Unsteady wall shear stress analysis from image-based computational fluid dynamic aneurysm models under Newtonian and Casson rheological models

Fractals and Chaos in the Hemodynamics of Intracranial Aneurysms

Computing the emerging flow in blood vessel sections by means of computational fluid dynamics is an often applied practice in hemodynamics research. One particular area for such investigations is related to the cerebral aneurysms, since their formation, pathogenesis, and the risk of a potential rupture may be flow-related. We present a study on the behavior of small advected particles in cerebral vessel sections in the presence of aneurysmal malformations. These malformations cause strong flow disturbances driving the system toward chaotic behavior. Within these flows, the particle trajectories can form a fractal structure, the properties of which are measurable by quantitative techniques. The measurable quantities are well established chaotic properties, such as the Lyapunov exponent, escape rate, and information dimension. Based on these findings, we propose that chaotic flow within blood vessels in the vicinity of the aneurysm might be relevant for the pathogenesis and development of this malformation.

Hemodynamics of anterior circulation intracranial aneurysms with daughter blebs: investigating the multidirectionality of blood flow fields

Recent advances in diagnostic neuroradiological imaging, allowed the detection of unruptured intracranial aneurysms (IAs). The shape - irregular or multilobular - of the aneurysmal dome, is considered as a possible rupture risk factor, independently of the size, the location and patient medical background. Disturbed blood flow fields in particular is thought to play a key role in IAs progression. However, there is an absence of widely-used hemodynamic indices to quantify the extent of a multi-directional disturbed flow. We simulated blood flow in twelve patient-specific anterior circulation unruptured intracranial aneurysms with daughter blebs utilizing the spectral/hp element framework Nektar++. We simulated three cardiac cycles using a volumetric flow rate waveform while we considered blood as a Newtonian fluid. To investigate the multidirectionality of the blood flow fields, besides the time-averaged wall shear stress (TAWSS), we calculated the oscillatory shear index (OSI), the relative residence time (RRT) and the time-averaged cross flow index (TACFI). Our CFD simulations suggest that in the majority of our vascular models there is a formation of complex intrasaccular flow patterns, resulting to low and highly oscillating WSS, especially in the area of the daughter blebs. The existence of disturbed multi-directional blood flow fields is also evident by the distributions of the RRT and the TACFI. These findings further support the theory that IAs with daughter blebs are linked to a potentially increased rupture risk.

Non-invasive diagnostics of blockage growth in the descending aorta-computational approach

Atherosclerosis causes blockages to the main arteries such as the aorta preventing blood flow from delivering oxygen to the organs. Non-invasive diagnosis of these blockages is difficult, particularly in primary healthcare. In this paper, the effect of arterial blockage development and growth is investigated at the descending aorta on some possible non-invasive assessment parameters including the blood pressure waveform, wall shear stress (WSS), time-average WSS (TAWSS) and the oscillation shear index (OSI). Blockage severity growth is introduced in a simulation model as 25%, 35%, 50% and 65% stenosis at the descending aorta based on specific healthy control aorta data clinically obtained. A 3D aorta model with invasive pulsatile waveforms (blood flow and pressure) is used in the CFD simulation. Blockage severity is assessed by using blood pressure measurements at the left subclavian artery. An arterial blockage growth more than 35% of the lumen diameter significantly affects the pressure. A strong correlation is also observed between the ascending aorta pressure values, pressure at the left subclavian artery and the relative residence time (RRT). An increase of RRT downstream from the stenosis indicates a 35% stenosis at the descending aorta which results in high systolic and diastolic pressure readings. The findings of this study could be further extended by transferring the waveform reading from the left subclavian artery to the brachial artery.

Graphical abstract

Reconstruction of carotid stenosis hemodynamics based on guidewire pressure data and computational modeling

A comparative analysis between intravascular guidewire-obtained and computational fluid dynamic (CFD) flow velocity and pressure data using simplified carotid stenosis models was performed. This information was used to evaluate the viability of using guidewire pressure data to provide inlet conditions for CFD flow, and to study the relationship between stenotic length and hemodynamic behavior. Carotid stenosis models differing in diameter and length were prepared and connected to a vascular pulsatile flow simulator. Time-dependent flow velocity and pressure measurements were taken by microcatheter guidewires and compared with CFD data. Guidewire and CFD-generated pressure profiles matched closely in all measurement locations. The guidewire was unable to reliably measure flow velocity at areas associated with higher CFD flow velocities (r = 0.92). CFD results showed that an increased length of stenosis generated expansive regions of elevated wall shear stress (WSS) within and distal to the stenosis. Low WSS was found immediately outside the stenosis outlet. An increase in stenotic length produced higher flow velocities with minimal lengthening of the distal high velocity flow jet due to faster dissipation of translational kinetic energy through turbulence. We found the accuracy of guidewire-obtained velocity measurements is limited to regions unaffected by disturbed flow. WSS and turbulence behavior distal to the stenosis may be important markers to evaluate the severity of atherosclerotic progression as a function of stenotic length.

Disturbed flow's impact on cellular changes indicative of vascular aneurysm initiation, expansion, and rupture: A pathological and methodological review

Aneurysms are malformations within the arterial vasculature brought on by the structural breakdown of the microarchitecture of the vessel wall, with aneurysms posing serious health risks in the event of their rupture. Blood flow within vessels is generally laminar with high, unidirectional wall shear stressors that modulate vascular endothelial cell functionality and regulate vascular smooth muscle cells. However, altered vascular geometry induced by bifurcations, significant curvature, stenosis, or clinical interventions can alter the flow, generating low stressor disturbed flow patterns. Disturbed flow is associated with altered cellular morphology, upregulated expression of proteins modulating inflammation, decreased regulation of vascular permeability, degraded extracellular matrix, and heightened cellular apoptosis. The understanding of the effects disturbed flow has on the cellular cascades which initiate aneurysms and promote their subsequent growth can further elucidate the nature of this complex pathology. This review summarizes the current knowledge about the disturbed flow and its relation to aneurysm pathology, the methods used to investigate these relations, as well as how such knowledge has impacted clinical treatment methodologies. This information can contribute to the understanding of the development, growth, and rupture of aneurysms and help develop novel research and aneurysmal treatment techniques.

Assessment and visualization of hemodynamic loading in aneurysm sac and neck: Effect of foam insertion

Shape memory polymer (SMP) foam is often proposed as the future alternative of coils in aneurysm treatment devices. Present work numerically investigates the unsteady, three-dimensional simulation of blood flow in a cerebral aneurysm filled with SMP foam. Simulations are conducted on patient-specific geometries with realistic blood velocity waveform imposed at the inlet while SMP foam is treated as a porous medium. The present study introduces a "loading risk map" that helps to visualize the hemodynamic effect of foam insertion on the aneurysm sac and neck. The loading risk maps suggest that while the SMP foam subdues the flow and wall shear pulsations in the aneurysm sac, the pressure distribution is minimally affected. The maps suggest that while the downstream lip is the most risk-prone site for both geometries, downstream vascular anatomy significantly influences foam efficiency in reducing pressure and wall shear stress loading.

Non-Newtonian Blood Modeling in Intracranial Aneurysm Hemodynamics: Impact on the Wall Shear Stress and Oscillatory Shear Index Metrics for Ruptured and Unruptured Cases

When simulating blood flow in intracranial aneurysms (IAs), the Newtonian model seems to be ubiquitous. However, analyzing the results from the few studies on this subject, the doubt remains on whether it is necessary to use non-Newtonian models in computational fluid dynamics (CFD) simulations of cerebral vascular flows. The objective of this study is to investigate whether different rheology models would influence the hemodynamic parameters related to the wall shear stress (WSS) for ruptured and unruptured IA cases, especially because ruptured aneurysms normally have morphological features, such as lobular regions and blebs, that could trigger non-Newtonian phenomena in the blood flow due to low shear rates. Using CFD in an open-source framework, we simulated four ruptured and four unruptured patient-specific aneurysms to assess the influence of the blood modeling on the main hemodynamic variables associated with aneurysm formation, growth, and rupture. Results for WSS and oscillatory shear index (OSI) and their metrics were obtained using Casson and Carreau-Yasuda non-Newtonian models and were compared with those obtained using the Newtonian model. We found that all differences between non-Newtonian and the Newtonian models were consistent among all cases irrespective of their rupture status. We further found that the WSS at peak systole is overestimated by more than 50% by using the non-Newtonian models, but its metrics based on time and surface averaged values are less affected-the maximum relative difference among the cases is 7% for the Casson model. On the other hand, the surface-averaged OSI is underestimated by more than 30% by the non-Newtonian models. These results suggest that it is recommended to investigate different blood rheology models in IAs simulations when specific parameters to characterize the flow are needed, such as peak-systole WSS and OSI.

Highly Electroconductive and Mechanically Strong Ti3C2Tx MXene Fibers Using a Deformable MXene Gel

Self-assembly of two-dimensional MXene sheets is used in various fields to create multiscale structures due to their electrical, mechanical, and chemical properties. In principle, MXene nanosheets are assembled by molecular interactions, including hydrogen bonds, electrostatic interactions, and van der Waals forces. This study describes how MXene colloid nanosheets can form self-supporting MXene hydrogels. Three-dimensional network structures of MXene gels are strengthened by reinforced electrostatic interactions between nanosheets. Stable gel networks are beneficial for fabricating highly aligned fibers because MXene gel can endure structural deformation. During wet spinning of highly concentrated MXene colloids in a coagulation bath, MXene sheets can be transformed into perfectly aligned fibers under a mechanical drawing force. Oriented MXene fibers exhibit a 1.5-fold increase in electrical conductivity (12 504 S cm^-1) and Young's modulus (122 GPa) compared with other fibers. The oriented MXene fibers are expected to have widespread applications, including electrical wiring and signal transmission.

Carbon nanotube-reduced graphene oxide fiber with high torsional strength from rheological hierarchy control

High torsional strength fibers are of practical interest for applications such as artificial muscles, electric generators, and actuators. Herein, we maximize torsional strength by understanding, measuring, and overcoming rheological thresholds of nanocarbon (nanotube/graphene oxide) dopes. The formed fibers show enhanced structure across multiple length scales, modified hierarchy, and improved mechanical properties. In particular, the torsional properties were examined, with high shear strength (914 MPa) attributed to nanotubes but magnified by their structure, intercalating graphene sheets. This design approach has the potential to realize the hierarchical dimensional hybrids, and may also be useful to build the effective network structure of heterogeneous materials.

Numerical investigation of patient-specific thoracic aortic aneurysms and comparison with normal subject via computational fluid dynamics (CFD)

Vascular hemodynamics play an important role in cardiovascular diseases. This work aimed to investigate the effects of an increase in ascending aortic diameter (AAD) on hemodynamics throughout a cardiac cycle for real patients. In this study, two scans of thoracic aortic aneurysm (TAA) subject with different AADs (42.94 mm and 48.01 mm) and a scan of a normal subject (19.81 mm) were analyzed to assess the effects of hemodynamics on the progression of TAA with the same flow rate. Real-patient aortic geometries were scanned by computed tomography angiography (CTA), and steady and pulsatile flow conditions were used to simulate real patient aortic geometries. Aortic arches were obtained from routine clinical scans. Computational fluid dynamics (CFD) simulations were performed with in vivo boundary conditions, and 3D Navier-Stokes equations were solved by a UDF (user-defined function) code defining a real cardiac cycle of one patient using Fourier series (FS). Wall shear stress (WSS) and pressure distributions were presented from normal subject to TAA cases. The results show that during the peak systolic phase pressure load increased by 18.56% from normal subject to TAA case 1 and by 23.8% from normal subject to TAA case 2 in the aneurysm region. It is concluded that although overall WSS increased in aneurysm cases but was low in dilatation areas. As a result, abnormal changes in WSS and higher pressure load may lead to rupture and risk of further dilatation. CFD simulations were highly effective to guide clinical predictions and assess the progress of aneurysm regions in case of early surgical intervention. Graphical abstract.

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.

Non-Newtonian Effects on Patient-Specific Modeling of Fontan Hemodynamics

The Fontan procedure is a common palliative surgery for congenital single ventricle patients. In silico and in vitro patient-specific modeling approaches are widely utilized to investigate potential improvements of Fontan hemodynamics that are related to long-term complications. However, there is a lack of consensus regarding the use of non-Newtonian rheology, warranting a systematic investigation. This study conducted in silico patient-specific modeling for twelve Fontan patients, using a Newtonian and a non-Newtonian model for each patient. Differences were quantified by examining clinically relevant metrics: indexed power loss (iPL), indexed viscous dissipation rate (iVDR), hepatic flow distribution (HFD), and regions of low wall shear stress (A_WSS). Four sets of "non-Newtonian importance factors" were calculated to explore their effectiveness in identifying the non-Newtonian effect. No statistical differences were observed in iPL, iVDR, and HFD between the two models at the population-level, but large inter-patient variations exist. Significant differences were detected regarding A_WSS, and its correlations with non-Newtonian importance factors were discussed. Additionally, simulations using the non-Newtonian model were computationally faster than those using the Newtonian model. These findings distinguish good importance factors for identifying non-Newtonian rheology and encourage the use of a non-Newtonian model to assess Fontan hemodynamics.

Simulation of GAP/HTPB phase behaviors in plasticizers and its application in composite solid propellant

Dissipative particle dynamics and molecular simulations were carried out to investigate the phase behaviors of glycidyl azide polymer (GAP)/hydroxyl-terminated polybutadiene (HTPB) polymer blend in dioctyl sebacate (DOS), and mixture of DOS and bis(2,2-dinitropropyl)formal/acetal (A3), respectively. The rheology of GAP/HTPB propellant slurry plasticized by A3/DOS was studied. First, single-phase aggregations of GAP and HTPB appear slightly in A3/DOS whereas it is conspicuous in DOS, which results from the small surface tension between the GAP/HTPB plasticized by A3/DOS and the weak thermal diffusion of this blend. Furthermore, with the plasticizing ratio (po/pl) increasing to 1.2, the GAP/HTPB propellant slurry plasticized by A3/DOS exhibits small viscosity and yield stress, and the Newtonian-like behavior of slurry improves its manufacturability. Finally, integral GAP/HTPB-based propellant can be obtained using A3/DOS as plasticizers.

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.

Monitoring Dynamic Morphological Changes With Electrocardiography-Gated Dynamic 4-Dimensional Computed Tomography Angiography to Predict Intraoperative Rupture of Intracranial Aneurysms

OBJECTIVE

This study aims to evaluate dynamic morphological changes of intracranial aneurysms to predict intraoperative aneurysm rupture (IAR) during clipping.

METHODS

Included in this study were 153 patients, who had ruptured and microsurgical-clipped aneurysms. All patients underwent dual-source computed tomography examination of electrocardiography-gated dynamic 4-dimensional computed tomography angiography before clipping. Original scanning data were reconstructed to produce 20 data sets of cardiac cycles with 5% time intervals. The aneurysm neck, transverse and longitudinal diameters, and volume from the 20 groups of images were measured to calculate their respective change rates. In addition, other data and clinical characteristics were recorded. Data were analyzed by logistic regression to identify factors associated with IAR.

RESULTS

Of the 153 patients, 24 patients experienced IAR. Multivariable analysis revealed that the aneurysm neck change rate (P = 0.0001; odds ratio, 1.276) and aspect ratio (height/neck ratio, P = 0.025; odds ratio, 2.387) are predictors for IAR. When the change rate was greater than or equal to 60%, and the sensitivity and specificity were 91.7% and 76.7%, respectively.

CONCLUSIONS

Aneurysm neck change rate is independent predictor of IAR.

Non-Newtonian versus numerical rheology: Practical impact of shear-thinning on the prediction of stable and unstable flows in intracranial aneurysms

Computational fluid dynamics (CFD) shows promise for informing treatment planning and rupture risk assessment for intracranial aneurysms. Much attention has been paid to the impact on predicted hemodynamics of various modelling assumptions and uncertainties, including the need for modelling the non-Newtonian, shear-thinning rheology of blood, with equivocal results. Our study clarifies this issue by contextualizing the impact of rheology model against the recently demonstrated impact of CFD solution strategy on the prediction of aneurysm flow instabilities. Three aneurysm cases were considered, spanning a range of stable to unstable flows. Simulations were performed using a high-resolution/accuracy solution strategy with Newtonian and modified-Cross rheology models and compared against results from a so-called normal-resolution strategy. Time-averaged and instantaneous wall shear stress (WSS) distributions, as well as frequency content of flow instabilities and dome-averaged WSS metrics, were minimally affected by the rheology model, whereas numerical solution strategy had a demonstrably more marked impact when the rheology model was fixed. We show that point-wise normalization of non-Newtonian by Newtonian WSS values tended to artificially amplify small differences in WSS of questionable physiological relevance in already-low WSS regions, which might help to explain the disparity of opinions in the aneurysm CFD literature regarding the impact of non-Newtonian rheology. Toward the goal of more patient-specific aneurysm CFD, we conclude that attention seems better spent on solution strategy and other likely "first-order" effects (eg, lumen segmentation and choice of flow rates), as opposed to "second-order" effects such as rheology.

A Review of Hemolysis Prediction Models for Computational Fluid Dynamics

Flow-induced hemolysis is a crucial issue for many biomedical applications; in particular, it is an essential issue for the development of blood-transporting devices such as left ventricular assist devices, and other types of blood pumps. In order to estimate red blood cell (RBC) damage in blood flows, many models have been proposed in the past. Most models have been validated by their respective authors. However, the accuracy and the validity range of these models remains unclear. In this work, the most established hemolysis models compatible with computational fluid dynamics of full-scale devices are described and assessed by comparing two selected reference experiments: a simple rheometric flow and a more complex hemodialytic flow through a needle. The quantitative comparisons show very large deviations concerning hemolysis predictions, depending on the model and model parameter. In light of the current results, two simple power-law models deliver the best compromise between computational efficiency and obtained accuracy. Finally, hemolysis has been computed in an axial blood pump. The reconstructed geometry of a HeartMate II shows that hemolysis occurs mainly at the tip and leading edge of the rotor blades, as well as at the leading edge of the diffusor vanes.

Virtual endovascular treatment of intracranial aneurysms: models and uncertainty

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

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

BACKGROUND

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 - 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

The numerical analysis of non-Newtonian blood flow in human patient-specific left ventricle

Recently, various non-invasive tools such as the magnetic resonance image (MRI), ultrasound imaging (USI), computed tomography (CT), and the computational fluid dynamics (CFD) have been widely utilized to enhance our current understanding of the physiological parameters that affect the initiation and the progression of the cardiovascular diseases (CVDs) associated with heart failure (HF). In particular, the hemodynamics of left ventricle (LV) has attracted the attention of the researchers due to its significant role in the heart functionality. In this study, CFD owing its capability of predicting detailed flow field was adopted to model the blood flow in images-based patient-specific LV over cardiac cycle. In most published studies, the blood is modeled as Newtonian that is not entirely accurate as the blood viscosity varies with the shear rate in non-linear manner. In this paper, we studied the effect of Newtonian assumption on the degree of accuracy of intraventricular hemodynamics. In doing so, various non-Newtonian models and Newtonian model are used in the analysis of the intraventricular flow and the viscosity of the blood. Initially, we used the cardiac MRI images to reconstruct the time-resolved geometry of the patient-specific LV. After the unstructured mesh generation, the simulations were conducted in the CFD commercial solver FLUENT to analyze the intraventricular hemodynamic parameters. The findings indicate that the Newtonian assumption cannot adequately simulate the flow dynamic within the LV over the cardiac cycle, which can be attributed to the pulsatile and recirculation nature of the flow and the low blood shear rate.

An automatic CFD-based flow diverter optimization principle for patient-specific intracranial aneurysms

The optimal treatment of intracranial aneurysms using flow diverting devices is a fundamental issue for neuroradiologists as well as neurosurgeons. Due to highly irregular manifold aneurysm shapes and locations, the choice of the stent and the patient-specific deployment strategy can be a very difficult decision. To support the therapy planning, a new method is introduced that combines a three-dimensional CFD-based optimization with a realistic deployment of a virtual flow diverting stent for a given aneurysm. To demonstrate the feasibility of this method, it was applied to a patient-specific intracranial giant aneurysm that was successfully treated using a commercial flow diverter. Eight treatment scenarios with different local compressions were considered in a fully automated simulation loop. The impact on the corresponding blood flow behavior was evaluated qualitatively as well as quantitatively, and the optimal configuration for this specific case was identified. The virtual deployment of an uncompressed flow diverter reduced the inflow into the aneurysm by 24.4% compared to the untreated case. Depending on the positioning of the local stent compression below the ostium, blood flow reduction could vary between 27.3% and 33.4%. Therefore, a broad range of potential treatment outcomes was identified, illustrating the variability of a given flow diverter deployment in general. This method represents a proof of concept to automatically identify the optimal treatment for a patient in a virtual study under certain assumptions. Hence, it contributes to the improvement of virtual stenting for intracranial aneurysms and can support physicians during therapy planning in the future.