Skip to main content
SpringerLink
Log in

Simulation of nonstationary spectral analysis of turbulence in the aorta using a modified autoregressive or maximum entropy (AR/ME) method

  • Biomechanics
  • Published:
Medical and Biological Engineering and Computing Aims and scope Submit manuscript

Abstract

A new method of parametric spectral calculation based on the ensemble average technique, which is a natural expansion of the Burg's maximum entropy method, is proposed. This method is applied to a set of numerical simulation data which simulate turbulent velocity fluctuations data measured in the canine aorta with a hot-film anemometer. The autoregressive order of the spectral calculation is chosen by the minimum AIC (Akaike's information criteria) method. It is shown that the proposed method used with the minimum AIC method has a very good performance calculating smooth averaged spectra in the short-time quasisteady spectral analysis of nonstationary processes such as turbulence in the aorta.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Akaike, H. (1969a) Fitting autoregressive models for prediction.Ann. Inst. Statist Math.,21, 243–247.

    MATH  MathSciNet  Google Scholar 

  • Akaike, H. (1969b) Power spectrum, estimation through autoregressive model fitting.——Ibid.,21., 407–419.

    MATH  MathSciNet  Google Scholar 

  • Akaike, H. (1974) A new look at the statistical model identification.IEEE Trans.,AC-19, 716–723.

    MATH  MathSciNet  Google Scholar 

  • Anderson, N. (1974) On the calculation of filter coefficients for maximum entropy spectral analysis.Geophysics,39, 69–72.

    Article  Google Scholar 

  • Bendat, J. S. andPiersol, A. G. (1971)Random data analysis and measurement procedures. Wiley-Interscience, New York, London, Sydney, Toronto, 325.

    MATH  Google Scholar 

  • Bradshaw, P. (1971)An introduction to turbulence and its measurement. Pergamon, Oxford, 22.

    MATH  Google Scholar 

  • Burg, J. P. (1967) Paper presented at the 37th Annual International Meeting, Society of Exploring Geophysicists, Oklahoma City, Oklahoma, 31st October 1967. Reprinted inModern spectrum analysis.Childers, D. G. (Ed.), IEEE Press, New York, 1978.

    Google Scholar 

  • Burg, J. P. (1972) The relationship between maximum entropy spectra and maximum likelihood spectra.Geophysics,37, 375–376.

    Article  Google Scholar 

  • Chen, W. Y. andStegen, G. R. (1974) Experiments with maximum entropy power spectra of sinusoids.J. Geophys., Res.,79, 3019–3022.

    Google Scholar 

  • Deshpande, M. D. andGiddens, D. P. (1980) Turbulence measurements in a constricted tube.J. Fluid Mech.,97, 65–89.

    Article  Google Scholar 

  • Giddens, D. P. andKitney, R. I. (1983) Autoregressive spectral estimation of poststenotic blood flow disturbance.J. Biomech. Eng.,105, 401–404.

    Google Scholar 

  • Haykin, S. andKesler, S. (1979) Prediction error filtering and maximum entropy spectral estimation. InNonlinear methods of spectral analysis. Topics in applied physics, vol. 34.Haykin, S. (Ed.), Springer-Verlag, Berlin, Heidelberg, New York, 9–72.

    Google Scholar 

  • Herring, R. W. (1980) The cause of line splitting in Burg maximum-entropy spectral analysis.IEEE Trans. ASSP,-28, 629–701.

    Google Scholar 

  • Hino, M., Kashiwayanagi, M., Nakayama, A. andHara, T. (1983) Experiments on the turbulence statistics and the structure of a reciprocating oscillatory flow.,J. Fluid Mech.,131, 363–400.

    Article  Google Scholar 

  • Jansen, B. H., Bourne, J. R. andWand, J. W. (1981) Autoregressive estimation of short segment spectra for computerised EEG analysis.IEEE Trans.,BME-28, 630–638.

    Google Scholar 

  • Jones, H. R. (1976) Autoregression order selection.Geophysics,41, 771–773

    Article  Google Scholar 

  • Kawai, S. (1979) Generation of initial wavelets by instability of a coupled shear flow and their evolution to wind waves.J. Fluid Mech.,93, 661–703.

    Article  Google Scholar 

  • Kay, S. M. (1979) The effects of noise on the autoregressive spectral estimator.IEEE Trans. ASSP,-27, 478–485.

    Article  MATH  MathSciNet  Google Scholar 

  • Kay, S. M. (1980) Noise compensation for autoregressive spectral estimates.IEEE Trans.,ASSP-28, 292–303.

    MATH  Google Scholar 

  • Khalifa, A. M. A. andGiddens, D. P. (1978) Analysis of disorder in pulsatile flows with application to post-stenotic blood velocity measurement in dogs.J. Biomech.,11, 129–141.

    Article  Google Scholar 

  • Khalifa, A. M. A. andGiddens, D. P. (1981) Characterisation and evolution of poststenotic flow disturbances.——Ibid..,14, 279–296.

    Article  Google Scholar 

  • Kitney, R. I. andGiddens, D. P. (1982) Extraction and characterisation of underlying velocity waveforms in poststenotic flow.IEE Proc. A,129, 651–662.

    Google Scholar 

  • Kitney, R. I. andGiddens, D. P. (1983) Analysis of blood velocity waveforms by phase shift averaging and autoregressive spectral estimation.J. Biomech. Eng.,105, 398–401.

    Google Scholar 

  • Lacoss, R. T. (1971) Data adaptive spectral analysis methods.Geophysics,36, 661–675.

    Article  Google Scholar 

  • Lawn, C. J. (1971) The determination of the rate of dissipation in turbulent pipe flow.J. Fluid Mech.,48, 477–505.

    Article  Google Scholar 

  • Parker, K. H. (1977) Instability in arterial blood flow. InCardiovascular flow dynamics and measurements Hwang, N. H. C. andNorman, N. A. (Eds.), University Park Press, Baltimore, 633–663.

    Google Scholar 

  • Radoski, H. R., Fougere, P. F. andZawalick, E. J. (1975) A comparison of power spectral estimates and applications of the maximum entropy method.J. Geophys. Res.,80, 610–625.

    Google Scholar 

  • Sakai, H. (1979) Statistical properties of AR spectral analysis.IEEE Trans. ASSP,-27, 402–409.

    MATH  Google Scholar 

  • Ulrych, T. J. (1972) Maximum entropy power spectrum of truncated sinusoids.J. Geophys. Res.,77, 1396–1400.

    Article  Google Scholar 

  • Ulyrch, T. J. andBishop, T. N. (1975) Maximum entropy spectral analysis and autoregressive decomposition.Rev. Geophys. Space Phys.,13, 183–200.

    Google Scholar 

  • Ulrych, T. J. andOoe, M. (1979) Autoregressive and mixed autoregressive-moving average models and spectra. InNonlinear methods of spectral analysis. (Topics in applied physics, vol. 34.) Haykin, S. (Ed.), Springer-Verlag, Berlin, Heidelberg, New York, 73–125.

    Google Scholar 

  • Yamaguchi, T., Yoshikawa, T., Kikkawa, S. andSugawara, M. (1980a) Turbulence intensity measured in the centre of canine ascending aorta with a hot-film anemometer. (In Japanese.)Trans. Soc. Instr. Control Eng. (Japan) 16, 754–760.

    Google Scholar 

  • Yamaguchi, T., Yoshikawa, T., Kikkawa, S. andSugawara, M. (1980b) A method for the analysis of turbulence measured in the canine aorta with a hot-film anemometer. (In Japanese.) ——Ibid.,16, 910–915.

    Google Scholar 

  • Yamaguchi, T., Kikkawa, S., Tanishita, K. andSugawara, M. (1981) Spectrum analysis of turbulence in the canine ascending aorta. (In Japanese)Jpn. J. Med. Electron. Biol. Eng.,19, 259–266.

    Google Scholar 

  • Yamaguchi, T., Kikkawa, S., Tanishita, K., Sugawara, M. andParker, K. H. (1982) Spectrum analysis of turbulence in the aorta. InBiomechanics: principles and applications.Huisks, R., van Campen, D. andDe Wijn, J. (Eds.), Martinus Nijhoff, The Hague, Boston, London, 359–366.

    Google Scholar 

  • Yamaguchi, T., Kikkawa, S., Yoshikawa, T..,Tanishita, K. andSugawara, M. (1983) Measurement of turbulence intensity in the centre of the canine ascending aorta with a hot-film anemometer.J. Biomech. Eng.,105, 177–187.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Vascular Physiology, National Cardiovascular Centre Research Institute, 5-7-1 Fujishiro-dai, 565, Suita, Osaka, Japan

    T. Yamaguchi

  2. Department of Surgical Science, The Heart Institute Japan, Tokyo Women's Medical College, Tokyo, Japan

    S. Kikkawa

  3. Physiological Flow Studies Unit, Imperial College, SW7 2AZ, London, UK

    K. H. Parker

Authors
  1. T. Yamaguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Kikkawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. H. Parker
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yamaguchi, T., Kikkawa, S. & Parker, K.H. Simulation of nonstationary spectral analysis of turbulence in the aorta using a modified autoregressive or maximum entropy (AR/ME) method. Med. Biol. Eng. Comput. 25, 533–542 (1987). https://doi.org/10.1007/BF02441746

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02441746

Keywords

Search

Navigation