Phase boundaries as electrically induced phosphenes

SIAM Journal on Applied Dynamical Systems

Volumn 5, Issue 4, 2006, Pages 529-551

  Drover, Jonathan D ^a   Bard Ermentrout, G ^b  

^a NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Phase boundaries; Phosphenes; Traveling waves

Indexed keywords

COMPUTER SIMULATION; DYNAMICAL SYSTEMS; PHASE BOUNDARIES;

ELECTRICAL STIMULATIONS; EXPERIMENTAL CHARACTERISTICS; INTEGRATE AND FIRES; PHOSPHENES; SPATIOTEMPORAL BEHAVIORS; STATIONARY SOLUTIONS; TRAVELING WAVE; TWO-DIMENSIONAL GRIDS;

VISION;

EID: 79951511116     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/050646469     Document Type: Article

References (24)

1. D. Attwell, Interaction of low frequency electric fields with the nervous system: The retina as a model system, Radiat. Prot. Dosimetry, 106 (2003), pp. 341–348.
2. P. Bates and A. Chmaj, An integrodifferential model for phase transitions: Stationary solutions in higher space dimensions, J. Statist. Phys., 95 (1999), pp. 1119–1139.
3. G. S. Brindley, The site of electrical excitation of the human eye, J. Physiol., 127 (1955), pp. 189–200.
4. R. H. S. Carpenter, Contour-like phosphenes from electrical stimulation of the human eye: Some new observations, J. Physiol., 229 (1973), pp. 767–785.
5. X. Chen, Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations, Adv. Differential Equations, 2 (1997), pp. 125–160.
6. J. Claussen, Visual sensations (phosphenes) produced by AC sine wave stimulation, Acta. Psychiatr. Neurol. Scand. Suppl., 94, pp. 1–10.
7. D. Crevier and M. Meister, Synchronous period-doubling in flicker vision of salamander and man, J. Neurophysiol., 79 (1998), pp. 1869–1878.
8. P. Dayan and L. Abbott, Theoretical Neuroscience, MIT Press, Cambridge, MA, 2001.
9. J. Drover, The Interplay of Intrinsic Dynamics and Coupling in Spatially Distributed Neuronal Networks, Ph.D. thesis, Mathematics Department, University of Pittsburgh, Pittsburgh, PA, 2005; available online at http://etd.library.pitt.edu/ETD/available/etd-08162005-135431.
10. G. B. Ermentrout, n:m phase-locking of weakly coupled oscillators, J. Math. Biol., 12 (1981), pp. 327–342.
11. B. Ermentrout, X. Chen, and Z. Chen, Transition fronts and localized structures in bistable reaction-diffusion equations, Phys. D, 108 (1997), pp. 147–167.
12. S. I. Firth, C.-T. Wang, and M. B. Feller, Retinal waves: Mechanisms and function in visual system development, Cell Calcium, 37 (2005), pp. 425–432.
13. J. R. Gibson, M. Beierlein, and B. W. Connors, Functional properties of electrical synapses between inhibitory interneurons of neocortical layer 4, J. Neurophysiol., 93 (2005), pp. 467–480.
14. L. E. Hallum, G. J. Suaning, and N. H. Lovell, Contribution to the theory of prosthetic vision, ASAIO J., 50 (2004), pp. 392–396.
15. S. Hidaka, T. Kato, and Y. Hashimoto, Structural and functional properties of homologous electrical synapses between retinal amacrine cells, J. Integr. Neurosci., 4 (2005), pp. 313–340.
16. E. H. Hu and S. A. Bloomfield, Gap junctional coupling underlies the short-latency spike synchrony of retinal alpha ganglion cells, J. Neurosci., 23 (2003), pp. 6768–6777.
17. G. T. Kenyon and D. W. Marshak, Gap junctions with amacrine cells provide a feedback pathway for ganglion cells within the retina, Proc. Biol. Sci., 265 (1998), pp. 919–925.
18. N. Kopell and G. B. Ermentrout, Symmetry and phaselocking in chains of weakly coupled oscillators, Comm. Pure Appl. Math., 39 (1986), pp. 623–660.
19. T. J. Lewis and J. Rinzel, Self-organized synchronous oscillations in a network of excitable cells coupled by gap junctions, Network, 11 (2000), pp. 299–320.
20. F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks of the Retina, Holden-Day, San Francisco, 1965.
21. C. W. Tyler, Some new entoptic phenomena, Vision Res., 18 (1978), pp. 1633–1639.
22. J. B. Willis, The modeling of neural circuitry, Progr. Neurobiol., 26 (1986), pp. 93–118.
23. M. Wilms, M. Eger, T. Schanze, and R. Eckhorn, Visual resolution with epi-retinal electrical stimulation estimated from activation profiles in cat visual cortex, Vis. Neurosci., 20 (2003), pp. 543–555.
24. H. R. Wilson, Computational evidence for a rivalry hierarchy in vision, Proc. Natl. Acad. Sci. USA, 100 (2003), pp. 14499–14503.