Scalp EEG is not a Blur: It Can See High Frequency Oscillations Although Their Generators are Small

Abstract

High frequency oscillations (HFOs) are emerging as biomarkers of epileptogenicity. They have been shown to originate from small brain regions. Surprisingly, spontaneous HFOs can be recorded from the scalp. To understand how is it possible to observe these small events on the scalp, one avenue is the analysis of the cortical correlates at the time of scalp HFOs. Using simultaneous scalp and intracranial recordings of 11 patients, we studied the spatial distribution of scalp events on the cortical surface. For typical interictal epileptiform discharges the subdural distributions were, as expected, spatially extended. On the contrary, for scalp HFOs the subdural maps corresponded to focal sources, consisting of one or a few small spatial extent activations. These topographies suggest that small cortical areas generated the HFOs seen on the scalp. Similar scalp distributions corresponded to distinct distributions on a standard 1 cm subdural grid and averaging similar scalp HFOs resulted in focal subdural maps. The assumption that a subdural grid “sees” everything that contributes to the potential of nearby scalp contacts was not valid for HFOs. The results suggest that these small extent events are spatially undersampled with standard scalp and grid inter-electrode distances. High-density scalp electrode distributions seem necessary to obtain a solid sampling of HFOs on the scalp. A better understanding of the influence of spatial sampling on the observation of high frequency brain activity on the scalp is important for their clinical use as biomarkers of epilepsy.

Appendix

Linear Model

There is a linear relation between subdural contacts and scalp, since tissue in between (skull, scalp, dura) is purely resistive at the frequencies of interest. Thus, it is possible to create a linear model of the form

$$mScalp_{M \times N} = G_{M \times K} \times mIEEG_{K \times N} ( + error)$$

(2)

or in matrix form (ignoring the error term)

$$\left[ {\begin{array}{*{20}c} {sScalp_{Ch1}^{HFO1} } & \ldots & {sScalp_{Ch1}^{HFON} } \\ \ldots & \ddots & \vdots \\ {sScalp_{ChM}^{HFO1} } & \ldots & {sScalp_{ChM}^{HFON} } \\ \end{array} } \right] = G_{M \times K} \left[ {\begin{array}{*{20}c} {sIEEG_{Ch1}^{HFO1} } & \ldots & {sIEEG_{Ch1}^{HFON} } \\ \ldots & \ddots & \vdots \\ {sIEEG_{ChK}^{HFO1} } & \ldots & {sIEEG_{ChK}^{HFON} } \\ \end{array} } \right]$$

where mScalp is an M×N matrix containing the concatenated scalp EEG signal ($sScalp_{Chi}^{HFOi} )$; mIEEG is a K×N matrix containing the concatenated intracranial EEG signal at the time of the scalp events ($sIEEG_{ChM}^{HFO1} )$; and G_M×K is the forward model to estimate. M is the number of scalp channels; K is the number of subdural channels; and N is the number of scalp events.

Assuming that the noise is Gaussian the matrix G_M×K can be obtained from the training set by

$$G_{M \times K } = (mIEEG_{train}^{'} \times mIEEG_{train} )^{ + } \times mIEEG_{train}^{'} \times mScalp_{train}$$

(3)

where train are the training events; ′ is the transpose operator; ⁺ is the inverse of the matrix (pseudo inverse since these are non-square matrices). G_M×K is estimated for all but one event at each run. We estimated the matrix G_M×K using the backslash operator in Matlab which provides the least square solution. At each run the estimated mScalp_test event was obtained as

$$mScalp_{test} = G_{M \times K} \times mIEEG_{test}$$

(4)

This procedure was repeated for all events in the leave one out schema.