Quantitative white matter fiber analysis: a short history (Part III)

Part III: Quantitative tract-based analysis

This is the third post in this three part series. Parts I and II are here
and here.


It is useful to classify white matter data analysis in the three decades that followed the introduction of the first MRI scans as volume-based or tract-based. The preprocessing path flows and possibilities for data interpretation differ in these two approaches.

Volume-based Anatomical structures or regions of interest are treated as volumes
and quantitative information is smoothed or averaged in such a way that the local variation
in individual tracts is not preserved. The white matter structures are usually segmented by thresholding FA maps though fiber tracts have also been used. Group-wise registration for population studies may be done at the voxel level or across individual volumes. A voxel-based coordinate system is used in the first case and a structure-based coordinate system in the second.

Tract-based The emphasis is on fiber tracts and parameters that vary along a fiber or anatomically defined bundle. Diffusion indices such as FA and physical descriptors such as shape are typically studied to assess fiber integrity or changes due to disease.



Tract-based image analysis was made possible only after the first tractography algorithms were introduced. In 1999, Mori et al. ushered in tract-based image analysis by reconstructing fiber pathways in a rat brain. Improvements to the basic tractography algorithm and work in clustering paved the way for data analysis. These three stages of what is a developing field are summarized below.

I) Tractography
Tractography or fiber tracking, as the name suggests, is a way to follow the direction of the local white matter diffusion from voxel to voxel. For DTI, the simplest algorithms follow the direction of the principal diffusion tensor eigenvector in a deterministic fashion. The reconstruction process, which includes curvature thresholds and other termination criteria, generates a tract or streamline. More sophisticated approaches include interpolations for smoother pathways, the use of anatomical and topological constraints to guide the tracking and ways to deal with the uncertainty at each voxel due to noise and registration errors.
Streamline tractography is also used in conjunction with high angular resolution (HARDI) methods.

II) Clustering
The mass of DTI fibers rendered was not immediately available for analysis. To organize and pare them down into meaningful fiber tracts, clustering was used and this led to a study of these methods.

III) Mathematical Frameworks
(Due to the length of this post, I will cover the data analysis frameworks in my next post.)

Bibliography
Mori, S., Crain, B. J., Chacko, V. P. and Van Zijl, P. C. M. (1999), Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Annals of Neurology, 45:265–269.

Quantitative white matter fiber analysis: a short history (Part II)

Part II: Imaging

This is the second of three parts. Parts I and III are here and here.


With the advent of soft tissue imaging technology--computed tomography (CT) in 1972 and magnetic resonance imaging (MRI) in 1977--it was possible to examine living brains. In 1982, physicians saw multiple sclerosis (MS) lesions for the first time in a live patient. Since then, clinicians have increasingly relied on brain scans for diagnosis and treatment. With this in vivo technology, disease progression in patients could be tracked by physicians and researchers, either individually, or as part of a longitudinal study of cohorts. This has led to a better understanding of white matter degenerative disease and has improved treatment options.

The MR signal can be assessed in different ways and the 1990s saw the emergence of two important MRI modalities. The first, Seiji Ogawa's 1990 proposal to use contrasts in blood oxygen response to map changes in brain activity, led to the development of functional magnetic resonance imaging (fMRI). The ability to view the brain in real time was a big step forward; it enabled us to study brain function and is responsible for the widespread use of fMRI among clinical neurologists, behavioral scientists, neuroscientists and others.

Diffusion tensor magnetic resonance imaging (DTI) was the second important MRI modality introduced. Water constitutes a big part of living tissue--white matter is 72% water--and the physical flow of fluid is described by a diffusion process. In 1994, Peter Basser, James Matiello and Denis Le Bihan, in a landmark paper, proposed a tensor model for diffusion where the flow of water was described by the magnitude and direction of the principal eigenvector at each image voxel. White matter fibers are inherently anisotropic and the first applications of DTI were studies of neural connectivity where fibers were tracked from end to end. Since the resolution of DTI is at the cellular level, it was also possible to detect disease--through indices such as fractional anisotropy (FA)--before it appeared in conventional MRI scans. Normal appearing white matter (NAWM) in MS is one example where compromised integrity manifests through lower FA values.

A second-order tensor model is adequate for DTI reproductions of coherent fiber tracks but in cases where fibers meet or cross, only one of these directions is retained. DTI tractography of callosal fibers, where the lateral projections are attenuated, is illustrative of this limitation. To overcome this shortcoming, high angular resolution diffusion imaging (HARDI) images acquired in several spatially uniform directions has been used. An orientation distribution function (ODF) that can model multiple maxima representing the different fiber directions replaces the simple tensor model at each voxel. HARDI datasets offer better resolution for important DTI applications such as connectivity studies and preoperative investigations.

Quantitative white matter fiber analysis: a short history (Part I)

Part I: Histological investigation
This is the first post in a three part series. Parts II and III are here and here.


The modern scientific study of white matter has its roots in the 19th century when links were being established between mental dysfunction and neuroanatomy. Correlations made between postmortem abnormalities in the brains of mental patients and clinical evaluations while they were living led to important discoveries. The identification of the arcuate fasciculus as a language pathway that connected the two language centers, the Broca and Wernicke regions, is one famous example. In that case, Carl Wernicke, who was developing language network models, made the association between lesions in the arcuate fasciculus and the various aphasias he had observed.

The impetus from these investigations crossed over to other developments. Theodor Meynert, the reputed neuroanatomist, had classified prominent white matter tracts or fasciculi, as they were known, based on the kinds of connections they made. Burdach and Déjérine published postmortem atlases, and both prominently included white matter dissections. New techniques for histopathological analysis were introduced. Notable among these was Camilio Golgi's staining method and Santiago Ramón y Cajal's use of it in his histolgical studies of nerve fibers.

Quantitative white matter fiber analysis benefited from these cumulative efforts which made studies in fiber thinning, demyelination and microstuctural damage possible. Today, postmortem dissections still give the most precise quantitative assessments.


Note of appreciation: This write-up was compiled based partly on Marco Catani's--I have pointed him out before--voluminous publications. He writes exceedingly well on the subject of language networks and related themes.

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.

USA yesterday, France today

The interlude is now over and I am back to overcast Rennes. A world away in the Florida bible belt, Anuj Srivastava is doing very interesting work with Riemannian shape spaces and one of its applications is to DTI white matter fibers. In working with anatomical brain data sets, I have found that for successful classification, we need to use a combination of physical features. So although Dr Srivastava's primary interest is in shape spaces, some of our work in the last year has been to define joint manifolds which can be used for a variety of classification tasks--clustering, labeling, atlas building and quantitative analysis for differential diagnosis. These manifolds may be extended to enable joint analysis that uses not just physical features but also scalar functions.

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.