Cognitive Neurodynamics

, Volume 13, Issue 4, pp 379–392 | Cite as

Complex temporal patterns processing by a neural mass model of a cortical column

  • Daniel Malagarriga
  • Antonio J. Pons
  • Alessandro E. P. VillaEmail author
Research Article


It is well known that neuronal networks are capable of transmitting complex spatiotemporal information in the form of precise sequences of neuronal discharges characterized by recurrent patterns. At the same time, the synchronized activity of large ensembles produces local field potentials that propagate through highly dynamic oscillatory waves, such that, at the whole brain scale, complex spatiotemporal dynamics of electroencephalographic (EEG) signals may be associated to sensorimotor decision making processes. Despite these experimental evidences, the link between highly temporally organized input patterns and EEG waves has not been studied in detail. Here, we use a neural mass model to investigate to what extent precise temporal information, carried by deterministic nonlinear attractor mappings, is filtered and transformed into fluctuations in phase, frequency and amplitude of oscillatory brain activity. The phase shift that we observe, when we drive the neural mass model with specific chaotic inputs, shows that the local field potential amplitude peak appears in less than one full cycle, thus allowing traveling waves to encode temporal information. After converting phase and amplitude changes obtained into point processes, we quantify input–output similarity following a threshold-filtering algorithm onto the amplitude wave peaks. Our analysis shows that the neural mass model has the capacity for gating the input signal and propagate selected temporal features of that signal. Finally, we discuss the effect of local excitatory/inhibitory balance on these results and how excitability in cortical columns, controlled by neuromodulatory innervation of the cerebral cortex, may contribute to set a fine tuning and gating of the information fed to the cortex.


Nonlinear time series analysis Deterministic nonlinear dynamics Information processing Neural mass model Brain dynamics 



The authors acknowledge the partial support by the Swiss National Science Foundation Grant No. CR13I1-138032. AJP’s work was supported, in part, by the Spanish MINECO FIS2015-66503-C3-2-P. All authors conceived and designed the simulations, which were performed primarily by DM. DM and AEPV wrote the paper, and all authors have read and approved the final manuscript.

Compliance with ethical standards

Conflict of interest

The authors declares no conflict of interest.


  1. Abeles M (1982a) Local cortical circuits. An electrophysiological study, studies of brain function, vol 6. Springer, BerlinGoogle Scholar
  2. Abeles M (1982b) Quantification, smoothing, and confidence limits for single-units’ histograms. J Neurosci Methods 5(4):317–325Google Scholar
  3. Abeles M (2014) Revealing instances of coordination among multiple cortical areas. Biol Cybern 108(5):665–75Google Scholar
  4. Abeles M, Gerstein GL (1988) Detecting spatiotemporal firing patterns among simultaneously recorded single neurons. J Neurophysiol 60(3):909–924Google Scholar
  5. Abeles M, Bergman H, Margalit E, Vaadia E (1993) Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. J Neurophysiol 70(4):1629–1638Google Scholar
  6. Abeysuriya RG, Hadida J, Sotiropoulos SN, Jbabdi S, Becker R, Hunt BAE, Brookes MJ, Woolrich MW (2018) A biophysical model of dynamic balancing of excitation and inhibition in fast oscillatory large-scale networks. PLoS Comput Biol 14(2):e1006007Google Scholar
  7. Akam T, Kullmann DM (2010) Oscillations and filtering networks support flexible routing of information. Neuron 67(2):308–20Google Scholar
  8. Albéri L, Lintas A, Kretz R, Schwaller B, Villa AEP (2013) The calcium-binding protein parvalbumin modulates the firing properties of the reticular thalamic nucleus bursting neurons. J Neurophysiol 109(11):2827–2841Google Scholar
  9. Andrzejak RG, Lehnertz K, Mormann F, Rieke C, David P, Elger CE (2001) Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: dependence on recording region and brain state. Phys Rev E Stat Nonlinear Soft Matter Phys 64(6 Pt 1):061907Google Scholar
  10. Asai Y, Villa AEP (2008) Reconstruction of underlying nonlinear deterministic dynamics embedded in noisy spike trains. J Biol Phys 34:325–340Google Scholar
  11. Asai Y, Villa AEP (2012) Integration and transmission of distributed deterministic neural activity in feed-forward networks. Brain Res 1434:17–33Google Scholar
  12. Asai Y, Guha A, Villa AEP (2008) Deterministic neural dynamics transmitted through neural networks. Neural Netw 21(6):799–809Google Scholar
  13. Benes FM, Taylor JB, Cunningham MC (2000) Convergence and plasticity of monoaminergic systems in the medial prefrontal cortex during the postnatal period: implications for the development of psychopathology. Cereb Cortex 10(10):1014–27Google Scholar
  14. Bonzon P (2017) Towards neuro-inspired symbolic models of cognition: linking neural dynamics to behaviors through asynchronous communications. Cogn Neurodyn 11(4):327–353Google Scholar
  15. Brama H, Guberman S, Abeles M, Stern E, Kanter I (2015) Synchronization among neuronal pools without common inputs: in vivo study. Brain Struct Funct 220(6):3721–31Google Scholar
  16. Brette R (2012) Computing with neural synchrony. PLoS Comput Biol 8(6):e1002561Google Scholar
  17. Brunel N, Hakim V (1999) Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Comput 11(7):1621–71Google Scholar
  18. Brunel N, Hansel D (2006) How noise affects the synchronization properties of recurrent networks of inhibitory neurons. Neural Comput 18(5):1066–110Google Scholar
  19. Buzsáki G, Anastassiou CA, Koch C (2012) The origin of extracellular fields and currents-EEG, ECoG, LFP and spikes. Nat Rev Neurosci 13(6):407–20Google Scholar
  20. Caillard O, Moreno H, Schwaller B, Llano I, Celio MR, Marty A (2000) Role of the calcium-binding protein parvalbumin in short-term synaptic plasticity. Proc Natl Acad Sci USA 97(24):13372–13377Google Scholar
  21. Carlén M, Meletis K, Siegle JH, Cardin JA, Futai K, Vierling-Claassen D, Rühlmann C, Jones SR, Deisseroth K, Sheng M, Moore CI, Tsai LH (2012) A critical role for NMDA receptors in parvalbumin interneurons for gamma rhythm induction and behavior. Mol Psychiatry 17(5):537–548Google Scholar
  22. Celletti A, Froeschlé C, Tetko IV, Villa AEP (1999) Deterministic behaviour of short time series. Meccanica 34:145–152Google Scholar
  23. Chen G, Ueta T (1999) Yet another chaotic attractor. Int J Bifurc Chaos 9(7):1465–1466Google Scholar
  24. Cutsuridis V (2012) Bursts shape the NMDA-R mediated spike timing dependent plasticity curve: role of burst interspike interval and GABAergic inhibition. Cogn Neurodyn 6(5):421–41Google Scholar
  25. David O, Friston KJ (2003) A neural mass model for MEG/EEG: coupling and neuronal dynamics. NeuroImage 20(3):1743–1755Google Scholar
  26. Deng B, Cai L, Li S, Wang R, Yu H, Chen Y, Wang J (2017) Multivariate multi-scale weighted permutation entropy analysis of EEG complexity for Alzheimer’s disease. Cogn Neurodyn 11(3):217–231Google Scholar
  27. Ermentrout B (2002) Simulating, analyzing, and animating dynamical systems: a guide to Xppaut for researchers and students (software, environments, tools). Society for Industrial and Applied Mathematics, PhiladelphiaGoogle Scholar
  28. Ermentrout B (2012) XPPAUT. In: Le Novère N (ed) Computational systems neurobiology. Springer, Berlin, pp 519–531 (chap 17) Google Scholar
  29. Feldman DE (2012) The spike-timing dependence of plasticity. Neuron 75(4):556–71Google Scholar
  30. Fries P, Womelsdorf T, Oostenveld R, Desimone R (2008) The effects of visual stimulation and selective visual attention on rhythmic neuronal synchronization in macaque area v4. J Neurosci 28(18):4823–35Google Scholar
  31. Fukushima Y, Tsukada M, Tsuda I, Yamaguti Y, Kuroda S (2007) Spatial clustering property and its self-similarity in membrane potentials of hippocampal CA1 pyramidal neurons for a spatio-temporal input sequence. Cogn Neurodyn 1(4):305–16Google Scholar
  32. Furth KE, Mastwal S, Wang KH, Buonanno A, Vullhorst D (2013) Dopamine, cognitive function, and gamma oscillations: role of d4 receptors. Front Cell Neurosci 7:102–102Google Scholar
  33. Gao J, Hu J, Tung WW (2011) Complexity measures of brain wave dynamics. Cogn Neurodyn 5(2):171–82Google Scholar
  34. García-Ojalvo J, Sancho J (1999) Noise in spatially extended systems. Springer, New YorkGoogle Scholar
  35. Gollo LL, Mirasso C, Villa AEP (2010) Dynamic control for synchronization of separated cortical areas through thalamic relay. Neuroimage 52(3):947–955Google Scholar
  36. Gross J, Hoogenboom N, Thut G, Schyns P, Panzeri S, Belin P, Garrod S (2013) Speech rhythms and multiplexed oscillatory sensory coding in the human brain. PLoS Biol 11(12):e1001752Google Scholar
  37. Gruart A, Delgado-García JM, Lintas A (2016) Effect of parvalbumin deficiency on distributed activity and interactions in neural circuits activated by instrumental learning. In: Wang R, Pan X (eds) Advances in cognitive neurodynamics (V). Springer, Singapore, pp 111–117Google Scholar
  38. Guyonneau R, Van Rullen R, Thorpe SJ (2005) Neurons tune to the earliest spikes through stdp. Neural Comput 17:859–879Google Scholar
  39. Hénon M (1976) A two-dimensional mapping with a strange attractor. Communi Math Phys 50(1):69–77Google Scholar
  40. Iglesias J, Villa AEP (2010) Recurrent spatiotemporal firing patterns in large spiking neural networks with ontogenetic and epigenetic processes. J Physiol Paris 104:137–146Google Scholar
  41. Iglesias J, Chibirova O, Villa A (2007) Nonlinear dynamics emerging in large scale neural networks with ontogenetic and epigenetic processes. Lect Notes Comput Sci 4668:579–588Google Scholar
  42. Jansen BH, Rit VG (1995) Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biol Cybern 73(4):357–366Google Scholar
  43. Jansen BH, Zouridakis G, Brandt ME (1993) A neurophysiologically-based mathematical model of flash visual evoked potentials. Biol Cybern 68(3):275–283Google Scholar
  44. Korn H, Faure P (2003) Is there chaos in the brain? II. Experimental evidence and related models. C R Biol 326(9):787–840Google Scholar
  45. Lee AT, Vogt D, Rubenstein JL, Sohal VS (2014) A class of gabaergic neurons in the prefrontal cortex sends long-range projections to the nucleus accumbens and elicits acute avoidance behavior. J Neurosci 34(35):11519–11525Google Scholar
  46. Lintas A (2014) Discharge properties of neurons recorded in the parvalbumin-positive (pv1) nucleus of the rat lateral hypothalamus. Neurosci Lett 571:29–33Google Scholar
  47. Lintas A, Schwaller B, Villa AEP (2013) Visual thalamocortical circuits in parvalbumin-deficient mice. Brain Res 1536:107–118Google Scholar
  48. Longtin A (1993) Nonlinear forecasting of spike trains from sensory neurons. Int J Bifurc Chaos 3(03):651–661Google Scholar
  49. Makarenko V, Llinás R (1998) Experimentally determined chaotic phase synchronization in a neuronal system. Proc Natl Acad Sci USA 95(26):15747–52Google Scholar
  50. Malagarriga D, Villa AEP, García-Ojalvo J, Pons AJ (2014) Excitation/inhibition patterns in a system of coupled cortical columns. In: Wermter S, Weber C, Duch W, Honkela T, Koprinkova-Hristova P, Magg S, Palm G, Villa AEP (eds) Artificial neural networks and machine learning—ICANN 2014. Lecture Notes in Computer Science, vol 8681. Springer, Cham, pp 651–658Google Scholar
  51. Malagarriga D, García-Vellisca MA, Villa AEP, Buldú JM, García-Ojalvo J, Pons AJ (2015a) Synchronization-based computation through networks of coupled oscillators. Front Comput Neurosci 9:00097Google Scholar
  52. Malagarriga D, Villa AEP, Garcia-Ojalvo J, Pons AJ (2015b) Mesoscopic segregation of excitation and inhibition in a brain network model. PLoS Comput Biol 11(2):e1004007Google Scholar
  53. Manseau F, Marinelli S, Mendez P, Schwaller B, Prince DA, Huguenard JR, Bacci A (2010) Desynchronization of neocortical networks by asynchronous release of GABA at autaptic and synaptic contacts from fast-spiking interneurons. PLoS Biol 8(9):e1000492Google Scholar
  54. Markram H, Lübke J, Frotscher M, Sakmann B (1997) Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275(5297):213–5Google Scholar
  55. Mateos DM, Guevara Erra R, Wennberg R, Perez Velazquez JL (2018) Measures of entropy and complexity in altered states of consciousness. Cogn Neurodyn 12(1):73–84Google Scholar
  56. Montbrió E, Pazó D, Roxin A (2015) Macroscopic description for networks of spiking neurons. Phys Rev X 5(2):021028Google Scholar
  57. Muller L, Chavane F, Reynolds J, Sejnowski TJ (2018) Cortical travelling waves: mechanisms and computational principles. Nat Rev Neurosci 19(5):255–268Google Scholar
  58. Myers MH, Kozma R (2018) Mesoscopic neuron population modeling of normal/epileptic brain dynamics. Cogn Neurodyn 12(2):211–223Google Scholar
  59. Ng BSW, Logothetis NK, Kayser C (2013) EEG phase patterns reflect the selectivity of neural firing. Cereb Cortex 23(2):389–98Google Scholar
  60. Nobukawa S, Yamanishi T, Nishimura H, Wada Y, Kikuchi M, Takahashi T (2019) Atypical temporal-scale-specific fractal changes in Alzheimer’s disease EEG and their relevance to cognitive decline. Cogn Neurodyn 13(1):1–11Google Scholar
  61. Nunez P (1995) Neocortical dynamics and human EEG rhythms. Oxford University Press, New YorkGoogle Scholar
  62. Ozaki TJ, Sato N, Kitajo K, Someya Y, Anami K, Mizuhara H, Ogawa S, Yamaguchi Y (2012) Traveling EEG slow oscillation along the dorsal attention network initiates spontaneous perceptual switching. Cogn Neurodyn 6(2):185–98Google Scholar
  63. Panzeri S, Brunel N, Logothetis NK, Kayser C (2010) Sensory neural codes using multiplexed temporal scales. Trends Neurosci 33(3):111–20Google Scholar
  64. Parker TS, Chua LO (1989) Poincaré maps. Springer, New York, pp 31–56Google Scholar
  65. Parnavelas JG, Papadopoulos GC (1989) The monoaminergic innervation of the cerebral cortex is not diffuse and nonspecific. Trends Neurosci 12(9):315–9Google Scholar
  66. Qu J, Wang R, Yan C, Du Y (2014) Oscillations and synchrony in a cortical neural network. Cogn Neurodyn 8(2):157–66Google Scholar
  67. Rabinovich MI, Varona P (2011) Robust transient dynamics and brain functions. Front Comput Neurosci 5:24Google Scholar
  68. Reinoso JA, Torrent MC, Masoller C (2016) Emergence of spike correlations in periodically forced excitable systems. Phys Rev E 94(3–1):032218Google Scholar
  69. Reynolds GP, Abdul-Monim Z, Neill JC, Zhang ZJ (2004) Calcium binding protein markers of GABA deficits in schizophrenia-postmortem studies and animal models. Neurotox Res 6(1):57–61Google Scholar
  70. Rubino D, Robbins KA, Hatsopoulos NG (2006) Propagating waves mediate information transfer in the motor cortex. Nat Neurosci 9(12):1549–57Google Scholar
  71. Schroeder CE, Lakatos P (2009) Low-frequency neuronal oscillations as instruments of sensory selection. Trends Neurosci 32(1):9–18Google Scholar
  72. Schwaller B, Tetko IV, Tandon P, Silveira DC, Vreugdenhil M, Henzi T, Potier MC, Celio MR, Villa AEP (2004) Parvalbumin deficiency affects network properties resulting in increased susceptibility to epileptic seizures. Mol Cell Neurosci 25(4):650–663Google Scholar
  73. Segundo JP (2003) Nonlinear dynamics of point process systems and data. Int J Bifurcat Chaos 13(08):2035–2116Google Scholar
  74. Singer W (1993) Synchronization of cortical activity and its putative role in information processing and learning. Annu Rev Physiol 55:349–74Google Scholar
  75. Singer W (1999) Neuronal synchrony: a versatile code for the definition of relations? Neuron 24(1):49–65Google Scholar
  76. Spiegler A, Kiebel SJ, Atay FM, Knösche TR (2010) Bifurcation analysis of neural mass models: impact of extrinsic inputs and dendritic time constants. Neuroimage 52(3):1041–1058Google Scholar
  77. Stam CJ (2005) Nonlinear dynamical analysis of EEG and MEG: review of an emerging field. Clin Neurophysiol 116(10):2266–2301Google Scholar
  78. Tal I, Abeles M (2016) Temporal accuracy of human cortico–cortical interactions. J Neurophysiol 115(4):1810–20Google Scholar
  79. Tal I, Abeles M (2018) Imaging the spatiotemporal dynamics of cognitive processes at high temporal resolution. Neural Comput 30(3):610–630Google Scholar
  80. Tetko IV, Villa AEP (2001) A pattern grouping algorithm for analysis of spatiotemporal patterns in neuronal spike trains. 2. Application to simultaneous single unit recordings. J Neurosci Methods 105(1):15–24Google Scholar
  81. Tewarie P, Hunt BAE, O’Neill GC, Byrne A, Aquino K, Bauer M, Mullinger KJ, Coombes S, Brookes MJ (2018) Relationships between neuronal oscillatory amplitude and dynamic functional connectivity. Cereb Cortex. Google Scholar
  82. Theiler J, Rapp PE (1996) Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram. Electroencephalogr Clin Neurophysiol 98(3):213–22Google Scholar
  83. Villa AEP, Abeles M (1990) Evidence for spatiotemporal firing patterns within the auditory thalamus of the cat. Brain Res 509(2):325–327Google Scholar
  84. Villa AEP, Fuster JM (1992) Temporal correlates of information processing during visual short-term memory. Neuroreport 3(1):113–116Google Scholar
  85. Vogels TP, Abbott LF (2009) Gating multiple signals through detailed balance of excitation and inhibition in spiking networks. Nat Neurosci 12(4):483–91Google Scholar
  86. Vogt SM, Hofmann UG (2012) Neuromodulation of STDP through short-term changes in firing causality. Cogn Neurodyn 6(4):353–66Google Scholar
  87. von der Malsburg C, Schneider W (1986) A neural cocktail-party processor. Biol Cybern 54(1):29–40Google Scholar
  88. Wennekers T (2008) Tuned solutions in dynamic neural fields as building blocks for extended EEG models. Cogn Neurodyn 2(2):137–46Google Scholar
  89. Whittington MA, Traub RD (2003) Interneuron diversity series: inhibitory interneurons and network oscillations in vitro. Trends Neurosci 26(12):676–82Google Scholar
  90. Zaslavsky G (1978) The simplest case of a strange attractor. Phys Lett A 69(3):145–147Google Scholar
  91. Zylberberg A, Fernández Slezak D, Roelfsema PR, Dehaene S, Sigman M (2010) The brain’s router: a cortical network model of serial processing in the primate brain. PLoS Comput Biol 6(4):e1000765Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Departament de FísicaUniversitat Politècnica de CatalunyaTerrassaSpain
  2. 2.Neuroheuristic Research GroupUniversity of LausanneLausanneSwitzerland

Personalised recommendations