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Time and Frequency Domain Analysis of Spike Train and Time Series Data

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Modern Techniques in Neuroscience Research

Abstract

The concept of a spike triggered average will be familiar to many neurophysiologists. The first application in neurophysiology by Mendell and Henneman (1968, 1971) was used to examine the magnitude of monosynaptic excitatory postsynaptic potentials (EPSP) from muscle spindle la afferents onto homonymous motoneurons, which provided a major piece of evidence in the development of the size principle for motoneuron recruitment (see Henneman and Mendell, 1981). The technique has gained widespread acceptance, and been widely used to investigate the strength of synaptic connections in the mammalian central nervous system (e.g. Watt et al., 1976; Stauffer et al., 1976; Kirkwood and Sears, 1980; Cope et al., 1987), leading to new insights and an increased understanding of basic neurophysiological mechanisms.

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References

  • Amjad AM, Halliday DM, Rosenberg JR, Conway BA (1997) An extended difference of coherence test for comparing and combining independent estimates: theory and application to the study of motor units and physiological tremor. J. Neurosci. Meth. 73: 69–79

    Google Scholar 

  • Baldissera F, Gustafsson B (1974) Afterhyperpolarization conductance time course in lumbar motoneurones of the cat. Acta Physiol Scand 91: 512–527

    Article  PubMed  CAS  Google Scholar 

  • Bartlett MS (1948) Smoothing periodograms from time series with continuous spectra. Nature 161: 686–687

    Article  Google Scholar 

  • Bartlett MS (1963) The spectral analysis of point processes. J Roy Statist Soc 25: 264–281

    Google Scholar 

  • Blackman RB, Tukey JW (1958) The measurement of power spectra from the point of view of corn-munications engineering. Bell Sys Tech J 37: 183–282, 485–569 ( Reprinted Dover Press, New-York, 1959 )

    Google Scholar 

  • Bloomfield P(1976) Fourier Analysis of Time Series: An Introduction. Wiley, New York.

    Google Scholar 

  • Breeze P, Emhemmed YM, Halliday DM, Rosenberg JR (1994) Likelihood analysis of a model for neuronal input-output data. J Physiol 479P: 112 P

    Google Scholar 

  • Brillinger DR (1972) The spectral analysis of stationary interval functions. In: LeCam LM, Ney-man J, Scott E (eds) Proceedings 6th Berkeley Symposium Mathematics Statistics Probability, Univ California Press, Berkeley, pp 483–513

    Google Scholar 

  • Brillinger DR (1974) Fourier analysis of stationary processes. Proc IEEE 62: 1628–1643

    Article  Google Scholar 

  • Brillinger DR (1975) Identification of point process systems. Ann Probability 3: 909–929

    Article  Google Scholar 

  • Brillinger DR (1976) Estimation of second-order intensities of a bivariate stationary point proc-ess. J Roy Statist Soc B38: 60–66

    Google Scholar 

  • Brillinger DR (1978) Comparative aspects of the study of ordinary time series and of point processes. In: Krishnaiah PR (ed) Developments in Statistics, vol 1. Academic Press, New York, pp 33–133

    Google Scholar 

  • Brillinger DR (1981) Time Series - Data Analysis and Theory, 2nd edn. Holden Day, San Francisco

    Google Scholar 

  • Brillinger DR (1983) The finite Fourier transform of a stationary process. In: Brillinger DR, Krishnaiah PR (eds) Handbook of Statistics, Elsevier, pp 21–37

    Google Scholar 

  • Brillinger DR (1988a) Maximum likelihood analysis of spike trains of interacting nerve cells. Biol Cybernet 59: 198–200

    Article  Google Scholar 

  • Brillinger DR (1988b). The maximum likelihood approach to the identification of neuronal interactions. Ann Biomed Eng 16: 3–16

    Article  PubMed  CAS  Google Scholar 

  • Brillinger DR, Tukey JW (1984) Spectrum analysis in the presence of noise: Some issues and examples. In: The collected works of John W Tukey, Volume II, Time series: 1965–1984. Wadsworth, Belmont, CA, pp 1001–1141

    Google Scholar 

  • Conway BA, Halliday DM, Rosenberg JR (1993) Detection of weak synaptic interactions between single Ia-afferents and motor-unit spike trains in the decerebrate cat. J Physiol 471: 379–409

    PubMed  CAS  Google Scholar 

  • Conway BA, Halliday DM, Farmer, SF, Shahani U, Maas P, Weir AI, Rosenberg JR (1995a) Synchronization between motor cortex and spinal motoneuronal pool during the performance of a maintained motor task in man. J Physiol 489: 917–924

    PubMed  CAS  Google Scholar 

  • Conway BA, Farmer, SF, Halliday DM, Rosenberg JR (1995b) On the relation between motor unit discharge and physiological tremor. In: Taylor A, Gladden MH, Durbaba R (eds) Alpha and Gamma Motor Systems. Plenum Press, New York, pp 596–598

    Chapter  Google Scholar 

  • Conway BA, Halliday DM, Bray K, Cameron M, McLelland D, Mulcahy E, Farmer SF, Rosenberg JR (1998) Inter-muscle coherence during co-contraction of finger and wrist muscles in man. J Physiol 509: 175 P

    Google Scholar 

  • Cope TC, Fetz EE, Matsumura M (1987) Cross-correlation assessment of synaptic strength of sin-gle Ia fibre connections with triceps surae motoneurones in cats. J Physiol 390: 161–188

    PubMed  CAS  Google Scholar 

  • Cox DR (1965) On the estimation of the intensity function of a stationary point process. J Roy Sta-tist Soc B27: 332–337

    Google Scholar 

  • Cox DR, Isham V (1980) Point Processes. Chapman and Hall, London

    Google Scholar 

  • Cox DR, Lewis PAW (1972) Multivariate point processes. In: LeCam LM, Neyman J, Scott E (eds) Proceedings 6th Berkeley Symposium Mathematics Statistics Probability, vol 3. University of California Press, Berkeley pp 401–488

    Google Scholar 

  • Daley DJ, Vere-Jones D (1988) An introduction to the Theory of Point Processes. Springer, New York

    Google Scholar 

  • Datta AK, Stephens JA (1990) Short-term synchronization of motor unit activity during voluntary contractions in man. J Physiol 422: 397–419

    PubMed  CAS  Google Scholar 

  • Emhemmed YM (1995) Maximum likelihood analysis of neuronal spike trains. PhD Thesis, University of Glasgow, 246 pp

    Google Scholar 

  • Fetz EE (1992) Are movement parameters recognizably coded in the activity of single neurons. Behavioral Brain Sci, 15: 679–690

    Google Scholar 

  • Farmer SF, Bremner FD, Halliday DM, Rosenberg JR, Stephens JA (1993) The frequency content of common synaptic inputs to motoneurones studied during voluntary isometric contraction in man. J Physiol 470: 127–155

    PubMed  CAS  Google Scholar 

  • Getting PA (1989) Reconstruction of small networks. In: Koch C, Segev I (eds) Methods in neuronal modeling: From synapses to networks, MIT Press, pp 171–194

    Google Scholar 

  • Gibbs J, Harrison LM, Stephens JA (1995) Organization of inputs to motoneuron pools in man. J Physiol, 485: 245–256

    PubMed  CAS  Google Scholar 

  • Griffith JS, Horn G (1963) Functional coupling between cells in the visual cortex of the unrestrained cat. Nature, 199: 873, 893–895

    Google Scholar 

  • Halliday DM, Murray-Smith DJ, Rosenberg JR (1992) A frequency domain identification approach to the study of neuromuscular systems - a combined experimental and modelling study. Trans Inst MC, 14: 79–90

    Article  Google Scholar 

  • Halliday DM (1995) Effects of electronic spread of EPSPs on synaptic transmission in motoneurones - A simulation Study. In: Taylor A, Gladden MH, Durbaba R (eds) Alpha and Gamma Motor Systems. Plenum Press, New York, pp 337–339

    Chapter  Google Scholar 

  • Halliday DM, Rosenberg JR, Amjad AM, Breeze P, Conway BA, Farmer SF (1995a) A framework for the analysis of mixed time series/point process data - Theory and application to the study of physiological tremor, single motor unit discharges and electromyograms. Prog Biophys molec Biol, 64: 237–278

    Article  CAS  Google Scholar 

  • Halliday DM, Kakuda N, Wessberg J, Vallbo AB, Conway BA, Rosenberg JR (1995b) Correlation between Ia afferent discharges, EMG and torque during steady isometric contractions of human finger muscles. In: Taylor A, Gladden MH, Durbaba R (eds) Alpha and Gamma Motor Systems. Plenum Press, New York, pp 547–549

    Chapter  Google Scholar 

  • Halliday DM, Conway BA, Farmer SF, Rosenberg JR (1998) Using electroencephalography to study functional coupling between cortical activity and electromyograms during voluntary contractions in humans. Neurosci Lett, 241: 5–8

    Article  PubMed  CAS  Google Scholar 

  • Hille B (1984) Ionic channels of excitable membranes. Sinauer

    Google Scholar 

  • Henneman E, Mendell LM (1981) Functional organization of motoneuron pool and its inputs. In: Brookhart JM, Mountcastle VB (eds) Handbook of Physiology, Section 1, Vol 2, Part 1, The nervous system: Motor control. American Physiological Society, Bethesda, MD, pp 423 –507

    Google Scholar 

  • Hepp-Raymond M-C, Huesler EJ, Maier MA (1996) Precision grip in humans: Temporal and spatial synergies. In: Wing AM, Haggard P, Flanagan JR (eds) Hand and Brain, the neurophysiology and psychology of hand movements. Academic Press, London, pp 37–68

    Google Scholar 

  • Jenkins GM, Watts DG (1968) Spectral analysis and its applications. Holden-Day.

    Google Scholar 

  • Kendall DG, Stuart A (1966) The advanced theory of statistics, vol 1. Griffin, London. Kirkwood PA, Sears TA (1978) The synaptic connections to intercostal motoneurones revealed by the average common excitation potential. J Physiol, 275: 103–134

    Google Scholar 

  • Kirkwood PA, Sears, TA (1980) The measurement of synaptic connections in the mammalian central nervous system by means of spike triggered averaging. In: Desmedt JE (ed) Progress in Clinical Neurophysiology, vol 8, Spinal and supraspinal mechanisms of voluntary motor control and locomotion. Basel, S Karger, pp 44–71

    Google Scholar 

  • Löscher H-R (1990) Transmission failure and its relief in the spinal monosynaptic reflex arc. In: Binder MD, Mendell LM (eds) The segmental motor system, Oxford University Press, pp 328348 McCullagh P, Nelder JA (1992) General Linear Models (2nd edition). Monographs on statistics and Applied Probability 37. Chapman Hall, London

    Google Scholar 

  • Mendel J (1991) Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications. Proc IEEE, 79: 278–305

    Article  Google Scholar 

  • Mendell LM, Henneman E (1968) Terminals of single Ia fibres: Distribution within a pool of 300 homonymous motoneurones. Science 160: 96–98

    Article  PubMed  CAS  Google Scholar 

  • Mendell LM, Henneman E (1971) Terminals of single Ia fibres: location, density and distribution within a pool of 300 homonymous motor neurons. J Neurophysiol, 34: 171–187

    PubMed  CAS  Google Scholar 

  • Moore GP, Segundo JP, Perkel DH, Levitan H (1970) Statistical signs of synaptic interaction in neurones. Biophys J 10: 876–900

    Article  PubMed  CAS  Google Scholar 

  • Parzen E (1961) Mathematical considerations in the estimation of spectra. Technometrics, 3: 167190 Press WH, Flannery BP, Teukolsky SA, Vetterling WT ( 1989 ) Numerical recipes. Cambridge University Press

    Google Scholar 

  • Rall W (1967) Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic inputs. J Neurophysiol 30: 1138–1168

    PubMed  CAS  Google Scholar 

  • Rall W (1977) Core conductor theory and cable properties of neurones. In: Kandel ER, Brookhart JM, Mountcastle VB (eds) Handbook of physiology: The nervous system, vol 1, part 1. Williams and Wilkins, Maryland, pp 39–97

    Google Scholar 

  • Rigas A (1983) Point Processes and Time Series Analysis: Theory and Applications to Complex Physiological Systems. PhD Thesis, University of Glasgow, 330 pp

    Google Scholar 

  • Rosenberg JR, Murray-Smith DJ, Rigas A (1982) An introduction to the application of system identification techniques to elements of the neuromuscular system. Trans Inst MC 4: 187–201

    Article  Google Scholar 

  • Rosenberg JR, Amjad AM, Breeze P, Brillinger DR, Halliday DM (1989) The Fourier approach to the identification of functional coupling between neuronal spike trains. Prog Biophys molec Biol, 53: 1–31

    Article  CAS  Google Scholar 

  • Rosenberg JR, Halliday DM, Breeze P, Conway BA (1998) Identification of patterns of neuronal ac-tivity - partial spectra, partial coherence, and neuronal interactions. J Neurosci Meth 83: 57–72

    Article  CAS  Google Scholar 

  • Rosenblatt M (1983) Cumulants and Cumulant Spectra. In: Brillinger DR, Krishnaiah PR (eds) Handbook of Statistics vol 3. North Holland, New York, pp 369–382

    Google Scholar 

  • Schuster A (1898) On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomenon. Terr Mag, 3: 13–41

    Article  Google Scholar 

  • Sears TA, Stagg D (1976) Short-term synchronization of intercostal motoneurone activity. J Physiol 263: 357–387

    PubMed  CAS  Google Scholar 

  • Sorensen HV, Jones DL, Heideman MT, Burrus CS (1987) Real valued Fast Fourier Transform Algorithms. Proc IEEE ASSP, 35: 849–863; Corrections p 1353

    Google Scholar 

  • Srinivasan SK (1974) Stochastic Point Processes and their Applications. Monograph No 34. Griffin, London

    Google Scholar 

  • Stauffer EK, Watt DGD, Taylor A, Reinking RM, Stuart DG (1976) Analysis of muscle receptor connections by spike triggered averaging. 2. Spindle group II afferents. J Neurophysiol, 39: 1393–1402

    Google Scholar 

  • Stiles RN, Randall JE (1967) Mechanical factors in human tremor frequency. J App Physiol 23: 324–330

    CAS  Google Scholar 

  • Tukey JW (1961) Discussion, emphasizing the connection between analysis of variance and spectrum analysis. Technometrics, 3: 191–219

    Article  Google Scholar 

  • Tukey JW (1980) Can we predict where “time series” should go next? In: Brillinger DR, Tiao GC(eds) Directions in Time Series IMS, Hayward, California, pp 1–31

    Google Scholar 

  • Vallbo AB, Hagbarth K-E (1968) Activity from skin mechanoreceptors recorded percutaneously in awake human subjects. Exp Neurol 21: 270–289

    Article  PubMed  CAS  Google Scholar 

  • Watt DGD, Stauffer EK, Taylor A, Reinking RM, Stuart DG (1976) Analysis of muscle receptor connections by spike triggered averaging. I. Spindle primary and tendon organ afferents. J Neurophysiol 39: 1375–1392

    Google Scholar 

  • Wiener N (1930) Generalized harmonic analysis. Acta Math 55: 117–258

    Article  Google Scholar 

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Authors
  1. David M. Halliday
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  2. Jay R. Rosenberg
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Editor information

Editors and Affiliations

  1. Center of Musculoskeletat Research, National Institute for Working Life, Petrus Laestadius väg, 90713, Umeå, Sweden

    Uwe Windhorst  & Håkan Johansson  & 

  2. Department of Clinical Neurosciences and Department of Physiology and Biophysics Faculty of Medicine, The University of Calgary, 333 Hospital Drive N.W., Calgary, Alberta, T2N 4N1, Canada

    Uwe Windhorst

  3. Zentrum Physiologie und Pathophysiologie, Universität Göttingen, Humboldtallee 23, 37073, Göttingen, Germany

    Uwe Windhorst

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Halliday, D.M., Rosenberg, J.R. (1999). Time and Frequency Domain Analysis of Spike Train and Time Series Data. In: Windhorst, U., Johansson, H. (eds) Modern Techniques in Neuroscience Research. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58552-4_18

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  • DOI: https://doi.org/10.1007/978-3-642-58552-4_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63643-1

  • Online ISBN: 978-3-642-58552-4

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