Tracking EEG Thalamic and Cortical Focal Brain Activity using Standardized Kalman Filtering with Kinematics Modeling

TL;DR

This work addresses EEG source localization under depth bias by extending standardized Kalman filtering with higher-order kinematics. The Dynamical Standardized Kalman Filter (DSKF) incorporates first- and second-order state evolution for dipole activity and its velocity/acceleration, combined with a power-weighted post hoc standardization that mitigates depth bias. Simulation results with simultaneous thalamic and cortical sources show that 2-DSKF and 3-DSKF provide smoother, temporally distinct estimates and superior focal localization compared to SKF and SSKF, particularly under high noise. The approach holds promise for dynamic EEG applications such as epilepsy monitoring and real-time brain tracking, with future work including validation on real data, multimodal fusion, and adaptive parameter learning.

Abstract

Kalman filtering has proven to be effective for estimating brain activity using EEG recordings. In particular, the introduced post hoc standardization step of the algorithm, inspired by the sLORETA time-invariant method, reduces the depth bias and thus allows the estimation to appear at the correct depth from the electrode surface. In the current work, we propose first and second-order kinematic evolution models, where the state-space vector includes not only the dipolar source activity but also its velocity and acceleration. Compared to our previous study, this motion model yields smoother and more physically plausible estimates of brain activity even when the measurement noise is high, for both superficial and deep sources. In addition, we introduce a tunable power parameter that enhances the computational efficiency of the algorithm. Our simulation study, which involves thalamic and cortical activity in the somatosensory region, demonstrates that accurate estimation and tracking of both superficial and deep brain activity are feasible.

Figures (9)

• Figure 1: The first and third rows present the locations and directions of cortical (somatosensory cortex (first row), visual cortex (third row)) and deep (thalamic) dipolar sources used in data simulation. The sources are presented as black quivers within the brain model obtained from MRI data. The second and fourth rows show the regions of interest from which the activity strength is averaged for source strength tracking.
• Figure 2: Left: Plots of the simulated EEG data without noise and with the experimented noise levels: 30, 20, and 10 dB of noise. The x-axis shows the time in milliseconds, and the y-axis shows the signal strength scaled to 1. Right: The graph presents the time evolution of the activity strengths for the deep source placed in the thalamus (green) and the cortical source placed in the somatosensory cortex (turquoise). The x-axis shows the time in seconds, and the y-axis shows the activity strength in nanoampere-meters.
• Figure 3: Brain activity strength evolution in thalamus (green) and somatosensory cortex (blue). The solid, darker line represents the median over 20 estimations with different measurement noise realizations. Time runs on the x-axis, presented in milliseconds, and the y-axis shows the strength.
• Figure 4: Normalized cross-correlations of the estimated tracks of the activity in somatosensory and thalamus presented in Figure \ref{['fig:DynamicKFTracks']}. The colored area covers the 10 and 90 % interval around the median. A bold, solid curve presents the median track. The solid red horizontal line is the mean cross-correlation over the whole time period. This mean value is presented numerically on the right side of the graphs.
• Figure 5: Normalized cross-correlations of the estimated tracks of the thalamic activity (presented by green in Figure \ref{['fig:DynamicKFTracks']}) against the true track presented in Figure \ref{['fig:trueevolution']}. The colored area covers the 10 and 90 % interval around the median. A bold, solid curve presents the median track. The dashed light red horizontal line is the highest point of the median cross-correlation. This maximum value is presented numerically on the right side of the graphs.