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Multidimensional encoding of brain connectomes - PubMed

  • ️Sun Jan 01 2017

Multidimensional encoding of brain connectomes

Cesar F Caiafa et al. Sci Rep. 2017.

Abstract

The ability to map brain networks in living individuals is fundamental in efforts to chart the relation between human behavior, health and disease. Advances in network neuroscience may benefit from developing new frameworks for mapping brain connectomes. We present a framework to encode structural brain connectomes and diffusion-weighted magnetic resonance (dMRI) data using multidimensional arrays. The framework integrates the relation between connectome nodes, edges, white matter fascicles and diffusion data. We demonstrate the utility of the framework for in vivo white matter mapping and anatomical computing by evaluating 1,490 connectomes, thirteen tractography methods, and three data sets. The framework dramatically reduces storage requirements for connectome evaluation methods, with up to 40x compression factors. Evaluation of multiple, diverse datasets demonstrates the importance of spatial resolution in dMRI. We measured large increases in connectome resolution as function of data spatial resolution (up to 52%). Moreover, we demonstrate that the framework allows performing anatomical manipulations on white matter tracts for statistical inference and to study the white matter geometrical organization. Finally, we provide open-source software implementing the method and data to reproduce the results.

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Conflict of interest statement

The authors declare that they have no competing interests.

Figures

Figure 1
Figure 1

Connectome encoding using multidimensional arrays. (a) Top. Two white matter fascicles (f 1 and f 2) and three voxels (v 1, v 2 and v 3). Bottom. Tensor encoding of fascicles’ spatial and geometrical properties. Yellow f 1, dark blue f 2, cyan v 2. Non-zero entries in Φ_ indicate fascicles orientation (1st mode), position (voxel, 2nd mode) and identity (3rd mode). (b) Top. Two major human white matter tracts (connectome edges). The corticospinal tract and Arcuate fasciculus. Bottom. Tensor encoding of connectome edges. The corticospinal tract and Arcuate fasciculus are encoded as collections of frontal slices–blue and yellow subtensors. (c) Top. Two human cortical areas (connectome nodes). Wernicke’s territory and Broca’s area. Bottom. Tensor encoding of connectome nodes. We show examples of a large temporal area comprising also Wernicke’s territory and Broca’s area encoded as collections of lateral slices–red and green subtensors (areas defined using Freesurfer–,).

Figure 2
Figure 2

Tensor decomposition of the Linear Fascicle Evaluation method. (a) The tensor decomposition model, LiFET (see Supplementary Section 2.1 for details). LiFET uses a dictionary (matrix D) of precomputed diffusion predictions in combination with the sparse tensor, Φ_, and a vector of fascicles weights (w) to model the measured dMRI signal (matrix Y). (b) Comparison of the error in predicting diffusion. Scatter plot of the global r.m.s error (e¯rms; equation (8), Methods) in predicting diffusion measurements for LiFEM and LiFET in ten brains, three dataset (HCP3T, STN and STN150) and two tracking methods (tensor-based deterministic and probabilistic tractography). The r.m.s is virtually identical. (c) top LiFET error in approximating the LiFEM matrix (e M; Equation (9); Methods) computed for ten brains (HCP3T, STN and STN150 datasets, probabilistic tractography, L max = 10). Bottom. Error (e w; Equation (10); Methods) of LiFET in recovering the fascicle contributions (vector w) assigned by LiFEM. (N = 10, probabilistic tractography L max = 10) (d) Model compression. Measured size of LiFEM (matrix M) and the decomposed model, LiFET, (tensor Φ_ and matrix D; N = 20). Matrices and tensors all stored using double floating-point precision avoiding zero entries,.

Figure 3
Figure 3

Connectome resolution and anatomical reliability as function of data and method. (a) Scatter plot of number of found fascicles and global r.m.s error in LiFET optimized connectomes (mean ±5 standard error of the mean, s.e.m., N = 1,490, n = 12 subjects, m = 10 repeated tracking, using either 13 or 9 different L max values for either STN, HCP3T or HCP7T). Inset shows the relation between the number of found fascicles (ordinate) and r.m.s. error (abscissa) and L max (color) in one subject from the HCP3T dataset. (b) Reproducibility of connectome anatomy. Twenty major human white matter tracts, two repeated estimates in a single subject probabilistic (top) and deterministic (bottom) tracking, HCP3T dataset. Tracts anatomy is very similar between repeated estimates when using a single tracking method (compare between columns, top and bottom). Estimated tracts anatomy differs within a single subject when the different tracking methods are used (compare between rows, left or right). (c) A different subject from the HCP3T dataset.

Figure 4
Figure 4

Virtual lesion of white matter tracts using the tensor encoding framework. (a) Anatomical representation of the arcuate fasciculus and its path-neighborhood, blue and red respectively. (b) Identification of the arcuate fasciculus and its path-neighborhood. Top. Arcuate fascicles encoded as frontal slices collated by a permutation (F, blue). Middle. Ensemble of all voxels touched by the arcuate (lateral tensor slices, yellow) collated by a permutation. Bottom. The path-neighborhood (P F, red) contained in the non-empty frontal slices of V F. (c) The virtual lesion using the encoding framework. Top. Diffusion prediction (Y) in the arcuate voxels by the arcuate and its path-neighborhood. Bottom. Diffusion prediction (Y′) associated to P F, (arcuate fasciculus weights are set to zero, white). (d) Statistical evidence for twenty human major white matter tracts established using the sparse tensor encoding framework. Error bars show ±1 s.e.m.

Figure 5
Figure 5

Quantifying variability of estimates for angles of incidence between fascicles in the human white matter. (a) Arcuate (Arc, blue) and corticospinal tract (CST, yellow) fascicles identified in frontal slices of Φ_. (b) Voxels shared between Arc and CST located by finding lateral slices in Φ_ (green) with non-zero entries in the yellow and blue subtensors. (c) Measurement of the angle of incidence in the voxels shared by Arc and CST (green). Angles are determined by finding the indices in the first dimension of Φ_ (1st mode). (d) Depiction of angles being computed in brain space. (e) Distribution of crossing angles between Arc and CST. (f) Distribution of angles incidence between Arc and SLF. (g) Distribution of crossing angles between Arc and its neighborhood. Angles computed on Probabilistic (blue) and Deterministic (orange) connectomes (L max = 10, STN and HCP3T). Analyses based only on fascicles with positive weight. Histograms show mean across subjects (n = 8). Bar plots show peak angle (μ) and width-at-half height (σ). Error bars ±1 standard error of the mean, s.e.m, across subjects (n = 8).

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