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IPAM gratefully acknowledges support for participants from the Center for Imaging Science at Johns Hopkins University.

Graduate Summer School: Mathematics in Brain Imaging

July 12 - 23, 2004

Program Poster PDF

Organizing Committee

Michael Miller (Johns Hopkins University)
Thomas Nichols (University of Michigan)
Stanley Osher (IPAM)
Russell Poldrack (UCLA)
Paul Thompson (UCLA)

Scientific Background

This two-week intensive workshop will focus on mathematical techniques that can be applied to brain images to measure, map and model brain structure and function. Experts who are pioneers in medical image analysis will describe the mathematics used in brain imaging today. Topics will range from modeling anatomical structures in MRI scans, and mapping connectivity in diffusion tensor images, to statistical analysis of functional brain images from fMRI, EEG, and MEG. Current applications in radiology and neuroscience will be highlighted, as well as new directions in the mathematics of structural and functional image analysis. Mathematical topics covered will include computational anatomy, statistical analysis of functional images and time-series, ICA and random field theory, metric pattern theory, differential geometry, and computer vision approaches used in computational anatomy and functional imaging. Software implementing a wide range of algorithms will also be demonstrated, and tutorial notes will be provided. Talks will be of interest to newcomers and experts in the field.


Week 1: Computational Anatomy (July 12 - 16, 2004)

The first course will cover mathematical methods for extracting, representing and analyzing the shapes of biological structures in brain images. These methods show enormous promise in understanding how diseases such as Alzheimer's, schizophrenia, tumor growth and abnormal development emerge in the brain, and help in investigating their effects. Deformable models also help understand how biological structures, such as the brain during surgery, change dynamically over time. They can also capture statistics on how anatomy and physiology vary in healthy and diseased populations. We will cover the mathematics and algorithms to model anatomical elements in the brain as parameterized manifolds. Methods for comparing these structures will be outlined, including flat mappings of the cortex, conformal mappings, and high-dimensional image registration using elastic and fluid mappings. Statistical techniques will be described that combine geometrical models of anatomy and make inferences about disease effects, anatomical connectivity, and brain changes over time. We will introduce the underlying mathematics as well as its applications, drawing on techniques from differential geometry and topology, tensor mapping, non-linear image registration and segmentation, metric pattern theory, and random field theory.

Week 2: Functional Brain Mapping (July 19 - 23, 2004)

This second one-week course will cover the mathematics of functional brain imaging. Diverse mathematical techniques are now widely used for analyzing functional images of the brain. These include the analysis of time-series of images from functional MRI scanning, positron emission tomography, as well as MEG, EEG, and optical imaging of the cortex. Each technique has given rise to sophisticated mathematics for detecting and analyzing the underlying features in these images. Methods will be outlined for Bayesian analysis of fMRI time-series, as well as statistical analysis using ICA and PCA, random field theory, and integration of multiple functional brain imaging techniques.


John Ashburner (Institute of Neurology)
Nicholas Ayache (INRIA Sophia Antipolis)
Christian Beckmann (Oxford University)
David Boas (Massachusetts General Hospital)
Edward Bullmore (Cambridge University)
Richard Buxton (University of California at San Diego)
Tony Chan (UCLA)
Mark Cohen (UCLA)
John Csernansky (Washington University)
Anders Dale (Massachusetts General Hospital)
Jan de Leeuw (UCLA)
Mathieu Desbrun (University of Southern California)
Ivo Dinov (UCLA)
James Duncan (Yale University)
Steve Engel (UCLA)
Olivier Faugeras (INRIA Sophia Antipolis)
Bruce Fischl (Massachusetts General Hospital)
James Gee (University of Pennsylvania)
Chris Genovese (Carnegie Mellon University)
Guido Gerig (University of North Carolina)
Anil Hirani (California Institute of Technology)
Darryl D. Holm (Los Alamos National Laboratory)
Monica Hurdal (Florida State University)
P. S. Krishnaprasad (University of Maryland)
Richard Leahy (University of Southern California)
Thomas Liu (University of California at San Diego)
Jean-Francois Mangin (CEA Saclay, France)
Randy McIntosh (University of Toronto)
Michael Miller (Johns Hopkins University)
Tom Mitchell (Carnegie Mellon University)
Susumu Mori (Johns Hopkins University)
David Mumford (Brown University)
Thomas Nichols (University of Michigan)
Douglas Noll (University of Michigan)
Will Penny (UCLA)
Jerry Prince (Johns Hopkins University)
J. Tilak Ratnanather (Johns Hopkins University)
David Rex (UCLA)
Denis Riviere (CEA Saclay, France)
Guillermo Sapiro (University of Minnesota)
David Shattuck (UCLA)
Steve Smith (Oxford University)
Ken Stephenson (University of Tennessee,Knoxville)
Steven Strother (University of Minnesota)
Jonathan Taylor (Stanford University)
Paul Thompson (UCLA)
Art Toga (UCLA)
Alain Trouvé (Ecole Normale Supérieure, France)
David van Essen (Washington University)
Lei Wang (Washington University/School of Medicine)
Thomas D. Wickens (University of California at Berkeley)
Keith Worsley (McGill University)
Laurent Younes (Ecole Normale Supérieure, France)
Alan Yuille (UCLA)

Other Links and Events

Application For Funding/Registration

Registration is now closed and we are no longer accepting applications for funding. We are very gratified by the tremendous response of the the scientific community to this program. Because of this large response and space considerations we can no longer accept registrations. In addition there is a waiting list for any potentially available slots. We welcome your interest in IPAM programs. Check this website for updates about online program materials and other options.

Contact Us:

Institute for Pure and Applied Mathematics (IPAM)
Attn: MBI2004
460 Portola Plaza
Los Angeles CA 90095-7121
Phone: 310 825-4755
Fax: 310 825-4756
Email: ipam@ucla.edu
Website: http://www.ipam.ucla.edu/programs/mbi2004/

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