The corpus callosum and interhemispheric communication

The corpus callosum (CC), with over 300 million fibers, is the largest white matter fiber bundle in the human brain. (It is easily identifiable in conventional MRI scans.) Topographically, it is centered along the midsagittal plane with radiations that extend to the prefrontal and frontal cortex in the anterior brain, the sensory-motor cortex in the middle and the parietal, temporal and occipital lobes in the posterior half of the brain.

This large and heterogeneous collection of fibers is responsible for interhemispheric communication. Michael Gazzaniga, a neuroscientist at Dartmouth College, has being studying the nature of this left brain- right brain communication for over 30 years. Here he explains some of his fascinating findings to Alan Alda, former hawkeye, now host of Scientific American Frontiers. And this is one of Gazzaniga's papers. (A similar account of the mysterious workings of the brain first got me interested in brain imaging. The book in question was V.S. Ramachandran's Phantoms in the Brain.)

Because of the important role it plays, the CC is the focus of many studies. Some are concerned with changes in the shape, size or structure of the CC. These changes may occur due to aging or degenerative disease. On one end of the spectrum, work is being done to provide tools to measure and monitor these changes. At the other end are the clinical studies. An example of a clinical study might be one that links the different stages of the disease or aging process with physical alterations.

White Matter Fiber Analysis

Shape, scale, orientation and position, the physical features associated with white matter fibers, can, either individually or in combination, be used to define feature spaces designed for specific end-applications. Such a treatment is useful since the quantitative analysis of white matter fibers has diverse applications, each with a different focus and objective.

In recent work, we describe a Riemannian framework in which various combinations of these features are considered. (This was presented at the ISBI 2010 conference. The slides are here, a version of the paper here.)

The framework also provides tools for computing statistical summaries of curves which enables us to perform a full statistical analysis. In the context of DTI fibers, a mean and variance that describes the essential characteristics of the fiber bundle can be used to represent a set of fibers. We can then proceed to tasks of statistical inference such as parameter estimation and hypothesis testing.

I am currently using the tools and metrics defined within this mathematical framework to show how morphological changes due to disease progression can be studied. Shape distances in tandem with distances defined within other manifolds like the shape+orientation manifold give us very encouraging results.

ISBI 2010

I'll be in Rotterdam in mid-April to present our paper entitled A Comprehensive Riemannian Framework for the Analysis of White Matter Fiber Tracts at the ISBI conference. This is the abstract:

A quantitative analysis of white matter fibers is based on different physical features (shape, scale, orientation and position) of the fibers, depending on the specific application. Due to the different properties of these features, one usually designs different metrics and spaces to treat them individually. We propose a comprehensive Riemannian framework that allows for a joint analysis of these features in a consistent manner. For each feature combination, we provide a formula for the distance, i.e. quantification of differences between fibers and a formula for geodesics, i.e. optimal deformations of fibers into each other. We illustrate this framework in the context of clustering fiber tracts from the corpus callosum and study the results from different combinations of features.

This is work I did with Anuj Srivastava and his student Sebastian Kurtek.

Topographical classification of the corpus callosum

The corpus callosum(CC) has no obvious landmarks. This is more true for the large central corpus than the more distinct genu and splenium. Methodologies for partitioning the CC are summarized here.

The Witelson scheme, the oldest, dating back to 1989, is used as a reference in this paper, to initialize bundles for clustering by Expectation Maximization (EM).

Creating DTI fiber bundles with spectral clustering

Recent work (2004-2007) at the Harvard LMI lab has shown that spectral clustering can be successfully used to create bundles from DTI fiber tracts. These clusters do not always correspond to anatomical bundles but they do to a large extent.
The picture on the right shows DTI fiber tracts extracted from the corpus callosum.
Some of my results of spectral clustering, applied to this data set, are presented below.





The clusters are consistent across 12 same-sex subjects--we get bundles from the rostrum, genu, corpus and splenium, the 4 sections of the corpus callosum, in each case. The distance measure is the mean closest point described in this paper by O'Donnell and Westin. Interestingly, a median closest point distance failed to produce more than one cluster--i.e. the distances between individual fibers were all the same in this case.