Lattice Boltzmann Solver for Multiphase Flows: Application to High Weber and Reynolds Numbers.

The lattice Boltzmann method, now widely used for a variety of applications, has also been extended to model multiphase flows through different formulations. While already applied to many different configurations in low Weber and Reynolds number regimes, applications to higher Weber/Reynolds numbers or larger density/viscosity ratios are still the topic of active research. In this study, through a combination of a decoupled phase-field formulation-the conservative Allen-Cahn equation-and a cumulant-based collision operator for a low-Mach pressure-based flow solver, we present an algorithm that can be used for higher Reynolds/Weber numbers. The algorithm was validated through a variety of test cases, starting with the Rayleigh-Taylor instability in both 2D and 3D, followed by the impact of a droplet on a liquid sheet. In all simulations, the solver correctly captured the flow dynamics andmatched reference results very well. As the final test case, the solver was used to model droplet splashing on a thin liquid sheet in 3D with a density ratio of 1000 and kinematic viscosity ratio of 15, matching the water/air system at We = 8000 and Re = 1000. Results showed that the solver correctly captured the fingering instabilities at the crown rim and their subsequent breakup, in agreement with experimental and numerical observations reported in the literature.

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.

Computational Fluid Dynamics-Based Design Optimization Method for Archimedes Screw Blood Pumps.

An optimization method suitable for improving the performance of Archimedes screw axial rotary blood pumps is described in the present article. In order to achieve a more robust design and to save computational resources, this method combines the advantages of the established pump design theory with modern computer-aided, computational fluid dynamics (CFD)-based design optimization (CFD-O) relying on evolutionary algorithms and computational fluid dynamics. The main purposes of this project are to: (i) integrate pump design theory within the already existing CFD-based optimization; (ii) demonstrate that the resulting procedure is suitable for optimizing an Archimedes screw blood pump in terms of efficiency. Results obtained in this study demonstrate that the developed tool is able to meet both objectives. Finally, the resulting level of hemolysis can be numerically assessed for the optimal design, as hemolysis is an issue of overwhelming importance for blood pumps.

Cerebral blood flow in a healthy Circle of Willis and two intracranial aneurysms: computational fluid dynamics versus four-dimensional phase-contrast magnetic resonance imaging.

Computational fluid dynamics (CFD) opens up multiple opportunities to investigate the hemodynamics of the human vascular system. However, due to numerous assumptions the acceptance of CFD among physicians is still limited in practice and validation through comparison is mandatory. Time-dependent quantitative phase-contrast magnetic resonance imaging PC-MRI measurements in a healthy volunteer and two intracranial aneurysms were carried out at 3 and 7 Tesla. Based on the acquired images, three-dimensional (3D) models of the aneurysms were reconstructed and used for the numerical simulations. Flow information from the MR measurements were applied as boundary conditions. The four-dimensional (4D) velocity fields obtained by CFD and MRI were qualitatively as well as quantitatively compared including cut planes and vector analyses. For all cases a high similarity of the velocity patterns was observed. Additionally, the quantitative analysis revealed a good agreement between CFD and MRI. Deviations were caused by minor differences between the reconstructed vessel models and the actual lumen. The comparisons between diastole and systole indicate that relative differences between MRI and CFD are intensified with increasing velocity. The findings of this study lead to the conclusion that CFD and MRI agree well in predicting intracranial velocities when realistic geometries and boundary conditions are provided. Due to the considerably higher temporal and spatial resolution of CFD compared to MRI, complex flow patterns can be further investigated in order to evaluate their role with respect to aneurysm formation or rupture. Nevertheless, special care is required regarding the vessel reconstruction since the geometry has a major impact on the subsequent numerical results.

Impact of stents and flow diverters on hemodynamics in idealized aneurysm models.

Cerebral aneurysms constitute a major medical challenge as treatment options are limited and often associated with high risks. Statistically, up to 3% of patients with a brain aneurysm may suffer from bleeding for each year of life. Eight percent of all strokes are caused by ruptured aneurysms. In order to prevent this rupture, endovascular stenting using so called flow diverters is increasingly being regarded as an alternative to the established coil occlusion method in minimally invasive treatment. Covering the neck of an aneurysm with a flow diverter has the potential to alter the hemodynamics in such a way as to induce thrombosis within the aneurysm sac, stopping its further growth, preventing its rupture and possibly leading to complete resorption. In the present study the influence of different flow diverters is quantified considering idealized patient configurations, with a spherical sidewall aneurysm placed on either a straight or a curved parent vessel. All important hemodynamic parameters (exchange flow rate, velocity, and wall shear stress) are determined in a quantitative and accurate manner using computational fluid dynamics when varying the key geometrical properties of the aneurysm. All simulations are carried out using an incompressible, Newtonian fluid with steady conditions. As a whole, 72 different cases have been considered in this systematic study. In this manner, it becomes possible to compare the efficiency of different stents and flow diverters as a function of wire density and thickness. The results show that the intra-aneurysmal flow velocity, wall shear stress, mean velocity, and vortex topology can be considerably modified thanks to insertion of a suitable implant. Intra-aneurysmal residence time is found to increase rapidly with decreasing stent porosity. Of the three different implants considered in this study, the one with the highest wire density shows the highest increase of intra-aneurysmal residence time for both the straight and the curved parent vessels. The best hemodynamic modifications are always obtained for a small aneurysm diameter.

Central moments multiple relaxation time LBM for hemodynamic simulations in intracranial aneurysms: An in-vitro validation study using PIV and PC-MRI.

The lattice Boltzmann method (LBM) has recently emerged as an efficient alternative to classical Navier-Stokes solvers. This is particularly true for hemodynamics in complex geometries. However, in its most basic formulation, i.e. with the so-called single relaxation time (SRT) collision operator, it has been observed to have a limited stability domain in the Courant/Fourier space, strongly constraining the minimum time-step and grid size. The development of improved collision models such as the multiple relaxation time (MRT) operator in central moments space has tremendously widened the stability domain, while allowing to overcome a number of other well-documented artifacts, therefore opening the door for simulations over a wider range of grid and time-step sizes. The present work focuses on implementing and validating a specific collision operator, the central Hermite moments multiple relaxation time model with the full expansion of the equilibrium distribution function, to simulate blood flows in intracranial aneurysms. The study further proceeds with a validation of the numerical model through different test-cases and against experimental measurements obtained via stereoscopic particle image velocimetry (PIV) and phase-contrast magnetic resonance imaging (PC-MRI). For a patient-specific aneurysm both PIV and PC-MRI agree fairly well with the simulation. Finally, low-resolution simulations were shown to be able to capture blood flow information with sufficient accuracy, as demonstrated through both qualitative and quantitative analysis of the flow field while leading to strongly reduced computation times. For instance in the case of the patient-specific configuration, increasing the grid-size by a factor of two led to a reduction of computation time by a factor of 14 with very good similarity indices still ranging from 0.83 to 0.88.

Hemodynamic Data Assimilation in a Subject-specific Circle of Willis Geometry.

PURPOSE: The anatomy of the circle of Willis (CoW), the brain's main arterial blood supply system, strongly differs between individuals, resulting in highly variable flow fields and intracranial vascularization patterns. To predict subject-specific hemodynamics with high certainty, we propose a data assimilation (DA) approach that merges fully 4D phase-contrast magnetic resonance imaging (PC-MRI) data with a numerical model in the form of computational fluid dynamics (CFD) simulations. METHODS: To the best of our knowledge, this study is the first to provide a transient state estimate for the three-dimensional velocity field in a subject-specific CoW geometry using DA. High-resolution velocity state estimates are obtained using the local ensemble transform Kalman filter (LETKF). RESULTS: Quantitative evaluation shows a considerable reduction (up to 90%) in the uncertainty of the velocity field state estimate after the data assimilation step. Velocity values in vessel areas that are below the resolution of the PC-MRI data (e.g., in posterior communicating arteries) are provided. Furthermore, the uncertainty of the analysis-based wall shear stress distribution is reduced by a factor of 2 for the data assimilation approach when compared to the CFD model alone. CONCLUSION: This study demonstrates the potential of data assimilation to provide detailed information on vascular flow, and to reduce the uncertainty in such estimates by combining various sources of data in a statistically appropriate fashion.

Transient flow prediction in an idealized aneurysm geometry using data assimilation.

Hemodynamic simulations are restricted by modeling assumptions and uncertain initial and boundary conditions, whereas Phase-Contrast Magnetic Resonance Imaging (PC-MRI) data is affected by measurement noise and artifacts. To overcome the limitations of both techniques, the current study uses a Localization Ensemble Transform Kalman Filter (LETKF) to fully incorporate noisy, low-resolution Phase-Contrast MRI data into an ensemble of high-resolution numerical simulations. The analysis output provides an improved state estimate of the three-dimensional blood flow field in an intracranial aneurysm model. Benchmark measurements are carried out in a silicone phantom model of an idealized aneurysm under pulsatile inflow conditions. Validation is ensured with high-resolution Particle Imaging Velocimetry (PIV) obtained in the symmetry plane of the same geometry. Two data assimilation approaches are introduced, which differ in their way to propagate the ensemble members in time. In both cases the velocity noise is significantly reduced over the whole cardiac cycle. Quantitative and qualitative results indicate an improvement of the flow field prediction in comparison to the raw measurement data. Although biased measurement data reveal a systematic deviation from the truth, the LETKF is able to account for stochastically distributed errors. Through the implementation of the data assimilation step, physical constraints are introduced into the raw measurement data. The resulting, realistic high-resolution flow field can be readily used to assess further patient-specific parameters in addition to the velocity distribution, such as wall shear stress or pressure.

Direct Numerical Simulations of Hotspot-induced Ignition in Homogeneous Hydrogen-air Pre-mixtures and Ignition Spot Tracking.

A systematic study relying on Direct Numerical Simulations (DNS) of premixed hydrogen-air mixtures has been performed to investigate the hotspot ignition characteristics and ignition probability under turbulent conditions. An ignition diagram is first obtained under laminar conditions by a parametric study. The impact of turbulence intensity on ignition delays and ignition probability is then quantified in a statistically-significant manner by repeating a large number of independent DNS realizations. By tracking in a Lagrangian frame the ignition spot, the balance between heat diffusion and heat of chemical reaction is observed as function of time. The evolution of each chemical species and radicals at the ignition spot is checked and the mechanism leading to ignition or misfire are analyzed. It is observed that successful ignition is mostly connected to a sufficient build-up of a HO2 pool, ultimately initiating production of OH. Turbulence always delays ignition, and ignition probability goes to zero at sufficiently high turbulence intensity when keeping temperature and size of the initial hotspot constant.

Tomographic particle image velocimetry for the validation of hemodynamic simulations in an intracranial aneurysm.

Image-based blood flow simulations can provide detailed hemodynamic information in diseased vessels such as intracranial aneurysms. However, validation is essential to evaluate the accuracy of these computations and further improve their acceptance among physicians. In this regard, tomographic particle image velocimetry was used to measure the flow characteristics in a patient specific aneurysm phantom model. Additionally, computational fluid dynamics (CFD) simulations were carried out using a well accepted commercial software package and a clinical research prototype, respectively. The comparison between in-vitro measurement and in-silico computations reveals a good qualitative agreement. Further, computations based on classical CFD agreed well with results from a clinical research prototype. Hence, the results of this study demonstrate the usability of numerical methods to obtain realistic blood flow predictions in a clinical context.

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.

Realistic virtual intracranial stenting and computational fluid dynamics for treatment analysis.

In order to support the decisions of medical experts and to develop better stent designs, the availability of a simulation tool for virtual stenting would be extremely useful. An innovative virtual stenting technique is described in this work, which is directly applicable for complex patient-specific geometries. A basilar tip aneurysm provided for the Virtual Intracranial Stenting Challenge 2010 is considered to demonstrate the advantages of this approach. A free-form deformation is introduced for a wall-tight stent deployment. Numerical flow simulations on sufficiently fine computational meshes are performed for different configurations in order to characterize the inflow rate into the aneurysm and the corresponding residence time in the aneurysm sac. A Neuroform and a SILK stent have been deployed at various locations and the computed residence times have been evaluated and compared, demonstrating the advantage associated with a lower stent porosity. It has been found that the SILK stent leads to a large increase in the residence time and to a significant reduction in the maximum wall shear stress in the aneurysm sac. This is only observed when placing the stent in the appropriate position, showing that virtual stenting might be employed for operation support.

Recommendations for accurate numerical blood flow simulations of stented intracranial aneurysms.

The number of scientific publications dealing with stented intracranial aneurysms is rapidly increasing. Powerful computational facilities are now available; an accurate computational modeling of hemodynamics in patient-specific configurations is, however, still being sought. Furthermore, there is still no general agreement on the quantities that should be computed and on the most adequate analysis for intervention support. In this article, the accurate representation of patient geometry is first discussed, involving successive improvements. Concerning the second step, the mesh required for the numerical simulation is especially challenging when deploying a stent with very fine wire structures. Third, the description of the fluid properties is a major challenge. Finally, a founded quantitative analysis of the simulation results is obviously needed to support interventional decisions. In the present work, an attempt has been made to review the most important steps for a high-quality computational fluid dynamics computation of virtually stented intracranial aneurysms. In consequence, this leads to concrete recommendations, whereby the obtained results are not discussed for their medical relevance but for the evaluation of their quality. This investigation might hopefully be helpful for further studies considering stent deployment in patient-specific geometries, in particular regarding the generation of the most appropriate computational model.

Experimental validation of numerical simulations on a cerebral aneurysm phantom model.

The treatment of cerebral aneurysms, found in roughly 5% of the population and associated in case of rupture to a high mortality rate, is a major challenge for neurosurgery and neuroradiology due to the complexity of the intervention and to the resulting, high hazard ratio. Improvements are possible but require a better understanding of the associated, unsteady blood flow patterns in complex 3D geometries. It would be very useful to carry out such studies using suitable numerical models, if it is proven that they reproduce accurately enough the real conditions. This validation step is classically based on comparisons with measured data. Since in vivo measurements are extremely difficult and therefore of limited accuracy, complementary model-based investigations considering realistic configurations are essential. In the present study, simulations based on computational fluid dynamics (CFD) have been compared with in situ, laser-Doppler velocimetry (LDV) measurements in the phantom model of a cerebral aneurysm. The employed 1:1 model is made from transparent silicone. A liquid mixture composed of water, glycerin, xanthan gum and sodium chloride has been specifically adapted for the present investigation. It shows physical flow properties similar to real blood and leads to a refraction index perfectly matched to that of the silicone model, allowing accurate optical measurements of the flow velocity. For both experiments and simulations, complex pulsatile flow waveforms and flow rates were accounted for. This finally allows a direct, quantitative comparison between measurements and simulations. In this manner, the accuracy of the employed computational model can be checked.

Experimental characterization of flow conditions in 2- and 20-L bioreactors with wave-induced motion.

Quantifying the influence of flow conditions on cell viability is essential for a successful control of cell growth and cell damage in major biotechnological applications, such as in recombinant protein and antibody production or vaccine manufacturing. In the last decade, new bioreactor types have been developed. In particular, bioreactors with wave-induced motion show interesting properties (e.g., disposable bags suitable for cGMP manufacturing, no requirement for cleaning and sterilization of cultivation vessels, and fast setup of new production lines) and are considered in this study. As an additional advantage, it is expected that cultivations in such bioreactors result in lower shear stress compared with conventional stirred tanks. As a consequence, cell damage would be reduced as cell viability is highly sensitive to hydrodynamic conditions. To check these assumptions, an experimental setup was developed to measure the most important flow parameters (liquid surface level, liquid velocity, and liquid and wall shear stress) in two cellbag sizes (2 and 20 L) of Wave Bioreactors®. The measurements confirm in particular low shear stress values in both cellbags, indicating favorable hydrodynamic conditions for cell cultivation.

Characterization of flow conditions in 2 L and 20 L wave bioreactors using computational fluid dynamics.

Characterization of flow conditions is of great importance to control cell growth and cell damage in animal cell culture because cell viability is influenced by the flow properties in bioreactors. Alternative reactor types like Wave Bioreactors have been proposed in recent years, leading to markedly different results in cell growth and product formation. An advantage of Wave Bioreactors is the disposability of the Polyethylenterephthalet-bags after one single use (fast setup of new production facilities). Another expected advantage is a lower shear stress compared to classical stirred-tank reactors, due to the gentle liquid motion in the rocking cellbag. This property would considerably reduce possible cell damage. The purpose of the present study is to investigate in a quantitative manner the key flow properties in Wave Bioreactors, both numerically and experimentally. To describe accurately flow conditions and shear stress in Wave Bioreactors using numerical simulations, it is necessary to compute the unsteady flow applying Computational Fluid Dynamics (CFD). Corresponding computations for two reactor scales (2 L and 20 L cellbags) are presented using the CFD code ANSYS-FLUENT. To describe correctly the free liquid surface, the present simulations employ the Volume of Fluid (VOF) method. Additionally, experimental measurements have been carried out to determine liquid level, flow velocity and liquid shear stress, which are used as a validation of the present CFD simulations. It is shown that the obtained flows stay in the laminar regime. Furthermore, the obtained shear stress levels are well below known threshold values leading to damage of animal cells.