The detection of transient abnormalities in the EEG of epileptic patients, known as “Interictal Epileptic Spikes”, may be used to determine the location of the “focus” or place of origin of the neurological malfunction. Epileptic Focus localization is important in the planning and performance of respective brain surgery for epilepsy.

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Interictal Epileptic “spikes” like the one indicated above in the EEG record really represent events in the time-varying surface potential field. These field events are characterized by their spatial and temporal sharpness.

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This Bubble Diagram of a focal interictal spike agrees with the hypothesis.

A “Bubble Diagram” displays a spatiotemporal EEG sample from  a 3 x 4 electrode array as a circle of radius proportional to the magnitude of the voltage. Shaded circles are negative voltages.


Two  independent and separable transformations are applied to the spatiotemporal data samples: The Spatial Laplacian (SL) , which measures the saptial sharpness of a spatio-temporal sample with respect to the rest of the samples collected at the same time.

The Temporal Laplacian (TL), which measures the temporal sharpness of a spatio-temporal sample with respect to data collected before and after, but in the same electrode location.

The space-time images of these transformations are multiplied on a point-to-point basis to obtain the Spatio-Temporal Laplacian (STL) field. In this field only data samples that were sharp in both space and time are emphasized.

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The STL Field is the product of the SL Filed and the TL Filed. In the STL Field only data samples that are sharp in both space 7 Time are emphasized. 


The STL Transformation is capable of isolating events in the time-varying surface potential field that are simultaneously sharp in space and in time, which characterizes focal interictal events in the EEG. If an event is only sharp in time (such as muscle artifact) or only sharp in space the STL transformation will not emphasize it.