A Numerical Analysis of the Hemodynamic Functionality of Human Coronary Stenosis Under Different Physiologic Conditions and Boundary Condition Formulations

2019 ◽  
Author(s):  
Iyad Fayssal ◽  
Fadl Moukalled
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Functional Significance ◽  
Diffusion Flux ◽  
Computational Effort ◽  
Patient Specific ◽  
Computational Domain ◽  
Artery Disease ◽  
Outflow Boundary

Abstract Coronary artery disease (CAD) is among the foremost causes for human death worldwide. This study aims at investigating the performance of different boundary condition model types to characterize CAD functional significance. In addition, alternate models to estimate FFR using any different combination of boundary conditions at inlet and outlet were analyzed. In the first type of boundary condition, an outflow resistance model is used combined with a fixed pressure at inlet. In the second model of boundary conditions, constant pressure values are imposed at the domain inlet and outlet/s sections. In the third model, a zero diffusion flux is applied at outlet with a pre-specified flow rate at inlet. Numerical simulations performed on healthy and stenosed idealized and physiological arterial models revealed the superiority of the first type of boundary condition to directly capture the level of ischemia in diseased arteries. However, in this model, special numerical treatment at the outflow boundary is needed to dampen pseudo numerical reflections entering the computational domain. Alternative simple methods are developed to tackle the problem incurred in the second and third types of boundary condition types. The alternate models are effective for carrying extensive parametric studies with minimal computational effort. The new developed methods allow results generated via generic simulations under any specified boundary condition type to correctly estimate CAD functional significance. The obtained surrogate models account for the effects of the patient-specific physiologic parameters and can be easily incorporated without modifying existing CFD codes. Moreover, where it is unfeasible to experimentally incorporate the downstream effects of a given diseased arterial segment, an important aspect the alternative models provide is that they can be easily adopted by experimentalists through building in-vitro arterial models to assess the functional significance of the obstruction caused by the disease and its relation to any given patient specific physiologic parameter.

MRI-Based Inflow Boundary Conditions for Patient Specific Fluid Structure Interaction Modeling of Abdominal Aortic Aneurysms

2012 ◽  
Author(s):  
Santanu Chandra ◽  
Samarth Raut ◽  
Anirban Jana ◽  
Robert W. Biederman ◽  
Mark Doyle ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Wall Thickness ◽  
Wall Stress ◽  
Patient Specific ◽  
Structure Interaction ◽  
Outflow Boundary Conditions ◽  
Abdominal Aortic ◽  
Outflow Boundary ◽  
Fully Coupled

Rupture of abdominal aortic aneurysm (AAA) is the 10th leading cause of death for men over age of 50 in US. The decision for surgical intervention is currently based on aneurysm diameter or its expansion rate. However, the use of these criteria for all patients is debatable. For example, small aneurysms do rupture or become symptomatic before reaching the critical diameter. Computationally predicted mechanical wall stress is considered a viable alternative criterion for rupture risk assessment. Hence, it is important to evaluate the effect of different modeling approaches on the accuracy of the predicated AAA wall stress. For computational solid stress (CSS) analysis or finite element analysis (FEA), a uniform static or transient intraluminal pressure is generally applied on the wall-lumen surface whereas in fluid-structure interaction (FSI) modeling the wall-lumen surface experiences transient and non-uniform fluid stress. An earlier comparison on idealized AAA models [1] revealed that static and transient CSS underestimate the peak wall stress (PWS) by an average 20–30% for variable wall thickness and 10% for uniform wall thickness when compared to fully coupled FSI. However, FSI-predicted stresses and strains were observed to be sensitive to inflow and outflow boundary conditions, warranting further study on a more accurate approach for FSI modeling. Though significant work has been performed on modeling outflow boundary conditions [2], studies on the sensitivity of computed stress or strain to the type of FSI inflow boundary condition is scarce [2–4]. We hypothesize that a FSI framework with a patient specific velocity boundary condition derived from magnetic resonance imaging (MRI) data applied to patient specific AAA geometry would provide better accuracy of PWS calculations compared to a FEA model. In this work, we present a framework where the AAA geometry is reconstructed from computed tomography (CT) images, on which FSI simulations were performed with inlet velocity components extracted from patient MR images of the abdominal aorta. Fully coupled FSI simulations were performed and results were compared with CSS simulations with uniform transient pressure boundary conditions.

The Effects of Geometry and Static Boundary Conditions on Microvessel Outgrowth in a 3D Model of Angiogenesis

2010 ◽  
Author(s):  
Clayton J. Underwood ◽  
Laxminarayanan Krishnan ◽  
Lowell T. Edgar ◽  
Steve Maas ◽  
James B. Hoying ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Direct Relationship ◽  
3D Model ◽  
Mechanical Strain ◽  
Matrix Stiffness ◽  
Collagen Gels ◽  
3D Collagen ◽  
In Vitro Angiogenesis

We reported previously that, in addition to mechanical strain, a constrained boundary condition alone can alter the organization of microvessel outgrowth during in vitro angiogenesis [1]. After 6 days of culture in vitro, microvessels aligned parallel to the long axis of rectangular 3D collagen gels that had constrained edges on the ends. However, unconstrained cultures did not show any alignment of microvessels. The ability to direct microvessel outgrowth during angiogenesis has significant implications for engineering prevascularized grafts and tissues in vitro, therefore an understanding of this process is important. Since there is direct relationship between the ability of endothelial cells to contract 3D gels and matrix stiffness [2], we hypothesize that some constrained boundary conditions will increase the apparent matrix stiffness and in turn will limit gel contraction, prevent microvessel alignment, and reduce microvessel outgrowth. The objective of this study was to compare microvessel growth and alignment under several different static boundary conditions.

The Validity of Approximate Boundary Conditions for Natural Convection With Thermal Radiation in Open Cavities

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Om Singh ◽  
Shireesh B. Kedare ◽  
Suneet Singh
Keyword(s):  
Natural Convection ◽  
Boundary Conditions ◽  
Significant Loss ◽  
Computational Effort ◽  
Computational Domain ◽  
Maximum Difference ◽  
Open Cavities ◽  
Shallow Cavities ◽  
Approximate Boundary Conditions ◽  
The Difference

Abstract The use of approximate boundary conditions at the opening of the cavities leads to restriction of the computational domain and, hence, the reduction in computational effort. However, the accuracy of the restricted domain approach (RDA) had been evaluated only for the natural convection inside open cavities and that too only for one aspect ratio (AR). The validity of the approach had not been evaluated for inclined, as well as, shallow cavities. This study focuses on the analysis of the accuracy of RDA against extended domain approach (EDA) in open cavities of different ARs, at different inclinations and different Rayleigh numbers (Ra). The results show that the difference between the approaches is only significant in very shallow cavities (AR is defined as the height of the hot wall divided by the depth of the cavity) at low Ra. For Ra higher than  106 and an AR greater than 0.2, the maximum difference between the two approaches is around 5% and hence RDA can be recommended in these ranges, resulting in increased computational efficiency without significant loss in the accuracy. Moreover, the maximum difference in the results for the two methods is for intermediate inclinations. Even there, an increase in the difference is more pronounced at lower Ra. Furthermore, distribution of the exit velocity and temperature at the opening as well as the distribution of the Nusselt number at the hot wall is compared for RDA and EDA to explain the behavior of error at different ARs and inclinations.

Numerical Simulation of Nonlinear Water Wave Propagation Over Rippled Bed

2007 ◽  
Author(s):  
Gerasimos A. Kolokythas ◽  
Athanassios A. Dimas
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Water Waves ◽  
Stokes Equations ◽  
Surface Flow ◽  
Surface Boundary ◽  
Computational Domain ◽  
Time Step ◽  
Outflow Boundary ◽  
Rippled Bed

In the present study, numerical simulations of the free-surface flow, developing by the propagation of nonlinear water waves over a rippled bottom, are performed assuming that the corresponding flow is two-dimensional, incompressible and viscous. The simulations are based on the numerical solution of the Navier-Stokes equations subject to the fully-nonlinear free-surface boundary conditions and the suitable bottom, inflow and outflow boundary conditions. The equations are properly transformed so that the computational domain becomes time-independent. For the spatial discretization, a hybrid scheme with finite-differences and Chebyshev polynomials is applied, while a fractional time-step scheme is used for the temporal discretization. A wave absorption zone is placed at the outflow region in order to efficiently minimize reflection of waves by the outflow boundary. The numerical model is validated by comparison to the analytical solution for the laminar, oscillatory, current flow which develops a uniform boundary layer over a horizontal bottom. For the propagation of finite-amplitude waves over a rigid rippled bed, the case with wavelength to water depth ratio λ/d0 = 6 and wave height to wavelength ratio H0/λ = 0.05 is considered. The ripples have parabolic shape, while their dimensions — length and height — are chosen accordingly to fit laboratory and field data. Results indicate that the wall shear stress over the ripples and the form drag forces on the ripples increase with increasing ripple height, while the corresponding friction force is insensitive to this increase. Therefore, the percentage of friction in the total drag force decreases with increasing ripple height.

Numerical Simulation of Nonlinear Wave Diffraction by a Vertical Cylinder in a Narrow Flume, Wide Tank, and Infinitely Wide Tank

2003 ◽  
Author(s):  
Alaa M. Mansour ◽  
A. Neil Williams
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Nonlinear Wave ◽  
Wave Diffraction ◽  
Open Boundary ◽  
Computational Domain ◽  
Open Boundary Condition ◽  
Lateral Direction ◽  
Cylinder Diameter ◽  
Side Walls

In this paper, a three dimensional numerical wave tank model has been used to simulate fully nonlinear wave diffraction by a uniform vertical circular cylinder. The cylinder has been placed in a narrow flume of a width equal to four times the cylinder diameter. The runup and the hydrodynamic forces on the cylinder has been compared to the results when a similar cylinder is placed in a similar tank but with a width equal to sixteen times the cylinder diameter. The model has been further extended by applying an open boundary condition to the side-walls to simulate an infinitely wide tank and hence more realistically simulate open sea condition. The proposed open boundary condition in the lateral direction is based on coupling of two prescribed boundary conditions, namely, numerical beach and Orlanski boundary conditions. The use of this coupled boundary condition has been found to be very efficient in eliminating any significant wave reflection from the side-walls back into the computational domain.

scholarly journals In Vitro Validation of Finite-Element Model of AAA Hemodynamics Incorporating Realistic Outlet Boundary Conditions

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Ethan O. Kung ◽  
Andrea S. Les ◽  
Francisco Medina ◽  
Ryan B. Wicker ◽  
Michael V. McConnell ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Numerical Simulations ◽  
In Silico ◽  
Physiological State ◽  
Patient Specific ◽  
Experimental Measurements ◽  
Windkessel Model ◽  
Measured Velocity ◽  
Good Agreement

The purpose of this study is to validate numerical simulations of flow and pressure in an abdominal aortic aneurysm (AAA) using phase-contrast magnetic resonance imaging (PCMRI) and an in vitro phantom under physiological flow and pressure conditions. We constructed a two-outlet physical flow phantom based on patient imaging data of an AAA and developed a physical Windkessel model to use as outlet boundary conditions. We then acquired PCMRI data in the phantom while it operated under conditions mimicking a resting and a light exercise physiological state. Next, we performed in silico numerical simulations and compared experimentally measured velocities, flows, and pressures in the in vitro phantom to those computed in the in silico simulations. There was a high degree of agreement in all of the pressure and flow waveform shapes and magnitudes between the experimental measurements and simulated results. The average pressures and flow split difference between experiment and simulation were all within 2%. Velocity patterns showed good agreement between experimental measurements and simulated results, especially in the case of whole-cycle averaged comparisons. We demonstrated methods to perform in vitro phantom experiments with physiological flows and pressures, showing good agreement between numerically simulated and experimentally measured velocity fields and pressure waveforms in a complex patient-specific AAA geometry.

Cyclic Breathing Simulations in Large-Scale Models of the Lung Airway From the Oronasal Opening to the Terminal Bronchioles

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
D. Keith Walters ◽  
Greg W. Burgreen ◽  
Robert L. Hester ◽  
David S. Thompson ◽  
David M. Lavallee ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Mass Flow ◽  
Flow Rate ◽  
Large Scale ◽  
Whole Body ◽  
Patient Specific ◽  
Computational Domain ◽  
Scale Models ◽  
Fully Coupled ◽  
Conducting Zone

Computational fluid dynamics (CFD) simulations were performed using large-scale models of the human lung airway and unsteady periodic breathing conditions. The computational domain included fully coupled representations of the orotracheal region and large conducting zone up to generation four (G4) obtained from patient-specific CT data, and the small conducting zone (to the 16th generation) obtained from a stochastically generated airway tree with statistically realistic morphological characteristics. A reduced-geometry airway model was used, in which several airway branches in each generation were truncated, and only select flow paths were retained to the 16th generation. The inlet and outlet flow boundaries corresponded to the oral opening, the physical inlet/outlet boundaries at the terminal bronchioles, and the unresolved airway boundaries created from the truncation procedure. The total flow rate was specified according to the expected ventilation pattern for a healthy adult male, which was supplied by the whole-body modeling software HumMod. The unsteady mass flow distribution at the distal boundaries was prescribed based on a preliminary steady-state simulation with an applied flow rate equal to the average flow rate during the inhalation phase of the breathing cycle. In contrast to existing studies, this approach allows fully coupled simulation of the entire conducting zone, with no need to specify distal mass flow or pressure boundary conditions a priori, and without the use of impedance or one-dimensional (1D) flow models downstream of the truncated boundaries. The results show that: (1) physiologically realistic flow is obtained in the model, in terms of cyclic mass conservation and approximately uniform pressure distribution in the distal airways; (2) the predicted alveolar pressure is in good agreement with correlated experimental data; and (3) the use of reduced-order geometry modeling allows accurate and efficient simulation of large-scale breathing lung flow, provided care is taken to use a physiologically realistic geometry and to properly address the unsteady boundary conditions.

Tuning a Multiscale Model of Abdominal Aortic Hemodynamics to Incorporate Patient-Specific Features of Flow and Pressure Waveforms

2009 ◽  
Author(s):  
Ryan L. Spilker ◽  
Charles A. Taylor
Keyword(s):  
Boundary Conditions ◽  
Computational Models ◽  
Multiscale Model ◽  
Patient Specific ◽  
Vascular Walls ◽  
Outflow Boundary Conditions ◽  
Abdominal Aortic ◽  
Cardiovascular Models ◽  
Outflow Boundary ◽  
Aortic Hemodynamics

Computational models enable the calculation of quantities that are impractical or impossible to measure and the prediction of physiological changes due to interventions. In order to be useful, cardiovascular models must be both rooted in physical principles and designed such that measured or otherwise desired features of the cardiovascular system are reproduced. The former requirement has motivated the development of image-based anatomic models, patient-specific inflow boundary conditions, deformable vascular walls, outflow boundary conditions that represent the influence of the downstream circulation, and multiscale models. The development of approaches to address the latter requirement, reproducing desired features of the circulation, is a critical area of modeling research that has received comparatively little attention.

On the Formulation of Nonreflecting Boundary Conditions for Turbomachinery Configurations: Part II — Application and Analysis

2020 ◽  
Author(s):  
Nina Wolfrum ◽  
Patrick Bechlars ◽  
Maximilian Beck ◽  
Christian Frey ◽  
Daniel Schlüß
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Meridional Flow ◽  
Computational Domain ◽  
Two Dimensional ◽  
Elementary Model ◽  
Nonreflecting Boundary Conditions ◽  
First Case ◽  
Geometrical Features ◽  
Rotational Surfaces

Abstract The flow in turbomachinery components is complex due to the relative motion of rotating and non-rotating elements. A proper design and prediction of physical phenomena requires reliable CFD tools. One important aspect is the incorporation of sophisticated algorithms at the boundaries of the computational domain. For inviscid, one-dimensional and two-dimensional Euler-flows there exist analytical solutions for the formulation of a boundary condition. Realistic applications, however, are viscous and consist of a complex three-dimensional character. Nevertheless, the analytical 2D nonreflecting boundary conditions are commonly used in CFD codes for their high computational efficiency and numerical robustness. The application becomes more challenging when the boundaries are close to geometrical features such as blades and vanes. In practical applications, the position of the boundaries is dictated by geometrical constraints and hence the proximity to the blading cannot always be avoided. The interaction of rotating and non-rotating geometrical features in a turbomachine produces complex flow patterns that propagate in the form of acoustic, vorticity and entropy waves. A boundary condition must be implemented in such a way that waves can propagate undisturbed out of the computational domain. Any reflection may unphysically affect the solution within the computational domain which is especially harmful to sensitive values such as unsteady aeroelastic quantities. But also steady-state computations may suffer from errors produced by reflective boundary conditions. The following paper is the second of two papers on the formulation of unsteady boundary conditions based on a two-dimensional analytical approach. The first part of this paper [6] explains how to extend 2D nonreflecting boundary conditions to real 3D annular domains by applying them in certain conical rotational surfaces. Two different formulations are discussed referring to the orientation of said rotational surfaces. In the first case the surfaces are oriented perpendicular to the boundary panel. In the second case the surfaces are aligned with the circumferentially averaged meridional flow velocity. In the present paper a thorough analysis of the two different approaches will be given. Both formulations of the boundary algorithm are validated on the basis of several elementary model flows. The behavior is analyzed for various unsteady wave patterns of different propagation directions with respect to the boundary. It will be shown that the alignment of the rotational surfaces with the meridional flow has a beneficial effect on the reflective behavior for the majority of the investigated flow conditions. The boundary conditions are then tested on realistic turbomachinery components in order to analyze their applicability on complex flows.

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