Tuesday, November 30, 2010

Offshoring work for medical diagnosis

A Wall Street Journal blog article headline states: India is benign for radiologists. It turns out that:

... reading such images relies heavily on what the two economists call “tacit knowledge.” Pattern-recognition software, which could make the work routine, doesn’t work very well in identifying malignancies and other problems,

The paper the blog refers to, was of course, talking about clinical diagnosis but one step removed from this is medical image analysis. Studies usually require databases (some very large) of subjects/cohorts who fit a common description. We might be quite far from full automatic diagnosis, but tasks can be broken down and piecemeal solutions can cetainly be outsourced. (I've been tempted more than once to go this route with the data I use or would use if only I could process them all.)

Suppose we want to build a database of twin brains or multiple sclerosis brains or whatever. Some of the tasks that are routine and could be outsourced are: registering the brains to a common template, segmenting specific sections of anatomy, representing the data in a certain way (in a representation space). Now with close supervision someone with basic training could easily do this. So the problem might be that there are not enough people who can supervise such work. And the people who can have not thought of setting up shop in India. Big pharma is interested in such studies so it could be a lucrative outsourcing venture if someone could put it all together.

Thursday, November 25, 2010

Tract-based white matter fiber analysis: what to study

The difficult problem in white matter fiber analysis (obtained from DTI or HARDI sources) is to efficiently handle the large volume of fibers. This may be achieved by clustering the fibers, by clustering using approximations such as the Nyström method, by sampling from the data in a fiber bundle or computing representative means as suggested here.

Volume-based methods side-step this issue by treating a white matter structure as a single anatomical unit. With tract-based analysis, however, processing individual fibers is usually a requirement. Tractography and clustering algorithms have made this possible. Improvements are needed but it is my view that making the pre-processing pipeline more efficient is an engineering effort.

While tedious processing is a disadvantage, tract-based methods offer the potential to study local parameters along a tract. This is important in the study of white matter disease
and, at this juncture, it is here that the maximum contributions to the medical community can be made.

C. Fowlkes, S. Belongie, F. Chung, J. Malik. "Spectral Grouping Using the Nyström Method", TPAMI. 26 (2) p.214-225.

Monday, November 15, 2010

White matter fiber analysis: why we need statistical summaries (means)

A key concept in medical image analysis is the idea of a mean template, i.e., a statistical average around which deviations can be assessed. In the context of white matter fiber analysis, we seek to represent an anatomically defined fiber bundle with a mean and variance that describes its essential characteristics. This mean is of interest for practical reasons that go beyond atlas construction. From my hard-won experience working with DTI fibers, these are 3 reasons we need to compute means:

1.There are a large number of fibers involved in white matter fiber analysis. The corpus callosum has over 300 million fibers alone, the whole brain, 100 billion! fibers--source: Mori's atlas. The tractography output which is some fraction of this can still be several thousand fibers. Due to this large volume, a practical first step in any study, and one that is advocated by me, is to compute a representative mean of a fiber bundle.

2. The tractography output is subject to error. Noise, imperfections in the image and the presence of regions of low anisotropy due to fiber crossings all contribute to this.
In order to make the streamline output more robust we can average over the fiber bundle. This strategy is also useful when a representative bundle is sought and there are discontinuities and other fiber damage due to disease.

3. To facilitate statistical analysis for population studies where the underlying problem is one of assigning membership to a group.

Means may be computed for the following situations:

i)for a group of fibers within a fiber bundle
ii) for an intra- or inter-subject collection of fibers from many bundles
iii)for an intra- or inter-subject collection of means of fiber bundles

The computation of statistical summaries is usually part of any framework for white matter
fiber analysis. Some of these frameworks are listed in my previous post on Mathematical frameworks.

Saturday, November 6, 2010

Tract-based quantitative white matter fiber analysis: Mathematical frameworks

This is a standalone post. It is also part of the Quantitative white matter fiber analysis
series posted here.

There are three steps in tract-based data analysis: pre-processing, modeling and statistical analysis. The pre-processing may involve registration, tractography segmentation or clustering and the information contained in these results is often incorporated into the data analysis model. Fractional anisotropy (FA) is one such artifact and the analysis of FA profiles along tracts is usually included in most studies. The quantitative frameworks use both simple ideas such as the alignment of fibers for statistical analysis and more advanced mathematical concepts such as currents or techniques in Riemannian geometry.
These methods for tract-based analysis are listed below:

1) Fiber-tract oriented statistics
This model by Corouge et al.[1] is a prototype for computing statistics along a fiber bundle. The core idea was to give a compact description of the geometry and diffusion properties of a fiber bundle along its length profile. Corresponding points for a set of fibers are aligned and averages of DTI indices along the cross-section are computed. This can be done with linear or nonlinear Riemannian spaces.
This basic idea has also been extended to a population atlas where information contained in tractography results[2] or registration results[3] are evaluated along a tract-based coordinate system.

2) Statistical modeling and EM clustering of white matter fiber bundles
Individual fibers are parameterized and aligned with the goal of performing tract-oriented analysis over a population. A statistical model of pre-segmented fiber bundles is then calculated which serves as a prior for mixture model clustering. The Expectation-Maximization algorithm is used to infer membership probabilities and cluster parameters. Atlas guided clustering gives anatomically meaningful bundles. This is work by Maddah et al. [4].

3) Statistical model of white matter fiber bundles based on currents
This is a flexible framework where fiber bundles (a collection of curves) are modeled as currents. The space of currents is a vector space equipped with an inner product and norm which defines the distance between two bundles. This is a global distance that does not use point-wise correspondences [5]. Durrleman et al. give a statistical model for a fiber bundle atlas and it variability in a population.

4) Comprehensive Riemannian Framework
In this framework, Mani et al.[6] use various combinations of shape, scale, orientation and position, the physical features associated with white matter fibers, to define Riemannian feature spaces. This is useful since applications have different objectives and often need different sets of tools and metrics for optimal results. For each joint manifold, a (geodesic) distance metric that quantifies differences between fibers as well as tools for computing statistical summaries of samples are defined. Correspondences between fibers are implicitly established during these pairwise comparisons. The framework may be extended to accomodate features such as scalar diffusion indices.

5) Statistical mapping of medial models of white matter tracts
Yushkevich et al.[7] use a different geometric model by giving major fiber tracts a medial representation. While this is strictly not a tract-based model, it is included here because local statistics of tensor-based features can be computed.


1) Isabelle Corouge, P.Thomas Fletcher, Sarang Joshi, Sylvain Gouttard, Guido Gerig, "Fiber Tract-Oriented Statistics for Quantitative Diffusion Tensor MRI Analysis," Medical Image Analysis 10 (2006), pp. 786-798.

2) Lauren J. O'Donnell, Carl-Fredrik Westin and Alexandra J. Golby. "Tract-Based Morphometry for White Matter Group Analysis," NeuroImage. Volume 45, Issue 3, (2009), pp. 832-844.

3) Casey B. Goodlett, P. Thomas Fletcher, John H. Gilmore, and Guido Gerig. "Group Analysis of DTI Fiber Tract Statistics with Application to Neurodevelopment," NeuroImage. (2009), 45(1 Suppl): S133–S142.

4) Maddah M., Grimson W.E.L., Warfield S.K. "Statistical Modeling and EM Clustering of White Matter Fiber Tracts", Proceedings of the 3rd IEEE International Symposium on Biomedical Imaging. (2006);1, pp. 53-56.

5) M. Vaillant and J. Glaunès, "Surface matching via Currents", Proceedings of Information Processing in Medical Imaging, Lecture Notes in Computer Science vol. 3565, Springer (2005), pp. 381–392.

6)Meena Mani, Sebastian Kurtek, Christian Barillot, Anuj Srivastava. "A Comprehensive Riemannian Framework for the Analysis of White Matter Fiber Tracts," In ISBI'2010, pp. 1101-1104.

7) Yushkevich P.A., Zhang H., Simon T.J., Gee J.C., "Structure-specific statistical mapping of white matter tracts," (2008) NeuroImage, 41 (2), pp. 448-461.