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Structure-function multilayer network integration and cognition in multiple sclerosis.

Code ↔ Paper

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The 2 matches
  1. [1] § METHODS › Network Construction › Multilayer networks. ↔ multinetx/core/multilayer.py, lines 53–138 · score 0.67 · MultiNetX, adjacency matrices, diagonal, NetworkX, Python, multilayer
  2. [2] § METHODS › Network Construction › Multilayer networks. ↔ multinetx/__init__.py, lines 27–41 · score 0.53 · NetworkX, multiNetX, Python, multilayer

Paper

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The authors' code

Python · 266 lines · 9.4 KB · no license · 1 match

  1. #! /usr/bin/env python
  2. # -*- coding: utf-8 -*-
  3. ########################################################################
  4. #
  5. # multiNetX -- a python package for general multilayer graphs
  6. #
  7. # (C) Copyright 2013-2019, Nikos E Kouvaris
  8. # multiNetX is part of the deliverables of the LASAGNE project
  9. # (multi-LAyer SpAtiotemporal Generalized NEtworks),
  10. # EU/FP7-2012-STREP-318132 (http://complex.ffn.ub.es/~lasagne/)
  11. #
  12. # multiNetX is free software: you can redistribute it and/or modify
  13. # it under the terms of the GNU General Public License as published
  14. # by the Free Software Foundation, either version 3 of the License,
  15. # or (at your option) any later version.
  16. #
  17. # multiNetX is distributed in the hope that it will be useful,
  18. # but WITHOUT ANY WARRANTY; without even the implied warranty of
  19. # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
  20. # See the GNU General Public License for more details.
  21. #
  22. # You should have received a copy of the GNU General Public License
  23. # along with this program. If not, see http://www.gnu.org/licenses/.
  24. ########################################################################
  25. """
  26. MultilayerGraph: Base class for a multi-layer network
  27. """
  28. from multinetx.core.exceptions import multinetxError
  29. # import copy
  30. try:
  31. from networkx import Graph, disjoint_union_all
  32. except ImportError:
  33. raise ImportError("NetworkX is required")
  34. try:
  35. from numpy import zeros
  36. except ImportError:
  37. raise ImportError("NumPy is required")
  38. try:
  39. from scipy.sparse import lil_matrix
  40. except ImportError:
  41. raise ImportError("SciPy is required")
  42. class MultilayerGraph(Graph):
  43. """"Define constructor of the class"""
  44. def __init__(self, list_of_layers=None, inter_adjacency_matrix=None, **attr):
  45. """Constructor of a MultilayerGraph.
  46. It creates a symmetric (undirected) MultilayerGraph object
  47. inheriting methods from networkx.Graph
  48. Parameters:
  49. -----------
  50. list_of_layers : Python list of networkx.Graph objects
  51. inter_adjacency_matrix : a lil sparse matrix (NxN) with zero
  52. diagonal elements and off-diagonal
  53. block elements defined by the
  54. inter-connectivity architecture.
  55. Return: a MultilayerGraph object
  56. Examples:
  57. ---------
  58. import multinetx as mx
  59. import numpy as np
  60. N = 10
  61. g1 = mx.erdos_renyi_graph(N,0.07,seed=218)
  62. g2 = mx.erdos_renyi_graph(N,0.07,seed=211)
  63. g3 = mx.erdos_renyi_graph(N,0.07,seed=211)
  64. adj_block = mx.lil_matrix(np.zeros((N*3,N*3)))
  65. adj_block[0: N, N:2*N] = np.identity(N) # L_12
  66. adj_block[0: N,2*N:3*N] = np.identity(N) # L_13
  67. #adj_block[N:2*N,2*N:3*N] = np.identity(N) # L_23
  68. adj_block += adj_block.T
  69. mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3],
  70. inter_adjacency_matrix=adj_block)
  71. mg.set_edges_weights(inter_layer_edges_weight=4)
  72. mg.set_intra_edges_weights(layer=0,weight=1)
  73. mg.set_intra_edges_weights(layer=1,weight=2)
  74. mg.set_intra_edges_weights(layer=2,weight=3)
  75. """
  76. # Give an empty graph in the list_of_layers
  77. if list_of_layers is None:
  78. self.list_of_layers = [Graph()]
  79. self.num_nodes_in_layers = []
  80. else:
  81. self.list_of_layers = list_of_layers
  82. self.num_nodes_in_layers = [
  83. layer.number_of_nodes() for layer in list_of_layers
  84. ]
  85. # Number of nodes
  86. self.num_nodes = sum(self.num_nodes_in_layers)
  87. # Create the MultilayerGraph without inter-layer links.
  88. try:
  89. Graph.__init__(self, Graph(disjoint_union_all(self.list_of_layers), **attr))
  90. except multinetxError:
  91. raise multinetxError("Multiplex cannot inherit Graph properly")
  92. # Make a zero lil matrix for inter_adjacency_matrix
  93. if inter_adjacency_matrix is None:
  94. inter_adjacency_matrix = lil_matrix(zeros((self.num_nodes, self.num_nodes)))
  95. # Check if the matrix inter_adjacency_matrix is lil
  96. try:
  97. assert inter_adjacency_matrix.format == "lil"
  98. except AssertionError:
  99. raise multinetxError(
  100. "interconnecting_adjacency_matrix\
  101. is not scipy.sparse.lil"
  102. )
  103. # Lists for intra-layer and inter-layer edges
  104. if list_of_layers is None:
  105. self.intra_layer_edges = []
  106. else:
  107. self.intra_layer_edges = self.edges()
  108. self.inter_layer_edges = []
  109. # Inter-layer connection
  110. self.layers_interconnect(inter_adjacency_matrix)
  111. # MultiNetX name
  112. self.name = "multilayer"
  113. for layer in self.list_of_layers:
  114. self.name += "_" + layer.name
  115. # Constructor
  116. # Define methods of the class
  117. def add_layer(self, layer, **attr):
  118. if self.num_nodes is 0:
  119. self.list_of_layers = [layer]
  120. else:
  121. self.list_of_layers.append(layer)
  122. self.num_nodes_in_layers.append(layer.number_of_nodes())
  123. self.num_nodes = sum(self.num_nodes_in_layers)
  124. for i, j in layer.edges():
  125. self.intra_layer_edges.append(
  126. (
  127. i + (len(self.list_of_layers) - 1) * layer.number_of_nodes(),
  128. j + (len(self.list_of_layers) - 1) * layer.number_of_nodes(),
  129. )
  130. )
  131. try:
  132. Graph.__init__(
  133. self, Graph(disjoint_union_all(self.list_of_layers), **attr)
  134. )
  135. except multinetxError:
  136. raise multinetxError("Multiplex cannot inherit Graph properly")
  137. def layers_interconnect(self, inter_adjacency_matrix=None):
  138. """Parameters:
  139. -----------
  140. Examples:
  141. ---------
  142. """
  143. # Make a zero lil matrix for inter_adjacency_matrix
  144. if inter_adjacency_matrix is None:
  145. inter_adjacency_matrix = lil_matrix(zeros((self.num_nodes, self.num_nodes)))
  146. # Check if the matrix inter_adjacency_matrix is lil
  147. try:
  148. assert inter_adjacency_matrix.format == "lil"
  149. except AssertionError:
  150. raise multinetxError(
  151. "interconnecting_adjacency_matrix\
  152. is not scipy.sparse.lil"
  153. )
  154. for i, row in enumerate(inter_adjacency_matrix.rows):
  155. for pos, j in enumerate(row):
  156. if i > j:
  157. self.inter_layer_edges.append((i, j))
  158. self.add_edges_from(self.inter_layer_edges)
  159. def get_number_of_layers(self):
  160. """Return the number of graphs"""
  161. return len(self.list_of_layers)
  162. def get_number_of_nodes_in_layers(self):
  163. """Return the number of nodes in each graph"""
  164. return self.num_nodes_in_layers
  165. def get_number_of_nodes(self):
  166. return self.num_nodes
  167. def get_intra_layer_edges(self):
  168. """Return a list with the intra-layer edges"""
  169. return self.intra_layer_edges
  170. def get_intra_layer_edges_of_layer(self, layer=0):
  171. """Return a list with the intra-layer edges of layer"""
  172. edge_list = self.get_layer(layer).edges()
  173. # liste of previous layer
  174. past = [self.num_nodes_in_layers[i] for i in range(layer)]
  175. # number of previous nodes
  176. num_past = sum(past)
  177. elist = []
  178. for i, j in edge_list:
  179. elist.append((num_past + i, num_past + j))
  180. return elist
  181. def get_inter_layer_edges(self):
  182. """Return a list with the inter-layer edges"""
  183. return self.inter_layer_edges
  184. def get_list_of_layers(self):
  185. """Return a list with the graphs of the layers"""
  186. return self.list_of_layers
  187. def get_layer(self, layer_number):
  188. """Return the networkx graph of the layer layer_number"""
  189. return self.list_of_layers[layer_number]
  190. def set_edges_weights(
  191. self, intra_layer_edges_weight=None, inter_layer_edges_weight=None
  192. ):
  193. """Set the weights of the MultilayerGraph edges
  194. ---
  195. intra_layer_edges_weight
  196. inter_layer_edges_weight
  197. ---
  198. Set the "intra_layer_edges_weight" and "inter_layer_edges_weight"
  199. as an edge attribute with the name "weight"
  200. """
  201. if intra_layer_edges_weight is not None:
  202. self.add_edges_from(self.intra_layer_edges, weight=intra_layer_edges_weight)
  203. if inter_layer_edges_weight is not None:
  204. self.add_edges_from(self.inter_layer_edges, weight=inter_layer_edges_weight)
  205. def set_intra_edges_weights(self, layer=0, weight=None):
  206. """Set the weights of the MultilayerGraph edges
  207. ---
  208. intra_layer_edges_weight
  209. ---
  210. Set the "intra_layer_edges_weight" and "intra_layer_edges_weight"
  211. as an edge attribute with the name "weight"
  212. """
  213. elist = self.get_intra_layer_edges_of_layer(layer=layer)
  214. self.add_edges_from(elist, weight=weight)
  215. def info(self):
  216. """Returns some information of the object MultilayerGraph"""
  217. info = "{}-layer graph,\
  218. intra_layer_edges:{},\
  219. inter_layer_edges:{},\
  220. number_of_nodes_in_layer:{} ".format(
  221. len(self.list_of_layers),
  222. len(self.intra_layer_edges),
  223. len(self.inter_layer_edges),
  224. self.num_nodes_in_layers,
  225. )
  226. return info

multilayer.py at commit 0f1d808, no license · at the source

Overview

Authors: Lucas C Breedt1, Giuseppe Pontillo2,3,4,5, Fernando A N Santos1,6, Chris Vriend1,7, Ferran Prados2,8,9, Alle Meije Wink2,4, Alvino Bisecco10, Alessandro Cagol11,12,13,14, Massimiliano Calabrese15, Marco Castellaro15,16, Sara Collorone3, Rosa Cortese17, Nicola De Stefano17, Christian Enzinger18, Massimo Filippi19,20,21,22,23, Michael A Foster3, Antonio Gallo10, Gabriel Gonzalez-Escamilla24, Cristina Granziera11,12,13, Sergiu Groppa24
and 18 other authorsEinar A Høgestøl25,26,27, Sara Llufriu28, Eloy Martinez-Heras28, Elisabeth Solana28, Silvia Messina29, Marcello Moccia3,30, Gro O Nygaard25,27, Jacqueline Palace29, Daniela Pinter18, Mara A Rocca19,20,23, Ahmed Toosy3, Paola Valsasina19, Olga Ciccarelli3, Eva M Strijbis2,31, Frederik Barkhof2,3,4,8,32, Menno M Schoonheim1,2, Linda Douw1, MAGNIMS study group
32 affiliations
  1. Department of Anatomy and Neurosciences, Amsterdam Neuroscience, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
  2. MS Center Amsterdam, Amsterdam Neuroscience, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
  3. Queen Square Multiple Sclerosis Centre, Department of Neuroinflammation, UCL Queen Square Institute of Neurology, University College London, London, United Kingdom
  4. Department of Radiology and Nuclear Medicine, MS Center Amsterdam, Amsterdam Neuroscience, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
  5. Departments of Advanced Biomedical Sciences and Electrical Engineering and Information Technology, University of Naples “Federico II,” Naples, Italy
  6. Dutch Institute for Emergent Phenomena (DIEP), Institute for Advanced Studies, University of Amsterdam, Amsterdam, The Netherlands
  7. Department of Psychiatry, Amsterdam Neuroscience, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
  8. Centre for Medical Image Computing, Department of Medical Physics and Biomedical Engineering, University College London, London, United Kingdom
  9. E-Health Center, Universitat Oberta de Catalunya, Barcelona, Spain
  10. Department of Advanced Medical and Surgical Sciences, University of Campania “Luigi Vanvitelli,” Naples, Italy
  11. Translational Imaging in Neurology (ThINK) Basel, Department of Biomedical Engineering, Faculty of Medicine, University Hospital Basel and University of Basel, Basel, Switzerland
  12. Department of Neurology, University Hospital Basel, Basel, Switzerland
  13. Research Center for Clinical Neuroimmunology and Neuroscience Basel (RC2NB), University Hospital Basel and University of Basel, Basel, Switzerland
  14. Dipartimento di Scienze della Salute, Università degli Studi di Genova
  15. Department of Neurosciences, Biomedicine and Movement Sciences, University of Verona, Verona, Italy
  16. Department of Information Engineering, University of Padova, Padova, Italy
  17. Department of Medicine, Surgery and Neuroscience, University of Siena, Siena, Italy
  18. Department of Neurology, Medical University of Graz, Graz, Austria
  19. Neuroimaging Research Unit, Division of Neuroscience, IRCCS San Raffaele Scientific Institute, Milan, Italy
  20. Neurology Unit, IRCCS San Raffaele Scientific Institute, Milan, Italy
  21. Neurorehabilitation Unit, IRCCS San Raffaele Scientific Institute, Milan, Italy
  22. Neurophysiology Service, IRCCS San Raffaele Scientific Institute, Milan, Italy
  23. Vita-Salute San Raffaele University, Milan, Italy
  24. Movement Disorders, Neurostimulation and Neuroimaging, University Medicine Mainz, Mainz, Germany
  25. Department of Neurology, Oslo University Hospital, Oslo, Norway
  26. Department of Psychology, University of Oslo, Oslo, Norway
  27. Institute of Clinical Medicine, University of Oslo, Oslo, Norway
  28. Neuroimmunology and Multiple Sclerosis Unit and Laboratory of Advanced Imaging in Neuroimmunological Diseases (ImaginEM), Hospital Clinic and Institut d’Investigacions Biomèdiques August Pi i Sunyer (IDIBAPS), University of Barcelona, Barcelona, Spain
  29. Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, United Kingdom
  30. Department of Molecular Medicine and Medical Biotechnology, University of Naples “Federico II,” Naples, Italy
  31. Department of Neurology, MS Center Amsterdam, Amsterdam Neuroscience, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
  32. Dementia Research Centre, UCL Queen Square Institute of Neurology, University College London, London, United Kingdom
Journal: Network neuroscience (Cambridge, Mass.), volume 10, issue 2, pages 400-417
Dates: received 31 March 2025; accepted 22 December 2025; published online 22 April 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1162/netn.a.545 · PMID 42039096 · PMCID PMC13108497 · OpenAlex W7124219763
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: structural MRI / diffusion (modality), fMRI (modality), multiple sclerosis (population), cognitive (subfield)
Methods: Spectral & time-frequency, Connectivity, Smoothing, state filtering, decompositions, Machine learning, Preprocessing, Statistics, fMRI & imaging
Keywords: Executive functioning, Graph theory, Functional connectivity, Structural connectivity, Multilayer networks
Topic: Functional Brain Connectivity Studies (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Citations: not cited yet (Europe PMC); 71 references in the paper

Abstract

People with multiple sclerosis (MS) often present with cognitive deficits that cannot fully be attributed to focal brain alterations. Whole-brain network changes show stronger relations, but MS network insights have mostly focused on either structural or functional (single-layer) networks, while recent work has shown the importance of multilayer frontoparietal network integration for cognition. Here, we explored the cognitive relevance of multilayer integration of the frontoparietal network in relapsing–remitting MS (n = 780) using diffusion and resting-state fMRI. Cognitive relations were first assessed for nodal multilayer eigenvector centrality, averaged over frontoparietal network nodes as a measure of integration, and post hoc for mean eccentricity for both single layer and multilayers. Higher multilayer frontoparietal network centrality was associated with worse Symbol Digit Modalities Test (SDMT) performance (β = −.117, p = .005). Mean eccentricity of single-layer diffusion (β = −.123, p < .001) and multilayer networks (β = .085, p = .018) were associated with SDMT performance. However, results could not be replicated using a different anatomical parcellation. This study showed that cognition in MS is related to multilayer network parameters. Nevertheless, correlations were weak and atlas specific, suggesting that a binary structure–function multilayer network approach is not particularly relevant as a correlate of cognition in MS.

Reproduced under the paper's license (CC BY), from the paper cited above.

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python.org

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networkx

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At the source: github.com/networkx

nkoub/multinetx

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Commit: 0f1d80869cb5ba8138988bd778ec480b9a099268, 5 August 2024
Languages: Jupyter (10), Python (7)
Size: 54 files, 17 scripts
Software Heritage: archived
Found in: the text, “Multilayer networks.”
Holds: README, environment (requirements.txt, setup.cfg, setup.py), documentation, 5 notebooks
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18 files

multinetlab-amsterdam

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Data

No dataset and no data link were found in the paper.

Data Availability Statement

The code used for the analyses in this study are available upon request; please contact L.D.

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Versions

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Recorded: type, language, journal, volume, issue, pages, dates, 38 authors, 5 keywords, 68 references.

Cite

This paper

Breedt, L. C., Pontillo, G., Santos, F. A. N., Vriend, C., Prados, F., Wink, A. M., Bisecco, A., Cagol, A., Calabrese, M., Castellaro, M., Collorone, S., Cortese, R., De Stefano, N., Enzinger, C., Filippi, M., Foster, M. A., Gallo, A., Gonzalez-Escamilla, G., Granziera, C., . . . MAGNIMS study group. (2026). Structure-function multilayer network integration and cognition in multiple sclerosis. Network neuroscience (Cambridge, Mass.), 10(2), 400-417. https://doi.org/10.1162/netn.a.545

BibTeX

@article{breedt2026structure,
author = {Breedt, Lucas C and Pontillo, Giuseppe and Santos, Fernando A N and Vriend, Chris and Prados, Ferran and Wink, Alle Meije and Bisecco, Alvino and Cagol, Alessandro and Calabrese, Massimiliano and Castellaro, Marco and Collorone, Sara and Cortese, Rosa and De Stefano, Nicola and Enzinger, Christian and Filippi, Massimo and Foster, Michael A and Gallo, Antonio and Gonzalez-Escamilla, Gabriel and Granziera, Cristina and Groppa, Sergiu and Høgestøl, Einar A and Llufriu, Sara and Martinez-Heras, Eloy and Solana, Elisabeth and Messina, Silvia and Moccia, Marcello and Nygaard, Gro O and Palace, Jacqueline and Pinter, Daniela and Rocca, Mara A and Toosy, Ahmed and Valsasina, Paola and Ciccarelli, Olga and Strijbis, Eva M and Barkhof, Frederik and Schoonheim, Menno M and Douw, Linda and {MAGNIMS study group}},
title = {{Structure-function multilayer network integration and cognition in multiple sclerosis}},
journal = {Network neuroscience (Cambridge, Mass.)},
year = {2026},
month = apr,
volume = {10},
number = {2},
pages = {400--417},
publisher = {MIT Press},
issn = {2472-1751},
doi = {10.1162/netn.a.545},
url = {https://doi.org/10.1162/netn.a.545},
pmid = {42039096},
pmcid = {PMC13108497}
}

RIS

TY - JOUR
AU - Breedt, Lucas C
AU - Pontillo, Giuseppe
AU - Santos, Fernando A N
AU - Vriend, Chris
AU - Prados, Ferran
AU - Wink, Alle Meije
AU - Bisecco, Alvino
AU - Cagol, Alessandro
AU - Calabrese, Massimiliano
AU - Castellaro, Marco
AU - Collorone, Sara
AU - Cortese, Rosa
AU - De Stefano, Nicola
AU - Enzinger, Christian
AU - Filippi, Massimo
AU - Foster, Michael A
AU - Gallo, Antonio
AU - Gonzalez-Escamilla, Gabriel
AU - Granziera, Cristina
AU - Groppa, Sergiu
AU - Høgestøl, Einar A
AU - Llufriu, Sara
AU - Martinez-Heras, Eloy
AU - Solana, Elisabeth
AU - Messina, Silvia
AU - Moccia, Marcello
AU - Nygaard, Gro O
AU - Palace, Jacqueline
AU - Pinter, Daniela
AU - Rocca, Mara A
AU - Toosy, Ahmed
AU - Valsasina, Paola
AU - Ciccarelli, Olga
AU - Strijbis, Eva M
AU - Barkhof, Frederik
AU - Schoonheim, Menno M
AU - Douw, Linda
AU - MAGNIMS study group
TI - Structure-function multilayer network integration and cognition in multiple sclerosis
T2 - Network neuroscience (Cambridge, Mass.)
J2 - Netw Neurosci
PY - 2026
DA - 2026/04/22
VL - 10
IS - 2
SP - 400
EP - 417
SN - 2472-1751
PB - MIT Press
DO - 10.1162/netn.a.545
UR - https://doi.org/10.1162/netn.a.545
LA - en
ER -

CSL-JSON

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"id": "10.1162/netn.a.545",
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"given": "Gabriel"
},
{
"family": "Granziera",
"given": "Cristina"
},
{
"family": "Groppa",
"given": "Sergiu"
},
{
"family": "Høgestøl",
"given": "Einar A"
},
{
"family": "Llufriu",
"given": "Sara"
},
{
"family": "Martinez-Heras",
"given": "Eloy"
},
{
"family": "Solana",
"given": "Elisabeth"
},
{
"family": "Messina",
"given": "Silvia"
},
{
"family": "Moccia",
"given": "Marcello"
},
{
"family": "Nygaard",
"given": "Gro O"
},
{
"family": "Palace",
"given": "Jacqueline"
},
{
"family": "Pinter",
"given": "Daniela"
},
{
"family": "Rocca",
"given": "Mara A"
},
{
"family": "Toosy",
"given": "Ahmed"
},
{
"family": "Valsasina",
"given": "Paola"
},
{
"family": "Ciccarelli",
"given": "Olga"
},
{
"family": "Strijbis",
"given": "Eva M"
},
{
"family": "Barkhof",
"given": "Frederik"
},
{
"family": "Schoonheim",
"given": "Menno M"
},
{
"family": "Douw",
"given": "Linda"
},
{
"literal": "MAGNIMS study group"
}
],
"container-title-short": "Netw Neurosci",
"volume": "10",
"issue": "2",
"page": "400-417",
"DOI": "10.1162/netn.a.545",
"PMID": "42039096",
"PMCID": "PMC13108497",
"ISSN": "2472-1751",
"publisher": "MIT Press",
"URL": "https://doi.org/10.1162/netn.a.545",
"language": "en",
"issued": {
"date-parts": [
[
2026,
4,
22
]
]
}
}

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