Bi-spectral analysis makes medication more manageable

Most biological systems, including the brain, are nonlinear systems that generate sinusoidal waves of different frequencies. The bioelectrical activity of millions of neurons in the brain contributes to the formation of an electroencephalogram (EEG) signal with complex nonlinear dynamics. The EEG signal is composed of complex waveforms that represent brain activity. Like other waveforms, they can be decomposed into a series of overlapping sinusoidal waves.

Bi-spectral analysis makes medication more manageable

Nassib Chamoun

Most biological systems, including the brain, are nonlinear systems that generate sinusoidal waves of different frequencies. The bioelectrical activity of millions of neurons in the brain contributes to the formation of an electroencephalogram (EEG) signal with complex nonlinear dynamics. The EEG signal is composed of complex waveforms that represent brain activity. Like other waveforms, they can be decomposed into a series of overlapping sinusoidal waves.

Most EEG equipment plots the frequencies and amplitudes of these sine waves using power spectral analysis, a technique that measures signal amplitude as a function of frequency. However, this cannot be used to determine relationships between sine waves of different frequencies because it performs only a linear interpretation of the signals. Nonlinear variations of sine waves and their relationships that result from subtle physiological changes in the brain cannot be detected.

Linear systems (top group of figures) produce independent component sine waves. In nonlinear systems (bottom group of figures), the interaction of two sine waves at 2 and 3 Hz produces a 5-Hz harmonic. As a result, any one of the three component sine waves can depend on each other or one in relationship to the other two.

Power spectral analysis represents the amplitudes of component sine waves as a function of their frequencies and cannot discern nonlinearities that exist. Therefore, the power spectrum of the signal generated by the linear system is identical to that generated by the nonlinear one.

Bi-spectral analysis quantifies the interaction between the component sine waves, and the bi-spectrum produces different results for signals generated by linear and nonlinear systems. In linear systems, no interaction of component sine waves is evident because all component waveforms are independent.

Bi-spectral analysis quantifies nonlinear relationships between waves by measuring the dependence of the phase angle of one component on the phase angles of other components. Finding such relationships provides information about subtle changes in EEG waveforms, and changes in brain activity due to the effects of administering anesthesia are easier to determine.

Aspect Medical Systems

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Natick, MA 01760

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