Structural MRI scans were collected from one healthy young subject at Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital. The subject gave written informed consent, and the study protocol was approved by the Massachusetts General Hospital Human Research Committee. Brain structural anatomical details were obtained from a T1-weighted multi-echo sequence (MEMPRAGE, TR/TE/TI = 2,530/1.64/1,200 ms, 7° flip angle, 1.0 × 1.0 × 1.0 mm³ voxel resolution) and a fast low-angle shot gradient echo sequence (FLASH, TR/TE = 20/1.85 ms, 5° flip angle, 1.3 mm sagittal slice thickness, 1.3 × 1.0 mm² in-plane resolution) using a 12-channel RF receive coil array on a 3T Siemens TrioTM MR scanner. An equidistant 128-channel montage (WaveguardTM, ANT Neuro, The Netherlands) was used for EEG electrode placement, and electrode positions were digitized using the Polhemus FastSCAN II laser scanner, aligned to the subject's structural MRI based on fiducial points (nasion and preauricular points) using the iterative closest point algorithm, and projected onto the scalp surface.

We used forward models to quantify changes in the EEG signal that would occur under varying levels of cortical shrinkage. A forward model maps the cortical currents to electric potentials on scalp, measured in EEG (Sarvas, 1987; Mosher et al., 1999). Following well-established methods developed for EEG/MEG source localization and brain stimulation, we represented cortical currents as distributed current dipoles normal to the cortical mantle (Dale and Sereno, 1993) and calculated the corresponding scalp surface potentials using the Boundary Element Method (BEM) (De Munck, 1992; Gramfort et al., 2014). BEM formulates the bioelectric volume conduction problem using well-known surface integral equations that are solved in discretized form using triangulated boundary surfaces (Geselowitz, 1970; Horacek, 1973; Hamalainen and Sarvas, 1989). Many BEM modeling problems require only three layers: the skin, the skull, and the brain. In this work, an additional CSF layer was incorporated to capture the effect of altered conductivity distribution due to an expanded CSF compartment during aging.

We constructed both spherical and realistic MRI-based EEG volume conductor models. Current dipoles were fixed with orientations normal to the cortical surface, motivated by the understanding that the primary currents producing the EEG signals are believed to come from pyramidal cells aligned perpendicularly to the cortical surface (He et al., 2018). Four-layer spherical volume conductor models were built using the MNE-Python software (Gramfort et al., 2013) evaluated with spherical harmonic expansion (Berg and Scherg, 1994). Since scalp potentials in spherical models are solved with closed-form expressions, these models provide theoretical verification and generalization of the results in realistic models based on the single MRI scan. The layers are constituted of skin, skull, CSF, and brain with relative outer radii of 1.0, 0.90, 0.83, and 0.78. These radii were empirically derived from distances on the subject's T1 structural scan, using the average of distances measured in Freeview from the origin of the scan acquisition to the most anterior, posterior, and superior points of respective tissue types. A total of 2562 source dipoles were positioned on a sphere just beneath the brain sphere (0.99 times the brain radius). Based on existing literature describing the range of electrical conductivities for different head tissues (Mahdavi et al., 2018; Saturnino et al., 2019), conductivity values of 0.3, 0.006, 1.5, and 0.3 S/m were assigned to skin, skull, CSF, and brain tissues, respectively.

In the four-layer MRI-based realistic volume conductor models, we computed the electromagnetic field using the BEM solutions to approximate boundary surface potentials. Tissue segmentation and mesh construction of boundary surfaces were initialized by running two SimNIBS processing pipelines using default settings: (1) “mri2mesh” based on a FreeSurfer 6.0 reconstruction (Windhoff et al., 2013), and (2) “headreco” based on the CAT12 and SPM12 toolboxes (Nielsen et al., 2018). FLASH images were used in place of the T2-weighted images that are typically used in the SimNIBS pipeline to improve tissue segmentation. The initial pial surface output of “mri2mesh” was corrected for “over-grabbing” of skull regions on the brainmask as often described in FreeSurfer quality control pipelines (http://freesurfer.net/fswiki), and “mri2mesh” was repeated with this corrected pial surface to provide an improved, updated tissue segmentation.

The gray matter/white matter boundary surface from “mri2mesh” was used to construct the source space in MNE-Python using a total of 20484 current dipole sources spanning the cortical surface. The pial, cerebellum, and inner skull (CSF) surfaces were obtained from “mri2mesh.” For the outer skull surface, CAT12 within the “headreco” pipeline provided more accurate segmentation of bone structures compared to “mri2mesh.” However, “headreco” outlined facial bone structures that were too detailed than appropriate for BEM solutions. Therefore, we constructed a hybrid outer skull surface combining the superior and posterior quadrants obtained with “headreco” and the anterior-inferior (facial) quadrant obtained using “mri2mesh” (see Supplementary Material for more details). Finally, the skin surface was extracted using the FreeSurfer watershed algorithm, which produced smoother surface estimates more appropriate for BEM modeling than “mri2mesh” or “headreco.” Figure 1 shows the final BEM surfaces. Additional details about the forward model, including smoothing parameters and vertex numbers, are included in the Supplementary Material. We assigned skin, skull, CSF, and brain tissues with conductivity values of 0.3, 0.006, 1.5, and 0.3 S/m, respectively, just as in the spherical models. The compartments inside the cerebellum and pial surfaces were both labeled as brain tissue.

Forward model gain matrices for the realistic models were obtained by solving the four-layer BEM problem. A direct non-iterative solver can be applied to the standard BEM formulation although this limits the resolution of the volume conductor model. Approaches utilizing the Fast Multipole Method (FMM) acceleration have been developed (Kybic et al., 2005) for high-resolution models but iterative numerical solvers are needed (Makarov et al., 2021). Here, the standard BEM formulation allows modeling CSF with adequate spatial resolution, and we selected a validated and efficient linear collocation BEM solver using the isolated source approach (Stenroos and Nummenmaa, 2016).

We simulated the overall structural effect of brain atrophy by shrinking the radius of the brain while maintaining the dimensions of the other tissue layers, i.e., skull and scalp. This “brain shrinkage” moves cortical dipoles away from the scalp and expands the CSF layer, in a manner analogous to age-related brain atrophy. This whole-brain shrinkage was implemented by reducing the distance from each source to the median centroid of all source dipoles by varying percentages of 0-30% in increments of 5% in both the spherical and realistic MRI-based models. We maintained the same number of dipoles across all levels of shrinking. For the spherical models, due to symmetry, only a single electrode was needed to characterize power reductions measured on the scalp (Figure 2A). To simulate the EEG signal changes, a patch of 20 source dipoles (~3.5 cm²) closest to the scalp EEG electrode was activated, while keeping the other sources silent. Each dipole in the active patch was assumed to have the same amplitude. The power reduction for each shrinkage value was calculated directly from the forward model gain matrices (see Supplementary Material for details).

In the realistic models, simulated shrinkage affected different cortical regions slightly differently due to anatomical variations and non-spherical geometry. The pial surface and the dipole locations were shrunk over the same range of percentages, 0-30% in 5% increments, to model the expansion of the CSF layer under cortical atrophy (Figure 2B). We estimated the corresponding average CSF thickness for each shrinkage value by computing the mean nodal projection distance from the CSF surface vertices to the pial/cerebellum surfaces (0% = 2.9 mm, 5% = 5.8 mm, 10% = 8.9 mm, 15% = 12.0 mm, 20% = 15.3 mm, 25% = 18.6 mm, 30% = 22.0 mm). CSF thickness can be estimated to be between 3-6 mm in normal aging (Pfefferbaum, 1990; Salat et al., 2004), while severe AD patients have been reported to have CSF thicknesses of up to 10 mm (Ancora et al., 2018). Thus, cortical shrinkage values of up to 10% (8.9mm) are within a physiologically plausible range, but global shrinkage above 10% would be implausible. Power reductions were computed at each of 128 electrodes to adequately sample EEG signals across the whole scalp. Similar to the approach for the spherical models, for each EEG electrode position, we activated the top 20 source dipoles with the highest squared gain magnitudes and estimated the power reduction over a local neighborhood of 4 to 7 electrodes. This procedure was repeated for each electrode position to estimate the average overall power reduction. We show a 2D topological plot of the electrode montage and neighboring electrodes in the Supplementary Material (Supplementary Figure 1). All active dipoles were assumed to have the same amplitude. Therefore, power reductions were calculated directly from the forward model gain matrices (see Supplementary Material for details). The final power reduction for each shrinkage value was represented using the mean and standard deviation of dB differences across all 128 electrodes.

As described earlier, we set the tissue conductivities in our models to values at the midpoints of the published ranges. However, multiple studies have highlighted how uncertainties in skull and CSF conductivities can impact on the accuracy of forward models (Gençer and Acar, 2004; Stenroos and Nummenmaa, 2016; Saturnino et al., 2019; Vorwerk et al., 2019; Koulouri and Rimpilainen, 2020). In addition, several studies have noted that tissue conductivities can change with advancing age (Wendel et al., 2010; Moskalenko et al., 2011; Mohammed et al., 2017; Thomas et al., 2018). To better understand the sensitivity of EEG power reductions to variations in CSF and skull conductivities, we repeated the cortical shrinkage simulations employing the full ranges of reported CSF and skull conductivity values (CSF: 1.2–1.8 S/m in 100 steps, skull: 0.003–0.015 S/m in 100 steps). The conductivities were varied in a spherical model with a fixed shrinkage percentage of 10%, which corresponds to a mean CSF thickness of 8.9 mm in the realistic models, approximating the largest physiologically plausible shrinkage encountered in aging. Spherical models instead of realistic models were used for this analysis to increase generalizability of the results and to decrease computation time in sampling the conductivity space with high resolution.

Figure 3A shows the EEG power reductions observed in spherical models at different levels of cortical shrinkage. At the unrealistically high 30% level of shrinkage, we observed a power reduction of less than 10 dB compared to the original spherical volume conductor model. At more physiologically plausible shrinkage values of 5 and 10%, simulated power reductions were 2.5 and 4.4 dB, respectively. In Figure 3A, we also illustrate the difference in the lead field matrix (LFM) absolute gain for a given electrode at 30% shrinkage compared to no shrinkage. The highest attenuation of measured source activity occurred directly below the measured electrode, as one would predict from principles of volume conduction. This observation corroborates our decision to activate the 20 dipole sources nearest to the electrode (see Supplementary Figure 2), since doing so provides an approximate upper bound on the power reductions that could be expected from a given level of shrinkage.

Figure 3B shows the EEG power reductions (mean and standard deviation) across different levels of brain shrinkage, averaged across all active source patches and electrode positions. Power reduction values in these realistic models were similar to those observed under the spherical models. At the highest level of shrinkage (30%, mean CSF thickness = 22.0 mm) simulations produced less than 10-dB power reductions compared to the intact model with no shrinkage. Meanwhile, at physiologically plausible 5% and 10% levels of shrinkage, we obtained power reductions of 2.1 dB (std = 0.9) and 3.7 dB (std = 1.1), respectively. In Figure 3B, we plot the difference in the LFM absolute gain for a frontal electrode at 30% shrinkage compared to no shrinkage. Similar to the spherical models, gain magnitudes decreased with increasing distance from the electrode, albeit with variations that reflect the changing dipole orientations along cortical folds. Since the quasistatic approximation of Maxwell's equations applies in EEG at physiological frequencies <100 Hz, the shrinkage-dependent attenuation we calculate here is frequency independent in the frequency range of interest (Supplementary Figure 3).

Figure 3C shows, for a fixed cortical shrinkage of 10%, how the EEG attenuation changes as a function of varying CSF and skull conductivities. This analysis shows that changes in conductivity across wide ranges can alter the EEG attenuation by at most 0.5 dB. EEG signal attenuation is therefore relatively insensitive to uncertainties in tissue conductivity. This result is compatible with previous findings of the sensitivity of EEG amplitudes to tissue conductivities (Stenroos and Nummenmaa, 2016), as the power reduction quantified here in the dB scale takes the ratio between shrinkage values, which normalizes out absolute changes on EEG amplitudes.