Chaotic Properties of Hemodynamic Responsein Functional Near Infrared Spectroscopic Measurement of Brain Activity
Functional near infrared spectroscopy (fNIRS) is a
practical non-invasive optical technique to detect characteristic of
hemoglobin density dynamics response during functional activation of
the cerebral cortex. In this paper, fNIRS measurements were made in
the area of motor cortex from C4 position according to international
10-20 system. Three subjects, aged 23 - 30 years, were participated in
the experiment.
The aim of this paper was to evaluate the effects of different motor
activation tasks of the hemoglobin density dynamics of fNIRS signal.
The chaotic concept based on deterministic dynamics is an important
feature in biological signal analysis. This paper employs the chaotic
properties which is a novel method of nonlinear analysis, to analyze
and to quantify the chaotic property in the time series of the
hemoglobin dynamics of the various motor imagery tasks of fNIRS
signal. Usually, hemoglobin density in the human brain cortex is
found to change slowly in time. An inevitable noise caused by various
factors is to be included in a signal. So, principle component analysis
method (PCA) is utilized to remove high frequency component. The
phase pace is reconstructed and evaluated the Lyapunov spectrum, and
Lyapunov dimensions. From the experimental results, it can be
conclude that the signals measured by fNIRS are chaotic.
[1] J. Decety, "The neurophysiological basis of motor imagery", Behavioral
Brain Research, vol. 77(1-2), pp. 45-52, 1996.
[2] G. Pfurtscheller, C. Neuper, and N. Birbaumer," Human brain-computer
interface". In E. Vaadia and A. Riehle (Eds.), Motor cortex in voluntary
movements: A distributed system for distributed functions. Series:
Methods and new frontiers in neuroscience, pp. 367-401, 2005. Boca
Raton, FL: CRC Press.
[3] M. Nakagawa,"Chaos and fractals in engineering", World Scientific,
Singapore, pp. 113, 1999.
[4] M. Phothisonothai and M. Nakagawa, "EEG-Based Fractal Analysis of
Different Motor Imagery Tasks using Critical Exponent Method",
International Journal of Biomedical Science, vol. 1, no.3, pp 1306-1216,
2006.
[5] Ni Ni Soe and M. Nakagawa, "Chaos and fractal analysis of EEG signals
during different imaginary motor movement tasks", J. Phys. Soc. Jpn.,
(submitted for publication).
[6] G. Hori, K. Aihara, Y. Mizuno and Y. Okuma, "Blind source separation
and chaotic analysis of EEG for judgment of brain death", Artif. Life
Robotics., vol. 5, no. 1, pp. 10-14, 2001.
[7] V. Vuksanović and V. Gal, "Nonlinear and chaos characteristics of heart
period time series: healthy aging and postural change", Autonomic
Neuroscience: Basic and Clinical, vol. 121, pp. 94 - 100, 2005.
[8] H. Koga and M. Nakagawa," A Chaotic Synthesis Model of Vowels ", J.
Phys. Soc. Jpn., vol. 72, no.3, pp. 751-761, 2003.
[9] T. J. Huppert, R. D. Hoge, S. G. Diamond, M. A. Franceschini, and D. A.
Boas," A temporal comparison of BOLD, ASL, and NIRS hemodynamic
responses to motor stimuli in adult human", NeuroImage, vol. 29, pp.
368-382, 2006.
[10] V. Y. Toronov, X. Zhang and A. G. Webb," A spatial and temporal
comparison of hemodynamic signals measured using optical and
functional magnetic resonance imaging during activation in human
primary visual cortex", NeuroImage, vol. 34, pp. 1136-1148, 2007.
[11] Barbara Stuart, "Infrared Spectroscopy: Fundamental and applications",
John Wiley and sons, 2004.
[12] C. B. Akg├╝l, B. Sankur and A. Akin, "Extraction of cognitive
activity-related waveforms from functional near-infrared spectroscopy
signals", Med. Bio. Eng. Comput., vol. 44, pp. 945-958, 2006
[13] R. N. Aslin, and J. Mehler," Near-infrared spectroscopy for functional
studies of brain activity in human infants: promise, prospects, and
challenges", Journal of Biomedical Optics, vol.10, no.1, pp. 011009,
2005.
[14] C. B. Akg├╝l, B. Sankur and A. Akin," Spectral analysis of event-related
hemodynamic responses in functional near infrared spectroscopy",
Journal of Computational Neuroscience, vol. 18, pp. 67-83, 2005.
[15] M. Okamoto and I. Dan, "Functional near-infrared spectroscopy for
human brain mapping of tase-related cognitive functions", Journal of
Bioscience and Bioengineering, vol. 103, no.3, pp. 207-215, 2007.
[16] R. Sitaram, et al., "Temporal classification of multichannel near-infrared
spectroscopy signals of motor imagery for developing a brain computer
interface", NeuroImage, vol. 34, pp. 1416-1427, 2007.
[17] S. Coyle, T. Ward, and C. Markham," Brain-computer interface using a
simplified functional near-infrared spectroscopy system", Journal of
Neural Engineering, vol. 4, pp. 219-226, 2007.
[18] S. Coyle, T. Ward, C. Markham and G. McDarby," On the suitability of
near-infrared (NIR) systems for next-generation brain computer
interface", Physiological Measurement, vol. 25, pp. 815-822, 2004.
[19] D. Friedman, R. Leeb, A. Antley, M. Garau, C. Guger, C. Keinrath, A.
Steed, G. Pfurtscheller, and M. Slater," Navigating virtual reality by
thought: What is it like?", Presence: Teleoperators and Virtual
Environments, vol.16 (1), pp.100-110, 2007.
[20] A. H. Nayfeh and B. Balachandran, "Applied nonlinear dynamics:
analytical, computational, and experimental methods", New York, John
Wiley and Sons, 1995.
[21] H.G. Schuster, "Deterministic chaos: an introduction", Weinheim,
Wiley-VCH, 1989.
[22] E. Ott, "Chaos in dynamical systems", Cambridge, Cambridge University
Press, 2002.
[23] S. H. Strogatz, "Nonlinear dynamics and chaos", Boston (MA),
Addison-Wesley, 1994.
[24] D. T. Kaplan and L. Class,"Understanding nonlinear dynamics", New
York, Springer, 1995.
[25] J. C. Sprott, "Chaos and Time-Series Analysis", Oxford University, New
York, 2003.
[26] R. C. Hilborn, "Chaos and Nonlinear Dynamics: An Introduction for
Scientists and Engineers", Oxford University, New York, 2nd ed., pp.
323, 2000.
[27] E. Ott, T. Sauer and J. Yorke, "Coping with chaos", John Wiley and Sons,
Inc. New York, 1994.
[28] "Handbook of chaos control",ed. H. G. Schustetr, Wiley-VCH,
Weinheim, 1999.
[29] F. Takens. "Detecting strange attractors in turbulence", Lecture Notes in
Mathematics of Dynamical Systems of Turbulence (Springer-Verlag,
Berlin, 1981), Vol. 898, pp. 365-381.
[30] A. M. Fraser and H. L. Swinney," Independent coordinates for strange
attractors from mutual information", Phys. Rev. A, vol. 33, pp. 1134-1140,
1986.
[31] M. B. Kennel, R. Brown and H. D. I. Abarbanel," Determining embedding
dimension for phase-space reconstruction using a geometrical
construction", Phys. Rev. A, vol. 45, pp. 3403-3411, 1992.
[32] M. T. Rosenstein, J. J. Collins and C. J. De Luca, "A practical method for
calculating largest Lyapunov exponents from small data sets", Physica D,
vol. 65, pp. 117-134, 1993.
[33] I. Shimada and T. Nagashima, "A numerical approach to ergodic problem
of dissipative dynamical systems", Prog. Theor. Phys., Vol. 611, no.6, pp.
1605-1616, 1979. [in Japanese].
[34] A.Wolf, J.B. Swift, H.L. Swinney, and J.A. Vastano, "Determining
Lyapunov exponents from a time series" Physica D, vol. 16, pp. 285-317,
1985.
[35] M.Sano and Y. Sawada, "Measurement of the Lyapunov spectrum from a
chaotic time series", Phys. Rev. Lett., vol. 55, no.10, pp. 1082-1085, 1985.
[36] S. Sato, M. Sano and Y. Sawada, "Practical methods of measuring the
generalized dimension and the largest Lyapunov exponent in high
dimensional chaotic systems", Prog. Theor. Phys., vol. 77, no.1, pp.1-5,
1987.
[37] P. Bryant, R. Brown, and H. D. I. Abarbanel, "Lyapunov exponents from
observed time series", Phys. Rev. A, vol. 65, pp.1523-1526, 1990.
[38] R. Brown, P. Bryant, and H. D. I. Abarbanel," Computing the Lyapunov
spectrum of a dynamical system from observed time series", Phys. Rev. A,
vol. 43, pp. 2787-2806, 1991.
[39] P. Frederickson, J. Kaplan, E. Yorke and J. Yorke, "The Lyapunov
dimension of Strange Attractors", J. Diff. Eqs., vol. 49, pp 185-207 ,1983.
[40] P. Gruber, et.at., "Denoising using local ICA and a generalized
eigendecomposition with time-delayed signals", In LNCS 3195, Proc.
ICA- 2004, pp 993-1000, Granada, 2004.
[1] J. Decety, "The neurophysiological basis of motor imagery", Behavioral
Brain Research, vol. 77(1-2), pp. 45-52, 1996.
[2] G. Pfurtscheller, C. Neuper, and N. Birbaumer," Human brain-computer
interface". In E. Vaadia and A. Riehle (Eds.), Motor cortex in voluntary
movements: A distributed system for distributed functions. Series:
Methods and new frontiers in neuroscience, pp. 367-401, 2005. Boca
Raton, FL: CRC Press.
[3] M. Nakagawa,"Chaos and fractals in engineering", World Scientific,
Singapore, pp. 113, 1999.
[4] M. Phothisonothai and M. Nakagawa, "EEG-Based Fractal Analysis of
Different Motor Imagery Tasks using Critical Exponent Method",
International Journal of Biomedical Science, vol. 1, no.3, pp 1306-1216,
2006.
[5] Ni Ni Soe and M. Nakagawa, "Chaos and fractal analysis of EEG signals
during different imaginary motor movement tasks", J. Phys. Soc. Jpn.,
(submitted for publication).
[6] G. Hori, K. Aihara, Y. Mizuno and Y. Okuma, "Blind source separation
and chaotic analysis of EEG for judgment of brain death", Artif. Life
Robotics., vol. 5, no. 1, pp. 10-14, 2001.
[7] V. Vuksanović and V. Gal, "Nonlinear and chaos characteristics of heart
period time series: healthy aging and postural change", Autonomic
Neuroscience: Basic and Clinical, vol. 121, pp. 94 - 100, 2005.
[8] H. Koga and M. Nakagawa," A Chaotic Synthesis Model of Vowels ", J.
Phys. Soc. Jpn., vol. 72, no.3, pp. 751-761, 2003.
[9] T. J. Huppert, R. D. Hoge, S. G. Diamond, M. A. Franceschini, and D. A.
Boas," A temporal comparison of BOLD, ASL, and NIRS hemodynamic
responses to motor stimuli in adult human", NeuroImage, vol. 29, pp.
368-382, 2006.
[10] V. Y. Toronov, X. Zhang and A. G. Webb," A spatial and temporal
comparison of hemodynamic signals measured using optical and
functional magnetic resonance imaging during activation in human
primary visual cortex", NeuroImage, vol. 34, pp. 1136-1148, 2007.
[11] Barbara Stuart, "Infrared Spectroscopy: Fundamental and applications",
John Wiley and sons, 2004.
[12] C. B. Akg├╝l, B. Sankur and A. Akin, "Extraction of cognitive
activity-related waveforms from functional near-infrared spectroscopy
signals", Med. Bio. Eng. Comput., vol. 44, pp. 945-958, 2006
[13] R. N. Aslin, and J. Mehler," Near-infrared spectroscopy for functional
studies of brain activity in human infants: promise, prospects, and
challenges", Journal of Biomedical Optics, vol.10, no.1, pp. 011009,
2005.
[14] C. B. Akg├╝l, B. Sankur and A. Akin," Spectral analysis of event-related
hemodynamic responses in functional near infrared spectroscopy",
Journal of Computational Neuroscience, vol. 18, pp. 67-83, 2005.
[15] M. Okamoto and I. Dan, "Functional near-infrared spectroscopy for
human brain mapping of tase-related cognitive functions", Journal of
Bioscience and Bioengineering, vol. 103, no.3, pp. 207-215, 2007.
[16] R. Sitaram, et al., "Temporal classification of multichannel near-infrared
spectroscopy signals of motor imagery for developing a brain computer
interface", NeuroImage, vol. 34, pp. 1416-1427, 2007.
[17] S. Coyle, T. Ward, and C. Markham," Brain-computer interface using a
simplified functional near-infrared spectroscopy system", Journal of
Neural Engineering, vol. 4, pp. 219-226, 2007.
[18] S. Coyle, T. Ward, C. Markham and G. McDarby," On the suitability of
near-infrared (NIR) systems for next-generation brain computer
interface", Physiological Measurement, vol. 25, pp. 815-822, 2004.
[19] D. Friedman, R. Leeb, A. Antley, M. Garau, C. Guger, C. Keinrath, A.
Steed, G. Pfurtscheller, and M. Slater," Navigating virtual reality by
thought: What is it like?", Presence: Teleoperators and Virtual
Environments, vol.16 (1), pp.100-110, 2007.
[20] A. H. Nayfeh and B. Balachandran, "Applied nonlinear dynamics:
analytical, computational, and experimental methods", New York, John
Wiley and Sons, 1995.
[21] H.G. Schuster, "Deterministic chaos: an introduction", Weinheim,
Wiley-VCH, 1989.
[22] E. Ott, "Chaos in dynamical systems", Cambridge, Cambridge University
Press, 2002.
[23] S. H. Strogatz, "Nonlinear dynamics and chaos", Boston (MA),
Addison-Wesley, 1994.
[24] D. T. Kaplan and L. Class,"Understanding nonlinear dynamics", New
York, Springer, 1995.
[25] J. C. Sprott, "Chaos and Time-Series Analysis", Oxford University, New
York, 2003.
[26] R. C. Hilborn, "Chaos and Nonlinear Dynamics: An Introduction for
Scientists and Engineers", Oxford University, New York, 2nd ed., pp.
323, 2000.
[27] E. Ott, T. Sauer and J. Yorke, "Coping with chaos", John Wiley and Sons,
Inc. New York, 1994.
[28] "Handbook of chaos control",ed. H. G. Schustetr, Wiley-VCH,
Weinheim, 1999.
[29] F. Takens. "Detecting strange attractors in turbulence", Lecture Notes in
Mathematics of Dynamical Systems of Turbulence (Springer-Verlag,
Berlin, 1981), Vol. 898, pp. 365-381.
[30] A. M. Fraser and H. L. Swinney," Independent coordinates for strange
attractors from mutual information", Phys. Rev. A, vol. 33, pp. 1134-1140,
1986.
[31] M. B. Kennel, R. Brown and H. D. I. Abarbanel," Determining embedding
dimension for phase-space reconstruction using a geometrical
construction", Phys. Rev. A, vol. 45, pp. 3403-3411, 1992.
[32] M. T. Rosenstein, J. J. Collins and C. J. De Luca, "A practical method for
calculating largest Lyapunov exponents from small data sets", Physica D,
vol. 65, pp. 117-134, 1993.
[33] I. Shimada and T. Nagashima, "A numerical approach to ergodic problem
of dissipative dynamical systems", Prog. Theor. Phys., Vol. 611, no.6, pp.
1605-1616, 1979. [in Japanese].
[34] A.Wolf, J.B. Swift, H.L. Swinney, and J.A. Vastano, "Determining
Lyapunov exponents from a time series" Physica D, vol. 16, pp. 285-317,
1985.
[35] M.Sano and Y. Sawada, "Measurement of the Lyapunov spectrum from a
chaotic time series", Phys. Rev. Lett., vol. 55, no.10, pp. 1082-1085, 1985.
[36] S. Sato, M. Sano and Y. Sawada, "Practical methods of measuring the
generalized dimension and the largest Lyapunov exponent in high
dimensional chaotic systems", Prog. Theor. Phys., vol. 77, no.1, pp.1-5,
1987.
[37] P. Bryant, R. Brown, and H. D. I. Abarbanel, "Lyapunov exponents from
observed time series", Phys. Rev. A, vol. 65, pp.1523-1526, 1990.
[38] R. Brown, P. Bryant, and H. D. I. Abarbanel," Computing the Lyapunov
spectrum of a dynamical system from observed time series", Phys. Rev. A,
vol. 43, pp. 2787-2806, 1991.
[39] P. Frederickson, J. Kaplan, E. Yorke and J. Yorke, "The Lyapunov
dimension of Strange Attractors", J. Diff. Eqs., vol. 49, pp 185-207 ,1983.
[40] P. Gruber, et.at., "Denoising using local ICA and a generalized
eigendecomposition with time-delayed signals", In LNCS 3195, Proc.
ICA- 2004, pp 993-1000, Granada, 2004.
@article{"International Journal of Medical, Medicine and Health Sciences:64111", author = "Ni Ni Soe and Masahiro Nakagawa", title = "Chaotic Properties of Hemodynamic Responsein Functional Near Infrared Spectroscopic Measurement of Brain Activity", abstract = "Functional near infrared spectroscopy (fNIRS) is a
practical non-invasive optical technique to detect characteristic of
hemoglobin density dynamics response during functional activation of
the cerebral cortex. In this paper, fNIRS measurements were made in
the area of motor cortex from C4 position according to international
10-20 system. Three subjects, aged 23 - 30 years, were participated in
the experiment.
The aim of this paper was to evaluate the effects of different motor
activation tasks of the hemoglobin density dynamics of fNIRS signal.
The chaotic concept based on deterministic dynamics is an important
feature in biological signal analysis. This paper employs the chaotic
properties which is a novel method of nonlinear analysis, to analyze
and to quantify the chaotic property in the time series of the
hemoglobin dynamics of the various motor imagery tasks of fNIRS
signal. Usually, hemoglobin density in the human brain cortex is
found to change slowly in time. An inevitable noise caused by various
factors is to be included in a signal. So, principle component analysis
method (PCA) is utilized to remove high frequency component. The
phase pace is reconstructed and evaluated the Lyapunov spectrum, and
Lyapunov dimensions. From the experimental results, it can be
conclude that the signals measured by fNIRS are chaotic.", keywords = "Chaos, hemoglobin, Lyapunov spectrum, motorimagery, near infrared spectroscopy (NIRS), principal componentanalysis (PCA).", volume = "2", number = "3", pages = "123-10", }
