The brain atlas concordance problem: quantitative comparison of anatomical parcellations

Abstract

Many neuroscientific reports reference discrete macro-anatomical regions of the brain which were delineated according to a brain atlas or parcellation protocol. Currently, however, no widely accepted standards exist for partitioning the cortex and subcortical structures, or for assigning labels to the resulting regions, and many procedures are being actively used. Previous attempts to reconcile neuroanatomical nomenclatures have been largely qualitative, focusing on the development of thesauri or simple semantic mappings between terms. Here we take a fundamentally different approach, discounting the names of regions and instead comparing their definitions as spatial entities in an effort to provide more precise quantitative mappings between anatomical entities as defined by different atlases. We develop an analytical framework for studying this brain atlas concordance problem, and apply these methods in a comparison of eight diverse labeling methods used by the neuroimaging community. These analyses result in conditional probabilities that enable mapping between regions across atlases, which also form the input to graph-based methods for extracting higher-order relationships between sets of regions and to procedures for assessing the global similarity between different parcellations of the same brain. At a global scale, the overall results demonstrate a considerable lack of concordance between available parcellation schemes, falling within chance levels for some atlas pairs. At a finer level, this study reveals spatial relationships between sets of defined regions that are not obviously apparent; these are of high potential interest to researchers faced with the challenge of comparing results that were based on these different anatomical models, particularly when coordinate-based data are not available. The complexity of the spatial overlap patterns revealed points to problems for attempts to reconcile anatomical parcellations and nomenclatures using strictly qualitative and/or categorical methods. Detailed results from this study are made available via an interactive web site at http://obart.info.

Figure 1. Illustration of the brain atlas concordance problem.

A: Rendering of three anatomical regions in the left temporal lobe as delineated by two different brain atlases. The largest region, Superior Temporal from the ICBM atlas (see Materials and Methods for atlas descriptions), shown in yellow, overlaps both the Superior Temporal Gyrus (blue) and the Middle Temporal Gyrus (red) regions in the AAL atlas to differing degrees. B: The same region boundaries drawn as projections in the three cardinal directions. An examination of the patterns of overlap in just 3 regions points to the complexity of the concordance problem.

Figure 2. Venn diagram illustrating the formulation of conditional probability measures P_ij.

Three different hypothetical regions r₁, r₂, and r₃ are shown in two dimensions in different spatial arrangements. At bottom, the calculation of each conditional probability based on the areas (volumes in 3-D) of the shaded regions is shown.

Figure 3. Region-level concordance analysis across eight anatomical parcellations.

A: Overall non-symmetric concordance matrix P. Entry P_ij gives P(i|j), the probability that a voxel is in region i given that it is in region j in another parcellation scheme. Each row and column corresponds to a particular anatomical region, and regions are grouped by parcellation method (separated by the gray horizontal and vertical lines). B: The column (top) and row (bottom) from the matrix P corresponding to the Superior Temporal region as delineated by the ICBM atlas (see arrows in A) were extracted and the corresponding conditional probability values rendered as the heights of bars. The orange bars give the fraction of the ICBM Superior Temporal region contained in other regions, and the blue bars (below) give the fraction of other regions contained in the ICBM region. The names of the example overlapping regions corresponding to the annotated bars are as follows: 1. AAL superior temporal gyrus; 2. AAL middle temporal gyrus; 3. ICBM superior temporal; 4. LPBA40 superior temporal gyrus; 5. TALg superior temporal gyrus; 6. CYTO TE1.2; 7. H-O superior temporal gyrus, anterior division; 8. T&G anterior superior temporal gyrus; 9. T&G posterior dorsal superior temporal sulcus; 10. TALc Brodmann Area 41; 11. TALg transverse temporal gyrus. C: Histogram of the mean number of regions from any parcellation R′ that overlap a single region drawn from a different parcellation R.

Figure 4. Scatter plot of computed spatial conditional probability values for all region pairs.

For each two regions (r_i, r_j), max(P(i|j), P(j|i)) is plotted vs. min(P(i|j), P(j|i)) (see also [27]). Histograms shown adjacent to either axis are log scale counts of these measures taken across all region pairs.

Figure 5. Visualization of region-level concordance results.

A: P_ij matrix after permuting the indices (region labels) independently within each block in order to reduce matrix bandwidth. The blocks can not be completely diagonalized because of the lack of one-to-one correspondence between regions in pairs of parcellations. B: Visualization of region labels using multi-dimensional scaling. Top: 2-D landscape of computed coordinates for each anatomical region, with the parcellation from which each region is drawn indicated by the marker type. Bottom: magnified portion of the 2-D landscape above revealing the anatomical regions and their labels that occupy this segment of the space (the highlighted rectangular area in top).

Figure 6. Extraction of approximate higher order spatial relationships using bipartite graphs.

A: Initial bipartite graph constructed by connecting vertices on the left (corresponding to the H-O parcellation) with vertices on the right (corresponding to the LPBA40 parcellation) when the corresponding parcels overlap. The undirected edge weights were determined by the maximum conditional probability value for each region pair. The graph is fully connected. B: Final bipartite graph representation of the same parcellations after pruning all edges with weight less than 0.25. The graph is partitioned into 9 connected components (rendered in different colors); for each component, the union of regions on the left is approximately equivalent to the union of regions on the right.

Figure 7. Random parcellations.

A: Sections through the AAL parcellation of the test brain with different colors indicating different parcels. B: a random parcellation of the same test brain.

Figure 8. Global concordance between parcellations.

A: Results using Adjusted Rand Index (ARI). B: Results using the S index. In each subfigure the values in the upper diagonal entries are the concordance indices for particular pairs of atlases, with above chance values in green. The lower diagonal entries show the sorted distribution of chance concordance values obtained by comparison of 1000 random size-matched parcellations (curved line) and the actual value obtained for this atlas pair as a horizontal line.

Figure 9. Comparison of Adjusted Rand Index and S index.

The values of both computed indices of global concordance plotted against each other for each atlas pair.