Vessel calibre and flow splitting relationships at the internal carotid artery terminal bifurcation

Comparison of computational fluid dynamics with transcranial Doppler ultrasound in response to physiological stimuli

Cerebrovascular haemodynamics are sensitive to multiple physiological stimuli that require synergistic response to maintain adequate perfusion. Understanding haemodynamic changes within cerebral arteries is important to inform how the brain regulates perfusion; however, methods for direct measurement of cerebral haemodynamics in these environments are challenging. The aim of this study was to assess velocity waveform metrics obtained using transcranial Doppler (TCD) with flow-conserving subject-specific three-dimensional (3D) simulations using computational fluid dynamics (CFD). Twelve healthy participants underwent head and neck imaging with 3 T magnetic resonance angiography. Velocity waveforms in the middle cerebral artery were measured with TCD ultrasound, while diameter and velocity were measured using duplex ultrasound in the internal carotid and vertebral arteries to calculate incoming cerebral flow at rest, during hypercapnia and exercise. CFD simulations were developed for each condition, with velocity waveform metrics extracted in the same insonation region as TCD. Exposure to stimuli induced significant changes in cardiorespiratory measures across all participants. Measured absolute TCD velocities were significantly higher than those calculated from CFD (P range < 0.001-0.004), and these data were not correlated across conditions (r range 0.030-0.377, P range 0.227-0.925). However, relative changes in systolic and time-averaged velocity from resting levels exhibited significant positive correlations when the distinct techniques were compared (r range 0.577-0.770, P range 0.003-0.049). Our data indicate that while absolute measures of cerebral velocity differ between TCD and 3D CFD simulation, physiological changes from resting levels in systolic and time-averaged velocity are significantly correlated between techniques.

Non-invasive estimation of the parameters of a three-element windkessel model of aortic arch arteries in patients undergoing thoracic endovascular aortic repair

Background: Image-based computational hemodynamic modeling and simulations are important for personalized diagnosis and treatment of cardiovascular diseases. However, the required patient-specific boundary conditions are often not available and need to be estimated. Methods: We propose a pipeline for estimating the parameters of the popular three-element Windkessel (WK3) models (a proximal resistor in series with a parallel combination of a distal resistor and a capacitor) of the aortic arch arteries in patients receiving thoracic endovascular aortic repair of aneurysms. Pre-operative and post-operative 1-week duplex ultrasound scans were performed to obtain blood flow rates, and intra-operative pressure measurements were also performed invasively using a pressure transducer pre- and post-stent graft deployment in arch arteries. The patient-specific WK3 model parameters were derived from the flow rate and pressure waveforms using an optimization algorithm reducing the error between simulated and measured pressure data. The resistors were normalized by total resistance, and the capacitor was normalized by total resistance and heart rate. The normalized WK3 parameters can be combined with readily available vessel diameter, brachial blood pressure, and heart rate data to estimate WK3 parameters of other patients non-invasively. Results: Ten patients were studied. The medians (interquartile range) of the normalized proximal resistor, distal resistor, and capacitor parameters are 0.10 (0.07-0.15), 0.90 (0.84-0.93), and 0.46 (0.33-0.58), respectively, for common carotid artery; 0.03 (0.02-0.04), 0.97 (0.96-0.98), and 1.91 (1.63-2.26) for subclavian artery; 0.18 (0.08-0.41), 0.82 (0.59-0.92), and 0.47 (0.32-0.85) for vertebral artery. The estimated pressure showed fairly high tolerance to patient-specific inlet flow rate waveforms using the WK3 parameters estimated from the medians of the normalized parameters. Conclusion: When patient-specific outflow boundary conditions are not available, our proposed pipeline can be used to estimate the WK3 parameters of arch arteries.

Characterizing Intracranial Hemodynamics in Sickle Cell Anemia: Impact of Patient-Specific Viscosity

PURPOSE

Pediatric and adult patients with sickle cell anemia (SCA) are at increased risk of stroke and cerebrovascular accident. In the general adult population, there is a relationship between arterial hemodynamics and pathology; however, this relationship in SCA patients remains to be elucidated. The aim of this work was to characterize circle of Willis hemodynamics in patients with SCA and quantify the impact of viscosity choice on pathophysiologically-relevant hemodynamics measures.

METHODS

Based on measured vascular geometries, time-varying flow rates, and blood parameters, detailed patient-specific simulations of the circle of Willis were conducted for SCA patients (n = 6). Simulations quantified the impact of patient-specific and standard blood viscosities on wall shear stress (WSS).

RESULTS

These results demonstrated that use of a standard blood viscosity introduces large errors into the estimation of pathophysiologically-relevant hemodynamic parameters. Standard viscosity models overpredicted peak WSS by 55% and 49% for steady and pulsatile flow, respectively. Moreover, these results demonstrated non-uniform, spatial patterns of positive and negative WSS errors related to viscosity, and standard viscosity simulations overpredicted the time-averaged WSS by 32% (standard deviation = 7.1%). Finally, differences in shear rate demonstrated that the viscosity choice alters the simulated near-wall flow field, impacting hemodynamics measures.

CONCLUSIONS

This work presents simulations of circle of Willis arterial flow in SCA patients and demonstrates the importance and feasibility of using a patient-specific viscosity in these simulations. Accurately characterizing cerebrovascular hemodynamics in SCA populations has potential for elucidating the pathophysiology of large-vessel occlusion, aneurysms, and tissue damage in these patients.

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.

Fluid-structure interaction simulation of tissue degradation and its effects on intra-aneurysm hemodynamics

Tissue degradation plays a crucial role in vascular diseases such as atherosclerosis and aneurysms. Computational modeling of vascular hemodynamics incorporating both arterial wall mechanics and tissue degradation has been a challenging task. In this study, we propose a novel finite element method-based approach to model the microscopic degradation of arterial walls and its interaction with blood flow. The model is applied to study the combined effects of pulsatile flow and tissue degradation on the deformation and intra-aneurysm hemodynamics. Our computational analysis reveals that tissue degradation leads to a weakening of the aneurysmal wall, which manifests itself in a larger deformation and a smaller von Mises stress. Moreover, simulation results for different heart rates, blood pressures and aneurysm geometries indicate consistently that, upon tissue degradation, wall shear stress increases near the flow-impingement region and decreases away from it. These findings are discussed in the context of recent reports regarding the role of both high and low wall shear stress for the progression and rupture of aneurysms.

On the Potential Self-Amplification of Aneurysms Due to Tissue Degradation and Blood Flow Revealed From FSI Simulations

Tissue degradation plays a crucial role in the formation and rupture of aneurysms. Using numerical computer simulations, we study the combined effects of blood flow and tissue degradation on intra-aneurysm hemodynamics. Our computational analysis reveals that the degradation-induced changes of the time-averaged wall shear stress (TAWSS) and oscillatory shear index (OSI) within the aneurysm dome are inversely correlated. Importantly, their correlation is enhanced in the process of tissue degradation. Regions with a low TAWSS and a high OSI experience still lower TAWSS and higher OSI during degradation. Furthermore, we observed that degradation leads to an increase of the endothelial cell activation potential index, in particular, at places experiencing low wall shear stress. These findings are robust and occur for different geometries, degradation intensities, heart rates and pressures. We interpret these findings in the context of recent literature and argue that the degradation-induced hemodynamic changes may lead to a self-amplification of the flow-induced progressive damage of the aneurysmal wall.

Assessment of cerebrovascular responses to physiological stimuli in identical twins using multimodal imaging and computational fluid dynamics

There is acknowledged variability in the Circle of Willis (CoW) in the general population, yet the structure and function relationship of the cerebrovasculature is poorly understood. We aimed to demonstrate the feasibility of combining high-resolution imaging techniques and computational fluid dynamics (CFD) to describe cerebrovascular structure and function in vivo. We tested our methodology by examining the null hypothesis that monozygotic twins (18-30 yr) would exhibit similar CoW structure and function. Six twin pairs underwent 3T magnetic resonance angiography of the head and neck and B-mode Doppler ultrasound for velocity and diameter recordings in the vertebral and internal carotid arteries under three conditions (rest, hypercapnia, and exercise). Artery diameter, length, tortuosity, and bifurcation angle were assessed in regions of interest of the CoW. We simulated hemodynamics to determine the cardiac-cycle time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), and relative residence time (RRT). We observed low and insignificant intraclass correlations (ICC) between twins in all regions for diameter (ICC range 0.000-0.657, P > 0.05), two of four regions for length (ICC range 0.355-0.368, P > 0.05), all regions for tortuosity (ICC range 0.270-0.505, P > 0.05), and all bifurcation angles (ICC range 0.000-0.547, P > 0.05). Similarly, no significant correlations were apparent for cerebral blood flow or CFD-derived measures of TAWSS, OSI, and RRT, at rest or in response to hypercapnia or exercise. Therefore, differences exist in CoW structure and associated shear stress in response to physiological stimulation. These data suggest that the structure, function, and health of cerebrovascular arteries are not primarily genetically dependent.NEW & NOTEWORTHY There is acknowledged variability in the Circle of Willis in the general population, yet the structure and function relationship of the cerebrovasculature is poorly understood. Using a combination of magnetic resonance imaging, high-resolution Doppler ultrasound, and computational fluid dynamic modeling, we show that monozygotic twins exhibit differences in cerebrovascular structure and function when exposed to physiological stimuli. These data suggest that the morphology, function, and health of cerebrovascular arteries are not primarily genetically determined.

How patient specific are patient-specific computational models of cerebral aneurysms? An overview of sources of error and variability

Computational modeling of cerebral aneurysms, derived from clinical 3D angiography, has become widespread over the past 15 years. While such "image-based" or "patient-specific" models have shown promise for the assessment of rupture risk, much debate remains about their reliability in light of necessary modeling assumptions and incomplete or uncertain model input parameters derived from the clinic. The aims of this review were to walk through the various steps of this so-called patient-specific modeling pipeline and to highlight evidence supporting those steps that we can or cannot rely on. The relative importance of the different sources of error and variability on hemodynamic predictions is summarized, with recommendations to standardize for those that can be avoided and to pay closer attention those to that cannot.

A review on the reliability of hemodynamic modeling in intracranial aneurysms: why computational fluid dynamics alone cannot solve the equation

Computational blood flow modeling in intracranial aneurysms (IAs) has enormous potential for the assessment of highly resolved hemodynamics and derived wall stresses. This results in an improved knowledge in important research fields, such as rupture risk assessment and treatment optimization. However, due to the requirement of assumptions and simplifications, its applicability in a clinical context remains limited.This review article focuses on the main aspects along the interdisciplinary modeling chain and highlights the circumstance that computational fluid dynamics (CFD) simulations are embedded in a multiprocess workflow. These aspects include imaging-related steps, the setup of realistic hemodynamic simulations, and the analysis of multidimensional computational results. To condense the broad knowledge, specific recommendations are provided at the end of each subsection.Overall, various individual substudies exist in the literature that have evaluated relevant technical aspects. In this regard, the importance of precise vessel segmentations for the simulation outcome is emphasized. Furthermore, the accuracy of the computational model strongly depends on the specific research question. Additionally, standardization in the context of flow analysis is required to enable an objective comparison of research findings and to avoid confusion within the medical community. Finally, uncertainty quantification and validation studies should always accompany numerical investigations.In conclusion, this review aims for an improved awareness among physicians regarding potential sources of error in hemodynamic modeling for IAs. Although CFD is a powerful methodology, it cannot provide reliable information, if pre- and postsimulation steps are inaccurately carried out. From this, future studies can be critically evaluated and real benefits can be differentiated from results that have been acquired based on technically inaccurate procedures.

Inter-patient variations in flow boundary conditions at middle cerebral artery from 7T PC-MRI and influence on Computational Fluid Dynamics of intracranial aneurysms

BACKGROUND

Computational fluid dynamics(CFD) of intracranial aneurysms requires flow boundary conditions(BCs) as inputs. Patient-specific BCs are usually unavailable and substituted by literature-derived generic BCs. Therefore, we investigated inter-patient BC variations and their influence on middle cerebral artery aneurysmal hemodynamics.

METHOD

We retrospectively collected CT angiography and 7-T Phase-Contrast(PC)-MRI data from eight middle-cerebral-artery bifurcation aneurysms to reconstruct the geometry and measure the arterial flowrates, respectively. The coefficient of variation(CoV) was calculated for the inlet flowrate and the pulsatility index(PI). The outflow split estimated by Murray's law was compared with PC-MRI measurements. For each aneurysm, we performed seven simulations: "baseline" using PC-MRI-derived BCs and the other six with changing BCs to explore the influence of BC variations on hemodynamics.

RESULTS

From PC-MRI, the inlet flowrate was 1.94 ± 0.71 cm³/s(CoV = 36%) and PI was 0.37 ± 0.13(CoV = 34%). The outflow split estimated by Murray's law deviated by 15.3% compared to PC-MRI. Comparing to "baseline" models, ±36% variations in inlet flowrate caused -61% to +89% changes in time-averaged wall shear stress(WSS), -37% to +32% in normalized WSS(NWSS; by parent-artery), and -42% to +126% in oscillatory shear index(OSI). The ±34% variations in PI caused, -46% to +67% in OSI. Applying ±15% variations in outflow split led to inflow jet deflection and -41% to +52% changes in WSS, -41% to +47% in NWSS, and -44% to +144% in OSI.

CONCLUSION

Inflow rate and outflow split have a drastic impact on hemodynamics of intracranial aneurysms. Inlet waveform has a negligible impact on WSS and NWSS but major impact on OSI. CFD-based models need to consider such sensitivity.

Blood flow rate and wall shear stress in seven major cephalic arteries of humans

Blood flow rate ( Q ˙ ) in relation to arterial lumen radius (r_i ) is commonly modelled according to theoretical equations and paradigms, including Murray's Law ( Q ˙ ∝ r i 3 ) and da Vinci's Rule ( Q ˙ ∝ r i 2 ). Wall shear stress (τ) is independent of r_i with Murray's Law (τ ∝  r i 0 ) and decreases with da Vinci's Rule (τ ∝  r i - 1 ). These paradigms are tested empirically with a meta-analysis of the relationships between Q ˙ and r_i in seven major arteries of the human cephalic circulation from 19 imaging studies in which both variables were presented. The analysis shows that Q ˙ ∝ r i 2.16 and τ ∝  r i - 1.02 , more consistent with da Vinci's Rule than Murray's Law. This meta-analysis provides standard values for Q ˙ , r_i and τ in the human cephalic arteries that may be a useful baseline in future investigations. On average, the paired internal carotid arteries supply 75%, and the vertebral arteries supply 25%, of total brain blood flow. The internal carotid arteries contribute blood entirely to the anterior and middle cerebral arteries and also partly to the posterior cerebral arteries via the posterior communicating arteries of the circle of Willis. On average, the internal carotid arteries provide 88% of the blood flow to the cerebrum and the vertebral arteries only 12%.

Correlation of flow complexity parameter with aneurysm rupture status

Ruptured aneurysms are known to have complex flow patterns and concentrated inflow jet, but a quantifiable measure for the degree of flow complexity in patient-specific geometries has not been established. Previously, we proposed a flow complexity parameter that provides a quantitative description of the complexity of flow patterns through calculated curvature and torsion of the flow field. The purpose of the current study was to provide an analytic solution of the flow complexity parameter and assess a possible correlation with the rupture status of cerebral aneurysms by analyzing the parameter on five ruptured and five unruptured aneurysms from anterior communicating artery. We analyzed the flow complexity parameter in jet and non-jet regions in order to measure the concentration of the jet flow and the complexity of the non-jet flow. We found that on average, in a ruptured case the jet region is significantly less complex (4.5 times) than the jet region in an unruptured case, while the non-jet region is significantly more complex (3.5 times) than the non-jet region in an unruptured case. We also found a strong positive correlation of the non-jet complexity with dome volume in ruptured cases, but no correlation of jet complexity with dome volume. These findings suggest that a ruptured aneurysm has more than 4 times more concentrated inflow jet and more than 3 times more complex flow patterns in non-jet region than an unruptured aneurysm. This newly implemented kinematic parameter provides a measurable degree of complexity of flow patterns in cerebral aneurysms that can better assess aneurysm rupture risk.

Real-World Variability in the Prediction of Intracranial Aneurysm Wall Shear Stress: The 2015 International Aneurysm CFD Challenge

Purpose

Image-based computational fluid dynamics (CFD) is widely used to predict intracranial aneurysm wall shear stress (WSS), particularly with the goal of improving rupture risk assessment. Nevertheless, concern has been expressed over the variability of predicted WSS and inconsistent associations with rupture. Previous challenges, and studies from individual groups, have focused on individual aspects of the image-based CFD pipeline. The aim of this Challenge was to quantify the total variability of the whole pipeline.

Methods

3D rotational angiography image volumes of five middle cerebral artery aneurysms were provided to participants, who were free to choose their segmentation methods, boundary conditions, and CFD solver and settings. Participants were asked to fill out a questionnaire about their solution strategies and experience with aneurysm CFD, and provide surface distributions of WSS magnitude, from which we objectively derived a variety of hemodynamic parameters.

Results

A total of 28 datasets were submitted, from 26 teams with varying levels of self-assessed experience. Wide variability of segmentations, CFD model extents, and inflow rates resulted in interquartile ranges of sac average WSS up to 56%, which reduced to < 30% after normalizing by parent artery WSS. Sac-maximum WSS and low shear area were more variable, while rank-ordering of cases by low or high shear showed only modest consensus among teams. Experience was not a significant predictor of variability.

Conclusions

Wide variability exists in the prediction of intracranial aneurysm WSS. While segmentation and CFD solver techniques may be difficult to standardize across groups, our findings suggest that some of the variability in image-based CFD could be reduced by establishing guidelines for model extents, inflow rates, and blood properties, and by encouraging the reporting of normalized hemodynamic parameters.

Better Than Nothing: A Rational Approach for Minimizing the Impact of Outflow Strategy on Cerebrovascular Simulations

BACKGROUND AND PURPOSE

Computational fluid dynamics simulations of neurovascular diseases are impacted by various modeling assumptions and uncertainties, including outlet boundary conditions. Many studies of intracranial aneurysms, for example, assume zero pressure at all outlets, often the default ("do-nothing") strategy, with no physiological basis. Others divide outflow according to the outlet diameters cubed, nominally based on the more physiological Murray's law but still susceptible to subjective choices about the segmented model extent. Here we demonstrate the limitations and impact of these outflow strategies, against a novel "splitting" method introduced here.

MATERIALS AND METHODS

With our method, the segmented lumen is split into its constituent bifurcations, where flow divisions are estimated locally using a power law. Together these provide the global outflow rate boundary conditions. The impact of outflow strategy on flow rates was tested for 70 cases of MCA aneurysm with 0D simulations. The impact on hemodynamic indices used for rupture status assessment was tested for 10 cases with 3D simulations.

RESULTS

Differences in flow rates among the various strategies were up to 70%, with a non-negligible impact on average and oscillatory wall shear stresses in some cases. Murray-law and splitting methods gave flow rates closest to physiological values reported in the literature; however, only the splitting method was insensitive to arbitrary truncation of the model extent.

CONCLUSIONS

Cerebrovascular simulations can depend strongly on the outflow strategy. The default zero-pressure method should be avoided in favor of Murray-law or splitting methods, the latter being released as an open-source tool to encourage the standardization of outflow strategies.