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Brain-heart interactions in late-onset major depressive disorder revealed by multimodal HRV-driven fMRI.

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 of them tie a paragraph to a whole file, not to given lines: a weak match, whose lines are not tinted
  1. [1] § Materials and methods › HRV regressors ↔ code/TVAR/modelloAR_TVAR.m, the whole file · a weak match · score 0.66 · forgetting factor, prediction error, algorithm, vector, temporal, matrices
  2. [2] § Materials and methods › HRV regressors ↔ code/TVAR/stimaPSD_TVAR_mia.m, lines 1–63 · score 0.59 · cross spectrum, model coefficients, PSD11, PSD12, partial spectra, power

Paper

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The authors' code

MATLAB · 97 lines · 2.7 KB · no license · 1 match

  1. function [coef,ve] = modelloAR_TVAR(dati,p,lambda)
  3. % Time-varying analysis -> COMPUTATION OF MODEL COEFFICIENTS.
  4. % INPUT:
  5. % dati = T x M matrix (T = number of samples, M = number of signals to analyze)
  6. % p = model order
  7. % lambda = forgetting factor
  8. % OUTPUT:
  9. % coef = model coefficient matrix (rows = M; columns = p*M; third dimension = T)
  10. % ve = prediction error variance matrix (rows = M; columns = p*M; third dimension = T)
  12. T = size(dati,1); % number of samples
  13. M = size(dati,2); % number of signals
  15. % Vector initializations
  16. p = round(p); % p must be an integer
  17. THETA = zeros(M, M*p); % AR model parameters: a matrix with
  18. % as many rows as signals and a number of columns equal
  19. % to the total number of parameters
  21. % The THETA matrix defined at time instant n is equivalent to
  22. % An = [An(1) An(2) ... An(p)]
  25. % la matrice THETA definita per l'istante temporale n, equivale alla
  26. % matrice An=[An(1) An(2) ... An(p)]
  28. P = 1 * eye(M*p); % covariance matrix
  29. fi_tot = zeros(M*p,1); % observation vector
  31. % matrices returned as output
  32. coef = zeros(M, M*p, T);
  33. ve = zeros(M, M, T);
  35. if p > T % if there are not enough samples
  36. return;
  37. end
  39. % initialization of the observation vector using all signals
  40. for sig = 1:M
  41. fi = dati(1:p, sig);
  42. fi_tot(sig:M:end) = fi(end:-1:1);
  43. end
  45. % initialization of variables that will contain the quantities of interest
  46. varep = zeros(M, M);
  47. oldvarep = zeros(M, M);
  50. w = eye(M) * lambda;
  52. W = ones(M*p)*lambda;
  54. % Algorithm
  55. for i = p+1:T
  57. Pfi_tot = P * fi_tot;
  58. denom = mean(diag(w)) + fi_tot' * Pfi_tot;
  59. % time-varying gain
  60. K = Pfi_tot / denom;
  61. % covariance matrix update
  62. P = (P - K * fi_tot' * P) ./ W;
  63. % the previous lines are all correct
  65. sample = dati(i,:);
  66. % a priori error
  67. E = sample' - THETA * fi_tot;
  68. % a priori error variance
  69. % vvv = (E*E').*(1-w) + oldvvv.*w;
  71. % model coefficient update
  72. THETA = THETA + E * K';
  73. % a posteriori error computed with the updated coefficients
  74. Ep = sample' - THETA * fi_tot;
  75. % prediction error variance (a posteriori prediction error)
  76. varep = (Ep * Ep') .* (1-w) + oldvarep .* w;
  78. % observation vector update
  79. fi_tot = [sample'; fi_tot(1:M*p - M)];
  80. oldvarep = varep;
  81. % oldvvv = vvv;
  83. THETA(2,1:2:end) = 0; % constraint to obtain an ARX model
  85. % save parameters
  86. coef(:,:,i) = THETA;
  87. ve(:,:,i) = varep;
  89. end
  91. % Make the first 2p rows have the coefficients found at rows 2p+1 and 2p+2,
  92. % corresponding to the (p+1)-th sample of the signal.
  93. % Do the same for the forgetting factor and for the prediction error variance.
  94. for ll = 1:p
  95. coef(:,:,ll) = coef(:,:,p+1);
  96. ve(:,:,ll) = ve(:,:,p+1);
  97. end

modelloAR_TVAR.m, no license · at the source

Overview

Authors: Federica Goffi1, Paolo Enrico2, Pierluigi Reali1, Gabriele Torino2,3, Maria Pia Marra2, Lorena Di Consoli2, Adele Ferro2, Giandomenico Schiena2, Yvan Torrente4,5, Luciano Lombardi6, Fabio M Triulzi6, Anna M Bianchi1,7, Paolo Brambilla2,3, Eleonora Maggioni1,2
ORCID iDs: Federica Goffi, Pierluigi Reali, Gabriele Torino, Yvan Torrente, Fabio M Triulzi, Anna M Bianchi, Paolo Brambilla
  1. Department of Electronics Information and Bioengineering, Politecnico di Milano, Milan, Italy
  2. Department of Neurosciences and Mental Health, Fondazione IRCCS Ca’ Granda Ospedale Maggiore Policlinico, Milan, Italy
  3. Department of Pathophysiology and Transplantation, Università degli Studi di Milano, Milan, Italy
  4. Neurology Unit, Fondazione IRCCS Ca’ Granda Ospedale Maggiore Policlinico, Milan, Italy
  5. Stem Cell Laboratory, Dino Ferrari Center, Department of Pathophysiology and Trasplantation, Università degli Studi di Milano, Milan, Italy
  6. Neuroradiology Unit, Fondazione IRCCS Ca’ Granda Ospedale Maggiore Policlinico, Milan, Italy
  7. Fondazione IRCCS Ca’ Granda Ospedale Maggiore Policlinico, Milan, Italy
Institutions: Politecnico di Milano (Italy); Fondazione IRCCS Ca' Granda Ospedale Maggiore Policlinico (Italy); University of Milan (Italy)
Journal: Communications biology, volume 9, issue 1, article 956
Dates: received 11 October 2025; accepted 20 April 2026; published online 8 May 2026
Type: Research article · Language: English
License: CC BY-NC-ND
Identifiers: DOI 10.1038/s42003-026-10156-5 · PMID 42098292 · PMCID PMC13369760 · OpenAlex W7160557179
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: fMRI (modality), other (modality), human (organism), depression (population)
Methods: Spectral & time-frequency, Preprocessing, Connectivity, Statistics, fMRI & imaging, Smoothing, state filtering, decompositions, Evoked potentials, Physiology & signal measures, Machine learning
Keywords: Neurophysiology, Depression, Autonomic nervous system, Functional magnetic resonance imaging, Computational neuroscience
MeSH: Autonomic Nervous System*, Brain*, Heart*, Heart Rate*, Magnetic Resonance Imaging*, Major Depressive Disorder*, Brain Mapping, Electrocardiography, Female, Humans, Male, Middle Aged (* major topic)
Topic: Heart Rate Variability and Autonomic Control (Cardiology and Cardiovascular Medicine, Medicine), according to OpenAlex
Funding: Telethon (GJC21084)
Citations: not cited yet (Europe PMC); 171 references in the paper

Abstract

The abstract is not reproduced here: the paper's license (CC BY-NC-ND) does not allow it. Read it in the paper, at the publisher or on Europe PMC.

Repository

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

OSF 7gp6y

License: none: the authors keep all their rights
State: the link answers, verified on 28 September 2026
Evidence: files inventoried
Languages: MATLAB (10)
Size: 24 files, 10 scripts
Software Heritage: not checked
Found in: “Code availability”
Holds: 6 notebooks
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 28 September 2026: the link answers (HTTP 200)
  • 28 September 2026: the link answers (HTTP 200)
10 files
At the source: osf.io/7gp6y/?view_only=f44d17b1fdd3434fac1586cf7a09b75b

Code availability statement

The paper has a code availability statement. Its license (CC BY-NC-ND) does not allow reproducing it here; in short, from what the harvester recognized in it:

  • it points to the authors' code: OSF 7gp6y
  • it says that the code is available on request

Read it in the paper: doi.org/10.1038/s42003-026-10156-5.

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;
  • 10 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 statement

The paper has a data availability statement. Its license (CC BY-NC-ND) does not allow reproducing it here; in short, from what the harvester recognized in it:

  • it says that the data are available on request

Read it in the paper: doi.org/10.1038/s42003-026-10156-5.

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, 14 authors, 5 keywords, 12 MeSH terms, 1 funder, 165 references.

Cite

This paper

Goffi, F., Enrico, P., Reali, P., Torino, G., Marra, M. P., Di Consoli, L., Ferro, A., Schiena, G., Torrente, Y., Lombardi, L., Triulzi, F. M., Bianchi, A. M., Brambilla, P., & Maggioni, E. (2026). Brain-heart interactions in late-onset major depressive disorder revealed by multimodal HRV-driven fMRI. Communications biology, 9(1), 956. https://doi.org/10.1038/s42003-026-10156-5

BibTeX

@article{goffi2026brain,
author = {Goffi, Federica and Enrico, Paolo and Reali, Pierluigi and Torino, Gabriele and Marra, Maria Pia and Di Consoli, Lorena and Ferro, Adele and Schiena, Giandomenico and Torrente, Yvan and Lombardi, Luciano and Triulzi, Fabio M and Bianchi, Anna M and Brambilla, Paolo and Maggioni, Eleonora},
title = {{Brain-heart interactions in late-onset major depressive disorder revealed by multimodal HRV-driven fMRI}},
journal = {Communications biology},
year = {2026},
month = may,
volume = {9},
number = {1},
pages = {956},
publisher = {Nature Publishing Group},
issn = {2399-3642},
doi = {10.1038/s42003-026-10156-5},
url = {https://doi.org/10.1038/s42003-026-10156-5},
pmid = {42098292},
pmcid = {PMC13369760}
}

RIS

TY - JOUR
AU - Goffi, Federica
AU - Enrico, Paolo
AU - Reali, Pierluigi
AU - Torino, Gabriele
AU - Marra, Maria Pia
AU - Di Consoli, Lorena
AU - Ferro, Adele
AU - Schiena, Giandomenico
AU - Torrente, Yvan
AU - Lombardi, Luciano
AU - Triulzi, Fabio M
AU - Bianchi, Anna M
AU - Brambilla, Paolo
AU - Maggioni, Eleonora
TI - Brain-heart interactions in late-onset major depressive disorder revealed by multimodal HRV-driven fMRI
T2 - Communications biology
J2 - Commun Biol
PY - 2026
DA - 2026/05/08
VL - 9
IS - 1
SP - 956
SN - 2399-3642
PB - Nature Publishing Group
DO - 10.1038/s42003-026-10156-5
UR - https://doi.org/10.1038/s42003-026-10156-5
LA - en
ER -

CSL-JSON

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