Abstract
Mean-field theory of brain dynamics is applied to explain the properties of gamma (≳30 Hz) oscillations of cortical activity often seen during vision experiments. It is shown that mm-scale patchy connections in the primary visual cortex can support collective gamma oscillations with the correct frequencies and spatial structure, even when driven by uncorrelated inputs. This occurs via resonances associated with the the periodic modulation of the network connections, rather than being due to single-cell properties alone. Near-resonant gamma waves are shown to obey the Schrödinger equation, which enables techniques and insights from quantum theory to be used in exploring these classical oscillations. Resulting predictions for gamma responses to stimuli account in a unified way for a wide range of experimental results, including why oscillations and zero-lag synchrony are associated, and variations in correlation functions with time delay, intercellular distance, and stimulus features. They also imply that gamma oscillations may enable a form of frequency multiplexing of neural signals. Most importantly, it is shown that correlations reproduce experimental results that show maximal correlations between cells that respond to related features, but little correlation with other cells, an effect that has been argued to be associated with segmentation of a scene into separate objects. Consistency with infill of missing contours and increase in response with length of bar-shaped stimuli are discussed. Background correlations expected in the absence of stimulation are also calculated and shown to be consistent in form with experimental measurements and similar to stimulus-induced correlations in structure. Finally, possible links of gamma instabilities to certain classes of photically induced seizures and visual hallucinations are discussed.
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References
Abramowitz M and Stegun IA (1965). Handbook of mathematical functions. Dover, New York
Bosking WH, Zhang Y, Schofield B and Fitzpatrick D (1997). Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. J Neurosci 17: 2112
Breakspear M, Roberts JA, Terry JR, Rodrigues S, Mahant N and Robinson PA (2006). A unifying explanation of generalized seizures through nonlinear brain modeling and bifurcation analysis. Cerebral Cortex 16: 1296
Bressler SL, Coppola R and Nakamura R (1993). Episodic multiregional cortical coherence at multiple frequncies during visual task performance. Nature 366: 153
Bressloff PC (2002). Bloch waves, periodic feature maps and cortical pattern formation. Phys Rev Lett 89: 088101
Bressloff PC and Cowan JD (2002). SO(3) symmetry breaking mechanism for orientation and spatial frequency tuning in the visual cortex. Phys Rev Lett 88: 078102
Bressloff PC, Cowan JD, Golubitsky M, Thomas PJ and Wiener MC (2001). Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex. Philos Trans R Soc Lond B 356: 299
Coombes S, Venkov NA, Shiau L, Bojak I, Liley DTJ, Laing CR (2007) Integral neural field equations, axonal delays, patchy connections, and an equivalent PDE model in 2+1 dimensions (submitted)
Dayan P, Abbott LF (2001) Theoretical neuroscience. MIT Press, Cambridge
Destexhe A and Paré D (1999). Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. J Neurophysiol 81: 1531
De Valois RL and De Valois KK (1990). Spatial vision. Oxford University Press, Oxford
Eckhorn R, Bauer R, Jordan W, Brosch M, Kruse W, Munk M and Reitboeck HJ (1988). Coherent oscillations: a mechanism of feature linking in the visual cortex. Biol Cybernet 60: 121
Engel AK, König P, Gray CM and Singer W (1990). Stimulus-dependent neuronal oscillations in cat visual cortes: inter-columnar interaction as determined by cross-correlation analysis. Eur J Neurosci 2: 588
Engel AK, König P, Kreiter AK, Schillen TB and Singer W (1992). Temporal coding in the visual cortex: new vistas on integration in the nervous system. Trends Neurosci 15: 218
Engel AK, König P, Kreiter AK and Singer W (1991). Interhemispheric synchronization of oscillatory neuronal responses in cat visual cortex. Science 252: 1177
Engel AK, König P and Singer W (1991). Direct physiological evidence for scene segmentation by temporal coding. Proc Natl Acad Sci USA 88: 9136
Engel AK, Kreiter AK, König P and Singer W (1991). Synchronization of oscillatory neuronal responses between striate and extrastriate visual cortical areas of the cat. Proc Natl Acad Sci USA 88: 6048
Engel AK, Roelfsema PR, Fries P, Brecht M and Singer W (1997). Role of the temporal domain for response selection and perceptual binding. Cerebral Cortex 7: 571
Engel AK and Singer W (2001). Temporal binding and the neural correlates of sensory awareness. Trends Cogn Sci 5: 16
Freeman WJ (1975). Mass action in the nervous system. Academic, New York
Frien A, Eckhorn R, Bauer R, Woelbern T and Kehr H (1994). Stimulus-specific fast oscillations at zero phase between visual areas V1 and V2 of awake monkey. Neuro Report 5: 2273
Fries P, Roelfsema PR, Engel AK, König P and Singer W (1997). Synchronization of oscillatory responses in visual cortex correlates with perception in interocular rivalry. Proc Nat Acad Sci USA 94: 12699
Gray CM, König P, Engel AK and Singer W (1989). Oscillatory responses in cat visual cortex exhibit intercolumnar synchronization which reflects global stimulus properties. Nature 338: 334
Gray CM and Singer W (1989). Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proc Natl Acad USA 86: 1698
Jirsa VK and Haken H (1996). Field theory of electromagnetic brain activity. Phys Rev Lett 77: 960
Kandel ER, Schwartz JH, Jessell TM (eds) (1991) Principles of neural science, 3rd edn. Appleton and Lange
Koch C (1999). Biophyics of computation. Oxford University Press, Oxford
König P and Engel AK (1995). Correlated firing in sensory-motor systems. Curr Opin Neurobiol 5: 511
König P, Engel AK and Singer W (1995). Relation between oscillatory activity and long-range synchronization in cat visual cortex. Proc Nat Acad Sci USA 92: 290
Kreiter AK and Singer W (1992). Oscillatory neuronal responses in the visual cortex of the awake macaque monkey. Eur J Neurosci 4: 369
Lopes da Silva FH, Hoeks A, Smits H and Zetterberg LH (1974). Model of brain rhythmic activity: the alpha rhythm of the thalamus. Kybernetic 15: 27
Lund JS, Angelucci A and Bressloff PC (2003). Anatomical substrates for functional columns in macaque monkey primary visual cortex. Cerebral Cortex 12: 15
Maldonado PE, Friedman-Hill S and Gray CM (2000). Dynamics of striate cortical activity in the alert macaque: II. Fast time scale synchronization. Cerebral Cortex 10: 1117
McPhedran RC, Botten LC, Asatryan AA, Nicorovici NA, Robinson PA and de Sterke CM (1999). Calculation of electromagnetic properties of regular and random arrays of metallic and dielectric cylinders. Phys Rev E 60: 7614
Murthy VN and Fetz EE (1992). Coherent 25- to 35-Hz oscillations in the sensorimotor cortex of awake behaving monkeys. Proc Natl Acad Sci USA 89: 5670
Nunez PL (1974). Wave-like properties of the alpha rhythm. IEEE Trans Biomed Eng 21: 473
Nunez PL (1995). Neocortical dynamics and human EEG rhythms. Oxford University Press, Oxford
Nunez PL and Srinivasan R (2006). Electric fields of the brain: the neurophysics of EEG, 2nd edn. Oxford University Press, Oxford
Obermayer K, Sejnowski TJ (eds) (2001) Self-organizing map formation: foundations of neural computation, MIT Press, Cambridge
O’Connor SC and Robinson PA (2003). Wave-number spectrum of electrocorticographic signals. Phys Rev E 67: 051912
Parra J, Kalitzin SN, Iriarte J, Blanes W, Velis DN and Lopesda Silva FH (2003). Gamma-band phase clustering and photosensitivity: is there an underlying mechanism common to photosensitive epilepsy and visual perception. Brain 126: 1164
Rennie CJ, Robinson PA and Wright JJ (2002). Unified neurophysical model of EEG spectra and evoked potentials. Biol Cybern 86: 457
Rennie CJ, Wright JJ and Robinson PA (2000). Mechanisms of cortical electrical activity and emergence of gamma rhythm. J Theor Biol 205: 17
Robinson PA (2003). Neurophysical theory of coherence and correlations of electroencephalographic and electrocorticographic signals. J Theor Biol 222: 163
Robinson PA (2005). Propagator theory of brain dynamics. Phys Rev E 72: 011904
Robinson PA (2006). Patchy propagators, cortical dynamics and the generation of spatially structured gamma oscillations. Phys Rev E 73: 041904
Robinson PA, Rennie CJ and Rowe DL (2002). Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Phys Rev E 65: 041924
Robinson PA, Rennie CJ, Rowe DL and O’Connor SC (2004). Estimation of multiscale neurophysiologic parameters by electroencephalographic means. Human Brain Mapp 23: 53
Robinson PA, Rennie CJ and Wright JJ (1997). Propagation and stability of waves of electrical activity in the cerebral cortex. Phys Rev E 56: 826
Robinson PA, Rennie CJ, Wright JJ, Bahramali H, Gordon E and Rowe DL (2001). Prediction of electroencephalographic spectra from neurophysiology. Phys Rev E 63: 021903
Roelfsema PR, Engel AK, König P and Singer W (1997). Visuomotor integration is associated with zero time-lag synchronization among cortical areas. Nature 385: 157
Roelfsema PR, König P, Engel AK, Sireteanu R and Singer W (1994). Reduced synchronization in the visual cortex of cats with strabismic amblyopia. Eur J Neurosci 6: 1645
Rowe DL, Robinson PA and Rennie CJ (2004). Estimation of neurophysiological parameters from the waking EEG using a biophysical model of brain dynamics. J Theor Biol 231: 413
Salinas E and Sejnowski TJ (2001). Correlated neuronal activity and the flow of neural information. Nat Rev Neurosci 2: 539
Shadlen MN and Movshon JA (1999). Synchrony unbound: A critical evaluation of the temporal binding hypothesis. Neuron 24: 67
Singer W (1993). Synchronization of cortical activity and its putative role in information processing and learning. Ann Rev Physiol 55: 349
Singer W and Gray CM (1995). Visual feature integration and the temporal correlation hypothesis. Ann Rev Neurosci 18: 555
Somers DC, Todorov EV, Siapas AG, Toth LJ, Kim D-S and Sur M (1998). A local circuit approach to understanding integration of long-range inputs in primary visual cortex. Cerebral Cortex 8: 204
Steriade M (2000). Corticothalamic resonance, states of vigilance and mentation. Neurosci 101: 243–276
Steyn-Ross ML, Steyn-Ross DA, Sleigh JW and Liley DTJ (1999). Theoretical electroencephalogram stationary spectrum for a white-noise-driven cortex: Evidence for a general anesthetic-induced phase transition. Phys Rev E 60: 7299
T’so DY, Gilbert CD and Wiesel TN (1986). Relationships between horizontal interactions and functional architecture in cat striate cortex as revealed by cross-correlation analysis. J Neurosci 6: 1160
Wilson HR and Cowan JD (1973). A mathematical theory for the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13: 55
Wright JJ and Liley DTJ (1996). Dynamics of the brain at global and microscopic scales: neural networks and the EEG. Behav Brain Sci 19: 285
Worrell GA, Parish L, Cranstoun SD, Jonas R, Baltuch G and Litt B (2004). High-frequency oscillations and seizure generation in neocortical epilepsy. Brain 127: 1496
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Robinson, P.A. Visual gamma oscillations: waves, correlations, and other phenomena, including comparison with experimental data. Biol Cybern 97, 317–335 (2007). https://doi.org/10.1007/s00422-007-0177-x
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DOI: https://doi.org/10.1007/s00422-007-0177-x