SIFT: Spherical-deconvolution informed filtering of tractograms

Abstract

Diffusion MRI allows the structural connectivity of the whole brain (the ‘tractogram’) to be estimated in vivo non-invasively using streamline tractography. The biological accuracy of these data sets is however limited by the inherent biases associated with the reconstruction method. Here we propose a method to retrospectively improve the accuracy of these reconstructions, by selectively filtering out streamlines from the tractogram in a manner that improves the fit between the streamline reconstruction and the underlying diffusion images. This filtering is guided by the results of spherical deconvolution of the diffusion signal, hence the acronym SIFT: spherical-deconvolution informed filtering of tractograms. Data sets processed by this algorithm show a marked reduction in known reconstruction biases, and improved biological plausibility. Emerging methods in diffusion MRI, particularly those that aim to characterise and compare the structural connectivity of the brain, should benefit from the improved accuracy of the reconstruction.

Introduction

Diffusion MRI allows for the investigation of tissue microstructure in vivo non-invasively, by exploiting the random, thermally-driven motion of water molecules to generate image contrast (Johansen-Berg and Behrens, 2009, Jones, 2011). This method is of particular interest in probing the white matter of the brain, where coherent organisation of the underlying neuronal axons exists at the millimetre scale. By encoding a series of images according to the diffusion of water in a number of non-collinear directions, and assessing the data using appropriate mathematical models, properties of the underlying structure (such as the orientations of axonal bundles) can be estimated (Tournier et al., 2011).

These properties are now being used in an attempt to infer the structural connectivity of the human brain in vivo. As the local orientations of these bundles can be estimated, it should be possible to infer the total path of a bundle by tracing a three-dimensional path (known as a ‘streamline’) that follows these orientations in a step-wise fashion until some termination criterion is achieved. By repeating this process many times from a distribution of unique starting points throughout the brain, an estimate of the structural connections of the whole brain (herein referred to as the ‘tractogram’) can be reconstructed.

The biological accuracy of these whole-brain reconstructions is however limited by the mechanisms by which the reconstructions are generated. In addition to the limitations imposed by the diffusion MRI acquisition itself, the greedy, locally-optimal nature of streamline propagation can introduce biases into the tractogram; this can result in the tractogram having attributes that are due to the reconstruction method and are not reflective of the underlying biology. These factors include, but are not limited to:

• Streamline seeding: longer white matter pathways present a greater volume from which to seed, and therefore tend to be over-defined by the streamline reconstruction.

• Selection of fibre orientation: in regions of complex architecture, most streamline algorithms simply follow the most collinear fibre orientation. In the case of a branching tract, streamlines will tend to follow the straightest path, introducing an imbalance in the streamline densities.

• White matter volume: because individual streamlines do not have a volume associated with them during streamline tractography, the physical constraint of fitting the volume occupied by structural connections into the relevant white matter volume is not taken into account.

This is by no means a comprehensive list of streamlines reconstruction biases, and others may exist that are specific to particular diffusion models or streamline algorithms. These biases are nontrivial to predict and/or measure, and their manifestations in the data will vary; but one common effect is that the density of reconstructed streamlines does not represent the density of underlying biological connections. This will inevitably influence the results of any subsequent analyses performed using these reconstructions.

The methods proposed thus far for addressing these reconstruction issues fall into two general approaches, classified by the mechanisms by which they improve the quality of the reconstruction:

• One is to replace the streamline paradigm (where plausible connections are generated independently and in a step-wise fashion) with a reconstruction that produces all structural connections simultaneously, considering factors such as the plausibility of each individual path, how well the connections fit into the given volume, and/or how well the total reconstruction fits the diffusion signal given a particular model; this is known as ‘global tractography’ (e.g. Jbabdi et al., 2007, Kreher et al., 2008, Reisert et al., 2011). Although promising, these approaches are highly computationally expensive, and are thus far limited in the total number of connections that they can feasibly generate.

• The other is to reconstruct a very large number of streamlines, and select some subset of streamlines that best fits the diffusion signal. We are aware of two methods that have used this approach. BlueMatter (Sherbondy et al., 2009) used a massive database of 180 billion streamlines, along with a BlueGene supercomputer and a model of Gaussian diffusion to identify a subset of around 200,000 streamlines that best fit the diffusion data for an example subject. In MicroTrack (Sherbondy et al., 2010), an appropriate subset of streamlines as well as the microstructural properties associated with each pathway are estimated concurrently, with each used to better inform the other. This approach also requires a large amount of computation power, and is limited in the scale or complexity of the solution.

Here we propose a novel algorithm for improving the biological accuracy of a streamline reconstruction, using the approach of finding a subset of streamlines that best matches the diffusion signal. Compared with the methods described above, it requires minimal assumptions regarding the contribution of each streamline to the diffusion signal, yields tractograms that still consist of very large numbers of streamlines, and executes in an acceptable time on a desktop computer. This method uses the results of spherical deconvolution of the diffusion signal to determine which streamlines to remove from the data set, hence the acronym SIFT: spherical-deconvolution informed filtering of tractograms. After undergoing this filtering operation, streamline data sets show a decrease in known reconstruction biases, and improved plausibility in terms of reconstruction of the underlying biology.