Experimental investigation of the neuromuscular system involves not only analysis of continuous signals but also necessitates the study of sequences of action potentials recorded from individual neurones together with the interactions between several sequences. Trains of action potentials may be regarded as realisations of stochastic point processes and techniques for the identification of point process systems can provide valuable experimental tools for the investigation of neuromuscular systems. Computational methods are presented for estimating the finite Fourier transform of a point process, and the associated spectral estimation procedures are described. An example is presented to illustrate the application of linear point process model identification techniques to the muscle spindle receptor. Using this example, simulation techniques are applied to demonstrate that spectral estimates can provide valuable physiological insight.
Amjad, A.M.1989Point Process Identification Techniques Applied to Complex Physiological Systems, PhD Thesis, University of Glasgow .
2.
Anderson, B.F., Lennerstrand, and Thoden, U.1968. ' Response characteristics of muscle spindle endings at constant length to variations in fusimotor activation', Acta Physiol Scand, 74, 301-318.
3.
Angelini, F. and Petracchi, D.1978. 'Significance of phase-locking measurements as a test for neural encoding models', Biol Cybernetics, 30, 169-177.
4.
Angers, D. and Delisle, G.Y.1971. 'A study of the action of static and dynamic fusimotor fibres with a mechanical model of the mammalian muscle spindle', IEEE Trans Bio-med Engng, BME18, 175-180.
5.
Bartlett, M.S.1963. 'The spectral analysis of point processes' J R Statist Soc, B25, 264-280.
6.
Brillinger, D.R.1972. 'The spectral analysis of stationary interval functions ', in Proc of 6th Berkeley Symp Math Statist Probab , 1 (Le Cam, L. M., Neyman, J. and Scott, E. L. eds), University of California Press, Berkeley, USA, 483-513.
7.
Brillinger, D.R.1975a. 'The identification of point process systems', Ann Probab, 3, 909-929.
8.
Brillinger, D.R.1975b. 'Estimation of product densities', in Comp Sci Statist, 8th Ann Symp on the Interface, UCLA, Los Angeles, USA, 431-438.
9.
Brillinger, D.R.1975c. 'Statistical inference for stationary point processes ', in Stochastic processes and related topics, 1 (Puri M. I. ed) Academic Press, New York, USA, 55-79.
10.
Brillinger, D.R.1978. 'Comparative aspects of the study of ordinary time series and of point processes' in Developments in Statistics, 1 (Krishnaiah, P. R. ed), Academic Press, New York, USA, 33-134.
11.
Brillinger, D.R.1983. 'The finite Fourier transform of a stationary process ', in Handbook of Statistics, 3 (Brillinger, F. R. & Krishnaiah, P. R.), Elsevier, Amsterdam, Netherlands, 21-37.
12.
Brillinger, D.R., Bryant, H.L. Jr. and Segundo, J.P.1976. 'Identification of synaptic interactions'. Biol Cybernetics, 22, 213-228.
13.
Clark, F.J., Matthews, P.B.C. and Muir, R.B.1981. 'Response of Ia afferents to vibration in the presence of the tonic vibration reflex', J Physiol, 311, 97-112.
14.
Cox, D.R.1965. 'On the estimation of the intensity function of a stationary point process', J R Statist Soc. B27, 322-337.
15.
Cox, D.R. and Isham, V.1980. Point Processes, Chapman and Hall, London.
16.
Cox, D.R. and Lewis, P.A.W.1968. The Statistical Analysis of Series of Events, Methuen, London.
17.
Cox, D.R. and Lewis, P.A.W.1972. 'Multivariable point processes', in Proc 6th Berkeley Symp Math Statis probab 3 (Le Cam, L. M., Neyman, J. & Scott, E. L. eds), University of California Press, Berkeley , USA, 401-448.
18.
Daly, D.J. and Vere-Jones, D.1988. An Introduction to the Theory of Point Processes, Springer, New York, USA
19.
Downie, I.C. and Murray-Smith, D.J.1981. 'Simulation of systems involving pulse frequency modulation with special reference to modelling of muscle spindle receptors', Proc 1981 UKSC Conf on Computer Simulation , Harrogate, Westbury House, Guildford, 143-152.
20.
French, A.S. and Holden, A.V.1971. 'Alias-free sampling of neuronal spike trains', Kybernetik, 8, 165-171.
21.
Jenkins, G. and Watts, D.G.1968. Spectral Analysis and its Applications, Holden-Day, San Francisco, USA.
22.
Karlin, S. and Taylor, H.M.1975. A First Course in Stochastic Processes, (2nd edn), Academic Press, New York, USA, Ch 1.
23.
Lago, P.J.A. and Jones, N.B.1982. 'Note on the spectral analysis of neural spike trains' , Med Biol Engng and Comput, 20, 44-48.
24.
Lewis, P.A.W.1972. 'Remarks on the theory, computation and application of the spectral analysis of series of events', J Sound and Vibration , 12, 353-375.
25.
Meyer, A.U.1961. Pulse Frequency Modulation and its Effect in Feedback Systems, PhD Dissertation, Northwestern University, USA.
26.
Moore, G.P. and Auriemma, R.A.1985. 'Prediction of muscle stretch receptor behaviour using Wiener kernels', Brain Res, 337, 185-109.
27.
Pavlides, T. and Jury, E.I.1965. 'Analysis of a new class of pulse-frequency modulated feedback systems', IEEE Trans Auto Cont, AC10, 35-43.
28.
Priestly, M.B.1963. 'Contribution to a discussion of paper by M. S. Bartlett ', J R Statist Soc, B25, 288-290.
29.
Rigas, A.G.1983. Point Processes and Time Series Analysis: Theory and Applications to Complex Biological Problems, PhD Thesis, University of Glasgow.
30.
Rosenberg, J.R., Murray-Smith, D.J. and Rigas, A.1982. 'An introduction to the application of system identification techniques to elements of the neuromuscular system', Trans Inst MC, 4, 187-201.
31.
Rosenberg, J.R., Amjad, A.M.Breeze, P., Brillinger, D.R. and Halliday, D.M.1989. 'The Fourier approach to the identification of functional coupling between neuronal spike trains', Prog Biophys Molec Biol, 53, 1-31.
