Fnd of Computatnl Sci
Fnd of Computatnl Sci CSI 701
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This 57 page Class Notes was uploaded by Summer Kreiger on Monday September 28, 2015. The Class Notes belongs to CSI 701 at George Mason University taught by Juan Cebral in Fall. Since its upload, it has received 52 views. For similar materials see /class/215157/csi-701-george-mason-university in Computer & Information Science at George Mason University.
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Date Created: 09/28/15
RPJNE Introduction What is Computational Sciences Computer simulations Writing scienti c software Example Natural sciences Physics Biology Astronomy Chemistry Medicine Sciences Abstract sciences Mathematical sciences Data sciences Computerscience Natural Sciences Experimental Observational Sciences Sciences Natural Phenomena Computational Theoretical Sciences Sciences Methodologies Theoretical sciences Abstract science development Modeling physical phenomena Correlation with experiments Observational sciences Instrumentation Hypothesis formulation Testing of theories Experimental sciences Instrumentation Physical experimentation Testing of theories Computational sciences Methodology development Computational experimentation Correlation with experiments Testing of theories hypothesis Numbers in Science Greeks Numbers and formulas to describe the world geometry algebra Newton amp Co Functions not numbers differential equations Modern sciences Return of the numbers numerical solutions Computational sciences numerical models Themes of Computational Sciences Modeling and Simulation Numerical Methods Data Analysis Databases Data mining Visualization High Performance Computing Traditional Computational Sciences Computational Physics Computational Astrophysics Molecular dynamics Particle physics Material science Galactic collisions Solar physics Cosmology Computational Bioloqy Drug design Protein folding Cellular signaling pathways Genome analysis Computational Mathematics Computational geometry Computational topology Multidisciplinary computational sciences Computational climate dynamics Fluid mechanics radiation transport ecology geography image analysis Computational social sciences Economics psychology Computational medicine Biomechanics anatomy physiology cell biology image analysis Computational blast dynamics Fluid mechanics structural dynamics fracture mechanics optimization techniques databases Computational Sciences at GMU Fluid dynamics Material sciences Space physics Earth sciences Climate dynamics Neuroscience Bioinformatics Social sciences Bioengineering Biomedical sciences Some Terminology Modeling Simulation Numerical Work Computational Work Algorithm Modeling A model tries to reproduce the salient features of a system The objective of modeling is not to produce an exact copy of the system Since models are based on approximations it is understood that models are imperfect representations of the system Models are valid only in some regimes and conditions and are always imprecise by a certain amount Models can be mathematical experimental computational statistical Simulation Attempts to imitate the dynamic behavior of a system and to predict or calculate subsequent events A simulation realizes a model for a particular choice of physical parameters object geometry initial and boundary conditions Numerical Work Numerical work a general theoretical subject whose main practical application is to solve problems on computers and is not always computational Numerical work includes Solving algebraic equations root finding Solving algebraic systems of equations numerical linear algebra Solving ordinary and partial differential equations Interpolation and data fitting Computational Work Computational work is not always numerical Computational work includes Searching Computational geometry Text manipulation Graphics Distribution parallelization Communications Algorithm An algorithm is a solution procedure to implement a model An algorithm is not a model An algorithm is not necessarily numerical Computer simulations I Physical Model I V I Mathematical Model I V I Numerical Model I V I Visualization I V I Data Analysis I Physical Models Detailed or Microscopic Models Fundamental models that describe the properties or behavior of a system starting from basic assumptions or first principles Averaqed or Macroscopic Models Used when the scales of the physical system are too disparate to resolve consistently in one calculation Phenomenoloqical Models Based on a simple theory for the phenomenon being modeled do not provide detailed information about the physical processes descnbed Empirical Models Direct fits of data mathematical formulas or data tables Mathematical Models Geometrical models Dimensionality OD 1D 2D 3D 4D Infinite domains periodicity Finite domains idealized realistic geometries Mathematical equations Algebraic equations Ordinary differential equations Partial differential equations Coupled systems Numerical Models Discretization techniques Spatial discretization Temporal discretization Parameter space discretization Equation discretization Solution techniques Matrix solvers Numerical integration Interpolation Visualization Use of colors and glyphs to represent amp explore data 2D graphs XY plots charts 3D graphics Animations 4D Visualization of multidimensional data Data Analysis Data interpretation Link to theories experiments Data reduction Data mining Extraction of most relevant information Knowledge discovery from large scientific databases Statistics Establish statistical significance of the results Example Aerodynamics problem need to know the forces acting on the wing of an airplane in order to create a better design Analytic solutions available only for simple geometries Experiments possible but expensive gt would like to perform only a few Perform computational experiments to gain knowledge and to guide the experimental work Physical Model Continuous hypothesis Air is a continuous medium Valid for scales large compared to molecules mean free path lnviscid fluid Air has no friction Valid for high Reynolds number ReLuu lncompressible flow Propagation of information is instantaneous Valid for low Mach number Mavc lrrotational flow No vorticity rotation of fluid elements Valid for inviscid fluid far from solid walls Mathematical Model Incompressible fluid V V O lrrotational flow VX V O gt V V Laplace s equation V2 0 1 V2 const 2 Bernoulli s equation p Two dimensions Problem Specification Geometrical Model 2D Boundary Conditions in ow rigid walls Numerical Model Spatial discretization Unstructured grid Values at the nodes Grid generation Tn39angular mesh Numerical solution Finite elements Matrix solver Algorithm Solve Laplace s eq 3 I Calc gradient 3 v Calc pressure Bernoulli s eq 3 p Calc force 3 f JpndS body Visualization amp Data Analysis Pressure field if Velocty gt Analyze forces on wing and try new design Computational models Sensitivity Independence of model parameters eg grid size Variability with physical parameters eg wind speed Validation Analytic solutions eg cylinder Experiments observations eg wind tunnel Other numerical results eg 3D calculations Knowledqe discovery Isolate control effects eg angle of attack wind speed Data mining eg create DB amp find most important variable Predictive sciences eg predict performance for a new condition Transforming Observational Sciences Computational sciences allow to transform an observational science into a predictive science Example astrophysics Create models of galactic collisions Perform simulations predicting shapes of merging galaxies Compare with observations Predict future evolution 450mm In 3322 Computational Hemodynamics in Cerebrovascular Diseases Juan R Cebrall Christopher Putman2 1 Center for Computational Fluid DynamicsKrasnow GM U Zlnterventional Neuroradiology nova Fairfax Hospital email jcebralgmuedu httpwwwc0sgmuedujcebral Stroke brain or hemorrgic bleeding into terrain Ischemic strokes are most commonly caused by occlusion of a feeding artery typically the carotid artery due to atherosclerosis Hemorrhagic strokes are most commonly caused by the rupture of a cerebral aneurysm Who to Treat Intracranial aneurysms are pathological dilatations of the cerebral arteries and tend to be silent ie no symptoms until they rupture The mortality rate associated with intracranial hemorrhage due to a ruptured aneurysm is approximately 50 and of the surviving patients only about 40 recover a normal life after the hemorrhage Cerebral aneurysms is a high prevalence disease approximately 8 of the population has undetected unruptured aneurysms However they carry a relatively low rupture risk of approx 01 annually Because the prognosis of cerebral hemorrhage is very poor preventive treatment is commonly practiced However treatment always carries a risk which can be higher than the risk of stroke gt The best practice would be to treat only those patients at higher risk This requires a better understanding of the disease process Hemodynamics The initiation progression and outcome of these cerebrovascular diseases are not well understood However it is widely accepted that hemodynamics blood flow plays a fundamental role in these diseases Unfortunately there are no reliable imaging techniques to quantify blood flow patterns in vivo Computational models offer an attractive alternative since they can deal with any artery geometry and can be made patient specific We use imagebased patientspecific computational models to study the hemodynamics in cerebrovascular diseases in order to better assess the risk of stroke How to Treat Surgical treatment for cerebrovascular diseases is no longer the first line of therapy especially for patients at high surgical risk Minimally invasive endovascular interventions catheterization are increasingly used for these patients These endovascular therapies aim at restoring the normal hemodynamic conditions in the affected arteries The effectiveness of these interventions depends on the fulfillment of this goal Therefore understanding the hemodynamics after endovascular interventions is important for improving and personalizing these procedures We use personalized imagebased computational models to design better endovascular devices such as stents and coils and select the best treatment option for a given patient Development ImageBased Computational Modeling Tools Image AcquisitiOIF lter blur lthcgnIent regi grsm ge Eft i39 39 39 quot 39 39 quot 39 L mini Force Visuali Peak Pressure F ragga Vilsllzllztllloznzl39 Eigl ent Cal 1 39 n bllttja39 tmga ogr igctmgrggbg 1133 C c l a 1 Validation Analytic amp In Vitro Data o n Analytlc m plpe ows 39 i a E a Glass model MRI w 7 W W 39 mu m 39 39 601 Glass model Em pressure Ex 2200 7 V B 100 39 i M 7 00 as 1n ms 20 275 nance Glass model i u 39 quot g u m u w i u au o i 0 3 l J 3 1 0 3 1 o 0quot M Validation In Vivo Data Stenosed carotid artery Normal carotid a ms mow FAIRFAX HosPnAL cumin m MRA Model H 1 w P LAN mp in Map a PRF mas PC MR Aneurysm jso intensity surfaces of TOF MRA images I iso velocity surfaces frond CFD simulation Sensitivity Geometry Solver Modality Solver EDNA Basile lirl aneurysm 2 39 1 f 2 A 36 Parent vessel 2 Imaging modality Clinical Database of Aneurysm Models Study Hemodynamics amp Rupture Small Small Study of Aneurysm Wall Motion from Dynamic DSA WalT Tracking complete model E e artery E aneurysmal sac lobule 9 m E h 7 8 a m 39D g 123456789101112 Frame Wall Motlon Quantl ca uon Study Hemodynamics amp Wall Injury Aneurysm Treatment Anew 34323236 7quot 1 o 39 v 39039 to u I Cllhlllr Aneurysm 4 I mm Shmzmin Clipped aneurysm Stemng Surgical Clipping Coiling Coiling and Stenting Modeling Endovascular Procedures 3 b Stenting of Idealized Terminal Aneurysm v mm v mm um i m 1 Pressure y 1 Wm p 1 man p a mm 1 mmlr 7 gm 1 us ma 5m 3 1 all Shear 94 Stress msz m m Virtual Stenting Design Cylinder Map Cylinder Map different designs to cylinder Alteration of Hemodynamics Flow patterns Conclusions We are using patientspecific computational modeling to obtain biofluid mechanical information othenvise unavailable Patientspecific computational models are capable of realistically representing the in vivo hemodynamic conditions These models can be used to connect hemodynamic variables to clinical events in order to better understand the mechanisms of initiation and progression of cerebrovascular diseases Personalized models of aneurysmal flow alterations caused by endovascular interventions can be useful for selecting the best therapy and to optimize the design of endovascular devices for each individual Hopefully this will result in improved patient management Messages Computational sciences can be used to formulate and test hypotheses about natural phenomena In particular they can transform observational sciences into predictive sciences Computational models need to be verified to ensure that the numerical solution is appropriate Computational models need to be validated to ensure that they properly represent the phenomena being studied Computational models can help guide new experiments Computational models can provide useful information for engineering purposes eg diagnosis treatment planning Software Development Design lt V V V I Maintenance 39 Code Design Time to Decide Problem definition Requirements Scope and limitations Architecture design Detailed design Program organization Modules Data structures Error handling Naming convention Implementation plan Buy vs code decisions Code Implementation Time to Code Prototyping proof of concept matlab Data structures Basic algorithms Routines Tuning for efficiency Code assembly Documentation Code Testing Time to Try Compilation Unit testing System testing Debugging Benchmarking Maintenance Time to Improve Corrective maintenance Functional enhancement Revision control system Some Design Criteria Speed Extensibility Software reusability Portability Libraries Layenng Graphical user interface Speed Programming language Data structures amp algorithms Code optimization Parallelization
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