On the usage of linear regression models to reconstruct limb kinematics from low frequency EEG signals

Abstract

Several works have reported on the reconstruction of 2D/3D limb kinematics from low-frequency EEG signals using linear regression models based on positive correlation values between the recorded and the reconstructed trajectories. This paper describes the mathematical properties of the linear model and the correlation evaluation metric that may lead to a misinterpretation of the results of this type of decoders. Firstly, the use of a linear regression model to adjust the two temporal signals (EEG and velocity profiles) implies that the relevant component of the signal used for decoding (EEG) has to be in the same frequency range as the signal to be decoded (velocity profiles). Secondly, the use of a correlation to evaluate the fitting of two trajectories could lead to overly-optimistic results as this metric is invariant to scale. Also, the correlation has a non-linear nature that leads to higher values for sinus/cosinus-like signals at low frequencies. Analysis of these properties on the reconstruction results was carried out through an experiment performed in line with previous studies, where healthy participants executed predefined reaching movements of the hand in 3D space. While the correlations of limb velocity profiles reconstructed from low-frequency EEG were comparable to studies in this domain, a systematic statistical analysis revealed that these results were not above the chance level. The empirical chance level was estimated using random assignments of recorded velocity profiles and EEG signals, as well as combinations of randomly generated synthetic EEG with recorded velocity profiles and recorded EEG with randomly generated synthetic velocity profiles. The analysis shows that the positive correlation results in this experiment cannot be used as an indicator of successful trajectory reconstruction based on a neural correlate. Several directions are herein discussed to address the misinterpretation of results as well as the implications on previous invasive and non-invasive works.

Figure 1. Illustration of the model and metric properties.

The left panel shows three datasets of temporal signals representing predictor variables at , and . The upper panel shows the predictands variables , which are identical to the predictors (i.e. they correspond to a linear model with ). Each dataset contains signals and 90% of them was used to train a linear regression model while the remaining 10% was used to evaluate performance. The linear regression model was used predict each dataset from itself and the others. For each case, the reconstructed signals and correlation results are shown in the middle panel. The effect of the artifact is revealed in the usage of the regression model and correlation to validate datasets 1 and 2, where the correlation values are approximately 0.23, despite having different frequencies.

Figure 2. Experimental design.

(A) Snapshot of the experimental setup showing a participant with the EEG electrodes (electrode locations are shown in the upper left of the picture), the visual reflective markers attached to the body, and the reaching apparatus. The participant has given written informed consent to publication of their photograph. (B) Examples of recorded trajectories for the hand of one subject during the reaching operations towards the target locations.

Figure 3. Scalp topography of power spectra changes of the EEG (relative to baseline from −1 to −0.6 s) averaged across all trials and participants.

Time in abscissa from −0.8 s to 0.8 s. Frequency in ordinate from 0 to 50 Hz at a resolution of 2 Hz. Movement onset occurs at s (solid black line in all graphs). Sensors above the contralateral and ipsilateral motor areas revealed a power increase in the slow wave range (4)Hz and a de-synchronization in the (8-12)Hz and (14-30)Hz frequency bands. Graph at the right lower corner represents the average across-sensors relative power spectra changes of the recorded EEG.

Figure 4. Topographies of changes in the power spectra averaged for all trials and participants (relative to baseline from −1 to −0.6 s with respect to the movement onset) in the (A) , (B) and (C) frequency bands.

Power increase in the slow wave range started at 300 ms prior to the movement onset and remained until 200ms relative to the movement onset. The de-synchronization in the and bands started 400 ms prior to the movement onset and remained until the end of the movement. (d) The source localization of the underlying EEG activity averaged for all trials and participants revealed a network of activation in the motor-related and neighboring areas prior to the movement onset, and the activation of the contralateral motor cortex during the execution of the movement.

Figure 5. (A,B) Distributions of and for all participants for decoding models evaluated with EEG in the very low (0–1) Hz, (8–12) Hz, (12,15) Hz, (14–30) Hz and (0–40) Hz frequency bands.

In the , and frequency bands, the distributions of have a significant zero-median distribution in X-, Y- and Z-dimension of the velocity. For the very low and the (0–40) Hz frequency bands the distributions of were positive and significantly different from zero, although the medians of the distributions obtained in the very low are notably higher than for the (0–40) Hz band. These results support the selection of the very low band to further study the decoding of hand velocity. (C,D) Decoding results using the very low (0–1) Hz frequency band. meanstd values of and in the decoding of hand velocity profiles using the very low frequency band for all participants plus overall mean.

Figure 6. Analysis of low frequency decoding results.

(A-E) Neural sources involved in encoding hand kinematic projected onto sagittal MRI slices, with dotted lines indicating the source location with the greatest contribution. Contralateral motor regions of the brain provided the greatest contribution in the decoding models that used (A) recorded and (B) shuffled data. No motor related brain region is involved in the decoding model that used (C) Random EEG&VEL, (D) Random EEG and (E) Random VEL. (F–G) Distributions of (F) and (G) for all participants for the real model (Recorded data) and the chance level models (Shuffled data, Random EEG&VEL, Random EEG and Artificial VEL). These results revealed no significant differences between the real model and the chance level models.

Figure 7. Examples for one of the participants of the source contribution and recorded vs estimated 3D velocity profiles and the corresponding trajectories in two of the targets (obtained with the decoding model that utilizes recorded data, shuffled data and random EEG data).

First column displays the measured velocity profiles and trajectories; the second, third and fourth columns display the time course of the reconstructed velocity profiles and the reconstructed trajectories.

Figure 8. Results of the decoding models for the progressive elimination of the number of electrodes.

(A–F) Neural sources involved in encoding hand kinematic projected onto sagittal MRI slices, with dotted lines indicating the source location with the greatest contribution. Contralateral motor regions of the brain provided the greatest contribution in the decoding models with 26, 25 and 23 sensors. No motor related brain region is involved in the other decoding models. (G–H) Distributions of (G) and (H) for all participants for decoding models built by progressive elimination of electrodes. These results indicate that significant similar results were obtained in the decoding models that utilize 26, 25, 23, 21 and 17 electrodes, but the results were significantly different and lower when utilizing 14 and 11 electrodes.

Figure 9. Examples for participant 1 for the decoding model that used recorded data with 26, 21 and 14 sensors.

Top: Location of the electrodes (black dots) used to built the decoding model and the removed electrodes (red crosses), and estimated neural sources involved in encoding hand kinematic projected onto sagittal MRI slices. Bottom: Recorded vs estimated 3D velocity profiles and trajectories in one of the targets. The first column displays the measured velocity profiles (upper panel) and trajectories (lower panel); the second, third and fourth columns display the time course of the reconstructed velocity profiles (upper panels) and the reconstructed trajectories (lower panel).