Lecture 10: Image-Based Modelling
|
|
- Megan Merritt
- 5 years ago
- Views:
Transcription
1 Computational Biology Group (CoBI), D-BSSE, ETHZ Lecture 10: Image-Based Modelling Prof Dagmar Iber, PhD DPhil MSc Computational Biology 2015
2 Contents 1 Image-based Domains for Simulations Staining & Imaging of the Tissue Image Processing Image Alignment Image Averaging Image segmentation Mesh Generation Model Simulation 2 Image-based Growth Fields for Simulations Basic Algorithms Extensions of the Algorithms Evaluation of Algorithms Final 2D Algorithm 3D Algorithms 3 Image-based Modelling 4 Model-based Domains & Growth Processes Computational Biology Group (CoBI), D-BSSE, ETHZ Prof Dagmar Iber, PhD DPhil Lecture 11 MSc Mai / 65
3 Human Embryonic Development Computational Biology Group (CoBI), D-BSSE, ETHZ Prof Dagmar Iber, PhD DPhil Lecture 11 MSc Mai / 65
4 Image-based Domains for Simulations Computational Biology Group (CoBI), D-BSSE, ETHZ Prof Dagmar Iber, PhD DPhil Lecture 11 MSc Mai / 65
5 15. Mai / 65 A Pipeline for Image-based Modelling Tissue / Organ of Interest Labelling & Imaging 3D Image Image Processing & Segmentation Static Computational Domain Clonal Analysis of realistic shape Morphing Cell Tracking Mesh Generation & Import Growth Fields Moving, growing Domains of Realistic Shapes Model Formulation Computational Models of Organ Development Parameter Optimization Gene Expression Domains: wildtype & mutants APPLICATIONS: - Define underlying Mechanisms - Test Consistency of Hypotheses with Biological Data - Predict & Explain Mutant Phenotypes - Biomedical Applications 1 Tissue Staining & Imaging 2 Image Processing Image Alignement & Averaging Image Segmentation 3 Mesh Generation 4 Model Simulation on Embryonic Domain Mesh Import Model Formulation PDE Solution
6 15. Mai / Staining & Imaging of the Tissue 1 obtain imaging data of the tissue of interest 2 If different sub-structures of interest label tissue accordingly. Data from Erkan Uenal The staining and imaging technique of choice depends on the tissue, the sub-structure of interest, and the desired resolution.
7 15. Mai / Image Processing Data from Erkan Uenal Several image processing software packages are available to perform these steps, e.g. Amira Imaris Drishti Simpleware Meshlab Rhino 3-D Slicer Alternatively, image processing can also be done with MATLAB.
8 15. Mai / Image Alignment If multiple image recordings of the organ or tissue are available at a given stage, then the 3D images can be aligned and averaged. The alignment procedure is a computationally non-trivial problem. Data from Erkan Uenal In Amira a number of iterative hierarchical optimization algorithms (e.g. QuasiNewton) are available as well as similarity measures (e.g. Euclidean distance) to be minimized.
9 15. Mai / Image Averaging Average pixel intensities of corresponding pixels in multiple datasets of the same size and resolution. helps to assess the variability between embryos identifies common features. reduces variability due to experimental handling UT averaging of badly aligned datasets can result in loss of biologically relevant spatial information run the alignment algorithm several times, starting with different initial positions of the objects, which are to be aligned.
10 15. Mai / Image segmentation During image segmentation, the digital image is partitioned into multiple subdomains, usually corresponding to anatomic features and gene expression regions. A variety of algorithms are available for image segmentation, most of which are based on differences in pixel intensity. Data from Erkan Uenal
11 15. Mai / 65 2-D Virtual Sections 3D Simulations are expensive and it can be helpful to extract 2-D sections first. A variety of algorithms are available for image segmentation, most of which are based on differences in pixel intensity. Data from Erkan Uenal
12 15. Mai / Mesh Generation To carry out finite element methods (FEM)-based simulations of the signaling networks, segmented images are subsequently converted into meshes of sufficient quality. Data from Erkan Uenal
13 15. Mai / Mesh Quality The quality of the mesh can be assessed according to the following two parameters: Mesh size: The linear size of the mesh should be much smaller than any feature of interest in the computational solution, i.e. if the gradient length scale in the model is 50 µm then the linear size of the mesh should be at least several times less than 50 µm. The ratio of the sides of the mesh elements: The length of the shortest side to the longest side should be 0.1 or more. To confirm the convergence of the simulation, the model must be solved on a series of refined meshes.
14 15. Mai / Mesh Import To exchange meshes between image processing software and the simulation software, suitable file formats need to be chosen. To exchange between AMIRA and COMSOL: save AMIRA mesh as I-DEAS universal data format read into Gmesh and save as Nastran Bulk data file change file extension from UNV to DAT import into COMSOL
15 15. Mai / Model Simulation Available PDE solver include Commercial: Ansis, Abaqus, COMSOL Open Source: DUNE, FEniCS, FreeFEM, LiveV Data from Erkan Uenal
16 Image-based Growth Fields for Simulations Computational Biology Group (CoBI), D-BSSE, ETHZ Prof Dagmar Iber, PhD DPhil Lecture 11 MSc Mai / 65
17 15. Mai / 65 Reaction-diffusion equation on a growing domain c i t + (c i u) = D i c i + R(c i ). (1) x x indicates that the time derivative is performed while keeping x constant. The terms u c i and c i u describe advection and dilution, respectively. If the domain is incompressible, i.e. u = 0, the equations further simplify.
18 15. Mai / 65 Image-based Displacement Fields Data from Odysse Michos, Sanger Insitute, Cambridge, UK
19 15. Mai / 65 Image-based Displacement Fields To obtain the displacement field from experimental data, tissue geometries need to be extracted at sequential time points. This requires the following steps: 1 imaging of the tissue at distinct developmental time points 2 image segmentation 3 meshing of the segmented domain 4 warping (morphing) of images at various developmental stages. Subsequently a mathematical regulatory network model can be solved on the deforming physiological domain. In the following we will discuss the different steps in detail.
20 Calculating the Displacement Field To simulate the signaling models on growing domains we need to determine the displacement fields between the different stages. The displacement field between two consecutive stages can be calculated by morphing two subsequent stages onto each other. In other words we are looking for a function which returns a point on a surface at time t + t which corresponds to a point on a surface at time t. Data from Erkan Uenal Computational Biology Group (CoBI), D-BSSE, ETHZ Prof Dagmar Iber, PhD DPhil Lecture 11 MSc Mai / 65
21 15. Mai / 65 Landmark-based Bookstein algorithm Data from Denis Menshykau The landmark-based Bookstein algorithm (Bookstein, 1989), which is implemented in Amira, uses paired thin-plate splines to interpolate surfaces over landmarks defined on a pair of surfaces. The landmark points need to be placed by hand on the two 3D geometries to identify corresponding points on the pair of surfaces.
22 15. Mai / 65 Limitations of landmark-based Bookstein Algorithm The exact shape of the computed warped surface therefore depends on the exact position of landmarks; landmarks must therefore be placed with great care. While various stereoscopic visualization technologies are available this process is time-consuming and in parts difficult for complex surfaces such as the epithelium of the embryonic lung or kidney, in particular if the developmental stages are further apart.
23 15. Mai / 65 Alternative Approaches to determine displacement fields (a) displacement field of entire domain (b) local displacement field
24 15. Mai / 65 Basic Algorithms 1 Minimal Distance Mapping 2 Normal Mapping: intersection of C 1 normal vector and C 2 3 Diffusion Mapping: This mapping is obtained by solving the diffusion equation u u = 0, (2) t for steady flow: u = 0 4 Uniform Mapping: interpolate N points equidistantly along both curves and connect them
25 Extensions of the Algorithms 1 Reverse Mapping: apply algorithm from C 2 to C 1 2 Transformation Mapping: scale and align before mapping 3 Curve Segment Mapping: curves are split into segments according to the intersection points Computational Biology Group (CoBI), D-BSSE, ETHZ Prof Dagmar Iber, PhD DPhil Lecture 11 MSc Mai / 65
26 15. Mai / 65 Extensions of the Algorithms: Curve Segment Mapping (a) global mapping (b) segment mapping
27 15. Mai / 65 Evaluation of Algorithms 1 Qualitative Evaluation 2 Theoretical Reasoning 3 Quantitative Evaluation
28 15. Mai / 65 Evaluation of Algorithms Qualitative Evaluation
29 15. Mai / 65 Minimal Distance Mapping (a) minimal distance mapping (b) reverse minimal distance mapping (c) transformed minimal distance mapping
30 15. Mai / 65 Minimal Distance Mapping (d) Minimal Distance (e) Reverse Minimal Distance
31 15. Mai / 65 Normal Mapping (a) normal mapping (b) reverse normal mapping(c) transfomed normal mapping
32 15. Mai / 65 Normal Mapping (d) Normal Mapping (e) Reverse Normal Mapping
33 15. Mai / 65 Diffusion Mapping (a) Normal Mapping fails (b) Minimal Distance fails
34 15. Mai / 65 Diffusion Mapping (c) solution of diffusion equation (d) streamlines (e) diffusion mapping
35 15. Mai / 65 Diffusion Mapping (f) diffusion mapping (g) reverse diffusion mapping (h) transformed diffusion mapping
36 15. Mai / 65 Uniform Mapping (a) good (b) bad
37 15. Mai / 65 Transformed Mapping (a) minimal distance mapping (b) C 1 scaled indicated by dashed line
38 15. Mai / 65 Transformed Mapping (c) minimal distance mapping from C t onto C 2 (d) displacement field starting points are transformed back onto C 1
39 15. Mai / 65 Summary of Qualitative Evaluation 1 Minimal distance fails when mapping onto a curve with much bigger curvature 2 Normal mapping leads to crossings if C 1 is locally concave and far away from C 2 3 Diffusion and uniform mapping solve these problems but in many cases do not give very nice results
40 15. Mai / 65 Theoretical Reasoning Minimal distance mapping will always be orthogonal on a smooth and closed curve minimal distance solution normal mapping solution Normal mapping is preferred: more natural, no crossings if point density is low, better solutions on boundary and other non smooth regions
41 Quantitative Evaluation of Mapping Algorithms Computational Biology Group (CoBI), D-BSSE, ETHZ Prof Dagmar Iber, PhD DPhil Lecture 11 MSc Mai / 65
42 15. Mai / 65 Quantitative Evaluation of Mapping Algorithms ( ) 2 Li QM 1 = 1. αl i (3) A i QM 2 = ( < A i > 1)2 (4) QM = QM 1 QM 2 = ( L i 1) 2 A i ( αl i < A i > 1)2 (5)
43 15. Mai / 65 Quality Measures applied to Circle Ellipse Mapping QM 1 QM 2 QM minimal distance mapping reverse minimal distance transformed minimal distance normal mapping reveres normal transformed normal diffusion mapping reverse diffusion transformed diffusion
44 Quality Measures applied to Circle Ellipse Computational Biology Group (CoBI), D-BSSE, ETHZ Prof Dagmar Iber, PhD DPhil Lecture 11 MSc Mai / 65
45 15. Mai / 65 Quality Measures applied to Kidney Data (a) minimal distance mapping (b) reverse minimal distance mapping
46 15. Mai / 65 Quality Measures applied to Kidney Data (c) normal mapping (d) reverse normal mapping
47 15. Mai / 65 Quality Measures applied to Kidney Data (e) reverse diffusion mapping (f) uniform mapping
48 15. Mai / 65 Quantitative Evaluation of Mapping Algorithms QM( =1h) QM( =2h) minimal distance 1.755E E-2 reverse minimal distance 1.937E E-2 normal 0.591E E-2 reverse normal 8.686E E-2 diffusion 1.163E E-2 reverse diffusion 3.896E E-2 uniform mapping 0.120E E-2
49 15. Mai / 65 Quantitative Evaluation of Mapping Algorithms QM( =4h) QM( =8h) minimal distance E reverse minimal distance E normal 9.247E reverse normal diffusion E reverse diffusion uniform mapping 0.951E
50 15. Mai / 65 Final 2D Algorithm For each curve intersection segment: 1 try normal mapping 2 if crossings occur try normal mapping with scaling 3 if crossings occur do reverse diffusion For open curves: first scale and connect!
51 15. Mai / 65 3D Algorithms (g) minimal distance mapping (h) normal mapping (i) diffusion mapping
52 3D Normal Mapping applied to Lung Data Computational Biology Group (CoBI), D-BSSE, ETHZ Prof Dagmar Iber, PhD DPhil Lecture 11 MSc Mai / 65
53 Image-based Modelling Computational Biology Group (CoBI), D-BSSE, ETHZ Prof Dagmar Iber, PhD DPhil Lecture 11 MSc Mai / 65
54 15. Mai / 65 Image-based Modelling Once the correspondence between two surfaces has been defined, a displacement field can be calculated by determining the difference between the positions of points on the two surface meshes as illustrated for the embryonic lung sequence in the next slide.
55 Image-based Displacement Fields Computational Biology Group (CoBI), D-BSSE, ETHZ 15. Mai / 65 Prof Dagmar Iber, PhD DPhil Lecture 11 MSc 2015
56 15. Mai / 65 Image-based Displacement Fields (a,b) The segmented epithelium and mesenchyme of the developing lung at two consecutive stages. (c) The displacement field between the two stages in panels a and b. (d) The growing part of the lung. The coloured vectors indicate the strength of the displacement field. (e) The solution of the Turing model (Equations 10) on the segmented lung of the stage in panel a. (f) Comparison of the simulated Turing model (solid surface) and the embryonic displacement field (arrows). The images processing was carried out in AMIRA; the simulations were carried out in COMSOL Multiphysics 4.3a.
57 15. Mai / 65 Simulation of Signaling Dynamics using FEM To carry out the FEM-based simulations the mesh and displacement field need to be imported into a FEM solver. To avoid unnecessary interpolation of the vector field, the displacement field should be calculated for exactly the same surface mesh as was used to generate the volume mesh. A number of commercial (COMSOL Multiphysics, Ansis, Abaqus etc) and open (FreeFEM, DUNE etc) FEM solvers are available.
58 15. Mai / 65 Reaction-diffusion equation on a growing domain c i t + (c i u) = D i c i + R(c i ). (6) x x indicates that the time derivative is performed while keeping x constant. The terms u c i and c i u describe advection and dilution, respectively. If the domain is incompressible, i.e. u = 0, the equations further simplify.
59 15. Mai / 65 Prescribed Growth In prescribed growth models an initial domain and a spatio-temporal velocity or displacement field are defined. The domain with initial coordinate vectors X is then moved according to this velocity field u(x, t), i.e. X(t) t = x t = u(x, t) (7) X
60 15. Mai / 65 Model-based Displacement Fields The velocity field u(x, t) can be captured in a functional form that represents either the observed growth and/or signaling kinetics. In the simplest implementation the displacement may be applied only normal to the boundary, i.e. u = µn, (8) where n is the normal vector to the boundary and µ is the local growth rate.
61 15. Mai / 65 Model-based Displacement Fields Growth processes often depend on signaling networks that evolve on the tissue domain. The displacement field u(x, t) may thus dependent on the local concentration of some growth or signaling factor. We then have u = µ(c)n, (9) where c is the local concentration of the signaling factor.
62 15. Mai / 65 Model Implementation These approaches can be readily implemented in the commercially available finite element solver COMSOL Multiphysics. Details of the implementation will be discussed in the tutorial.
63 15. Mai / 65 Example: Schnakenberg Turing Model c 1 t + (c 1u) = c 1 + γ(a c 1 + c1 2 c 2 ) c 2 t + (c 2u) = d c 2 + γ(b c1 2 c 2 ); (10) a, b, γ, and d are constant parameters in the Turing model.
64 Prescribed Domain Growth under Control of a Signaling Model. The figure shows as an example a 2D sheet that deforms within a 3D domain according to the strength of the signaling field normal to its surface, i.e. u = µc12 c2 n, where c1 and c2 are the two variables that are governed by the Schnakenberg-type Turing model. Computational Biology Group (CoBI), D-BSSE, ETHZ 15. Mai / 65 Prof Dagmar Iber, PhD DPhil Lecture 11 MSc 2015
65 15. Mai / 65 Thanks!! Thanks for your attention! Slides for this talk will be available at:
ADAPTIVE FINITE ELEMENT
Finite Element Methods In Linear Structural Mechanics Univ. Prof. Dr. Techn. G. MESCHKE SHORT PRESENTATION IN ADAPTIVE FINITE ELEMENT Abdullah ALSAHLY By Shorash MIRO Computational Engineering Ruhr Universität
More informationFinite Element Convergence for Time-Dependent PDEs with a Point Source in COMSOL 4.2
Finite Element Convergence for Time-Dependent PDEs with a Point Source in COMSOL 4.2 David W. Trott and Matthias K. Gobbert Department of Mathematics and Statistics, University of Maryland, Baltimore County,
More information1.2 Numerical Solutions of Flow Problems
1.2 Numerical Solutions of Flow Problems DIFFERENTIAL EQUATIONS OF MOTION FOR A SIMPLIFIED FLOW PROBLEM Continuity equation for incompressible flow: 0 Momentum (Navier-Stokes) equations for a Newtonian
More informationIntroduction to Finite Element Analysis using ANSYS
Introduction to Finite Element Analysis using ANSYS Sasi Kumar Tippabhotla PhD Candidate Xtreme Photovoltaics (XPV) Lab EPD, SUTD Disclaimer: The material and simulations (using Ansys student version)
More informationMethod of Finite Elements I
Institute of Structural Engineering Page 1 Held by Prof. Dr. E. Chatzi, Dr. P. Steffen Assistants: Adrian Egger (HIL E 13.3), Harry Mylonas (HIL H33.1), Konstantinos Tatsis (HIL H33.1) Lectures homepage:
More informationVCell Tutorial. FRAP with binding
VCell Tutorial FRAP with binding Create a simple biomodel and spatial (PDE) application to simulate a photobleaching experiment with both diffusion and binding. In this tutorial Gain a basic introduction
More informationParticle Velocimetry Data from COMSOL Model of Micro-channels
Particle Velocimetry Data from COMSOL Model of Micro-channels P.Mahanti *,1, M.Keebaugh 1, N.Weiss 1, P.Jones 1, M.Hayes 1, T.Taylor 1 Arizona State University, Tempe, Arizona *Corresponding author: GWC
More informationSUPPLEMENTARY FILE S1: 3D AIRWAY TUBE RECONSTRUCTION AND CELL-BASED MECHANICAL MODEL. RELATED TO FIGURE 1, FIGURE 7, AND STAR METHODS.
SUPPLEMENTARY FILE S1: 3D AIRWAY TUBE RECONSTRUCTION AND CELL-BASED MECHANICAL MODEL. RELATED TO FIGURE 1, FIGURE 7, AND STAR METHODS. 1. 3D AIRWAY TUBE RECONSTRUCTION. RELATED TO FIGURE 1 AND STAR METHODS
More informationUnstructured Mesh Generation for Implicit Moving Geometries and Level Set Applications
Unstructured Mesh Generation for Implicit Moving Geometries and Level Set Applications Per-Olof Persson (persson@mit.edu) Department of Mathematics Massachusetts Institute of Technology http://www.mit.edu/
More informationLecture 32: Sysnoise and Structural Models Computational Acoustics, c V. Sparrow/PSU, 2000
Lecture 32: Sysnoise and Structural Models Computational Acoustics, c V. Sparrow/PSU, 2000 References: - Sysnoise Rev. 5.4User s Manuals, LMS Numerical Technologies, Leuven, Belgium. - Sysnoise Rev. 5.4Examples
More informationModelling With Comsol: Gradients and Pattern Formation Direct questions and suggestions to Denis
Modelling With Comsol: Gradients and Pattern Formation Direct questions and suggestions to Denis (dzianis.menshykau@bsse.ethz.ch) Problem 1 Solve simple diffusion equation (no reactions!) on a 1D domain.
More informationGuidelines for proper use of Plate elements
Guidelines for proper use of Plate elements In structural analysis using finite element method, the analysis model is created by dividing the entire structure into finite elements. This procedure is known
More informationOpenFOAM and Third Party Structural Solver for Fluid Structure Interaction Simulations
OpenFOAM and Third Party Structural Solver for Fluid Structure Interaction Simulations Robert L. Campbell rlc138@arl.psu.edu Fluids and Structural Mechanics Office Applied Research Laboratory The Pennsylvania
More informationOutline. COMSOL Multyphysics: Overview of software package and capabilities
COMSOL Multyphysics: Overview of software package and capabilities Lecture 5 Special Topics: Device Modeling Outline Basic concepts and modeling paradigm Overview of capabilities Steps in setting-up a
More informationLecture 2 Unstructured Mesh Generation
Lecture 2 Unstructured Mesh Generation MIT 16.930 Advanced Topics in Numerical Methods for Partial Differential Equations Per-Olof Persson (persson@mit.edu) February 13, 2006 1 Mesh Generation Given a
More informationCHAPTER 4. Numerical Models. descriptions of the boundary conditions, element types, validation, and the force
CHAPTER 4 Numerical Models This chapter presents the development of numerical models for sandwich beams/plates subjected to four-point bending and the hydromat test system. Detailed descriptions of the
More informationCSE 554 Lecture 7: Deformation II
CSE 554 Lecture 7: Deformation II Fall 2011 CSE554 Deformation II Slide 1 Review Rigid-body alignment Non-rigid deformation Intrinsic methods: deforming the boundary points An optimization problem Minimize
More informationMicrowell Mixing with Surface Tension
Microwell Mixing with Surface Tension Nick Cox Supervised by Professor Bruce Finlayson University of Washington Department of Chemical Engineering June 6, 2007 Abstract For many applications in the pharmaceutical
More informationStep 1: Problem Type Specification. (1) Open COMSOL Multiphysics 4.1. (2) Under Select Space Dimension tab, select 2D Axisymmetric.
Step 1: Problem Type Specification (1) Open COMSOL Multiphysics 4.1. (2) Under Select Space Dimension tab, select 2D Axisymmetric. (3) Click on blue arrow next to Select Space Dimension title. (4) Click
More informationCOMPUTER AIDED ENGINEERING. Part-1
COMPUTER AIDED ENGINEERING Course no. 7962 Finite Element Modelling and Simulation Finite Element Modelling and Simulation Part-1 Modeling & Simulation System A system exists and operates in time and space.
More information3D Finite Element Software for Cracks. Version 3.2. Benchmarks and Validation
3D Finite Element Software for Cracks Version 3.2 Benchmarks and Validation October 217 1965 57 th Court North, Suite 1 Boulder, CO 831 Main: (33) 415-1475 www.questintegrity.com http://www.questintegrity.com/software-products/feacrack
More informationApplication of Finite Volume Method for Structural Analysis
Application of Finite Volume Method for Structural Analysis Saeed-Reza Sabbagh-Yazdi and Milad Bayatlou Associate Professor, Civil Engineering Department of KNToosi University of Technology, PostGraduate
More informationLagrangian methods and Smoothed Particle Hydrodynamics (SPH) Computation in Astrophysics Seminar (Spring 2006) L. J. Dursi
Lagrangian methods and Smoothed Particle Hydrodynamics (SPH) Eulerian Grid Methods The methods covered so far in this course use an Eulerian grid: Prescribed coordinates In `lab frame' Fluid elements flow
More informationProblem description. The FCBI-C element is used in the fluid part of the model.
Problem description This tutorial illustrates the use of ADINA for analyzing the fluid-structure interaction (FSI) behavior of a flexible splitter behind a 2D cylinder and the surrounding fluid in a channel.
More informationProposal of Research Activity. PhD Course in Space Sciences, Technologies and Measurements (STMS)
Proposal of Research Activity PhD Course in Space Sciences, Technologies and Measurements (STMS) Curriculum: Sciences and Technologies for Aeronautics and Satellite Applications (STASA) XXXIV Cycle PhD
More informationFEMLAB Exercise 1 for ChE366
FEMLAB Exercise 1 for ChE366 Problem statement Consider a spherical particle of radius r s moving with constant velocity U in an infinitely long cylinder of radius R that contains a Newtonian fluid. Let
More informationDr. Ulas Bagci
Lecture 9: Deformable Models and Segmentation CAP-Computer Vision Lecture 9-Deformable Models and Segmentation Dr. Ulas Bagci bagci@ucf.edu Lecture 9: Deformable Models and Segmentation Motivation A limitation
More informationCoupled Analysis of FSI
Coupled Analysis of FSI Qin Yin Fan Oct. 11, 2008 Important Key Words Fluid Structure Interface = FSI Computational Fluid Dynamics = CFD Pressure Displacement Analysis = PDA Thermal Stress Analysis = TSA
More informationThe 3D DSC in Fluid Simulation
The 3D DSC in Fluid Simulation Marek K. Misztal Informatics and Mathematical Modelling, Technical University of Denmark mkm@imm.dtu.dk DSC 2011 Workshop Kgs. Lyngby, 26th August 2011 Governing Equations
More informationFemap Version
Femap Version 11.3 Benefits Easier model viewing and handling Faster connection definition and setup Faster and easier mesh refinement process More accurate meshes with minimal triangle element creation
More informationCHAPTER 8 FINITE ELEMENT ANALYSIS
If you have any questions about this tutorial, feel free to contact Wenjin Tao (w.tao@mst.edu). CHAPTER 8 FINITE ELEMENT ANALYSIS Finite Element Analysis (FEA) is a practical application of the Finite
More informationIsotropic Porous Media Tutorial
STAR-CCM+ User Guide 3927 Isotropic Porous Media Tutorial This tutorial models flow through the catalyst geometry described in the introductory section. In the porous region, the theoretical pressure drop
More informationRevised Sheet Metal Simulation, J.E. Akin, Rice University
Revised Sheet Metal Simulation, J.E. Akin, Rice University A SolidWorks simulation tutorial is just intended to illustrate where to find various icons that you would need in a real engineering analysis.
More informationVOLCANIC DEFORMATION MODELLING: NUMERICAL BENCHMARKING WITH COMSOL
VOLCANIC DEFORMATION MODELLING: NUMERICAL BENCHMARKING WITH COMSOL The following is a description of the model setups and input/output parameters for benchmarking analytical volcanic deformation models
More informationCoustyx Tutorial Indirect Model
Coustyx Tutorial Indirect Model 1 Introduction This tutorial is created to outline the steps required to compute radiated noise from a gearbox housing using Coustyx software. Detailed steps are given on
More informationOverview and Recent Developments of Dynamic Mesh Capabilities
Overview and Recent Developments of Dynamic Mesh Capabilities Henrik Rusche and Hrvoje Jasak h.rusche@wikki-gmbh.de and h.jasak@wikki.co.uk Wikki Gmbh, Germany Wikki Ltd, United Kingdom 6th OpenFOAM Workshop,
More informationA NURBS-BASED APPROACH FOR SHAPE AND TOPOLOGY OPTIMIZATION OF FLOW DOMAINS
6th European Conference on Computational Mechanics (ECCM 6) 7th European Conference on Computational Fluid Dynamics (ECFD 7) 11 15 June 2018, Glasgow, UK A NURBS-BASED APPROACH FOR SHAPE AND TOPOLOGY OPTIMIZATION
More informationParallel Performance Studies for COMSOL Multiphysics Using Scripting and Batch Processing
Parallel Performance Studies for COMSOL Multiphysics Using Scripting and Batch Processing Noemi Petra and Matthias K. Gobbert Department of Mathematics and Statistics, University of Maryland, Baltimore
More informationRevision of the SolidWorks Variable Pressure Simulation Tutorial J.E. Akin, Rice University, Mechanical Engineering. Introduction
Revision of the SolidWorks Variable Pressure Simulation Tutorial J.E. Akin, Rice University, Mechanical Engineering Introduction A SolidWorks simulation tutorial is just intended to illustrate where to
More informationModeling of Laminar Flow Static Mixers
Modeling of Laminar Flow Static Mixers Nagi Elabbasi, Xiaohu Liu, Stuart Brown ( ) Mike Vidal, Matthew Pappalardo (Nordson EFD) COMSOL Conference 2012, Boston, MA Excerpt from the Proceedings of the 2012
More informationCS337 INTRODUCTION TO COMPUTER GRAPHICS. Describing Shapes. Constructing Objects in Computer Graphics. Bin Sheng Representing Shape 9/20/16 1/15
Describing Shapes Constructing Objects in Computer Graphics 1/15 2D Object Definition (1/3) Lines and polylines: Polylines: lines drawn between ordered points A closed polyline is a polygon, a simple polygon
More informationVCell Tutorial. FRAP: Fluorescence Redistribution After Photo bleaching
VCell Tutorial FRAP: Fluorescence Redistribution After Photo bleaching Create a simple biomodel and spatial (PDE) application to simulate a photobleaching experiment and view the results. In this tutorial
More informationcomputational Fluid Dynamics - Prof. V. Esfahanian
Three boards categories: Experimental Theoretical Computational Crucial to know all three: Each has their advantages and disadvantages. Require validation and verification. School of Mechanical Engineering
More informationDigital Image Processing. Prof. P.K. Biswas. Department of Electronics & Electrical Communication Engineering
Digital Image Processing Prof. P.K. Biswas Department of Electronics & Electrical Communication Engineering Indian Institute of Technology, Kharagpur Image Segmentation - III Lecture - 31 Hello, welcome
More informationA Procedure for the 3D Reconstruction of Biological Organs from 2D Image Sequences
A Procedure for the 3D Reconstruction of Biological Organs from 2D Image Sequences Kirana Kumara P Centre for Product Design and Manufacturing Indian Institute of Science Bangalore, 560 012 India Ashitava
More informationFinite Element Logan Solution Manual
Logan Solution Manual Free PDF ebook Download: Logan Solution Manual Download or Read Online ebook finite element logan solution manual in PDF Format From The Best User Guide Database Analysis. Mechanical
More informationCS123 INTRODUCTION TO COMPUTER GRAPHICS. Describing Shapes. Constructing Objects in Computer Graphics 1/15
Describing Shapes Constructing Objects in Computer Graphics 1/15 2D Object Definition (1/3) Lines and polylines: Polylines: lines drawn between ordered points A closed polyline is a polygon, a simple polygon
More information10.1 Overview. Section 10.1: Overview. Section 10.2: Procedure for Generating Prisms. Section 10.3: Prism Meshing Options
Chapter 10. Generating Prisms This chapter describes the automatic and manual procedure for creating prisms in TGrid. It also discusses the solution to some common problems that you may face while creating
More informationVariational Methods II
Mathematical Foundations of Computer Graphics and Vision Variational Methods II Luca Ballan Institute of Visual Computing Last Lecture If we have a topological vector space with an inner product and functionals
More informationOptimizing Bio-Inspired Flow Channel Design on Bipolar Plates of PEM Fuel Cells
Excerpt from the Proceedings of the COMSOL Conference 2010 Boston Optimizing Bio-Inspired Flow Channel Design on Bipolar Plates of PEM Fuel Cells James A. Peitzmeier *1, Steven Kapturowski 2 and Xia Wang
More informationMODELING OF A MICRO-GRIPPER COMPLIANT JOINT USING COMSOL MULTIPHYSICS SIMULATION
MODELING OF A MICRO-GRIPPER COMPLIANT JOINT USING COMSOL MULTIPHYSICS SIMULATION Mihăiţă Nicolae ARDELEANU, Veronica DESPA, Ioan Alexandru IVAN Valahia University from Targoviste E-mail: mihai.ardeleanu@valahia.ro,
More information2008 International ANSYS Conference
2008 International ANSYS Conference FEM AND FSI SIMULATIONS OF IMPACT LOADS ON GRP SUBSEA COMPOSITE COVERS Kjetil Rognlien, MSc Technical Consultant EDR AS, Norway 2008 ANSYS, Inc. All rights reserved.
More informationIntroduction to C omputational F luid Dynamics. D. Murrin
Introduction to C omputational F luid Dynamics D. Murrin Computational fluid dynamics (CFD) is the science of predicting fluid flow, heat transfer, mass transfer, chemical reactions, and related phenomena
More informationMoving Interface Problems: Methods & Applications Tutorial Lecture II
Moving Interface Problems: Methods & Applications Tutorial Lecture II Grétar Tryggvason Worcester Polytechnic Institute Moving Interface Problems and Applications in Fluid Dynamics Singapore National University,
More informationScilab Element Finite Cylinder
Scilab Element Finite Cylinder Free PDF ebook Download: Scilab Element Finite Cylinder Download or Read Online ebook scilab element finite cylinder in PDF Format From The Best User Guide Database Scilab
More informationAcoustic Field Comparison of High Intensity Focused Ultrasound by using Experimental Characterization and Finite Element Simulation
Acoustic Field Comparison of High Intensity Focused Ultrasound by using Experimental Characterization and Finite Element Simulation J. L. Teja, A. Vera, and L. Leija Department of Electrical Engineering,
More informationChapter 3. Automated Segmentation of the First Mitotic Spindle in Differential Interference Contrast Microcopy Images of C.
Chapter 3 Automated Segmentation of the First Mitotic Spindle in Differential Interference Contrast Microcopy Images of C. elegans Embryos Abstract Differential interference contrast (DIC) microscopy is
More informationHow to plot the gradients of magnetic field
How to plot the gradients of magnetic field Background 3D magnetic problems are solved in COMSOL using vector (curl) elements. The solution to these problems is the magnetic vector potential (A). The magnetic
More informationPartial Differential Equations
Simulation in Computer Graphics Partial Differential Equations Matthias Teschner Computer Science Department University of Freiburg Motivation various dynamic effects and physical processes are described
More informationComputational Study of Laminar Flowfield around a Square Cylinder using Ansys Fluent
MEGR 7090-003, Computational Fluid Dynamics :1 7 Spring 2015 Computational Study of Laminar Flowfield around a Square Cylinder using Ansys Fluent Rahul R Upadhyay Master of Science, Dept of Mechanical
More informationFlow and Heat Transfer in a Mixing Elbow
Flow and Heat Transfer in a Mixing Elbow Objectives The main objectives of the project are to learn (i) how to set up and perform flow simulations with heat transfer and mixing, (ii) post-processing and
More information"The real world is nonlinear"... 7 main Advantages using Abaqus
"The real world is nonlinear"... 7 main Advantages using Abaqus FEA SERVICES LLC 6000 FAIRVIEW ROAD, SUITE 1200 CHARLOTTE, NC 28210 704.552.3841 WWW.FEASERVICES.NET AN OFFICIAL DASSAULT SYSTÈMES VALUE
More informationAdjoint Solver Workshop
Adjoint Solver Workshop Why is an Adjoint Solver useful? Design and manufacture for better performance: e.g. airfoil, combustor, rotor blade, ducts, body shape, etc. by optimising a certain characteristic
More informationSimulating Organogenesis in COMSOL: Comparison Of Methods For Simulating Branching Morphogenesis
Simulating Organogenesis in COMSOL: Comparison Of Methods For Simulating Branching Morphogenesis Lucas D. Wittwer 1, Michael Peters 1,2, Sebastian Aland 3, Dagmar Iber *1,2 1 D-BSSE, ETH Zürich, Zurich,
More informationStrömningslära Fluid Dynamics. Computer laboratories using COMSOL v4.4
UMEÅ UNIVERSITY Department of Physics Claude Dion Olexii Iukhymenko May 15, 2015 Strömningslära Fluid Dynamics (5FY144) Computer laboratories using COMSOL v4.4!! Report requirements Computer labs must
More informationCHAPTER 1. Introduction
ME 475: Computer-Aided Design of Structures 1-1 CHAPTER 1 Introduction 1.1 Analysis versus Design 1.2 Basic Steps in Analysis 1.3 What is the Finite Element Method? 1.4 Geometrical Representation, Discretization
More informationCFD MODELING FOR PNEUMATIC CONVEYING
CFD MODELING FOR PNEUMATIC CONVEYING Arvind Kumar 1, D.R. Kaushal 2, Navneet Kumar 3 1 Associate Professor YMCAUST, Faridabad 2 Associate Professor, IIT, Delhi 3 Research Scholar IIT, Delhi e-mail: arvindeem@yahoo.co.in
More informationSmart point landmark distribution for thin-plate splines
Smart point landmark distribution for thin-plate splines John Lewis a, Hea-Juen Hwang a, Ulrich Neumann a, and Reyes Enciso b a Integrated Media Systems Center, University of Southern California, 3740
More informationImage-based Modelling of Organogenesis
Image-based Modelling of Organogenesis Dagmar Iber 1,2,*, Zahra Karimaddini 1,2, Erkan Ünal 1,2,3 Affiliations: 1 Department of Biosystems, Science and Engineering (D-BSSE), ETH Zurich, Switzerland 2 -
More informationRBF Morph An Add-on Module for Mesh Morphing in ANSYS Fluent
RBF Morph An Add-on Module for Mesh Morphing in ANSYS Fluent Gilles Eggenspieler Senior Product Manager 1 Morphing & Smoothing A mesh morpher is a tool capable of performing mesh modifications in order
More informationAppendix A: Mesh Nonlinear Adaptivity. ANSYS Mechanical Introduction to Structural Nonlinearities
Appendix A: Mesh Nonlinear Adaptivity 16.0 Release ANSYS Mechanical Introduction to Structural Nonlinearities 1 2015 ANSYS, Inc. Mesh Nonlinear Adaptivity Introduction to Mesh Nonlinear Adaptivity Understanding
More informationMorphometric Analysis of Biomedical Images. Sara Rolfe 10/9/17
Morphometric Analysis of Biomedical Images Sara Rolfe 10/9/17 Morphometric Analysis of Biomedical Images Object surface contours Image difference features Compact representation of feature differences
More informationVolume Illumination & Vector Field Visualisation
Volume Illumination & Vector Field Visualisation Visualisation Lecture 11 Institute for Perception, Action & Behaviour School of Informatics Volume Illumination & Vector Vis. 1 Previously : Volume Rendering
More informationVolume Illumination and Segmentation
Volume Illumination and Segmentation Computer Animation and Visualisation Lecture 13 Institute for Perception, Action & Behaviour School of Informatics Overview Volume illumination Segmentation Volume
More informationTurbulent Premixed Combustion with Flamelet Generated Manifolds in COMSOL Multiphysics
Turbulent Premixed Combustion with Flamelet Generated Manifolds in COMSOL Multiphysics Rob J.M Bastiaans* Eindhoven University of Technology *Corresponding author: PO box 512, 5600 MB, Eindhoven, r.j.m.bastiaans@tue.nl
More informationChapter 6 Visualization Techniques for Vector Fields
Chapter 6 Visualization Techniques for Vector Fields 6.1 Introduction 6.2 Vector Glyphs 6.3 Particle Advection 6.4 Streamlines 6.5 Line Integral Convolution 6.6 Vector Topology 6.7 References 2006 Burkhard
More informationHydro-elastic analysis of a propeller using CFD and FEM co-simulation
Fifth International Symposium on Marine Propulsors smp 17, Espoo, Finland, June 2017 Hydro-elastic analysis of a propeller using CFD and FEM co-simulation Vesa Nieminen 1 1 VTT Technical Research Centre
More informationThe Finite Element Method for the Analysis of Non-Linear and Dynamic Systems. Prof. Dr. Eleni Chatzi, J.P. Escallo n Lecture December, 2013
The Finite Element Method for the Analysis of Non-Linear and Dynamic Systems Prof. Dr. Eleni Chatzi, J.P. Escallo n Lecture 11-17 December, 2013 Institute of Structural Engineering Method of Finite Elements
More informationMesh Morphing and the Adjoint Solver in ANSYS R14.0. Simon Pereira Laz Foley
Mesh Morphing and the Adjoint Solver in ANSYS R14.0 Simon Pereira Laz Foley 1 Agenda Fluent Morphing-Optimization Feature RBF Morph with ANSYS DesignXplorer Adjoint Solver What does an adjoint solver do,
More informationAn advanced RBF Morph application: coupled CFD-CSM Aeroelastic Analysis of a Full Aircraft Model and Comparison to Experimental Data
An advanced RBF Morph application: coupled CFD-CSM Aeroelastic Analysis of a Full Aircraft Model and Comparison to Experimental Data Dr. Marco Evangelos Biancolini Tor Vergata University, Rome, Italy Dr.
More informationEffects of Solvers on Finite Element Analysis in COMSOL MULTIPHYSICS
Effects of Solvers on Finite Element Analysis in COMSOL MULTIPHYSICS Chethan Ravi B.R Dr. Venkateswaran P Corporate Technology - Research and Technology Center Siemens Technology and Services Private Limited
More informationMeshless Modeling, Animating, and Simulating Point-Based Geometry
Meshless Modeling, Animating, and Simulating Point-Based Geometry Xiaohu Guo SUNY @ Stony Brook Email: xguo@cs.sunysb.edu http://www.cs.sunysb.edu/~xguo Graphics Primitives - Points The emergence of points
More information3. Preprocessing of ABAQUS/CAE
3.1 Create new model database 3. Preprocessing of ABAQUS/CAE A finite element analysis in ABAQUS/CAE starts from create new model database in the toolbar. Then save it with a name user defined. To build
More informationSETTLEMENT OF A CIRCULAR FOOTING ON SAND
1 SETTLEMENT OF A CIRCULAR FOOTING ON SAND In this chapter a first application is considered, namely the settlement of a circular foundation footing on sand. This is the first step in becoming familiar
More informationMatching. Compare region of image to region of image. Today, simplest kind of matching. Intensities similar.
Matching Compare region of image to region of image. We talked about this for stereo. Important for motion. Epipolar constraint unknown. But motion small. Recognition Find object in image. Recognize object.
More informationSolid and shell elements
Solid and shell elements Theodore Sussman, Ph.D. ADINA R&D, Inc, 2016 1 Overview 2D and 3D solid elements Types of elements Effects of element distortions Incompatible modes elements u/p elements for incompressible
More informationDgp _ lecture 2. Curves
Dgp _ lecture 2 Curves Questions? This lecture will be asking questions about curves, their Relationship to surfaces, and how they are used and controlled. Topics of discussion will be: Free form Curves
More informationFluent User Services Center
Solver Settings 5-1 Using the Solver Setting Solver Parameters Convergence Definition Monitoring Stability Accelerating Convergence Accuracy Grid Independence Adaption Appendix: Background Finite Volume
More informationNon-Linear Finite Element Methods in Solid Mechanics Attilio Frangi, Politecnico di Milano, February 3, 2017, Lesson 1
Non-Linear Finite Element Methods in Solid Mechanics Attilio Frangi, attilio.frangi@polimi.it Politecnico di Milano, February 3, 2017, Lesson 1 1 Politecnico di Milano, February 3, 2017, Lesson 1 2 Outline
More informationLecture 12 Level Sets & Parametric Transforms. sec & ch. 11 of Machine Vision by Wesley E. Snyder & Hairong Qi
Lecture 12 Level Sets & Parametric Transforms sec. 8.5.2 & ch. 11 of Machine Vision by Wesley E. Snyder & Hairong Qi Spring 2017 16-725 (CMU RI) : BioE 2630 (Pitt) Dr. John Galeotti The content of these
More informationDeformations. Recall: important tmodel dlof shape change is the deformation of one form into another.
Deformations Recall: important tmodel dlof shape change is the deformation of one form into another. Dates back to D Arcy Thompson s (1917) transformation grids. Deformation maps a set of morphological
More informationExample 24 Spring-back
Example 24 Spring-back Summary The spring-back simulation of sheet metal bent into a hat-shape is studied. The problem is one of the famous tests from the Numisheet 93. As spring-back is generally a quasi-static
More informationENERGY-224 Reservoir Simulation Project Report. Ala Alzayer
ENERGY-224 Reservoir Simulation Project Report Ala Alzayer Autumn Quarter December 3, 2014 Contents 1 Objective 2 2 Governing Equations 2 3 Methodolgy 3 3.1 BlockMesh.........................................
More informationSIMULATION OF METAL FORMING PROCESSES. Konstantin SOLOMONOV a, Victor SVIRIN b
SIMULATION OF METAL FORMING PROCESSES Konstantin SOLOMONOV a, Victor SVIRIN b a Moscow State University of Railway Engineering (Voronezh branch), 75а, Uritskogo street, 394026, Voronezh, Russia, E-mail
More informationANSYS User s Group Non-Linear Adaptive Meshing (NLAD)
19.2 Release ANSYS User s Group Non-Linear Adaptive Meshing (NLAD) Sriraghav Sridharan Application Engineer, ANSYS Inc Sriraghav.Sridharan@ansys.com 1 2017 ANSYS, Inc. October 10, 2018 Topics Background
More informationThe Level Set Method THE LEVEL SET METHOD THE LEVEL SET METHOD 203
The Level Set Method Fluid flow with moving interfaces or boundaries occur in a number of different applications, such as fluid-structure interaction, multiphase flows, and flexible membranes moving in
More informationSecond International Workshop on Scientific Computing and Applications. Kananaskis, Canada, May 28 - June 1, 2000
Second International Workshop on Scientific Computing and Applications. Kananaskis, Canada, May 28 - June 1, 2000 Program May 28 (Sunday) 19:00-21:00 Registration and reception Session Chairman: Y. Wong
More informationSIMULATION OF A DETONATION CHAMBER TEST CASE
SIMULATION OF A DETONATION CHAMBER TEST CASE Daniel Hilding Engineering Research Nordic AB Garnisonen I4, Byggnad 5 SE-582 10 Linköping www.erab.se daniel.hilding@erab.se Abstract The purpose of a detonation
More informationFinite Element Method. Chapter 7. Practical considerations in FEM modeling
Finite Element Method Chapter 7 Practical considerations in FEM modeling Finite Element Modeling General Consideration The following are some of the difficult tasks (or decisions) that face the engineer
More informationCalculate a solution using the pressure-based coupled solver.
Tutorial 19. Modeling Cavitation Introduction This tutorial examines the pressure-driven cavitating flow of water through a sharpedged orifice. This is a typical configuration in fuel injectors, and brings
More information