Strategy for modeling flow diverters in cerebral aneurysms as a porous medium

Numerical simulation of flow-diverting stent: comparison between branches in bifurcation brain aneurysm

The usage of flow-diverting stents in the treatment of intracranial aneurysms is widespread due to their high success and low complication rates. However, their use is still not officially recommended for bifurcation aneurysms, as there is a risk of generating ischemic complications due to the reduced blood flow to the jailed branch. Many works utilize computational fluid dynamics (CFD) to study how hemodynamic variables respond to flow diverter placement, but few seem to use it to verify flow variation between branches of bifurcation aneurysms and to aid in the choice of the best ramification for device placement. This investigation was performed in the present work, by comparing wall shear stress (WSS) and flowrates for a patient-specific scenario of a middle cerebral artery (MCA) aneurysm, considering device placement on each branch. A secondary objective was to follow a methodology that provides fast results, envisioning application to daily medical practice. The device was simplified as a homogeneous porous medium, and extreme porosity values were simulated for comparison. Results suggest that stent placement on either branch is both safe and effective, significantly reducing WSS and flow into the aneurysm while maintaining flow to the different ramifications within acceptable thresholds.

Assessing a heterogeneous model for accounting for endovascular devices in hemodynamic simulations of cerebral aneurysms

The heterogeneous model developed by Berod et al [Int J Numer Method Biomed Eng 38, 2021] for representing the hemodynamic effects of endovascular prostheses is applied to a series of 10 patient specific cerebral aneurysms, 6 being treated by flow diverters, 4 being equipped with WEBs. Two markers correlated with the medical outcome of the treatment are used to assess the potential of the model, namely the saccular mean velocity and the inflow rate at the neck of the aneurysm. The comparison with the corresponding wire-resolved simulations is very favorable in both cases, and the model-based simulations also retrieve the jetting-type flows generated downstream of the struts. Noteworthy, the very same model was used for representing the flow diverters and the WEBs, showing the versatility and robustness of the heterogeneous modeling of the devices.

Numerical Assessment of the Risk of Abnormal Endothelialization for Diverter Devices: Clinical Data Driven Numerical Study

Numerical modeling is an effective tool for preoperative planning. The present work is devoted to a retrospective analysis of neurosurgical treatments for the occlusion of cerebral aneurysms using flow-diverters and hemodynamic factors affecting stent endothelization. Several different geometric approaches have been considered for virtual flow-diverters deployment. A comparative analysis of hemodynamic parameters as a result of computational modeling has been carried out basing on the four clinical cases: one successful treatment, one with no occlusion and two with in stent stenosis. For the first time, a quantitative assessment of both: the limiting magnitude of shear stresses that are necessary for the occurrence of in stent stenosis (MaxWSS > 1.23) and for conditions in which endothelialization is insufficiently active and occlusion of the cervical part of the aneurysm does not occur (MaxWSS < 1.68)—has been statistacally proven (p < 0.01).

A heterogeneous model of endovascular devices for the treatment of intracranial aneurysms

Numerical computations of hemodynamics inside intracranial aneurysms treated by endovascular braided devices such as flow-diverters contribute to understanding and improving such treatment procedures. Nevertheless, these simulations yield high computational and meshing costs due to the heterogeneity of length scales between the dense weave of the fine struts of the device and the arterial volume. Homogeneous strategies developed over the last decade to circumvent this issue substitute local dissipations due to the wires with a global effect in the form of a pressure-drop across the device surface. However, these methods cannot accurately reproduce the flow-patterns encountered near the struts, the latter strongly dictating the intra-saccular flow environment. In this work, a versatile theoretical framework which aims at correctly reproducing the local flow heterogeneities due to the wires while keeping memory consumption, meshing and computational times as low as possible is introduced. This model reproduces the drag forces exerted by the device struts onto the fluid, thus producing local and heterogeneous effects on the flow. Extensive validation for various flow and geometric configurations using an idealized device is performed. To further illustrate the method capabilities, a real patient-specific aneurysm endovascularly treated with a flow-diverter is used, enabling quantitative comparisons with classical approaches for both intra-saccular velocities and computational costs reduction. The proposed heterogeneous model endeavors to bridge the gap between computational fluid dynamics and clinical applications and ushers in a new era of numerical treatment planning with minimally costing computational tools.

Cerebral aneurysm flow diverter modeled as a thin inhomogeneous porous medium in hemodynamic simulations

Rapid and accurate simulation of cerebral aneurysm flow modifications by flow diverters (FDs) can help improving patient-specific intervention and predicting treatment outcome. However, when FD devices are explicitly represented in computational fluid dynamics (CFD) simulations, flow around the stent wires must be resolved, leading to high computational cost. Classic porous medium (PM) methods can reduce computational expense but cannot capture the inhomogeneous FD wire distribution once implanted on a cerebral artery and thus cannot accurately model the post-stenting aneurysmal flow. We report a novel approach that models the FD flow modification as a thin inhomogeneous porous medium (iPM). It improves over the classic PM approaches in two ways. First, the FD is more appropriately treated as a thin screen, which is more accurate than the classic 3D-PM-based Darcy-Forchheimer relation. Second, pressure drop is calculated cell-by-cell using the local FD geometric parameters across an inhomogeneous PM. We applied the iPM technique to simulating the post-stenting hemodynamics of three patient-specific aneurysms. To test its accuracy and speed, we compared the results from the iPM technique against CFD simulations with explicit FD devices. The iPM CFD ran 500% faster than the explicit CFD while achieving 94%-99% accuracy; thus, iPM is a promising clinical bedside modeling tool to assist endovascular interventions with FD and stents.

Flow diverter modeled as heterogeneous and anisotropic porous medium: Simulation, experimental validation and case analysis

Simulation of flow diverter (FD) treated aneurysm can evaluate treatment efficacy and aid treatment planning. However, explicit modeling of thin wires of FD impose extremely high demand of computational resources and time, which limit its use in time-sensitive presurgical planning. One alternative approach is to model FD as homogenous porous medium, which saves time but with compromise in accuracy. We proposed a new method to model FD as heterogeneous and anisotropic porous medium whose properties were determined from local porosity. The new method was validated by comparing with PIV measurement from an in-vitro phantom. Simulation result was in good agreement with experimental measurement. Four patient cases were further analyzed to compare the new method with the homogenous porous media method. Results showed that in patient cases with curved artery, new method was preferred over the homogenous method, as the assumption of homogenous porosity led to overpredicted flow reduction effect by as much as 87.9%, which may lead to overoptimistic decision making and poor prognosis. Our new method can provide timely and accurate simulation to aid in the treatment planning of aneurysms.

Implementation of computer simulation to assess flow diversion treatment outcomes: systematic review and meta-analysis

Introduction

Despite a decade of research into virtual stent deployment and the post-stenting aneurysmal hemodynamics, the hemodynamic factors which correlate with successful treatment remain inconclusive. We aimed to examine the differences in various post-treatment hemodynamic parameters between successfully and unsuccessfully treated cases, and to quantify the additional flow diversion achievable through stent compaction or insertion of a second stent.

Methods

A systematic review and meta-analysis were performed on eligible studies published from 2000 to 2019. We first classified cases according to treatment success (aneurysm occlusion) and then calculated the pooled standardized mean differences (SMD) of each available parameter to examine their association with clinical outcomes. Any additional flow diversion arising from the two common strategies for improving the stent wire density was quantified by pooling the results of such studies.

Results

We found that differences in the aneurysmal inflow rate (SMD −6.05, 95% CI −10.87 to −1.23, p=0.01) and energy loss (SMD −5.28, 95% CI −7.09 to −3.46, p<0.001) between the successfully and unsuccessfully treated groups were indicative of statistical significance, in contrast to wall shear stress (p=0.37), intra-aneurysmal average velocity (p=0.09), vortex core-line length (p=0.46), and shear rate (p=0.09). Compacting a single stent could achieve additional flow diversion comparable to that by dual-stent implantation.

Conclusions

Inflow rate and energy loss have shown promise as identifiers to discriminate between successful and unsuccessful treatment, pending future research into their diagnostic performance to establish optimal cut-off values.

Stenting as porous media in anatomically accurate geometries. A comparison of models and spatial heterogeneity

Modelling intracranial aneurysm blood flow after flow diverter treatment has proven to be of great scientific and clinical interest. One of the reasons for not having CFD as an everyday clinical tool yet is the time required to set-up such simulations plus the required computational time. The speed-up of these simulations can have a considerable impact during treatment planning and device selection. Modelling flow diverters as a porous medium (PM) can considerably improve the computational time. Many models have been presented in literature, but quantitative comparisons between models are scarce. In this study, the untreated case, the explicit definition of the flow diverter wires as no-slip boundary condition and five different porous medium models were chosen for comparison, and evaluated on intracranial aneurysm of 14 patients with different shapes, sizes, and locations. CFD simulations were made using finite volume method on steady flow conditions. Velocities, kinetic energy, wall shear stress, and computational time were assessed for each model. Then, all models are compared against the no-slip boundary condition using non parametric Kolmogorov-Smirnov test. The model with least performance showed a mean K-S statistic of 0.31 and deviance of 0.2, while the model with best values always gave K-S statistics below 0.2. Kinetic energy between PM models varied between an over estimation of 218.3% and an under estimation of 73.06%. Also, speedups were between 4.75x and 5.3x (stdev: 0.38x and 0.15x) when using PM models. Flow diverters can be simulated with PM with a good agreement to standard CFD simulations were FD wires are represented with no-slip boundary condition in less than a quarter of the time. Best results were obtained on PM models based on geometrical properties, in particular, when using a heterogeneous medium based on equations for flat rhomboidal wire frames.

Optimization of porous stents for endovascular repair of abdominal aortic aneurysms

This study presents a simulation-based methodology to design porous stents to induce suitable hemodynamic environments inside abdominal aortic aneurysm (AAA) sacs. In the proposed methodology, an optimization algorithm iteratively modifies the porosity distribution of the stent and executes a computational fluid dynamics (CFD) simulation to determine the effect of these changes on the hemodynamic conditions inside the aneurysm sac. The optimization iterations proceed until relevant hemodynamic parameters are within ranges prescribed a priori by the user as desirable to control the progression of the AAA. The resulting porosity distribution uniquely describes the porous stent design that can control the hemodynamic environment (eg, shear stress at the aneurysm wall, pressure distribution, residence time), reducing AAA rupture risks and improving treatment efficacy. To demonstrate its potential, the proposed methodology is applied to idealized AAA geometry under steady-state flow conditions, though it may be easily applied to more complex AAA geometries under transient, pulsatile flow conditions. The proposed methodology has the potential to enable the design of a new generation of porous stents tailored to patient-specific geometries and flow conditions, to improve patient outcomes.

Hemodynamics of Cerebral Aneurysms: Connecting Medical Imaging and Biomechanical Analysis

In the last two decades, numerous studies have conducted patient-specific computations of blood flow dynamics in cerebral aneurysms and reported correlations between various hemodynamic metrics and aneurysmal disease progression or treatment outcomes. Nevertheless, intra-aneurysmal flow analysis has not been adopted in current clinical practice, and hemodynamic factors usually are not considered in clinical decision making. This review presents the state of the art in cerebral aneurysm imaging and image-based modeling, discussing the advantages and limitations of each approach and focusing on the translational value of hemodynamic analysis. Combining imaging and modeling data obtained from different flow modalities can improve the accuracy and fidelity of resulting velocity fields and flow-derived factors that are thought to affect aneurysmal disease progression. It is expected that predictive models utilizing hemodynamic factors in combination with patient medical history and morphological data will outperform current risk scores and treatment guidelines. Possible future directions include novel approaches enabling data assimilation and multimodality analysis of cerebral aneurysm hemodynamics.

A comparative study of porous medium CFD models for flow diverter stents: Advantages and shortcomings

In computational fluid dynamics, there is a high interest in modeling flow diverter stents as porous media due to its reduced computational loads. One of the main difficulties of such models is proper parameter setup. Most authors assume flow diverter's wire screen as an isotropic and homogeneous medium, while others proposes anisotropic configurations, yet very little is discussed about the effect of these assumptions on model's accuracy. In this paper, we compare the effect of different models on hemodynamics in relation to their parameters. The fidelity and efficiency of the different models to capture wire screen effect on fluid flow are quantitatively analyzed and compared.

Model for pressure drop and flow deflection in the numerical simulation of stents in aneurysms

The numerical simulation of flow diverters like stents contributes to the development and improvement of endovascular stenting procedures, leading ultimately to an improved treatment of intracranial aneurysms. Due to the scale difference between the struts of flow diverters and the full artery, it is common to avoid fully resolved simulations at the level of the stent porosity. Instead, the effect of stents on the flow is represented by a heuristic continuum model. However, the commonly used porous media models describe the properties of flow diverters only partially, because they do not explicitly account for the deflection of the flow direction by the stent. We show that this deficiency can be circumvented by adopting the theoretical framework of screen models. The article first reviews existing screen models. It then proposes an explicit formula for the drag and the deflection coefficient, as predicted by each model, for both perpendicular and inclined angles. The results of 2D numerical simulations are used to formulate a generalization of these formulas, to achieve best results in the case of stent modeling. The obtained model is then validated, again through 2D numerical simulation.

Virtual endovascular treatment of intracranial aneurysms: models and uncertainty

Virtual endovascular treatment models (VETMs) have been developed with the view to aid interventional neuroradiologists and neurosurgeons to pre-operatively analyze the comparative efficacy and safety of endovascular treatments for intracranial aneurysms. Based on the current state of VETMs in aneurysm rupture risk stratification and in patient-specific prediction of treatment outcomes, we argue there is a need to go beyond personalized biomechanical flow modeling assuming deterministic parameters and error-free measurements. The mechanobiological effects associated with blood clot formation are important factors in therapeutic decision making and models of post-treatment intra-aneurysmal biology and biochemistry should be linked to the purely hemodynamic models to improve the predictive power of current VETMs. The influence of model and parameter uncertainties associated to each component of a VETM is, where feasible, quantified via a random-effects meta-analysis of the literature. This allows estimating the pooled effect size of these uncertainties on aneurysmal wall shear stress. From such meta-analyses, two main sources of uncertainty emerge where research efforts have so far been limited: (1) vascular wall distensibility, and (2) intra/intersubject systemic flow variations. In the future, we suggest that current deterministic computational simulations need to be extended with strategies for uncertainty mitigation, uncertainty exploration, and sensitivity reduction techniques. WIREs Syst Biol Med 2017, 9:e1385. doi: 10.1002/wsbm.1385 For further resources related to this article, please visit the WIREs website.

In Vitro Investigation of a New Thin Film Nitinol-Based Neurovascular Flow Diverter

Fusiform and wide-neck cerebral aneurysms (CAs) can be challenging to treat with conventional endovascular or surgical approaches. Recently, flow diverters have been developed to treat these cases by diverting flow away from the aneurysm rather than occluding it. The pipeline embolization device (PED), which embodies a single-layer braided design, is best known among available flow diverters. While the device has demonstrated success in recent trials, late aneurysmal rupture after PED treatment has been a concern. More recently, a new generation of dual-layer devices has emerged that includes a novel hyperelastic thin film nitinol (HE-TFN)-covered design. In this study, we compare fluid dynamic performance between the PED and HE-TFN devices using particle image velocimetry (PIV). The PED has a pore density of 12.5–20 pores/mm2 and a porosity of 65–70%. The two HE-TFN flow diverters have pore densities of 14.75 pores/mm2 and 40 pores/mm2, and porosities of 82% and 77%, respectively. Conventional wisdom suggests that the lower porosity PED would decrease intra-aneurysmal flow to the greatest degree. However, under physiologically realistic pulsatile flow conditions, average drops in root-mean-square (RMS) velocity (VRMS) within the aneurysm of an idealized physical flow model were 42.8–73.7% for the PED and 68.9–82.7% for the HE-TFN device with the highest pore density. Interestingly, examination of collateral vessel flows in the same model also showed that the HE-TFN design allowed for greater collateral perfusion than the PED. Similar trends were observed under steady flow conditions in the idealized model. In a more clinically realistic scenario wherein an anatomical aneurysm model was investigated, the PED affected intra-aneurysmal VRMS reductions of 64.3% and 56.3% under steady and pulsatile flow conditions, respectively. In comparison, the high pore density HE-TFN device reduced intra-aneurysmal VRMS by 88% and 71.3% under steady and pulsatile flow conditions, respectively. We attribute the superior performance of the HE-TFN device to higher pore density, which may play a more important role in modifying aneurysmal fluid dynamics than the conventional flow diverter design parameter of greatest general interest, absolute porosity. Finally, the PED led to more elevated intra-aneurysmal pressures after deployment, which provides insight into a potential mechanism for late rupture following treatment with the device.