Mathematical Aspects of Imaging, Modelling and Visualization in Multiscale Biology

Mathematical Aspects of Imaging, Modeling and Visualization in Multiscale Biology

March 31 – April 4, 2009

The University of Texas at Austin

Austin, Texas, USA

This Workshop will be held under the auspices of the international partnership between the University of Texas at Austin and Portuguese Universities, a part of the International Collaboratory for Emerging Technologies.

Speakers	Organizers
Program	Lodging & Travel
Abstracts	Registration

Introduction

The Workshop will focus on a selected range of interdisciplinary topics handled from both mathematical and engineering applications perspectives, aimed at prompting interesting dialogue among the conveners. The target audience is mathematicians and engineers as well as graduate students interested in doing research on problems related to Mathematics, Medical Imaging, Biomechanics, Biology, and Bioengineering.

The Workshop will consist of a series of 45 minute plenary sessions, given by eight Portuguese speakers and thirteen American speakers.

Some contributed papers by PhD Students and Postdoctoral researchers will be selected to be on display during poster sessions.

Portuguese Speakers

João P. Barreto, Electrical and Computer Engineer, University of Coimbra

“Image Geometry in Medical Endoscopy by Embedding the Projective Plane into a Higher Dimensional Space”

Paulo Fernandes, Mechanical Engineer, IST Lisbon

“A Multi-scale Model of Bone Tissue Adaptation”

José Augusto Ferreira, Mathematician, University of Coimbra

“Memory in Diffusion Phenomena”

Eduardo Borges Pires, Civil Engineer, IST Lisbon

“Biomechanical Modeling of the Femoro-Acetabular Impingement of the CAM Type”

Adélia Sequeira, Mathematician, IST Lisbon

“Multiscale Modeling and Simulation in Hemodynamics”

João Manuel R.S. Tavares, Mechanical Engineer, University of Porto

“A Computer Analysis of Structures in Image Sequences: Methods and Applications”

United States Speakers

Timothy Baker, Biochemist and Molecular Biologist, University of California San Diego

“Strategies and Challenges in Three-Dimensional Reconstruction of Viruses”

Thomas Bartol, Neurobiologist, Salk Institute

“Realistic Modeling of Neuronal Cell Signaling with MCell”

Lisa Fauci, Mathematician, Tulane University

“Interaction of Elastic Biological Structures with Complex Fluids”

Irene Fonseca, Mathematician, Carnegie Mellon University

“A Higher Order Model for Image Restoration”

Ozan Öktem, Mathematician, Comsol AB and KTH - Royal Institute of Technology

“Local Tomography in Electron Microscopy”

Pawel Penczek, Molecular Biochemist, University of Texas-Houston Medical School

“Analysis of Conformational Variability of Macromolecules in Cryo-electron Microscopy”

Michael Reed, Mathematician, Duke University

“What Can Mathematics Do for Biology? Lessons from Cell Metabolism”

Kristian Sandberg, Mathematician, University of Colorado at Boulder

“Orientation Based Methods for Image Segmentation”

University of Texas at Austin Speakers

Inderjit Dhillon, Computer Scientist

“Multilevel Graph Clustering”

Ron Elber, Biochemist

“Coarse Grained Molecular Times with Non-Markovian Modeling”

Irene Gamba, Mathematician

“Statistical Charged Transport Models: Simulations and Multiscale Analysis in Heterogeneous Nano Structures”

Kristen Harris, Neurobiologist

“Analysis of Complete 3D Reconstructions of Brain Ultrastructure at High Resolution”

Pierre-Louis Lions, Mathematician (visiting from Paris Dauphine University)

“Some Examples of Mean Field Games Models”

Tinsley Oden, Mathematician

“Real-Time Control of Laser Treatment of Cancer Using Computational Models of Nonlinear Bio-Heat Transfer”

David Ress, Neurobiologist

“Analysis of High-Resolution Brain Volume Anatomies Acquired Using Magnetic Resonance Imaging”

John Wallingford, Molecular Biologist

“Visualizing Embryo Development Big & Small: In vivo 4-dimensional Imaging of Tissues, Cells, and Molecules”

Lexing Ying, Mathematics

“Butterfly Algorithm and Its Applications”

Poster Session Authors

** Poster authors: please click here to read instructions for poster presentations **

Marco Barchiesi, Mathematician, Carnegie Mellon University

“Homogenization of fiber reinforced brittle materials”
Filippo Cagnetti, Mathematician, Carnegie Mellon University

“Shape analysis with the Mumford-Shah functional”
Alberto Gambaruto, Biomedical Engineer, IST Lisbon

“Topological structures in physiological flows”

Stefan Kroemer, Mathematician, Carnegie Mellon University

“Multiscale analysis in the presence of linear differential constraints”

Daniel Simões Lopes, Biomedical Engineer, IST Lisbon
“Modeling and Visualization of Complex Biomechanical Structures by Means of Superquadric Surface

Representations”

Zhen Ma, Mechanical Engineer, University of Porto

“Organs segmentation in MR images of the pelvic cavity”

Francisco P. M. Oliveira, Mechanical Engineer, University of Porto

“Alignment of Image Data based on Geometric Information and Optimization”

Giuseppe Romanazzi, Mathematician, University of Coimbra
“A Multiscale Model for Tracking Epithelial Cells in Colonic Crypts”

Luís Miguel Francisco Santos, Biomedical Engineer, IST Lisbon
“A DXA validation of a bone adaptation model for the assessment of osteoporotic bone quality”

Pascoal Martins da Silva, Mathematician, University of Coimbra

“Modeling drug release through contact lenses”

Organizers

Chandrajit Bajaj, Computer Scientist, University of Texas at Austin

Luis Caffarelli, Mathematician, University of Texas at Austin

Isabel Narra Figueiredo, Mathematician, University of Coimbra

Andrew Gillette, Mathematician, University of Texas at Austin

Hélder Rodrigues, Mechanical Engineer, Instituto Superior Técnico, Lisbon

Program

Talks will take place in the ACES building on the campus of the University of Texas at Austin. Each talk will be a maximum of 50-55 minutes followed by time for questions. Please make note of the room assignments for each day. The schedule of talks is below or you can download a pdf of the schedule. Talk abstracts appear below.

Tuesday March 31: talks held in ACES 4.304

Morning chairs: Luis Caffarelli and Chandrajit Bajaj

Afternoon chair: Hélder Rodrigues,

8:00-8:30	Registration – ACES 4.304
8:25-8:30	Opening remarks – Chandrajit Bajaj and Luis Caffarelli
8:30-9:30	Tinsley Oden “Real-Time Control of Laser Treatment of Cancer Using Computational Models of Nonlinear Bio-Heat Transfer”
9:30-9:45	Coffee break
9:45-10:45	Kristian Sandberg “Orientation Based Methods for Image Segmentation”
11:00-12:00	Irene Fonseca “A Higher Order Model for Image Restoration”
2:00-2:45	Inderjit Dhillon “Multilevel Graph Clustering”
2:45-3:00	Coffee break
3:00-4:00	Irene Gamba “Statistical Charged Transport Models: Simulations and Multiscale Analysis in Heterogeneous Nano Structures”
6:00-6:30	ACES Connector Lobby: Presentation of posters (5 min each) by M. Barchiesi, F. Cagnetti, A. Gambaruto, S. Kroemer, D. Lopes. (Beverages will be served)
6:30-8:00	ACES Connector Lobby: Reception for registered participants and invited guests (all posters will be on display)

Instructions for Poster Presentations: Poster presentations will be placed on vertical boards with maximum display dimensions of 900 mm X 1200 mm (A0-portrait, about 35 inches x 47 inches). The poster should contain the title of the presentation, the authors’ names and authors’ affiliations.

Wednesday April 1: talks held in ACES 4.304

Morning chair: Isabel Narra Figueiredo

Afternoon chair: Eduardo Borges Pires

8:30-9:30	Adélia Sequeira “Multiscale Modeling and Simulation in Hemodynamics”
9:30-9:45	Coffee break
9:45-10:45	Eduardo Borges Pires “Biomechanical Modeling of the Femoro-Acetabular Impingement of the CAM Type”
11:00-12:00	João P. Barreto “Image Geometry in Medical Endoscopy by Embedding the Projective Plane into a Higher Dimensional Space”
1:30-2:30	David Ress, "Analysis of High-Resolution Brain Volume Anatomies Acquired Using Magnetic Resonance Imaging”
2:30-2:45	Coffee break
2:45-3:45	Michael Reed “What Can Mathematics Do for Biology? Lessons from Cell Metabolism”
6:00-6:30	ACES Connector Lobby: Presentation of posters (5 min each) by Z. Ma, F. Oliveira, G. Romanazzi, L. Santos, P. Silva (Beverages will be served)
6:30-8:00	ACES Connector Lobby: Poster session (all posters will be on display)

Thursday April 2: talks held in ACES 4.304

Morning chair: Adélia Sequeira

Afternoon chair: Andrew Gillette

8:30-9:30	Paulo Fernandes “A Multi-scale Model of Bone Tissue Adaptation”
9:30-9:45	Coffee break
9:45-10:45	Kristen Harris “Analysis of Complete 3D Reconstructions of Brain Ultrastructure at High Resolution”
11:00-12:00	José Augusto Ferreira “Memory in Diffusion Phenomena”
1:30-2:30	Thomas Bartol “Realistic Modeling of Neuronal Cell Signaling with MCell”
2:30-2:45	Coffee break
2:45-3:45	João Manuel R.S. Tavares “A Computer Analysis of Structures in Image Sequences: Methods and Applications”
6:00 pm	O’s Cafe: Banquet for registered participants and invited guests.

Friday April 3: talks held in ACES 6.304

Morning chair: Chandrajit Bajaj

Afternoon chair: Diogo Aguiar Gomes

8:30-9:30	Ozan Oktem, “Local Tomography in Electron Microscopy”
9:30-9:45	Coffee break
9:45-10:45	Timothy Baker, “Strategies and Challenges in Three-Dimensional Reconstruction of Viruses”
11:00-12:00	Pawel Penczek, “Analysis of Conformational Variability of Macromolecules in Cryo-electron Microscopy”
1:30-2:30	John Wallingford “Visualizing Embryo Development Big & Small: In vivo 4-dimensional Imaging of Tissues, Cells, and Molecules”
2:30-2:45	Coffee break
2:45-3:45	Ron Elber “Coarse Grained Molecular Times with Non-Markovian Modeling”
4:00-4:30	ACES 2.404a: Tour of the TACC Visualization Lab

Saturday April 4: talks held in ACES 2.402

Morning chair: Luis Caffarelli

8:30-9:30

Lisa Fauci “Interaction of Elastic Biological Structures with Complex Fluids”

9:45-10:45

Lexing Ying “Butterfly Algorithm and Its Applications”

11:00-12:00

Pierre-Louis Lions “Some Examples of Mean Field Games Models”

Abstracts

Timothy Baker: Strategies and Challenges in Three-Dimensional Reconstruction of Viruses

The use of image processing to reconstruct the three-dimensional structures of viruses from images of unstained, frozen-hydrated specimens recorded in transmission electron microscopes has progressed very rapidly, especially in the past five years. In a few instances, the structures of viruses with icosahedrally-symmetric capsids have reached near atomic resolution (<4 Å), which is high enough to clearly follow the backbones of polypeptide chains and to distinguish bulky, amino acid residues. The talk will provide a brief overview of the broad field of virus structure determination and highlight some of the current challenges such as finding ways to drastically reduce the timeframe between acquisition of primary image data to computation of reliable, high-resolution structural results of both highly-symmetric and asymmetric viruses and finally visualization and interpretation of these 3D volumetric data.

João P. Barreto: Image Geometry in Medical Endoscopy by Embedding the Projective Plane into a Higher Dimensional Space

Endoscopy is broadly employed in medicine enabling minimally invasive procedures with little or no injury to healthy organs and tissues. Such procedures are very difficult to execute and even the best trained professionals make mistakes with inevitable consequences for the patient. Systems for computer aided surgery (CAS), relying on the processing of intra-operative endoscopic video, can be extremely helpful in changing this scenario.

Unfortunately medical endoscopes are non-conventional cameras with strong non-linear distortions. Unlike perspective cameras, the projection is non linear in homogeneous coordinates which precludes the application of standard computer vision concepts and techniques. This is a serious obstacle for the development of image-based CAS systems. In this talk we propose to overcome the problem by lifting the projective plane using Veronese maps. The embedding in a higher dimensional space provides an excellent insight about the image geometry, and enables us to prove the existence of a projection matrix, planar homography and essential/fundamental matrix. These results are explored to establish camera calibration methods that take into account the operational constraints inherent to the medical environment. Additionally we show how the calibration can be helpful in enhancing doctor's perception of the scene and registering pre-operative models to intra-operative images.

Thomas Bartol: Realistic Modeling of Neuronal Cell Signaling with MCell

Biochemical signaling pathways are integral to the information storage, transmission, and transformation roles played by neurons in the nervous system. Far from behaving as well-mixed bags of biochemical soup, the intra- and inter-cellular environments in and around neurons are highly organized reaction-diffusion systems, with some subcellular specializations consisting of just a few copies each of the various molecular species they contain. For example, glutamtergic dendritic spines in area CA1 hippocampal pyramidal cells contain perhaps 100 AMPA receptors, 20 NMDA receptors, 10 CaMKII complexes, and 5 free Ca++ ions in the spine head. Much experimental data has been gathered about the neuronal signaling pathways involved in processes such as synaptic plasticity, especially recently, thanks to new molecular probes and advanced imaging techniques. Yet, fitting these observations into a clear and consistent picture that is more than just a cartoon but rather can provide biophysically accurate predictions of function has proven difficult due to the complexity of the interacting pieces and their relationships. Gone are the days when one could do a simple thought experiment based on the known quantities and imagine the possibilities with any degree of accuracy. This is especially true of biological reaction-diffusion systems where the number of discrete interacting particles is small, the spatial relationships are highly organized, and the reaction pathways are non-linear and stochastic. Biophysically accurate computational experiments performed on cell signaling pathways is a powerful way to study such systems and to help formulate and test new hypotheses in conjunction with bench experiments.

MCell was designed for the purpose of simulating exactly these sorts of cell signaling systems. Here I will present an introduction to the computational algorithms employed in MCell Version 3, and how to use MCell's Model Description Language to build 3D models of virtually any biochemical signaling pathway in the context of its cellular ultrastructure. Finally, I will introduce fundamental concepts of cell signaling processes in organized, compact spaces that have been studied using MCell including: 1) glutamatergic synaptic transmission and calcium dynamics in hippocampal area CA1 dendritic spines; and 2) Presynaptic calcium dynamics and modulation of release probability in Schaffer collateral multisynaptic boutons.

Ron Elber: Coarse Grained Molecular Times with Non-Markovian Modeling

Milestoning is a combination of the reaction path approach and molecular dynamics simulations that uses coarser representation of space and time to extract a stochastic model and compute rates in complex systems. The theory and the algorithm will be described and applications to peptide folding and conformational transitions in proteins will be discussed.

Lisa Fauci: Interaction of Elastic Biological Structures with Complex Fluids

The biofluiddynamics of reproduction provide wonderful examples of fluid-structure interactions. Peristaltic pumping by wave-like muscular contractions is a fundamental mechanism for ovum transport in the oviduct and uterus. While peristaltic pumping of a Newtonian fluid is well understood, in many important applications the fluids have non-Newtonian responses. Similarly, mammalian spermatozoa encounter complex, non-Newtonian fluid environments as they make their way through the female reproductive tract. The beat form realized by the flagellum varies tremendously along this journey. We will present recent progress on the development of computational models of pumping and swimming in a complex fluid. An immersed boundary framework is used, with the complex fluid represented either by a continuum Oldroyd-B model, or a Newtonian fluid overlaid with discrete viscoelastic elements.

Paulo Fernandes: A Multiscale Model of Bone Tissue Adaptation

Bone is a hierarchical structural material, and several organizational levels can be identified from macroscale to nanoscale. The two top levels corresponding to the entire bone and trabecular structure respectively show a suitable distribution of physical properties, such as bone density and corresponding mechanical properties, to achieve the functional requirements of bone tissue.

In this work a multi-scale model is presented, where the process of bone tissue adaptation is described with respect to functional demands to obtain the bone apparent density distribution (at the macroscale) and the trabecular structure (at the microscale). At global scale bone is assumed as a continuum material characterized by equivalent mechanical properties. At local scale, a periodic cellular material model approaches bone trabecular anisotropy. The law of bone remodeling assumes that bone adapts in order to satisfy a multi-criteria objective based on structural stiffness and metabolic cost of bone formation. Biological requirements, such as porosity and permeability constraints, are considered for a better representation of bone tissue adaptation. Computationally, the multi-scale model implies the iterative solution of one problem at macro scale and many problems at local scale to define the bone microstructure (local problem). Since the local problems can be uncoupled, the solution can be obtained using parallel computing techniques.

The model is able to provide a density distribution that fairly approximates the real femur bone at macroscale. At microscale the microstructures give a good mechanically characterization of the local microstructure of trabecular bone with the respective anisotropic properties. This model represents a new approach to computational prediction of bone adaptation, both for apparent density and trabecular architecture mechanical behavior. Thus, it can be a valuable tool to medical diagnoses, to gain insight into the fine structure of bone, namely on osteoporosis, as well as to support scaffolds design in tissue engineering.

José Augusto Ferreira: Memory in Diffusion Phenomena

This talk focuses on the mathematical study from analytical and numerical view points of some non Brownian models for diffusion phenomena within different fields of applications, namely drug release, heat conduction and reaction-diffusion phenomena. Those models were introduced in the literature to overcome some discrepancies between experimental data and simulation results obtained using classical models. From analytical point of view stability estimates that allow the well-posedness of the mathematical problems are established. Numerical methods that lead to to approximations of analytical solutions are studied.

Irene Fonseca: A Higher Order Model for Image Restoration

The higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is proposed, and it is proved analytically that the higher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals. This is work in collaboration with Gianni DAl Maso, Giovanni Leoni and Massimiliano Morini.

Irene Gamba: Statistical Charged Transport Models: Simulations and Multiscale Analysis in Heterogeneous Nano Structures

Statistical and stochastic charged transport models given by kinetic systems, exhibit fundamental differences in terms of their possible steady states under strong relative forces due to the inhomogeneity an nano-scale, such as short based channels. The corresponding reduced macroscopic model will depend on the nature of their interaction as well on the boundary conditions. We will discuss the difference between collisional models BTE (Boltzmann Transport Equations) vs stochastic ones FP (Fokker Plank) in the applications to short channels and their corresponding macroscopic approximations, both by means of numerical simulations and asymptotic analysis methods.

Tinsley Oden: Real-Time Control of Laser Treatment of Cancer Using Computational Models of Nonlinear Bio-Heat Transfer

Collaborators: David Fuentes, Yusheng Feng, J. M. Bass, Ivo Babuska, Chandrajit Bajaj, Ken Diller, J. C. Browne, John Hazle, Jason Staflord, and Andrea Hawkins

Cancer cells die when heated to around 44º C or higher for sustained periods of time. This fact is the basis for several cancer therapies such as laser treatments in which a concentrated power source is provided to ablate cells in tumors in such organs as the prostate. The challenge in these therapies is to supply enough heat to eradicate the cancer while minimizing damage to healthy tissue. This lecture describes a dynamic control system in which a computational model of bio-heat transfer in heterogeneous living tissue is used to guide remotely the location, frequency, and power of a laser used to heat tissue in or near prostate tumors. The actual therapy, performed at M. D. Anderson Cancer Center in Houston, Texas, on a laboratory animal, is monitored by a MRTI device that can produce MRI images as well as 3D temperature fields. The MRTI images are sent to ICES in Austin where a 3D finite element model of the prostate is generated and a temperature field is computed using a nonlinear bio-heat transfer model. Temperature measurements are used to calibrate the model. The predicted temperature fields are used to control the laser location and power to optimize the process. A cell damage model is developed to describe cell death as a function of time and temperature, and this is used in the adaptive-control strategy. Several generalizations of these methodologies are also described, including the effects of nano-shells and the derivation of more general models of tumor growth.

Ozan Öktem: Local Tomography in Electron Microscopy

We present a new local tomographic algorithm applicable to electron microscope tomography. Our algorithm applies to the standard data acquisition method, single-axis tilting, as well as to more arbitrary acquisition methods including double axis and conical tilt. Using microlocal analysis we put the reconstructions in a mathematical context, explaining which singularities are stably visible from the limited data given by the data collection protocol in the electron microscope. We provide reconstructions of real specimens from electron tomography data to show the merits of local tomography. Finally we conclude with a discussion of the possible role of microlocal analysis within variational regularisation and Bayesian inference.

Eduardo Borges Pires: Biomechanical Modeling of the Femoro-Acetabular Impingement of the CAM Type

The conflict known as femoro-acetabular impingement depends on an abnormal morphological relation between the femoral head and the acetabular cavity. The “Cam” type impingement is due to the presence of a non-spherical portion of the femoral head, usually located at the antero-superior quadrant of the region of transition with the anatomical neck. This asphericity may exert an excessive pressure on the acetabular cartilage during flexural movements and/or internal rotation. This abnormal compression may occur in sport or in some cases even in day-by-day activities, particularly in young individuals. The objective of this study is to evaluate the order of magnitude of the normal and tangential stresses at the cartilage of the femoral head as a result of the abnormal contact between the different tissues.

In this paper a 2-D finite element model of the hip joint is analyzed. The distinguishing anatomical structures are: the head and the anatomical neck of the femur, the femoral cartilage, the acetabulum, the acetabular cartilage and the cotyloid edge. To obtain the finite element mesh, use was made of arthoscopic magnetic resonance images (MRA). The region of interest consists of a transversal-oblique cut of the hip joint containing the axis of the anatomical neck. The different structures of the corresponding radial image were manually segmented with spline curves to obtain the 2-D geometrical model. The image segmentation was performed with the software Blender3D and the finite element mesh was obtained with CUBIT. Quadrilateral elements were used for each structure of the model. Boundary and interface conditions were prescribed. With respect to the interface conditions, definition of the contact areas between the femoral cartilage and the acetabular cartilage and the cotyloid edge was required. Applied loads related to the compression of the femur on the cotyloid cavity and with the internal rotation movement were considered.

This work is part of a more general study that has the purpose of showing that the Cam type femoro-acetabular conflict, i.e. the lack of sphericity of the femur head, with the cephalic radius growing from the equator to the region of transition neck/head, corresponds to an increased risk of osteoarthritis of the hip that may be prevented by anticipated surgery or, at least, by reduction or modification of the physical activities that are decisive in this conflict.

Michael Reed: What Can Mathematics Do for Biology? Lessons from Cell Metabolism

Biological systems are complex and difficult to understand because they were selected, not designed. The purpose of mathematical models is not to reproduce what is currently known, but to allow in silico investigation of biological hypotheses that would be difficult, expensive, or unethical to conduct experimentally. However, the details really matter, so overly simplified models that present nice mathematical questions may not advance biological understanding. Examples will be discussed from recent work on one-carbon metabolism, glutathione synthesis, and dopamine metabolism.

David Ress: Analysis of High-Resolution Brain Volume Anatomies Acquired Using Magnetic Resonance Imaging

It is often useful to segment brain tissue into gray matter and white matter in the cerebral cortex. A variety of image processing schemes have been implemented in various packages (e.g., FreeSurfer and FSL) to perform such segmentations, but all of them require extensive interaction with an expert human operator. In fact, tedious manual editing of the segmentation is generally required if there is a need for high precision in the segmentation. All of these problems are strongly exacerbated at high spatial resolution, e.g., voxel sizes <1 mm.

We have been examining the issues associated with segmenting brain volumes collected with 0.6—0.7-mm voxels. The problems include multi-scale spatial inhomogeneity patterns associated with surface-coil arrays, and substantial spatial variations in tissue contrast between the gray and white matter. We show some simple, largely manual methods for reducing these problems that greatly improve the quality of subsequent automatic segmentations. Our results may form the basis for improvements to automatic segmentation techniques.

Kristian Sandberg: Orientation Based Methods for Image Segmentation

The Line Filter Transform (LFT) and the Orientation Filter Transform (OFT) are two recently proposed non-linear filtering techniques for image enhancement and segmentation. Areas of applications has so far included biological, medical, and seismic imaging.

The LFT is particularly effective for enhancing curve-like structures of low-contrast in noisy data sets. The LFT can also be used for generating an orientation field associated with an image. Orientation fields can be remarkably uniform along structures of weak or non-uniform contrast. The OFT can be used for finding correlations in the orientation field and detect objects in situations when the contrast of the objects may prevent the usage of more traditional segmentation tools.

In this talk we will review these transforms and also discuss enhancements and generalizations to these techniques that will allow us to segment a broad variety of shapes and structures. The techniques will be illustrated by segmenting challenging data sets of cellular structures collected by electron microscopy.

Adélia Sequeira: Multiscale Modeling and Simulation in Hemodynamics

Hemodynamics is the study of the forces and physical mechanisms associated with blood flow in the cardiovascular system. Hemodynamic features such as flow separation, flow recirculation, and low and oscillatory wall shear stress are believed to play important roles in the localization and development of vascular diseases such as atherosclerosis, cerebral aneurysms, post-stenotic dilatations and arteriovenous malformations. Over the past few years, developments in computational science and technology have become increasingly important in the progress of biomedical research and predictive biomedicine. The advancements in the power of modern computers along with the progress in imaging, visualization and geometry reconstruction techniques, as well as the improvement of sophisticated numerical algorithms, allow for the development and analysis of highly complex mathematical models. The final goal is to set up patient-specific models and simulations incorporating data and measurements taken from each single patient, that will be able to predict the results of medical diagnosis and therapeutic planning with reasonable accuracy and using non-invasive means. According to the most recent statistics, cardiovascular diseases represent the major cause of death in developed countries. An increasing demand from the medical community for scientifically rigorous and quantitative investigations of cardiovascular diseases has given a major impulse to the development of mathematical models and numerical tools for the computer simulation of the human cardiovascular system, in both healthy and pathological states. However, the circulatory system is highly integrated and modeling its various functions is an incredibly challenging problem, which still requires many fundamental issues to be addressed.

In this talk some recent mathematical models of the cardiovascular system will be introduced and analyzed. The geometrical multiscale approach, consisting in coupling a hierarchy of models with different levels of complexity and detail will be discussed and some numerical simulations illustrating its effectiveness will be shown. A few test cases of clinical interest will also be presented.

João Manuel R.S. Tavares: A Computer Analysis of Structures in Image Sequences: Methods and Applications

The computer analysis of structures in image sequences is a very complex and challenging matter as it usually involves automatic tasks for detection, matching, tracking, motion analysis, deformation estimation as well as 3D shape reconstruction. Despite its inherent difficulties, this computational analysis provides a wide range of important applications in our society such as is the case of medical diagnosis systems, surveillance systems, tools used to develop virtual reality environments, biomechanical modeling, in addition to simulation and bioengineering systems.

As a result of the extent of the purposes of this vast process, several difficulties can arise, such as is the case of the simultaneous analysis of manifold structures, cases of temporary occlusion of the structure from the image scene or even its definitive disappearance, alterations of the viewpoints which have been taken into consideration or alternatively, of the illumination conditions, or even of the non-rigid deformations that non-rigid structures may undergo along image sequences.

In this presentation, we will provide an overview of several of the methods that we have developed in order to analyze structures in image sequences; more specifically, those which are used for the segmentation, tracking and matching of images, as well as the estimation of the deformation involved between images and the 3D shape reconstruction from images. Some application examples will be presented which take into consideration medical, face, traffic and surveillance images amongst others.

Lexing Ying: Butterfly Algorithm and Its Applications

Oscillatory integral transforms and equations arise in many direct and inverse problems pertaining to wave propagation phenomena. Examples abound in fields including seismic imaging, acoustic and electromagnetic wave scattering, and radar imaging. However, the rapid
evaluation of these transforms is an challenging task due to the oscillatory nature of the kernel.

In this talk, we first review the butterfly algorithm, which was recently developed as a general approach for the rapid evaluation of these oscillatory integrals. However, sometimes the practical efficiency of the butterfly algorithm is limited by its high preprocessing time and high storage requirement. In the second part of this talk, we discuss two applications: (1) sparse Fourier transform and (2) partial Fourier transform, where in each case these constraints can be removed by using tools such as tensor product decomposition and non-standard Chebyshev interpolation.

Lodging and Travel Info

Travel arrangements and booking are the responsibility of the individual participants. The workshop will begin at 9am on March 31 and end at 5pm on April 4.

Arrival and Departure

The Austin Bergstrom International Airport (AUS) is the closest airport to Austin and the University of Texas. For transportation to and from the airport, feel free to take a taxi or the Super Shuttle. Super Shuttle can be reached at (512) 258-3826 or 1-800-BLUE VAN or online at http://www.supershuttle.com/ or you can book a ride upon arrival.

Lodging

We have reserved a block of rooms for this conference at the Extended Stay America Suites located at 601 Guadalupe St. for arrival beginning 03/30/09 and check out by 04/05/09. The phone number for the hotel is (011) 512-457-9994. To get the special conference rate, please specify mention the conference code "UT Mathematics." The rate is $80.00 per night plus city taxes. You must contact the hotel directly to receive this rate. It is not available through their online booking system.

Extended Stay America has restaurants, grocery stores and other conveniences nearby. To see their website visit:

http://www.extendedstayamerica.com/minisite/?HotelID=842

Local Transportation

For transportation to campus, the Capitol Metro Airport Flyer (#100) bus route (inbound) stops one block from the Extended Stay America hotel at 6th & Lavaca approximately every 35 minutes. The fare is $0.75 per trip or $1.50 for a 24 hour pass on any Capital Metro bus. The #100 bus stops on the University campus at Dean Keeton and Speedway, near the math building (RLM) and one block north of the conference location (ACES). The schedule of the #100 route and map is available here:

http://www.capmetro.org/riding/schedules.asp?f1=100

Many other bus routes service the University from Congress avenue, a few blocks east of the hotel, including routes 1L, 1M, 5, and 7. For more information, visit the Capital Metro website:

http://www.capmetro.org/riding/schedulesandmaps.asp

Maps of the UT campus are available here:

http://www.ma.utexas.edu/dev/math/Maps_and_Directions/

Registration

Registration for the workshop is closed. Non-registered participants are welcome to attend the talks but are asked to yield seats to registered participants as space is limited.