Unsupervised white matter fiber clustering and tract probability map generation: Applications of a Gaussian process framework for white matter fibers

Abstract

With the increasing importance of fiber tracking in diffusion tensor images for clinical needs, there has been a growing demand for an objective mathematical framework to perform quantitative analysis of white matter fiber bundles incorporating their underlying physical significance. This paper presents such a novel mathematical framework that facilitates mathematical operations between tracts using an inner product based on Gaussian processes, between fibers which span a metric space. This metric facilitates combination of fiber tracts, rendering operations like tract membership to a bundle or bundle similarity simple. Based on this framework, we have designed an automated unsupervised atlas-based clustering method that does not require manual initialization nor an a priori knowledge of the number of clusters. Quantitative analysis can now be performed on the clustered tract volumes across subjects thereby avoiding the need for point parametrization of these fibers, or the use of medial or envelope representations as in previous work. Experiments on synthetic data demonstrate the mathematical operations. Subsequently, the applicability of the unsupervised clustering framework has been demonstrated on a 21 subject dataset.

Registration, atlas estimation and variability analysis of white matter fiber bundles modeled as currents

“…Then, fibers may be selected and gathered into anatomically relevant clusters, called fiber bundles in the sequel. This clustering may be done either manually or via the help of registration like in Ziyan & Westin (2009), or via automatic clustering algorithm like in Savadjiev et al (2008); Wassermann et al (2010) for instance. These fiber bundles give an estimation of the anatomy of the true underlying neural pathways.…”

Processing and Visualization of Diffusion MRI

“…a fiber of any length can be encoded with only the mean and covariance of points along its path and then use the L 2 distance [25]. An altogether different approach is to consider the spatial overlap between fibers [127,128]. Since full-brain tractography often contains many small broken fragments as it tries to trace out bundles, such fragments are often separated from their actual cluster.…”

“…For example, one can efficiently group directly on the induced manifold by iteratively joining fibers most similar until the desired clustering emerges [128]. Fig.…”

A novel approach for improved tractography and quantitative analysis of probabilistic fibre tracking curves

“…Generally, the mathematical frameworks described in the literature to date (Maddah et al, 2008;Wassermann et al, 2010) have aimed to facilitate subsequent clustering and group-based statistical analysis of fibre bundles. Recently, Wassermann et al (2010) presented a mathematical framework that facilitates mathematical operations between tracts using an inner product between fibres with the aim of producing an automated clustering method. While analysing fibre tracking curves geometrically is a promising notion, relatively little attention has been paid to this area, with a few exceptions.…”