Algorithm:GATech:DWMRI Musings

DW-MRI Musings

Back to Georgia Tech DW-MRI Geodesic Active Contours.

This page contains a hodge podge of thoughts on Diffusion-Weighted MRI (DW-MRI) processing. From a bird's eye view, the most general question for a DW-MRI data processor is: What clinically relevant information can be leveraged from DW-MRI data and used for scientific and clinical studies? Furthermore, what algorithms, programming constructs, clinical guidance, and training are needed to make this happen? The following are some quick thoughts that may be considered when attempting to answer these questions, in no particular order:

DW-MRI vs DT-MRI

In answering the questions posed above, it is common for people to assume from the onset that we are using terminology related to tensors (i.e. DT-MRI, DTI). The raw data coming out of the scanner is referred to as DW-MRI or DWI. The difference between the "T" and the "W" is that the "T" has undergone a preprocessing step which computes tensors at each voxel which are a function of the original "W" data. Hence, the data resulting from this preprocessing step is referred to at DT-MRI. There are advantages and disadvantages to using this preprocessing tensor construction step. The point here is that when we think about trying to find ways to go from the scanner data to clinical answers, we are talking about going from DW-MRI data to clinical answers. In other words, it is okay to think outside the box and to consider ways in which ellipsoidal constraints arising from the tensor model may be meaningfully relaxed.

A Spaghetti Fancy

In this line of research, the most common figures one can expect in the key Neuroimage, Science, Nature, etc. publications are pretty pictures of a bunch of open curves (or fibers) sprawling through the brain. These images are so common, that some people have come to presuppose that this is the kind of output one should expect from algorithms which process DW-MRI or DT-MRI data. Of course, these images are the result of streamline techniques, which is one important branch of DW-MRI research. But if you consider recent 2006-2007 publications on DW-MRI and DT-MRI algorithms, you quickly realize that the bent of research has recently experience a shift to other optimal path / volumetric segmentation type approaches, which do not produce these kinds of sprawling fiber figures. So, in current and future publications, one can expect to see a greater variety of visualizations which reflect the other branches of research emerging in DW-MRI processing.

Synchronizing Terminology

An important step in approaching the questions above is the development of a set of common terms which we can use to describe our work. The following is a list of commonly used and confused terms in this line of research with corresponding definitions. Note that some things (such as fractional anisotropy (FA), b-values, etc) have straightforward definitions and need no further attempt at solidifying. These definitions are certainly not perfect and could benefit greatly from community input:

• DW-MRI, DWI - Diffusion-Weighted Magnetic Resonance Imagery - the raw data coming out of the scanner - small values correspond to strong diffusion.
• DT-MRI, DTI - Diffusion-Tensor Magnetic Resonance Imagery - the 6-component data resulting from the construction of tensors from DW-MRI data - high eigenvalues correspond to strong diffusion.
• fibers, tracts - open curves representing possible diffusion paths through the brain - while the paths themselves certainly do not correspond to any micro-architecture, they provide possible paths through which particles may diffuse through the volume.
• streamlines - these are a particular subset of fibers and tracts which are produced via streamline-based algorithms - streamline-based algorithms employ a local decision-making methodology, propagating paths until a particular termination criterion is reached - streamlines are not mathematically optimal with respect to any particular metric.
• fiber bundles - volumetric bundles of axons which are large enough to be resolved with the typical 1-3mm resolution of MRI scanners - whether or not this term permits structures with branchings is still an open question.
• fiber clusters - anatomically equivalent to fiber bundles - algorithmically different from fiber bundles because clusters refer to the fact that fiber clusters are formed by analyzing the group behavior of many streamlines.
• optimal fiber, optimal tract, optimal path, anchor tract - the best open curve connecting two ROIs, as determined via an optimization of an energy functional or probability measure - note that the underlying metric which is optimized may be different in the various algorithms, but the essential concept is the same wherein the optimal path connecting two ROIs is found according to the particular choice of metric.
• fiber tractography - algorithms which take raw DW-MRI or DT-MRI data as an input and produce tracts or an optimal tract as an output - note that this term was used first to describe streamline techniques, but has since been applied to optimization techniques - therefore, one must be careful when using this term to describe algorithms since two very different classes of algorithms have borrowed the term.
• fiber bundle segmentation - algorithms which take raw DW-MRI or DT-MRI data as an input and produce volumetric segmentations of fiber bundles as an output.
• connectivity maps - these are maps which indicate the connectivity of a particular region with the rest of the domain (typically the entire brain) - these connectivity maps come in a variety of flavors, as probability maps, as arrival time maps resulting from energy minimization techniques, etc. - note that it is possible for algorithms to generate connectivity maps which indicate the degree of connectivity of two ROIs, without ever explicitly segmenting a single fiber or fiber bundle.

Streamline Ups and Downs

coming soon

Validation Soap Box

When we consider assessing the utility of a particular tool in serving the needs of our clinical customers, we should stop and consider the factors upon which our assessment is based and biased. This is particular important when attempting to validate results in an environment absent of ground truth. In the absence of ground truth, tools are judged according to: visual appeal, reproducibility, user-friendliness, and (if you're shooting for the stars and want something for which there is ground truth) accuracy in diagnosis.

Broadly speaking, each tool consists of four components which contribute toward the utility of the tool: the algorithm, the engineering, the incorporation of clinical knowledge, and the training. It is common to interchange the terms tool and algorithm when assessing the utility of a tool. However, especially in an environment where results are primarily judged by the visual appeal and user-friendliness, this is misleading. The fear here is that streamline-based algorithms which have been around the longest and have enjoyed a great deal of engineering input, clinical guidance, and community training, will somehow be inordinately attended to because the judgment criterion used for these tools is based on these non-algorithmic components. It is useful to ask the question, "If algorithm A had received as much engineering, clinical input, and training as algorithm B, how would this change things?"

Algorithm Categorization

coming soon

Beware of the Segmentation Discrimination Paradox

coming soon

Beware of Mr. Legendre

coming soon