Cerliani, L.

Falkiewicz, M.

Margulies, D.

English

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Characterizing gradients in cortical connectivity: Assessment and applications of manifold learningFalkiewicz, M.1, Cerliani, L.2 & Margulies, D.S.1 1. Neuroanatomy & Connectivity Research Group, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germanymfalkiewicz@cbs.mpg.deIntroductionResultsConclusionsMethodsConfernce, Year2. Institut du Cerveau et de la moelle epiniere, Hopital Pitie-Salpetriere, Paris, France1. Gradients derived from RS represent well-known networks and relationships between them (Fig 2)2.  Gradients show remarkable consistency across subjects and sessions (Fig. 3)3. Relatively good classification accuracy could be achieved by manually drawing lines on a 2D plane (Fig. 4)4. Very small subsets of gradients allow to achieve high classification accura-cies of states within tasks (Fig. 5 and 6)5. Low-frequency gradients perform best for tasks which engage consistent sets of large-scale networks (Fig. 6)6. Further research is needed for devel-opment and interpretation of individual connectivity gradientsAnatomical description of the human connectome has largely focused on delineating distinct cortical areas and network modules using various forms of categorical clustering. However, such approaches are limited in revealing the presence of: 1. broader gradations across distinct parcels; and, 2. gradual transitions between distinct areas, as previously demonstrated in cytoarchitectonic data. Evidence from gold-standard tract- tracing studies in the macaque monkey indicates the presence of stepwise gradations in patterns of connec-tivity. For example, direct projections occur predominantly between areas that are one level away in the architectonic hierarchy. In the frontal lobe, this pattern of progressive architectonic differentiation is spatially organized along orthogonal gradients spanning the dor-so-ventral and rostro-caudal axes. Nonetheless, current applications of clustering methods to connectivity data acquired with MRI are not optimized to capture these overarching patterns. Previous studies have used MRI-based in vivo methods to investigate the similarity in the connectivity profiles of thousands of voxels simultaneously, and has shown the ability to identify boundaries between regions featuring a sharp transitions. However the presence of gradients of connectivity across regions has been thus far been neglected. Here we employed an original manifold learning method to recover com-plex connectivity structure, such as the overlapping gradients docu-mented by the neuroanatomical literature.We have used the ‘dense connectome’ derived from Human Connectome Project (HCP) [3,4] as the input to manifold learning algorithm, consisting of total 91282 cortical and sub-cortical nodes. The connectome was non-linearly decomposed into a set of spatial maps, which we call connectivity gradients (Fig 1a) [2]. The gradients represent sets of well-known resting state networks and relationships between them. Here we hy-pothesized that the set of gradients derived from resting state can be used as a basis set for the macroscale connectivity pat-terns [1]. To test this hypothesis, we have tested if the gradients can ap-proximate the activation patterns observed in 7 tasks used in HCP.  For each task, we have re-expressed each volume in time-series as a linear combination of 300 gradients derived from resting state (Fig 1b). For each subject and state, the weights of respective gradients were averaged. We have trained a SVM with L1-penalty to classify between states within each task - fixation, control task and main task. L1 penalty allowed to get a sparse solution. The goal was to get reasonable classification accuracy with the most sparse set of gradients possible. We report accuracies for training, test and validation sets, each consisting of approximately 90 subjectsReferencesa).1. Atasoy, S., Donnelly, I., & Pearson, J. (2016). Human brain networks function in connectome-specific harmonic waves. Nature communications, 7.2. Margulies, D.S., Ghosh, S., Goulas, A., Falkiewicz, M., Huntenburg, J.M., Langs, G., Bezgin, G., Eickhoff, S., Castellanos, F. X., Petrides, M., Jeffries, E. & Smallwood, J. (in press). Situating the default-mode network in a principal gradient of macroscale cortical connectivity. PNAS (in press).3. Smith, S. M., Beckmann, C. F., Andersson, J., Auerbach, E. J., Bijsterbosch, J., Douaud, G., ... & Kelly, M. (2013). Resting-state fMRI in the human connectome project. Neuroimage, 80, 144-168.4. Smith, S. M., Hyvärinen, A., Varoquaux, G., Miller, K. L., & Beckmann, C. F. (2014). Group-PCA for very large fMRI datasets. NeuroImage, 101, 738-749.1b)3Fig. 2 Average gradients timecourses (N=50) in WM task. Blue line represents run 1, orange - run 2. Red background represent 2-back condition, green - 0-back, white - fixation, brown - 2-back and 0-back switched between runs.4Fig. 3. States within WM task in space defined by 3 gradients. The plotsindicate that conditions within n-back task are clearly separated in this space.5Fig. 4. Model selection procedure. 3 gradients are sufficient to achieve very high classification accuracywithin the n-back task.6Fig. 5. Classification accuracies and selected gradientsfor all 7 HCP tasks. TR - training set, TE1 - test set 1, TE2, TE3 - independent test sets (different subjects)Fig. 2. Ten gradients based on resting state connectivity.123456789102

Characterizing gradients in cortical connectivity: Assessment and applications of manifold learning

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