Experimental and CFD flow studies in an intracranial aneurysm model with Newtonian and non-Newtonian fluids

A hemodynamic analysis of energy loss in abdominal aortic aneurysm using three-dimension idealized model

Objective: The aim of this study is to perform specific hemodynamic simulations of idealized abdominal aortic aneurysm (AAA) models with different diameters, curvatures and eccentricities and evaluate the risk of thrombosis and aneurysm rupture. Methods: Nine idealized AAA models with different diameters (3 cm or 5 cm), curvatures (0° or 30°) and eccentricities (centered on or tangent to the aorta), as well as a normal model, were constructed using commercial software (Solidworks; Dassault Systemes S.A, Suresnes, France). Hemodynamic simulations were conducted with the same time-varying volumetric flow rate extracted from the literature and 3-element Windkessel model (3 EWM) boundary conditions were applied at the aortic outlet. Several hemodynamic parameters such as time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), relative residence time (RRT), endothelial cell activation potential (ECAP) and energy loss (EL) were obtained to evaluate the risk of thrombosis and aneurysm rupture under different conditions. Results: Simulation results showed that the proportion of low TAWSS region and high OSI region increases with the rising of aneurysm diameter, whereas decreases in the curvature and eccentric models of the corresponding diameters, with the 5 cm normal model having the largest low TAWSS region (68.5%) and high OSI region (40%). Similar to the results of TAWSS and OSI, the high ECAP and high RRT areas were largest in the 5 cm normal model, with the highest wall-averaged value (RRT: 5.18 s, ECAP: 4.36 Pa-1). Differently, the increase of aneurysm diameter, curvature, and eccentricity all lead to the increase of mean flow EL and turbulent EL, such that the highest mean flow EL (0.82 W · 10-3) and turbulent EL (1.72 W · 10-3) were observed in the eccentric 5 cm model with the bending angle of 30°. Conclusion: Collectively, increases in aneurysm diameter, curvature, and eccentricity all raise mean flow EL and turbulent flow EL, which may aggravate the damage and disturbance of flow in aneurysm. In addition, it can be inferred by conventional parameters (TAWSS, OSI, RRT and ECAP) that the increase of aneurysm diameter may raise the risk of thrombosis, whereas the curvature and eccentricity appeared to have a protective effect against thrombosis.

Hemodynamic characteristics in a cerebral aneurysm model using non-Newtonian blood analogues

This study aims to develop an experimentally validated computational fluid dynamics (CFD) model to estimate hemodynamic characteristics in cerebral aneurysms (CAs) using non-Newtonian blood analogues. Blood viscosities varying with shear rates were measured under four temperatures first, which serves as the reference for the generation of blood analogues. Using the blood analogue, particle image velocimetry (PIV) measurements were conducted to quantify flow characteristics in a CA model. Then, using the identical blood properties in the experiment, CFD simulations were executed to quantify the flow patterns, which were used to compare with the PIV counterpart. Additionally, hemodynamic characteristics in the simplified Newtonian and non-Newtonian models were quantified and compared using the experimentally validated CFD model. Results showed the proposed non-Newtonian viscosity model can predict blood shear-thinning properties accurately under varying temperatures and shear rates. Another developed viscosity model based on the blood analogue can well represent blood rheological properties. The comparisons in flow characteristics show good agreements between PIV and CFD, demonstrating the developed CFD model is qualified to investigate hemodynamic factors within CAs. Furthermore, results show the differences of absolute values were insignificant between Newtonian and non-Newtonian fluids in the distributions of wall shear stress (WSS) and oscillatory shear index (OSI) on arterial walls. However, not only does the simplified Newtonian model underestimate WSS and OSI in most regions of the aneurysmal sac, but it also makes mistakes in identifying the high OSI regions on the sac surface, which may mislead the hemodynamic assessment on the pathophysiology of CAs.

A Hemodynamic Analysis of the Thrombosis Within Occluded Coronary Arterial Fistulas With Terminal Aneurysms Using a Blood Stasis Model

Objective: The aim of this study is to numerically evaluate thrombosis risk within occluded coronary arterial fistulas (CAF) with terminal aneurysms, and provide guidance in choosing occlusion positions, with clinical observations as reference. Method: Four patients with CAF were studied, with different occlusion positions in actual treatments. Hemodynamics simulations were conducted, with blood residue predicted using the blood stasis model. Three types of models (untreated model, aneurysm-reserved model and aneurysm-removed model) were studeid for each patient. Four metrics, i.e., proportion of high oscillatory shear index (OSI), area of high OSI, old blood volume fraction (OBVF)) and old blood volume (OBV) was obtained to distinguish the thrombosis risk of different treatments (proximal or distal occlusion), comparing with the follow-up CTA. Results: For all the postopertive models, the high OBVF, high OSI(>0.3) and low time-averaged wall shear stress (TAWSS) regions were mainly at the distal fistula, indicating these regions were prone to thrombosis. The regions where blood residue remains are roughly regions of high OSI, corresponding well with clinical observations. In contrast, TAWSS failed to distinguish the difference in thrombosis risk. Absolute values (area of high OSI, OBV) can better reflect the degree of thrombosis risk between treatment types compared with percentage values (proportion of high OSI, OBVF). By comparing with the actual clinical treatments and observations, the OBV is superior to the area of high OSI in determining treatment type. Conclusion: The OBV, a volumetric parameter for blood stasis, can better account for the CAF thrombosis and reflect the degree of blood stasis compared with OSI or TAWSS, is a more appropriate metric for thrombosis in the fistula. Together with morphological parameters, the OBV could guide clinicians to formulate more appropriate surgical plans, which is of great significance for the preoperative evaluation and treatment prognosis of CAF patients.

Comparison of Newtonian and Non-newtonian Fluid Models in Blood Flow Simulation in Patients With Intracranial Arterial Stenosis

Background

Newtonian fluid model has been commonly applied in simulating cerebral blood flow in intracranial atherosclerotic stenosis (ICAS) cases using computational fluid dynamics (CFD) modeling, while blood is a shear-thinning non-Newtonian fluid. We aimed to investigate the differences of cerebral hemodynamic metrics quantified in CFD models built with Newtonian and non-Newtonian fluid assumptions, in patients with ICAS.

Methods

We built a virtual artery model with an eccentric 75% stenosis and performed static CFD simulation. We also constructed CFD models in three patients with ICAS of different severities in the luminal stenosis. We performed static simulations on these models with Newtonian and two non-Newtonian (Casson and Carreau-Yasuda) fluid models. We also performed transient simulations on another patient-specific model. We measured translesional pressure ratio (PR) and wall shear stress (WSS) values in all CFD models, to reflect the changes in pressure and WSS across a stenotic lesion. In all the simulations, we compared the PR and WSS values in CFD models derived with Newtonian, Casson, and Carreau-Yasuda fluid assumptions.

Results

In all the static and transient simulations, the Newtonian/non-Newtonian difference on PR value was negligible. As to WSS, in static models (virtual and patient-specific), the rheological difference was not obvious in areas with high WSS, but observable in low WSS areas. In the transient model, the rheological difference of WSS areas with low WSS was enhanced, especially during diastolic period.

Conclusion

Newtonian fluid model could be applicable for PR calculation, but caution needs to be taken when using the Newtonian assumption in simulating WSS especially in severe ICAS cases.

Simulation analysis of aneurysm embolization surgery: Hemorheology of aneurysms with different embolization rates (CTA)

BACKGROUND

Embolization degree acts as an important factor affecting recurrence of aneurysm.

OBJECTIVE

To analyze the role of hemodynamics parameters of different degrees of embolization in the occurrence, development and post-treatment of aneurysms, and to determine the specific factors causing the occurrence and recurrence of aneurysms after hemodynamics treatment. Our study provides a theoretical basis for the prevention and treatment of aneurysms.

METHODS

Computed tomography angiography data of a patient with cerebral aneurysm was used to model 0%, 24%, 52%, 84% and 100% of endovascular embolization, respectively. The time average wall shear stress, time average wall shear stress, oscillatory shear index, hemodynamics formation index and relative retentive time were used to analyze the changes of hemodynamics indexes in different embolic models.

RESULTS

With the increase of embolic rate, the values of time average wall shear stress, time average wall shear stress grade and aneurysm index formation gradually increased, and the values of relative retention time gradually decreased. Oscillatory shear index was higher in patients with incomplete embolization and decreased in patients with complete embolization.

CONCLUSIONS

As the degree of embolization increased, the blood flow tended to stabilize, reducing the risk of cerebral aneurysm rupture, and finding that the wall of the vessel junction was susceptible to injury.

Numerical study on the energy cascade of pulsatile Newtonian and power-law flow models in an ICA bifurcation

The complex physics and biology underlying intracranial hemodynamics are yet to be fully revealed. A fully resolved direct numerical simulation (DNS) study has been performed to identify the intrinsic flow dynamics in an idealized carotid bifurcation model. To shed the light on the significance of considering blood shear-thinning properties, the power-law model is compared to the commonly used Newtonian viscosity hypothesis. We scrutinize the kinetic energy cascade (KEC) rates in the Fourier domain and the vortex structure of both fluid models and examine the impact of the power-law viscosity model. The flow intrinsically contains coherent structures which has frequencies corresponding to the boundary frequency, which could be associated with the regulation of endothelial cells. From the proposed comparative study, it is found that KEC rates and the vortex-identification are significantly influenced by the shear-thinning blood properties. Conclusively, from the obtained results, it is found that neglecting the non-Newtonian behavior could lead to underestimation of the hemodynamic parameters at low Reynolds number and overestimation of the hemodynamic parameters by increasing the Reynolds number. In addition, we provide physical insight and discussion onto the hemodynamics associated with endothelial dysfunction which plays significant role in the pathogenesis of intracranial aneurysms.

Particle Image Velocimetry Measurements of the Flow-Diverting Effects of a New Generation of the eCLIPs Implant for the Treatment of Intracranial Bifurcation Aneurysms

Flow diverters (FDs) for the endovascular treatment of intracranial aneurysms are effective for sidewall aneurysms, but their use at a bifurcation is problematic because FDs only partially cover the aneurysm neck and impede flow into a daughter branch; they are thus not employed routinely in this anatomy. eCLIPs was developed as a non-tubular implant to completely cover the neck of an aneurysm and serve as a coil retention device necessary for the adequate treatment of wide-neck bifurcation aneurysms. eCLIPs has shown some flow diversion effects in bifurcation anatomy but not equal to those exhibited by clinically accepted flow diverters in sidewall anatomy. A new generation of eCLIPs implant, the eCLIPs bifurcation flow diverter (eBFD), with higher metal coverage, was developed to achieve a similar flow diversion as a Pipeline Embolization Device (PED), a prototypical FD. Particle image velocimetry was used to capture the fluid dynamics and velocity reduction within silicone aneurysm replicas. A circulatory mimicking loop was developed to circulate the flow through the silicone models. All generations of eCLIPs implants had some flow-diverting effect, with increasing metal coverage density of the implant proportionately increasing the flow diversion effect. The eBFD, with a metal density of 35%, showed greater flow diversion than PED, with 30% metal density, for bifurcation anatomy. The eBFD showed similar reduction of flow in a bifurcation anatomy to PED in a sidewall, both sufficient to permit early thrombosis of the aneurysm. Thus, the eBFD can potentially provide sufficient flow diversion for the treatment of bifurcation aneurysms to avoid adjunctive coiling.

A Brush-Spin-Coating Method for Fabricating In Vitro Patient-Specific Vascular Models by Coupling 3D-Printing

PURPOSE

In vitro patient-specific flexible vascular models are helpful for understanding the haemodynamic changes before and after endovascular treatment and for effective training of neuroendovascular interventionalists. However, it is difficult to fabricate models of overall unified or controllable thickness using existing manufacturing methods. In this study, we developed an improved and easily implemented method by combining 3D printing and brush-spin-coating processes to produce a transparent silicone model of uniform or varied thickness.

METHODS

First, a water-soluble inner-skeleton model, based on clinical data, was printed on a 3D printer. The skeleton model was subsequently fixed in a single-axis-rotation machine to enable continuous coating of silicone, the thickness of which was manually controlled by adsorption and removal of excess silicone in a brush-spinning operation. After the silicone layer was solidified, the inner skeleton was further dissolved in a hot water bath, affording a transparent vascular model with real geometry. To verify the controllability of the coating thickness by using this method, a straight tube, an idealised aneurysm model, a patient-specific aortic arch model, and an abdominal aortic aneurysm model were manufactured.

RESULTS

The different thicknesses of the manufactured tubes could be well controlled, with the relative standard deviations being 5.6 and 8.1% for the straight and aneurysm tubes, respectively. Despite of the diameter changing from 33 to 20 mm in the patient-specific aorta, the thickness of the fabricated aortic model remains almost the same along the longitudinal direction with a lower standard deviation of 3.1%. In the more complex patient-specific abdominal aneurysm model, varied thicknesses were realized to mimic the measured data from the CT images, where the middle of the aneurysm was with 2 mm and abdominal aorta as well as the iliac arteries had the normal thickness of 2.3 mm.

CONCLUSION

Through the brush-spin-coating method, models of different sizes and complexity with prescribed thickness can be manufactured, which will be helpful for developing surgical treatment strategies or training neuroendovascular interventionalists.

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.

How Flow Reduction Influences the Intracranial Aneurysm Occlusion: A Prospective 4D Phase-Contrast MRI Study

BACKGROUND AND PURPOSE

Flow-diverter stents are widely used for the treatment of wide-neck intracranial aneurysms. Various parameters may influence intracranial aneurysm thrombosis, including the flow reduction induced by flow-diverter stent implantation, which is assumed to play a leading role. However, its actual impact remains unclear due to the lack of detailed intra-aneurysmal flow measurements. This study aimed to clarify this relationship by quantitatively measuring the intra-aneurysmal flow using 4D phase-contrast MR imaging.

MATERIALS AND METHODS

We acquired prospective pre- and post-stent implantation 4D phase-contrast MR imaging data of a consecutive series of 23 patients treated with flow-diverter stents. Velocity field data were combined with the intraprocedural 3D angiogram vessel geometries for precise intracranial aneurysm extraction and partial volume correction. Intra-aneurysmal hemodynamic modifications were compared with occlusion outcomes at 6 and 12 months.

RESULTS

The averaged velocities at systole were lower after flow-diverter stent implantation for all patients and ranged from 21.7 ± 7.1 cm/s before to 7.2 ± 2.9 cm/s after stent placement. The velocity reduction was more important for the group of patients with aneurysm thrombosis at 6 months (68.8%) and decreased gradually from 66.2% to 55% for 12-month thrombosis and no thrombosis, respectively (P = .08).

CONCLUSIONS

We propose an innovative approach to measure intracranial flow changes after flow-diverter stent implantation. We identified a trend between flow reduction and thrombosis outcome that brings a new insight into current understanding of the flow-diversion treatment response.

Evaluation of flow changes after telescopic stenting of a giant fusiform aneurysm of the vertebrobasilar junction

BACKGROUND

The use of flow-diverters for non-saccular cerebral posterior circulation aneurysms requires complex deployment techniques and is associated with high mortality and morbidity. Therefore, further studies are required to clarify the effect of stenting on post-treatment hemodynamics in such aneurysms. In this study, we evaluated flow alterations in a treated giant fusiform aneurysm of the vertebrobasilar junction and correlated them with the clinical outcome.

METHODS

A patient-specific aneurysm model was acquired by rotational angiography, and three SILK flow-diverters (4.5 × 40, 5 × 40 and 5.5 × 40 mm) were virtually deployed in series along the basilar and right vertebral arteries. Image-based blood flow simulations before and after the treatment were performed under realistic pulsatile flow conditions. The flow reduction, velocity and wall shear stress (WSS) distribution, streamlines and WSS-derived parameters were evaluated before and after the treatment.

RESULTS

The computed velocity streamlines showed substantial alterations of the flow pattern in the aneurysm and successful redirection of blood flow along the series of flow-diverters with no flow through the overlapping stents. The obtained flow reduction of 86% was sufficient to create thrombogenic flow conditions. Moreover, a 6.2-fold increase in relative residence time and a decrease by 87% of time-averaged WSS contributed to a successful treatment outcome observed during the follow-up.

CONCLUSIONS

We found a correlation between the numerically predicted flow alterations and the available treatment outcome. This shows the potential of image-based simulations to be used in clinical practice for treatment planning and estimation of possible risk factors associated with a complex stent deployment in fusiform aneurysms of the posterior circulation.

Evidence for non-Newtonian behavior of intracranial blood flow from Doppler ultrasonography measurements

Computational fluid dynamics (CFD) studies of intracranial hemodynamics often use Newtonian viscosity model to close the shear rate term in the Navier-Stokes equation. This is based on a commonly accepted hypothesis which state that non-Newtonian effects can be neglected in intracranial blood flow. This study aims to examine the validity of such hypothesis to guide future CFD studies of intracranial hemodynamics. Doppler ultrasonography (DUS) measurements of systolic and diastolic vessel diameter and blood velocity were conducted on 16 subjects (mean age 50.6). The measurements were conducted on the internal carotid (ICA), middle cerebral (MCA), and anterior communicating (AComA) arteries. Systolic and diastolic wall shear stress (WSS) values were calculated via the Hagen-Poiseuille exact solution using Newtonian and three different non-Newtonian models: namely Carreau, power-law and Herschel-Bulkley models. The Weissenberg-Rabinowitsch correction for blood shear-thinning viscosity was applied to the non-Newtonian models. The error percentage between the two sets of models was calculated and discussed. The Newtonian hypothesis was tested statistically and discussed using paired t tests. Significant differences (P < 0.0001) were found between the Newtonian and non-Newtonian WSS in ICA. In MCA and AComA, similar differences were found except in the systole and diastole for the Herschel-Bulkley and power-law models (P = 0.0669, P = 0.7298), respectively. The error between the Newtonian and non-Newtonian models ranged from - 27 to 30% (0.2 to 2.2 Pa). These values could affect the physical interpretation of IA CFD studies. Evidence suggests that the Newtonian assumption may be inappropriate to investigate intracranial hemodynamics. Graphical abstract The WSS estimation error resulting from using the Newtonian assumption compared to three non-Newtonian models for ICA, MCA, and AComA in systole and diastole conditions, based on TCCD measurements of 16 subjects. The error due to the Newtonian assumption ranged from 0.2 to 2.2 Pa (- 27 to 30%). These values could affect the physical interpretation of IA CFD studies.

NEWTONIAN AND NON-NEWTONIAN BLOOD FLOW AT A 90∘-BIFURCATION OF THE CEREBRAL ARTERY: A COMPARATIVE STUDY OF FLUID VISCOSITY MODELS

The majority of numerical simulations assumes blood as a Newtonian fluid due to an underestimation of the effect of non-Newtonian blood behavior on hemodynamics in the cerebral arteries. In the present study, we evaluated the effect of non-Newtonian blood properties on hemodynamics in the idealized 90[Formula: see text]-bifurcation model, using Newtonian and non-Newtonian fluids and different flow rate ratios between the parent artery and its branch. The proposed Local viscosity model was employed for high-precision representation of blood viscosity changes. The highest velocity differences were observed at zones with slow recirculating flow. During the systolic peak the average difference was 17–22%, whereas at the end of diastole the difference increased to 27–60% depending on the flow rate ratio. The main changes in the viscosity distribution were observed distal to the flow separation point, where the non-Newtonian fluid model produced 2.5 times higher viscosity. A presence of such high viscosity region substantially affected the size of the flow recirculation zone. The observed differences showed that non-Newtonian blood behavior had a significant effect on hemodynamic parameters and should be considered in the future studies of blood flow in cerebral arteries.

Phase-contrast MRI versus numerical simulation to quantify hemodynamical changes in cerebral aneurysms after flow diverter treatment

Cerebral aneurysms are a major risk factor for intracranial bleeding with devastating consequences for the patient. One recently established treatment is the implantation of flow-diverters (FD). Methods to predict their treatment success before or directly after implantation are not well investigated yet. The aim of this work was to quantitatively study hemodynamic parameters in patient-specific models of treated cerebral aneurysms and its correlation with the clinical outcome. Hemodynamics were evaluated using both computational fluid dynamics (CFD) and phase contrast (PC) MRI. CFD simulations and in vitro MRI measurements were done under similar flow conditions and results of both methods were comparatively analyzed. For preoperative and postoperative distribution of hemodynamic parameters, CFD simulations and PC-MRI velocity measurements showed similar results. In both cases where no occlusion of the aneurysm was observed after six months, a flow reduction of about 30-50% was found, while in the clinically successful case with complete occlusion of the aneurysm after 6 months, the flow reduction was about 80%. No vortex was observed in any of the three models after treatment. The results are in agreement with recent studies suggesting that CFD simulations can predict post-treatment aneurysm flow alteration already before implantation of a FD and PC-MRI could validate the predicted hemodynamic changes right after implantation of a FD.