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Brain Topography

, Volume 32, Issue 1, pp 28–65 | Cite as

A Blind Module Identification Approach for Predicting Effective Connectivity Within Brain Dynamical Subnetworks

  • Fadi N. KaramehEmail author
  • Ziad Nahas
Original Paper

Abstract

Model-based network discovery measures, such as the brain effective connectivity, require fitting of generative process models to measurements obtained from key areas across the network. For distributed dynamic phenomena, such as generalized seizures and slow-wave sleep, studying effective connectivity from real-time recordings is significantly complicated since (i) outputs from only a subnetwork can be practically measured, and (ii) exogenous subnetwork inputs are unobservable. Model fitting, therefore, constitutes a challenging blind module identification or model inversion problem for finding both the parameters and the many unknown inputs of the subnetwork. We herein propose a novel estimation framework for identifying nonlinear dynamic subnetworks in the case of slowly-varying, otherwise unknown local inputs. Starting with approximate predictions obtained using Cubature Kalman filtering, residuals of local output predictions are utilized to improve upon local input estimates. The algorithm performance is tested on both simulated and clinical EEG of induced seizures under electroconvulsive therapy (ECT). For the simulated network, the algorithm significantly boosted the estimation accuracy for inputs and connections from noisy EEG. For the clinical data, the algorithm predicted increased subnetwork inputs during the pre-stimulus anesthesia condition. Importantly, it predicted an increased frontocentral connectivity during the generalized seizure that is commensurate with electrode placement and that corroborates the clinical hypothesis of increased frontal focality of therapeutic ECT seizures. The proposed framework can be extended to account for several input configurations and can in principle be applied to study effective connectivity within brain subnetworks defined at the microscale (cortical lamina interaction) or at the macroscale (sensory integration).

Keywords

Model inversion Effective connectivity Kalman filtering Neuronal modeling Blind deconvolution Brain subnetworks 

Notes

Funding

This work has been supported by the Lebanese National Council for Scientific Research (LNCSR, Award No. 102630) and the following internal grant programs at AUB (1) the F Jabre Award for biomedical research, and (2) University Research Board award.

Compliance with Ethical Standards

Conflict of Interest

Fadi N. Karameh has no conflict of interest. Ziad Nahas has had research funding from MECTA Inc. in form of FEAST device loan.

Ethical Approval

All procedures performed in studies involving human participants were approved by the institutional review board (IRB) at the American University of Beirut under a FDA investigation device exemption and in accordance with the 1964 Helsinki declaration and its later amendments.

Informed Consent

Informed consent was obtained from all individual participants included in the study.

Research Involving Human Participants and/or Animals

This article does not contain any studies with animals performed by any of the authors

References

  1. Ackermann RF, Engel J, Baxter L (1986) Positron emission tomography and autoradiographic studies of glucose utilization following electroconvulsive seizures in humans and rats. Annal N Y Acad Sci 462(1):263–269Google Scholar
  2. Ambrogioni L, Hinne M, Van Gerven M, Maris E (2017) Gp cake: effective brain connectivity with causal kernels. In: Advances in Neural Information Processing Systems, pp 951–960Google Scholar
  3. Arasaratnam I, Haykin S (2009) Cubature kalman filters. IEEE Trans Autom Control 54(6):1254–1269Google Scholar
  4. Arasaratnam I, Haykin S, Hurd TR (2010) Cubature kalman filtering for continuous-discrete systems: theory and simulations. IEEE Trans Signal Process 58(10):4977–4993Google Scholar
  5. Barrett AB, Murphy M, Bruno MA, Noirhomme Q, Boly M, Laureys S, Seth AK (2012) Granger causality analysis of steady-state electroencephalographic signals during propofol-induced anaesthesia. PLoS ONE 7(1):e29–072Google Scholar
  6. Bastos AM, Litvak V, Moran R, Bosman CA, Fries P, Friston KJ (2015) A dcm study of spectral asymmetries in feedforward and feedback connections between visual areas v1 and v4 in the monkey. Neuroimage 108:460–475Google Scholar
  7. Beierlein M, Gibson JR, Connors BW (2003) Two dynamically distinct inhibitory networks in layer 4 of the neocortex. J Neurophysiol 90(5):2987–3000Google Scholar
  8. Bell AJ, Sejnowski TJ (1995) An information-maximization approach to blind separation and blind deconvolution. Neural Comput 7(6):1129–1159Google Scholar
  9. Bielczyk NZ, Llera A, Buitelaar JK, Glennon JC, Beckmann CF (2017) Increasing robustness of pairwise methods for effective connectivity in magnetic resonance imaging by using fractional moment series of bold signal distributions. arXiv:160608724v3
  10. Cammarota M, Losi G, Chiavegato A, Zonta M, Carmignoto G (2013) Fast spiking interneuron control of seizure propagation in a cortical slice model of focal epilepsy. J Physiol 591(4):807–822Google Scholar
  11. Canolty RT, Knight RT (2010) The functional role of cross-frequency coupling. Trends Cogn Sci 14(11):506–515Google Scholar
  12. Correa N, Adalı T, Calhoun VD (2007) Performance of blind source separation algorithms for fmri analysis using a group ica method. Magn Reson Imaging 25(5):684–694Google Scholar
  13. Cruikshank SJ, Ahmed OJ, Stevens TR, Patrick SL, Gonzalez AN, Elmaleh M, Connors BW (2012) Thalamic control of layer 1 circuits in prefrontal cortex. J Neurosci 32(49):17Google Scholar
  14. Crunelli V, David F, Lőrincz ML, Hughes SW (2015) The thalamocortical network as a single slow wave-generating unit. Curr Opin Neurobiol 31:72–80Google Scholar
  15. Damaraju E, Allen E, Belger A, Ford J, McEwen S, Mathalon D, Mueller B, Pearlson G, Potkin S, Preda A et al (2014) Dynamic functional connectivity analysis reveals transient states of dysconnectivity in schizophrenia. NeuroImage 5:298–308Google Scholar
  16. Dankers A, Van den Hof PM, Bombois X, Heuberger PS (2015) Errors-in-variables identification in dynamic networks-consistency results for an instrumental variable approach. Automatica 62:39–50Google Scholar
  17. Dankers A, Van den Hof PM, Bombois X, Heuberger PS (2016) Identification of dynamic models in complex networks with prediction error methods: predictor input selection. IEEE Trans Autom Control 61(4):937–952Google Scholar
  18. Dankers A, Van den Hof PM, Bombois X, Heuberger PS (2013) Predictor input selection for two stage identification in dynamic networks. In: Control Conference (ECC), 2013 European, IEEE, pp 1422–1427Google Scholar
  19. David O, Kiebel SJ, Harrison LM, Mattout J, Kilner JM, Friston KJ (2006) Dynamic causal modeling of evoked responses in eeg and meg. NeuroImage 30(4):1255–1272Google Scholar
  20. De Curtis M, Gnatkovsky V (2009) Reevaluating the mechanisms of focal ictogenesis: the role of low-voltage fast activity. Epilepsia 50(12):2514–2525Google Scholar
  21. Deng ZD, Lisanby SH, Peterchev AV (2011) Electric field strength and focality in electroconvulsive therapy and magnetic seizure therapy: a finite element simulation study. J Neural Eng 8(1):016007Google Scholar
  22. Destexhe A, Rudolph M, Paré D (2003) The high-conductance state of neocortical neurons in vivo. Nat Rev Neurosci 4(9):739Google Scholar
  23. Diez I, Bonifazi P, Escudero I, Mateos B, Muñoz MA, Stramaglia S, Cortes JM (2015) A novel brain partition highlights the modular skeleton shared by structure and function. Sci Rep 5(srep10):532Google Scholar
  24. Dijkstra N, Zeidman P, Ondobaka S, Gerven MA, Friston K (2017) Distinct top-down and bottom-up brain connectivity during visual perception and imagery. Sci Rep 7(1):5677Google Scholar
  25. Dubeau S, Havlicek M, Beaumont E, Ferland G, Lesage F, Pouliot P (2012) Neurovascular deconvolution of optical signals as a proxy for the true neuronal inputs. J Neurosci Methods 210(2):247–258Google Scholar
  26. Enev M, McNally KA, Varghese G, Zubal IG, Ostroff RB, Blumenfeld H (2007) Imaging onset and propagation of ect-induced seizures. Epilepsia 48(2):238–244Google Scholar
  27. Engel AK, Fries P, Singer W (2001) Dynamic predictions: oscillations and synchrony in top-down processing. Nat Rev Neurosci 2(10):704Google Scholar
  28. Everitt N (2017) Module identification in dynamic networks: parametric and empirical bayes methods. PhD thesis, KTH Royal Institute of TechnologyGoogle Scholar
  29. Everitt N, Bottegal G, Rojas CR, Hjalmarsson H (2016) Identification of modules in dynamic networks: an empirical bayes approach. In: 2016 IEEE 55th Conference on Decision and control (CDC), IEEE, pp 4612–4617Google Scholar
  30. Fontolan L, Morillon B, Liegeois-Chauvel C, Giraud AL (2014) The contribution of frequency-specific activity to hierarchical information processing in the human auditory cortex. Nat Commun 5:4694Google Scholar
  31. Franks NP (2008) General anaesthesia: from molecular targets to neuronal pathways of sleep and arousal. Nat Rev Neurosci 9(5):370Google Scholar
  32. Frässle S, Lomakina EI, Kasper L, Manjaly ZM, Leff A, Pruessmann KP, Buhmann JM, Stephan KE (2018) A generative model of whole-brain effective connectivity. NeuroImage 179:505–529Google Scholar
  33. Freestone DR, Karoly PJ, Nešić D, Aram P, Cook MJ, Grayden DB (2014) Estimation of effective connectivity via data-driven neural modeling. Front Neurosci 8:383Google Scholar
  34. Friston KJ (2011) Functional and effective connectivity: a review. Brain Connect 1(1):13–36Google Scholar
  35. Friston K, Moran R, Seth AK (2013) Analysing connectivity with granger causality and dynamic causal modelling. Curr Opin Neurobiol 23(2):172–178Google Scholar
  36. Garrido MI, Friston KJ, Kiebel SJ, Stephan KE, Baldeweg T, Kilner JM (2008) The functional anatomy of the mmn: a dcm study of the roving paradigm. Neuroimage 42(2):936–944Google Scholar
  37. Goebel R, Roebroeck A, Kim DS, Formisano E (2003) Investigating directed cortical interactions in time-resolved fmri data using vector autoregressive modeling and granger causality mapping. Magn Reson Imaging 21(10):1251–1261Google Scholar
  38. Grover S, Mattoo SK, Gupta N (2005) Theories on mechanism of action of electroconvulsive therapy. German J Psychiatry 8:70–84Google Scholar
  39. Havlicek M, Jan J, Brazdil M, Calhoun VD (2010) Dynamic granger causality based on kalman filter for evaluation of functional network connectivity in fmri data. Neuroimage 53(1):65–77Google Scholar
  40. Havlicek M, Friston KJ, Jan J, Brazdil M, Calhoun VD (2011) Dynamic modeling of neuronal responses in fmri using cubature kalman filtering. NeuroImage 56(4):2109–2128Google Scholar
  41. Hilgetag CC, Kötter R, Stephan KE, Sporns O (2002) Computational methods for the analysis of brain connectivity. In: Ascoli G (ed) Computational neuroanatomy. Springer, New York, pp 295–335Google Scholar
  42. Holland R, Leff AP, Penny WD, Rothwell JC, Crinion J (2016) Modulation of frontal effective connectivity during speech. NeuroImage 140:126–133Google Scholar
  43. Honey CJ, Kötter R, Breakspear M, Sporns O (2007) Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proc Natl Acad Sci 104(24):10240–10245Google Scholar
  44. Hu L, Zhang Z, Hu Y (2012) A time-varying source connectivity approach to reveal human somatosensory information processing. Neuroimage 62(1):217–228Google Scholar
  45. Hyafil A, Giraud AL, Fontolan L, Gutkin B (2015) Neural cross-frequency coupling: connecting architectures, mechanisms, and functions. Trends Neurosci 38(11):725–740Google Scholar
  46. Hyvarinen A (1999) Fast and robust fixed-point algorithms for independent component analysis. IEEE Trans Neural Netw 10(3):626–634Google Scholar
  47. Jann K, Kottlow M, Dierks T, Boesch C, Koenig T (2010) Topographic electrophysiological signatures of fmri resting state networks. PLoS ONE 5(9):e12–945Google Scholar
  48. 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
  49. Jones SR, Pritchett DL, Stufflebeam SM, Hämäläinen M, Moore CI (2007) Neural correlates of tactile detection: a combined magnetoencephalography and biophysically based computational modeling study. J Neurosci 27(40):10751–10764Google Scholar
  50. Karameh FN, Awada M, Mourad F, Zahed K, Abou-Faycal IC, Nahas Z (2014) Modeling of neuronal population activation under electroconvulsive therapy. In: Biosignals, pp 229–238Google Scholar
  51. Kiebel SJ, Garrido MI, Moran R, Chen CC, Friston KJ (2009) Dynamic causal modeling for EEG and MEG. Hum Brain Mapp 30(6):1866–1876Google Scholar
  52. Lee U, Kim S, Noh GJ, Choi BM, Hwang E, Mashour GA (2009) The directionality and functional organization of frontoparietal connectivity during consciousness and anesthesia in humans. Conscious Cogn 18(4):1069–1078Google Scholar
  53. Lee WH, Deng ZD, Kim TS, Laine AF, Lisanby SH, Peterchev AV (2012) Regional electric field induced by electroconvulsive therapy in a realistic finite element head model: influence of white matter anisotropic conductivity. Neuroimage 59(3):2110–2123Google Scholar
  54. Lee U, Ku S, Noh G, Baek S, Choi B, Mashour GA (2013) Disruption of frontal-parietal communication by ketamine, propofol, and sevoflurane. J Am Soc Anesthesiol 118(6):1264–1275Google Scholar
  55. Li B, Daunizeau J, Stephan KE, Penny W, Hu D, Friston K (2011) Generalised filtering and stochastic DCM for fMRI. Neuroimage 58(2):442–457Google Scholar
  56. Lisanby SH (2007) Electroconvulsive therapy for depression. N Engl J Med 357(19):1939–1945Google Scholar
  57. Ljung L (1999) System identification, Wiley Encyclopedia of Electrical and Electronics EngineeringGoogle Scholar
  58. Madi MK, Karameh FN (2017) Hybrid cubature kalman filtering for identifying nonlinear models from sampled recording: estimation of neuronal dynamics. PLoS ONE 12(7):1–49Google Scholar
  59. Madi MK, Karameh FN (2018) Adaptive optimal input design and parametric estimation of nonlinear dynamical systems: application to neuronal modeling. J Neural Eng 15(4):046028Google Scholar
  60. Mankad MV, Beyer JL, Weiner RD, Krystal A (2010) Clinical manual of electroconvulsive therapy. American Psychiatric Pub, Washington, DCGoogle Scholar
  61. Markram H, Toledo-Rodriguez M, Wang Y, Gupta A, Silberberg G, Wu C (2004) Interneurons of the neocortical inhibitory system. Nat Rev Neurosci 5(10):793Google Scholar
  62. McCormick DA, Bal T (1997) Sleep and arousal: thalamocortical mechanisms. Annu Rev Neurosci 20(1):185–215Google Scholar
  63. Merkl A, Heuser I, Bajbouj M (2009) Antidepressant electroconvulsive therapy: mechanism of action, recent advances and limitations. Experim Neurol 219(1):20–26Google Scholar
  64. Moran RJ, Kiebel SJ, Stephan K, Reilly R, Daunizeau J, Friston KJ (2007) A neural mass model of spectral responses in electrophysiology. NeuroImage 37(3):706–720Google Scholar
  65. Moran RJ, Stephan KE, Seidenbecher T, Pape HC, Dolan RJ, Friston KJ (2009) Dynamic causal models of steady-state responses. Neuroimage 44(3):796–811Google Scholar
  66. Moscrip TD, Terrace HS, Sackeim HA, Lisanby SH (2006) Randomized controlled trial of the cognitive side-effects of magnetic seizure therapy (MST) and electroconvulsive shock (ECS). Int J Neuropsychopharmacol 9(1):1–11Google Scholar
  67. Mouraux A, Iannetti GD (2008) Across-trial averaging of event-related eeg responses and beyond. Magn Reson Imaging 26(7):1041–1054Google Scholar
  68. Müller-Linow M, Hilgetag CC, Hütt MT (2008) Organization of excitable dynamics in hierarchical biological networks. PLoS Comput Biol 4(9):e1000–190Google Scholar
  69. Nahas Z, Short B, Burns C, Archer M, Schmidt M, Prudic J, Nobler MS, Devanand D, Fitzsimons L, Lisanby SH et al (2013) A feasibility study of a new method for electrically producing seizures in man: focal electrically administered seizure therapy. Brain Stimul 6(3):403–408Google Scholar
  70. Nobler MS, Sackeim HA, Prohovnik I, Moeller JR, Mukherjee S, Schnur DB, Prudic J, Devanand D (1994) Regional cerebral blood flow in mood disorders, III: treatment and clinical response. Arch General Psychiatry 51(11):884–897Google Scholar
  71. Nobler MS, Oquendo MA, Kegeles LS, Malone KM, Campbell C, Sackeim HA, Mann JJ (2001) Decreased regional brain metabolism after ECT. Am J Psychiatry 158(2):305–308Google Scholar
  72. Pagerols J, Rojo J (2009) Electrophysiological mechanisms of action of electroconvulsive therapy. Actas Esp Psiquiatr 37(6):343–351Google Scholar
  73. Palmer L, Murayama M, Larkum M (2012) Inhibitory regulation of dendritic activity in vivo. Front Neural Circuits 6:26Google Scholar
  74. Palva S, Palva JM (2012) Discovering oscillatory interaction networks with m/EEG: challenges and breakthroughs. Trends Cogn Sci 16(4):219–230Google Scholar
  75. Park HJ, Friston K (2013) Structural and functional brain networks: from connections to cognition. Science 342(6158):1238–411Google Scholar
  76. Park HJ, Friston K, Pae C, Park B, Razi A (2017) Dynamic effective connectivity in resting state fMRI. NeuroImage.  https://doi.org/10.1016/j.neuroimage.2017.11.033 Google Scholar
  77. Pereda E, Quiroga RQ, Bhattacharya J (2005) Nonlinear multivariate analysis of neurophysiological signals. Prog Neurobiol 77(1):1–37Google Scholar
  78. Pfeffer CK, Xue M, He M, Huang ZJ, Scanziani M (2013) Inhibition of inhibition in visual cortex: the logic of connections between molecularly distinct interneurons. Nat Neurosci 16(8):1068–1076Google Scholar
  79. Pinotsis D, Geerts J, Pinto L, FitzGerald T, Litvak V, Auksztulewicz R, Friston K (2017) Linking canonical microcircuits and neuronal activity: dynamic causal modelling of laminar recordings. NeuroImage 146:355–366Google Scholar
  80. Plomp G, Quairiaux C, Kiss JZ, Astolfi L, Michel CM (2014) Dynamic connectivity among cortical layers in local and large-scale sensory processing. Eur J Neurosci 40(8):3215–3223Google Scholar
  81. Proix T, Spiegler A, Schirner M, Rothmeier S, Ritter P, Jirsa VK (2016) How do parcellation size and short-range connectivity affect dynamics in large-scale brain network models? NeuroImage 142:135–149Google Scholar
  82. Rennie CJ, Robinson PA, Wright JJ (2002) Unified neurophysical model of EEG spectra and evoked potentials. Biol Cybern 86(6):457–471Google Scholar
  83. Roebroeck A, Formisano E, Goebel R (2011) The identification of interacting networks in the brain using fmri: model selection, causality and deconvolution. Neuroimage 58(2):296–302Google Scholar
  84. Rosch R, Friston K, Tisdall M, Thornton R (2017) Patient-specific modelling of epileptogenic networks from stereotactic EEG recordings.  https://doi.org/10.6084/m9.figshare.5311198.v1
  85. Rubinov M, Sporns O (2010) Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52(3):1059–1069Google Scholar
  86. Sackeim HA (1999) The anticonvulsant hypothesis of the mechanisms of action of ECT: current status. J ECT 15(1):5–26Google Scholar
  87. Sackeim HA, Luber B, Katzman GP, Moeller JR, Prudic J, Devanand D, Nobler MS (1996) The effects of electroconvulsive therapy on quantitative electroencephalograms: relationship to clinical outcome. Arch General Psychiatry 53(9):814–824Google Scholar
  88. Sackeim HA, Prudic J, Nobler MS, Fitzsimons L, Lisanby SH, Payne N, Berman RM, Brakemeier EL, Perera T, Devanand D (2008) Effects of pulse width and electrode placement on the efficacy and cognitive effects of electroconvulsive therapy. Brain Stimul 1(2):71–83Google Scholar
  89. Sedigh-Sarvestani M, Schiff SJ, Gluckman BJ (2012) Reconstructing mammalian sleep dynamics with data assimilation. PLoS Comput Biol 8(11):e1002–788Google Scholar
  90. Sellers KK, Bennett DV, Hutt A, Williams JH, Fröhlich F (2015) Awake vs. anesthetized: layer-specific sensory processing in visual cortex and functional connectivity between cortical areas. J Neurophysiol 113(10):3798–3815Google Scholar
  91. Sengupta B, Friston KJ, Penny WD (2015) Gradient-free mcmc methods for dynamic causal modelling. NeuroImage 112:375–381Google Scholar
  92. Shayegh F, Fattahi RA, Sadri S, Ansari-Asl K (2011) A brief survey of computational models of normal and epileptic eeg signals: a guideline to model-based seizure prediction. J Med Signals Sens 1(1):62Google Scholar
  93. Spellman T, Peterchev AV, Lisanby SH (2009) Focal electrically administered seizure therapy (feast): a novel form of ect illustrates the roles of current directionality, polarity, and electrode configuration in seizure induction. Neuropsychopharmacology 34(8):2002Google Scholar
  94. Sporns O (2014) Contributions and challenges for network models in cognitive neuroscience. Nat Neurosci 17(5):652–660Google Scholar
  95. Sporns O, Betzel RF (2016) Modular brain networks. Annu Rev Psychol 67:613–640Google Scholar
  96. Staiger JF, Freund TF, Zilles K (1997) Interneurons immunoreactive for vasoactive intestinal polypeptide (vip) are extensively innervated by parvalbumin-containing boutons in rat primary somatosensory cortex. Eur J Neurosci 9(11):2259–2268Google Scholar
  97. Stephan KE, Hilgetag CC, Burns GA, O’Neill MA, Young MP, Kotter R (2000) Computational analysis of functional connectivity between areas of primate cerebral cortex. Philos Trans R Soc London B 355(1393):111–126Google Scholar
  98. Tamás G, Szabadics J, Lörincz A, Somogyi P (2004) Input and frequency-specific entrainment of postsynaptic firing by ipsps of perisomatic or dendritic origin. Eur J Neurosci 20(10):2681–2690Google Scholar
  99. Thompson WH, Fransson P (2015) The frequency dimension of fmri dynamic connectivity: network connectivity, functional hubs and integration in the resting brain. NeuroImage 121:227–242Google Scholar
  100. Trevelyan AJ, Schevon CA (2013) How inhibition influences seizure propagation. Neuropharmacology 69:45–54Google Scholar
  101. Uhrig L, Dehaene S, Jarraya B (2014) Cerebral mechanisms of general anesthesia. Annales francaises d’anesthesie et de reanimation 33:72–82Google Scholar
  102. Van Den Heuvel MP, Sporns O (2011) Rich-club organization of the human connectome. J Neurosci 31(44):15775–15786Google Scholar
  103. Van den Hof PM, Dankers A, Heuberger PS, Bombois X (2013) Identification of dynamic models in complex networks with prediction error methods-basic methods for consistent module estimates. Automatica 49(10):2994–3006Google Scholar
  104. van Rotterdam A, Da Silva FL, Van den Ende J, Viergever M, Hermans A (1982) A model of the spatial-temporal characteristics of the alpha rhythm. Bull Math Biol 44(2):283–305Google Scholar
  105. Varela F, Lachaux JP, Rodriguez E, Martinerie J (2001) The brainweb: phase synchronization and large-scale integration. Nat Rev Neurosci 2(4):229Google Scholar
  106. Von Stein A, Sarnthein J (2000) Different frequencies for different scales of cortical integration: from local gamma to long range alpha/theta synchronization. Int J Psychophysiol 38(3):301–313Google Scholar
  107. Weaver KE, Wander JD, Ko AL, Casimo K, Grabowski TJ, Ojemann JG, Darvas F (2016) Directional patterns of cross frequency phase and amplitude coupling within the resting state mimic patterns of fmri functional connectivity. Neuroimage 128:238–251Google Scholar
  108. Wendling F, Bartolomei F, Bellanger J, Chauvel P (2002) Epileptic fast activity can be explained by a model of impaired gabaergic dendritic inhibition. Eur J Neurosci 15(9):1499–1508Google Scholar
  109. Wendling F, Hernandez A, Bellanger JJ, Chauvel P, Bartolomei F (2005) Interictal to ictal transition in human temporal lobe epilepsy: insights from a computational model of intracerebral EEG. J Clin Neurophysiol 22(5):343Google Scholar
  110. Xiang W, Yang C, Karfoul A, Jeannès RLB (2016) Quantifying connectivity in a physiology based model using adaptive dynamic causal modelling. In: Engineering in Medicine and Biology Society (EMBC), 2016 IEEE 38th Annual International Conference of the, IEEE, pp 2818–2821Google Scholar
  111. Yamamura D, Sano A, Tateno T (2017) An analysis of current source density profiles activated by local stimulation in the mouse auditory cortex in vitro. Brain Res 1659:96–112Google Scholar

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Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringAmerican University of BeirutBeirutLebanon
  2. 2.Department of PsychiatryAmerican University of BeirutBeirutLebanon
  3. 3.Department of PsychiatryUniversity of MinnesotaMinneapolisUSA

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