An application of fractal dimension to the detection of transients in the electroencephalogram

Abstract

It is sometimes desirable to identify a brief seizure, occasional spike, single evoked potential, or other transient in the EEG. Transient detection in an EEG can be a difficult task, often requiring prior knowledge of the characteristics of the transient. A fractal is a shape which retains structural detail despite magnification (scaling). The complexity of the structure of such a set, invariant under this scaling, can be characterized by a single number: the fractal dimension. Regarding the EEG as a fractal, we have shown that transient deterministic data in the EEG have a fractal dimension different from the quasirandom background. An extensive introduction to fractals is presented with the assumption that the reader is unfamiliar with the theory. In the preliminary results presented here, analysis by fractal dimension is shown to be a promising method of transient detection, requiring no prior knowledge of the characteristics of the transient. Possible applications of the technique to evoked potential technology and epilepsy surgery are discussed. Other applications to biology, neuroscience and medicine are reviewed.