220 research outputs found
Boundary Layers
No full text1 1 Boundary-Layer Behavior 1 2 Extension Theorems 5 3 Regularization 8 4 Matching Asymptotic Approximations 16 Index 20 iv ASYMPTOTIC ANALYSIS Working Note #3 BOUNDARY LAYERS by Marc Garbey and Hans G. Kaper Abstract In this chapter we discuss the asymptotic approximation of functions that display boundary-layer behavior. Our purpose here is to introduce the basic concepts underlying the phenomenon, to illustrate its importance, and to describe some of the fundamental tools available for its analysis. To achieve our purpose in the clearest way possible, we shall work with functions that are assumed to be given explicitly---that is, functions f : (0; ffl 0 ) ! X whose expressions are known, at least in principle. Only in the following chapter shall we begin the study of functions that are given implicitly as solutions of boundary value problems---the real stuff of which singular perturbation theory is made. Boundary-layer behavior is associated with asymptotic expansions that are..
A robust construction algorithm of the centerline skeleton for complex aortic vascular structure using computational fluid dynamics
No full textCenterlines of blood vessels are useful tools to make important anatomical measurements (length, diameter, area),
which cannot be accurately obtained using 2D images. In this paper a brand new method for centerline extraction
of vascular trees is presented. By using computational fluid dynamics (CFD) we are able to obtain a robust and
purely functional centerline allowing us to support better measurements than classic purely geometrical-based
centerlines. We show that the CFD-based centerline is within a few pixels from the geometrical centerline where
the latter is defined (far away from inlet/outlets and from the branches). We show that the centerline computed
with our method is not affected by traditional errors of other classical volume-based algorithms such as topo-
logical thinning, and could be a potential alternative to be considered for future studies
Basic Concepts And Definitions
No full text1 1 From Euler to Poincar'e 1 2 Order Relations 3 3 Order Functions 5 4 Asymptotic Sequences and Asymptotic Series 5 5 Gauge Sets 7 6 Asymptotic Approximations and Asymptotic Expansions 7 7 Regular Initial Value Problems 10 References 14 Index 16 iv ASYMPTOTIC ANALYSIS Working Note #1 BASIC CONCEPTS AND DEFINITIONS by Marc Garbey and Hans G. Kaper Abstract In this note we introduce the basic concepts of asymptotic analysis. After some comments of historical interest (Section 1), we begin by defining the order relations O, o, and O ] , which enable us to compare the asymptotic behavior of functions of a small positive parameter ffl as ffl # 0 (Section 2). Next, we introduce order functions (Section 3), asymptotic sequences of order functions (Section 4), and more general gauge sets of order functions (Section 5) and define the concepts of an asymptotic approximation and an asymptotic expansion with respect to a given gauge set (Section 6). This string of definitions culminates in..
Approximation Of Integrals
No full text1 1 Integration by Parts 1 2 Laplace Integrals 3 3 Laplace's Method 5 4 Fourier Integrals 8 5 Stokes' Method of Stationary Phase 11 References 16 Index 17 iv ASYMPTOTIC ANALYSIS Working Note #2 APPROXIMATION OF INTEGRALS by Marc Garbey and Hans G. Kaper Abstract In this note we discuss the approximation of integrals that depend on a parameter. The basic tool is simple, namely, integration by parts (Section 1). Of course, the power of the tool is evidenced in applications. The applications are many; they include Laplace integrals (Section 2), generalized Laplace integrals (Section 3), Fourier integrals (Section 4), and Stokes' method of stationary phase for generalized Fourier integrals (Section 5). These results illustrate beautifully Hardy's concept of applications of mathematics, that is, "certain regions of mathematical theory in which the notation and the ideas of the [method of integration by parts] may be used systematically with a great gain in clearness and simplicity" [G...
Computational surgery and dual training: computing, robotics and imaging
No full textThis critical volume focuses on the use of medical imaging, medical robotics, simulation, and information technology in surgery. It offers a road map for computational surgery success, discusses the computer-assisted management of disease and surgery, and provides a rational for image processing and diagnostic. This book also presents some advances on image-driven intervention and robotics, as well as evaluates models and simulations for a broad spectrum of cancers as well as cardiovascular, neurological, and bone diseases. Training and performance analysis in surgery assisted by robotic systems is also covered. This book also: · Provides a comprehensive overview of the use of computational surgery and disease management · Discusses the design and use of medical robotic tools for orthopedic surgery, endoscopic surgery, and prostate surgery · Provides practical examples and case studies in the areas of image processing, virtual surgery, and simulation training Computational Surgery and Dual Training: Computing, Robotics and Imaging is an ideal book for graduate students and professionals in the area of bioengineering, computational science, computational medicine, and medical residents in surgery
A fully coupled computational fluid dynamics – agent-based model of atherosclerotic plaque development: Multiscale modeling framework and parameter sensitivity analysis
No full textBackground: Peripheral Artery Disease (PAD) is an atherosclerotic disorder that leads to impaired lumen patency through intimal hyperplasia and the build-up of plaques, mainly localized in areas of disturbed flow. Computational models can provide valuable insights in the pathogenesis of atherosclerosis and act as a predictive tool to optimize current interventional techniques. Our hypothesis is that a reliable predictive model must include the atherosclerosis development history. Accordingly, we developed a multiscale modeling framework of atherosclerosis that replicates the hemodynamic-driven arterial wall remodeling and plaque formation.
Methods: The framework was based on the coupling of Computational Fluid Dynamics (CFD) simulations with an Agent-Based Model (ABM). The CFD simulation computed the hemodynamics in a 3D artery model, while 2D ABMs simulated cell, Extracellular Matrix (ECM) and lipid dynamics in multiple vessel cross-sections. A sensitivity analysis was also performed to evaluate the oscillation of the ABM output to variations in the inputs and to identify the most influencing ABM parameters.
Results: Our multiscale model qualitatively replicated both the physiologic and pathologic arterial configuration, capturing histological-like features. The ABM outputs were mostly driven by cell and ECM dynamics, largely affecting the lumen area. A subset of parameters was found to affect the final lipid core size, without influencing cell/ECM or lumen area trends.
Conclusion: The fully coupled CFD-ABM framework described atherosclerotic morphological and compositional changes triggered by a disturbed hemodynamics
A Multiscale Model of Atherosclerotic Plaque Development: Toward a Coupling Between an Agent-Based Model and CFD Simulations
No full textComputational models have been widely used to predict the efficacy of surgical interventions in response to Peripheral Occlusive Diseases. However, most of them lack a multiscale description of the development of the disease, which, in our hypothesis, is the key to develop an effective predictive model. Accordingly, in this work we present a multiscale computational framework that simulates the generation of atherosclerotic arterial occlusions. Starting from a healthy artery in homeostatic conditions, the perturbation of specific cellular and extracellular dynamics led to the development of the pathology, with the final output being a diseased artery. The presented model was developed on an idealized portion of a Superficial Femoral Artery (SFA), where an Agent-Based Model (ABM), locally replicating the plaque development, was coupled to Computational Fluid Dynamics (CFD) simulations that define the Wall Shear Stress (WSS) profile at the lumen interface. The ABM was qualitatively validated on histological images and a preliminary analysis on the coupling method was conducted. Once optimized the coupling method, the presented model can serve as a predictive platform to improve the outcome of surgical interventions such as angioplasty and stent deployment
A Clinical Protocol to Validate a Breast Conservative Therapy Outcome Model
No full textBreast cancer is the most common cancer among women around the world. Regarding the different treatments modalities for breast cancer, one is Breast Conservative Therapy (BCT) where the complete tumor and a margin of healthy tissues are surgically removed and the remaining breast tissue receives radiotherapy. From a patient point of view, preserving the shape of her breast is essential for her quality of life and hence, BCT may be a good treatment option. Although the outcome of this treatment usually provides good clinical results, some cosmetic defects like asymmetry may emerge. The goal of our team is to offer surgeons a tool that predicts the shape of the breast after BCT. Therefore, a multiscale model has been implemented by members of our team and is being validated and fine-tuned. A clinical study has been designed. The objective of this Master's thesis is to determine whether the predicted shape of the breast is realistic or not by:
- acquiring numerical data during the patients' follow-up,
- providing a confident 3D-reconstruction of the breast at certain point in time,
- understanding the main steps during the healing process.Computer Science, Department o
A code-independent technique for computational verification of fluid mechanics and heat transfer problems
No full textInternational audienceThe goal of this paper is to present a versatile framework for solution verification of PDE’s. We first generalize the Richardson Extrapolation technique to an optimized extrapolation solution procedure that constructs the best consistent solution from a set of two or three coarse grid solution in the discrete norm of choice. This technique generalizes the Least Square Extrapolation method introduced by one of the author and W. Shyy. We second establish the conditioning number of the problem in a reduced space that approximates the main feature of the numerical solution thanks to a sensitivity analysis. Overall our method produces an a posteriori error estimation in this reduced space of approximation. The key feature of our method is that our construction does not require an internal knowledge of the software neither the source code that produces the solution to be verified. It can be applied in principle as a postprocessing procedure to off the shelf commercial code. We demonstrate the robustness of our method with two steady problems that are separately an incompressible back step flow test case and a heat transfer problem for a battery. Our error estimate might be ultimately verified with a near by manufactured solution. While our procedure is systematic and requires numerous computation of residuals, one can take advantage of distributed computing to get quickly the error estimate
Hands off Coding
No full textThe goal of this paper is to present a versatile framework for solution verification of PDEs. We first generalize the Richardson Extrapolation technique to an optimized extrapolation solution procedure that constructs the best consistent solution from a set of two or three coarse grid solution in the discrete norm of choice. This technique generalizes the Least Square Extrapolation method introduced by one of the author and W.Shyy. We second establish the conditioning number of the problem in a reduced space that approximates the main feature of the numerical solution thanks to a sensitivity analysis. Overall our method produces an a posteriori error estimation in this reduced space of approximation. The key feature of our method is that our construction does not require an internal knowledge of the software neither the source code that produces the solution to be verified. It can be applied in principle as a postprocessing procedure to off the shelf commercial code. We demonstrate the robustness of our method with two steady problems that are respectively an incompressible back step flow test case and a heat transfer problem for a battery. Both test cases are solved by the Finite Element package ADINA. Our error estimate might be ultimately verified with a near by manufactured solution. While our procedure is systematic and requires numerous computation of residuals, one can take advantage of grid computing to get quickly the error estimate
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