Computational Flow Model Research Articles

Binary collision dynamics of immiscible Newtonian and non-Newtonian fluid droplets

This experimental and theoretical study is devoted to the investigation of head-on collisions of two immiscible Newtonian and non-Newtonian droplets. The density of the two droplets is similar, and the viscosity of 0.3% carboxymethyl cellulose droplet is slightly larger than 10 cSt silicone oil. The sizes and relative velocity of the colliding droplets close to the point of impact are measured by means of image processing. The deformed states after the impact and their evolution with time are studied by experimental visualization and the energy evolution with time are discussed by numerical results. The accuracy of the two-dimensional axisymmetric three-phase flow computational model is validated. We study the effects of collisions of non-Newtonian droplets with Newtonian droplets and the subsequent retraction kinetics. Droplet “cannibalization” is commonly observed: after collision and spreading, the droplet retracts rapidly, resulting in a Newtonian droplet wrapping around a non-Newtonian droplet. We show the whole process of droplet collision captured by a high-speed camera and obtain the cloud and velocity vector maps of the droplets by numerical simulation. The droplet wrapping phenomenon is produced by different three-phase interfacial tensions and viscosities. We delineate the different phases of the collision process and discuss the dominant forces in each phase. We calculate the energy evolution of the spreading phase and use it to derive a predictive model for the dimensionless maximum spreading diameter and spreading time.

Biomechanical Analysis of Age-Dependent Changes in Fontan Power Loss.

The hemodynamics in Fontan patients with single ventricles rely on favorable flow and energetics, especially in the absence of a subpulmonary ventricle. Age-related changes in energetics for extracardiac and lateral tunnel Fontan procedures are not well understood. Vorticity (VOR) and viscous dissipation rate (VDR) are two descriptors that can provide insights into flow dynamics and dissipative areas in Fontan pathways, potentially contributing to power loss. This study examined power loss and its correlation with spatio-temporal flow descriptors (vorticity and VDR). Data from 414 Fontan patients were used to establish a relationship between the superior vena cava (SVC) to inferior vena cava (IVC) flow ratio and age. Computational flow modeling was conducted for both extracardiac conduits (ECC, n = 16) and lateral tunnels (LT, n = 25) at different caval inflow ratios of 2, 1, and 0.5 that corresponded with ages 3, 8, and 15+. In both cohorts, vorticity and VDR correlated well with PL, but ECC cohort exhibited a slightly stronger correlation for PL-VOR (>0.83) and PL-VDR (>0.89) than that for LT cohort (>0.76 and > 0.77, respectively) at all ages. Our data also suggested that absolute and indexed PL increase (p < 0.02) non-linearly as caval inflow changes with age and are highly patient-specific. Comparison of indexed power loss between our ECC and LT cohort showed that while ECC had a slightly higher median PL for all 3 caval inflow ratio examined (3.3, 8.3, 15.3) as opposed to (2.7, 7.6, 14.8), these differences were statistically non-significant. Lastly, there was a consistent rise in pressure gradient across the TCPC with age-related increase in IVC flows for both ECC and LT Fontan patient cohort. Our study provided hemodynamic insights into Fontan energetics and how they are impacted by age-dependent change in caval inflow. This workflow may help assess the long-term sustainability of the Fontan circulation and inform the design of more efficient Fontan conduits.

Computational modeling of left ventricular flow using PC-CMR-derived four-dimensional wall motion.

Intracardiac hemodynamics plays a crucial role in the onset and development of cardiac and valvular diseases. Simulations of blood flow in the left ventricle (LV) have provided valuable insight into assessing LV hemodynamics. While fully coupled fluid-solid modelings of the LV remain challenging due to the complex passive-active behavior of the LV wall myocardium, the integration of imaging-driven quantification of structural motion with computational fluid dynamics (CFD) modeling in the LV holds the promise of feasible and clinically translatable characterization of patient-specific LV hemodynamics. In this study, we propose to integrate two magnetic resonance imaging (MRI) modalities with the moving-boundary CFD method to characterize intracardiac LV hemodynamics. Our method uses the standard cine cardiac magnetic resonance (CMR) images to estimate four-dimensional myocardial motion, eliminating the need for involved myocardial material modeling to capture LV wall behavior. In conjunction with CMR, phase contrast-MRI (PC-MRI) was used to measure temporal blood inflow rates at the mitral orifice, serving as an additional boundary condition. Flow patterns, including velocity streamlines, vortex rings, and kinetic energy, were characterized and compared to the available data. Moreover, relationships between LV wall kinematic markers and flow characteristics were determined without myocardial material modeling and using a non-rigid image registration (NRIR) method. The fidelity of the simulation was quantitatively evaluated by validating the flow rate at the aortic outflow tract against respective PC-MRI measures. The proposed methodology offers a novel and feasible toolset that works with standard PC-CMR protocols to improve the clinical assessment of LV characteristics in prognostic studies and surgical planning.

Realization of Bio-Coal Injection into the Blast Furnace

The steel industry accounts, according to the International Energy Agency, for ~6.7% of global CO2 emissions, and the major portion of its contribution is from steelmaking via the blast furnace (BF) route. In the short term, a significant reduction in fossil CO2 emissions can be achieved through the introduction of bio-coal into the BF as part of cold bonded briquettes, by injection, or as part of coke. The use of bio-coal-containing residue briquettes was previously demonstrated in industrial trials in Sweden, whereas bio-coal injection was only tested on a pilot scale or in one-tuyere tests. Therefore, industrial trials replacing part of the pulverized coal (PC) were conducted. It was concluded that the grinding, conveying, and injection of up to 10% of charcoal (CC) with PC can be safely achieved without negative impacts on PC injection plant or BF operational conditions and without losses of CC with the dust. From a process point of view, higher addition is possible, but it must be verified that grinding and conveying is feasible. Through an experimentally validated computational fluid flow model, it was shown that a high moisture content and the presence of oversized particles delay devolatilization and ignition, lowering the combustion efficiency. By using CC with similar heating value to PC, compositional variations in the injected blend are not critical.

The effect of flow-derived mechanical cues on the growth and morphology of platelet aggregates under low, medium, and high shear rates

Platelet aggregation is a dynamic process that can obstruct blood flow, leading to cardiovascular diseases. While many studies have demonstrated clear connections between shear rate and platelet aggregation, the impact of flow-derived mechanical signals on this process is not fully understood. The objective of this work is to investigate the role of flow conditions on platelet aggregation dynamics, including effects on growth, shape, density composition, and their potential correlation with binding processes that are characterised by longer (e.g., via αIIbβ3 integrin) and shorter (e.g., via VWF) initial binding times. In vitro blood perfusion experiments were conducted at wall shear rates of 800, 1600 and 4000 s-1. Detailed analysis of two modalities of experimental images was performed to offer insights into the morphology of platelet aggregates. A consistent structural pattern was observed across all samples: a high-density core enveloped by a low-density outer shell. An image-based 3D computational blood flow model was subsequently employed to study the local flow conditions, including binding availability time and flow-derived mechanical signals via shear rate and rate of elongation. The results show substantial dependence of the aggregation dynamics on these flow parameters. We found that the different binding mechanisms that prefer different flow regimes do not have a monotonic cross-over in efficiency as the flow increases. There is a significant dip in the cumulative aggregation potential in-between the preferred regimes. The results suggest that treatments targeting the biomechanical pathways could benefit from creating conditions that exploit these low-efficiency zones of aggregation.

Research on ignition matching for magnesium-based water ramjet engines

This paper addresses the ignition compatibility issues of the water ramjet engine (WRE). It studies the impact of several engine parameters on the ignition process and performance, including the primary water injection angle, primary water-fuel ratio, igniter mass, and igniter position. Based on the specified parameters, a multiphase flow computational model for the ignition process of the WRE developed. The obtained results show that the ignition performance of the engine is significantly affected by the primary water-fuel ratio, igniter mass, and igniter location. When the primary water-fuel ratio increases, the equilibrium temperature in the combustion chamber tends to initially increase and then decrease, reaching a maximum value for a ratio of 0.55. Criteria are then proposed to determine whether the WRE can transition into the self-sustained combustion phase. These ignition criteria are established by considering the relationship between the mass of the igniter charge, its location, and the surface area of the burning surface of the propellant. The results obtained by the proposed model demonstrate that the engine will not extinguish when this value is greater than 46.65.

Particle-based modeling and GPU-accelerated simulation of cellular blood flow

Computational modeling and simulation of cellular blood flow is highly desired for understanding blood microcirculation and blood-related diseases such as thrombosis and tumor, but it remains a challenging task primarily because blood in microvessels should be described as a dense suspension of different types of deformable cells. The focus of the present work is on the development of a particle-based and GPU-accelerated numerical method that is able to quickly simulate the various behaviors of deformable cells in three-dimensional arbitrarily complex geometries. We employ a two-fluid model to describe blood flow, incorporating the deformation and aggregation of cells. A smoothed dissipative particle dynamics is used to solve the two-fluid model, and a discrete microstructure model is applied for the cell deformation, as well as a Morse potential model for the cell aggregation. The heterogeneous CPU-GPU environment is established, where each GPU thread is dedicated to a particle, and the CPU is mainly responsible for loading and exporting data. Five test cases are conducted against analytical theory, experimental data, and previous numerical results, for pure fluid, cell deformation, cell aggregation, cell suspension and the cellular flow in a complex network, respectively. It is shown that the methodology can accurately predict various behaviors of cells, and the GPU is well suited for particle-based modeling. Especially for cellular blood flow, where calculating cellular forces is a compute-intensive and time-consuming task, the GPU offers exceptional parallel capabilities, significantly enhancing the simulation efficiency. The speedup is about 3.5 times faster than the CPU parallelization with 96 cores for the pure fluid, and this acceleration nearly reaches 20 times when cells are included in the simulations. Particularly, the calculations for deformation and aggregation forces demonstrate a substantial speedup, achieving the improvements of up to 120 and 640 times, respectively, compared to their serial counterparts. The present methodology can effectively integrate various behaviors of cells, and has the potential in simulating very large microvascular networks at organ levels.

Flow Analysis of Central Venous Outflow Tract: A New Approach to Understanding Pulse-Synchronous Tinnitus.

Pulse-synchronous tinnitus (PST) has been linked to multiple anatomical variants of the central venous outflow tract (CVOT) including sigmoid sinus (SS) dehiscence and diverticulum. This study investigates flow turbulence, pressure, and wall shear stress along the CVOT and proposes a mechanism that results in SS dehiscence and PST. Case series. Tertiary Academic Center. Venous models were reconstructed from computed tomography scans of 3 patients with unilateral PST. Two models for each patient are obtained: a symptomatic and contralateral asymptomatic side. A turbulent model-enabled commercial flow solver was used to simulate the pulsatile blood flow over the cardiac cycle through the models. Fluid flow through the transverse and SS junction was analyzed to observe the velocity, pressure, turbulent kinetic energy (TKE), and shear stress over a simulated cardiac cycle. Fluid flow on the symptomatic side showed increased vorticity in the presence of an SS diverticulum. Higher TKE with periodicity following the cardiac cycle was observed on the symptomatic side, and a sharp increase was observed if SS diverticulum was present. Shear stress was highest near the narrowest segments of the vessel. Pressure was observed to be lower on the symptomatic side at the transverse-SS junction for all 3 patients. Computational fluid dynamics modeling of blood flow through the CVOT in PST suggests that low pressure may be the cause of dehiscence, and tinnitus may result from periodic increases in TKE.

Mapping the blood vasculature in an intact human kidney using hierarchical phase-contrast tomography.

The architecture of the kidney vasculature is essential for its function. Although structural profiling of the intact rodent kidney vasculature has been performed, it is challenging to map vascular architecture of larger human organs. We hypothesised that hierarchical phase-contrast tomography (HiP-CT) would enable quantitative analysis of the entire human kidney vasculature. Combining label-free HiP-CT imaging of an intact kidney from a 63-year-old male with topology network analysis, we quantitated vasculature architecture in the human kidney down to the scale of arterioles. Although human and rat kidney vascular topologies are comparable, vascular radius decreases at a significantly faster rate in humans as vessels branch from artery towards the cortex. At branching points of large vessels, radii are theoretically optimised to minimise flow resistance, an observation not found for smaller arterioles. Structural differences in the vasculature were found in different spatial zones of the kidney reflecting their unique functional roles. Overall, this represents the first time the entire arterial vasculature of a human kidney has been mapped providing essential inputs for computational models of kidney vascular flow and synthetic vascular architectures, with implications for understanding how the structure of individual blood vessels collectively scales to facilitate organ function.

Computational modelling of micropolar blood-based magnetised hybrid nanofluid flow over a porous curved surface in the presence of artificial bacteria.

This work provides a brief comparative analysis of the influence of heat creation on micropolar blood-based unsteady magnetised hybrid nanofluid flow over a curved surface. The Powell-Eyring fluid model was applied for modelling purposes, and this work accounted for the impacts of both viscous dissipation and Joule heating. By investigating the behaviours of Ag and TiO2 nanoparticles dispersed in blood, we aimed to understand the intricate phenomenon of hybridisation. A mathematical framework was created in accordance with the fundamental flow assumptions to build the model. Then, the model was made dimensionless using similarity transformations. The problem of a dimensionless system was then effectively addressed using the homotopy analysis technique. A cylindrical surface was used to calculate the flow quantities, and the outcomes were visualised using graphs and tables. Additionally, a study was conducted to evaluate skin friction and heat transfer in relation to blood flow dynamics; heat transmission was enhanced to raise the Biot number values. According to the findings of this study, increasing the values of the unstable parameters results in increase of the blood velocity profile.

From cine-MRI to computational models of blood flow within the heart

From cine-MRI to computational models of blood flow within the heart

Influence of Slip Boundary Conditions on Jeffrey Fluid Flow in Tapered Conduit with Hall Current and Soret–Dufour Effects

AbstractThe present work examines the computational analysis and mathematical modeling of peristaltic blood flow in a tapered channel, taking into account slip boundary conditions, Hall current, and Soret–Dufour forces. By neglecting the wave number and employing a long‐wavelength approximation to analyze the fluid model, the investigation was conducted within the framework of a low Reynolds number regime. The study reveals that the values of the Soret number, Dufour number, Prandtl number, and Schmidt number exhibit an upward trend as the fluid temperature rises. In contrast, a rise in the thermal slip parameter causes the fluid temperature to fall. It has been shown that when the mass slip parameter increases, the fluid's concentration rises. The skin friction coefficient rises within the range of x = 0.55 to x = 1 as the velocity, concentration slip parameter, Soret number, and Dufour number increase. Conversely, the skin friction coefficient decreases as the thermal slip parameter increases. The selected characteristics exhibit realism since they find use in many fields such as medical biology, biomechanics, heat exchangers, gas turbines, and several other domains.

Computational fluid dynamics modeling of coronary artery blood flow using OpenFOAM: Validation with the food and drug administration benchmark nozzle model.

Cardiovascular disease (CVD), a global health concern, particularly coronary artery disease (CAD), poses a significant threat to well-being. Seeking safer and cost-effective diagnostic alternatives to invasive coronary angiography, noninvasive coronary computed tomography angiography (CCTA) gains prominence. This study employed OpenFOAM, an open-source Computational Fluid Dynamics (CFD) software, to analyze hemodynamic parameters in coronary arteries with serial stenoses. Patient-specific three-dimensional (3D) models from CCTA images offer insights into hemodynamic changes. OpenFOAM breaks away from traditional commercial software, validated against the FDA benchmark nozzle model for reliability. Applying this refined methodology to seventeen coronary arteries across nine patients, the study evaluates parameters like fractional flow reserve computed tomography simulation (FFRCTS), fluid velocity, and wall shear stress (WSS) over time. Findings include FFRCTS values exceeding 0.8 for grade 0 stenosis and falling below 0.5 for grade 5 stenosis. Central velocity remains nearly constant for grade 1 stenosis but increases 3.4-fold for grade 5 stenosis. This research innovates by utilizing OpenFOAM, departing from previous reliance on commercial software. Combining qualitative stenosis grading with quantitative FFRCTS and velocity measurements offers a more comprehensive assessment of coronary artery conditions. The study introduces 3D renderings of wall shear stress distribution across stenosis grades, providing an intuitive visualization of hemodynamic changes for valuable insights into coronary stenosis diagnosis.

Numerical simulation of unsteady blood based Carreau nanofluid flow in an inclined porous saturated artery having overlapping stenosis with electro-osmosis

The present paper focuses on the computational modeling of the unsteady non-Newtonian electro-magnetohydrodynamic flow of nano-blood through the inclined and tapered saturated porous artery with overlapping stenosis. The Carreau fluid model is adopted to simulate the non-Newtonian behavior of the blood. This study also uses a modified form of Darcy’s law applied to the Carreau model. Blood is doped with a suspension of homogeneous biocompatible nanoparticles of different shapes. In addition, a combination of a magnetic field and an electric field has also been taken into account. The significance of this work rests in the ability to enhance comprehension of the complicated behavior of hemodynamic flow when exposed to external fields and porous media with the addition of nanoparticles, which has substantial implications for the regulation and treatment of cardiovascular diseases. The finite-difference method is used to obtain the solution of the resulting equations. The simulations are applicable to targeted magnetic therapy for stenotic artery disease and the delivery of nanomedicines.

A one-dimensional computational model for blood flow in an elastic blood vessel with a rigid catheter.

Strokes are one of the leading causes of death in the United States. Stroke treatment involves removal or dissolution of the obstruction (usually a clot) in the blocked artery by catheter insertion. A computer simulation to systematically plan such patient-specific treatments needs a network of about 105 blood vessels including collaterals. The existing computational fluid dynamic (CFD) solvers are not employed for stroke treatment planning as they are incapable of providing solutions for such big arterial trees in a reasonable amount of time. This work presents a novel one-dimensional mathematical formulation for blood flow modeling in an elastic blood vessel with a centrally placed rigid catheter. The governing equations are first-order hyperbolic partial differential equations, and the hypergeometric function needs to be computed to obtain the characteristic system of these hyperbolic equations. We employed the Discontinuous Galerkin method to solve the hyperbolic system and validated the implementation by comparing it against a well-established 3D CFD solver using idealized vessels and a realistic truncated arterial network. The results showed clinically insignificant differences in steady flow cases, with overall variations between 1D and 3D models remaining below 10%. Additionally, the solver accurately captured wave reflection phenomena at domain discontinuities in unsteady cases. A primary advantage of this model over 3D solvers is its ease in obtaining a discretized geometry of complex vasculatures with multiple arterial branches. Thus, the 1D computational model offers good accuracy and applicability in simulating complex vasculatures, demonstrating promising potential for investigating patient-specific endovascular interventions in strokes.

An individualised 3D computational flow and particle model to predict the deposition of inhaled medicines — A case study using a nebuliser

Background and objective: Drug inhalation is generally accepted as the preferred administration method for treating respiratory diseases. To achieve effective inhaled drug delivery for an individual, it is necessary to use an interdisciplinary approach that can cope with inter-individual differences. The paper aims to present an individualised pulmonary drug deposition model based on Computational Fluid and Particle Dynamics simulations within a time frame acceptable for clinical use. Methods:We propose a model that can analyse the inhaled drug delivery efficiency based on the patient’s airway geometry as well as breathing pattern, which has the potential to also serve as a tool for a sub-regional diagnosis of respiratory diseases. The particle properties and size distribution are taken for the case of drug inhalation by using nebulisers, as they are independent of the patient’s breathing pattern. Finally, the inhaled drug doses that reach the deep airways of different lobe regions of the patient are studied. Results:The numerical accuracy of the proposed model is verified by comparison with experimental results. The difference in total drug deposition fractions between the simulation and experimental results is smaller than 4.44% and 1.43% for flow rates of 60 l/min and 15 l/min, respectively. A case study involving a COVID-19 patient is conducted to illustrate the potential clinical use of the model. The study analyses the drug deposition fractions in relation to the breathing pattern, aerosol size distribution, and different lobe regions. Conclusions:The entire process of the proposed model can be completed within 48 h, allowing an evaluation of the deposition of the inhaled drug in an individual patient’s lung within a time frame acceptable for clinical use. Achieving a 48-hour time window for a single evaluation of patient-specific drug delivery enables the physician to monitor the patient’s changing conditions and potentially adjust the drug administration accordingly. Furthermore, we show that the proposed methodology also offers a possibility to be extended to a detection approach for some respiratory diseases.

Dynamic wetting performance and resin-flow behavior of two-level selective laser-etched metal surface in resin transfer moulding process of fiber-metal laminates

ABSTRACT In selective laser etching for the interfacial strengthening of Fiber Metal Laminates (FMLs), the wettability of customized structured features significantly affects their overall mechanical properties. For two-level features, their complicated geometry makes the evaluation of wettability difficult, which introduces challenges to feature design. In this study, a sandwich FMLs comprising an AA2024-O metal skin and a plain-woven carbon-fiber fabric core is investigated. Three types of two-level feature interfaces are designed and introduced into the FMLs structure. To understand the effect of two-level features on the resin flow and dynamic wetting progress in resin transfer molding, two-phase flow Computational Fluid Dynamics numerical models coupled with porous media and level-set numerical methods are built. The feasibility of the numerical simulation in the qualitative analysis was verified by comparing the results with those of the testing porosity values from X-ray scanning. In addition, the mechanisms of pore formation and transportation are revealed. These results indicate that the deeper groove structure in the etched features plays an important role in discharging residual air and determining the transformation of pores to reduce porosity. The permeability orientations of the porous media and surface structure both have significant impacts on the flow behavior and formation of pores.

Computer modeling of supersonic gas flow in variable cross-section channels using OpenFOAM

Computer modeling of supersonic gas flow in variable cross-section channels using OpenFOAM

Transcranial electric stimulation modulates firing rate at clinically relevant intensities

BackgroundNotwithstanding advances with low-intensity transcranial electrical stimulation (tES), there remain questions about the efficacy of clinically realistic electric fields on neuronal function. ObjectiveTo measure electric fields magnitude and their effects on neuronal firing rate of hippocampal neurons in freely moving rats, and to establish calibrated computational models of current flow. MethodsCurrent flow models were calibrated on electric field measures in the motor cortex (n = 2 anesthetized rats) and hippocampus. A Neuropixels 2.0 probe with 384 channels was used in an in-vivo rat model of tES (n = 4 freely moving and 2 urethane anesthetized rats) to detect effects of weak fields on neuronal firing rate. High-density field mapping and computational models verified field intensity (1 V/m in hippocampus per 50 μA of applied skull currents). ResultsElectric fields of as low as 0.35 V/m (0.25–0.47) acutely modulated average firing rate in the hippocampus. At these intensities, firing rate effects increased monotonically with electric field intensity at a rate of 11.5 % per V/m (7.2–18.3). For the majority of excitatory neurons, firing increased for soma-depolarizing stimulation and diminished for soma-hyperpolarizing stimulation. While more diverse, the response of inhibitory neurons followed a similar pattern on average, likely as a result of excitatory drive. ConclusionIn awake animals, electric fields modulate spiking rate above levels previously observed in vitro. Firing rate effects are likely mediated by somatic polarization of pyramidal neurons. We recommend that all future rodent experiments directly measure electric fields to insure rigor and reproducibility.

Blood flow assessment technology in aortic surgery: a narrative review.

Blood flow assessment is an emerging technique that allows for assessment of hemodynamics in the heart and blood vessels. Recent advances in cardiovascular imaging technologies have made it possible for this technique to be more accessible to clinicians and researchers. Blood flow assessment typically refers to two techniques: measurement-based flow visualization using echocardiography or four-dimensional flow magnetic resonance imaging (4D flow MRI), and computer-based flow simulation based on computational fluid dynamics modeling. Using these methods, blood flow patterns can be visualized and quantitative measurements of mechanical stress on the walls of the ventricles and blood vessels, most notably the aorta, can be made. Thus, blood flow assessment has been enhancing the understanding of cardiac and aortic diseases; however, its introduction to clinical practice has been negligible yet. In this article, we aim to discuss the clinical applications and future directions of blood flow assessment in aortic surgery. We then provide our unique perspective on the technique's translational impact on the surgical management of aortic disease. Articles from the PubMed database and Google Scholar regarding blood flow assessment in aortic surgery were reviewed. For the initial search, articles published between 2013 and 2023 were prioritized, including original articles, clinical trials, case reports, and reviews. Following the initial search, additional articles were considered based on manual searches of the references from the retrieved literature. In aortic root pathology and ascending aortic aneurysms, blood flow assessment can elucidate postoperative hemodynamic changes after surgical reconfiguration of the aortic valve complex or ascending aorta. In cases of aortic dissection, analysis of blood flow can predict future aortic dilatation. For complicated congenital aortic anomalies, surgeons may use preoperative imaging to perform "virtual surgery", in which blood flow assessment can predict postoperative hemodynamics for different surgical reconstructions and assist in procedural planning even before entering the operating room. Blood flow assessment and computational modeling can evaluate hemodynamics and flow patterns by visualizing blood flow and calculating biomechanical forces in patients with aortic disease. We anticipate that blood flow assessment will become an essential tool in the treatment planning and understanding of the progression of aortic disease.