The effect of inlet waveforms on computational hemodynamics of patient-specific intracranial aneurysms

Due to the lack of patient-specific inlet flow waveform measurements, most computational fluid dynamics (CFD) simulations of intracranial aneurysms usually employ waveforms that are not patient-specific as inlet boundary conditions for the computational model. The current study examined how this assumption affects the predicted hemodynamics in patient-specific aneurysm geometries. We examined wall shear stress (WSS) and oscillatory shear index (OSI), the two most widely studied hemodynamic quantities that have been shown to predict aneurysm rupture, as well as maximal WSS (MWSS), energy loss (EL) and pressure loss coefficient (PLc). Sixteen pulsatile CFD simulations were carried out on four typical saccular aneurysms using 4 different waveforms and an identical inflow rate as inlet boundary conditions. Our results demonstrated that under the same mean inflow rate, different waveforms produced almost identical WSS distributions and WSS magnitudes, similar OSI distributions but drastically different OSI magnitudes. The OSI magnitude is correlated with the pulsatility index of the waveform. Furthermore, there is a linear relationship between aneurysm-averaged OSI values calculated from one waveform and those calculated from another waveform. In addition, different waveforms produced similar MWSS, EL and PLc in each aneurysm. In conclusion, inlet waveform has minimal effects on WSS, OSI distribution, MWSS, EL and PLc and a strong effect on OSI magnitude, but aneurysm-averaged OSI from different waveforms has a strong linear correlation with each other across different aneurysms, indicating that for the same aneurysm cohort, different waveforms can consistently stratify (rank) OSI of aneurysms.     

Vascular wall flow-induced forces in a progressively enlarged aneurysm model

The current study is focused on the numerical investigation of the flow field induced by the unsteady flow in the vicinity of an abdominal aortic aneurysm model. The computational fluid dynamics code used is based on the finite volume method, and it has already been used in various bioflow studies. For modelling the rheological behaviour of blood, the Quemada non-Newtonian model is employed, which is suitable for simulating the two-phase character of blood namely a suspension of blood cells in plasma. For examining its non-Newtonian effects a comparison with a corresponding Newtonian flow is carried out. Furthermore, the investigation is focused on the distribution of the flow-induced forces on the interior wall of the aneurysm and in order to study the development of the distribution with the gradual enlargement of the aneurysm, three different degrees of aneurysm-growth have been assumed. Finally and for examining the effect of the distribution on the aneurysm growth, a comparison is made between the pressure and wall shear-stress distributions at the wall for each growth-degree.     

Direct numerical simulation of transitional flow in a stenosed carotid bifurcation

The blood flow dynamics of a stenosed, subject-specific, carotid bifurcation were numerically simulated using the spectral element method. Pulsatile inlet conditions were based on in vivo color Doppler ultrasound measurements of blood velocity. The results demonstrated the transitional or weakly turbulent state of the blood flow, which featured rapid velocity and pressure fluctuations in the post-stenotic region of the internal carotid artery (ICA) during systole and laminar flow during diastole. High-frequency vortex shedding was greatest downstream of the stenosis during the deceleration phase of systole. Velocity fluctuations had a frequency within the audible range of 100-300Hz. Instantaneous wall shear stress (WSS) within the stenosis was relatively high during systole ( approximately 25-45Pa) compared to that in a healthy carotid. In addition, high spatial gradients of WSS were present due to flow separation on the inner wall. Oscillatory flow reversal and low pressure were observed distal to the stenosis in the ICA. This study predicts the complex flow field, the turbulence levels and the distribution of the biomechanical stresses present in vivo within a stenosed carotid artery.     

Haemodynamic effects of stent diameter and compaction ratio on flow-diversion treatment of intracranial aneurysms: A numerical study of a successful and an unsuccessful case

Background: Compacting a flow-diverting (FD) stent is an emerging technique to create a denser configuration of wires across the aneurysm ostium. However, quantitative analyses of post-stenting haemodynamics affected by the compaction level of different stent sizes remain inconclusive.Objective: To compare the aneurysmal haemodynamic alterations after virtual FD treatments with different device diameters at different compaction ratios.Methods: We virtually implanted three sizes of FD stent, with each size deployed at four compaction ratios, into two patient aneurysms previously treated with the Silk + FD—one successful case and the other unsuccessful. Wire configurations of the FD in the 24 treatment scenarios were examined, and aneurysmal haemodynamic alterations were resolved by computational fluid dynamics (CFD) simulations. We investigated the aneurysmal flow patterns, aneurysmal average velocity (AAV), mass flowrate (MF), and energy loss (EL) in each scenario.Results: Compactions of the stent in the successful case resulted in a greater metal coverage rate than that achieved in the unsuccessful one. A 25% increment in compaction ratio further decreased the AAV (12%), MF (11%), and EL (9%) in both cases (average values). The averaged maximum differences attributable to device size were 10% (AAV), 8% (MF), and 9% (EL).Conclusions: Both stent size and compaction level could markedly affect the FD treatment outcomes. It is therefore important to individualise the treatment plan by selecting the optimal stent size and deployment procedure. CFD simulation can be used to investigate the treatment outcomes, thereby assisting doctors in choosing a favourable treatment plan.     

Pressure and flow in the umbilical cord

A fluid dynamic study of blood flow within the umbilical vessels of the human maternal-fetal circulatory system is considered. It is found that the umbilical coiling index (UCI) is unable to distinguish between cords of significantly varying pressure and flow characteristics, which are typically determined by the vessel curvature, torsion and length. Larger scale geometric non-uniformities superposed over the inherent coiling, including cords exhibiting width and/or local UCI variations as well as loose true knots, typically produce a small effect on the total pressure drop. Crucially, this implies that a helical geometry of mean coiling may be used to determine the steady vessel pressure drop through a more complex cord. The presence of vessel constriction, however, drastically increases the steady pressure drop and alters the flow profile. For pulsatile-flow within the arteries, the steady pressure approximates the time-averaged value with high accuracy over a wide range of cords. Furthermore, the relative peak systolic pressure measured over the period is virtually constant and approximately 25% below the equivalent straight-pipe value for a large range of non-straight vessels. Interestingly, this suggests that the presence of vessel helicity dampens extreme pressures within the arterial cycle and may provide another possible evolutionary benefit to the coiled structure of the cord.     

High-resolution computational fluid dynamics detects flow instabilities in the carotid siphon: Implications for aneurysm initiation and rupture?

The carotid siphon is by nature a tortuous vessel segment with sharp bends and large area variations, and of relevance to the study of intracranial aneurysm initiation and rupture. The aim of this paper was to determine whether the siphon might harbor flow instabilities, if care is taken to resolve them. This study focused on five consecutive internal carotid artery (ICA) aneurysm cases from the open-source Aneurisk dataset. The aneurysm, always downstream of the siphon, was digitally removed using previously developed and verified tools. Computational fluid dynamic (CFD) models included long cervical segments upstream, and middle and anterior cerebral arteries downstream. High-resolution pulsatile simulations were performed using the equivalent of ~24$~24$ million linear tetrahedra on average (range 16-32 M) and 30,000 time-steps/cycle. Two of the five cases were laminar with mild flow instabilities right after peak systole. One of the cases experienced strong periodic vortex shedding at a frequency of around 100 Hz. The remaining two cases harbored higher frequency flow instabilities and complex 3D vortical structures, extending to the cerebral arteries downstream. Our findings suggest that the carotid siphon, a conduit to the majority of anterior intracranial aneurysms, may experience flow instabilities, consistent with in vitro reports, but seemingly at odds with the majority of CFD studies, which have been done at lower resolutions. This has obvious implications for elucidating the forces involved in aneurysm initiation; and propagation of flow instabilities into ICA or downstream aneurysms could also impact understanding of the forces involved in aneurysm rupture.     

Errors in power-law estimations of inflow rates for intracranial aneurysm CFD

Patient-specific inflow rates are rarely available for computational fluid dynamics (CFD) studies of intracranial aneurysms. Instead, inflow rates are often estimated from parent artery diameters via power laws, i.e. Q ∝ Dⁿ, reflecting adaptation of conduit arteries to demanded flow. The present study aimed to validate the accuracy of these power laws. Internal carotid artery (ICA) flow rates were measured from 25 ICA aneurysm patients via 2D phase contrast MRI. ICA diameters, derived from 3D segmentation of rotational angiograms, were used to estimate inflow rates via power laws from the aneurysm CFD literature assuming the same inlet wall shear stress (WSS) (n = 3), velocity (n = 2) or flow rate (n = 0) for all cases. To illustrate the potential impact of errors in flow rate estimates, pulsatile CFD was carried out for four cases having large errors for at least one power law. Flow rates estimated by n = 3 and n = 0 power laws had significant (p < 0.01) mean biases of −22% to +32%, respectively, but with individual errors ranging from −78% to +120%. The n = 2 power law had no significant bias, but had non-negligible individual errors of −58% to +71%. CFD showed similarly large errors for time-averaged sac WSS; however, these were reduced after normalizing by parent artery WSS. High frequency WSS fluctuations, evident in 2/4 aneurysms, were also sensitive to inflow rate errors. Care should therefore be exercised in the interpretation of aneurysm CFD studies that rely on power law estimates of inflow rates, especially if absolute (vs. normalized) WSS, or WSS instabilities, are of interest.     

Biomechanical behaviour of cerebral aneurysm and its relation with the formation of intraluminal thrombus: a patient-specific modelling study

Cerebral aneurysm is an irreversible dilatation causing intracranial haemorrhage with severe complications. It is assumed that the biomechanical factor plays a significant role in the development of cerebral aneurysm. However, reports on the correlations between the formation of intraluminal thrombus and the flow pattern, wall shear stress (WSS) distribution of the cerebral aneurysm as well as wall compliance are still limited. In this research, patient-specific numerical simulation was carried out for three cerebral aneurysms based on magnetic resonance imaging (MRI) data-sets. The interaction between pulsatile blood and aneurysm wall was taken into account. The biomechanical behaviour of cerebral aneurysm and its relation with the formation of intraluminal thrombus was studied systematically. The results of the numerical simulation indicated that the region of low blood flow velocity and the region of swirling recirculation were nearly coincident with each other. Besides, there was a significant correlation between the slow swirling flow and the location of thrombus deposition. Excessively low WSS was also found to have strong association with the regions of thrombus formation. Moreover, the relationship between cerebral aneurysm compliance and thrombus deposition was discovered. The patient-specific modelling study based on fluid–structure interaction) may provide a basis for future investigation on the prediction of thrombus formation in cerebral aneurysm.     

Numerical simulations of the blood flow in the patient-specific arterial cerebral circle region

The Cerebral Circle Region, also known as the Circle of Willis (CoW), is a loop of arteries that form arterial connections between supply arteries to distribute blood throughout the cerebral mass. Among the population, only 25% to 50% have a complete system of arteries forming the CoW. 3D time-varying simulations for three different patient-specific artery anatomies of CoW were performed in order to gain a better insight into the phenomena existing in the cerebral blood flow. The models reconstructed on the basis of computer tomography images start from the aorta and include the largest arteries that supply the CoW and the arteries of CoW. Velocity values measured during the ultrasound examination have been compared with the results of simulations. It is shown that the flow in the right anterior artery in some cases may be supplied from the left internal carotid artery via the anterior communicating artery. The investigations conducted show that the computational fluid dynamic tool, which provides high resolution in both time and space domains, can be used to support physicians in diagnosing patients of different ages and various anatomical arterial structures.     

In-stent graft helical flow intensity reduces the risk of migration after endovascular aortic repair

During the last years endovascular aneurysm repair (EVAR) became the elective treatment for abdominal aortic aneurysms (AAAs) thanks to lower mortality and morbidity rates than open surgery. In face of these advantages, stent-graft performances are still clinically suboptimal. In particular, post-surgical complications derive from device migration as a consequence of the hemodynamic forces acting on the endograft. In this regard, while the importance of hemodynamic surface forces is well recognized, the role of the in-stent flow is still unclear. Here we hypothesize that in-stent helical blood flow patterns might influence the distribution of the displacement forces (DFs) acting on the stent-graft and, ultimately, the risk of stent migration. To test this hypothesis, the hemodynamics of 20 post-EVAR models of patients treated with two different commercial endografts was analyzed using computational hemodynamics.The main findings of the study indicate that: (1) helical flow intensity decreases the risk of endograft migration, as given by an inverse correlation between helicity intensity (h₂) and time-averaged displacement forces (TADFs) (p < 0.05); (2) unbalanced counter-rotating helical structures in the legs of the device contribute, in particular along the systole, to significantly suppress TADFs (p < 0.01); (3) as expected, helical flow intensity is positively correlated with pressure drop and resistance to flow (p < 0.001). The findings of this study suggest that a design strategy promoting in-stent helical flow structures could contribute to minimize the risk of migration of implanted EVAR devices.     

Validated numerical fluid simulation of a thin‐layer cascade photobioreactor in OpenFOAM

Recently, microalgae have been considered as a promising alternative for the production of biofuels from CO₂. For the efficient cultivation of these microalgae, several types of photobioreactors have been designed and Pilot scale photobioreactors have been used to assess the performance of these reactors. Therein the primarily investigated reactor type is the Raceway Pond. However, the less researched Thin‐Layer Cascade Photobioreactor (TLC) shows a high potential for efficient production processes. Unfortunately, for low‐value products like biofuels costs must be kept to a minimum for an economic operation. To facilitate this, 3D Computational Fluid Dynamic simulations can be employed to estimate performance of reactor variants e.g. with respect to power input and mixing. Since up to now little effort has been put into the modelling of TLC reactors, this report aims to present a simulation approach for these reactors types that allows simple adaptation to different geometric or operational boundary conditions. All models have been generated for a two‐phase mixture in OpenFOAM. To demonstrate its applicability, validation measurements with a physical unit have been performed and were compared to the simulation results. With errors in the order of 10 % a successful simulation of the reactor geometry could be proven.     

Approximating hemodynamics of cerebral aneurysms with steady flow simulations

Computational fluid dynamics (CFD) simulations can be employed to gain a better understanding of hemodynamics in cerebral aneurysms and improve diagnosis and treatment. However, introduction of CFD techniques into clinical practice would require faster simulation times. The aim of this study was to evaluate the use of computationally inexpensive steady flow simulations to approximate the aneurysm's wall shear stress (WSS) field. Two experiments were conducted. Experiment 1 compared for two cases the time-averaged (TA), peak systole (PS) and end diastole (ED) WSS field between steady and pulsatile flow simulations. The flow rate waveform imposed at the inlet was varied to account for variations in heart rate, pulsatility index, and TA flow rate. Consistently across all flow rate waveforms, steady flow simulations accurately approximated the TA, but not the PS and ED, WSS field. Following up on experiment 1, experiment 2 tested the result for the TA WSS field in a larger population of 20 cases covering a wide range of aneurysm volumes and shapes. Steady flow simulations approximated the space-averaged WSS with a mean error of 4.3%. WSS fields were locally compared by calculating the absolute error per node of the surface mesh. The coefficient of variation of the root-mean-square error over these nodes was on average 7.1%. In conclusion, steady flow simulations can accurately approximate the TA WSS field of an aneurysm. The fast computation time of 6 min per simulation (on 64 processors) could help facilitate the introduction of CFD into clinical practice.     

Hemodynamic analysis of a novel stent graft design with slit perforations in thoracic aortic aneurysm

Thoracic endovascular aortic repair (TEVAR) has been introduced as a less invasive approach to the treatment of thoracic aortic aneurysm (TAA). However, the effectiveness of TEVAR in the treatment of TAA is often limited due to the complex anatomy of aortic arch. Flow preservation at the three supra-aortic branches further increases the overall technical difficulty. This study proposes a novel stent graft design with slit perforations that can positively alter the hemodynamics at the aortic arch while maintaining blood flow to supra-aortic branches. We carried out a computational fluid dynamic (CFD) analysis to evaluate flow characteristics near stented aortic arch in simplified TAA models, followed by in-vitro experiments using particle image velocimetry (PIV) in a mock circulatory loop. The hemodynamics result was studied in terms of time-averaged wall shear stress (TAWSS), oscillating shear index (OSI), and endothelial cell action potential (ECAP). The results showed that the stent graft with slit perforations can reduce the disturbed flow region considerably. Furthermore, the effect of the slits on flow preservation to the supra-aortic branches was simulated and compared with experimental results. The effectiveness of the stent graft with slit perforations in preserving flow to the branches was demonstrated by both simulated and experimental results. Low TAWSS and elevated ECAP were observed in the aortic arch aneurysm after the placement of the stent graft with slits, implying the potential of thrombus formation in the aneurysm. On the other hand, the effects of the stent grafts with full-slit design and half-slit design on the shear stress did not differ significantly. The present analysis indicated that not only could the stent graft with slit perforations shield the aneurysm from rupture, but also it resulted in a favorable environment for thrombus that can contribute to the shrinkage of the aneurysm.     

椎动脉狭窄内血液两相流动数值模拟分析

目的:对应用三维重构得到的人体真实椎动脉进行血液两相流数值模拟,与经典单相流牛顿血液模型对比,分析动脉粥样硬化等病因与椎动脉狭窄处的血流动力学关系。方法:把考虑血细胞和血浆的两相流血液模型应用到逆向工程方法构建的基于人体生理解剖特征的椎动脉三维几何模型中去进行数值模拟,分析血细胞分布情况等血流动力学参数,并与单相流模型的模拟结果进行对比。结果:通过瞬态模拟计算,得到了椎动脉在心动周期内不同时刻的两相流和单相流模型的血流动力学参数。结论:通过对比单相流数值模拟结果,得出血管狭窄处血细胞出现聚集,血流更加复杂和低壁面切应力分布等与动脉粥样硬化及血栓的形成相关的结论。并且与两相流模型相比,单相流模型存在如无法获得如血细胞分布等不足,为进一步深入研究椎动脉等疾病的发病机理提供方法和理论支持。     

DPD simulation of non-Newtonian electroosmotic fluid flow in nanochannel

We use the dissipative particle dynamics (DPD) method to simulate the non-Newtonian electroosmotic flow (EOF) through nanochannels. Contrary to a large amount of past computational efforts dedicated to the study of EOF profile, this work pays attention to the EOF of non-Newtonian fluids, which has been rarely touched in past publications. Practically, there are many MEMS/NEMS devices, in which the EOF behaviour should be treated assuming both non-continuum and non-Newtonian conditions. Therefore, our concern in this work is to simulate the EOF through nanochannels considering both non-Newtonian fluid properties and non-continuum flow conditions. We have chosen DPD as our working tool because it provides several important advantages comparing with the classical time consuming molecular dynamics method. Using the DPD method, we explore the effect of a few important fluid properties and nanochannel parameters on the EOF behaviour and the resulting flow rate magnitudes. Our investigation will result in a number of findings, which have not been reported in past research works.     

Finite element modeling of embolic coil deployment: Multifactor characterization of treatment effects on cerebral aneurysm hemodynamics

Endovascular coiling is the most common treatment for cerebral aneurysms. During the treatment, a sequence of embolic coils with different stiffness, shapes, sizes, and lengths is deployed to fill the aneurysmal sac. Although coil packing density has been clinically correlated with treatment success, many studies have also reported success at low packing densities, as well as recurrence at high packing densities. Such reports indicate that other factors may influence treatment success. In this study, we used a novel finite element approach and computational fluid dynamics (CFD) to investigate the effects of packing density, coil shape, aneurysmal neck size, and parent vessel flow rate on aneurysmal hemodynamics. The study examines a testbed of 80 unique CFD simulations of post-treatment flows in idealized basilar tip aneurysm models. Simulated coil deployments were validated against in vitro and in vivo deployments. Among the investigated factors, packing density had the largest effect on intra-aneurysmal velocities. However, multifactor analysis of variance showed that coil shape can also have considerable effects, depending on packing density and neck size. Further, linear regression analysis showed an inverse relationship between mean void diameter in the aneurysm and mean intra-aneurysmal velocities, which underscores the importance of coil distribution and thus coil shape. Our study suggests that while packing density plays a key role in determining post-treatment hemodynamics, other factors such as coil shape, aneurysmal geometry, and parent vessel flow may also be very important.     

Evaluation of dentinal fluid flow behaviours: a fluid-structure interaction simulation

This study uses the fluid-structure interaction (FSI) method to investigate the fluid flow in dental pulp. First, the FSI method is used for the biomechanical simulation of dental intrapulpal responses during force loading (50, 100 and 150 N) on a tooth. The results are validated by comparison with experimental outcomes. Second, the FSI method is used to investigate an intact tooth subjected to a mechanical stimulus during loading at various loading rates. Force loading (0–100 N) is applied gradually to an intact tooth surface with loading rates of 125, 62.5, 25 and 12.5 N/s, respectively, and the fluid flow changes in the pulp are evaluated. FSI analysis is found to be suitable for examining intrapulpal biomechanics. An external force applied to a tooth with a low loading rate leads to a low fluid flow velocity in the pulp chamber, thus avoiding tooth pain.