Fast Approximation of EEG Forward Problem and Application to Tissue Conductivity Estimation

TL;DR

This paper introduces a fast approximation method for the EEG forward problem that reduces computation time by approximating the lead field matrix across multiple conductivity configurations, enabling efficient tissue conductivity estimation.

Contribution

The authors propose a novel approximation approach for the EEG forward problem that significantly accelerates computations while maintaining accuracy, facilitating non-invasive tissue conductivity estimation.

Findings

Approximation method reduces computation time substantially.

No bias introduced in conductivity estimation.

Effective with simulated and real EEG data.

Abstract

Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to the conductivity of the different head tissues. Conductivity values are subject dependent, so non-invasive methods for conductivity estimation are necessary to fine tune the EEG models. To do so, the EEG forward problem solution (so-called lead field matrix) must be computed for a large number of conductivity configurations. Computing one lead field requires a matrix inversion which is computationally intensive for realistic head models. Thus, the required time for computing a large number of lead fields can become impractical. In this work, we propose to approximate the lead field matrix for a set of conductivity configurations, using the exact solution only for a small set of basis points in the conductivity space. Our approach accelerates the computing time, while controlling the approximation error. Our method is tested for brain and skull conductivity estimation , with simulated and measured EEG data, corresponding to evoked somato-sensory potentials. This test demonstrates that the used approximation does not introduce any bias and runs significantly faster than if exact lead field were to be computed.