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See comment in PubMed Commons belowFront Neurosci. 2014 Mar 4;8:15. doi: 10.3389/fnins.2014.00015. eCollection 2014.
Connexel visualization: a software implementation of glyphs and edge-bundling for dense connectivity data using brainGL.
- 1
- Max Planck Research Group for Neuroanatomy & Connectivity, Max Planck Institute for Human Cognitive and Brain Sciences Leipzig, Germany.
- 2
- MEG and Cortical Networks Unit, Max Planck Institute for Human Cognitive and Brain Sciences Leipzig, Germany.
- 3
- Max Planck Research Group for Neuroanatomy & Connectivity, Max Planck Institute for Human Cognitive and Brain Sciences Leipzig, Germany ; Department of Neurophysics, Max Planck Institute for Human Cognitive and Brain Sciences Leipzig, Germany.
- 4
- Department of Neurology, Max Planck Institute for Human Cognitive and Brain Sciences Leipzig, Germany.
Abstract
The visualization of brain connectivity becomes progressively more challenging as analytic and computational advances begin to facilitate connexel-wise analyses, which include all connections between pairs of voxels. Drawing full connectivity graphs can result in depictions that, rather than illustrating connectivity patterns in more detail, obfuscate patterns owing to the data density. In an effort to expand the possibilities for visualization, we describe two approaches for presenting connexels: edge-bundling, which clarifies structure by grouping geometrically similar connections; and, connectivity glyphs, which depict a condensed connectivity map at each point on the cortical surface. These approaches can be applied in the native brain space, facilitating interpretation of the relation of connexels to brain anatomy. The tools have been implemented as part of brainGL, an extensive open-source software for the interactive exploration of structural and functional brain data.
KEYWORDS:
connectome; functional connectivity; magnetic resonance imaging; neuroanatomy; visualization software
Figure 1
Connectivity data can be described as connexels, six-dimensional pairs of three-dimensional spatial positions, and an associated connection strength. As in this example of functional connectivity, such data can be represented with the node positions of a cortical surface (Top left), and a matrix of connection strengths (Top right). Connexels can be visualized with straight lines connecting each pair of connected nodes, but the structure of the data is unclear when a large number of connexels are included (Bottom).
Front Neurosci. 2014;8:15.
Figure 2
(A) Edge-bundling groups together geometrically similar connexels. (B) First, a measure of similarity (compatibility) between connexels is calculated from four geometrical criteria: length, angle, distance, and overlap (based on Holten and van Wijk, ). (C) Mean-shift edge-bundling then iteratively subdivides the connexels, and shifts compatible subdivision points toward their common mean. (D) Using a mean-shift has the advantage of bundling connexels with different density equally, and makes our method applicable to different datasets with the same default parameters.
Front Neurosci. 2014;8:15.
Figure 3
Functional connectivity is calculated between each pair of nodes on a set of cortical surface representations, and thresholding yields a set of connections, here colored by orientation. The colors and geometry of the connections are then used to calculate diverse glyph representations of the connectivity profile at each node. The vector and point glyph geometry is influenced by the choice of surface on a spectrum from the anatomically determined pial geometry, to the spherical representation. Drawing points diminishes overdraw, while drawing vectors emphasizes long-range connections. After sorting the colors by their hue, the pie charts emphasize the ratio of connections with different orientations.
Front Neurosci. 2014;8:15.
Figure 4
The size of the pie charts is linearly interpolated between conveying the number of connected nodes (Left) and a constant radius (Right).
Front Neurosci. 2014;8:15.
Figure 5
After painting an area of interest (Left), anatomical background glyphs for an area-of-interest can be displayed. They can either show color-mapped values on their surface (Top right), or serve to support the simplified glyphs (Bottom right).
Front Neurosci. 2014;8:15.
Figure 6
Difference glyphs show the boundaries of the primary visual cortex (Left). The triangle mesh is overlaid to illustrate the placement of the difference glyphs in the middle of each triangle edge in order to show the difference in connectivity profile between two adjacent mesh nodes.
Front Neurosci. 2014;8:15.
Figure 7
Thresholded connectivity for an example point glyph, represented with different coloring options: the orientation of the connexel (Left) or the associated connectivity value (Right).
Front Neurosci. 2014;8:15.
Figure 8
Unthresholded (Left), thresholded (Middle) and transparent (Right) point glyphs. Thresholding the glyphs leads to characteristic shapes, which also work well when minimized. Drawing glyphs with alpha blending makes it possible to perceive different connectivity values.
Front Neurosci. 2014;8:15.
Figure 9
The user interface is divided into a list of loaded datasets, three-dimensional views of the data, as well as global and dataset-specific properties. Depending on which data type is currently selected, different buttons in the toolbar are made available.
Front Neurosci. 2014;8:15.
Figure 10
Synchronized views of the data in brainGL showing visualization properties (Left), glyphs (Middle) and the color-mapped connectivity of a selected point (Right). Clicking on a node leads to the display of coordinate markers in both 3D views, and the display of the associated connectivity map in the right view. This allows for simultaneous overview of differences between neighboring nodes and their detailed individual connectivity.
Front Neurosci. 2014;8:15.
Figure 11
Interactive exploration of the two free parameters of glyph visualization. This example demonstrates the effects of adjusting the thresholding (Left) and removing short connections (Right).
Front Neurosci. 2014;8:15.
Figure 12
(A) Point, (B) vector and (C) pie chart glyphs for a whole-brain average functional connectivity dataset (threshold: r > 0.5, minimum length = 20 mm). Colors represent orientation of the underlying connections. The motor network presents as a red belt due to its lateral connectivity, and the visual network presents as collection of red/blue glyphs in the back of the brain. A multitude of other areas are distinguishable, representing a subdivision of the cortex into areas with similar functional connectivity profiles.
Front Neurosci. 2014;8:15.
Figure 13
Correlations between age and functional connectivity-based connexels in a group of 65 participants: the distribution of correlation values (A) is thresholded (at ±0.43, minimum length 20 mm). The remaining connections (B) vary strongly with age: The thresholded connexels in (b, right) gain connectivity strength over age, while the connexels in (B left) decrease in value (color represents orientation with xyz mapped to rgb). Edge-bundling (B, bottom, C) clarifies the structure of the connectivity graph. The same correlations visualized with surface connectivity glyphs (D,E), which clarify the anatomical placement of the connections termination points on the pial (D) and inflated (E) surface representation. Combined visualization with glyphs and bundlings (F). In (C–F), positive and negative values are shown in the same visualization (yellow-to-red color scale for negative, green-to-blue color scale for positive correlation with age).
Front Neurosci. 2014;8:15.