Medical background information

The human brain consists of 100 billions of interconnected neurons performing tasks in information storage and processing. The transmission of information between neurons is based on changes in the electric potential of the electrically excitable neuron cells. Consequently the brain continously creates various electric fields; their non-periodically varying superposition can be measured at the surface of the scull. Similarly to the case of the electrocardiogram electrodes - typically 8 or more - located at different positions allow for a local measurement of the brain activity. The frequencies and amplitudes of the so-called brain waves thus obtained yield information about ongoing processes within the brain and can be used for diagnostic purposes.

ECG-recording of 3 heart beats

Typically the amplitudes of the measured EEG-potential lie in the range from 10 to 150 microvolt. Depending on their frequency brainwaves are roughly classified as alpha-waves with a frequency of 8-12 hertz and an amplitude below 50 microvolt, beta-waves possessing 14-32 hertz and amplitudes below 30 microvolt, and delta-waves with 1-4 Hertz and high amplitudes between 100 and 150 microvolt. It is known that alpha-waves normally appear when the brain rests, beta-waves are a typical phenomenon during thinking, while delta-waves shine up during sleep.

The EEG is one of the most complex biosignals of the human body and can be utilized as an indicator for external influences. In this context the project partner Rayonex Schwingungstechnik GmbH plans to use EEGs for the scientific investigation of the so-called Bioresonance method, a curative procedure not yet accepted in the traditional medical science, and therefore financially supports the development of improved methods of EEG analysis.

Frequency und Damping of EEG-Signal

Approach

A standard method in the analysis of biosignals consists of considering the signal as a superposition of simple components. The type and occurence of the various components appearing in a concrete signal are viewed as characterising the signal and can be utilized for example for the medical classification of the signal for diagnostic purposes. Simple signal components for example are harmonic oscillations of varying frequencies and amplitudes. In mathematics the standard procedure to decompose a signal into such harmonic components is the (harmonic) Fourier analysis. Fast decomposition algorithms are available since a long time.
However Fourier analysis has some drawbacks: the frequencies computed are always fractions of the signal length and thus a priori have no connection to signal-inherent frequencies, if the signal is a superposition of certain harmonic oscillations. In fact the inherent frequencies are approximated by the Fourier frequencies, however there exists no simple method to decide whether a certain Fourier frequency is signal-inherent or not. Furthermore it is difficult to extract damping coefficients from the data obtained by Fourier analysis of a signal that is known to be the superposition of damped harmonic oscillations. The latter problem can be solved theoretically by extending the set of simple signal components by damped harmonic oscillators with varying frequencies and damping coefficients. Then depending on the properties of the signal a choice has to be made among the infinitely many possibilites for the value of the frequency and the damping coefficient as to which ones fit best with the signal. Based on the theory of anharmonic Fourier series the project partner professor Joachim Petzold developped a method to perform this choice. In the project this method is implemented in the mathematical programming language Matlab and is tested. The method also includes a criterion to check whether a given frequency and amplitude is signal-inherent or not. The graphic shows frequencies (horizontal axis) and the associated damping coefficients (vertical axis) extracted from an EEG-signal of 20 seconds in length with the method just mentioned. The radius of the circles drawn around each data point corresponds to the dominance of the associated frequency within the EEG-signal.