Variability of computational fluid dynamics solutions for pressure and flow in a giant aneurysm: the ASME 2012 Summer Bioengineering Conference CFD Challenge

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.

Does the DSA reconstruction kernel affect hemodynamic predictions in intracranial aneurysms? An analysis of geometry and blood flow variations

BACKGROUND

Computational fluid dynamics (CFD) blood flow predictions in intracranial aneurysms promise great potential to reveal patient-specific flow structures. Since the workflow from image acquisition to the final result includes various processing steps, quantifications of the individual introduced potential error sources are required.

METHODS

Three-dimensional (3D) reconstruction of the acquired imaging data as input to 3D model generation was evaluated. Six different reconstruction modes for 3D digital subtraction angiography (DSA) acquisitions were applied to eight patient-specific aneurysms. Segmentations were extracted to compare the 3D luminal surfaces. Time-dependent CFD simulations were carried out in all 48 configurations to assess the velocity and wall shear stress (WSS) variability due to the choice of reconstruction kernel.

RESULTS

All kernels yielded good segmentation agreement in the parent artery; deviations of the luminal surface were present at the aneurysm neck (up to 34.18%) and in distal or perforating arteries. Observations included pseudostenoses as well as noisy surfaces, depending on the selected reconstruction kernel. Consequently, the hemodynamic predictions show a mean SD of 11.09% for the aneurysm neck inflow rate, 5.07% for the centerline-based velocity magnitude, and 17.83%/9.53% for the mean/max aneurysmal WSS, respectively. In particular, vessel sections distal to the aneurysms yielded stronger variations of the CFD values.

CONCLUSIONS

The choice of reconstruction kernel for DSA data influences the segmentation result, especially for small arteries. Therefore, if precise morphology measurements or blood flow descriptions are desired, a specific reconstruction setting is required. Furthermore, research groups should be encouraged to denominate the kernel types used in future hemodynamic studies.

A comparison of hemodynamic metrics and intraluminal thrombus burden in a common iliac artery aneurysm

Aneurysms of the common iliac artery (CIAA) are typically found in association with an abdominal aortic aneurysm (AAA). Isolated CIAAs, in the absence of an AAA, are uncommon. Similar to AAAs, CIAA may develop intraluminal thrombus (ILT). As isolated CIAAs have a contralateral common iliac artery for comparison, they provide an opportunity to study the hemodynamic mechanisms behind ILT formation. In this study, we compared a large isolated CIAA and the contralateral iliac artery using computational fluid dynamics to determine if hemodynamic metrics correlate with the location of ILT. We performed a comprehensive computational fluid dynamics study and investigated the residence time of platelets and monocytes, velocity fields, time-averaged wall shear stress, oscillatory shear index, and endothelial cell activation potential. We then correlated these data to ILT burden determined with computed tomography. We found that high cell residence times, low time-averaged wall shear stress, high oscillatory shear index, and high endothelial cell activation potential all correlate with regions of ILT development. Our results show agreement with previous hypotheses of thrombus formation in AAA and provide insights into the computational hemodynamics of iliac artery aneurysms.

Cerebral aneurysm blood flow simulations are sensitive to basic solver settings

Computational modeling of peri-aneurysmal hemodynamics is typically carried out with commercial software without knowledge of the sensitivity of the model to variation in input values. For three aneurysm models, we carried out a formal sensitivity analysis and optimization strategy focused on variation in timestep duration and model residual error values and their impact on hemodynamic outputs. We examined the solution sensitivity to timestep sizes of 10^-3s, 10^-4s, and 10^-5s while using model residual error values of 10^-4, 10^-5, and 10^-6 using ANSYS Fluent to observe compounding errors and to optimize solver settings for computational efficiency while preserving solution accuracy. Simulations were compared qualitatively and quantitatively against the most rigorous combination of timestep and residual parameters, 10^-5s and 10^-6, respectively. A case using 10^-4s timesteps, with 10^-5 residual errors proved to be a converged solution for all three models with mean velocity and WSS difference RMS errors less than <1% compared with baseline, and was computationally efficient with a simulation time of 62h per cardiac cycle compared to 392h for baseline for the model with the most complex flow simulation. The worst case of our analysis, using 10^-3s timesteps and 10^-4 residual errors, was still able to predict the dominant vortex in the aneurysm, but its velocity and WSS RMS errors reached 20%. Even with an appealing simulation time of 11h per cycle for the model with the most complex flow, the worst case analysis solution exhibited compounding errors from large timesteps and residual errors. To resolve time-dependent flow characteristics, CFD simulations of cerebral aneurysms require sufficiently small timestep size and residual error. Simulations with both insufficient timestep and residual resolution are vulnerable to compounding errors.

Hemodynamics of Flow Diverters

Cerebral aneurysms are pathological focal evaginations of the arterial wall at and around the junctions of the circle of Willis. Their tenuous walls predispose aneurysms to leak or rupture leading to hemorrhagic strokes with high morbidity and mortality rates. The endovascular treatment of cerebral aneurysms currently includes the implantation of fine-mesh stents, called flow diverters, within the parent artery bearing the aneurysm. By mitigating flow velocities within the aneurysmal sac, the devices preferentially induce thrombus formation in the aneurysm within hours to days. In response to the foreign implant, an endothelialized arterial layer covers the luminal surface of the device over a period of days to months. Organization of the intraneurysmal thrombus leads to resorption and shrinkage of the aneurysm wall and contents, eventually leading to beneficial remodeling of the pathological site to a near-physiological state. The devices' primary function of reducing flow activity within aneurysms is corollary to their mesh structure. Complete specification of the device mesh structure, or alternately device permeability, necessarily involves the quantification of two variables commonly used to characterize porous media—mesh porosity and mesh pore density. We evaluated the flow alteration induced by five commercial neurovascular devices of varying porosity and pore density (stents: Neuroform, Enterprise, and LVIS; flow diverters: Pipeline and FRED) in an idealized sidewall aneurysm model. As can be expected in such a model, all devices substantially reduced intraneurysmal kinetic energy as compared to the nonstented case with the coarse-mesh stents inducing a 65–80% reduction whereas the fine-mesh flow diverters induced a near-complete flow stagnation (∼98% reduction). We also note a trend toward greater device efficacy (lower intraneurysmal flow) with decreasing device porosity and increasing device pore density. Several such flow studies have been and are being conducted in idealized as well as patient-derived geometries with the overarching goals of improving device design, facilitating treatment planning (what is the optimal device for a specific aneurysm), and predicting treatment outcome (will a specific aneurysm treated with a specific device successfully occlude over the long term). While the results are generally encouraging, there is poor standardization of study variables between different research groups, and any consensus will only be reached after standardized studies are conducted on collectively large datasets. Biochemical variables may have to be incorporated into these studies to maximize predictive values.

SimVascular: An Open Source Pipeline for Cardiovascular Simulation

Patient-specific cardiovascular simulation has become a paradigm in cardiovascular research and is emerging as a powerful tool in basic, translational and clinical research. In this paper we discuss the recent development of a fully open-source SimVascular software package, which provides a complete pipeline from medical image data segmentation to patient-specific blood flow simulation and analysis. This package serves as a research tool for cardiovascular modeling and simulation, and has contributed to numerous advances in personalized medicine, surgical planning and medical device design. The SimVascular software has recently been refactored and expanded to enhance functionality, usability, efficiency and accuracy of image-based patient-specific modeling tools. Moreover, SimVascular previously required several licensed components that hindered new user adoption and code management and our recent developments have replaced these commercial components to create a fully open source pipeline. These developments foster advances in cardiovascular modeling research, increased collaboration, standardization of methods, and a growing developer community.

Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms

We develop efficient numerical methods for fractional order PDEs, and employ them to investigate viscoelastic constitutive laws for arterial wall mechanics. Recent simulations using one-dimensional models [1] have indicated that fractional order models may offer a more powerful alternative for modeling the arterial wall response, exhibiting reduced sensitivity to parametric uncertainties compared with the integer-calculus-based models. Here, we study three-dimensional (3D) fractional PDEs that naturally model the continuous relaxation properties of soft tissue, and for the first time employ them to simulate flow structure interactions for patient-specific brain aneurysms. To deal with the high memory requirements and in order to accelerate the numerical evaluation of hereditary integrals, we employ a fast convolution method [2] that reduces the memory cost to O(log(N)) and the computational complexity to O(N log(N)). Furthermore, we combine the fast convolution with high-order backward differentiation to achieve third-order time integration accuracy. We confirm that in 3D viscoelastic simulations, the integer order models strongly depends on the relaxation parameters, while the fractional order models are less sensitive. As an application to long-time simulations in complex geometries, we also apply the method to modeling fluid-structure interaction of a 3D patient-specific compliant cerebral artery with an aneurysm. Taken together, our findings demonstrate that fractional calculus can be employed effectively in modeling complex behavior of materials in realistic 3D time-dependent problems if properly designed efficient algorithms are employed to overcome the extra memory requirements and computational complexity associated with the non-local character of fractional derivatives.

Investigation of blood flow in the external carotid artery and its branches with a new 0D peripheral model

BACKGROUND

Patient-specific modelling in clinical studies requires a realistic simulation to be performed within a reasonable computational time. The aim of this study was to develop simple but realistic outflow boundary conditions for patient-specific blood flow simulation which can be used to clarify the distribution of the anticancer agent in intra-arterial chemotherapy for oral cancer.

METHODS

In this study, the boundary conditions are expressed as a zero dimension (0D) resistance model of the peripheral vessel network based on the fractal characteristics of branching arteries combined with knowledge of the circulatory system and the energy minimization principle. This resistance model was applied to four patient-specific blood flow simulations at the region where the common carotid artery bifurcates into the internal and external carotid arteries.

RESULTS

Results of these simulations with the proposed boundary conditions were compared with the results of ultrasound measurements for the same patients. The pressure was found to be within the physiological range. The difference in velocity in the superficial temporal artery results in an error of 5.21 ± 0.78 % between the numerical results and the measurement data.

CONCLUSIONS

The proposed outflow boundary conditions, therefore, constitute a simple resistance-based model and can be used for performing accurate simulations with commercial fluid dynamics software.

Multiscale modeling and simulation of brain blood flow

The aim of this work is to present an overview of recent advances in multi-scale modeling of brain blood flow. In particular, we present some approaches that enable the in silico study of multi-scale and multi-physics phenomena in the cerebral vasculature. We discuss the formulation of continuum and atomistic modeling approaches, present a consistent framework for their concurrent coupling, and list some of the challenges that one needs to overcome in achieving a seamless and scalable integration of heterogeneous numerical solvers. The effectiveness of the proposed framework is demonstrated in a realistic case involving modeling the thrombus formation process taking place on the wall of a patient-specific cerebral aneurysm. This highlights the ability of multi-scale algorithms to resolve important biophysical processes that span several spatial and temporal scales, potentially yielding new insight into the key aspects of brain blood flow in health and disease. Finally, we discuss open questions in multi-scale modeling and emerging topics of future research.

The Computational Fluid Dynamics Rupture Challenge 2013—Phase II: Variability of Hemodynamic Simulations in Two Intracranial Aneurysms

With the increased availability of computational resources, the past decade has seen a rise in the use of computational fluid dynamics (CFD) for medical applications. There has been an increase in the application of CFD to attempt to predict the rupture of intracranial aneurysms, however, while many hemodynamic parameters can be obtained from these computations, to date, no consistent methodology for the prediction of the rupture has been identified. One particular challenge to CFD is that many factors contribute to its accuracy; the mesh resolution and spatial/temporal discretization can alone contribute to a variation in accuracy. This failure to identify the importance of these factors and identify a methodology for the prediction of ruptures has limited the acceptance of CFD among physicians for rupture prediction. The International CFD Rupture Challenge 2013 seeks to comment on the sensitivity of these various CFD assumptions to predict the rupture by undertaking a comparison of the rupture and blood-flow predictions from a wide range of independent participants utilizing a range of CFD approaches. Twenty-six groups from 15 countries took part in the challenge. Participants were provided with surface models of two intracranial aneurysms and asked to carry out the corresponding hemodynamics simulations, free to choose their own mesh, solver, and temporal discretization. They were requested to submit velocity and pressure predictions along the centerline and on specified planes. The first phase of the challenge, described in a separate paper, was aimed at predicting which of the two aneurysms had previously ruptured and where the rupture site was located. The second phase, described in this paper, aims to assess the variability of the solutions and the sensitivity to the modeling assumptions. Participants were free to choose boundary conditions in the first phase, whereas they were prescribed in the second phase but all other CFD modeling parameters were not prescribed. In order to compare the computational results of one representative group with experimental results, steady-flow measurements using particle image velocimetry (PIV) were carried out in a silicone model of one of the provided aneurysms. Approximately 80% of the participating groups generated similar results. Both velocity and pressure computations were in good agreement with each other for cycle-averaged and peak-systolic predictions. Most apparent “outliers” (results that stand out of the collective) were observed to have underestimated velocity levels compared to the majority of solutions, but nevertheless identified comparable flow structures. In only two cases, the results deviate by over 35% from the mean solution of all the participants. Results of steady CFD simulations of the representative group and PIV experiments were in good agreement. The study demonstrated that while a range of numerical schemes, mesh resolution, and solvers was used, similar flow predictions were observed in the majority of cases. To further validate the computational results, it is suggested that time-dependent measurements should be conducted in the future. However, it is recognized that this study does not include the biological aspects of the aneurysm, which needs to be considered to be able to more precisely identify the specific rupture risk of an intracranial aneurysm.

The Effects That Cardiac Motion has on Coronary Hemodynamics and Catheter Trackability Forces for the Treatment of Coronary Artery Disease: An In Vitro Assessment

The coronary arterial tree experiences large displacements due to the contraction and expansion of the cardiac muscle and may influence coronary haemodynamics and stent placement. The accurate measurement of catheter trackability forces within physiological relevant test systems is required for optimum catheter design. The effects of cardiac motion on coronary flowrates, pressure drops, and stent delivery has not been previously experimentally assessed. A cardiac simulator was designed and manufactured which replicates physiological coronary flowrates and cardiac motion within a patient-specific geometry. A motorized delivery system delivered a commercially available coronary stent system and monitored the trackability forces along three phantom patient-specific thin walled compliant coronary vessels supported by a dynamic cardiac phantom model. Pressure drop variation is more sensitive to cardiac motion than outlet flowrates. Maximum pressure drops varied from 7 to 49 mmHg for a stenosis % area reduction of 56 to 90%. There was a strong positive linear correlation of cumulative trackability force with the cumulative curvature. The maximum trackability forces and curvature ranged from 0.24 to 0.87 N and 0.06 to 0.22 mm(-1) respectively for all three vessels. There were maximum and average percentage differences in trackability forces of (23-49%) and (1.9-5.2%) respectively when comparing a static pressure case with the inclusion of pulsatile flow and cardiac motion. Cardiac motion with pulsatile flow significantly altered (p value <0.001) the trackability forces along the delivery pathways with high local percentage variations and pressure drop measurements.

A unified method for estimating pressure losses at vascular junctions

In reduced-order (0D/1D) blood or respiratory flow models, pressure losses at junctions are usually neglected. However, these may become important where velocities are high and significant flow redirection occurs. Current methods for estimating losses rely on relatively complex empirical equations that are only valid for specific junction geometries and flow regimes. In pulsatile multi-directional flows, switching between empirical equations upon reversing flow may introduce unrealistic discontinuities in simulated haemodynamic waveforms. Drawing from work by Bassett et al. (SAE Trans 112:565-583, 2003), we therefore developed a unified method (Unified0D) for estimating loss coefficients that can be applied to any junction (i.e. any number of branches at any angle) and any flow regime. Discontinuities in simulated waveforms were avoided by extending Bassett et al.'s control volume-based method to incorporate a 'pseudodatum' supplier branch, an imaginary effective vessel containing all inflow to the junction. Energy exchange between diverging flow streams was also accounted for empirically. The formulation was validated using high resolution computational fluid dynamics in a wide range flow conditions and junction configurations. In a pulsatile 1D simulation exhibiting transitions between four different flow regimes, the new formulation produced smooth transitions in calculated pressure losses.

Patient-specific computational modeling of blood flow in the pulmonary arterial circulation

Computational fluid dynamics (CFD) modeling of the pulmonary vasculature has the potential to reveal continuum metrics associated with the hemodynamic stress acting on the vascular endothelium. It is widely accepted that the endothelium responds to flow-induced stress by releasing vasoactive substances that can dilate and constrict blood vessels locally. The objectives of this study are to examine the extent of patient specificity required to obtain a significant association of CFD output metrics and clinical measures in models of the pulmonary arterial circulation, and to evaluate the potential correlation of wall shear stress (WSS) with established metrics indicative of right ventricular (RV) afterload in pulmonary hypertension (PH). Right Heart Catheterization (RHC) hemodynamic data and contrast-enhanced computed tomography (CT) imaging were retrospectively acquired for 10 PH patients and processed to simulate blood flow in the pulmonary arteries. While conducting CFD modeling of the reconstructed patient-specific vasculatures, we experimented with three different outflow boundary conditions to investigate the potential for using computationally derived spatially averaged wall shear stress (SAWSS) as a metric of RV afterload. SAWSS was correlated with both pulmonary vascular resistance (PVR) (R(2)=0.77, P<0.05) and arterial compliance (C) (R(2)=0.63, P<0.05), but the extent of the correlation was affected by the degree of patient specificity incorporated in the fluid flow boundary conditions. We found that decreasing the distal PVR alters the flow distribution and changes the local velocity profile in the distal vessels, thereby increasing the local WSS. Nevertheless, implementing generic outflow boundary conditions still resulted in statistically significant SAWSS correlations with respect to both metrics of RV afterload, suggesting that the CFD model could be executed without the need for complex outflow boundary conditions that require invasively obtained patient-specific data. A preliminary study investigating the relationship between outlet diameter and flow distribution in the pulmonary tree offers a potential computationally inexpensive alternative to pressure based outflow boundary conditions.

Narrowing the Expertise Gap for Predicting Intracranial Aneurysm Hemodynamics: Impact of Solver Numerics versus Mesh and Time-Step Resolution

BACKGROUND AND PURPOSE

Recent high-resolution computational fluid dynamics studies have uncovered the presence of laminar flow instabilities and possible transitional or turbulent flow in some intracranial aneurysms. The purpose of this study was to elucidate requirements for computational fluid dynamics to detect these complex flows, and, in particular, to discriminate the impact of solver numerics versus mesh and time-step resolution.

MATERIALS AND METHODS

We focused on 3 MCA aneurysms, exemplifying highly unstable, mildly unstable, or stable flow phenotypes, respectively. For each, the number of mesh elements was varied by 320× and the number of time-steps by 25×. Computational fluid dynamics simulations were performed by using an optimized second-order, minimally dissipative solver, and a more typical first-order, stabilized solver.

RESULTS

With the optimized solver and settings, qualitative differences in flow and wall shear stress patterns were negligible for models down to ∼800,000 tetrahedra and ∼5000 time-steps per cardiac cycle and could be solved within clinically acceptable timeframes. At the same model resolutions, however, the stabilized solver had poorer accuracy and completely suppressed flow instabilities for the 2 unstable flow cases. These findings were verified by using the popular commercial computational fluid dynamics solver, Fluent.

CONCLUSIONS

Solver numerics must be considered at least as important as mesh and time-step resolution in determining the quality of aneurysm computational fluid dynamics simulations. Proper computational fluid dynamics verification studies, and not just superficial grid refinements, are therefore required to avoid overlooking potentially clinically and biologically relevant flow features.

The Computational Fluid Dynamics Rupture Challenge 2013—Phase I: prediction of rupture status in intracranial aneurysms

BACKGROUND AND PURPOSE

Rupture risk assessment for intracranial aneurysms remains challenging, and risk factors, including wall shear stress, are discussed controversially. The primary purpose of the presented challenge was to determine how consistently aneurysm rupture status and rupture site could be identified on the basis of computational fluid dynamics.

MATERIALS AND METHODS

Two geometrically similar MCA aneurysms were selected, 1 ruptured, 1 unruptured. Participating computational fluid dynamics groups were blinded as to which case was ruptured. Participants were provided with digitally segmented lumen geometries and, for this phase of the challenge, were free to choose their own flow rates, blood rheologies, and so forth. Participants were asked to report which case had ruptured and the likely site of rupture. In parallel, lumen geometries were provided to a group of neurosurgeons for their predictions of rupture status and site.

RESULTS

Of 26 participating computational fluid dynamics groups, 21 (81%) correctly identified the ruptured case. Although the known rupture site was associated with low and oscillatory wall shear stress, most groups identified other sites, some of which also experienced low and oscillatory shear. Of the 43 participating neurosurgeons, 39 (91%) identified the ruptured case. None correctly identified the rupture site.

CONCLUSIONS

Geometric or hemodynamic considerations favor identification of rupture status; however, retrospective identification of the rupture site remains a challenge for both engineers and clinicians. A more precise understanding of the hemodynamic factors involved in aneurysm wall pathology is likely required for computational fluid dynamics to add value to current clinical decision-making regarding rupture risk.

Presurgical planning using image-based in silico anatomical and functional characterization of Tetralogy of Fallot with associated anomalies

OBJECTIVES

The ideal vascular reconstruction strategy for anomalies associated with Tetralogy of Fallot (ToF) is often driven by observations made at the operating table. A method to conduct accurate studies to assess the virtues of a certain surgical technique to guide surgical decisions is found wanting. We hypothesize that patient-specific computed tomography (CT)-based morphometry followed by in silico reconstruction of viable surgical options with haemodynamic function assessment using computational fluid dynamics (CFD) can guide surgical decisions and help forecast functional outcomes without invasive measurements.

METHODS

A ToF patient associated with additional left pulmonary artery (LPA) stenosis and a patent ductus arteriosus (PDA) who underwent a successful correction using a single pericardial patch (SPP) was selected as a reference for morphological characterization after 3D anatomical reconstruction from CT images. A second patient with morphological similarities established after scaled, co-registration with the reference patient was selected for virtual correction using the same strategy (i.e. SPP repair). CFD was employed for functional analysis of pulmonary artery (PA) pressure gradients in the baseline preoperative and virtually corrected models, using patient-specific cardiac output and Qp/Qs information.

RESULTS

SPP repair was modelled in silico following surgical steps of PDA ligation, creation of an incision along the LPA and main PA (MPA) and finally suturing a rectangular SPP, effectively reducing MPA to LPA angle. Analysis of SPP repair revealed significant reduction in right ventricular outflow tract-LPA pressure gradient with improved left-right PA flow distribution in both patients.

CONCLUSIONS

In silico surgery followed by CFD evaluation has the potential in augmenting morphology-guided decisions on surgical strategy and holds promise in preoperatively determining optimal intervention strategy. This is a paradigm-shifting concept to evaluate patient-specific anomalies in a manner more objective than mere visual inspection of anatomical traits from radiology images. Present studies are focused on an analysis with a larger patient cohort to establish a library of ToF patients' successful surgical outcomes to inform morphology-based selection of surgical strategy.

Flow visualization of recurrent aneurysms after coil embolization by 3D phase-contrast MRI

BACKGROUND

Flow patterns in cerebral aneurysms are clinically important. Information on inflow patterns into aneurysms is especially helpful in preventing a recurrence after coil embolization. Computational fluid dynamics (CFD) simulations of patient-specific cerebral aneurysms are feasible and provide information on flow patterns. However, flow visualization by CFD simulations is challenging for recurrent aneurysms after coil embolization because coils make it difficult to obtain precise geometry of the recurrent aneurysms. In this study, we assessed the feasibility of flow visualization of recurrent aneurysms using 3D phase-contrast magnetic resonance imaging (PC-MRI).

METHOD

Time-of-flight magnetic resonance angiography and 3D PC-MRI were performed in eight cases of recurrent aneurysms after coil embolization. We attempted to visualize flow inside the aneurysms using data of 3D PC-MRI and evaluated the visualization. Additionally, CFD simulations were performed in a single case.

RESULTS

Inflow into aneurysms was visualized in all eight cases (100%). Flow patterns inside aneurysms were visualized in six cases (75%), and these were associated with a large size of recurrent aneurysms (mean size, 10.3 mm for visualized cases vs. 4.8 mm for unvisualized cases; p = 0.046, Mann-Whitney test). Flow patterns were similar between PC-MRI and CFD simulations. PC-MRI was faster and easier for observing inflow patterns than CFD simulations.

CONCLUSIONS

This is the first study to demonstrate that flow visualization of recurrent aneurysms by 3D PC-MRI is feasible. This technique may be more practical and easier than CFD simulations, and may provide clinically helpful information.

Proximal stenosis may induce initiation of cerebral aneurysms by increasing wall shear stress and wall shear stress gradient

Hemodynamic parameters, such as wall shear stress (WSS), WSS gradient (WSSG), aneurysm formation indicator (AFI), or gradient oscillatory number (GON), have been proposed to be linked to initiation of cerebral aneurysms. However, how such conditions occur in humans is unclear. We encountered a rare and interesting case to address this issue. A patient had a newly formed aneurysm with proximal stenosis, which was confirmed by serial imagings. We made two pre-aneurysm models: one with stenosis and the other without stenosis. We performed computational fluid dynamics simulations for these models. Owing to jet flow caused by the stenosis, the maximum WSS and WSSG on the aneurysm initiation site were approximately doubled and tripled, respectively. However, the oscillatory shear index (OSI), AFI, and GON did not change substantially by the stenosis. Computer simulations using artificial vascular models with different degrees of proximal stenosis at different distances demonstrated that oscillatory shear index, AFI, and GON did not change substantially by the stenosis. These results showed that proximal stenosis caused high WSS and high WSSG at the aneurysm initiation site, possibly leading to aneurysm initiation. Proximal stenosis may be a potential factor to induce initiation of one class of cerebral aneurysms by increasing WSS and WSSG.

Hemodynamic effects of stent struts versus straightening of vessels in stent-assisted coil embolization for sidewall cerebral aneurysms

Background

Recent clinical studies have shown that recanalization rates are lower in stent-assisted coil embolization than in coiling alone in the treatment of cerebral aneurysms.

Objective

This study aimed to assess and compare the hemodynamic effect of stent struts and straightening of vessels by stent placement on reducing flow velocity in sidewall aneurysms, with the goal of reducing recanalization rates.

Methods

We evaluated 16 sidewall aneurysms treated with Enterprise stents. We performed computational fluid dynamics simulations using patient-specific geometries before and after treatment, with or without stent struts.

Results

Stent placement straightened vessels by a mean (±standard deviation) of 12.9°±13.1° 6 months after treatment. Placement of stent struts in the initial vessel geometries reduced flow velocity in aneurysms by 23.1%±6.3%. Straightening of vessels without stent struts reduced flow velocity by 9.6%±12.6%. Stent struts had significantly stronger effects on reducing flow velocity than straightening (P = 0.004, Wilcoxon test). Deviation of the effects was larger by straightening than by stent struts (P = 0.01, F-test). The combination of stent struts and straightening reduced flow velocity by 32.6%±12.2%. There was a trend that larger inflow angles produced a larger reduction in flow velocity by straightening of vessels (P = 0.16).

Conclusion

In sidewall aneurysms, stent struts have stronger effects (approximately 2 times) on reduction in flow velocity than straightening of vessels. Hemodynamic effects by straightening vary in each case and can be predicted by inflow angles of pre-operative vessel geometry. These results may be useful to design a treatment strategy for reducing recanalization rates.

In Vitro Validation of Patient-Specific Hemodynamic Simulations in Coronary Aneurysms Caused by Kawasaki Disease

To perform experimental validation of computational fluid dynamics (CFD) applied to patient specific coronary aneurysm anatomy of Kawasaki disease. We quantified hemodynamics in a patient-specific coronary artery aneurysm physical phantom under physiologic rest and exercise flow conditions. Using phase contrast MRI (PCMRI), we acquired 3-component flow velocity at two slice locations in the aneurysms. We then performed numerical simulations with the same geometry and inflow conditions, and performed qualitative and quantitative comparisons of velocities between experimental measurements and simulation results. We observed excellent qualitative agreement in flow pattern features. The quantitative spatially and temporally varying differences in velocity between PCMRI and CFD were proportional to the flow velocity. As a result, the percent discrepancy between simulation and experiment was relatively constant regardless of flow velocity variations. Through 1D and 2D quantitative comparisons, we found a 5-17% difference between measured and simulated velocities. Additional analysis assessed wall shear stress differences between deformable and rigid wall simulations. This study demonstrated that CFD produced good qualitative and quantitative predictions of velocities in a realistic coronary aneurysm anatomy under physiological flow conditions. The results provide insights on factors that may influence the level of agreement, and a set of in vitro experimental data that can be used by others to compare against CFD simulation results. The findings of this study increase confidence in the use of CFD for investigating hemodynamics in the specialized anatomy of coronary aneurysms. This provides a basis for future hemodynamics studies in patient-specific models of Kawasaki disease.

Benefit of cone-beam CT angiography in visualizing aneurysm shape and identification of exact rupture site

While high-resolution cone-beam computational tomographic (CBCT) angiography has gained use in intracranial vascular imaging, digital subtraction angiography (DSA) and 3-dimensional-rotational angiography (3D-RA) remain the preferred acquisition modalities for intracranial aneurysm imaging. This case report highlights the utility of the greater spatial resolution afforded by CBCT for cerebral aneurysm imaging. A 54-year-old man presenting with subarachnoid hemorrhage was confirmed to harbor a ruptured anterior communicating artery aneurysm by conventional angiography. Due to varying contrast opacification captured by different acquisition methods, dramatic aneurysm shape difference was observed between 2- and 3-dimensional-angiographic and CBCT models. The greater resolution of CBCT revealed in an unequivocal fashion the exact site of rupture on the aneurysm dome, visualized as a discrete irregular and elongated bleb that was not seen on either 3D-RA or DSA. High-resolution CBCT visualized the shape of the target aneurysm in greater detail than the more conventional 2D-DSA and 3D-RA, enabling more precise computational fluid dynamics (CFD) simulations. Given that aneurysms most likely change shape either prior to rupture or upon rupture, future studies evaluating fluid dynamics using computer reconstructions should be cognizant of the differences in resolution provided by various imaging modalities.

Generalized versus patient-specific inflow boundary conditions in computational fluid dynamics simulations of cerebral aneurysmal hemodynamics

BACKGROUND AND PURPOSE

Attempts have been made to associate intracranial aneurysmal hemodynamics with aneurysm growth and rupture status. Hemodynamics in aneurysms is traditionally determined with computational fluid dynamics by using generalized inflow boundary conditions in a parent artery. Recently, patient-specific inflow boundary conditions are being implemented more frequently. Our purpose was to compare intracranial aneurysm hemodynamics based on generalized versus patient-specific inflow boundary conditions.

MATERIALS AND METHODS

For 36 patients, geometric models of aneurysms were determined by using 3D rotational angiography. 2D phase-contrast MR imaging velocity measurements of the parent artery were performed. Computational fluid dynamics simulations were performed twice: once by using patient-specific phase-contrast MR imaging velocity profiles and once by using generalized Womersley profiles as inflow boundary conditions. Resulting mean and maximum wall shear stress and oscillatory shear index values were analyzed, and hemodynamic characteristics were qualitatively compared.

RESULTS

Quantitative analysis showed statistically significant differences for mean and maximum wall shear stress values between both inflow boundary conditions (P < .001). Qualitative assessment of hemodynamic characteristics showed differences in 21 cases: high wall shear stress location (n = 8), deflection location (n = 3), lobulation wall shear stress (n = 12), and/or vortex and inflow jet stability (n = 9). The latter showed more instability for the generalized inflow boundary conditions in 7 of 9 patients.

CONCLUSIONS

Using generalized and patient-specific inflow boundary conditions for computational fluid dynamics results in different wall shear stress magnitudes and hemodynamic characteristics. Generalized inflow boundary conditions result in more vortices and inflow jet instabilities. This study emphasizes the necessity of patient-specific inflow boundary conditions for calculation of hemodynamics in cerebral aneurysms by using computational fluid dynamics techniques.

Large eddy simulation of the FDA benchmark nozzle for a Reynolds number of 6500

This work investigates the flow in a benchmark nozzle model of an idealized medical device proposed by the FDA using computational fluid dynamics (CFD). It was in particular shown that a proper modeling of the transitional flow features is particularly challenging, leading to large discrepancies and inaccurate predictions from the different research groups using Reynolds-averaged Navier-Stokes (RANS) modeling. In spite of the relatively simple, axisymmetric computational geometry, the resulting turbulent flow is fairly complex and non-axisymmetric, in particular due to the sudden expansion. The resulting flow cannot be well predicted with simple modeling approaches. Due to the varying diameters and flow velocities encountered in the nozzle, different typical flow regions and regimes can be distinguished, from laminar to transitional and to weakly turbulent. The purpose of the present work is to re-examine the FDA-CFD benchmark nozzle model at a Reynolds number of 6500 using large eddy simulation (LES). The LES results are compared with published experimental data obtained by Particle Image Velocimetry (PIV) and an excellent agreement can be observed considering the temporally averaged flow velocities. Different flow regimes are characterized by computing the temporal energy spectra at different locations along the main axis.

An In Vitro Assessment of the Cerebral Hemodynamics Through Three Patient Specific Circle of Willis Geometries

The Circle of Willis (CoW) is a complex pentagonal network comprised of fourteen cerebral vessels located at the base of the brain. The collateral flow feature within the circle of Willis allows the ability to maintain cerebral perfusion of the brain. Unfortunately, this collateral flow feature can create undesirable flow impact locations due to anatomical variations within the CoW. The interaction between hemodynamic forces and the arterial wall are believed to be involved in the formation of cerebral aneurysms, especially at irregular geometries such as tortuous segments, bends, and bifurcations. The highest propensity of aneurysm formation is known to form at the anterior communicating artery (AcoA) and at the junctions of the internal carotid and posterior communicating arteries (PcoAs). Controversy still remains as to the existence of blood flow paths through the communicating arteries for a normal CoW. This paper experimentally describes the hemodynamic conditions through three thin walled patient specific models of a complete CoW based on medical images. These models were manufactured by a horizontal dip spin coating method and positioned within a custom made cerebral testing system that simulated symmetrical physiological afferent flow conditions through the internal carotid and vertebral arteries. The dip spin coating procedure produced excellent dimensional accuracy. There was an average of less than 4% variation in diameters and wall thicknesses throughout all manufactured CoW models. Our cerebral test facility demonstrated excellent cycle to cycle repeatability, with variations of less than 2% and 1% for the time and cycle averaged flow rates, respectively. The peak systolic flow rates had less than a 4% variation. Our flow visualizations showed four independent flow sources originating from all four inlet arteries impacting at and crossing the AcoA with bidirectional cross flows. The flow paths entering the left and right vertebral arteries dissipated throughout the CoW vasculature from the posterior to anterior sides, exiting through all efferent vessels. Two of the models had five flow impact locations, while the third model had an additional two impact locations within the posterior circulation caused by an additional bidirectional cross flows along the PcoAs during the accelerating and part of the decelerating phases. For a complete CoW, bidirectional cross flows exist within the AcoA and geometrical variations within the CoW geometry can either promote uni- or bidirectional cross flows along the PcoAs.

Mind the gap: impact of computational fluid dynamics solution strategy on prediction of intracranial aneurysm hemodynamics and rupture status indicators

BACKGROUND AND PURPOSE

Computational fluid dynamics has become a popular tool for studying intracranial aneurysm hemodynamics, demonstrating success for retrospectively discriminating rupture status; however, recent highly refined simulations suggest potential deficiencies in solution strategies normally used in the aneurysm computational fluid dynamics literature. The purpose of the present study was to determine the impact of this gap.

MATERIALS AND METHODS

Pulsatile flow in 12 realistic MCA aneurysms was simulated by using both high-resolution and normal-resolution strategies. Velocity fields were compared at selected instants via domain-averaged error. We also compared wall shear stress fields and various reduced hemodynamic indices: cycle-averaged mean and maximum wall shear stress, oscillatory shear index, low shear area, viscous dissipation ratio, and kinetic energy ratio.

RESULTS

Instantaneous differences in flow and wall shear stress patterns were appreciable, especially for bifurcation aneurysms. Linear regressions revealed strong correlations (R(2) > 0.9) between high-resolution and normal-resolution solutions for all indices except kinetic energy ratio (R(2) = 0.25) and oscillatory shear index (R(2) = 0.23); however, for most indices, the slopes were significantly <1, reflecting a pronounced underestimation by the normal-resolution simulations. Some high-resolution simulations were highly unstable, with fluctuating wall shear stresses reflected by the poor oscillatory shear index correlation.

CONCLUSIONS

Typical computational fluid dynamics solution strategies may ultimately be adequate for augmenting rupture risk assessment on the basis of certain highly reduced indices; however, they cannot be relied on for predicting the magnitude and character of the complex biomechanical stimuli to which the aneurysm wall may be exposed. This impact of the computational fluid dynamics solution strategy is likely greater than that for other modeling assumptions or uncertainties.

Accuracy of computational cerebral aneurysm hemodynamics using patient-specific endovascular measurements

Computational hemodynamic simulations of cerebral aneurysms have traditionally relied on stereotypical boundary conditions (such as blood flow velocity and blood pressure) derived from published values as patient-specific measurements are unavailable or difficult to collect. However, controversy persists over the necessity of incorporating such patient-specific conditions into computational analyses. We perform simulations using both endovascularly-derived patient-specific and typical literature-derived inflow and outflow boundary conditions. Detailed three-dimensional anatomical models of the cerebral vasculature are developed from rotational angiography data, and blood flow velocity and pressure are measured in situ by a dual-sensor pressure and velocity endovascular guidewire at multiple peri-aneurysmal locations in 10 unruptured cerebral aneurysms. These measurements are used to define inflow and outflow boundary conditions for computational hemodynamic models of the aneurysms. The additional in situ measurements which are not prescribed in the simulation are then used to assess the accuracy of the simulated flow velocity and pressure drop. Simulated velocities using patient-specific boundary conditions show good agreement with the guidewire measurements at measurement locations inside the domain, with no bias in the agreement and a random scatter of ≈25%. Simulated velocities using the simplified, literature-derived values show a systematic bias and over-predicted velocity by ≈30% with a random scatter of ≈40%. Computational hemodynamics using endovascularly measured patient-specific boundary conditions have the potential to improve treatment predictions as they provide more accurate and precise results of the aneurysmal hemodynamics than those based on commonly accepted reference values for boundary conditions.

An experimental investigation of the hemodynamic variations due to aplastic vessels within three-dimensional phantom models of the circle of Willis

A complete circle of Willis (CoW) is found in approximately 30-50% of the population. Anatomical variations, such as absent or surgically clamped vessels, can result in undesirable flow patterns. These can affect the brain's ability to maintain cerebral perfusion and the formation of cerebral aneurysms. An experimental test system was developed to simulate cerebral physiological conditions through three flexible 3D patient-specific models of complete and incomplete CoW geometries. Flow visualizations were performed with isobaric dyes and the mapped dye streamlines were tracked throughout the models. Three to seven flow impact locations were observed for all configurations, corresponding to known sites for aneurysmal formation. Uni and bi-directional cross-flows occurred along the communicating arteries. The greatest shunting of flow occurred for a missing pre-communicating anterior (A1) and posterior (P1) cerebral arteries. The anterior cerebral arteries had the greatest reduction (15-37%) in efferent flow rates for missing either a unilateral A1 or bilateral P1 segments. The bi-directional cross-flows, with multiple afferent flow mixing, observed along the communicating arteries may explain the propensity of aneurysm formation at these sites. Reductions in efferent flow rates due to aplastic vessel configurations may affect normal brain function.

Numerical blood flow simulation in surgical corrections: what do we need for an accurate analysis?

BACKGROUND

Computational fluid dynamics has been increasingly used in congenital heart surgery to simulate pathophysiological blood flow, investigate surgical options, or design medical devices. Several commercial and research computational or numerical codes have been developed. They present different approaches to numerically solve the blood flow equations, raising the question whether these numerical codes are equally reliable to achieve accurate simulation results. Accordingly, we sought to examine the influence of numerical code selection in several complex congenital cardiac operations.

MATERIAL AND METHODS

The main steps of blood flow simulations are detailed (geometrical mesh, boundary conditions, and solver numerical methods) for congenital cardiac operations of increasing complexity. The first case tests different numerical solutions against an analytical, or exact, solution. In the second case, the three-dimensional domain is a patient-specific superior cavopulmonary anastomosis. As an analytical solution does not exist in such a complex geometry, different numerical solutions are compared. Finally, a realistic case of a systemic-to-pulmonary shunt is presented with both geometrically and physiologically challenging conditions. For all, solutions from a commercially available code and an open-source research code are compared.

RESULTS

In the first case, as the mesh or solver numerical method is refined, the simulation results for both codes converged to the analytical solution. In the second example, velocity differences between the two codes are greater when the resolution of the mesh were lower and less refined. The third case with realistic anatomy reveals that the pulsatile complex flow is very similar for both codes.

CONCLUSIONS

The precise setup of the numerical cases has more influence on the results than the choice of numerical codes. The need for detailed construction of the numerical model that requires high computational cost depends on the precision needed to answer the biomedical question at hand and should be assessed for each problem on a combination of clinically relevant patient-specific geometry and physiological conditions.

Considerations for numerical modeling of the pulmonary circulation--a review with a focus on pulmonary hypertension

Both in academic research and in clinical settings, virtual simulation of the cardiovascular system can be used to rapidly assess complex multivariable interactions between blood vessels, blood flow, and the heart. Moreover, metrics that can only be predicted with computational simulations (e.g., mechanical wall stress, oscillatory shear index, etc.) can be used to assess disease progression, for presurgical planning, and for interventional outcomes. Because the pulmonary vasculature is susceptible to a wide range of pathologies that directly impact and are affected by the hemodynamics (e.g., pulmonary hypertension), the ability to develop numerical models of pulmonary blood flow can be invaluable to the clinical scientist. Pulmonary hypertension is a devastating disease that can directly benefit from computational hemodynamics when used for diagnosis and basic research. In the present work, we provide a clinical overview of pulmonary hypertension with a focus on the hemodynamics, current treatments, and their limitations. Even with a rich history in computational modeling of the human circulation, hemodynamics in the pulmonary vasculature remains largely unexplored. Thus, we review the tasks involved in developing a computational model of pulmonary blood flow, namely vasculature reconstruction, meshing, and boundary conditions. We also address how inconsistencies between models can result in drastically different flow solutions and suggest avenues for future research opportunities. In its current state, the interpretation of this modeling technology can be subjective in a research environment and impractical for clinical practice. Therefore, considerations must be taken into account to make modeling reliable and reproducible in a laboratory setting and amenable to the vascular clinic. Finally, we discuss relevant existing models and how they have been used to gain insight into cardiopulmonary physiology and pathology.

Changes in wall shear stress magnitude after aneurysm rupture

Computational fluid dynamics (CFD) studies on cerebral aneurysms have attempted to identify surrogate hemodynamic parameters to predict rupture risk. We present a case of bilateral mirror image aneurysms, one of which ruptured soon after imaging. Wall shear stress values of the ruptured aneurysm changed by 20-30% after rupture because of change in the aneurysm shape. Findings from our case suggest that CFD studies comparing unruptured and ruptured aneurysms may not yield valid estimation on aneurysm rupture risk because of changes in aneurysm shape after rupture. Changes in aneurysm shape after rupture should be considered in CFD research.