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Spectral and Non-linear Analysis of Thalamocortical Neural Mass Model Oscillatory Dynamics

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Advanced Computational Approaches to Biomedical Engineering

Abstract

The chapter is organised in two parts: In the first part, the focus is on a combined power spectral and non-linear behavioural analysis of a neural mass model of the thalamocortical circuitry. The objective is to study the effectiveness of such “multi-modal” analytical techniques in model-based studies investigating the neural correlates of abnormal brain oscillations in Alzheimer’s disease (AD). The power spectral analysis presented here is a study of the “slowing” (decreasing dominant frequency of oscillation) within the alpha frequency band (8–13 Hz), a hallmark of electroencephalogram (EEG) dynamics in AD. Analysis of the non-linear dynamical behaviour focuses on the bifurcating property of the model. The results show that the alpha rhythmic content is maximal at close proximity to the bifurcation point—an observation made possible by the “multi-modal” approach adopted herein. Furthermore, a slowing in alpha rhythm is observed for increasing inhibitory connectivity—a consistent feature of our research into neuropathological oscillations associated with AD. In the second part, we have presented power spectral analysis on a model that implements multiple feed-forward and feed-back connectivities in the thalamo-cortico-thalamic circuitry, and is thus more advanced in terms of biological plausibility. This study looks at the effects of synaptic connectivity variation on the power spectra within the delta (1–3 Hz), theta (4–7 Hz), alpha (8–13 Hz) and beta (14–30 Hz) bands. An overall slowing of EEG with decreasing synaptic connectivity is observed, indicated by a decrease of power within alpha and beta bands and increase in power within the theta and delta bands. Thus, the model behaviour conforms to longitudinal studies in AD indicating an overall slowing of EEG.

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Notes

  1. 1.

    Interested readers may refer to [32, 71] for a background on non-linear dynamical analysis used in neuroscience research. For a tutorial on non-linear dynamical analysis applied to EEG, please see [48].

References

  1. Abuhassan, K., Coyle, D., Maguire, L.P.: Investigating the neural correlates of pathological cortical networks in Alzheimer’s disease using heterogeneous neuronal models. IEEE Trans. Biomed. Eng. 59, 890–896 (2012)

    Article  Google Scholar 

  2. Adeli, H., Ghosh-Dastidar, S., Dadmehr, N.: Alzheimer’s disease: models of computation and analysis of EEGs. Clin. EEG Neurosci. 36(3), 131–136 (2005)

    Google Scholar 

  3. Amsallem, B., Pollin, B.: Possible role of the nucleus reticularis thalami (nRT) in the control of specific, non-specific thalamic nuclei and cortex activity. Pain 18, S-283 (1984)

    Google Scholar 

  4. Aradi, I., Erdi, P.: Computational neuropharmacology: dynamical approaches in drug discovery. Trends Pharmacol. Sci. 27(5), 240–243 (2006)

    Article  Google Scholar 

  5. Babloyantz, A., Destexhe, A.: Low-dimensional chaos in an instance of epilepsy. Proc. Natl. Acad. Sci. USA 83, 3513–3517 (1986)

    Article  Google Scholar 

  6. Bhattacharya, B.S., Coyle, D., Maguire, L.P.: A computational modelling approach to investigate alpha rhythm slowing associated with Alzheimer’s Disease. In: Proceedings of the Brain Inspired Cognitive Systems (BICS), Madrid, pp. 382–392 (2010)

    Google Scholar 

  7. Bhattacharya, B.S., Coyle, D., Maguire, L.P.: Thalamocortical circuitry and alpha rhythm slowing: an empirical study based on a classic computational model. In: Proceedings of the International Journal of Neural Networks (IJCNN), Barcelona, pp. 3912–3918 (2010)

    Google Scholar 

  8. Bhattacharya, B.S., Coyle, D., Maguire, L.P.: Alpha and theta rhythm abnormality in Alzheimer’s disease: a study using a computational model. In: Hernandez, C., Gomez, J., Sanz, R., Alexander, I., Smith, L., Hussain, A., Chella, A. (eds.) Advances in Experimental Medicine and Biology, vol. 718, pp. 57–73. Springer, New York (2011)

    Google Scholar 

  9. Bhattacharya, B.S., Coyle, D., Maguire, L.P.: Assessing retino-geniculo-cortical connectivities in Alzheimer’s disease with a neural mass model. In: Proceedings of the IEEE Symposium Series in Computational Intelligence (SSCI), Paris, pp. 159–163 (2011)

    Google Scholar 

  10. Bhattacharya, B.S., Coyle, D., Maguire, L.P.: A thalamo-cortico-thalamic neural mass model to study alpha rhythms in Alzheimer’s disease. Neural Netw. 24, 631–645 (2011)

    Article  Google Scholar 

  11. Bhattacharya, B.S., Coyle, D., Maguire, L.P.: Assessing alpha band event-related synchronisation/desynchronisation with a mutually coupled thalamo-cortical circuitry model. J. Univers. Comput. Sci. 18, 1888–1904 (2012)

    Google Scholar 

  12. Bhattacharya, B.S., Cakir, Y., Serap-Sengor, N., Maguire, L., Coyle, D.: Model-based bifurcation and power spectral analyses of thalamocortical alpha rhythm slowing in Alzheimer’s disease. Neurocomputing 115, 11–22 (2013). http://dx.doi.org/10.1016/j.neucom.2012.10.023

    Google Scholar 

  13. Braak, H., Braak, E.: Alzheimer’s Disease affects limbic nuclei of the thalamus. Acta Neuropathol. 81, 261–268 (1991)

    Article  Google Scholar 

  14. Brenner, R.P., Ulrich, R.F., Spiker, D.G., Sclabassi, R.J., Reynolds, C.F., Marin, R.S., Boller, F.: Computerized EEG spectral analysis in elderly normal, demented and depressed subjects. Electroencephalogr. Clin. Neurophysiol. 64, 483–492 (1986)

    Article  Google Scholar 

  15. Cantero, J.L., Atienza, M., Salas, R.M.: Human alpha oscillations in wakefulness, drowsiness period, and REM sleep: different electroencephalographic phenomena within the alpha band. Clin. Neurophysiol. 32, 54–71 (2002)

    Article  Google Scholar 

  16. Cantero, J.L., Atienza, M., Cruz-Vadell, A., Suarez-Gonzalez, A., Gil-Neciga, E.: Increased synchronization and decreased neural complexity underlie thalamocortical oscillatory dynamics in mild cognitive impairment. Neuroimage 46, 938–948 (2009)

    Article  Google Scholar 

  17. da Silva, F.H.L., van Lierop, T.H.M.T., Schrijer, C.F., van Leeuwen, W.S.: Essential differences between alpha rhythms and barbiturate spindles: spectra and thalamo-cortical coherences. Electroencephalogr. Clin. Neurophysiol. 35, 641–645 (1973)

    Article  Google Scholar 

  18. Dauwels, J., Vialatte, F., Cichocki, A.: Diagnosis of Alzheimer’s disease from EEG signals: Where are we standing? Neuroimage 49, 668–693 (2010). doi:10.1016/j.neuroimage.2009.06.056

    Article  Google Scholar 

  19. de Jong, L.W., van der Hiele, K., Veer, I.M., Houwing, J.J., Westendorp, R.G.J., Bollen, E.L.E.M., de Bruin, P.W., Middelkoop, H.A.M., van Buchem, M.A., van der Grond, J.: Strongly reduced volumes of putamen and thalamus in Alzheimer’s disease: an MRI study. Brain 131, 3277–3285 (2008)

    Article  Google Scholar 

  20. Erdi, P., Kiss, T., Toth, J., Ujfalussy, B., Zalanyi, L.: From systems biology to dynamical neuropharmacology: proposal for a new methodology. IEEE Proc. Syst. Biol. 153(4), 299–308 (2006)

    Article  Google Scholar 

  21. Ermentrout, B.: Simulating, Analyzing, and Animating Dynamical Systems: A Guide to Xppaut for Researchers and Students (Software, Environments, Tools). Society for Industrial Mathematics, Philadelphia (2002)

    Book  Google Scholar 

  22. Ermentrout, B.: Xppaut. Scholarpedia 1(10), 1399 (2006)

    Google Scholar 

  23. Freeman, W.J.: Linear analysis of the dynamics of neural masses. Annu. Rev. Biophys. Bioeng. 1, 225–256 (1972)

    Article  Google Scholar 

  24. Freeman, W.J.: Mass Action in the Nervous System, 1st edn. Academic, New York (1975)

    Google Scholar 

  25. Freyer, F., Roberts, J.A., Becker, R., Robinson, P.A., Ritter, P., Breakspear, M.: Dynamic mechanisms of multistability in the human alpha rhythm. J. Neurosci. 31, 6353–6361 (2011)

    Article  Google Scholar 

  26. Gasser, U.S., Rousson, V., Hentschel, F., Sattel, H., Gasser, T.: Alzheimer disease versus mixed dementias: an EEG perspective. Clin. Neurophysiol. 119, 2255–2259 (2008)

    Article  Google Scholar 

  27. Grimbert, F., Faugeras, O.: Bifurcation analysis of Jansen’s neural mass model. Neural Comput. 18, 3052–3068 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  28. Hines, M.L., Morse, T., Migliore, M., Carnevale, N.T., Shepherd, G.M.: ModelDB: a database to support computational neuroscience. J. Comput. Neurosci. 17(1), 7–11 (2004)

    Article  Google Scholar 

  29. Horn, S.C.V., Erisir, A., Sherman, S.M.: Relative distribution of synapses in the A-laminae of the lateral geniculate nucleus of the cat. J. Comp. Neurol. 416, 509–520 (2000)

    Article  Google Scholar 

  30. Hornero, R., Abasolo, D., Escudero, J., Gomez, C.: Nonlinear analysis of electroencephalogram and magnetoencephalogram recordings in patients with Alzheimer’s disease. Philos. Trans. R. Soc. A 367, 317–336 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  31. Hughes, S.W., Crunelli, V.: Thalamocortical mechanisms in EEG alpha rhythms and their pathological implications. Neuroscientist 11(4), 357–372 (2005)

    Article  Google Scholar 

  32. Izhikevich, E.M.: Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. MIT, Cambridge (2007)

    Google Scholar 

  33. Jansen, B.H., Rit, V.G.: Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biol. Cybern. 73, 357–366 (1995)

    Article  MATH  Google Scholar 

  34. Jelles, B., Scheltens, P., van der Flier, W.M., Jonkman, E.J., da Silva, F.H.L., Stam, C.J.: Global dynamical analysis of the EEG in Alzheimer’s Disease: frequency-specific changes of functional interactions. Clin. Neurophysiol. 119, 837–841 (2008)

    Article  Google Scholar 

  35. Jeong, J.: Nonlinear dynamics of EEG in Alzheimer’s disease. Drug Dev. Res. 56, 57–66 (2002)

    Article  Google Scholar 

  36. Jeong, J.: EEG dynamics in patients with Alzheimer’s disease. Clin. Neurophysiol. 115, 1490–1505 (2004)

    Article  Google Scholar 

  37. Jones, E.G.: The Thalamus, vols. I and II, 1st edn. Cambridge University Press, Cambridge (2007)

    Google Scholar 

  38. Jonkman, E.J.: The role of the electroencephalogram in the diagnosis of dementia of the Alzheimer type: an attempt at technology assessment. Clin. Neurophysiol. 27, 211–219 (1997)

    Article  Google Scholar 

  39. Li, X., Coyle, D., Maguire, L.P., Watson, D., McGinnity, T.: Gray matter concentration and effective connectivity changes in Alzheimer’s disease: a longitudinal structural MRI study. Neuroradiology 53, 733–748 (2010)

    Article  Google Scholar 

  40. Marten, F., Rodrigues, S., Suffczynski, P., Richardson, M.P., Terry, J.R.: Derivation and analysis of an ordinary differential equation mean-field model for studying clinically recorded epilepsy dynamics. Phys. Rev. E 79(021911), 1–7 (2009)

    MathSciNet  Google Scholar 

  41. MATLAB: Version 7.10.0 (R2010a). The MathWorks Inc., Natick (2010)

    Google Scholar 

  42. McCormick, D.A.: Are thalamocortical rhythms the Rosetta Stone of a subset of neurological disorders? Nat. Med. 5(12), 1349–1351 (1999)

    Article  Google Scholar 

  43. McCormick, D.A., Bal, T.: Sleep and arousal: thalamocortical mechanisms. Annu. Rev. Neurosci. 20, 185–215 (1997)

    Article  Google Scholar 

  44. Moran, R., Kiebel, S., Stephan, K., Reilly, R., Daunizeau, J., Friston, K.: A neural mass model of spectral responses in electrophysiology. Neuroimage 37, 706–720 (2007)

    Article  Google Scholar 

  45. Moretti, D.V., Babiloni, C., Binetti, G., Cassetta, E., Forno, G.D., Ferreric, F., Ferri, R., Lanuzza, B., Miniussi, C., Nobili, F., Rodriguez, G., Salinari, S., Rossini, P.M.: Individual analysis of EEG frequency and band power in mild Alzheimer’s disease. Clin. Neurophysiol. 115, 299–308 (2004)

    Article  Google Scholar 

  46. Pons, A.J., Cantero, J.L., Atienza, M., Garcia-Ojalvo, J.: Relating structural and functional anomalous connectivity in the ageing brain via neural mass modelling. Neuroimage 52(3), 848–861 (2010)

    Article  Google Scholar 

  47. Prinz, P.N., Vitiello, M.V.: Dominant occipital (alpha) rhythm frequency in early stage Alzheimer’s Disease and depression. Electroencephalogr. Clin. Neurophysiol. 73, 427–432 (1989)

    Article  Google Scholar 

  48. Pritchard, W.S., Duke, D.W.: Measuring chaos in the brain: a tutorial review of nonlinear dynamical EEG analysis. Int. J. Neurosci. 67, 31–80 (1992)

    Article  Google Scholar 

  49. Robinson, P.A., Rennie, C.J., Rowe, D.L., O’Connor, S.C.: Estimation of multiscale neurophysiologic parameters by electroencephalographic means. Hum. Brain Mapp. 23, 53–72 (2004)

    Article  Google Scholar 

  50. Roth, C., Achermann, P., Borbely, A.A.: Alpha activity in the human REM sleep EEG: topography and effect of REM sleep deprivation. Clin. Neurophysiol. 110, 632–635 (1999)

    Article  Google Scholar 

  51. Scheibel, A.B.: Thalamus. In: Encyclopedia of the Neurological Sciences, pp. 501–508. Elsevier Science, Amsterdam (2003)

    Google Scholar 

  52. Sherman, S.M.: Interneurons and triadic circuitry of the thalamus. Trends Neurosci. 27(11), 670–675 (2004)

    Article  Google Scholar 

  53. Sherman, S.M.: Thalamus. Scholarpedia 1(9), 1583 (2006)

    Article  Google Scholar 

  54. Sherman, S.M., Guillery, R.W.: Exploring the Thalamus, 1st edn. Academic, New York (2001)

    Google Scholar 

  55. Soininen, H., Reinikainen, K., Partanen, J., Helkala, E.L., Paljarvi, L., Riekkinen, P.: Slowing of elctroencephalogram and choline acetyltransferase activity in post mortem frontal cortex in definite Alzheimer’s Disease. Neuroscience 49(3), 529–535 (1992)

    Article  Google Scholar 

  56. Sotero, R.C., Tujillo-Barreto, N.J., Iturria-Medina, Y.: Realistically coupled neural mass models can generate EEG rhythms. Neural Comput. 19, 479–512 (2007)

    Article  Google Scholar 

  57. Stam, C.: Nonlinear dynamical analysis of EEG and MEG: review of an emerging field. Clin. Neurophysiol. 116, 2266–2301 (2005)

    Article  Google Scholar 

  58. Stam, C., Pijn, J., Suffczyński, P., da Silva, F.L.: Dynamics of the human alpha rhythm: evidence for non-linearity? Clin. Neurophysiol. 110, 1801–1813 (1999)

    Article  Google Scholar 

  59. Steriade, M., Deschenes, M.: The thalamus as a neuronal oscillator. Brain Res. Rev. 8, 1–63 (1984)

    Article  Google Scholar 

  60. Steriade, M.M., McCarley, R.: Brain Control of Wakefulness and Sleep, 2nd edn. Kluwer, New York (2005)

    Google Scholar 

  61. Steriade, M., Gloor, P., Llinas, R.R., da Silva, F.H.L., Mesulam, M.M.: Basic mechanisms of cerebral rhythmic activities. Electroencephalogr. Clin. Neurophysiol. 76, 481–508 (1991)

    Article  Google Scholar 

  62. Stoller, A.: Slowing of the alpha-rhythm of the electroencephalogram and its association with mental deterioration and epilepsy. J. Mental Sci. 95, 972–984 (1949). doi:10.1192/bjp.95.401.972

    Google Scholar 

  63. Suffczyński, P.: Neural dynamics underlying brain thalamic oscillations investigated with computational models. Ph.D. Thesis, Institute of Experimental Physics, University of Warsaw (2000)

    Google Scholar 

  64. Suffczyński, P., Kalitzin, S., Silva, F.H.L.D.: Dynamics of non-convulsive epileptic phenomena modelled by a bistable neuronal network. Neuroscience 126, 467–484 (2004)

    Article  Google Scholar 

  65. Tai, Y., Yi, H., Ilinsky, I.A., Kultas-Ilinsky, K.: Nucleus reticularis thalami connections with the mediodorsal thalamic nucleus: a light and electron microscopic study in the monkey. Brain Res. Bull. 38(5), 475–488 (1995)

    Article  Google Scholar 

  66. Theiler, J.: On the evidence for low-dimensional chaos in an epileptic electroencephalogram. Phys. Lett. A 196, 335–341 (1995)

    Article  Google Scholar 

  67. Tognoli, E., Lagarde, J., DeGuzman, G.C., Kelso, J.A.S.: The phi complex as a neuromarker of human social coordination. Proc. Natl. Acad. Sci. USA 104(19), 8190–8195 (2006)

    Article  Google Scholar 

  68. Tombol, T.: Short neurons and their synaptic relations in the specific thalamic nuclei. Brain Res. 3, 307–326 (1967)

    Article  Google Scholar 

  69. Ursino, M., Cona, F., Zavaglia, M.: The generation of rhythms within a cortical region: analysis of a neural mass model. Neuroimage 52(3), 1080–1094 (2010)

    Article  Google Scholar 

  70. Wendling, F., Bartolomei, F., Bellanger, J.J., Chauvel, P.: Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. Eur. J. Neurosci. 15, 1499–1508 (2002)

    Article  Google Scholar 

  71. Wilson, H.: Spikes, Decisions and Actions. Oxford University Press, Oxford (1999)

    MATH  Google Scholar 

  72. Wilson, H.R., Cowan, J.D.: Excitatory and inhibitory interaction in localized populations of model neurons. J. Biophys. 12, 1–23 (1972)

    Article  Google Scholar 

  73. Wilson, H.R., Cowan, J.D.: A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13, 55–80 (1973)

    Article  MATH  Google Scholar 

  74. Xuereb, J.H., Perry, R.H., Candy, J.M., Perry, E.K., Marshall, E., Bonham, J.R.: Nerve cell loss in the thalamus in Alzheimer’s disease and Parkinson’s disease. Brain 114, 1363–1379 (1991)

    Article  Google Scholar 

  75. Zavaglia, M., Astolfi, L., Babiloni, F., Ursino, M.: A neural mass model for the simulation of cortical activity estimated from high resolution EEG during cognitive or motor tasks. J. Neurosci. Methods 157, 317–329 (2006)

    Article  Google Scholar 

  76. Zou, X., Coyle, D., Wong-Lin, K., Maguire, L.P.: Computational study of hippocampal-septal theta rhythm changes due to beta-amyloid-altered ionic channels. PLoS One 6, e21579 (2011)

    Article  Google Scholar 

  77. Zou, X., Coyle, D., Wong-Lin, K., Maguire, L.P.: Beta-amyloid induced changes in a-type k + current can alter hippocampo-septal network dynamics. J. Comput. Neurosci. 32(3), 465–477 (2012)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. University of Lincoln, Lincoln, UK

    Basabdatta Sen-Bhattacharya

  2. Istanbul Technical University, Istanbul, Turkey

    Neslihan Serap-Sengor & Yuksel Cakir

  3. University of Ulster, Magee Campus, Northern Ireland, UK

    Liam Maguire & Damien Coyle

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  1. Basabdatta Sen-Bhattacharya
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  2. Neslihan Serap-Sengor
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  3. Yuksel Cakir
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  4. Liam Maguire
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Correspondence to Basabdatta Sen-Bhattacharya .

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  1. Dept. of Electrical and Computer Engineering, University of Iowa, Iowa City, Iowa, USA

    Punam K. Saha

  2. Dept. of Computer Science and Engineering, Jadavpur University, Kolkata, West Bengal, India

    Ujjwal Maulik

  3. Dept. of Computer Science and Engineering, Jadavpur University, Kolkata, India

    Subhadip Basu

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Sen-Bhattacharya, B., Serap-Sengor, N., Cakir, Y., Maguire, L., Coyle, D. (2014). Spectral and Non-linear Analysis of Thalamocortical Neural Mass Model Oscillatory Dynamics. In: Saha, P., Maulik, U., Basu, S. (eds) Advanced Computational Approaches to Biomedical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41539-5_4

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