Establishing a direct relationship between regional boundaries based on diffusion imaging and borders between regions that perform different functions would not only be of great significance when interpreting functional results, but would also provide a first step towards the validation of diffusion-based anatomical connectivity studies.

The relationship between brain structure and brain function is fundamental to neuroscience. Early studies designed to parcellate human and non-human cortex into regions that were distinct in their structure (Brodman 1909; Vogt & Vogt 1919) acted under the hypothesis that these structurally defined regions also differed in their function. Such studies parcellate cortical regions on the basis of microstructural features such as cyto- or myeloarchitecture (Vogt et al. 1995; Roland & Zilles 1998; Zilles & Palomero-Gallagher 2001), which have direct implications for local cellular processing. Cortical regions, which may be delineated on the basis of cellular microstructure, have also been shown to differ in their connections to other brain regions (e.g. Jones & Burton 1976; Vogt 1993).

Independent of their respective relationships to cellular microstructure, there is good reason to expect a strong correspondence between regional brain function and connectional architecture. Anatomical connections constrain the nature of the information available to a region and the influence that it can exert over other regions in a distributed network: local structural organization can therefore be expected to determine local functional specialization. However, this relationship between circuitry and function has proved difficult to test directly in the absence of a mechanism for investigating connectivity in the functioning brain. Direct information relating to anatomical connections in the human brain is sparse and, until recently, only available post-mortem. More direct assessment of connectivity is feasible using invasive tracer techniques in non-human animals, but these approaches must be focused on specific regions, and assessment of function in the same animals is technically demanding (although excellent examples do exist; Yoshida et al. 2003).

Magnetic resonance diffusion imaging is able to characterize the local diffusion properties of water in tissue at a millimetre scale (Le Bihan 2003). In tissue with a high degree of directional organization, the self-diffusion of water is hindered more in some directions than others. For example, water diffusion in brain white matter is more hindered perpendicular than parallel to the major axis of a fibre bundle (Moseley et al. 1990), such that the direction of least resistance to diffusion (or principal diffusion direction) aligns well with the mean fibre orientation in an imaging voxel (Basser et al. 1994). Recent developments in diffusion tensor imaging techniques have enabled this diffusion anisotropy to be quantified, and for the principal diffusion direction to be computed at each voxel. Using these local fibre orientations, early studies were able to trace large white matter fibre tracts (Basser & Pierpaoli 1996; Mori et al. 1999; Catani et al. 2002), raising the possibility of explorations of anatomical connectivity in the living human brain. Using diffusion tractography, it has been possible to identify specific patterns of anatomical connectivity associated with grey matter ‘seed’ voxels (Conturo et al. 1999; Behrens et al. 2003a), and to demonstrate that spatially near, but functionally distinct, grey matter seed voxels have very different connectivity patterns (figure 1).

Figure 1 Tracing anatomical connections with diffusion imaging: (a) seeded from a single voxel in a ventral lateral location in thalamus. In macaque monkeys, ventral lateral nucleus of thalamus (VL) processes motor information and projects to primary motor cortex (more ...)

In this paper, we investigate whether it is possible to use diffusion-based connectivity information in a systematic fashion in order to parcellate grey matter according to its connectional architecture, and hence infer boundaries between discrete functional regions. We overview three possible approaches for parcellating the brain on the basis of diffusion MRI. These strategies differ not only in their technical approach to identifying boundaries, but also conceptually in the information they consider.

The first two applications aim to identify distinct regions in human thalamus (Behrens et al. 2003a; Wiegell et al. 2003). In Behrens et al. (2003a), prior knowledge of the major cortical connection sites of the thalamic nuclei in non-human primates is used to identify regions in human thalamus by associating thalamic seed voxels with their most probable cortical projection targets, as estimated by diffusion tractography. In Wiegell et al. (2003), thalamic nuclei are identified with no prior knowledge of their patterns of connectivity, discriminating instead on the basis of voxel-wise diffusion properties. Regions are effectively distinguished on the basis of the local properties of white matter fibres as they penetrate the thalamic grey matter.

In the third study reviewed here, the focus is on a region of cortical grey matter—medial area 6 (Johansen-Berg et al. 2004). White matter penetration in neocortex is substantially weaker than in subcortical structures such as thalamus; hence, in comparison to such structures, local diffusion properties are relatively homogeneous across cortical voxels, and tracking anatomical connections from cortical voxels to their remote cortical targets is relatively unreliable. Moreover, the evolution of neocortex is such that it is often difficult to make accurate predictions about the connectivity patterns from human cortical regions by examining only data from non-human primate. Here, supplementary motor area (SMA) and preSMA are distinguished with no prior knowledge of their connectional architecture by searching for a sharp change in the entire profiles of connectivity from the seed locations. The acting hypothesis is that, if the SMA and the preSMA perform different functions, they must require different connectional architecture, so that by searching for the boundary where this architecture changes, the functional border may be inferred.

Figure 2 Diffusion-based parcellation of grey matter: (a) Identifying thalamic nuclei on the basis of their remote cortical projections. (i) Cortex was first segmented into large anatomically defined regions corresponding to known connection areas of the major (more ...)

Although the correspondence between the clusters identified from connectivity data and histological sections of human thalamus is compelling (figure 2a(ii,iii)), the precise thalamic borders identified using diffusion data in this way depend on the borders that are initially manually defined on the cortex. This dependence is not ideal for a number of reasons. First, the correspondence between gross anatomical landmarks underlying cortical cytoarchitecture is debatable (e.g. Amunts et al. 1999). Also, the parcellation depends on prior knowledge of what constitute meaningful connectivity target regions. This is reasonably well achieved in the case of the thalamus, as thalamo-cortical relationships are well described, but may be more challenging for other regions.

The diffusion tensor is reconstructed at each thalamic voxel (figure 2b) and a metric is defined that allows the calculation of the dissimilarity or distance between any two diffusion tensors. The authors submit these diffusion tensor data to an automated clustering routine that attempts to partition the thalamus into groups of voxels that are close, both spatially and in terms of their diffusion tensors. Tensors are labelled as ‘close’ to one another if they are similar in properties such as diffusion anisotropy and mean diffusivity and if their principal orientations are well aligned. The resulting clusters (labelled in figure 2b) bear close resemblance to the connectivity-defined regions in figure 2a, and to previously reported histological segmentations of the thalamic nuclei. For comparison with the approach described in the previous section, again note the medial dorsal and anterior clusters of voxels whose principal axis of diffusion is in the anterior–posterior orientation (green), pointing towards prefrontal cortex, and note the lateral cluster of voxels whose principal axis is in the inferior–superior orientation (blue/purple) pointing towards sensorimotor cortices.

Parcellation with respect to local diffusion properties could provide a powerful means of subdividing grey matter. One strength of the technique is that it does not require prior specification of connectivity targets, and does not rely on the accuracy of diffusion-based tractography routines. However, the approach does rely on differences in remote connectivity being visible as differences in local diffusion properties. Cases will exist in which voxels with similar local diffusion properties (e.g. similar local fibre orientation) have divergent patterns of remote connectivity. In such cases, local information alone will not be enough to identify the connectional differences.

In Johansen-Berg et al. (2004), we propose a fundamentally different strategy for inferring structural parcellation from diffusion data that allows ‘blind’ discrimination of regions with different patterns of connection, and which benefits from the sensitivity gained by considering a seed point's remote targets without having to rely on a complete, or even accurate, representation of its connectivity. Instead of classifying a single seed point on the basis of its cortical target, we consider the entire ‘profile’ of connectivity from all seed points simultaneously. This allows us to find clusters of seed voxels with very similar patterns of connectivity or, equivalently, draw boundaries between adjacent brain areas whose patterns are markedly different.

The specific cortical focus in this paper is medial area 6—an area which provides an excellent test case. In macaque monkey, the medial part of the homologue of Brodmann's area 6 consists of two cytoarchitectonically distinct regions (Vogt & Vogt 1919; Matelli et al. 1991), thought to correspond to SMA proper and preSMA. These two regions exhibit different functional responses (Matsuzaka & Tanji 1996), have distinct connections (Luppino et al. 1993) and may be distinguished on the basis of gross anatomy as lying on the medial surface, either side of a plane approximately at rostro-caudal to the level of the bow of the arcuate sulcus. In the human brain there is consistent evidence for a functional distinction, at least between anterior and posterior parts of medial area 6, as functional imaging studies have found differential involvement of these regions in tasks engaging distinct cognitive or motor domains (Picard & Strick 1996; Rushworth et al. 2002). However, there is no local anatomical landmark that differentiates functionally defined SMA and preSMA in the human brain; the vertical line from the anterior commissure (VCA line) provides the best approximation (Zilles et al. 1996).

We aim to find a connectional dissociation within medial area 6 which corresponds to the known functional dissociation between SMA and preSMA. The hypothesis is that voxels within either one of the functionally dissociated regions will have very similar patterns of connectivity, but that there will be a sharp transition in connectivity at the functional boundary, such that the characteristic patterns will be very different between the two regions.

Connectivity distributions are seeded from voxels in a region in medial frontal cortex that includes both functional areas. Every connectivity distribution is correlated with every other, and the correlations between each of these pairs of distributions are stored in a matrix (figure 2c(i)). Each element in this matrix, therefore, represents the similarity between connectivity profiles of two specific medial frontal seed points. If the hypothesis of a connectional dissociation is accurate, then this matrix will contain high values at locations corresponding to the correlation between two voxels in the same brain region (demonstrating the similarity of their connectivity patterns), whereas the correlation between connectivity patterns originating from voxels in different brain regions should be low. In its original form, it is not possible to identify such patterns in the correlation matrix, as seed voxels are entered along the axes of the matrix in a random order. To test for this organization, the data are submitted to a spectral reordering algorithm (Johansen-Berg et al. 2004), which reorders the rows and columns of the similarity matrix, such that large element values in the matrix are forced towards the diagonal. Clusters emerge in the reordered matrix (figure 2c(i)) representing groups of seed voxels with similar patterns of connectivity, which, when mapped back onto the brain, correspond to discrete, spatially contiguous regions situated along the anterior–posterior axis of the medial frontal cortex (figure 2c(ii)). The boundary between clusters in the reordered matrix corresponds to a sharp change in connectivity in medial frontal cortex. This border appears close to the coronal plane of the VCA line, supporting the hypothesis that the clusters correspond to SMA and preSMA.

In each of the parcellation strategies described above, grey matter regions have been distinguished on the basis of differences in either local or remote white matter architecture. These differences may be interesting in their own right, but the associated hypothesis is that the connectional boundaries which they imply are also of cytoarchitectonic and functional relevance. In this section, we will examine possible strategies for testing this hypothesis, and hence of approaching the related problem of validating the connectivity-based parcellations.

The first of these approaches relies on a high degree of consistency across the population in connectional, and by inference histological, parcellations. Each of the studies described in §2 tests the population variability in the recovered parcellations and, in each case, demonstrates good reproducibility across a group of subjects.1 In both of the thalamic studies, where the histo-architecture is well defined, the authors are then able to make comparisons between group average measurements derived from their diffusion-based parcellations, and measurements derived from post-mortem histological atlases. Wiegell et al. choose to examine the geometric location of the recovered nuclei within thalamus, demonstrating good correspondence with the centres of mass of nuclei defined by characteristic fibre orientation measured histologically (Niemann et al. 2000; figure 3a). Johansen-Berg et al. (2005) demonstrate consistency between the relative volumes of thalamic regions projecting to each cortical zone and these same volumes estimated on the basis of a cytoarchitectonic atlas of thalamic nuclei (Morel et al. 1997).

Figure 3 Structural validation of diffusion-based grey matter parcellations: (a; taken from Wiegell et al. 2003) Comparison between centres of gravity of thalamic nuclei defined on the basis of local diffusion characteristics (white bars), and the same nuclei (more ...)

The ability to test the correspondence between cyto- and connectional architectures in the same brain in vivo relies on the existence of reliable alternative in vivo markers of cytoarchitecture. Such markers are rare, as in general, cytoarchitectonic boundaries do not align well with gross anatomical landmarks (e.g. Amunts et al. 1999). However, in thalamus, recent studies have been able to identify the medio-dorsal and ventral posterior nuclei using specifically designed structural MR protocols. By acquiring such images in the same subjects used for the connectivity-based thalamic parcellation, Sillery et al. (in preparation) are able to perform a direct in vivo comparison (figure 3b).

In Johansen-Berg et al. (2005) we test the hypothesis that connectivity-defined regions in thalamus co-localize with functional activations during tasks expected to involve specific thalamic nuclei and their cortical connectivity targets. Executive and memory tasks are expected to involve the thalamic region projecting to the prefrontal cortex, whereas sensorimotor tasks are predicted to activate thalamic regions projecting to sensory and motor cortices. We compare the locations of connectivity-defined regions grouped across individuals with those of centres of mass of previously reported functional activations in thalamus during executive and sensorimotor tasks (figure 4a). Note the spatial dissociation in thalamus between activations associated with the different tasks (figure 4a(i)). Centres of activation for the sensorimotor tasks fall within thalamic regions with high group probability of connection to sensorimotor and premotor areas (figure 4a(ii)). Similarly, activation centres for the executive and memory tasks fall within thalamic regions of high group probability of connection to prefrontal cortex (figure 4a(iii)).

Figure 4 Functional relevance of diffusion-based parcellations. (a) Functional relevance of connectivity-based parcellation of thalamus. In each figure, the pale grey surface represents the thalamus; the black arrow represents a posterior–anterior orientation; (more ...)

By acquiring functional and diffusion imaging data in the same group of subjects, it is possible to make direct comparisons between connectional and functional borders. Using functional MRI in conjunction with tasks designed to activate SMA and preSMA selectively, we are able to identify the functional boundary between the two regions (figure 4b(i); Johansen-Berg et al. 2004). The combination of the regions activating during each of the two functional tasks is chosen as a seed region in which to search for a connectional dissociation in the diffusion data. As before, probabilistic tractography is seeded from every voxel in this region; the connectivity profile correlation matrix is computed and submitted to spectral reordering; and clusters emerge in the reordered matrix. When mapped back onto the brain, the regions defined using connectivity information alone bear close resemblance to the functionally defined SMA and preSMA (figure 4b).

The connectional architecture of a brain region constrains the region's function. Magnetic resonance diffusion imaging offers information about this architecture that is unique among non-invasive measurement techniques. Using this information, it is possible to identify regions in cortical and subcortical grey matter that can be dissociated by features of their connectivity, and demonstrate that the connectional boundaries that these dissociations imply have relevance in terms of both cellular and functional architecture.

In addition to the studies reviewed in this article, recent and ongoing studies have successfully applied similar techniques to subdivide different brain areas. For example, in Lehericy et al. (2004), using remote cortical connectivity patterns, the authors are able to subdivide the striatum into regions belonging to distinct cortico-striatal circuits. In Sillery et al. (2004), differences in connectivity patterns reveal a dissociation between the internal and external globus pallidus. The authors demonstrate a correspondence between boundaries identified by changes in connectivity and those identified manually on a high-resolution proton-density-weighted MR scan.

A general relationship between boundaries in connectional architecture visible to diffusion imaging and borders between cytoarchitectonically and functionally distinct grey matter regions would be of great significance to future neuroimaging studies. Such a relationship would allow future functional imaging results to be interpreted in the context of local cytoarchitectonic borders. Functional data could be compared directly across studies with reference to the cytoarchitectonic region of the activation site. Functionally relevant boundaries could be preserved when aligning data from different subjects, allowing, for example, for more accurate measurements of variability in functional responses across a population. The ability to infer cytoarchitectonic boundaries in vivo would also have significance for studies of brain structure. Boundary locations, or regional volumes, could be compared across subject groups or brain hemispheres. Lesion locations could be estimated accurately with respect to the cytoarchitecture.

However, although the strategies reviewed in this article have allowed for initial demonstrations of the potential of diffusion data for inferring structural and functional parcellations, they are not yet in a position to provide generally applicable tools. Any technique designed to group data into dissociated clusters relies on the ability to make hard decisions about, for example, the number of clusters to choose and the membership of each cluster. To date, diffusion-based parcellation studies have relied on manual setting of these parameters—Weigell et al. (2003) chose to search for 14 thalamic nuclei. Johansen-Berg et al. (2004) identified clusters by eye in the reordered correlation matrices. Before these techniques can be generally applied to blind structural parcellation in grey matter, statistical techniques should be developed to provide an automated framework in which to make these decisions. This problem is closely related to problems faced by scientists attempting to infer similar parcellations from classical histology. Robust methods for making decisions about the existence and location of boundaries in cellular architecture are the subject of ongoing research (e.g. Schleicher et al. 2000).

The methods that we have described have all relied on explicit models of local diffusion in biological tissue. These models make simplifying assumptions, such as the existence of only a single characteristic fibre orientation within any voxel, which may preclude them from identifying boundaries in regions of the brain where these assumptions break down. Recent research has allowed the representation of local diffusion information within a voxel without the need for these restrictive models (Alexander et al. 2002; Tuch et al. 2003). This new technology will only improve the sensitivity and accuracy of all diffusion-based connectivity studies.

The spatial resolution of the parcellations is also limited by current technology. A set of diffusion-weighted images appropriate for tractography might take 40min to acquire, and have spatial resolution of only 2×2×2mm³. As MR scanner technology improves, the spatial resolution of the images will increase, allowing for finer anatomical parcellations.

Despite these limitations, we have shown that diffusion-based parcellations, carried out in controlled circumstances in which functional or cytoarchitectonic boundaries are available, have identified connectional borders which align well with the functional or structural data. In the cases where the inferred parcellations depend on the accuracy of the underlying diffusion tractography, the functional/structural validation of these parcellations may prove a first step towards validating the tractography process. Eventually, the validity of diffusion-based connectivity studies should be established by direct comparison with invasive tracer studies in non-human primates. However, at present, the voxel resolution available to diffusion studies (of the order of 1mm³) is such that only the largest fibre pathways are visible in a macaque brain (Parker et al. 2002). The demonstration of good correspondence between connectional, functional and cytoarchitectures inferred from diffusion imaging, functional imaging and histolology, respectively, not only promises to provide powerful tools for studying brain structure and function in vivo, but lends weight to the argument that diffusion imaging is providing measures relating to anatomical brain circuitry.