Numerical Modeling of Flow in the Cerebral Vasculature: Understanding Changes in Collateral Flow Directions in the Circle of Willis for a Cohort of Vasospasm Patients Through Image-Based Computational Fluid Dynamics.

The Circle of Willis (CoW) is a ring-like network of blood vessels that perfuses the brain. Flow in the collateral pathways that connect major arterial inputs in the CoW change dynamically in response to vessel narrowing or occlusion. Vasospasm is an involuntary constriction of blood vessels following subarachnoid hemorrhage (SAH), which can lead to stroke. This study investigated interactions between localization of vasospasm in the CoW, vasospasm severity, anatomical variations, and changes in collateral flow directions. Patient-specific computational fluid dynamics (CFD) simulations were created for 25 vasospasm patients. Computed tomographic angiography scans were segmented capturing the anatomical variation and stenosis due to vasospasm. Transcranial Doppler ultrasound measurements of velocity were used to define boundary conditions. Digital subtraction angiography was analyzed to determine the directions and magnitudes of collateral flows as well as vasospasm severity in each vessel. Percent changes in resistance and viscous dissipation were analyzed to quantify vasospasm severity and localization of vasospasm in a specific region of the CoW. Angiographic severity correlated well with percent changes in resistance and viscous dissipation across all cerebral vessels. Changes in flow direction were observed in collateral pathways of some patients with localized vasospasm, while no significant changes in flow direction were observed in others. CFD simulations can be leveraged to quantify the localization and severity of vasospasm in SAH patients. These factors as well as anatomical variation may lead to changes in collateral flow directions. Future work could relate localization and vasospasm severity to clinical outcomes like the development of infarct.

A Computational Investigation of the Effects of Temporal Synchronization of Left Ventricular Assist Device Speed Modulation with the Cardiac Cycle on Intraventricular Hemodynamics.

Patients with advanced heart failure are implanted with a left ventricular assist device (LVAD) as a bridge-to-transplantation or destination therapy. Despite advances in pump design, the risk of stroke remains high. LVAD implantation significantly alters intraventricular hemodynamics, where regions of stagnation or elevated shear stresses promote thrombus formation. Third generation pumps incorporate a pulsatility mode that modulates rotational speed of the pump to enhance in-pump washout. We investigated how the timing of the pulsatility mode with the cardiac cycle affects intraventricular hemodynamic factors linked to thrombus formation. Computational fluid dynamics simulations with Lagrangian particle tracking to model platelet behavior in a patient-specific left ventricle captured altered intraventricular hemodynamics due to LVAD implantation. HeartMate 3 incorporates a pulsatility mode that modulates the speed of the pump every two seconds. Four different timings of this pulsatility mode with respect to the cardiac cycle were investigated. A strong jet formed between the mitral valve and inflow cannula. Blood stagnated in the left ventricular outflow tract beneath a closed aortic valve, in the near-wall regions off-axis of the jet, and in a large counterrotating vortex near the anterior wall. Computational results showed good agreement with particle image velocimetry results. Synchronization of the pulsatility mode with peak systole decreased stasis, reflected in the intraventricular washout of virtual contrast and Lagrangian particles over time. Temporal synchronization of HeartMate 3 pulsatility with the cardiac cycle reduces intraventricular stasis and could be beneficial for decreasing thrombogenicity.

In Vitro Investigation of the Effect of the Timing of Left Ventricular Assist Device Speed Modulation on Intraventricular Flow Patterns.

Thromboembolic events remain a common complication for left ventricular assist device (LVAD) patients. To prevent in-pump thrombosis, third-generation LVADs use speed modulation, which is not synchronized with the native left ventricle (LV) contractility. This study aims to investigate the effect of speed modulation on intraventricular flow patterns, and specifically, the impact of timing relative to pressure variations in the LV. Stereo-particle image velocimetry measurements were performed in a patient-derived LV implanted with an LVAD, for different timings of the speed modulation and speed. Speed modulation has a strong effect on instantaneous afterload and flowrate (-16% and +20%). The different timings of the speed modulation resulted in different flowrate waveforms, exhibiting different maxima (5.3-5.9 L/min, at constant average flowrate). Moreover, the timing of the speed modulation was found to strongly influence intraventricular flow patterns, specifically, stagnation areas within the LV. These experiments highlight, once more, the complex relationship between LVAD speed, hemodynamic resistance, and intraventricular pressure. Overall, this study demonstrates the importance of considering native LV contractility in future LVAD controls, to improve hemocompatibility and reduce the risk of thromboembolic complications.

A Novel Patient-Specific Computational Fluid Dynamics Study of the Activation of Primary Collateral Pathways in the Circle of Willis During Vasospasm.

The Circle of Willis (CoW) is a redundant network of blood vessels that perfuses the brain. The ringlike anatomy mitigates the negative effects of stroke by activating collateral pathways that help maintain physiological perfusion. Previous studies have investigated the activation of these pathways during embolic stroke and internal carotid artery occlusion. However, the role of collateral pathways during cerebral vasospasm-an involuntary constriction of blood vessels after subarachnoid hemorrhage-is not well-documented. This study presents a novel technique to create patient-specific computational fluid dynamics (CFD) simulations of the Circle of Willis before and during vasospasm. Computed tomographic angiography (CTA) scans are segmented to model the vasculature, and transcranial Doppler ultrasound (TCD) measurements of blood flow velocity are applied as boundary conditions. Bayesian analysis leverages information about the uncertainty in the measurements of vessel diameters and velocities to find an optimized parameter set that satisfies mass conservation and that is applied in the final simulation. With this optimized parameter set, the diameters, velocities, and flow rates fall within typical literature values. Virtual angiograms modeled using passive scalar transport agree closely with clinical angiography. A sensitivity analysis quantifies the changes in collateral flow rates with respect to changes in the inlet and outlet flow rates. This analysis can be applied in the future to a cohort of patients to investigate the relationship between the locations and severities of vasospasm, the patient-to-patient anatomical variability in the Circle of Willis, and the activation of collateral pathways.

Endothelial Responses to Curvature-Induced Flow Patterns in Engineered Cerebral Aneurysms.

Hemodynamic factors have long been associated with clinical outcomes in the treatment of cerebral aneurysms. Computational studies of cerebral aneurysm hemodynamics have provided valuable estimates of the mechanical environment experienced by the endothelium in both the parent vessel and aneurysmal dome walls and have correlated them with disease state. These computational-clinical studies have recently been correlated with the response of endothelial cells (EC) using either idealized or patient-specific models. Here, we present a robust workflow for generating anatomic-scale aneurysm models, establishing luminal cultures of ECs at physiological relevant flow profiles, and comparing EC responses to curvature mediated flow. We show that flow patterns induced by parent vessel curvature produce changes in wall shear stress (WSS) and wall shear stress gradients (WSSG) that are correlated with differences in cell morphology and cellular protein localization. Cells in higher WSS regions align better with the flow and display strong Notch1-extracellular domain (ECD) polarization, while, under low WSS, differences in WSSG due to curvature change were associated with less alignment and attenuation of Notch1-ECD polarization in ECs of the corresponding regions. These proof-of-concept results highlight the use of engineered cellularized aneurysm models for connecting computational fluid dynamics to the underlying endothelial biology that mediates disease.

Modeling Flow in Cerebral Aneurysm After Coils Embolization Treatment: A Realistic Patient-Specific Porous Model Approach.

PURPOSE: Computational fluid dynamics (CFD) has been used to evaluate the efficiency of endovascular treatment in coiled cerebral aneurysms. The explicit geometry of the coil mass cannot typically be incorporated into CFD simulations since the coil mass cannot be reconstructed from clinical images due to its small size and beam hardening artifacts. The existing methods use imprecise porous medium representations. We propose a new porous model taking into account the porosity heterogeneity of the coils deployed in the aneurysm. METHODS: The porosity heterogeneity of the coil mass deployed inside two patients' cerebral aneurysm phantoms is first quantified based on 3D X-ray synchrotron images. These images are also used to compute the permeability and the inertial factor arising in porous models. A new homogeneous porous model (porous crowns model), considering the coil's heterogeneity, is proposed to recreate the flow within the coiled aneurysm. Finally, the validity of the model is assessed through comparisons with coil-resolved simulations. RESULTS: The strong porosity gradient of the coil measured close to the aneurysmal wall is well captured by the porous crowns model. The permeability and the inertial factor values involved in this model are closed to the ideal homogeneous porous model leading to a mean velocity in the aneurysmal sac similar as in the coil-resolved model. CONCLUSION: The porous crowns model allows for an accurate description of the mean flow within the coiled cerebral aneurysm.

The effect of Dean, Reynolds and Womersley numbers on the flow in a spherical cavity on a curved round pipe. Part 2. The haemodynamics of intracranial aneurysms treated with flow-diverting stents.

The flow in a spherical cavity on a curved round pipe is a canonical flow that describes well the flow inside a sidewall aneurysm on an intracranial artery. Intracranial aneurysms are often treated with a flow-diverting stent (FDS), a low-porosity metal mesh that covers the entrance to the cavity, to reduce blood flow into the aneurysm sac and exclude it from mechanical stresses imposed by the blood flow. Successful treatment is highly dependent on the degree of reduction of flow inside the cavity, and the resulting altered fluid mechanics inside the aneurysm following treatment. Using stereoscopic particle image velocimetry, we characterize the fluid mechanics in a canonical configuration representative of an intracranial aneurysm treated with a FDS: a spherical cavity on the side of a curved round pipe covered with a metal mesh formed by an actual medical FDS. This porous mesh coverage is the focus of Part 2 of the paper, characterizing the effects of parent vessel Re, De and pulsatility, Wo, on the fluid dynamics, compared with the canonical configuration with no impediments to flow into the cavity that is described in Part 1 (Chassagne et al., J. Fluid Mech., vol. 915, 2021, A123). Coverage with a FDS markedly reduces the flow Re in the aneurysmal cavity, creating a viscous-dominated flow environment despite the parent vessel Re > 100. Under steady flow conditions, the topology that forms inside the cavity is shown to be a function of the parent vessel De. At low values of De, flow enters the cavity at the leading edge and remains attached to the wall before exiting at the trailing edge, a novel behaviour that was not found under any conditions of the high-Re, unimpeded cavity flow described in Part 1. Under these conditions, flow in the cavity co-rotates with the direction of the free-stream flow, similar to Stokes flow in a cavity. As De increases, the flow along the leading edge begins to separate, and the recirculation zone grows with increasing De, until, above De ≈ 180, the flow inside the cavity is fully recirculating, counter-rotating with respect to the free-stream flow. Under pulsatile flow conditions, the vortex inside the cavity progresses through the same cycle - switching from attached and co-rotating with the free-stream flow at the beginning of the cycle (low velocity and positive acceleration) to separated and counter-rotating as De reaches a critical value. The location of separation within the harmonic cycle is shown to be a function of both De and Wo. The values of aneurysmal cavity Re based on both the average velocity and the circulation inside the cavity are shown to increase with increasing values of De, while Wo is shown to have little influence on the time-averaged metrics. As De increases, the strength of the secondary flow in the parent vessel grows, due to the inertial instability in the curved pipe, and the flow rate entering the cavity increases. Thus, the effectiveness of FDS treatment to exclude the aneurysmal cavity from the haemodynamic stresses is compromised for aneurysms located on high-curvature arteries, i.e. vessels with high De, and this can be a fluid mechanics criterion to guide treatment selection.

The effect of Dean, Reynolds, and Womersley number on the flow in a spherical cavity on a curved round pipe. Part 1. Fluid mechanics in the cavity as a canonical flow representing intracranial aneurysms.

Flow in side-wall cerebral aneurysms can be ideally modelled as the combination of flow over a spherical cavity and flow in a curved circular pipe, two canonical flows. Flow in a curved pipe is known to depend on the Dean number De, combining the effects of Reynolds number, Re, and of the curvature along the pipe centreline, κ. Pulsatility in the flow introduces a dependency on the Womersley number Wo. Using stereo PIV measurements, this study investigated the effect of these three key non-dimensional parameters, by modifying pipe curvature (De), flow-rate (Re), and pulsatility frequency (Wo), on the flow patterns in a spherical cavity. A single counter-rotating vortex was observed in the cavity for all values of pipe curvature κ and Re, for both steady and pulsatile inflow conditions. Increasing the pipe curvature impacted both the flow patterns in the pipe and the cavity, by shifting the velocity profile towards the cavity opening and increasing the flow rate into the cavity. The circulation in the cavity was found to collapse well with only the Dean number, for both steady and pulsatile inflows. For pulsatile inflow, the counter-rotating vortex was unstable and the location of its centre over time was impacted by the curvature of the pipe, as well as the Re and the Wo in the freestream. The circulation in the cavity was higher for steady inflow than for the equivalent average Reynolds and Dean number pulsatile inflow, with very limited impact of the Womersley in the range studied.

Computational fluid dynamics modeling aiding surgical planning in a toddler with Parkes Weber syndrome.

Parkes Weber syndrome is a fast-flow and slow-flow vascular anomaly with limb overgrowth that can lead to congestive heart failure and limb ischemia. Current management strategies have focused on symptom management with focal embolization. A pediatric case with early onset heart failure is reported. We discuss the use of computational fluid dynamics (CFD) modeling to guide a surgical management strategy in a toddler with an MAP2K1 mutation.

Lagrangian Trajectory Simulation of Platelets and Synchrotron Microtomography Augment Hemodynamic Analysis of Intracranial Aneurysms Treated With Embolic Coils.

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.