Transitional flow in aneurysms and the computation of haemodynamic parameters

Influence of Blood Rheology and Turbulence Models in the Numerical Simulation of Aneurysms

An aneurysm is a vascular malformation that can be classified according to its location (cerebral, aortic) or shape (saccular, fusiform, and mycotic). Recently, the study of blood flow interaction with aneurysms has gained attention from physicians and engineers. Shear stresses, oscillatory shear index (OSI), gradient oscillatory number (GON), and residence time have been used as variables to describe the hemodynamics as well as the origin and evolution of aneurysms. However, the causes and hemodynamic conditions that promote their growth are still under debate. The present work presents numerical simulations of three types of aneurysms: two aortic and one cerebral. Simulation results showed that the blood rheology is not relevant for aortic aneurysms. However, for the cerebral aneurysm case, blood rheology could play a relevant role in the hemodynamics. The evaluated turbulence models showed equivalent results in both cases. Lastly, a simulation considering the fluid-structure interaction (FSI) showed that this phenomenon is the dominant factor for aneurysm simulation.

Is Accurate Lumen Segmentation More Important than Outlet Boundary Condition in Image-Based Blood Flow Simulations for Intracranial Aneurysms?

PURPOSE

Image-based blood flow simulations are increasingly used to investigate the hemodynamics in intracranial aneurysms (IAs). However, a strong variability in segmentation approaches as well as the absence of individualized boundary conditions (BCs) influence the quality of these simulation results leading to imprecision and decreased reliability. This study aims to analyze these influences on relevant hemodynamic parameters within IAs.

METHODS

As a follow-up study of an international multiple aneurysms challenge, the segmentation results of five IAs differing in size and location were investigated. Specifically, five possible outlet BCs were considered in each of the IAs. These are comprised of the zero-pressure condition (BC1), a flow distribution based on Murray's law with the exponents n = 2 (BC2) and n = 3 (BC3) as well as two advanced flow-splitting models considering the real vessels by including circular cross sections (BC4) or anatomical cross sections (BC5), respectively. In total, 120 time-dependent blood flow simulations were analyzed qualitatively and quantitatively, focusing on five representative intra-aneurysmal flow and five shear parameters such as vorticity and wall shear stress.

RESULTS

The outlet BC variation revealed substantial differences. Higher shear stresses (up to Δ9.69 Pa), intrasaccular velocities (up to Δ0.15 m/s) and vorticities (up to Δ629.22 1/s) were detected when advanced flow-splitting was applied compared to the widely used zero-pressure BC. The tendency of outlets BCs to over- or underestimate hemodynamic parameters is consistent across different segmentations of a single aneurysm model. Segmentation-induced variability reaches Δ19.58 Pa, Δ0.42 m/s and Δ957.27 1/s, respectively. Excluding low fidelity segmentations, however, (a) reduces the deviation drastically (>43%) and (b) leads to a lower impact of the outlet BC on hemodynamic predictions.

CONCLUSION

With a more realistic lumen segmentation, the influence of the BC on the resulting hemodynamics is decreased. A realistic lumen segmentation can be ensured, e.g., by using high-resolved 2D images. Furthermore, the selection of an advanced outflow-splitting model is advised and the use of a zero-pressure BC and BC based on Murray's law with exponent n = 3 should be avoided.

Computerized Differentiation of Growth Status for Abdominal Aortic Aneurysms: A Feasibility Study

Fast-growing abdominal aortic aneurysms (AAA) have a high rupture risk and poor outcomes if not promptly identified and treated. Our primary objective is to improve the differentiation of small AAAs' growth status (fast versus slow-growing) through a combination of patient health information, computational hemodynamics, geometric analysis, and artificial intelligence. 3D computed tomography angiography (CTA) data available for 70 patients diagnosed with AAAs with known growth status were used to conduct geometric and hemodynamic analyses. Differences among ten metrics (out of ninety metrics) were statistically significant discriminators between fast and slow-growing groups. Using a support vector machine (SVM) classifier, the area under receiving operating curve (AUROC) and total accuracy of our best predictive model for differentiation of AAAs' growth status were 0.86 and 77.50%, respectively. In summary, the proposed analytics has the potential to differentiate fast from slow-growing AAAs, helping guide resource allocation for the management of patients with AAAs.

Recasting Current Knowledge of Human Fetal Circulation: The Importance of Computational Models

Computational hemodynamic simulations are becoming increasingly important for cardiovascular research and clinical practice, yet incorporating numerical simulations of human fetal circulation is relatively underutilized and underdeveloped. The fetus possesses unique vascular shunts to appropriately distribute oxygen and nutrients acquired from the placenta, adding complexity and adaptability to blood flow patterns within the fetal vascular network. Perturbations to fetal circulation compromise fetal growth and trigger the abnormal cardiovascular remodeling that underlies congenital heart defects. Computational modeling can be used to elucidate complex blood flow patterns in the fetal circulatory system for normal versus abnormal development. We present an overview of fetal cardiovascular physiology and its evolution from being investigated with invasive experiments and primitive imaging techniques to advanced imaging (4D MRI and ultrasound) and computational modeling. We introduce the theoretical backgrounds of both lumped-parameter networks and three-dimensional computational fluid dynamic simulations of the cardiovascular system. We subsequently summarize existing modeling studies of human fetal circulation along with their limitations and challenges. Finally, we highlight opportunities for improved fetal circulation models.

Aneurysmal degeneration of the hood of a cryopreserved vein allograft two years after thrombosis

Cryopreserved vein allografts are used as alternative conduits for infrainguinal bypass but are prone to aneurysmal degeneration. A 60-year-old man presented with a pulsatile, tender right groin mass 2 years after thrombosis of a cryopreserved vein jump graft emanating from a prosthetic axillary to profunda bypass. Intraoperatively, the aneurysm was consistent with isolated dilatation of the hood of the thrombosed cryopreserved vein graft. This was excised and repaired with bovine pericardial patch angioplasty. The patient recovered with no recurrence for 2 years. Aneurysmal degeneration of the cryopreserved vein allograft can occur even after graft thrombosis.

On the prevalence of flow instabilities from high-fidelity computational fluid dynamics of intracranial bifurcation aneurysms

High-fidelity computational fluid dynamics (HF-CFD) has revealed the potential for high-frequency flow instabilities (aka "turbulent-like" flow) in intracranial aneurysms, consistent with classic in vivo and in vitro reports of bruits and/or wall vibrations. However, HF-CFD has typically been performed on limited numbers of cases, often with unphysiological inflow conditions or focused on sidewall-type aneurysms where flow instabilities may be inherently less prevalent. Here we report HF-CFD of 50 bifurcation aneurysm cases from the open-source Aneurisk model repository. These were meshed using quadratic finite elements having an average effective spatial resolution of 0.065 mm, and solved under physiologically-pulsatile flow conditions using a well-validated, minimally-dissipative solver with 20,000 time-steps per cardiac cycle Flow instability was quantified using the recently introduced spectral power index (SPI), which quantifies, from 0 to 1, the power associated with velocity fluctuations above those of the driving inflow waveform. Of the 50 cases, nearly half showed regions within the sac having SPI up to 0.5, often with non-negligible power into the 100's of Hz, and roughly 1/3 had sac-averaged SPI > 0.1. High SPI did not significantly predict rupture status in this cohort. Proper orthogonal decomposition of cases with highest SPI_avg revealed time-varying energetics consistent with transient turbulence. Our reported prevalence of high-frequency flow instabilities in HF-CFD modelling of aneurysms suggests that care must be taken to avoid routinely overlooking them if we are to understand the highly dynamic mechanical forces to which some aneurysm walls may be exposed, and their prevalence in vivo.

Effect of foam insertion in aneurysm sac on flow structures in parent lumen: relating vortex structures with disturbed shear

Numerous studies suggest that disturbed shear, causing endothelium dysfunction, can be related to neighboring vortex structures. With this motivation, this study presents a methodology to characterize the vortex structures. Precisely, we use mapping and characterization of vortex structures' changes to relate it with the hemodynamic indicators of disturbed shear. Topological features of vortex core lines (VCLs) are used to quantify the changes in vortex structures. We use the Sujudi-Haimes algorithm to extract the VCLs from the flow simulation results. The idea of relating vortex structures with disturbed shear is demonstrated for cerebral arteries with aneurysms virtually treated by inserting foam in the sac. To get physiologically realistic flow fields, we simulate blood flow in two patient-specific geometries before and after foam insertion, with realistic velocity waveform imposed at the inlet, using the Carreau-Yasuda model to mimic the shear-thinning behavior. With homogenous porous medium assumption, flow through the foam is modeled using the Forchheimer-Brinkman extended Darcy model. Results show that foam insertion increases the number of VCLs in the parent lumen. The average length of VCL increases by 168.9% and 55.6% in both geometries. For both geometries under consideration, results demonstrate that the region with increased disturbed shear lies in the same arterial segment exhibiting an increase in the number of oblique VCLs. Based on the findings, we conjecture that an increase in oblique VCLs is related to increased disturbed shear at the neighboring portion of the arterial wall.

Arterial pulse wave propagation across stenoses and aneurysms: assessment of one-dimensional simulations against three-dimensional simulations and in vitro measurements

One-dimensional (1-D) arterial blood flow modelling was tested in a series of idealized vascular geometries representing the abdominal aorta, common carotid and iliac arteries with different sizes of stenoses and/or aneurysms. Three-dimensional (3-D) modelling and in vitro measurements were used as ground truth to assess the accuracy of 1-D model pressure and flow waves. The 1-D and 3-D formulations shared identical boundary conditions and had equivalent vascular geometries and material properties. The parameters of an experimental set-up of the abdominal aorta for different aneurysm sizes were matched in corresponding 1-D models. Results show the ability of 1-D modelling to capture the main features of pressure and flow waves, pressure drop across the stenoses and energy dissipation across aneurysms observed in the 3-D and experimental models. Under physiological Reynolds numbers (Re), root mean square errors were smaller than 5.4% for pressure and 7.3% for the flow, for stenosis and aneurysm sizes of up to 85% and 400%, respectively. Relative errors increased with the increasing stenosis and aneurysm size, aneurysm length and Re, and decreasing stenosis length. All data generated in this study are freely available and provide a valuable resource for future research.

Implementation and characterization of a physiologically relevant flow waveform in a 3D microfluidic model of the blood-brain barrier

Previous in vitro studies interrogating the endothelial response to physiologically relevant flow regimes require specialized pumps to deliver time-dependent waveforms that imitate in vivo blood flow. The aim of this study is to create a low-cost and broadly adaptable approach to mimic physiological flow, and then use this system to characterize the effect of flow separation on velocity and shear stress profiles in a three-dimensional (3D) topology. The flow apparatus incorporates a programmable linear actuator that superposes oscillations on a constant mean flow driven by a peristaltic pump to emulate flow in the carotid artery. The flow is perfused through a 3D in vitro model of the blood-brain barrier designed to induce separated flow. Experimental flow patterns measured by microparticle image velocimetry and modeled by computational fluid dynamics reveal periodic changes in the instantaneous shear stress along the channel wall. Moreover, the time-dependent flow causes periodic flow separation zones, resulting in variable reattachment points during the cycle. The effects of these complex flow regimes are assessed by evaluating the integrity of the in vitro blood-brain barrier model. Permeability assays and immunostaining for proteins associated with tight junctions reveal barrier breakdown in the region of disturbed flow. In conclusion, the flow system described here creates complex, physiologically relevant flow profiles that provide deeper insight into the fluid dynamics of separated flow and pave the way for future studies interrogating the cellular response to complex flow regimes.

Mathematical model of atherosclerotic aneurysm

Atherosclerosis is a major cause of abdominal aortic aneurysm (AAA) and up to 80% of AAA patients have atherosclerosis. Therefore it is critical to understand the relationship and interactions between atherosclerosis and AAA to treat atherosclerotic aneurysm patients more effectively. In this paper, we develop a mathematical model to mimic the progression of atherosclerotic aneurysms by including both the multi-layer structured arterial wall and the pathophysiology of atherosclerotic aneurysms. The model is given by a system of partial differential equations with free boundaries. Our results reveal a 2D biomarker, the cholesterol ratio and DDR1 level, assessing the risk of atherosclerotic aneurysms. The efficacy of different treatment plans is also explored via our model and suggests that the dosage of anti-cholesterol drugs is significant to slow down the progression of atherosclerotic aneurysms while the additional anti-DDR1 injection can further reduce the risk.

Computational fluid dynamics simulations of cerebral aneurysm using Newtonian, power-law and quasi-mechanistic blood viscosity models

Cerebral aneurysm is a fatal neurovascular disorder. Computational fluid dynamics simulation of aneurysm haemodynamics is one of the most important research tools which provide increasing potential for clinical applications. However, computational fluid dynamics modelling of such delicate neurovascular disorder involves physical complexities that cannot be easily simplified. Recently, it was shown that the Newtonian simplification used to close the shear stress tensor of the Navier-Stokes equation is not sufficient to explore aneurysm haemodynamics. This article explores the differences between the latter simplification, non-Newtonian power-law model and a newly proposed quasi-mechanistic model. The modified Krieger model, which treats blood as a suspension of plasma and particles, was implemented in computational fluid dynamics context here for the first time and is made available to the readers in a C# code in the supplementary material of this article. Two middle-cerebral artery and two anterior-communicating artery aneurysms, all ruptured, were utilized here as case studies. It was shown that the modified Krieger model had higher sensitivity for wall shear stress calculations in comparison with the other two models. The modified Krieger model yielded lower wall shear stress values consistently in comparison with the other two models. Moreover, the modified Krieger model has generally predicted higher pressure in the aneurysm models. Based on published aneurysm rupture studies, it is believed that ruptured aneurysms are usually correlated with lower wall shear stress values than unruptured ones. Therefore, this work concludes that the modified Krieger model is a potential candidate for providing better clinical relevance to aneurysm computational fluid dynamics simulations.

What does computational fluid dynamics tell us about intracranial aneurysms? A meta-analysis and critical review

Despite the plethora of published studies on intracranial aneurysms (IAs) hemodynamic using computational fluid dynamics (CFD), limited progress has been made towards understanding the complex physics and biology underlying IA pathophysiology. Guided by 1733 published papers, we review and discuss the contemporary IA hemodynamics paradigm established through two decades of IA CFD simulations. We have traced the historical origins of simplified CFD models which impede the progress of comprehending IA pathology. We also delve into the debate concerning the Newtonian fluid assumption used to represent blood flow computationally. We evidently demonstrate that the Newtonian assumption, used in almost 90% of studies, might be insufficient to describe IA hemodynamics. In addition, some fundamental properties of the Navier-Stokes equation are revisited in supplementary material to highlight some widely spread misconceptions regarding wall shear stress (WSS) and its derivatives. Conclusively, our study draws a roadmap for next-generation IA CFD models to help researchers investigate the pathophysiology of IAs.

Transition to turbulence in an oscillatory flow through stenosis

Onset of flow transition in a sinusoidally oscillating flow through a rigid, constant area circular pipe with a smooth sinusoidal obstruction in the center of the pipe is studied by performing direct numerical simulations, with resolutions close to the Kolmogorov microscales. The studied pipe is stenosed in the center with a 75% reduction in area in two distinct configurations-one that is symmetric to the axis of the parent pipe and the other that is offset by 0.05 diameters to introduce an eccentricity, which disturbs the flow thereby triggering the onset of flow transition. The critical Reynolds number at which the flow transitions to turbulence for a zero-mean oscillatory flow through a stenosis is shown to be nearly tripled in comparison with studies of pulsating unidirectional flow through the same stenosis. The onset of transition is further explored with three different flow pulsation frequencies resulting in a total of 90 simulations conducted on a supercomputer. It is found that the critical Reynolds number at which the oscillatory flow transitions is not affected by the pulsation frequencies. The locations of flow breakdown and re-stabilization post-stenosis are, however, respectively shifted closer to the stenosis throat with increasing pulsation frequencies. The results show that oscillatory physiological flows, while more stable, exhibit fluctuations due to geometric complexity and have implications in studies of dispersion and solute transport in the cerebrospinal fluid flow and understanding of pathological conditions.

Numerical Investigation of Turbulence in Abdominal Aortic Aneurysms

Computational fluid dynamics (CFD) is a powerful method to investigate aneurysms. The primary focus of most investigations has been to compute various hemodynamic parameters to assess the risk posed by an aneurysm. Despite the occurrence of transitional flow in aneurysms, turbulence has not received much attention. In this article, we investigate turbulence in the context of abdominal aortic aneurysms (AAA). Since the clinical practice is to diagnose an AAA on the basis of its size, hypothetical axisymmetric geometries of various sizes are constructed. In general, just after the peak systole, a vortex ring is shed from the expansion region of an AAA. As the ring advects downstream, an azimuthal instability sets in and grows in amplitude thereby destabilizing the ring. The eventual breakdown of the vortex ring into smaller vortices leads to turbulent fluctuations. A residence time study is also done to identify blood recirculation zones, as a recirculation region can lead to degradation of the arterial wall. In some of the geometries simulated, the enhanced local mixing due to turbulence does not allow a recirculation zone to form, whereas in other geometries, turbulence had no effect on them. The location and consequence of a recirculation zone suggest that it could develop into an intraluminal thrombus (ILT). Finally, the possible impact of turbulence on the oscillatory shear index (OSI), a hemodynamic parameter, is explored. To conclude, this study highlights how a small change in the geometric aspects of an AAA can lead to a vastly different flow field.

Morphology and Hemodynamics in Isolated Common Iliac Artery Aneurysms Impacts Proximal Aortic Remodeling

Objective—

Isolated common iliac artery aneurysms (CIAA) are rare. Their prognosis and influence on aortoiliac blood flow and remodeling are unclear. We evaluated the hypotheses that morphology at and distal to the aortic bifurcation, together with the associated hemodynamic changes, influence both the natural history of CIAA and proximal aortic remodeling.

Approach and Results—

Twenty-five isolated CIAAs (15 intact, 10 ruptured), in 23 patients were reconstructed and analyzed with computational fluid dynamics: all showed abnormal flow. Then we studied a series of 24 hypothetical aortoiliac geometries in silico with varying abdominal aortic deflection and aortic bifurcation angles: key findings were assessed in an independent validation cohort of 162 patients. Wall shear stress in isolated unilateral CIAAs was lower than the contralateral common iliac artery, 0.38±0.33 Pa versus 0.61±0.24 Pa, inversely associated with CIAA diameter ( P <0.001) and morphology (high shear stress in variants distal to a sharp kink). Rupture usually occurred in regions of elevated low and oscillatory shear with a wide aortic bifurcation angle. Abdominal aortas deflected towards the CIAA for most unilateral isolated CIAAs (14/21). In silico, wider bifurcation angles created high focal regions of low and oscillatory shear in the common iliac artery. The associations of unilateral CIAA with aortic deflection and common iliac artery diameter with bifurcation angle were confirmed in the validation cohort.

Conclusions—

Decreasing wall shear stress is strongly associated with CIAA progression (larger aneurysms and rupture), whereas abnormal blood flow in the CIAA seems to promote proximal aortic remodeling, with adaptive lateral deflection of the abdominal aorta towards the aneurysmal side.

Biomechanical Investigation of Disturbed Hemodynamics-Induced Tissue Degeneration in Abdominal Aortic Aneurysms Using Computational and Experimental Techniques

Abdominal aortic aneurysm (AAA) is the dilatation of the aorta beyond 50% of the normal vessel diameter. It is reported that 4-8% of men and 0.5-1% of women above 50 years of age bear an AAA and it accounts for ~15,000 deaths per year in the United States alone. If left untreated, AAA might gradually expand until rupture; the most catastrophic complication of the aneurysmal disease that is accompanied by a striking overall mortality of 80%. The precise mechanisms leading to AAA rupture remains unclear. Therefore, characterization of disturbed hemodynamics within AAAs will help to understand the mechanobiological development of the condition which will contribute to novel therapies for the condition. Due to geometrical complexities, it is challenging to directly quantify disturbed flows for AAAs clinically. Two other approaches for this investigation are computational modeling and experimental flow measurement. In computational modeling, the problem is first defined mathematically, and the solution is approximated with numerical techniques to get characteristics of flow. In experimental flow measurement, once the setup providing physiological flow pattern in a phantom geometry is constructed, velocity measurement system such as particle image velocimetry (PIV) enables characterization of the flow. We witness increasing number of applications of these complimentary approaches for AAA investigations in recent years. In this paper, we outline the details of computational modeling procedures and experimental settings and summarize important findings from recent studies, which will help researchers for AAA investigations and rupture mechanics.

A non-dimensional parameter for classification of the flow in intracranial aneurysms. II. Patient-specific geometries

A simple parameter, called the Aneurysm number (An) which is defined as the ratio of transport to vortex time scales, has been shown to classify the flow mode in simplified aneurysm geometries. Our objective is to test the hypothesis that An can classify the flow in patient-specific intracranial aneurysms (IA). Therefore, the definition of this parameter is extended to anatomic geometries by using hydraulic diameter and the length of expansion area in the approximate direction of the flow. The hypothesis is tested using image-based flow simulations in five sidewall and four bifurcation geometries, i.e., if An ≲ 1 (shorter transport time scale), then the fluid is transported across the neck before the vortex could be formed, creating a quasi-stationary shear layer (cavity mode). By contrast, if An ≳ 1 (shorter vortex time scale), a vortex is formed. The results show that if An switches from An ≲ 1 to An ≳ 1, then the flow mode switches from the cavity mode to the vortex mode. However, if An does not switch, then the IAs stay in the same mode. It is also shown that IAs in the cavity mode have significantly lower An, temporal fluctuations of wall shear stress and oscillatory shear index (OSI) compared to the vortex mode (p < 0.01). In addition, OSI correlates with An in each flow mode and with pulsatility index in each IA. This suggests An to be a viable hemodynamic parameter which can be easily calculated without the need for detailed flow measurements/ simulations.

Patient-Specific Prediction of Abdominal Aortic Aneurysm Expansion Using Bayesian Calibration

Translating recent advances in abdominal aortic aneurysm (AAA) growth and remodeling (G&R) knowledge into a predictive, patient-specific clinical treatment tool requires a major paradigm shift in computational modeling. The objectives of this study are to develop a prediction framework that first calibrates the physical AAA G&R model using patient-specific serial computed tomography (CT) scan images, predicts the expansion of an AAA in the future, and quantifies the associated uncertainty in the prediction. We adopt a Bayesian calibration method to calibrate parameters in the G&R computational model and predict the magnitude of AAA expansion. The proposed Bayesian approach can take different sources of uncertainty; therefore, it is well suited to achieve our aims in predicting the AAA expansion process as well as in computing the propagated uncertainty. We demonstrate how to achieve the proposed aims by solving the formulated Bayesian calibration problems for cases with the synthetic G&R model output data and real medical patient-specific CT data. We compare and discuss the performance of predictions and computation time under different sampling cases of the model output data and patient data, both of which are simulated by the G&R computation. Furthermore, we apply our Bayesian calibration to real patient-specific serial CT data and validate our prediction. The accuracy and efficiency of the proposed method is promising, which appeals to computational and medical communities.

Flow instability detected in ruptured versus unruptured cerebral aneurysms at the internal carotid artery

Flow instability has emerged as a new hemodynamic metric hypothesized to have potential value in assessing the rupture risk of cerebral aneurysms. However, diverse findings have been reported in the literature. In the present study, high-resolution hemodynamic simulations were performed retrospectively on 35 aneurysms (10 ruptured & 25 unruptured) located at the internal carotid artery (ICA). Simulated hemodynamic parameters were statistically compared between the ruptured and unruptured aneurysms, with emphasis on examining the correlation of flow instability with the status of aneurysm rupture. Pronounced flow instability was detected in 20% (2 out of 10) of the ruptured aneurysms, whereas in 44% (11 out of 25) of the unruptured aneurysms. Statistically, the flow instability metric (quantified by the temporally and spatially averaged fluctuating kinetic energy over the aneurysm sac) did not differ significantly between the ruptured and unruptured aneurysms. In contrast, low wall shear stress area (LSA) and pressure loss coefficient (PLC) exhibited significant correlations with the status of aneurysm rupture. In conclusion, the present study suggests that the presence of flow instability may not correlate closely with the status of aneurysm rupture, at least for ICA aneurysms. On the other hand, the retrospective nature of the study and the small sample size may have to some extent compromised the reliability of the conclusion, and therefore large-scale prospective studies would be needed to further address the issue.

Hemodynamics in a giant intracranial aneurysm characterized by in vitro 4D flow MRI

Experimental and computational data suggest that hemodynamics play a critical role in the development, growth, and rupture of cerebral aneurysms. The flow structure, especially in aneurysms with a large sac, is highly complex and three-dimensional. Therefore, volumetric and time-resolved measurements of the flow properties are crucial to fully characterize the hemodynamics. In this study, phase-contrast Magnetic Resonance Imaging is used to assess the fluid dynamics inside a 3D-printed replica of a giant intracranial aneurysm, whose hemodynamics was previously simulated by multiple research groups. The physiological inflow waveform is imposed in a flow circuit with realistic cardiovascular impedance. Measurements are acquired with sub-millimeter spatial resolution for 16 time steps over a cardiac cycle, allowing for the detailed reconstruction of the flow evolution. Moreover, the three-dimensional and time-resolved pressure distribution is calculated from the velocity field by integrating the fluid dynamics equations, and is validated against differential pressure measurements using precision transducers. The flow structure is characterized by vortical motions that persist within the aneurysm sac for most of the cardiac cycle. All the main flow statistics including velocity, vorticity, pressure, and wall shear stress suggest that the flow pattern is dictated by the aneurysm morphology and is largely independent of the pulsatility of the inflow, at least for the flow regimes investigated here. Comparisons are carried out with previous computational simulations that used the same geometry and inflow conditions, both in terms of cycle-averaged and systolic quantities.

Direct numerical simulation of transitional hydrodynamics of the cerebrospinal fluid in Chiari I malformation: The role of cranio-vertebral junction

Obstruction to the cerebrospinal fluid (CSF) outflow caused by the herniation of cerebellar tonsils as a result of Chiari malformation type I leads to altered CSF hydrodynamics. This contribution explores the minutest characteristics of the CSF hydrodynamics in cervical subarachnoid space (SAS) of a healthy subject and 2 Chiari patients by performing highly resolved direct numerical simulation. The lattice Boltzmann method is used for the simulations because of its scalability on modern supercomputers that allow us to simulate up to approximately 10⁹ cells while resolving the Kolmogorov microscales. The results depict that whereas the complex CSF flow remains largely laminar in the SAS of a healthy subject, constriction of the cranio-vertebral junction in Chiari I patients causes manifold fluctuations in the hydrodynamics of the CSF. These fluctuations resemble a flow that is in a transitional regime rather than laminar or fully developed turbulence. The fluctuations confine near the cranio-vertebral junction and are triggered due to the tonsillar herniation, which perturbs the flow as a result of altered anatomy of the SAS.

Influence of overlapping pattern of multiple overlapping uncovered stents on the local mechanical environment: A patient-specific parameter study

BACKGROUND

Multiple overlapping uncovered stents (MOUS) system has shown potentials in managing complex aortic aneurysms with side branches involvement. It promotes the development of thrombus by modulating local flow pattern that reduces the wall tension, while maintaining patency of side branches. However the modulation of local hemodynamic parameters depends on various factors that have not been assessed comprehensively.

METHODS

Aneurysm 3D geometry was reconstructed based on CT images. One-way fluid-structure interaction analysis was performed to quantify structural stress concentration in the wall, and changes of blood velocity, wall shear stress (WSS), oscillatory shear index (OSI), relative residence time (RRT) and pressure in the sac due to the stent deployment.

RESULTS

High structural stress concentration due to stent deployment was found in the landing zone and it increased linearly with the number of stents deployed. The wall tension in the sac was unaffected by the stent deployment. Stress within the wall was insensitive to the different overlapping pattern. After one stent was deployed, the mean flow velocity in the sac reduced by 36.4%. The deployment of the 2nd stent further reduced the mean sac velocity by 10%. WSS decreased while both OSI and RRT increased after stent deployment, however pressure in the sac remained nearly unchanged. Except for the cases with complete stents struts alignment, different overlapping pattern had little effect on flow parameters.

CONCLUSIONS

Mechanical parameters modulated by the MOUS are insensitive to different overlapping pattern suggesting that endovascular procedure can be performed with less attention to the overlapping pattern.

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.

Transitional hemodynamics in intracranial aneurysms - Comparative velocity investigations with high resolution lattice Boltzmann simulations, normal resolution ANSYS simulations, and MR imaging

PURPOSE

Blood flow in intracranial aneurysms has, until recently, been considered to be disturbed but still laminar. Recent high resolution computational studies have demonstrated, in some situations, however, that the flow may exhibit high frequency fluctuations that resemble weakly turbulent or transitional flow. Due to numerous assumptions required for simplification in computational fluid dynamics (CFD) studies, the occurrence of these events, in vivo, remains unsettled. The detection of these fluctuations in aneurysmal blood flow, i.e., hemodynamics by CFD, poses additional challenges as such phenomena cannot be captured in clinical data acquisition with magnetic resonance (MR) due to inadequate temporal and spatial resolutions. The authors' purpose was to address this issue by comparing results from highly resolved simulations, conventional resolution laminar simulations, and MR measurements, identify the differences, and identify their causes.

METHODS

Two aneurysms in the basilar artery, one with disturbed yet laminar flow and the other with transitional flow, were chosen. One set of highly resolved direct numerical simulations using the lattice Boltzmann method (LBM) and another with adequate resolutions under laminar flow assumption were conducted using a commercially available ANSYS Fluent solver. The velocity fields obtained from simulation results were qualitatively and statistically compared against each other and with MR acquisition.

RESULTS

Results from LBM, ANSYS Fluent, and MR agree well qualitatively and quantitatively for one of the aneurysms with laminar flow in which fluctuations were <80 Hz. The comparisons for the second aneurysm with high fluctuations of > ∼ 600 Hz showed vivid differences between LBM, ANSYS Fluent, and magnetic resonance imaging. After ensemble averaging and down-sampling to coarser space and time scales, these differences became minimal.

CONCLUSIONS

A combination of MR derived data and CFD can be helpful in estimating the hemodynamic environment of intracranial aneurysms. Adequately resolved CFD would suffice gross assessment of hemodynamics, potentially in a clinical setting, and highly resolved CFD could be helpful in a detailed and retrospective understanding of the physiological mechanisms.

On the quantification and visualization of transient periodic instabilities in pulsatile flows

Turbulent-like flows without cycle-to-cycle variations are more frequently being reported in studies of cardiovascular flows. The associated stimuli might be of mechanobiological relevance, but how to quantify them objectively is not obvious. Classical Reynolds decomposition, where the flow is separated into mean and fluctuating velocity components, is not applicable as the phase-average is zero. We therefore expanded on established techniques and present the idea, analogous to Reynolds decomposition, to decompose a flow with transient instabilities into low- versus high frequency components, respectively, to discriminate flow instabilities from the underlying cardiac pulsatility. Transient wall shear stress and velocity signals derived from computational fluid dynamic simulations were transferred to the frequency domain. A high-pass filter was applied to subtract the 99% most-energy-containing frequencies, which gave a cut-off frequency of 25Hz. We introduce here the spectral power index, and compute the fluctuating kinetic energy, based on the high-pass filtered velocity components, both being frequency-based operators. The efficacy was evaluated in an aneurysm model for multiple flow rates demonstrating transition to turbulent-like flows. The frequency-based operators were found to better correlate with the qualitatively observed flow instabilities compared to conventional descriptors, like time-averaged wall shear stress or oscillatory shear index. We demonstrate how the high frequencies beyond the physiological range could be analyzed and/or transferred back to the time domain for quantification and visualization purposes. We have introduced general frequency-based operators, easily extendable to other cardiovascular territories based on a posteriori heuristic filtering that allows for separation, isolation, and quantification of cycle-invariant turbulent-like flows.

Effects of Reynolds and Womersley Numbers on the Hemodynamics of Intracranial Aneurysms

The effects of Reynolds and Womersley numbers on the hemodynamics of two simplified intracranial aneurysms (IAs), that is, sidewall and bifurcation IAs, and a patient-specific IA are investigated using computational fluid dynamics. For this purpose, we carried out three numerical experiments for each IA with various Reynolds (Re = 145.45 to 378.79) and Womersley (Wo = 7.4 to 9.96) numbers. Although the dominant flow feature, which is the vortex ring formation, is similar for all test cases here, the propagation of the vortex ring is controlled by both Re and Wo in both simplified IAs (bifurcation and sidewall) and the patient-specific IA. The location of the vortex ring in all tested IAs is shown to be proportional to Re/Wo² which is in agreement with empirical formulations for the location of a vortex ring in a tank. In sidewall IAs, the oscillatory shear index is shown to increase with Wo and 1/Re because the vortex reached the distal wall later in the cycle (higher resident time). However, this trend was not observed in the bifurcation IA because the stresses were dominated by particle trapping structures, which were absent at low Re = 151.51 in contrast to higher Re = 378.79.

Characterizations and Correlations of Wall Shear Stress in Aneurysmal Flow

Wall shear stress (WSS) is one of the most studied hemodynamic parameters, used in correlating blood flow to various diseases. The pulsatile nature of blood flow, along with the complex geometries of diseased arteries, produces complicated temporal and spatial WSS patterns. Moreover, WSS is a vector, which further complicates its quantification and interpretation. The goal of this study is to investigate WSS magnitude, angle, and vector changes in space and time in complex blood flow. Abdominal aortic aneurysm (AAA) was chosen as a setting to explore WSS quantification. Patient-specific computational fluid dynamics (CFD) simulations were performed in six AAAs. New WSS parameters are introduced, and the pointwise correlation among these, and more traditional WSS parameters, was explored. WSS magnitude had positive correlation with spatial/temporal gradients of WSS magnitude. This motivated the definition of relative WSS gradients. WSS vectorial gradients were highly correlated with magnitude gradients. A mix WSS spatial gradient and a mix WSS temporal gradient are proposed to equally account for variations in the WSS angle and magnitude in single measures. The important role that WSS plays in regulating near wall transport, and the high correlation among some of the WSS parameters motivates further attention in revisiting the traditional approaches used in WSS characterizations.

Study on the role of Cathepsin B and JNK signaling pathway in the development of cerebral aneurysm

OBJECTIVE

To investigate the correlation between JNK signal and the apoptosis of VSMC as well as the expression of Cathepsin B and to explore the role of JNK signal in the development of cerebral aneurysm.

METHODS

Rat models of cerebral aneurysm were established and histopathologic changes of cerebral aneurysm and the apoptosis of VSMC were analyzed. Rat models were respectively subject to subcutaneous injection of Cathepsin B siRNA and JNK inhibitor SP600125. Western blot technique was used to detect the expression of proteins like Cathepsin B, Caspase-3, and p-JNK. Spearman's rho was used to examine the correlation between p-JNK and Cathepsin B, as well as the expression of relevant proteins.

RESULTS

The success rate of modeling rats with cerebral aneurysm was 88.75%. After the respective injection of Cathepsin B siRNA, SP600125 and their combination, the cell densities of VSMC of rats with cerebral aneurysm all increased significantly (P < 0.05 or P < 0.01), but the apoptosis rate of VSMC decreased significantly (P < 0.01). Compared with normal rats, the expression of Cathepsin B, Caspase-3 and p-JNK in Cerebral aneurysm models increased significantly. Effectively intervening Cathepsin B genes with Cathepsin B siRNA could significantly inhibit the expression of Cathepsin B and Caspase-3, but hardly influence the expression of p-JNK. JNK inhibitor SP600125 had no influence on the expression of Cathepsin B and Caspase-3, but effectively inhibited the expression of p-JNK. In cerebral aneurysm tissues, positive correlation was observed between the expression of p-JNK and Cathepsin B, the correlation coefficient was r = 0.640.

CONCLUSION

After the attack of cerebral aneurysm, proteins like Cathepsin B, Caspase-3 and p-JNK are all involved in the apoptosis of VSMCs. This process may be realized by Cathepsin B which activates the apoptosis mechanism of Caspase-3 and mediate the apoptosis of VSMC through the JNK signaling pathway. Therefore, silencing Cathepsin B gene or inhibiting the conduction through JNK signaling pathway can mitigate the apoptosis of vascular smooth muscle cells in cerebral aneurysm.