High-Resolution EEG Source Reconstruction from PCA-Corrected BEM-FMM Reciprocal Basis Funcions: A Study with Visual Evoked Potentials from Intermittent Photic Stimulation

Abstract

Modern automated human head segmentations can generate high-resolution computational meshes involving many non-nested tissues. However, most source reconstruction software is limited to 3 -4 nested layers of low resolution and a small number of dipolar sources ~10,000. Recently, we introduced modeling techniques for source reconstruction of magnetoencephalographic (MEG) signals using the reciprocal approach and the boundary element fast multipole method (BEM-FMM). The technique of BEM-FMM can process both nested and non-nested models with as many as 4 million surface elements. In this paper, we present an analogue technique for source reconstruction of electroencephalographic (EEG) signals based on cortical global basis functions. The present work uses Helmholtz reciprocity to relate the reciprocally-generated lead-field matrices to their direct counterpart, while resolving the issue of possible biases toward the reference electrode. Our methodology is tested with experimental EEG data collected from a cohort of 12, young and healthy, volunteers subjected to intermittent photic stimulation (IPS). Our novel high-resolution source reconstruction models can have impact on mental health screening as well as brain-computer interfaces.

Figure A1:

A. Circuital reciprocity theorem. B. Its application to a distributed circuit – a volume conductor.

Figure B1:

Source localization results for volunteers P01 and P03: the calcarine sulcus has been tagged in the WM and inflated WM surfaces with a magenta line. The corresponding P100 peaks of activation appeared in latencies 104 and 111 ms, respectively. The regularization and depth parameters were $\lambda =0.8$ and $\gamma =1.4$ for both volunteers.

Figure B2:

Source localization results for volunteers P05 and P06: the calcarine sulcus has been tagged in the WM and inflated WM surfaces with a magenta line. The corresponding P100 peaks of activation appeared in latencies 99 and 133 ms, respectively. The regularization and depth parameters were $\lambda =0.8$ and $\gamma =1.4$ for both volunteers.

Figure B3:

Source localization results for volunteers P08 and P10: the calcarine sulcus has been tagged in the WM and inflated WM surfaces with a magenta line. The corresponding P100 peaks of activation appeared in latencies 103 and 84 ms, respectively. The regularization parameters were $\lambda =0.8$ and $\lambda =2$ for each volunteer, respectively. The depth parameter $\gamma =1.4$ was used for both volunteers.

Figure B4:

Source localization results for volunteers P13 and P14: the calcarine sulcus has been tagged in the WM and inflated WM surfaces with a magenta line. The corresponding P100 peaks of activation appeared in latencies 90 and 85 ms, respectively. The regularization parameters were $\lambda =1.5$ and $\lambda =0.8$ for each volunteer, respectively. The depth parameter $\gamma =1.4$ was used for both volunteers.

Figure B5:

Source localization results for volunteers P15 and P16: the calcarine sulcus has been tagged in the WM and inflated WM surfaces with a magenta line. The corresponding P100 peaks of activation appeared in latencies 117 and 122 ms, respectively. The regularization parameters were $\lambda =0.8$ and $\gamma =1.4$ for both volunteers.

Figure B6:

Source localization results for volunteers P20 and P21: the calcarine sulcus has been tagged in the WM and inflated WM surfaces with a magenta line. The corresponding P100 peaks of activation appeared in latencies 97 and 112 ms, respectively. The regularization parameters were $\lambda =0.8$ and $\lambda =1.5$ for each volunteer, respectively. The depth parameter $\gamma =1.4$ was used for both volunteers.

Figure 1:

61-channel EEG system placement on volunteer P01 (facial features are blurred for the purpose of privacy). The reference electrode is indicated with a red sphere. After co-registration of electrodes, these are imprinted into the model by refining the skin mesh so as to represent a circular contact surface accurately.

Figure 2:

An example of the effect of applying projections to a basis function (central image). Here we show a basis function for volunteer P01, with the EEG electrode in blue and the reference electrode in red. The basis function has clear peaks near the EEG and reference electrodes. Notice how the average basis function (upper-left) —i.e., the average over the rows of the leadfield matrix— has the largest magnitude near the reference electrode. After subtracting this average to obtain the mean corrected basis function (upper-right), there is still a high magnitude near the reference (purple dashed circle). In comparison, when projecting to the space orhtogonal to the largest PCA component of the leadfield matrix (lower-left), the peak in potential near the reference is removed (lower-right).

Figure 3:

Source localization results for volunteer P01: the calcarine sulcus has been tagged in the WM and inflated WM surfaces with a magenta line. The corresponding P100 peaks of activation appeared at latency 104 ms, respectively. The regularization and depth parameters were $\lambda =0.8$ and $\gamma =1.4$, respectively.

Figure 4:

Source localization results for volunteer P20: the calcarine sulcus has been tagged in the WM and inflated WM surfaces with a magenta line. The corresponding P100 peaks of activation appeared at latency 97 ms, respectively. The regularization and depth parameters were $\lambda =0.8$ and $\gamma =1.4$, respectively.