Dynamical instability determines the effect of ongoing noise on neural firing

JARO - Journal of the Association for Research in Otolaryngology

Volumn 10, Issue 2, 2009, Pages 251-267

  O'Gorman, David E ^a,b,c   White, John A ^c   Shera, Christopher A ^a,b,d  

^a MASSACHUSETTS EYE AND EAR INFIRMARY   (United States)

^b HARVARD MIT DIVISION OF HEALTH SCIENCES AND TECHNOLOGY   (United States)

^c Boston University   (United States)

^d HARVARD MEDICAL SCHOOL   (United States)

Author keywords

Auditory nerve; Chaos; Cochlear implant; Desynchronization; Electrical stimulation; Firing irregularity; Lyapunov exponent

Indexed keywords

VOLTAGE GATED SODIUM CHANNEL;

ARTICLE; AUDITORY RESPONSE; COCHLEA PROSTHESIS; COCHLEAR NERVE; CONTROLLED STUDY; CORTICAL SYNCHRONIZATION; ELECTROSTIMULATION; NERVE CELL EXCITABILITY; NERVE CELL STIMULATION; NOISE; NONLINEAR SYSTEM; PRIORITY JOURNAL; SIGNAL NOISE RATIO; SPIKE WAVE; STIMULUS RESPONSE;

ACOUSTIC STIMULATION; ACTION POTENTIALS; AUDITORY THRESHOLD; COCHLEAR IMPLANTS; COCHLEAR NERVE; COMPUTER SIMULATION; ELECTRIC STIMULATION; MODELS, NEUROLOGICAL; NONLINEAR DYNAMICS;

EID: 67349125922     PISSN: 15253961     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10162-008-0148-5     Document Type: Article

References (85)

1. CL Adamson MA Reid ZL Mo J Bowne-English RL Davis 2002 Firing features and potassium channel content of murine spiral ganglion neurons vary with cochlear location J. Comp. Neurol. 447 331 350 (Pubitemid 34478059)
2. K Aihara G Matsumoto Y Ikegaya 1984 Periodic and non-periodic responses of a periodically forced Hodgkin-Huxley oscillator J. Theor. Biol. 109 249 269 (Pubitemid 14039147)
3. KF Bonhoeffer 1948 Activation of passive iron as a model for the excitation of nerve J. Gen. Physiol. 32 69 91
4. IC Bruce LS Irlicht MW White SJ O'Leary S Dynes E Javel GM Clark 1999 A stochastic model of the electrically stimulated auditory nerve: pulse-train response IEEE Trans. Biomed. Eng. 46 630 637 (Pubitemid 29245053)
5. C Chen 1997 Hyperpolarization-activated current (I-h) in primary auditory neurons Hear. Res. 110 179 190 (Pubitemid 27364331)
6. JR Clay LJ DeFelice 1983 Relationship between membrane excitability and single channel open-close kinetics Biophys. J. 42 151 157
7. JR Clay 1998 Excitability of the squid giant axon revisited J. Neurophysiol. 80 903 913 (Pubitemid 28387668)
8. Cleveland WS. Visualizing Data. Summit, New Jersey, Hobart, 1993.
9. V Colletti RV Shannon 2005 Open set speech perception with auditory brainstem implant Laryngoscope 115 1974 1978 (Pubitemid 44391659)
10. S Coombes AH Osbaldestin 2000 Period-adding bifurcations and chaos in a periodically stimulated excitable neural relaxation oscillator Phys. Rev. E. 62 4057 4066
11. Dayan P, Abbott LF. Theoretical neuroscience: computational and mathematical modeling of neural systems. Cambridge, Mass, MIT Press, p. 460, 2001.
12. S Doi 1989 A chaotic map with a flat segment can produce a noise-induced order J. Stat. Phys. 55 941 964
13. SJ Doi S Sato 1995 The global bifurcation structure of the BVP neuronal model driven by periodic pulse trains Math. Biosci. 125 229 250
14. Dynes SBC. Discharge characteristics of auditory nerve fibers for pulsatile electrical stimuli. PhD Thesis, MIT, Cambridge, MA, 1996.
15. J-P Eckmann D Ruelle 1985 Ergodic theory of chaos and strange attractors Rev. Mod. Phys. 57 617 656 (Pubitemid 16461131)
16. GB Ermentrout 1984 Period doublings and possible chaos in neural models SIAM J. Appl. Math. 44 80 95 (Pubitemid 14569381)
17. P Faure H Korn 1997 A nonrandom dynamic component in the synaptic noise of a central neuron Proc. Natl. Acad. Sci. USA 94 6506 6511 (Pubitemid 27270715)
18. M Feingold DL Gonzales O Piro H Viturro 1988 Phase locking, period doubling, and chaotic phenomena in externally driven excitable systems Phys. Rev. A 37 4060 4063
19. FitzHugh F. Mathematical models of excitation and propagation in nerve. In: Schwan HP (ed) Biological Engineering. New York, McGraw-Hill, 1969.
20. R FitzHugh 1961 Impulses and physiological states in theoretical models of nerve membrane Biophys. J. 1 445 465
21. QJ Fu RV Shannon 2000 Effect of stimulation rate on phoneme recognition by Nucleus-22 cochlear implant listeners J. Acoust. Soc. Am. 107 589 597 (Pubitemid 30039183)
22. QJ Fu 2002 Temporal processing and speech recognition in cochlear implant users Neuroreport 13 1635 1639
23. E Glowatzki PA Fuchs 2002 Transmitter release at the hair cell ribbon synapse Nat. Neurosci. 5 147 154 (Pubitemid 34121582)
24. J Guckenheimer RA Oliva 2002 Chaos in the Hodgkin-Huxley Model SIAM J. Appl. Dyn. Syst. 1 105 114 (Pubitemid 38818562)
25. P Heil H Neubauer DRF Irvine M Brown 2007 Spontaneous activity of auditory-nerve fiber stochastic processes at ribbon synapses J. Neurosci. 27 8457 8474 (Pubitemid 47219628)
26. JL Hindmarsh RM Rose 1982 A model of the nerve impulse using two first-order differential equations Nature 296 162 164 (Pubitemid 12160915)
27. JL Hindmarsh RM Rose 1984 A model of neuronal bursting using 3 coupled 1st order differential-equations Proc. R. Soc. Lond. B Biol. Sci. 221 87 102
28. Hirsch MW, Smale S. Differential Equations, Dynamical Systems, and Linear Algebra. New York, Academic, 1974.
29. IJ Hochmair-Desoyer ES Hochmair H Motz F Rattay 1984 A model for the electrostimulation of the nervus acusticus Neuroscience 13 553 562 (Pubitemid 15211957)
30. AL Hodgkin AF Huxley 1952 A quantitative description of membrane current and its application to conduction and excitation in nerve J. Physiol. 117 500 544
31. RS Hong JT Rubinstein 2003 High-rate conditioning pulse trains in cochlear implants: Dynamic range measures with sinusoidal stimuli J. Acoust. Soc. Am. 114 3327 3342 (Pubitemid 37553645)
32. N Ichinose K Aihara K Judd 1998 Extending the concept of isochrons from oscillatory to excitable systems for modeling an excitable neuron Int. J. Bifurcat. Chaos 8 2375 2385 (Pubitemid 128336009)
33. Javel E. Acoustic and electrical encoding of temporal information. In: Miller JM, Spelman FA (eds) Cochlear Implants: Models of the Electrically Stimulated Ear. New York, Springer, pp. 247-292, 1990.
34. E Javel NF Viemeister 2000 Stochastic properties of cat auditory nerve responses to electric and acoustic stimuli and application to intensity discrimination J. Acoust. Soc. Am 107 908 921 (Pubitemid 30082818)
35. DH Johnson NY Kiang 1976 Analysis of discharges recorded simultaneously from pairs of auditory nerve fibers Biophys. J. 16 719 734
36. DT Kaplan JR Clay T Manning L Glass MR Guevara A Shrier 1996 Subthreshold dynamics in periodically stimulated squid giant axons Phys. Rev. Lett. 76 4074 4077 (Pubitemid 126640420)
37. TB Kepler LF Abbott E Marder 1992 Reduction of conductance-based neuron models Biol. Cybern. 66 381 387
38. Kiang NY, Watanabe T, Thomas EC, Clark LF. Discharge Patterns of Single Fibers in the Cat's Auditory Nerve. Cambridge, MIT Press, 1965.
39. NY Kiang 1990 Curious oddments of auditory-nerve studies Hear. Res. 49 1 16 (Pubitemid 20370248)
40. EK Kosmidis K Pakdaman 2006 Stochastic chaos in a neuronal model Int. J. Bifurcat. Chaos 16 395 410
41. H Lecar R Nossal 1971 Theory of threshold fluctuations in nerves: I. Relationships between electrical noise and fluctuations in axon firing Biophys. J. 11 1048 1067
42. H Lecar R Nossal 1971 Theory of threshold fluctuations in nerves: II. Analysis of various sources of membrane noise Biophys. J. 11 1068 1084
43. KK Lin 2006 Entrainment and chaos in a pulse-driven Hodgkin-Huxley oscillator SIAM J. Appl. Dyn. Syst. 5 179 204
44. LM Litvak B Delgutte DK Eddington 2001 Auditory-nerve fiber responses to electric stimulation: Modulated and unmodulated pulse trains J. Acoust. Soc. Am. 110 368 379 (Pubitemid 32642577)
45. LM Litvak ZM Smith B Delgutte DK Eddington 2003 Desynchronization of electrically evoked auditory-nerve activity by high-frequency pulse trains of long duration J. Acoust. Soc. Am. 114 2066 2078 (Pubitemid 37266634)
46. LM Litvak B Delgutte DK Eddington 2003 Improved temporal coding of sinusoids in electric stimulation of the auditory nerve using desynchronizing pulse trains J. Acoust. Soc. Am. 114 2079 2098 (Pubitemid 37266635)
47. LM Litvak B Delgutte DK Eddington 2003 Improved neural representation of vowels in electric stimulation using desynchronizing pulse trains J. Acoust. Soc. Am. 114 2099 2111 (Pubitemid 37266636)
48. Longtin A. Effect of noise on nonlinear dynamics. In: Beuter A, Glass L, Mackey MC, and Titcombe M (eds) Nonlinear Dynamics in Physiology and Medicine. New York, 2003.
49. EN Lorenz 1963 Deterministic nonperiodic flow J. Atmos. Sci. 20 130 141
50. SB Lowen MC Teich 1992 Auditory-nerve action potentials form a nonrenewal point process over short as well as long time scales J. Acoust. Soc. Am. 92 803 806
51. G Matsumoto K Aihara Y Hanyu N Takahashi S Yoshizawa J Nagumo 1987 Chaos and phase locking in normal squid axons Phys. Lett. A 123 162 166
52. K Matsumoto I Tsuda 1983 Noise-induced order J. Stat. Phys. 31 87 106
53. K Matsumoto 1984 Noise-induced order II J. Stat. Phys. 34 111 127 (Pubitemid 15438318)
54. AJ Matsuoka JT Rubinstein PJ Abbas CA Miller 2001 The effects of interpulse interval on stochastic properties of electrical stimulation: Models and measurements IEEE Trans. Biomed. Eng. 48 416 424 (Pubitemid 32289875)
55. G Mayer-Kress H Haken 1981 The influence of noise on the logistic model J. Stat. Phys. 26 149 171
56. CA Miller PJ Abbas BK Robinson 2001 Response properties of the refractory auditory nerve fiber J. Assoc. Res. Otolaryngol. 2 216 232 (Pubitemid 32954927)
57. CA Miller N Hu F Zhang BK Robinson PJ Abbas 2008 Changes across time in the temporal responses of auditory-nerve fibers stimulated by electric pulse trains J. Assoc. Res. Otolaryngol. 9 122 137 (Pubitemid 47222433)
58. ZL Mo RL Davis 1997 Endogenous firing patterns of murine spiral ganglion neurons J. Neurophysiol. 77 1294 1305 (Pubitemid 27137025)
59. RP Morse EF Evans 1996 Enhancement of vowel coding for cochlear implants by addition of noise Nat. Med. 2 928 932 (Pubitemid 26296766)
60. F Moss F Chiou-Tan R Klinke 1996 Will there be noise in their ears Nat. Med. 2 860 862 (Pubitemid 26296753)
61. Moxon EC. Electric stimulation of the cat's cochlea: A study of discharge rates in single auditory nerve fibers. Masters Thesis, MIT, Cambridge, MA, 1967.
62. Moxon EC. Neural and mechanical responses to electric stimulation of the cat's inner ear. Ph.D. Thesis, MIT, Cambridge, MA 1971.
63. J Nagumo S Arimoto S Yoshizawa 1963 An active pulse transmission line stimulating nerve axon P. IRE 50 2061 2070
64. O'Gorman DE, Shera CA. Does the high-rate response of electrically stimulated neurons reflect nonclassical sodium gating? Assoc. Res. Otolaryngol. Abs. 24, 2001.
65. O'Gorman DE, Shera CA, White JW, Colburn HS. Realistically irregular and sensitive neural firing without physiological noise [abstract]. Proceedings of the 2007 Conference on Implantable Auditory Prostheses. Lake Tahoe, Nevada, 2007. p 139. Abstract B34.
66. HG Othmer M Xie 1999 Subharmonic resonance and chaos in forced excitable systems J. Math. Biol. 39 139 171
67. AS Pikovsky J Kurths 1997 Coherence resonance in a noise-driven excitable system Phys. Rev. Lett. 78 775 778 (Pubitemid 127648034)
68. A Rabinovitch R Thieberger M Friedman 1994 Forced Bonhoeffer-van der Pol oscillator in its excited mode Phys. Rev. E 50 1572 1578
69. A Rabinovitch I Rogachevskii 1999 Threshold, excitability and isochrones in the Bonhoeffer-van der Pol system Chaos 9 880 886
70. S Rajasekar M Lakshmanan 1988 Period doubling route to chaos for a BVP oscillator with periodic external force J. Theor. Biol. 133 473 477
71. S Rajasekar M Lakshmanan 1994 Bifurcation, chaos and suppression of chaos in FitzHugh-Nagumo nerve conduction model equation J. Theor. Biol. 166 275 288 (Pubitemid 24095569)
72. Rinzel J, Ermentrout GB. Analysis of neural excitability and oscillations. In: Koch C, Segev I (eds) Methods in Neuronal Modeling. Cambridge MA, MIT Press, pp. 251-291, 1998.
73. JT Rubinstein 1995 Threshold fluctuations in an N sodium channel model of the node of Ranvier Biophys. J. 68 779 785
74. JT Rubinstein BS Wilson CC Finley PJ Abbas 1999 Pseudospontaneous activity: stochastic independence of auditory-nerve fibers with electrical stimulation Hear. Res. 127 108 118 (Pubitemid 29023735)
75. Sakmann B, Neher E. Single-Channel Recording. New York, Plenum, 1983.
76. S Sato S Doi 1992 Response characteristics of the BVP neuron model to periodic pulse inputs Math. Biosci. 112 243 259 (Pubitemid 23019910)
77. JH Siegel 1992 Spontaneous synaptic potentials from afferent terminals in the guinea pig cochlea Hear. Res. 59 85 92
78. FJ Sigworth 1980 The variance of sodium current fluctuations at the node of Ranvier J. Physiol. (Lond) 307 97 129 (Pubitemid 11253739)
79. NG Stocks D Allingham RP Morse 2002 The application of suprathreshold stochastic resonance to cochlear implant coding Fluct. Noise Lett. 2 L169 L181
80. N Takahashi Y Hanyu T Musha R Kubo G Matsumoto 1990 Global bifurcation structure in periodically stimulated giant axons of squid Physica D 43 318 334
81. C Van den Honert PH Stypulkowski 1987 Temporal response patterns of single auditory nerve fibers elicited by periodic electrical stimuli Hear. Res. 29 207 222
82. AA Verveen HE Derksen 1968 Fluctuation phenomena in nerve membrane P. IEEE 56 906 916
83. JA White JT Rubinstein AR Kay 2000 Channel noise in neurons Trends Neurosci. 23 131 137 (Pubitemid 30110629)
84. Wolfram S. The Mathematica Book. Wolfram Media/Cambridge University Press, 2003.
85. F Zhang CA Miller BK Robinson PJ Abbas N Hu 2007 Changes across time in spike rate and spike amplitude of auditory nerve fibers stimulated by electric pulse trains J. Assoc. Res. Otolaryngol. 8 356 372 (Pubitemid 47222433)