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Emergence of multifrequency activity in a laminar neural mass model.

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The authors' code

Python · 107 lines · 4.5 KB · CC0-1.0

  1. ############################################
  2. #Auto07p script for the bifucation diagram of the LaNMM.
  3. #Plots are handled with Python's matplotlib.
  4. #Read the docs: https://github.com/auto-07p/auto-07p
  5. #Tutorial: https://github.com/pclus/auto-tutorial
  6. ############################################
  7. #run with #$: auto bifur_lanmm.py
  8. ############################################
  9. import numpy as np
  10. import matplotlib.pyplot as plt
  11. import matplotlib.colors as colors
  12. from matplotlib import rc
  13. from matplotlib.colors import LinearSegmentedColormap
  14. from matplotlib.colors import ListedColormap, Normalize
  15. '''latex configuration
  16. plt.rcParams.update({'font.size': 16})
  17. plt.rcParams.update({'figure.autolayout': True})
  19. rc('font', **{'family': 'serif', 'serif': ['Computer Modern Roman']})
  20. rc('text', usetex=True)
  21. '''
  22. ###############################################################
  23. ###############################################################
  24. ################# Useful functions ######################
  25. ###############################################################
  26. ###############################################################
  27. def truncate_colormap(cmap, minval=0.0, maxval=1.0, n=100):
  28. new_cmap = colors.LinearSegmentedColormap.from_list(
  29. 'trunc({n},{a:.2f},{b:.2f})'.format(n=cmap.name, a=minval, b=maxval),
  30. cmap(np.linspace(minval, maxval, n)))
  31. return new_cmap
  33. def pt_vals(f):
  34. return np.array([f[0][i]['PT'] for i in range(len(f[0]))])
  36. def bifs(f,par):
  37. exceptions = ['No Label', 'RG', 'EP', 'UZ'] # List of exceptions
  38. return [[f[0][i]['TY name'],f[0][i][par]] for i in range(len(f[0])) if f[0][i]['TY name'] not in exceptions]
  40. prop_cycle = plt.rcParams['axes.prop_cycle']
  41. colores = prop_cycle.by_key()['color']
  43. cmap = plt.get_cmap('Greys')
  45. greys = truncate_colormap(cmap, 0.25, 0.85)
  46. cblues = [(172/255,129/255,255/255),(95/255,14/255,255/255)]
  47. creds = [(255/255,148/255,115/255),(255/255,71/255,14/255)]
  48. cblues = LinearSegmentedColormap.from_list('cblues',cblues,N = 50)
  49. creds = LinearSegmentedColormap.from_list('creds',creds,N = 50)
  51. ###############################################################
  52. ###############################################################
  53. ################## AUTO-07p part ########################
  54. ###############################################################
  55. ###############################################################
  57. init = run('lanmm',IPS=-2,NMX=100000,PAR={'p1':-100.0, 'p2' : 90.0})
  58. ic = init(201)
  60. fp=run(ic,IPS=1,NMX=400000,ISW=1,ICP=[1,2,7,8],UZSTOP={'p1' : 500.0})
  62. hb1=fp('HB1')
  63. lc1=run(hb1,IPS=2,ISP=2,ICP=[1,11,2,3,4,5,6],NMX=500000,ISW=1, UZSTOP={'p1' : 500.0,'PERIOD':100.0})#p2_0 UZSTOP={'PERIOD' : 100.0})
  65. hb2=fp('HB2')
  66. lc2=run(hb2,IPS=2,ISP=2,ICP=[1,11,2,3,4,5,6],NMX=500000,ISW=1, UZSTOP={'p1' : 500.0,'PERIOD':100.0})#p2_90 UZSTOP={'PERIOD' : 100.0})
  68. ###############################################################
  69. ###############################################################
  70. ################## Plotting part ########################
  71. ###############################################################
  72. ###############################################################
  74. fig, axs = plt.subplots(2,1,figsize= (8,6))
  76. axs[0].scatter(fp['p1'], fp['vp1'], c= (pt_vals(fp)< 0), cmap=greys, s=0.5)
  77. axs[0].scatter(lc1['p1'],lc1['y1_min'],c=2 * (pt_vals(lc1) < 0), cmap=cblues, s=2)
  78. axs[0].scatter(lc1['p1'],lc1['y1_max'],c=2 * (pt_vals(lc1) < 0), cmap=cblues, s=2)
  79. axs[0].scatter(lc2['p1'],lc2['y1_min'],c=2 * (pt_vals(lc2) < 0), cmap=cblues, s=2)
  80. axs[0].scatter(lc2['p1'],lc2['y1_max'],c=2 * (pt_vals(lc2) < 0), cmap=cblues, s=2)
  83. axs[1].scatter(fp['p1'], fp['vp2'], c= (pt_vals(fp)< 0), cmap=greys, s=0.5)
  84. axs[1].scatter(lc1['p1'],lc1['y2_min'],c=2 * (pt_vals(lc1) < 0), cmap=creds, s=2)
  85. axs[1].scatter(lc1['p1'],lc1['y2_max'],c=2 * (pt_vals(lc1) < 0), cmap=creds, s=2)
  86. axs[1].scatter(lc2['p1'],lc2['y2_min'],c=2 * (pt_vals(lc2) < 0), cmap=creds, s=2)
  87. axs[1].scatter(lc2['p1'],lc2['y2_max'],c=2 * (pt_vals(lc2) < 0), cmap=creds, s=2)
  89. axs[1].set_ylabel(r'$v_{P_1}$')
  90. axs[1].set_ylabel(r'$v_{P_2}$')
  91. axs[1].set_xlabel(r'$p_1$')
  93. bfp = bifs(fp,'p1')
  94. blc1 = bifs(lc1,'p1')
  95. blc2 = bifs(lc2,'p1')
  97. for ax in axs:
  98. for i,b in enumerate(bfp):
  99. ax.axvline(b[1],color='k', ls="--",alpha=0.7)
  100. for i,b in enumerate(blc1):
  101. ax.axvline(b[1],color='k', ls="--",alpha=0.7)
  102. for i,b in enumerate(blc2):
  103. ax.axvline(b[1],color='k', ls="--",alpha=0.7)
  104. ax.set_xlim(fp['p1'][0],fp['p1'][-1])
  106. plt.show()
  107. clean()

bifur_lanmm.py at commit cb7ec2b, under CC0-1.0 · at the source

Overview

Authors: Raul de Palma Aristides1, Pau Clusella2, Roser Sanchez-Todo3,4, Giulio Ruffini4, Jordi Garcia-Ojalvo1
ORCID iDs: Raul de Palma Aristides, Jordi Garcia-Ojalvo
  1. Department of Medicine and Life Sciences, Universitat Pompeu Fabra, Barcelona, Spain
  2. Department of Mathematics, Universitat Politècnica de Catalunya, Manresa, Spain
  3. Center of Brain and Cognition, Universitat Pompeu Fabra, Barcelona, Spain
  4. Brain Modeling Department, Neuroelectrics, Barcelona, Spain
Institutions: Universitat Pompeu Fabra (Spain); Universitat Politècnica de Catalunya (Spain); Neuroelectrics Barcelona SLU (Spain) (Spain)
Journal: PLoS computational biology, volume 22, issue 4, article e1014022
Dates: received 18 June 2025; accepted 15 February 2026; published online 3 April 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1371/journal.pcbi.1014022 · PMID 41931533 · PMCID PMC13075798 · OpenAlex W7148989990
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: computational modeling (no new data) (modality), human (organism), Alzheimer's / dementia (population)
Methods: Single-unit activity, calcium imaging
MeSH: Brain*, Models, Neurological*, Nerve Net*, Neurons*, Action Potentials, Alzheimer Disease, Animals, Computational Biology, Computer Simulation, Humans (* major topic)
Journal subjects: Biology and Life Sciences, Cell Biology, Cellular Types, Animal Cells, Neurons, Neuroscience, Cellular Neuroscience, Physiology, Electrophysiology, Membrane Potential, Anatomy, Nervous System, Synapses, Medicine and Health Sciences, Neurophysiology, Population Biology, Population Dynamics, Postsynaptic Potentials, Biochemistry, Neurochemistry, Neurotransmitters, Mental Health and Psychiatry, Dementia, Alzheimer's Disease, Neurology, Medical Conditions, Neurodegenerative Diseases, Interneurons
Topic: Neural dynamics and brain function (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: EC | Horizon 2020 Framework Programme (EU Framework Programme for Research and Innovation H2020) (101017716); MICIU/AEI/10.13039/501100011033 and ERDF, UE (PID2024-155942NB-I00); Spanish Ministry of Science and Innovation, the Spanish State Research Agency and FEDER (Project Reference No. PID2024-160263NB-I00); ICREA Academia program; European Research Council (ERC Synergy CeLEARN-101167121, 855109)
Citations: cited by 1 paper (Europe PMC); 80 references in the paper

Abstract

Neural mass models (NMMs) aim to capture the principles underlying mesoscopic neural activity representing the average behavior of large neural populations in the brain. Recently, a biophysically grounded laminar NMM (LaNMM) has been proposed, capable of generating coupled slow and fast oscillations resulting from interactions between different cortical layers. This concurrent oscillatory activity provides a mechanistic framework for studying information processing mechanisms and various disease-related oscillatory dysfunctions. We show that this model can exhibit periodic, quasiperiodic, and chaotic oscillations. Additionally we demonstrate, through bifurcation analysis and numerical simulations, the emergence of rhythmic activity and various frequency couplings in the model, including delta-gamma, theta-gamma, and alpha-gamma couplings. We also examine how alterations linked with Alzheimer’s disease impair the model’s ability to display multifrequency activity. Furthermore, we show that the model remains robust when coupled to another neural mass. Together, our results offer a dynamical systems perspective of the laminar NMM model, thereby providing a foundation for future modeling studies and investigations into cognitive processes that depend on cross-frequency coupling.

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

Repository

Its files are read in the Code ↔ Paper reader above.

dsb-lab/LaNMM

License: CC0-1.0
State: the link answers, verified on 28 September 2026
Evidence: files inventoried
Commit: cb7ec2b64723fb0805c5fc1c6ac8a003f58a7aad, 2 October 2025
Languages: Python (2), Fortran (1), Julia (1)
Size: 7 files, 4 scripts
Software Heritage: not archived
Found in: “Data Availability”
Holds: README, license file
Not found: CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Matplotlib (2 files), NumPy (2 files), DifferentialEquations.jl (1 file), SciPy (1 file)
Availability: 1 check, the latest on 28 September 2026: the link answers
  • 28 September 2026: the link answers
6 files
At the source: github.com/dsb-lab/LaNMM

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

Tracing map

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  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
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Data

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Data Availability

The codes to reproduce the main results is publicly available (https://github.com/dsb-lab/LaNMM).

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

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Version 1, 28 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 5 authors, 10 MeSH terms, 5 funders, 74 references.

Cite

This paper

de Palma Aristides, R., Clusella, P., Sanchez-Todo, R., Ruffini, G., & Garcia-Ojalvo, J. (2026). Emergence of multifrequency activity in a laminar neural mass model. PLoS computational biology, 22(4), e1014022. https://doi.org/10.1371/journal.pcbi.1014022

BibTeX

@article{depalmaaristides2026emergence,
author = {de Palma Aristides, Raul and Clusella, Pau and Sanchez-Todo, Roser and Ruffini, Giulio and Garcia-Ojalvo, Jordi},
title = {{Emergence of multifrequency activity in a laminar neural mass model}},
journal = {PLoS computational biology},
year = {2026},
month = apr,
volume = {22},
number = {4},
pages = {e1014022},
publisher = {PLOS},
issn = {1553-734X},
doi = {10.1371/journal.pcbi.1014022},
url = {https://doi.org/10.1371/journal.pcbi.1014022},
pmid = {41931533},
pmcid = {PMC13075798}
}

RIS

TY - JOUR
AU - de Palma Aristides, Raul
AU - Clusella, Pau
AU - Sanchez-Todo, Roser
AU - Ruffini, Giulio
AU - Garcia-Ojalvo, Jordi
TI - Emergence of multifrequency activity in a laminar neural mass model
T2 - PLoS computational biology
J2 - PLoS Comput Biol
PY - 2026
DA - 2026/04/03
VL - 22
IS - 4
SP - e1014022
SN - 1553-734X
PB - PLOS
DO - 10.1371/journal.pcbi.1014022
UR - https://doi.org/10.1371/journal.pcbi.1014022
LA - en
ER -

CSL-JSON

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