Characterization of Interictal Epileptiform Discharges with Time-Resolved Cortical Current Maps Using the Helmholtz–Hodge Decomposition

Jeremy D. Slater, Sheraz Khan, Zhimin Li, Eduardo Castillo

Source estimates performed using a single equivalent current dipole (ECD) model for interictal epileptiform discharges (IEDs) which appear unifocal have proven highly accurate in neocortical epilepsies, falling within millimeters of that demonstrated by electrocorticography. Despite this success, the single ECD solution is limited, best describing sources which are temporally stable. Adapted from the field of optics, optical flow analysis of distributed source models of MEG or EEG data has been proposed as a means to estimate the current motion field of cortical activity, or "cortical flow." The motion field so defined can be used to identify dynamic features of interest such as patterns of directional flow, current sources, and sinks. The Helmholtz-Hodge Decomposition (HHD) is a technique frequently applied in fluid dynamics to separate a flow pattern into three components: (1) a non-rotational scalar potential U describing sinks and sources, (2) a non-diverging scalar potential A accounting for vortices, and (3) an harmonic vector field H. As IEDs seem likely to represent periods of highly correlated directional flow of cortical currents, the U component of the HHD suggests itself as a way to characterize spikes in terms of current sources and sinks. In a series of patients with refractory epilepsy who were studied with magnetoencephalography as part of their evaluation for possible resective surgery, spike localization with ECD was compared to HHD applied to an optical flow analysis of the same spike. Reasonable anatomic correlation between the two techniques was seen in the majority of patients, suggesting that this method may offer an additional means of characterization of epileptic discharges.