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Integrated anatomical and functional connectivity mapping in episodic migraine: a spectral graph theory approach.

Code ↔ Paper

2 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 2 matches
  1. [1] § Methodology › General pipeline ↔ Code/Error_Metrics/robustnessAnalysis_PIC.m, lines 1–76 · score 0.58 · Spectral mapping, structural matrix, robustness, functional matrix, power, diagonal
  2. [2] § Methodology › Connectivity matrices › Individual contributions of walk lengths ↔ Code/Error_Metrics/robustnessAnalysis_PIC.m, lines 84–122 · score 0.51 · rotation matrix, polynomial, Becker, functional matrix, powers, predict

Paper

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The authors' code

MATLAB · 146 lines · 3.9 KB · no license · 2 matches

  1. function robustnessAnalysis()
  2. % Investigate the robustness of individual spectral mapping with respect to noise
  3. % in the structural matrices using the multiplicative perturbation model.
  5. add_folders();
  7. % Parameters
  8. rho_values = 0:0.02:0.5; % Range of perturbation parameter rho
  9. k = 7; % Maximum power for polynomial expansion
  10. num_runs = 10000; % Number of runs for averaging
  12. % Define matrix F
  13. F = [
  14. 1.0000 0.0641 0.7277 0.3484;
  15. 0.0641 1.0000 0.1533 0.1546;
  16. 0.7277 0.1533 1.0000 0.1029;
  17. 0.3484 0.1546 0.1029 1.0000
  18. ];
  20. % Define matrix S
  21. S = [
  22. 1.0000 0.7355 0.6143 0.1188;
  23. 0.7355 1.0000 0.2711 0.4548;
  24. 0.6143 0.2711 1.0000 0.3465;
  25. 0.1188 0.4548 0.3465 1.0000
  26. ];
  28. % Symmetrize matrices
  29. S = (S + S') / 2;
  30. F = (F + F') / 2;
  32. % Set diagonal elements to 1
  33. S(1:size(S, 1) + 1:end) = 1;
  34. F(1:size(F, 1) + 1:end) = 1;
  36. % Train the model
  37. [a, R] = individual_train(S, F, k);
  39. % Initialize matrix to store average correlations
  40. average_correlations = zeros(1, length(rho_values));
  42. % Loop over rho values
  43. for idx = 1:length(rho_values)
  44. rho = rho_values(idx);
  45. temp_correlations = zeros(1, num_runs); % Store correlations for each run
  47. for run = 1:num_runs
  48. % Perturb the structural matrix using the multiplicative model
  49. Delta = (2 * rho * rand(size(S)) - rho); % Uniform perturbation in [-rho, rho]
  50. S_perturbed = (1 + Delta) .* S; % Apply multiplicative perturbation
  51. S_perturbed = (S_perturbed + S_perturbed') / 2; % Ensure symmetry
  53. % Predict functional matrix from perturbed structural matrix
  54. F_perturbed = individual_predict(S_perturbed, a, R);
  56. % Calculate correlation between original and perturbed functional matrices
  57. temp_correlations(run) = smcorr(F, F_perturbed);
  58. end
  60. % Compute the average correlation for this rho
  61. average_correlations(idx) = mean(temp_correlations);
  62. end
  64. % Plot results
  65. figure;
  66. plot(rho_values, average_correlations, '-o', 'LineWidth', 2);
  67. xlabel('\rho (Perturbation Parameter)');
  68. ylabel('Average Correlation (u_{corr})');
  69. title('Robustness of Spectral Mapping to Structural Noise');
  70. grid on;
  72. end
  74. % Funções auxiliares
  76. % private function to add toolbox folders to the matlab path
  77. function add_folders()
  79. parts = strsplit(mfilename('fullpath'),filesep);
  80. addpath(genpath([filesep fullfile(parts{1:end-2})]));
  82. end
  84. function [a,R] = individual_train(S,F,k)
  85. % INDIVIDUAL_TRAIN trains a mapping for single subjects based on a vector of
  86. % coefficents and a rotation matrix.
  87. %
  88. % Inputs:
  89. % S - symmetric structural matrix
  90. % F - symmetric functional matrix
  91. % k - the maximum power of the polynomial (paths length)
  92. %
  93. % Outputs:
  94. % a - vector of coefficients
  95. % R - rotation matrix
  96. %
  97. % See also INDIVIDUAL_PREDICT.
  98. %
  99. % Author: Cassiano Becker, June 2017
  100. %
  101. % ---- BEGIN CODE ----
  103. % perform ordered eigendecomposition
  104. %compute and order eigen values(V) and eigen vectors(lam) for both Matrices
  106. [V,lam] = oeig(S);
  107. [U,phi] = oeig(F);
  109. %compute the vandermonde matrix
  110. L = vandermonde(lam,k);
  112. %computes the pseudoinverse matrix
  113. Ldag = pinv(L);
  115. % vector of cofficients
  116. a = (Ldag*phi);
  118. % rotation matrix
  119. R = U*V';
  122. end
  124. function textMatrix(M)
  125. % Adiciona os valores da matriz como texto no gráfico
  126. [rows, cols] = size(M);
  127. for i = 1:rows
  128. for j = 1:cols
  129. text(j, i, sprintf('%.2f', M(i, j)), ...
  130. 'HorizontalAlignment', 'center', 'Color', 'black', 'FontSize', 10);
  131. end
  132. end
  133. end
  135. function Fhat = individual_predict(S,a,R)
  137. [V,lam] = oeig(S);
  139. k = length(a)-1;
  141. L = vandermonde(lam,k);
  143. % apply mapping
  144. Fhat = R*V*diag(L*a)*(V')*(R');
  146. end

robustnessAnalysis_PIC.m at commit e2ddae4, no license · at the source

Overview

Authors: Gonçalo Grácio1, Ana Matoso2, Inês Esteves2, Ana R Fouto2,3, Amparo Ruiz-Tagle2, Gina Caetano2, Raquel Gil-Gouveia4,5, Patrícia Figueiredo2, Rita G Nunes2, Sérgio Pequito1
ORCID iDs: Raquel Gil-Gouveia
  1. Institute for Systems and Robotics – Lisboa and Department of Electrical and Computer Engineering, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal
  2. Institute for Systems and Robotics - Lisboa and Department of Bioengineering, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal
  3. Algarve Biomedical Center, Faro, Portugal
  4. Neurology Department, Hospital da Luz, Lisbon, Portugal
  5. Center for Interdisciplinary Research in Health, Universidade Católica Portuguesa, Lisbon, Portugal
Institutions: University of Lisbon (Portugal); Instituto Superior Técnico (Portugal); Algarve Biomedical Center (Portugal); Universidade Católica Portuguesa (Portugal); Hospital da Luz (Portugal)
Journal: Scientific reports, volume 16, issue 1, article 22871
Dates: received 17 September 2025; accepted 13 May 2026; published online 20 May 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1038/s41598-026-53726-7 · PMID 42156507 · PMCID PMC13388938 · OpenAlex W4414994944
Open access: gold, a free copy (OpenAlex)
Preprint: doi:10.21203/rs.3.rs-7643639/v1
Status: code verified
Categories: structural MRI / diffusion (modality), fMRI (modality), human (organism), pain (population)
Methods: Spectral & time-frequency, Connectivity, Statistics, Machine learning, fMRI & imaging
Keywords: Neurology, Neuroscience
MeSH: Brain*, Brain Mapping*, Migraine Disorders*, Adult, Case-Control Studies, Diffusion Magnetic Resonance Imaging, Female, Humans, Magnetic Resonance Imaging, Nerve Net (* major topic)
Topic: Migraine and Headache Studies (Psychiatry and Mental health, Medicine), according to OpenAlex
Funding: Fundação para a Ciência e a Tecnologia (2023.03810.BDANA)
Citations: not cited yet (Europe PMC); 63 references in the paper

Abstract

Migraine disproportionately affects women, yet how migraine physiology reshapes large-scale brain communication remains unclear. We combined diffusion-weighted imaging (DWI) and resting-state fMRI in female participants (14 patients with episodic migraine without aura; 15 matched healthy controls) to test how direct and indirect anatomical communication paths in the brain can predict brain function. We used a spectral mapping framework that isolates the contribution of communication paths of a specific length and evaluated how well brain structure predicts brain function within individuals. Analyses of individual path lengths revealed a non-monotonic dissociation: no difference at one-step (direct) paths, but higher mapping accuracy in patients at intermediate indirect scales (four and five steps). At longer scales, contributions attenuated in both groups. Spatial correspondence analyses localized patient-specific effects to default mode network subsystems across multiple atlases. These findings indicate that migraine-related dysfunction reflects altered mesoscale structure-function integration along indirect anatomical routes, and they provide a general approach to dissect structure-function coupling by communication scale in disease.

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

Repository

Its files are read in the Code ↔ Paper reader above, with 2 matches between paragraphs and lines of code.

ggoncalo02/SpectralConnectivity

License: none: the authors keep all their rights
State: the link answers, verified on 28 September 2026
Evidence: files inventoried
Commit: e2ddae40ca73f1b0cb7179c07e09252b04d6904e, 25 September 2025
Languages: MATLAB (16), Jupyter (1)
Size: 26 files, 17 scripts
Software Heritage: not archived
Found in: “Data availability”
Holds: 1 notebook
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Statistics and Machine Learning Toolbox (9 files)
Availability: 1 check, the latest on 28 September 2026: the link answers
  • 28 September 2026: the link answers
17 files
At the source: github.com/ggoncalo02/SpectralConnectivity

The paper's code and data availability statement is in the Data section.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 17 scripts, each with its path and the digest of its content;
  • 2 matches between paragraphs of the paper and lines of the code (method lexical-v1);
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

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

Data availability

Example structural and functional connectivity matrices that allow replication of the main analyses are available in the Spectral Connectivity repository: https://github.com/ggoncalo02/SpectralConnectivity. The full neuroimaging dataset analysed during the current study is not publicly available due to patient privacy restrictions but is available from the corresponding author on reasonable request.

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

Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 1, 28 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 10 authors, 2 keywords, 10 MeSH terms, 1 funder, 59 references.

Cite

This paper

Grácio, G., Matoso, A., Esteves, I., Fouto, A. R., Ruiz-Tagle, A., Caetano, G., Gil-Gouveia, R., Figueiredo, P., Nunes, R. G., & Pequito, S. (2026). Integrated anatomical and functional connectivity mapping in episodic migraine: a spectral graph theory approach. Scientific reports, 16(1), 22871. https://doi.org/10.1038/s41598-026-53726-7

BibTeX

@article{gracio2026integrated,
author = {Grácio, Gonçalo and Matoso, Ana and Esteves, Inês and Fouto, Ana R and Ruiz-Tagle, Amparo and Caetano, Gina and Gil-Gouveia, Raquel and Figueiredo, Patrícia and Nunes, Rita G and Pequito, Sérgio},
title = {{Integrated anatomical and functional connectivity mapping in episodic migraine: a spectral graph theory approach}},
journal = {Scientific reports},
year = {2026},
month = may,
volume = {16},
number = {1},
pages = {22871},
publisher = {Nature Publishing Group},
issn = {2045-2322},
doi = {10.1038/s41598-026-53726-7},
url = {https://doi.org/10.1038/s41598-026-53726-7},
pmid = {42156507},
pmcid = {PMC13388938}
}

RIS

TY - JOUR
AU - Grácio, Gonçalo
AU - Matoso, Ana
AU - Esteves, Inês
AU - Fouto, Ana R
AU - Ruiz-Tagle, Amparo
AU - Caetano, Gina
AU - Gil-Gouveia, Raquel
AU - Figueiredo, Patrícia
AU - Nunes, Rita G
AU - Pequito, Sérgio
TI - Integrated anatomical and functional connectivity mapping in episodic migraine: a spectral graph theory approach
T2 - Scientific reports
J2 - Sci Rep
PY - 2026
DA - 2026/05/20
VL - 16
IS - 1
SP - 22871
SN - 2045-2322
PB - Nature Publishing Group
DO - 10.1038/s41598-026-53726-7
UR - https://doi.org/10.1038/s41598-026-53726-7
LA - en
ER -

CSL-JSON

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The tracing map gets a citation of its own once an author has validated it and it has a DOI.

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