each absent artery being depicted relative to the complete CoW anastomosis. A.Comm indicates anterior communicating artery; CoW, circle of Willis; L.ACA, left anterior cerebral artery; L.Comm, left communicating artery; L.ICA, left internal carotid artery; L.MCA, left middle cerebral artery; L.PCA, left posterior cerebral artery; L.P1, left P1 connector; R.ACA, right anterior cerebral artery; R.Comm, right communicating artery; R.ICA, right internal carotid artery; R.MCA, right middle cerebral artery; R.PCA, right posterior cerebral artery; and R.P1, right P1 connector.

Hemodynamics Simulation

Three‐dimensional simulations of blood flow using computational fluid dynamics were conducted for each of the 24 models. For these simulations, each model was discretized into a computational mesh comprising approximately 6.0 to 6.5 million linear tetrahedral elements, with the average element size being between 0.36 and 0.52 mm for each model. These parameters were chosen through mesh refinement analysis described in prior works. ¹⁶ Meshes were generated using the TetGen software tool, integrated within the SimVascular package. Blood flow was modeled using the classical Navier–Stokes equations for momentum balance and the continuity equation for mass balance. A Petrov‐Galerkin stabilized finite‐element method built into the SimVascular package was used to solve the mass and momentum equations for the velocity and pressure fields. ²² , ²³ A summary of the underlying mathematical equations is presented in Data S1. A pulsatile flow velocity profile was designated as an inlet boundary condition at the aortic root of the model. The profile was derived based on magnetic resonance measurements reported in Olufsen et al. ²⁴ This specified inlet flow led to a consistent average volumetric flow rate of 79 mL/s as the cardiac output for all models. To account for influence of the downstream vascular beds at each of the truncated arterial outlets, flow resistance boundary conditions were assigned to each outlet of the model. An average systolic and diastolic blood pressure of 120 and 80 mm Hg was assumed, leading to a mean arterial pressure of 93.33 mm Hg, which was used to compute a total arterial resistance as mean arterial pressure/cardiac output. Subsequently, a proportion of the total arterial resistance was assigned to each vessel outlet based on target flow divisions as outlined in prior work. ¹⁴ Briefly, (1) 65% of total flow was assumed to exit the descending aorta ²⁵ ; (2) flow rates at the 6 cerebral artery outlets were assigned based on measured magnetic resonance data reported in MacDonald and Frayne ²⁶ ; and (3) the remaining volumetric flow was designated to exit the external carotid and the subclavian artery outlets based on their cross‐sectional area. ²⁷ Multiple steady‐state flow simulations were conducted to tune the outlet resistance values for the boundary conditions, to match the target flow rates described here. ¹⁴ , ¹⁵ Once obtained, the cardiac output, mean arterial pressure, and outlet resistance values were kept the same across all patients and CoW variations to allow for controlled simulations of embolus transport. A total of 3 cardiac cycles of blood flow were simulated for each model, and the results from the third cardiac cycle was used further for embolus transport calculations. Extensive details on each underlying methodological piece have been described in a series of prior works. ¹⁵ , ¹⁶

Embolus Transport

Transport of thromboemboli across the arteries was modeled using a custom modified version of the Maxey‐Riley equation, ¹⁵ , ²⁸ which calculates the trajectories of individual particles moving through a fluid flow based on local velocities and particle properties. Individual thromboemboli were modeled as idealized spherical particles in accordance with the underlying physics of the Maxey‐Riley equation, with a density of 1.1 g/cm³ and elasticity of 1667.64 Pa as obtained from literature. ²⁹ , ³⁰ Our modifications to the classical form of Maxey‐Riley equations included incorporating (1) lift force produced by near‐wall shear gradients, (2) collisions between particles and the artery wall, and (3) elastohydrodynamic lubrication effects near‐wall. These are in addition to standard drag forces, added mass effects, and forces from the undisturbed background flow. Mathematical details of each of these physical forces are provided in Data S2. Particle‐particle collisions were not taken into account as the trajectory of individual particles were modeled independent of each other. Flow velocity data from the third cardiac cycle of hemodynamics simulations were stitched together 5 times to create a representative flow‐field spanning 5 cardiac cycles that has no cycle‐to‐cycle flow variations. This was used to compute the embolus trajectories across a 5 cardiac cycle duration. The integration of each particle trajectory was completed using a Euler time integration method with a time‐step of 0.05 ms. The embolus computation workflow is implemented in a set of custom computer codes built using C and Python with the Visualization Toolkit Libraries for preprocessing and postprocessing of flow velocity data and particle data, respectively. Extensive details on the individual mathematical expressions and algorithms can be found in our prior works. ¹⁴ , ¹⁵ , ¹⁶

In Silico Experiment Design

For this study, we used the simulation tools described in "Hemodynamics Simulation" and "Embolus Transport" to set up a parametric set of numerical experiments for embolus transport originating from carotid artery sources. The outline of the experiment design is illustrated in Figure 2. Specifically, for each of the 24 patient CoW anatomical variants modeled as stated in "Image‐Based Modeling of Vascular Anatomy", representative thromboembolic particles were released along the walls of the left and the right carotid arteries as indicated in Figure 1. Approximately 12 000 embolic particle samples were released for each case. Three different embolus sizes were used: 500 microns, 700 microns, and 1000 microns. As stated previously, each embolic particle trajectory integration was completed for 5 cardiac cycles during which all 12 000 particles exited into 1 of the vessel outlets. Across all parameter combinations, this led to a total of 144 simulations, each comprising 12 000 embolic particle samples, leading to distribution data spanning a total 1.728 million embolus samples. From each of the 144 simulations, we obtained the embolus distribution to the 6 cerebral arteries (left and right M1, A1, and P1) as a number fraction defined as N _k /N _cow , where N _k is the number of emboli that reached a specific cerebral artery (identified by k), and N _cow is the total number of emboli that reached the CoW from the carotid source.

Figure 2. The structure of in silico experiments comprising a total of 144 different embolus transport simulations.

These parameters include 4 patients, 6 CoW variations, 3 embolus sizes, and 2 release locations. AcoA indicates anterior communicating artery; CoW, circle of Willis; L.Comm, left communicating artery; L.P1, left P1 connector; R.Comm, right communicating artery; and R.P1, right P1 connector.

Results

Total Embolus Distribution

The total combined distribution statistics of emboli to each cerebral arteries across all the simulation cases are presented in Figure 3, categorized based on (1) left versus right carotid release sites and (2) embolus size. The first sample box plot in each panel represents the flow distribution to the respective cerebral artery across all simulation models. We observe that the majority of emboli travel to ipsilateral hemisphere sites: that is, the majority of emboli reach cerebral arteries on the same hemisphere side as the respective carotid release. We also observe that the majority of the emboli distribute to the left and right M1 segment outlets. Both of these observations are commonly expected based on the natural direct anatomical connection of the internal carotid artery into the MCA for left and right. However, the data in Figure 3 also indicate that there is a finite nonzero proportion of emboli that move into cerebral arteries on the contralateral side: that is, emboli reach cerebral arteries on the opposite hemisphere side as the respective carotid release. Based on our in silico experiment results, the contralateral distribution fractions are more notable in the ACA and MCA segments.

Figure 3. Total distribution of emboli to each cerebral vessel across all simulations.

Flow distribution to each cerebral vessel is depicted using the tag “Flow.” The distribution is represented as percentage of emboli/flow that reached the specific vessel to the total amount of emboli/flow entering the circle of Willis. ACA indicates anterior cerebral artery; CoW, circle of Willis; L.ACA, left anterior cerebral artery; L.MCA, left middle cerebral artery; L.PCA, left posterior cerebral artery; R.ACA, right anterior cerebral artery; R.MCA, right middle cerebral artery; and R.PCA, right posterior cerebral artery.

Throughout all of the cases considered, we note that embolus distribution to the cerebral arteries notably differs from flow distribution, thereby indicating that flow distribution alone is not a suitable indicator of the fractions in which emboli originating from a specific source will reach a cerebral artery. Specifically, a 1‐sample nonparametric Wilcoxon test for difference between the embolus distribution across all sizes and the flow distribution to each of the 6 cerebral arteries was conducted. The tests led to a P value ≤ 0.05 for right MCA, left MCA, right PCA, and left PCA, respectively; P values for the left ACA and right ACA were 0.06 and 0.32, respectively. This distinction from flow distribution has been also discussed in several prior works ¹³ , ¹⁶ , ³¹ ; and considering the CoW anastomosis variations, the results indicate that the proximal collateral design of the CoW along with embolus size‐dependent transport causes substantial variabilities in embolus destination and distribution. The variabilities were statistically characterized across all in silico experiments using the coefficient of variation of embolus distribution fractions to each of the 6 cerebral arteries. The coefficient of variation was calculated as the ratio of sample SD and sample mean for the embolus distribution fraction to each cerebral artery across all models and embolus sizes. The estimated coefficients of variation were 1.09, 1.04, and 3.87, respectively, for the left ACA, left MCA, and left PCA; and 1.11, 1.05, and 3.06, respectively, for the right ACA, right MCA, right PCA—indicating high variability with all values being >1.0, and most variability observed in right PCA and left PCA embolus distributions for emboli originating from carotid artery sources.

Extent of Contralateral Movement

In Figure 4, we specifically illustrate the extent of contralateral movement of emboli originating from the left and right carotid arteries, categorized across the 6 different CoW anastomoses and across the 4 patients. Specifically, we depict the percentage of emboli entering the CoW that travel to a cerebral artery contralateral to the carotid site from which it was released. The last bar in Figure 4 for each CoW anatomical variant depicts the average of the contralateral embolus distribution across all 4 patients. As stated in "Total Embolus Distribution," contralateral movement of emboli is observed in the majority of models. Specifically, for both left carotid and right carotid releases, 18 out of the 24 patient CoW anatomical variant models considered led to nonzero contralateral embolus distribution. Statistically, the null hypothesis that emboli released from left as well as right carotid sites do not travel contralaterally (that is the proportion of contralaterally traveling emboli=0) was rejected, with P values of 0.0003 and 0.0001, respectively (based on a 1‐sample nonparametric Wilcoxon rank test). For emboli originating from the left carotid sites, CoW variants with missing right communicating artery and missing right P1 led to the highest percentage of contralateral embolus distribution. For emboli originating from the right carotid sites, CoW variant with missing LP1 led to the highest percentage of contralateral embolus distribution. Additionally, cases with zero contralateral embolus distribution most consistently involved the CoW anastomosis with the missing AcoA, with only 1 case with missing AcoA leading to contralateral embolus transport.

Figure 4. The proportion of contralateral movement for both the left and right carotid releases across all 6 CoW variations.

Left figure shows the percentage of emboli entering the CoW that are released from the left carotid and travel to the right cerebral arteries. The right figure shows the percentage of emboli entering the CoW that are released from the right carotid and travel to the left cerebral arteries. AcoA indicates anterior communicating artery; CoW, circle of Willis; L.Comm, left communicating artery; L.P1, left P1 connector; R.Comm, right communicating artery; and R.P1, right P1 connector.

Embolus Size Dependence

Figure 5 illustrates the dependency of contralateral movement on embolus size. Panels A., B, and C, respectively, depict the percentage of contralaterally traveling emboli that are 500 μm, 750 μm, and 1000 μm diameter. Similar to Figure 4, each panel depicts the distribution categorized across the 6 CoW anatomical variants for each of the 4 patient anatomical models considered. For each CoW anatomical variant, the fifth bar depicts the average of the contralateral embolus distribution across all 4 patients. The results show that in the simulation cases considered, smaller emboli have a greater tendency to distribute contralaterally, with the 1000  μm embolus having the smallest proportion of contralateral embolus and the 500  μm embolus having the largest proportion of contralaterally traveling emboli.

Figure 5. The percentage of contralateral embolus movement decomposed based on embolus size.

The illustration indicates that smaller emboli held a larger proportion of contralateral movement in comparison to larger. AcoA indicates anterior communicating artery; L.Comm, left communicating artery; L.P1, left P1 connector; R.Comm, right communicating artery; and R.P1, right P1 connector.

Discussion

Simulation cases considered in this study demonstrate contralateral movement of emboli originating from carotid artery sites leading to otherwise nonintuitive embolus distributions. We note that CoW anastomosis is a key factor influencing the extent of contralateral embolus movement. In a prior work, we have quantified how the communicating arteries of the CoW recruit and route flow and cardiogenic emboli into the 6 major cerebral arteries across different CoW anastomosis. ¹⁶ As an embolus enters the CoW from the 3 major inlet vessels (left and right internal carotid artery and basilar artery), it can get entrained in the flow patterns across the CoW communicating vessels and ultimately travel across more than 1 vessel segments to reach its destination M1/A1/P1 segment in the left/right hemisphere. This interaction of collateral flow in CoW with the embolus is therefore one key factor that determines the propensity of contralateral embolus distribution. Specifically, emboli entering the CoW from 1 of the carotid arteries directly feeding the CoW may not reach a cerebral artery on the same side based on anatomical considerations alone but instead be entrained in CoW collateral flow to traverse several vessel segments and reach a cerebral artery on the opposite hemisphere.

As also observed in Figure 5, contralateral embolus distribution is influenced by embolus size. This can also be interpreted in terms of embolus interaction with collateral flow. Specifically, we refer to a physical parameter named momentum response time, which is a surrogate descriptor for the time that a particle takes to respond to changes in the background fluid flow in which it is immersed. Additional mathematical definitions and details are provided in Data S3 and Figure S1. For the same material (eg, thromboembolus considered here), the momentum response time is proportional to the square of the particle diameter. Thus, a smaller particle will have lesser momentum response time and will respond to and get entrained by the background flow faster. Particle size is directly related to particle inertia, and particles with finite inertia will therefore have a nonzero momentum response time and will not exactly follow the path of the flow. These factors taken together explain the observations that embolus distribution differs from flow distribution, and the distribution ultimately has a dependency on size. Specifically, the smaller emboli may be recruited by the collateral flow pathways of the CoW anastomosis more rapidly than the larger emboli, thereby explaining why smaller emboli show greater extent of contralateral movement aided by flow routing across the CoW vessels. This aspect of flow‐embolus interaction physics has also been discussed in mathematical detail in conjunction with embolus material properties and ratio of material density between embolus and blood in our prior work. ¹⁵ , ¹⁶

Among the communicating vessels in the CoW, the AcoA has been known to play a key role in collateralization of flow across hemispheres. High patency of AcoA is often related to contralateral microemboli as well. ³² Here, detailed quantitative data from our in silico experiments further support and substantiate this idea. We have shown in Figure 4 that most cases with 0 contralateral embolus distribution correspond to CoW anastomosis with a missing AcoA. Additionally, we present a case study of Patient 1 in Figure 6, panel A, where the left posterior communicating artery is missing, and we observe the collateral flow influencing the contralateral susceptibility for both the left and right carotid releases. This patient had 8% of emboli travel contralaterally, higher than the average 4% across all patient models. Detailed analysis of flow through the CoW as described in Mukherjee et al ¹⁶ indicates that right internal carotid artery flow rate is directed toward the anterior of the CoW, which allows for more particles to be influenced and routed by the high AcoA flow rate, which is directed from the right to left hemisphere. This potentially indicates that the AcoA is facilitating emboli from the right to left hemisphere and preventing movement of emboli from left to right. These dynamics are clearly visible in the embolus trajectory animation video provided in Data S4 with Videos S1 and S2.

Figure 6. Two case studies examining how collateral proximal flow of the CoW affects the ability for contralateral movement.

A, Patient 1 with an absent left posterior connector exhibits how the collateral flow rate allows for contralateral movement from the right to left hemisphere through the AcoA. The AcoA has a high right to left flow rate that is able to route emboli into it and to the left hemipshere. B, Patient 4 with a complete CoW anatomy completes contralateral movement through the posterior region. The R.Comm flow rate directed toward the posterior routes emboli into the basilar artery and allows for travel into the left hemisphere due to the L.P1 flow rate directed toward the L.PCA. AcoA indicates anterior communicating artery; CoW, circle of Willis; L.ACA, left anterior cerebral artery; L.ICA, left internal carotid artery; L.MCA, left middle cerebral artery; L.PCA, left posterior cerebral artery; L.P1, left P1 connector; R.ACA, right anterior cerebral artery; R.Comm, right communicating artery; R.ICA, right internal carotid artery; R.MCA, right middle cerebral artery; and R.PCA, right posterior cerebral artery.

Two additional observations are noted here based on detailed embolus trajectory data from our in silico experiments. First, although the AcoA was a key segment that enabled embolus transport contralaterally, it was not the only segment doing so. In Figure 6, panel B, we present another case of Patient 4 with a complete CoW network and emboli released from the right carotid site. In this case, emboli moved from the right internal carotid artery into the right communicating artery segment, then into the right P1 segment, and thereafter traveled over into the left PCA P1 segment. This embolus transport occurred over several cardiac cycles and is representative of the examples of nonintuitive embolus distribution dependent on flow‐embolus interaction mechanisms in the CoW. An animation of this posterior contralateral movement is provided in Data S4 with Video S3. Second, compared with systolic phase flow in the CoW vessels, diastolic flow exhibits significant retrograde and recirculating flow features. In several cases considered in this study, embolus interactions with these nonlinear flow features led to complex nonintuitive trajectories. An example animation of such dynamics is provided in Data S4 with Video S4, where 1 mm diameter thromboemboli move across Patient 3's CoW with a missing right communicating artery segment. Although initially systolic phase flow pushes the emboli into the ipsilateral A1 segment, the emboli interact with the retrograde diastolic flow and pass through the AcoA to move into the contralateral A1 and M1 segments. Both of these examples provide detailed evidence of highly nonintuitive embolus distribution patterns that (1) differ from those expected from flow distributions alone, (2) differ from those expected from highly patent AcoA alone, and together offer insights into mechanisms of contralateral transport that can be complicate pathogenesis sourcing for carotid origin strokes.

The data and insights presented here have multiple broad clinical implications. The role of CoW vessels in collateral circulation in conjunction with the leptomeningeal collateral flow is acknowledged to be critical in acute ischemic stroke, ³³ , ³⁴ , ³⁵ , ³⁶ even inspiring approaches toward collateral therapeutics. ³⁷ However, fewer details are known about CoW collateral pathways being a route for emboli and subsequent embolism sites in the brain—a potential contributing factor toward determining embolism pathogenesis in strokes. Additionally, the observation that smaller emboli are more prone to contralateral movement and routing across CoW collateral pathways is of significance in small emboli pathological mechanisms that lead to microembolic showers, ³⁸ lacunar and watershed infarcts, ³⁹ , ⁴⁰ , ⁴¹ and microstrokes leading to progressive vascular damage and dementia. ⁴² , ⁴³ Furthermore, understanding stroke risks from carotid stenosis has major implications for planning and outcomes of carotid revascularization therapy, such as carotid artery stenting or carotid endarterectomy. ⁸ Findings from this study are significant in advancing our understanding of peri‐ and postoperative stroke risks during revascularization procedures. A better understanding of when carotid lesions may lead to contralateral strokes could avoid false attributions of embolic sources and extensive or potentially harmful cardiac workups. It is relevant to note where such in silico models and analysis can find integration into direct patient cases. Currently, end‐to‐end computation time from standard‐of‐care images to embolus probabilities has an upper bound of 36 to 48 hours using reasonable state‐of‐the‐art computational resources. Ongoing research is aiming to further reduce the compute time, for example, by accelerating image‐segmentation using AI/ML based approaches. Hence, in their present form such in silico analyses would not be feasible within the rapid acute phase of standard‐of‐care, which focuses on reperfusion and tissue recovery. However, postacute phase secondary analysis of stroke pathogenesis is potentially feasible wherein it would be akin to running an in silico or laboratory test and obtaining the workup within a 36‐ to 48‐hour (or less) time window. Finally, we have validated the 1‐way coupling embolus transport model using high‐resolution computational fluid dynamics ¹³ and validated the predictions and trends for embolism statistics against data reported in other clinical and imaging studies of cardiogenic embolus destinations ⁴⁴ , ⁴⁵ and that of cardiogenic versus aortogenic embolus destinations ⁴⁶ (demonstrated in prior work ¹⁴ ). However, well‐controlled systematic comparison of the in silico framework against in vitro or benchtop models will further benefit the advancement of such modeling framework, which is an area of active investigation.

This study was based on several key assumptions. First, we assumed that the carotid sites did not have a visible severe stenosis. Presence of a severe stenosis will alter flow patterns through the carotid arteries into the CoW, ⁴⁷ which makes it difficult to isolate the effects of embolus‐flow interactions at the CoW vessels alone. Furthermore, carotid arteries can be suspect to varying forms of embolization such as postoperative embolic showers after carotid endarterectomy ⁴⁸ or endothelial trauma during catheterization, where stenosis severity will be low yet embolic phenomena may occur. These cases of nonsymptomatic or mild stenosis can lead to otherwise unexpected or nonintuitive adverse cerebrovascular embolic events. ⁴⁹ This aligns with the focus of this study on nonintuitive embolus transport in relation to flow distributions within the proximal collateral pathways as influenced by CoW anastomosis and embolus size. Additionally, the presence of higher‐degree stenosis will require reevaluation of hemodynamics as severe stenosis can alter hemodynamics within the heart‐to‐brain pathway. Incorporating these additional simulations within a parametric mechanistic study design as the one presented here would require a substantially more expensive computational effort that would be significantly beyond the scope of this article. Nevertheless, the approach presented here can be extended in future studies to specifically account for stenosis of varying severity and its influence on cerebral embolic events. Along similar lines, future efforts would also benefit from incorporating the simultaneous effects of contralateral carotid disease and vertebral artery disease to enable additional insights on embolic events from the cervical vessel sites. Second, we assume that the blood flow influences the emboli, but the emboli themselves do not significantly alter the flow (commonly referred to as one‐way coupling). This is a reasonable assumption considering that each embolus is modeled individually as a single particle released independently of the other (ie, there is not a large concentration of thrombo‐emboli suspended in blood to begin with). This assumption does limit our study to exclude cases where the embolus diameter approaches the sizes of the cerebral arteries themselves (ie, nearly occlusive emboli). ¹³ To mitigate this, we focused on transport only to the M1/A1/P1 segments. However, the computational models can be further improved in future investigations if detailed models of flow disturbance around an individual embolus can be incorporated. Third, our physics‐based embolus transport model assumes that the emboli are spherical particles. This is a widely adopted modeling choice originating primarily from the fact that presently there is no generalized physics‐model (such as Equation S5, for example) for arbitary nonspherical particle shapes, and derivation of a first‐principles physics model of this nature will require significant additional theoretical and computational effort, which is beyond the scope of the study presented here. Additionally, embolus stretching, deformation, and deviation from sphericity is governed by the flow‐induced forces, especially large gradations in shear forces as the embolus squeezes through a vessel. This effect is not dominant when we consider small‐to‐medium embolus sizes that do not approach the vessel diameters, which comprised the size regimen we focused on this study. Finally, owing to the computational complexity of the overall set of simulations considered, we were able to consider 4 human subjects and 6 CoW anastomoses for each. In order to expand the interpretations further larger number of subjects need to be included, which is a substantial computational undertaking of its own beyond the scope of this current study. Regardless, the 144 experiments spanning over 1.7 million embolus samples illustrate a rich set of evidence and mechanisms of contralateral embolus transport from carotid sites.

Conclusions

We completed an investigation on how emboli originating from the carotid arteries may exhibit contralateral hemispheric movement when reaching the cerebral vessels. We completed a systematic in silico study comprising 144 embolus transport simulations by varying particle size, CoW anastomosis variation, and carotid side (left/right). The in silico framework enabled obtaining high‐resolution embolus transport data across patient‐specific vascular anatomical models, with pulsatile hemodynamics—data that are otherwise challenging to obtain. Five frequently observed CoW variations were modeled across 4 healthy patients in order to assess the effects of CoW anatomy on embolus transport influenced by underlying CoW collateral flow patterns. Contralateral or transhemispheric embolus movement was found to be significantly nonzero across the anatomical models regardless of carotid release. Smaller emboli demonstrated higher probability of traveling contralaterally in comparison to larger emboli. Proximal collateral flow rate of the CoW can promote contralateral movement in either hemispheric direction through the anterior or posterior communicating vessels. These findings can illuminate the mechanisms of contralateral movement that can contribute to sourcing nondecipherable emboli occlusion pathogenesis.

Sources of Funding

The authors acknowledge funding support from National Institutes of Health Award: R21EB029736 for this study. This work used the Summit supercomputer, which is supported by the National Science Foundation (awards ACI‐1532235 and ACI‐1532236), the University of Colorado Boulder, and Colorado State University.

Disclosures

None.

Supporting information

Data S1–S4

Video S1

Video S2

Video S3

Video S4