The degree of irregularity apparent in the discharge patterns of electrically stimulated auditory-nerve fibers depends upon the stimulation rate (Moxon 1967; van den Honert and Stypulkowski 1987; Javel 1989). Whereas fibers fire regularly at low stimulation rates, the same fibers fire irregularly at high rates. The irregularity observed at high stimulation rates has been attributed to noise produced by the random opening and closing of voltage-gated ion channels (Rubinstein et al. 1999; Litvak et al. 2001). This explanation, however, is incomplete: an additional mechanism must be operating to account for the different effects of noise at the two stimulation rates.
In this talk, I will be illustrating such a rate-dependent mechanism. Specifically, I will show that in the Fitzhugh-Nagumo (FN) model (Fitzhugh 1961) the stability to perturbations such as noise depends upon the stimulation rate (O'Gorman, Shera, and White, to be submitted). At sufficiently high rates, a dynamical instability (Doi and Sato 1995) arises that accounts for the main statistical features of the irregular discharge pattern, even in the absence of ongoing physiological noise. In addition, I will show that this instability can account for the high sensitivity of the neural response to amplitude modulations applied to an ongoing stimulus (Litvak et al. 2003). In cochlear implants, amplitude modulations are used to encode acoustic information such as speech. Psychophysically, sensitivity to small modulations correlates strongly with speech perception ability (Fu 2002), suggesting a role for dynamical stability/instability in speech perception. I will also show that this rate-dependent stability/instability occurs in the classical Hodgkin-Huxley model (Hodgkin and Huxley 1952), as well as a biophysical model of the mammalian node of Ranvier (Schwarz and Eikhof 1987). Finally, in addition to discussing the above topics, and if time permits, I may also describe how this rate-dependent stability/instability in the FN model arises from the time-resetting produced by each individual stimulus pulse (Rabinovitch et al. 1994; O'Gorman 2006).
Citations
Doi, S. and S. Sato (1995). "The global bifurcation structure of the BVP (FN) neuronal model driven by periodic pulse trains." Mathematical Biosciences(125): 229-250.
Fitzhugh, R. (1961). "Impulses and physiological states in theoretical models of nerve membrane." Biophysical Journal 1: 445-465.
Fu, Q. J. (2002). "Temporal processing and speech recognition in cochlear implant users." Neuroreport 13(13): 1635-1639.
Hodgkin, A. L. and A. F. Huxley (1952). "A quantitative description of membrane current and its application to conduction and excitation in nerve." Journal of Physiology 117: 500-544.
Javel, E. (1989). Acoustic and electrical encoding of temporal information. in \underline{Cochlear implants: Models of the electrically stimulated ear}. J. M. Miller and F. A. Spelman.
Litvak, L., B. Delgutte, et al. (2001). "Auditory nerve fiber responses to electric stimulation: Modulated and unmodulated pulse trains." Journal of the Acoustical Society of America 110: 368-379.
Litvak, L. M., B. Delgutte, et al. (2003). "Improved temporal coding of sinusoids in electric stimulation of the auditory nerve using desynchronizing pulse trains." Journal of The Acoustical Society of America 114(4): 2079-2098.
Moxon, E. C. (1967). Electric stimulation of the cat's cochlea: A study of discharge rates in single auditory nerve fibers. Department of Electrical Engineering. Cambridge, Massachusetts Institute of Technology: 38.
O'Gorman, D. E. (2006). Dynamical mechanisms of neural firing irregularity and modulation sensitivity with applications to cochlear implants, Ph.D Thesis. Cambridge, MIT.
Rabinovitch, A., R. Thieberger, et al. (1994). "Forced Bonhoeffer - van der Pol (Fitzhugh-Nagumo) oscillator in its excited mode." Physical Review E 50(2): 1572-1578.
Rubinstein, J. T., B. S. Wilson, et al. (1999). "Pseudospontaneous activity: stochastic independence of auditory nerve fibers with electrical stimulation." Hearing Resesearch 127: 108-118.
Schwarz, J. R. and G. Eikhof (1987). "Na currents and action potentials in rat myelinated nerve fibres at 20 and 37 degrees C." Pflugers Archive 409(6): 569-77.
van den Honert, C. and P. H. Stypulkowski (1987). "Temporal response patterns of single auditory nerve fibers elicited by periodic electrical stimuli." Hearing Research 29(2-3): 207-22.