Linear inverse filtering improves spatial separation of nonlinear brain dynamics: a simulation study.

We examined topographic variations in nonlinear measures based on scalp voltages, which were generated by two simulated current dipoles each placed in a different hemisphere of a spherical volume conductor (three-shell model). Dipole dynamics were that of a three-torus and the x-component of the Lorenz-system and scalp voltage were calculated for a configuration of 29 electrode positions. Although estimates for correlation dimension D2 and Lyapunov exponent L1 were close to the theoretical values for the original time series, the simulated scalp voltage data showed almost no topographic resolution of dipole positions. In order to enhance topographic differentiation, we constructed linear inverse filters, to focus on brain activity from a specified brain region. It turned out that the nonlinear measures for the inversely filtered time series were much closer to the expected values (with respect to the location of the dipoles used in the simulation) than when using unfiltered data. Our preliminary results indicate that inverse filtering can improve the topographic resolution of nonlinear scalp EEG estimates.