**6. References**


Mendel, J. M. (1988). "Use of Higher Order Statistics in Signal Processing and System Theory: An Update," *Proceedings of SPIE, Advanced Algorithms and Architectures for Signal Processing III*, vol. 975, pp. 126-144.

52 Practical Applications in Biomedical Engineering

**Author details** 

Walid A. Zgallai *Berkshire, UK Dubai, UAE* 

**6. References** 

vol. 36, pp. 1351-1374.

to noise or non-linearity due to strong uterine contractions.

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Powers, and Zoubier, eds.), Ch. 7, pp. 213-267, 1995.

of Business and Economics Statistics, ASA, pp. 135-141.

*time series analysis*, vol. 3, No. 3, pp. 169-176.

*Speech and Signal Processing (ICASSP)*, pp. 2412-2415, NY, April.

wave-wave interactions," Signal Processing, vol. 42, pp. 291-309.

motion artefact on the detection of the QRS-complexes is not noticeable.

the motion artefact and the bicoherence squared of the EMG noise have frequencies that would potentially overlap with those of the QRS-complexes of the mother and the fetal, albeit at –20 dB level. The bicoherence squared of the EMG noise is spread over a wide band of frequencies, up to (120 Hz ,120 Hz). The carpet effect of the non-linearity attributed to the EMG noise will be significantly reduced by linearising the transabdominal signal prior to fetal QRS detection in the third-order statistical domain. Under broad signal and noise conditions, linearisation of the transabdominal ECG signals not only removes to a great extent the signal non-linearity, but also partially eliminates other types of non-linearity due

It could be deduced from Table 1 that there would be overlapping between the bispectral frequencies of motion artefact and those of the maternal and the fetal QRS-complexes, albeit at around –20 dB level. However, the level of noise at the QRS-complex spectra is comparatively small and by using QRS-complex tailor-made spectral windows, the effect of

Brillinger,D. R. (1965). "An Introduction to Polyspectra," *Annals of Mathematical Statistics*,

Brockett, P. L.; Hinich, M. J.; and Patterson, D. (1988). "Bispectral-Based Tests for the Detection of Gaussianity and Linearity in Time Series," Journal of the American

Friedlander, B. and Porat, P. (1988). "Performance analysis of MA parameter estimation algorithms based on higher-order moments*," Proceedings of IEEE Int Conf Acoustics,* 

Hinich, M. J. (1982). "Test for Gaussianity and linearity of a stationary time series," *Journal of* 

Kim, Y. and Powers, E. J. (1978). "Digital Bispectral Analysis of Self-Excited Fluctuation

Kim, S. B. and Powers, E. J. (1995). "Estimation of Volterra kernels via higher-order statistical signal processing," in *Higher order statistical signal processing*, (Boashash,

Kravtchenko-Berejnoi, V. et al. (1995). "On the use of tricoherent analysis to detect nonlinear

Lii, K. S. (1982). "Non-Gaussian ARMA model identification and estimation," Proceedings


Rosenblatt, M. (1985). *Statistical Sequences and Random Fields*, Birkhauser, USA.

Rosenblatt, M. (1983). "Cumulants and Cumulant Spectra," in *Handbook of Statistics*, vol. 3, (D. Brillinger, and P. Krishnaiah, eds.), Amesterdam, Holland, pp. 369-387.

**Chapter 3** 

© 2012 Papaioannou and Pneumatikos, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is

© 2012 Papaioannou and Pneumatikos, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Fractal Physiology, Breath-to-Breath Variability** 

Physiologic data measured at the bedside often display fluctuations at scales spanning several orders of magnitude. These fluctuations are extremely inhomogeneous and appear irregular and complex whereas in the medical literature, they are often regarded as noise and are neglected. However, they may carry information about the underlying structure or function of the heart and lungs. Examples include fluctuations in heart rate, respiratory rate, lung volume and blood flow [1]. The central task of statistical physics is to study macroscopic phenomena that result from continuous microscopic interactions among many different components. Particularly, physiologic systems such as the cardiovascular and respiratory systems, are good candidates for such an approach, since they include multiple components and are affected by varying neuro-autonomic inputs, continuously over time

Healthy state exhibits some degree of stochastic variability in physiologic variables, such as heart and respiratory rate. This variability is a measure of complexity that accompanies healthy systems and is responsible, according to Buchman, for their greater adaptability and functionality related to pathologic systems [2]. Loss of this variability has been shown to precede the onset of sepsis and multiple organ dysfunction syndrome (MODS) [3-6]. Studying physiological signals of critically ill patients, such as heart and respiratory rate can easily identify 'hidden' information concerning inherent dynamics and overall variability within time series [4]. Recognition that physiologic time series contain such information, related to an extraordinary complexity that characterizes physiologic systems, defies traditional mechanistic approaches based on conventional biostatistical methodologies and

**and Respiratory Diseases: An Introduction to** 

**Complex Systems Theory Application in** 

**Pulmonary and Critical Care Medicine** 

Vasilios Papaioannou and Ioannis Pneumatikos

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/3331

**1. Introduction** 

[1].

properly cited.

