Guided graph spectral embedding: Application to the <i>C. elegans</i> connectome

Petrovic, Miljan; Bolton, T. B.; Preti, Maria Giulia; Liégeois, Raphaël; Ville, Dimitri Van De

doi:10.1162/netn_a_00084

Cited by 13 publications

(10 citation statements)

References 55 publications

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“…In particular, because of the known retinotopic mapping between visual stimuli and neural activity, the visual cortex presents itself as a very interesting ROI for such developments [57]. Moving beyond neuronal populations and even the human brain, the mathematical framework of graph neural fields may also be used to implement single-neuron models directly on the full connectome graphs of simple organisms, such as C. Elegans, whose neuronal pathways have been experimentally mapped at the single-neuron level [22].…”

Section: Discussionmentioning

confidence: 99%

“…In short, MRI data is employed to obtain local graph edges based on the surface mesh; DTI data is employed to add long-range white-matter connections to the graph. The main difference with previous studies analyzing brain activity in terms of the anatomical connectome graph Laplacian [11] is that instead of constructing the combinatorial (binary) graph Laplacian, here we construct a distance-weighted graph Laplacian (Eqs (19)(20)(21)(22)). This allows us to take into account physical distance properties of the cortex that are relevant for graph neural fields, and that are otherwise lost.…”

Section: Author Summarymentioning

confidence: 99%

“…Graph neural fields present immediate application in the investigation of the relationship between individual anatomy, pathology, lesions, neuropharmacological alterations, with functional brain activity; and furthermore provide a modelbased approach to test novel graph signal processing neuroimaging hypotheses. While here we focus on the human connectome as a prime application for graph neural fields, the mathematical framework can also be used to implement and analyze single-neuron models directly on the connectome graphs of simple organisms, such as C. Elegans, whose full neuronal pathways have been experimentally mapped [22].…”

Section: Introductionmentioning

confidence: 99%

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Graph neural fields: A framework for spatiotemporal dynamical models on the human connectome

et al. 2021

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Tools from the field of graph signal processing, in particular the graph Laplacian operator, have recently been successfully applied to the investigation of structure-function relationships in the human brain. The eigenvectors of the human connectome graph Laplacian, dubbed “connectome harmonics”, have been shown to relate to the functionally relevant resting-state networks. Whole-brain modelling of brain activity combines structural connectivity with local dynamical models to provide insight into the large-scale functional organization of the human brain. In this study, we employ the graph Laplacian and its properties to define and implement a large class of neural activity models directly on the human connectome. These models, consisting of systems of stochastic integrodifferential equations on graphs, are dubbed graph neural fields, in analogy with the well-established continuous neural fields. We obtain analytic predictions for harmonic and temporal power spectra, as well as functional connectivity and coherence matrices, of graph neural fields, with a technique dubbed CHAOSS (shorthand for Connectome-Harmonic Analysis Of Spatiotemporal Spectra). Combining graph neural fields with appropriate observation models allows for estimating model parameters from experimental data as obtained from electroencephalography (EEG), magnetoencephalography (MEG), or functional magnetic resonance imaging (fMRI). As an example application, we study a stochastic Wilson-Cowan graph neural field model on a high-resolution connectome graph constructed from diffusion tensor imaging (DTI) and structural MRI data. We show that the model equilibrium fluctuations can reproduce the empirically observed harmonic power spectrum of resting-state fMRI data, and predict its functional connectivity, with a high level of detail. Graph neural fields natively allow the inclusion of important features of cortical anatomy and fast computations of observable quantities for comparison with multimodal empirical data. They thus appear particularly suitable for modelling whole-brain activity at mesoscopic scales, and opening new potential avenues for connectome-graph-based investigations of structure-function relationships.

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Section: Discussionmentioning

confidence: 99%

Section: Author Summarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Graph neural fields: A framework for spatiotemporal dynamical models on the human connectome

et al. 2021

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“…The lineage, morphology and synaptic connectivity of all 181 neurites is known 3,8 . While connectomic analyses have revealed network principles and circuit motifs [9][10][11][12][13][14][15][16][17][18][19][20][21][22] , we still lack an understanding of the design principles that underlie nerve ring neuropil architecture and function, and the developmental sequence that forms this functional architecture.…”

Section: Discussionmentioning

confidence: 99%

Structural and developmental principles of neuropil assembly inC. elegans

Moyle

Barnes

Kuchroo

et al. 2020

Preprint

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To visualize DC cluster relationships we developed C-PHATE, an extension of PHATE 30 capable of generating a 3D representation of the multigranular structures in the DC hierarchical tree ( Fig. 1a,b; see Methods). Quantitative comparisons of DC/C-PHATE results revealed similar clustering behaviors between the two separately analyzed nervering reconstructions (Adjusted Rand Index (ARI) of 0.7; Extended Data Fig. 1a,b), consistent with the long-accepted qualitative descriptions of the stereotyped structure for the C. elegans nerve ring 3,31 , and recent analyses of neurite adjacencies 22 . Examination of the cluster patterns through the iterations of DC revealed known cell-cell interactions and behavioral circuits ( Fig. 1b,c; Extended Data Fig. 2a,b; [32][33][34][35][36][37][38][39] ), consistent with behavioral and connectomic studies 10,19,20 . The multigranular outputs of the DC/C-PHATE results enabled understanding of the cell-cell interactions within the context of functional circuits, and the functional circuits within the context of the larger bundles of the neuropil.Comparisons of the modularity score, a measure of cluster robustness 40,41 , was highest when the majority of neurites were grouped into four super-clusters ( Fig. 1b; Extended Data Fig. 1a,b; Supplemental Video 1,2; see Methods). Overlaying our analysis of these four super-clusters (see Methods) onto the anatomy of the nerve ring revealed that they correspond to four distinct and tightly grouped bundles within the greater neuropil, circling the pharynx isthmus and stacked along the anterior-posterior axis of the animal. These clusters are herein called S1, S2, S3 and S4 for Stratum 1 etc. (Fig. 1c; Extended Data Fig. 1c-h; Supplemental Video 3 show details of these structures and single-cell identities). The stratified organization of the nerve ring neuropil, resolved here at single neurite level, is reminiscent of laminar organizations in the Drosophila nervous system 42,43 , and in the vertebrate retina and the brain cortex 44,45 .We observed that not all computationally clustered neurites followed simple bundled paths through the neuropil. In Strata 1 (S1), 32 anterior sensory neurons project perpendicular to the nerve ring bundle before making a 180º curl and returning to the anterior limits of the neuropil, where they terminate as synaptic endplates (Fig. 1d; Extended Data Fig. 3a-d; 3,46 ). These uniquely shaped S1 neurons looped at the borders of the S2/S3/S4 bundles. The anterior loops encase ~90% of S2, and the posterior loops encase ~84% of S3 and 100% of S4 ( Fig. 1d-g; Extended Data Fig. 3e-k ; SupplementalVideo 5; Supplemental Table 1). We found that the 32 axons form a six-fold symmetrical honeycomb structure along the neuropil's arc, creating a scaffold that encapsulates the different strata ( Fig. 1g; Extended Data Fig. 3e-h; Supplemental Video 4).The architecture of the neuropil reflects functional segregation of distinct sensory information streams and motor outputs.C. elegans neurons can be divided into three categories ...

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“…Graph Slepians have been recently launched as functions that generalize the standard Slepians for graph signals [47], [48], by introducing the notions of selectivity and bandwidth that correspond to the imposed constrains. The former refers to the original graph domain, while the latter to the graph spectral domain.…”

Section: Graph Slepiansmentioning

confidence: 99%

Covariation Informed Graph Slepians for Motor Imagery Decoding

Georgiadis

Adamos

Nikolopoulos

et al. 2021

IEEE Trans. Neural Syst. Rehabil. Eng.

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Graph signal processing (GSP) provides signal analytic tools for data defined in irregular domains, as is the case of non-invasive electroencephalography (EEG). In this work, the recently introduced technique of Graph Slepian functions is exploited for the robust decoding of motor imagery (MI) brain activity. The particular technique builds over the concept of graph Fourier transform (GFT) and provides additional flexibility in the subsequent data analysis by incorporating domain knowledge. Based on contrastive learning, we introduce an algorithmic pipeline that attains a data driven and subject specific design of Graph Slepian functions. These functions, by incorporating both the topology of the sensor array and the empirical evidence about the differential functional covariation, act as spatial filters that enhance the information conveyed by the multichannel signal and specifically relates to the participant's intention. The proposed technique for crafting Graph Slepians is incorporated in a MI-decoding scheme, in which the informed projections are fed to a support vector machine (SVM) that casts a prediction regarding the type of intended movement. The employed MI-decoder is evaluated based on two publicly available datasets and its superiority against popular alternatives in the field is established. Computational efficiency is listed among its main advantages, since it involves only simple matrix operations, allowing to consider its use in real-time implementations.

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Guided graph spectral embedding: Application to the C. elegans connectome

Cited by 13 publications

References 55 publications

Graph neural fields: A framework for spatiotemporal dynamical models on the human connectome

Graph neural fields: A framework for spatiotemporal dynamical models on the human connectome

Structural and developmental principles of neuropil assembly inC. elegans

Covariation Informed Graph Slepians for Motor Imagery Decoding

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