Talk
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from Talks
Fred
L. Bookstein (University of Michigan)
New
Applications of Geometry to Analysis of Brain Imagery
Recently a new methodological discipline, morphometrics, has
emerged as a combination of geometry, computer science, statistics,
and mathematical biology. The new techniques bridge two domains
of mathematics usually applied separately in medical imaging:
one, the domain of image acquisition, emphasizing physical noi
se models and the associated signal-processing task, and the
other, the domain of biometrical pattern analysis, emphasizing
the ties of image information to the larger world of covariance
structures, group averages, and scientific hypotheses . This
talk will sketch the flavor of the new discipline in two applications
to empirical investigations into ``endophrenology," the correlation
of brain form w ith behavior in disease. One application is
an algorithm for usefully parametrizin g stable localized shape
difference in the presence of substantial biological variation.
The other demonstrates a powerful modeling protocol for identifying
"the midline of the corpus callosum," an approximately
symmetric structure the shape of which turns out to be strongly
informative about embryological conditi ons associated with
the diagnosis of Fetal Alcohol Syndrome. In sketching these
applications my talk will touch on a range of classical topics
including Riemann ian geometry, analytic geometry of planes,
interpolation theory, and singularity theory.
William
Eddy (Carnegie Mellon University)
Combining Information Across Subjects
It has become common practice to average t statistics when pooling
subjects in a series of fMRI experiments. This talk will decry
this practice. I will also provide a brief review of other more
preferable methods. I will specifically advocate standard meta-analytic
methods when they are possible and Fisher's method when better
methods are not available. A single common example will be used
to illustrate each of the methods discussed.
Olivier
Faugeras (INRIA/MIT)
Reflections
on the Inverse EEG and MEG Problems
I discuss the problem of the three-dimensional reconstruction
of the electrical activity of the brain from electroencephalography
(EEG) and magnetoencephalography (MEG). I propose a variational
approach based upon three main methods and ideas. The first
one is the optimal control of systems governed by elliptic partial
differential equations, the second is the regularization of
the solutions while preserving the discontinuities (the edges),
and the third one is the use of geometric information obtained
from magnetic resonance images (MRI) to constrain the solutions
in an anatomically "reasonable'' way. Some preliminary results
of implementations of these ideas are presented.
Sheng
He (University of Minnesota)
Visual
Surfaces Representation in Human MT+ and SPL
Surface
extraction is of great importance to visual function and visually
guided action. Neurons in primate MT/V5 have been shown to be
both direction and disparity selective. Using fMRI, we demonstrate
that human MT+ respond more to two planes of oppositely moving
random dots if the two planes are placed in different stereo
depths. We also tested if the disparity sensitive areas are
capable of encoding global surface structures. Results suggest
that in addition to the MT+ areas, the Superior Parietal lobule
(SPL) is most sensitive to the global structure of visual surface.
Monica
Hurdal (Florida State University)
Quasi-conformal
Flat Maps of the Human Cerebellum
There is great interest in trying to create flat maps of the
cortical surface. It is believed that flat maps can assist in
identifying and localizing functional foci obtained from PET
and functional MRI data. Most current approaches attempt to
minimize or reduce a combination of linear, areal and angular
distortion between the flattened surface of the cortex and the
original cortical sheet. However, it is impossible to flatten
a surface without introducing linear and areal distortion. Nevertheless,
the Riemann Mapping Theorem from mathematics states that angle-preserving
(conformal) maps exist. A novel computational implementation
will be discussed which creates conformal flat maps of the cortical
surface using circle packings. This approach offers a number
of advantages over existing approaches such as no cuts need
to be introduced into the surface, the maps are mathematically
unique, maps can be created in the Euclidean and hyperbolic
planes and on a sphere, and canonical coordinate systems can
be imposed on these maps.
Seong-Gi
Kim/Kamil Ugurbil (University of Minnesota)
Are
fMRI Responses Localized to Sub-millimeter Functional Structures?
Recently
introduced fMRI techniques provide the capability of visualizing
elevat ed neuronal activity with spatiotemporal specificity
and resolution that has not be en previously available with
other non-invasive methods. Such a capability is essential for
a system level understanding of human brain function, which
posses ses unique attributes that are distinct from animal models
and cannot be investigate d with invasive techniques available
for animal studies. Despite the indispensable role of the BOLD
fMRI technique in mapping human brain function, ability of mapp
ing sub-millimeter functional structures such as cortical columns
is controversial. We have investigated spatial specificity and
resolution of fMRI using well-established anesthetized animal
models, rat forepaw stimulation and cat orientation column.
We found that columnar structures can be mapped by using metabolism-based
early negative BOLD signal or draining vessels-free perfusion-based
fMRI.
Jack
Lancaster (University of Texas Health Sciences Center
at San Antonio)
Representative
Brain Models for 3-D MR Brain Images
Our
long-term goal is to develop 3-D brain models that retain consistent
anatomical features of the group of brains from which they are
derived. Such brain models could serve as representative brains
for comparisons between groups of interest, i.e. testing for
anatomical differences between normal and disease groups. An
analysis method based on 3-D deformation fields is proposed
for developing representative brain models. The hypothesis is
that a target brain (our brain model) that represents the least
deformation effort for a group is the best overall representative
brain for the group. The process can be thought of as a two
step procedure, where the first step is to find the best target
brain within the group of brain images, followed by an optimization
process that transforms this best target brain into an optimal
brain model for the group. A target quality score to measure
deformation effort and anatomical variability was devised to
guide this processing. The complexity of the processing scheme
is O(n^2) where n is the number of brains in the group and number
of deformation fields to calculate. Even with high-speed regional
warping methods such as octree spatial normalization this would
be a lengthy process for large groups of brains. A fast algorithm
(O(n)) was found to provide similar results. A review of the
processing steps for the development of representative brain
models will be presented.
Nicholas
Lange (Laboratory for Statistical Neuroimaging and
Molecular Pharmacology Laboratory, Department of Psychiatry,
McLean Hospital and Harvard Medical School)
Analysis
of Drug Effects on Spatial Patterns of Gene Expression in MR
Neuroimaging and Microscopy
In
this talk, I will discuss recent findings on automatic identification
of c-fos gene expression in rat thalamus, amygdala and nucleus
accumbens post administration of typical and atypical antipsychotics,
a benzodiazepine and a sedative, all compared to a control condition.
I will provide background for these types of experiments, including
some current work in pharmacological magnetic resonance imaging
(phMRI). Relevant quantitative analytical considerations lead
one to question certain general methodological approaches taken
currently in similar animal and human microscopy. Additional
recent results will also be presented on one such issue: How
to count neurons in human neocortex -- presenting a challenge
to so-called ``unbiased" optical disector stereological methods.
Anthony Randal McIntosh (Rotman Research Institute
- Baycrest Ctr, University of Toronto) http://psych.utoronto.ca/~mcintosh
mcintosh@psych.utoronto.ca
Incoroporating Neurobiology into the Analysis
of Brain Imaging Data
Many approaches to the analysis of brain imaging
data have adopted conventional parametric statistics (e.g.,
t-test, ANOVA, MANOVA) for evaluation of brain imaging data.
There is a great deal of information that can be lost with such
approaches since they were developed for different purposes.
We have recently applied methods that are more suited for analysis
of systems that show characteristics similar to the brain, such
as high interdependency and high dimensionality. I will present
two of these methods, path analysis and partial least squares,
and discuss the new directions that analytic approaches need
to go in order to capitalize on the wealth of information brain
imaging can provide.
Michael
Miller (John Hopkins University)
Computational Anatomy: An Emerging Discipline
This talk with introduce geodesics on diffeomorphic
transformations for anatomic al variation and on geometric and
image transformation for growth and neoplasm development. Its
role in image matching and measuring anatomical deformation
wil l be shown through various example in brain imaging.
Partha
Mitra (Bell Labs)
mitra@bell-labs.com
A Frequency Localised Framework for Inference
in fMRI
Although fMRI time series have been subjected to a very large
number of studies, the noise models in use are generally unreliable
and inaccurate, as shown by the general scepticism about P-values.
We argue that since the noise sources in question, which are
primarily physiological in origin, are well segregated in the
frequency domain, most of the problems are obviated by confining
the inference to the frequency range relevant to the hemodynamic
response. We have developed and tested a methodology for statistical
inference as well as for exploratory analysis based on projections
of the time series data onto frequency localised basis sets,
following the framework of multitaper spectral analysis. The
associated statistical tests are both straightforward and provide
somewhat more sensible P-values, since Gaussian distributional
assumptions are more closely valid for narrowband processes
due to the central limit theorem.
Charles A. Nelson (University of Minnesota), canelson@tc.umn.edu
A Cognitive Neuroscience Perspective on Memory Development
In this talk I will illustrate the various approaches we have
adopted as a means of studying memory in infants and young children.
Here I will draw from our work with both typically developing
children and those who have might have incurred neurological
insults as a means of examing the ontogeny of memory. Work using
both event-related potentials and functional magnetic resoance
imaging will be highlighted.
Stephen Strother
(Minneapolis VA Medical Center)
The Quantitative Evaluation of Functional Neuroimaging
Experiments: The NPAIRS Data Analysis Framework
We introduce the NPAIRS (Non-parametric Prediction, Activation,
Influence and Reproducibility reSampling) data analysis framework
for evaluating the interaction between activation tasks and
the methodological choices involved in data acquisition, preprocessing,
data-analysis model selection and associated software tools.
NPAIRS provides a real-data driven alternative to simulations
and ROC curves by examining the relationship between model prediction
accuracy and activation image signal-to-noise ratios (SNR)--we
plot training-test set predictions of the experimental design
variables (e.g., scan state labels, covariates etc.; Morch et
al.,1997, Hansen et al.,1999) versus the reproducibility SNR
metrics in Strother et al. (1997). For a given spatial scale
we propose that methodological choices should be optimized by
maximizing the prediction accuracy and the reproducibility SNR
of the extracted activation images. NPAIRS also provides a Z-score
activation-image incorporating random subject effects for any
data-analysis model and a measure of each subject's relative
influence (Strother et al., 1998, 1999). We demonstrate NPAIRS
using the wide range of activation signal-to-noise ratios and
associated PAIR statistics obtained from [O-15]water PET studies
of twelve age and sex matched groups performing different motor
tasks (8 subjects/group). If time permits preliminary results
using NPAIRS to rank the importance of within-subject alignment,
temporal detrending and spatial smoothing in a fMRI task will
also be presented.
Keith
Worsley (McGill
University)
A
General Statistical Analysis for fMRI data
Many
methods are available for the statistical analysis of fMRI data
that range from a simple linear model for the response and a
global autoregressive model for the temporal errors (SPM), to
a more sophisticated non-linear model for the response with
a local state space model for the temporal errors (Purdon, et
al., 1998). We have written Matlab programs (http://www.bic.mni.mcgill.ca/users/keith)
that seek a compromise between validity, generality, simplicity
and execution speed. The method is based on linear models with
local AR(p) errors. The AR(p) model is fitted via the Yule-Walker
equations with a simple bias correction, then the parameters
are regularized by spatial smoothing. The resulting effects
are then combined across runs in the same session, across sessions
in the same subject, and across subjects within a population
by further linear models that perform a random effects analysis
in which the residual degrees of freedom are increased using
a form of regularization by spatial smoothing.
Material
from Talks
Minisymposium: Brain Imaging
2000-2001
Program: Mathematics in Multimedia
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