Estimating the crossing of nerve fibers in the human brain

Diffusion imaging is a variant of magnetic resonance imaging (MRI) that can noninvasively map the nerve fiber tracts of the human brain.1 Because fibrous tissue restricts the constant heat motion (i.e., diffusion) of water molecules in a characteristic way, diffusionmeasurements provide data about the position and orientation of major nerve fiber bundles. Nerve fiber paths reconstructed from diffusion images2 are depicted in Figure 1. Such information about the connectivity within the brain is of great interest for medical treatments as well as for understanding both normal brain function and neuronal diseases such as multiple sclerosis and schizophrenia. The interpretation of diffusion imaging data is relatively well understood for volume elements (voxels) in which a single fiber direction prevails. Unfortunately, voxels are much larger than the individual nerve cells that make up the fiber bundles. Thus, in areas where fibers touch or cross, many voxels can contain two or more distinct fiber populations. Our work proposes a novel method to deal with these difficult cases.3 Reconstructing directionally-dependent diffusion behavior requires multiple measurements in different directions. A common way to analyze the resulting data set is called ‘spherical deconvolution’.4 This approach produces an orientation distribution function (ODF) that is defined on the unit sphere and takes on high values in the assumed fiber directions. Figure 2(a) illustrates a 60◦ crossing, whose ODF is shown Figure 2(b). Reconstructing fiber pathways involves extracting discrete fiber orientations from such continuous ODFs as shown in Figure 2(c). Prior work simply assumed that fiber orientations coincide with the maxima of the ODF. However, spherical deconvolution is a linear model, and in a linear superposition of peaks that have a finite width, the original maxima interfere (see Figure 3). Interpreting the data amounts to finding a set of peaks that total the givenODF. Even though this problem does not have a unique solution, we propose that a plausible resolution can be obtained by Figure 1. Colored streamlines represent likely paths of nerve fiber bundles. This data was extracted from a diffusion imaging data set.