Physical mechanisms of human brain functions

Abstract

In recent years, exploring the physical mechanisms of brain functions has been a hot topic in the fields of nonlinear dynamics and complex networks, and many important achievements have been made, mainly based on the characteristic features of time series of human brain. To speed up the further study of this problem, herein we make a brief review on these important achievements, which includes the aspects of explaining: (i) the mechanism of brain rhythms by network synchronization, (ii) the mechanism of unihemispheric sleep by chimera states, (iii) the fundamental difference between the structural and functional brain networks by remote synchronization, (iv) the mechanism of stronger detection ability of human brain to weak signals by remote firing propagation, and (v) the mechanism of dementia patterns by eigen-microstate analysis. As a brief review, we will mainly focus on the aspects of basic ideas, research histories, and key results but ignore the tedious mathematical derivations. Moreover, some outlooks will be discussed for future studies.

Keywords

chimera states / eigenmode analysis / network synchronization / remote firing propagation / remote synchronization

References

[1] Gazzaniga MS , Ivry RB , Mangun GR . Cognitive neuroscience: the biology of the mind. New York: W. W. Norton & Company; 2013.

[2] Drubach D . The brain explained. New Jersey: Prentice-Hall; 2000.

[3] Herculano-Houzel S . The human brain in numbers: a linearly scaled-up primate brain. Front Hum Neurosci. 2009; 3: 31- 823.

[4] Drachman DA . Do we have brain to spare? Neurology. 2005; 64 (12): 2004- 5.

[5] Hagmann P , Cammoun L , Gigandet X , Meuli R , Honey CJ , Wedeen JV , et al. Mapping the structural core of human cerebral cortex. PLoS Biol. 2008; 6 (7): e159.

[6] Honey CJ , Sporns O , Cammoun L , Gigandet X , Thiran JP , Meuli R , et al. Predicting human resting-state functional connectivity from structural connectivity. Proc Natl Acad Sci USA. 2009; 106 (6): 2035- 40.

[7] Bansal K , Medaglia JD , Bassett DS , Vettel JM , Muldoon SF . Data-driven brain network models differentiate variability across language tasks. PLoS Comput Biol. 2018; 14 (10): e1006487.

[8] Bansal K , Garcia JO , Tompson SH , Verstynen T , Vettel JM , Muldoon SF . Cognitive chimera states in human brain networks. Sci Adv. 2019; 5 (4): eaau8535.

[9] van den Heuvel MP , Stam CJ , Kahn RS , Hulshoff Pol HE . Efficiency of functional brain networks and intel-lectual performance. J Neurosci. 2009; 29 (23): 7619- 24.

[10] Cao H , Liu Z . A novel synchronization transition and amplitude death in the local brain networks of cortical regions. Nonlinear Dyn. 2022; 108 (4): 2861- 74.

[11] Lord L , Stevner AB , Deco G , Kringelbach ML . Understanding principles of integration and segregation using whole-brain computational connectomics: implications for neuropsychiatric disorders. Phil Trans R Soc A. 2017; 375 (2096): 20160283.

[12] Wu T , Zhang X , Liu Z . Understanding the mechanisms of brain functions from the angle of synchronization and complex network. Front Phys. 2022; 17 (3): 31504.

[13] Fox MD , Snyder AZ , Vincent JL , Corbetta M , Van Essen DC , Raichle ME . The human brain is intrinsically organized into dynamic, anticorrelated functional networks. Proc Natl Acad Sci USA. 2005; 102 (27): 9673- 8.

[14] Avena-Koenigsberger A , Misic B , Sporns O . Communication dynamics in complex brain networks. Nat Rev Neurosci. 2018; 19 (1): 17- 33.

[15] Wang J , Lombardi F , Zhang X , Anaclet C , Ivanov PC . Non-equilibrium critical dynamics of bursts in θ and δ rhythms as fundamental characteristic of sleep and wake micro-architecture. PLoS Comput Biol. 2019; 15 (11): e1007268.

[16] Uhlhaas PJ , Singer W . Abnormal neural oscillations and synchrony in schizophrenia. Nat Rev Neurosci. 2010; 11 (2): 100- 13.

[17] Deng L , Huo S , Chen A , Liu Z . Coupling resonance of signal responses induced by heterogeneously mixed positive and negative couplings in cognitive subnetworks. Chaos Solit Fractals. 2024; 180: 114505.

[18] Buzsaki G . Rhythms of the brain. New York: Oxford University Press; 2006

[19] Fries P . A mechanism for cognitive dynamics: neuronal communication through neuronal coherence. Trends Cognit Sci. 2005; 9 (10): 474- 80.

[20] Sporns O , Chialvo DR , Kaiser M , Hilgetag CC . Organization, development and function of complex brain networks. Trends Cognit Sci. 2004; 8 (9): 418- 25.

[21] Eguiluz VM , Chialvo DR , Cecchi GA , Baliki M , Apkarian AV . Scale-free brain functional networks. Phys Rev Lett. 2005; 94 (1): 018102.

[22] Abdelnour F , Voss HU , Raj A . Network diffusion accurately models the relationship between structural and functional brain connectivity networks. Neuroimage. 2014; 90: 335- 47.

[23] Buzsaki G , Draguhn A . Neuronal oscillations in cortical networks. Science. 2004; 304 (5679): 1926- 9.

[24] Crick F , Koch C . Some reflections on visual awareness. Cold Spring Harb Symp Quant Biol. 1990; 55 (0): 953- 62.

[25] Ward LM . Synchronous neural oscillations and cognitive processes. Trends Cognit Sci. 2003; 7 (12): 553- 9.

[26] Phillips AJK , Robinson PA . A quantitative model of sleep-wake dynamics based on the physiology of the brainstem ascending arousal system. J Biol Rhythm. 2007; 22 (2): 167- 79.

[27] Ipina IP , Kehoe PD , Kringelbach M , Laufs H , Ibañez A , Deco G , et al. Modeling regional changes in dynamic stability during sleep and wakefulness. Neuroimage. 2020; 215: 116833.

[28] Volgushev M , Chauvette S , Mukovski M , Timofecv I . Precise long-range synchronization of activity and silence in neoconical neurons during slow-wave sleep. J Neurosci. 2006; 26 (21): 5665- 72.

[29] Buzsaki G . Two-stage model of memory trace formation: a role for “noisy” brain states. Neuroscience. 1989; 31 (3): 551- 70.

[30] Wilson MA , McNaughton BL . Reactivation of hippocampal ensemble memories during sleep. Science. 1994; 265 (5172): 676- 9.

[31] Bullmore E , Sporns O . Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci. 2009; 10 (3): 186- 98.

[32] Fornito A , Zalesky A , Breakspear M . The connectomics of brain disorders. Nat Rev Neurosci. 2015; 16 (3): 159- 72.

[33] Huo S , Tian C , Zheng M , Guan S , Zhou CS , Liu Z . Spatial multi-scaled chimera states of cerebral cortex network and its inherent structure-dynamics relationship in human brain. Natl Sci Rev. 2021; 8 (1): nwaa125.

[34] Margineanu DG . Epileptic hypersynchrony revisited. Neuroreport. 2010; 21 (15): 963- 7.

[35] Pikovsky A , Rosenblum M , Kurths J . Synchronization: a universal concept in nonlinear sciences. Cambridge: Cambridge University Press; 2001.

[36] Arenas A , Diaz-Guilera A , Kurths J , Moreno Y , Zhou C . Synchronization in complex networks. Phys Rep. 2008; 469 (3): 93- 153.

[37] Boccaletti S , Almendral JA , Guan S , Leyva I , Liu Z , Sendina-Nadal I , et al. Explosive transitions in complex networks structure and dynamics: percolation and synchronization. Phys Rep. 2016; 660: 1- 94.

[38] Wendling F , Bellanger JJ , Bartolomei F , Chauvel P . Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals. Biol Cybern. 2000; 83 (4): 367- 78.

[39] Zhou C , Zemanova L , Zamora-Lopez G , Hilgetag CC , Kurths J . Structure-function relationship in complex brain networks expressed by hierarchical synchronization. New J Phys. 2007; 9 (6): 178.

[40] Sacchet MD , LaPlante RA , Wan Q , Pritchett DL , Lee AK , Hämäläinen M , et al. Attention drives synchronization of alpha and beta rhythms between right inferior frontal and primary sensory neocortex. J Neurosci. 2015; 35 (5): 2074- 82.

[41] von Stein A , Rappelsberger P , Sarnthein J , Petsche H . Synchronization between temporal and parietal cortex during multimodal object processing in man. Cereb Cortex. 1999; 9 (2): 137- 50.

[42] Massimini M , Ferrarelli F , Huber R , Esser SK , Singh H , Tononi G . Breakdown of cortical effective connectivity during sleep. Science. 2005; 309 (5744): 2228- 32.

[43] Stam CJ , Jones BF , Nolte G , Breakspear M , Scheltens P . Small world networks and functional connectivity in Alzheimer’s disease. Cereb Cortex. 2007; 17 (1): 92- 9.

[44] Chavez M , Valencia M , Navarro V , Latora V , Martinerie J . Functional modularity of background activities in normal and epileptic brain networks. Phys Rev Lett. 2010; 104 (11): 118701.

[45] Huo S , Zou Y , Kaisere M , Liu Z . Time-limited self-sustaining rhythms and state transitions in brain networks. Phys Rev Res. 2022; 4 (2): 023076.

[46] Fan H , Wang Y , Wang X . Eigenvector-based analysis of cluster synchronization in general complex networks of coupled chaotic oscillators. Front Phys. 2023; 18 (4): 45302.

[47] Pecora LM , Carroll TL . Master stability functions for synchronized coupled systems. Phys Rev Lett. 1998; 80 (10): 2109- 12.

[48] Wu T , Huo S , Alfaro-Bittner K , Boccaletti S , Liu Z . Double explosive transition in the synchronization of multilayer networks. Phys Rev Res. 2022; 4 (3): 033009.

[49] Rattenborg NC , Amlaner CJ , Lima SL . Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep. Neurosci Biobehav Rev. 2000; 24 (8): 817- 42.

[50] Rattenborg NC , Lima SL , Amlaner CJ . Half-awake to the risk of predation. Nature. 1999; 397 (6718): 397- 8.

[51] Tamaki M , Bang J , Watanabe T , Sasaki Y . Night watch in one brain hemisphere during sleep associated with the first-night effect in humans. Curr Biol. 2016; 26 (9): 1190- 4.

[52] Panaggio MJ , Abrams DM . Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators. Nonlinearity. 2015; 28 (3): R67- 87.

[53] Majhi S , Bera BK , Ghosh D , Perc M . Chimera states in neuronal networks: a review. Phys Life Rev. 2019; 28: 100- 21.

[54] Wang Z , Liu Z . Partial synchronization in complex networks: chimera state, remote synchronization, and cluster synchronization. Acta Phys Sin. 2020; 69 (8): 088902.

[55] Wang Z , Liu Z . A brief review of chimera state in empirical brain networks. Front Physiol. 2020; 11: 724.

[56] Kuramoto Y , Battogtokh D . Coexistence of coherence and incoherence in nonlocally coupled phase oscillators: a soluble case. Nonlinear Phenom Complex Syst. 2002; 5: 380.

[57] Abrams DM , Strogatz SH . Chimera states for coupled oscillators. Phys Rev Lett. 2004; 93 (17): 174102.

[58] Abrams DM , Mirollo R , Strogatz SH , Wiley DA . Solvable model for chimera states of coupled oscillators. Phys Rev Lett. 2008; 101 (8): 084103.

[59] Ma R , Wang J , Liu Z . Robust features of chimera states and the implementation of alternating chimera states. Europhys Lett. 2010; 91 (4): 40006.

[60] Omelchenko I , Omelchenko E , Hovel P , Scholl E . When nonlocal coupling between oscillators becomes stronger: patched synchrony or multichimera states. Phys Rev Lett. 2013; 110 (22): 224101.

[61] Uhlhaas PJ , Singer W . Neural synchrony in brain disorders: relevance for cognitive dysfunctions and pathophysiology. Neuron. 2006; 52 (1): 155- 68.

[62] Laing CR , Chow CC . Stationary bumps in networks of spiking neurons. Neural Comput. 2001; 13 (7): 1473- 94.

[63] Zhu Y , Zheng Z , Yang J . Chimera states on complex networks. Phys Rev E. 2014; 89 (2): 022914.

[64] Osipov GV , Hu B , Zhou C , Ivanchenko MV , Kurths J . Three types of transitions to phase synchronization in coupled chaotic oscillators. Phys Rev Lett. 2003; 91 (2): 024101.

[65] Liu Z , Zhou J , Munakata T . Detecting generalized synchronization by the generalized angle. Europhys Lett. 2009; 87 (5): 50002.

[66] Sporns O . Network attributes for segregation and integration in the human brain. Curr Opin Neurobiol. 2013; 23 (2): 162- 71.

[67] Park HJ , Friston K . Structural and functional brain networks: from connections to cognition. Science. 2013; 342: 6158.

[68] Sporns O . Contributions and challenges for network models in cognitive neuroscience. Nat Neurosci. 2014; 17 (5): 652- 60.

[69] Attwell D , Laughlin SB . An energy budget for signaling in the grey matter of the brain. J Cereb Blood Flow Metab. 2001; 21 (10): 1133- 45.

[70] Kaiser M , Hilgetag CC . Nonoptimal component placement, but short processing paths, due to long distance projections in neural systems. PLoS Comput Biol. 2006; 2 (7): e95.

[71] Bullmore E , Sporns O . The economy of brain network organization. Nat Rev Neurosci. 2012; 13 (5): 336- 49.

[72] Varela F , Lachaux J-P , Rodriguez E , Martinerie J . The brainweb: phase synchronization and large-scale integration. Nat Rev Neurosci. 2001; 2 (4): 229- 39.

[73] Bergner A , Frasca M , Sciuto G , Buscarino A , Ngamga EJ , Fortuna L , et al. Remote synchronization in star networks. Phys Rew E. 2012; 85 (2): 026208.

[74] Okuda K , Kuramoto Y . Mutual entrainment between populations of coupled oscillators. Prog Theor Phys. 1991; 86 (6): 1159- 76.

[75] Kumar M , Rosenblum M . Two mechanisms of remote synchronization in a chain of Stuart-Landau oscillators. Phys Rev E. 2021; 104 (5): 054202.

[76] Ruvinsky I , Gibson-Brown JJ . Genetic and developmental bases of serial homology in vertebrate limb evolution. Development. 2000; 127 (24): 5233- 44.

[77] Rosenthal JE , Murphy GM . Group theory and the vibrations of polyatomic molecules. Rev Mod Phys. 1936; 8 (4): 317- 46.

[78] Nicosia V , Valencia M , Chavez M , Diaz-Guilera A , Latora V . Remote synchronization reveals network symmetries and functional modules. Phys Rev Lett. 2013; 110 (17): 174102.

[79] Cao H , Yang Z , Liu Z . Remote synchronization in multi-layered community networks with star-like topology. Chaos Solit Fractals. 2023; 166: 112893.

[80] Gambuzza LV , Cardillo A , Fiasconaro A , Fortuna L , Gómez-Gardeñes J , Frasca M . Analysis of remote synchronization in complex networks. Chaos. 2013; 23 (4): 043103.

[81] Kang L , Wang Z , Huo S , Tian C , Liu Z . Remote synchronization in human cerebral cortex network with identical oscillators. Nonlinear Dyn. 2020; 99 (2): 1577- 86.

[82] Yang Z , Chen D , Xiao Q , Liu Z . Phase frustration induced remote synchronization. Chaos. 2022; 32 (10): 103125.

[83] Shen Q , Liu Z . Remote firing propagation in the neural network of C.elegans. Phys Rev E. 2021; 103 (5): 052414.

[84] Wang Z , Liu Z . Effect of remote signal propagation in an empirical brain network. Chaos. 2021; 31 (6): 063126.

[85] Vuksanovic V , Hovel P . Functional connectivity of distant cortical regions: role of remote synchronization and symmetry in interactions. Neuroimage. 2014; 97: 1- 8.

[86] Yang Z , Chen D , Hu G , Liu Z . Partial remote synchronization in star-like networks with partial connections among leaf nodes. Phys Rev Res. 2023; 5 (4): 043253.

[87] Benzi R , Parisi G , Sutera A , Vulpiani A . Stochastic resonance in climatic change. Tellus. 1982; 34 (1): 10.

[88] Gammaitoni L , Hanggi P , Jung P , Marchesoni F . Stochastic resonance. Rev Mod Phys. 1998; 70 (1): 223- 87.

[89] Pikovsky AS , Kurths J . Coherence resonance in a noise-driven excitable system. Phys Rev Lett. 1997; 78 (5): 775- 8.

[90] Liu Z , Lai Y-C . Coherence resonance in coupled chaotic oscillators. Phys Rev Lett. 2001; 86 (21): 4737- 40.

[91] Acebron JA , Lozano S , Arenas A . Amplified signal response in scale-free networks by collaborative signaling. Phys Rev Lett. 2007; 99 (12): 128701.

[92] Liu Z , Munakata T . Scale-free topology induced double resonance in networked two-state systems. Phys Rev E. 2008; 78 (4): 046111.

[93] Zhou J , Zhou Y , Liu Z . Amplification of signal response at an arbitrary node of a complex network. Phys Rev E. 2011; 83 (4): 046107.

[94] Kondo T , Liu Z , Munakata T . One-body theory for amplified signal response in a scale-free network. Phys Rev E. 2010; 81 (4): 041115.

[95] Barabasi AL , Albert R . Emergence of scaling in random networks. Science. 1999; 286 (5439): 509- 12.

[96] Shu Y , Hasenstaub A , McCormick DA . Turning on and off recurrent balanced cortical activity. Nature. 2003; 423 (6937): 288- 93.

[97] Wehr M , Zador AM . Balanced inhibition underlies tuning and sharpens spike timing in auditory cortex. Nature. 2003; 426 (6965): 442- 6.

[98] Haider B , Duque A , Hasenstaub AR , McCormick DA . Neocortical network activity in vivo is generated through a dynamic balance of excitation and inhibition. J Neurosci. 2006; 26 (17): 4535- 45.

[99] Xue M , Atallah BV , Scanziani M . Equalizing excitation-inhibition ratios across visual cortical neurons. Nature. 2014; 511 (7511): 596- 600.

[100] Liang X , Liu C , Zhang X . Positive and negative couplings perform complementary roles in the signal amplification of globally coupled bistable oscillators. Phys Rev E. 2020; 101 (2): 022205.

[101] Liang X , Zhang X , Zhao L . Diversity-induced resonance for optimally suprathreshold signals. Chaos. 2020; 30 (10): 103101.

[102] Louzada VHP , Araujo NAM , Andrade JS Jr. , Herramnn HJ , How to suppress undesired synchronization. Sci Rep. 2012; 2 (1): 658.

[103] Hong H , Strogatz SH . Kuramoto model of coupled oscillators with positive and negative coupling parameters: an example of conformist and contrarian oscillators. Phys Rev Lett. 2011; 106 (5): 054102.

[104] Zhang X , Guan S , Zou Y , Chen X , Liu Z . Suppressing explosive synchronization by contrarians. Europhys Lett. 2016; 113 (2): 28005.

[105] Tessone CJ , Mirasso CR , Toral R , Gunton JD . Diversity-induced resonance. Phys Rev Lett. 2006; 97 (19): 194101.

[106] Shen Q , Liu Z . Unidirectional links prefer local firing propagation in the neural network of C. elegans. Chaos Solit Fractals. 2023; 174: 113850.

[107] Dynamic connetcome lab.

[108] Dhamala M , Jirsa VK , Ding M . Transitions to synchrony in coupled bursting neurons. Phys Rev Lett. 2004; 92 (2): 028101.

[109] Wang R , Liu M , Cheng X , Wu Y , Hildebrandt A , Zhou C . Segregation, integration, and balance of large-scale resting brain networks configure different cognitive abilities. Proc Natl Acad Sci USA. 2021; 118 (23): e2022288118.

[110] Raichle ME , Mintun MA . Brain work and brain imaging. Annu Rev Neurosci. 2006; 29 (1): 449- 76.

[111] Fox MD , Corbetta M , Snyder AZ , Vincent JL , Raichle ME . Spontaneous neuronal activity distinguishes human dorsal and ventral attention systems. Proc Natl Acad Sci USA. 2006; 103 (26): 10046- 51.

[112] Hilger K , Fukushima M , Sporns O , Fiebach CJ . Temporal stability of functional brain modules associated with human intelligence. Hum Brain Mapp. 2020; 41 (2): 362- 72.

[113] Fong AHC , Yoo K , Rosenberg MD , Zhang S , Li CSR , Scheinost D , et al. Dynamic functional connectivity during task performance and rest predicts individual differences in attention across studies. Neuroimage. 2019; 188: 14- 25.

[114] Deco G , Tononi G , Boly M , Kringelbach ML . Rethinking segregation and integration: contributions of whole-brain modelling. Nat Rev Neurosci. 2015; 16 (7): 430- 9.

[115] Fransson P , Schiffler BC , Thompson WH . Brain network segregation and integration during an epoch-related working memory fmri experiment. Neuroimage. 2018; 178: 147- 61.

[116] Wang R , Lin P , Liu M , Wu Y , Zhou T , Zhou C . Hierarchical connectome modes and critical state jointly maximize human brain functional diversity. Phys Rev Lett. 2019; 123 (3): 038301.

[117] Wang MB , Owen JP , Mukherjee P , Raj A . Brain network eigenmodes provide a robust and compact representation of the structural connectome in health and disease. PLoS Comput Biol. 2017; 13 (6): e1005550.

[118] Robinson PA . Neurophysical theory of coherence and correlations of electroencephalographic and electrocorticographic signals. J Theor Biol. 2003; 222 (2): 163- 75.

[119] Tewarie P , Abeysuriya R , Byrne A , O’Neill GC , Sotiropoulos SN , Brookes MJ , et al. How do spatially distinct frequency specific MEG networks emerge from one underlying structural connectome? The role of the structural eigenmodes. Neuroimage. 2019; 186: 211- 20.

[120] Robinson PA . Discrete spectral eigenmode-resonance network of brain dynamics and connectivity. Phys Rev E. 2021; 104 (3): 034411.

[121] Abdelnour F , Dayan M , Devinsky O , Thesen T , Raj A . Functional brain connectivity is predictable from anatomic network’s Laplacian eigen-structure. Neuroimage. 2018; 172: 728- 39.

[122] Raj A , Kuceyeski A , Weiner M . A network diffusion model of disease progression in dementia. Neuron. 2012; 73 (6): 1204- 15.

[123] Atasoy S , Donnelly I , Pearson J . Human brain networks function in connectome-specific harmonic waves. Nat Commun. 2016; 7 (1): 10340.

[124] Chen X , Ren H , Tang Z , Zhou K , Zhou L , Zuo Z , et al. Leading basic modes of spontaneous activity drive individual functional connectivity organization in the resting human brain. Commsbio. 2023; 6 (1): 892.

[125] Sun Y , Hu G , Zhang Y , Lu B , Lu Z , Fan J , et al. Eigen microstates and their evolutions in complex systems. Commun Theor Phys. 2021; 73 (6): 065603.

[126] Hu G , Liu T , Liu M , Chen W , Chen X . Condensation of eigen microstate in statistical ensemble and phase transition. Sci China Phys Mech Astron. 2019; 62 (9): 990511.

[127] Huo S , Liu Z . Condensation of eigenmodes in functional brain network and its correlation to chimera state. Commsphys. 2023; 6 (1): 285.

[128] Swadlow HA . Monitoring the excitability of neocortical efferent neurons to direct activation by extracellular current pulses. J Neurophysiol. 1992; 68 (2): 605- 19.

[129] Swadlow HA . Efferent neurons and suspected interneurons in motor cortex of the awake rabbit: axonal properties, sensory receptive fields, and subthreshold synaptic inputs. J Neurophysiol. 1994; 71 (2): 437- 53.

[130] Milton J , Jung P . Epilepsy as a dynamic disease. Berlin: Springer; 2003.

[131] Kandel ER , Schwartz JH , Jessell TM . Principles of neural science. 3rd ed. New York: Elsevier; 1991.

[132] Barres BA . The mystery and magic of glia: a perspective on their roles in health and disease. Neuron. 2008; 60 (3): 430- 40.

[133] Xu S , Lu J , Shao A , Zhang JH , Zhang J . Glial cells: role of the immune response in ischemic stroke. Front Immunol. 2020; 11: 294.

[134] Hay A , Popichak K , Moreno J , Zabel M . The role of glial cells in neurobiology and prion neuropathology. Cells. 2024; 13 (10): 832.

[135] Dietz AG , Goldman SA , Nedergaard M . Glial cells in schizophrenia: a unified hypothesis. Lancet Psychiatr. 2020; 7 (3): 272- 81.

[136] Zhao M , Jiang X , Zhang H , Sun J , Pei H , Ma L , et al. Interactions between glial cells and the blood-brain barrier and their role in Alzheimer’s disease. Ageing Res Rev. 2021; 72: 101483.

[137] Garcia-Bermudez MY , Freude KK , Mouhammad ZA , van Wijngaarden P , Martin KK , Kolko M . Glial cells in glaucoma: friends, foes, and potential therapeutic targets. Front Neurol. 2021; 12: 624983.

[138] Li Q , Haney MS . The role of glia in protein aggregation. Neurobiol Dis. 2020; 143: 105015.

[139] Hanani M , Spray DC . Emerging importance of satellite glia in nervous system function and dysfunction. Nat Rev Neurosci. 2020; 21 (9): 485- 98.

[140] Hernandez IH , Villa-Gonzalez M , Martin G , Soto M , Perez-Alvarez MJ . Glial cells as therapeutic approaches in brain ischemia-reperfusion injury. Cells. 2021; 10 (7): 1639.

[141] Wang Y , Wang L , Fan H , Ma J , Cao H , Wang X . Breathing cluster in complex neuron-astrocyte networks. Chaos. 2023; 33 (11): 113118.

[142] Dahms T , Lehnert J , Scholl E . Cluster and group synchronization in delay-coupled networks. Phys Rev E. 2012; 86 (1): 016202.

[143] Jalan S , Singh A , Acharyya S , Kurths J . Impact of a leader on cluster synchronization. Phys Rev E. 2015; 91 (2): 022901.

[144] Cho YS , Nishikawa T , Motter AE . Stable chimeras and independently synchronizable clusters. Phys Rev Lett. 2017; 119 (8): 084101.

[145] Siddique AB , Pecora L , Hart JD , Sorrentino F . Symmetry-and input-cluster synchronization in networks. Phys Rev E. 2018; 97 (4): 042217.

[146] Williams CRS , Murphy TE , Roy R , Sorrentino F , Dahms T , Scholl E . Experimental observations of group synchrony in a system of chaotic optoelectronic oscillators. Phys Rev Lett. 2013; 110 (6): 064104.

[147] Pecora LM , Sorrentino F , Hagerstrom AM , Murphy TE , Roy R . Cluster synchronization and isolated desynchronization in complex networks with symmetries. Nat Commun. 2014; 5 (1): 4079.

[148] Sorrentino F , Pecora LM , Hagerstrom M , Murphy TE , Roy R . Complete characterization of the stability of cluster synchronization in complex dynamical networks. Sci Adv. 2016; 2 (4): e1501737.

[149] Wang X . Synchronous patterns in complex networks. Sci Sin. 2020; 50 (1): 010503.

[150] Neuling T , Rach S , Herrmann C . Orchestrating neuronal networks: sustained after-effects of transcranial alternating current stimulation depend upon brain states. Front Hum Neurosci. 2013; 7: 161.

[151] Liu Z . Organization network enhanced detection and transmission of phase-locking. Europhys Lett. 2012; 100 (6): 60002.

[152] The 2014 nobel prize in physiology or medicine-press redlease.

[153] Cao L , Liu Z . How IQ depends on the running mode of brain network? Chaos. 2020; 30 (7): 073111.

[154] Hens C , Harush U , Haber S , Cohen R , Barzel B . Spatiotemporal signal propagation in complex networks. Nat Phys. 2019; 15 (4): 403- 12.

[155] Zhang X , Witthaut D , Timme M . Topological determinants of perturbation spreading in networks. Phys Rev Lett. 2020; 125 (21): 218301.

[156] Seidl AH . Regulation of conduction time along axons. Neuroscience. 2014; 276: 126- 34.

[157] Zhang Z , Chen Y , Mi Y , Hu G . Reconstruction of dynamic networks with time-delayed interactions in the presence of fast-varying noises. Phys Rev E. 2019; 99 (4): 042311.

[158] Wang X , Zhang Z , Li H , Chen Y , Mi Y , Hu G . Exploring node interaction relationship in complex networks by using high-frequency signal injection. Phys Rev E. 2021; 103 (2): 022317.

[159] Wang X , Mi Y , Zhang Z , Chen Y , Hu G , Li H . Reconstructing distant interactions of multiple paths between perceptible nodes in dark networks. Phys Rev E. 2022; 106 (1): 014302.

[160] Mishra A , Jalan S . Eigenvector localization in hyper-graphs: pairwise versus higher-order links. Phys Rev E. 2023; 107 (3): 034311.

[161] Wang L , Fan H , Xiao J , Lan Y , Wang X . Criticality in reservoir computer of coupled phase oscillators. Phys Rev E. 2022; 105 (5): L052201.

[162] Luo H , Du Y , Fan H , Wang X , Guo J , Wang X . Reconstructing bifurcation diagrams of chaotic circuits with reservoir computing. Phys Rev E. 2024; 109 (2): 024210.

[163] Sun W , Fu W , Mao W , Wang D , Wang Y . Low frequency repetitive transcranial magnetic stimulation for the treatment of refractory partial epilepsy. Clin EEG Neurosci. 2011; 42 (1): 40- 4.

[164] Cole J , Bernacki C , Helmer A , Pinninti N , O’reardon J . Efficacy of transcranial magnetic stimulation (TMS) in the treatment of schizophrenia: a review of the literature to date. Innov Clin Neurosci. 2015; 12: 12.

[165] Fried I . Brain stimulation in Alzheimers disease. J Alzheimers Dis. 2016; 54 (2): 789- 91.

[166] George MS , Taylor JJ , Short EB . The expanding evidence base for rTMS treatment of depression. Curr Opin Psychiatr. 2013; 26 (1): 13- 8.

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