Comparison of Correlation Dimension and Fractal Dimension in Estimating BIS index

ABSTRACT

This paper compares the correlation dimension (D2) and Higuchi fractal dimension (HFD) approaches in estimating BIS index based on of electroencephalogram (EEG). The single-channel EEG data was captured in both ICU and operating room and different anesthetic drugs, including propofol and isoflurane were used. For better analysis, application of adaptive segmentation on EEG signal for estimating BIS index is evaluated and compared to fixed segmentation. Prediction probability (PK) is used as a measure of correlation between the predictors and BIS index to evaluate the proposed methods. The results show the ability of these algorithms (specifically HFD algorithm) in predicting BIS index. Also, evolving fixed and adaptive windowing methods for segmentation of EEG reveals no meaningful difference in estimating BIS index.

This paper compares the correlation dimension (D2) and Higuchi fractal dimension (HFD) approaches in estimating BIS index based on of electroencephalogram (EEG). The single-channel EEG data was captured in both ICU and operating room and different anesthetic drugs, including propofol and isoflurane were used. For better analysis, application of adaptive segmentation on EEG signal for estimating BIS index is evaluated and compared to fixed segmentation. Prediction probability (PK) is used as a measure of correlation between the predictors and BIS index to evaluate the proposed methods. The results show the ability of these algorithms (specifically HFD algorithm) in predicting BIS index. Also, evolving fixed and adaptive windowing methods for segmentation of EEG reveals no meaningful difference in estimating BIS index.

KEYWORDS

Adaptive Segmentation, Bispectral Index, Depth of Anesthesia, Correlation Dimension, Fractal Dimension

Adaptive Segmentation, Bispectral Index, Depth of Anesthesia, Correlation Dimension, Fractal Dimension

Cite this paper

nullB. AHMADI and R. AMIRFATTAHI, "Comparison of Correlation Dimension and Fractal Dimension in Estimating BIS index,"*Wireless Sensor Network*, Vol. 2 No. 1, 2010, pp. 67-73. doi: 10.4236/wsn.2010.21010.

nullB. AHMADI and R. AMIRFATTAHI, "Comparison of Correlation Dimension and Fractal Dimension in Estimating BIS index,"

References

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[2] R. D. Miller, “Miller’s Anesthesia,” Sixth Edition, Elsevier Churchill Livingstone, pp. 1227–1264, 2005.

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[17] P. Pascolo, F. Barazza, and R. Carniel, “Considerations on the application of the chaos paradigm to describe the postural sway,” Chaos Solitons and Fractal, No. 27, pp. 1339–1346, 2006.

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[20] G. Widman, T. Schreiber, B. Rehberg, A. Hoerof, and C. E. Elger, “Quantification of depth of anesthesia by nonlinear time series analysis of brain electrical activity,” Physical Review E, No. 62, pp. 4898–4903, 2000.

[21] M. G. Lee, E. J. Park, J. M. Choi, and M. H. Yoon, “Electroencephalographic correlation dimension changes with depth of halothane,” Korean Journal of Physiology and Pharmacology, No. 3, pp. 491–499, 1999.

[22] R. Bender, B. Schultz, and U. Grouven, “Classification of EEG signals into general stages of anesthesia in real time using autoregressive models,” Conference Proceedings of the 16th Annual Conference of the Gesellschaft fur Klassifikatione, University of Dortmund, 1992

[23] S. Hagihira, M. Takashina, T. Mori, T. Mashimo, and I. Yoshiya, “Practical issues in bispectral analysis of electroencephalographic signals,” Anesthesia and Analgesia, Vol. 93, pp. 966–970, 2001.

[24] W. A. Brock, “Distiguishing random and determining the minimum embededding dimension of scalar time series,” Physica D, No. 110, pp. 43–50, 1986.

[25] F. Takens, “Detecting strange attractors in fluid turbulence,” In Rand D. A., Young L. S. (Eds), Dynamical System and Turbulence, Lecture Notes in Mathematics, Springer Verlag, Berlin, pp. 366–381, 1981.

[26] J. Theiler, “Efficient algorithm for etimating the correlation dimension from a set of discrete point,” Physical Review A, Vol. 36, No. 9, pp. 4456–4462.

[27] J. Theiler, “Spurious dimension from correlation algorithms applied to limited time series data,” Physical Review A, Vol. 34, No. 3, pp. 2427–2432.

[28] A. M. Fraser, et al., “Independent coordinate for strange attractors from mutual information,” Physical Review, 1986.

[29] C. D. Cutler, “Some results on the behavior and estimation of fractal dimension of distribuations on attractors,” Journal of Statistical Physics, Vol. 62, No. 3–4, pp. 651, 1991.

[30] R. M. Rangayyan, “Biomedical signal analysis: A case- study approach,” IEEE Press, NJ, pp. 405–416, 2001.

[31] W. D. Smith, R. C. Dutton, and N. T. Smith, “Measuring the performance of anesthetic depth indicators,” Anesthesiology, Vol. 84, No. 1, pp. 38–51, 1996.

[1] J. G. Jones, “Perception and memory during general anesthesia,” British Journal of Anaesthesia, No. 73, pp. 31–37, 1994.

[2] R. D. Miller, “Miller’s Anesthesia,” Sixth Edition, Elsevier Churchill Livingstone, pp. 1227–1264, 2005.

[3] E. Freye and J. V. Levy, “Cerebral monitoring in the operating room and the intensive care unit: An introductory for the clinician and a guide for the novice wanting to open a window to the brain,” Part I: The electroencephalogram, Journal of Clinical Monitoring and Computing, No. 19, pp. 1–76, 2005.

[4] L. C. Jameson and T. B. Sloan, “Using EEG to monitor anesthesia drug effects during surgery,” Journal of Clinical Monitoring and Computing, No. 20, pp. 445–472, 2006.

[5] I. J. Rampil, “A primer for EEG signal processing in anesthesia,” Anesthesiology, No. 89, pp. 980–1002, 1998.

[6] H. S. Traast and C. J. Kalkman, “Electroencephalographic Characteristics of emergence from propofol/ sufentanil total intravenous anesthesia,” Anesthesia and Analgesia, No. 81, pp. 366–371, 1995.

[7] R. Ferenets, T. Lipping, A. Anier, V. J?ntti, S. Melto, and S. Hovilehto, “Comparison of entropy and complexity measures for the assessment of depth of sedation,” IEEE Transactions on Biomedical Engineering, Vol. 53, No. 6, pp. 1067–1077, 2006.

[8] C. Robert, P. Karasinski, C. D. Arreto, and J. F. Gaudy, “Monitoring anesthesia using neural networks: A survey,” Journal of Clinical Monitoring and Computing, No. 17, pp. 259–267, 2002.

[9] V. Lalitha and C. Eswaran, “Automated detection of anesthetic depth levels using chaotic features with artificial neural networks,” Journal of Medical Systems, No. 31, pp. 445–452, 2007.

[10] R. Bender, B. Schultz, and U. Grouven, “Classification of EEG signals into general stages of anesthesia in real time using autoregressive models,” Conference Proceedings of the 16th Annual Conference of the Gesellschaft fur Klassifikatione, University of Dortmund, pp. 443–452, April 1–3, 1992.

[11] D. R. Drover, H. J. Lemmens, E. T. Pierce, G. Plourde, G. Loyd, E. Ornstein, L. S. Prichep, R. J. Chabot, and L. Gugino, “Patient state index: Titration of delivery and recovery from propofol, alfentanil, and nitrous oxide anesthesia,” Anesthesiology, No. 97, pp. 82–89, 2002.

[12] B. J. West, “Fractal physiology and chaos in medicine,” World Scientific, Singapore, Studies of Nonlinear Phenomena in Life Sciences, Vol. 1, 1990.

[13] P. Grassberger and I. Procaccia, “Characterization of strange attractors,” Physical Review Letters, No. 50, pp. 346–349, 1983.

[14] D. Hsieh, “Chaos and nonlinear dynamics: Applications to financial markets,” Journal of Finance, No. 46, pp. 1839–1877, 1991.

[15] J. Ulbikas and A. Cenys, “Nonlinear dynamics methods in EEG investigations,” Advances in Synergetics, Belarusian State University Press, Minsk, Vol. 1, pp. 110–120, 1994.

[16] I. M. Irurzun, P. Bergero, M. C. Cordero, M. M. Defeo, J. L. Vicente, and E. E. Mola, “Non-linear properties of R-R distributions as a measure of heart rate variability,” Chaos Solitons and Fractal, No. 16, pp. 699–708, 2003.

[17] P. Pascolo, F. Barazza, and R. Carniel, “Considerations on the application of the chaos paradigm to describe the postural sway,” Chaos Solitons and Fractal, No. 27, pp. 1339–1346, 2006.

[18] G. Mayer-Kress, S. P. layne, S. H. Koslow, A. J. Mandell, and M. F. shlesinger, “Perspectives in biomedical dynamics and theoretical medicine,” Annals of the New York Academy of Sciences, New York, USA, pp. 62–87, 1987.

[19] R. C. Watt and S. R. Hameroff, “Phase space electroencephalography (EEG): A new mode of intraoperative EEG analysis,” Journal of Clinical Monitoring and Computting, No. 5, pp. 3–13, 1988.

[20] G. Widman, T. Schreiber, B. Rehberg, A. Hoerof, and C. E. Elger, “Quantification of depth of anesthesia by nonlinear time series analysis of brain electrical activity,” Physical Review E, No. 62, pp. 4898–4903, 2000.

[21] M. G. Lee, E. J. Park, J. M. Choi, and M. H. Yoon, “Electroencephalographic correlation dimension changes with depth of halothane,” Korean Journal of Physiology and Pharmacology, No. 3, pp. 491–499, 1999.

[22] R. Bender, B. Schultz, and U. Grouven, “Classification of EEG signals into general stages of anesthesia in real time using autoregressive models,” Conference Proceedings of the 16th Annual Conference of the Gesellschaft fur Klassifikatione, University of Dortmund, 1992

[23] S. Hagihira, M. Takashina, T. Mori, T. Mashimo, and I. Yoshiya, “Practical issues in bispectral analysis of electroencephalographic signals,” Anesthesia and Analgesia, Vol. 93, pp. 966–970, 2001.

[24] W. A. Brock, “Distiguishing random and determining the minimum embededding dimension of scalar time series,” Physica D, No. 110, pp. 43–50, 1986.

[25] F. Takens, “Detecting strange attractors in fluid turbulence,” In Rand D. A., Young L. S. (Eds), Dynamical System and Turbulence, Lecture Notes in Mathematics, Springer Verlag, Berlin, pp. 366–381, 1981.

[26] J. Theiler, “Efficient algorithm for etimating the correlation dimension from a set of discrete point,” Physical Review A, Vol. 36, No. 9, pp. 4456–4462.

[27] J. Theiler, “Spurious dimension from correlation algorithms applied to limited time series data,” Physical Review A, Vol. 34, No. 3, pp. 2427–2432.

[28] A. M. Fraser, et al., “Independent coordinate for strange attractors from mutual information,” Physical Review, 1986.

[29] C. D. Cutler, “Some results on the behavior and estimation of fractal dimension of distribuations on attractors,” Journal of Statistical Physics, Vol. 62, No. 3–4, pp. 651, 1991.

[30] R. M. Rangayyan, “Biomedical signal analysis: A case- study approach,” IEEE Press, NJ, pp. 405–416, 2001.

[31] W. D. Smith, R. C. Dutton, and N. T. Smith, “Measuring the performance of anesthetic depth indicators,” Anesthesiology, Vol. 84, No. 1, pp. 38–51, 1996.