Cortical Signal Suppression (CSS) for Detection of Subcortical Activity Using MEG and EEG

Abstract

Magnetoencephalography (MEG) and electroencephalography (EEG) use non-invasive sensors to detect neural currents. Since the contribution of superficial neural sources to the measured M/EEG signals are orders-of-magnitude stronger than the contribution of subcortical sources, most MEG and EEG studies have focused on cortical activity. Subcortical structures, however, are centrally involved in both healthy brain function as well as in many neurological disorders such as Alzheimer’s disease and Parkinson’s disease. In this paper, we present a method that can separate and suppress the cortical signals while preserving the subcortical contributions to the M/EEG data. The resulting signal subspace of the data mainly originates from subcortical structures. Our method works by utilizing short-baseline planar gradiometers with short-sighted sensitivity distributions as reference sensors for cortical activity. Since the method is completely data-driven, forward and inverse modeling are not required. In this study, we use simulations and auditory steady state response experiments in a human subject to demonstrate that the method can remove the cortical signals while sparing the subcortical signals. We also test our method on MEG data recorded in an essential tremor patient with a deep brain stimulation implant and show how it can be used to reduce the DBS artifact in the MEG data by ~ 99.9% without affecting low frequency brain rhythms.

Appendix

ASSR

To differentiate signals of acoustic origin in the tubephones from those of neural origin, the sound output at one of the earpieces was measured using a coupler of model G.R.A.S. Sound & Vibration IEC 60126 2 cc (Nærum, Denmark) connected to a sound level meter of model Larson Davis SoundTrack LxT2 (Depew (NY), US). The average loudness was measured to be 83 dB (A), although the sound level in the actual experiment was somewhat lower because the subject expressed discomfort with the loudness and it was subsequently decreased. The power spectral density (PSD) of the acoustic signal was computed using Slepian tapers with 5 s windows and 0.25 overlap fraction between windows and is shown in Fig. 8. There are several spectral peaks of mechanical origin that was not in the stimulus spectrum: 70, 80, 90, 116, 120, 133, 153, 180, 183, 263 and 273 Hz were all not in the digital stimulus signal but present in the acoustic ASSR signal and must therefore be the result of acoustic modes in the tubephones. Some of these peaks are also seen in the neural response (Fig. 6). However, there was no significant acoustic signal power at $f=63$ and $103\,\text{Hz}$, both of which were prominent in the neural ASSR data. These signals must thus either be of acoustic origin from the ear canal or inner ear, or of neural origin. Tracing the origin of these signals is difficult as it would either require invasive sound measurement or CFD simulations with very exact subject-specific anatomy, because flows through confined channels such as the inner ear have been shown to be extremely sensitive to shape variations (Samuelsson et al. 2015) and is beyond the scope of this paper.

Fig. 8

Power spectral density (PSD) normalized to the peak value at $\text{f}=40\,\text{Hz}$ of ASSR sound stimulus measured in dB(A). PSD was computed using a multi-taper sequence of Slepian tapers with 5 s time windows and 0.25 overlap fraction

PLV

Phase locking value (PLV) is the vector sum of phase differences between different channels. In our case, we have also included the phase difference at different time points because the neural ASSR is steady throughout the epoch after the initial transients. See Bharadwaj and Shinn-Cunningham (2014) for details on how to calculate PLV. If there is only noise at a particular frequency, there will be no phase locking in the neural response and the phase difference at that frequency will be random, uniformly distributed around the unit circle in the complex plane. In such a case, the magnitude of the average of the phase differences will be close to zero. Because we know that the neural response is phase-locked to the modulation wave form of the auditory stimulus, PLV is a good metric for SNR; a higher PLV implies a stronger neural phase locking response and a higher SNR.

How Does CSS Relate to a Wiener Filter?

Suppose that we have a contaminated signal $x$ and a signal of interest $y$ so that $x=y+n$ where $n$ is noise or some other signal of no interest. One can then filter the signal using a Wiener filter by

$$Y\left( z \right)=H\left( z \right)X\left( z \right),$$

where capital letter denotes the Z-transform of the signal and $H\left(z\right)$ is the Z-transform of the Wiener filter $h$ with the transfer function $H\left(z\right)=\sum _{i=0}^{N}{a}_{i}{z}^{-i}$, where ${a}_{i}$ are constants specific to the filter $h$. An optimal estimate $\widehat{y}$ of the signal of interest $y$ based on the measured signal $x$ is given by

$$\hat {y}={Z^{ - 1}}\left\{ {H\left( z \right)X\left( z \right)} \right\},$$

where H$\left(z\right)$ is found by solving the equation

$$\mathop \sum \limits_{{i=0}}^{N} h[i]{R_{xx}}\left[ {t - i} \right]={R_{yx}}\left[ t \right],$$

where $h\left[i\right]$ is the impulse response of the filter $h$, ${R_{xx}}[t - i]$ is the autocorrelation of x shifted by i time steps and ${R_{yx}}[t]$ is the cross-correlation between measured signal x and target process y. If the Wiener filter is of zeroth order, this equation simplifies to

$$\begin{aligned} h\left[ 0 \right]{R_{xx}}\left[ t \right] & ={R_{yx}}[t] \\ & =>h\left[ 0 \right]=\frac{{{R_{yx}}\left[ t \right]}}{{{R_{xx}}\left[ t \right]}}=\frac{{{C_{yx}}}}{{{C_{xx}}}}, \\ \end{aligned}$$

and the processed signal is simply

$$\hat {y}\left[ t \right]={Z^{ - 1}}\left\{ {H\left( z \right)X\left( z \right)} \right\}=h\left[ 0 \right]{Z^{ - 1}}\left\{ {X\left( z \right)} \right\}=\frac{{{C_{yx}}}}{{{C_{xx}}}}x\left[ t \right].$$

If our target process is the cortical signal in the magnetometer data $\widehat{{M}_{c}}$, an estimate can be obtained by Wiener filtering the gradiometer signal $G$ by using $M$ as the target process;

$$\widehat {{{M_c}}}={C_{mg}}C_{{gg}}^{{ - 1}}G.$$

This Wiener filter of zeroth order simply finds the common temporal subspace between the gradiometers and magnetometers, which represents the cortical component of the magnetometer data, as mentioned above. This cortical component of the magnetometer data can then be removed by an orthogonal projection to this Wiener filter on the raw signal M:

$$\widehat {{{M_d}}}=M - \widehat {{{M_c}}}=M\left( {I - {G^T}C_{{gg}}^{{ - 1}}G} \right),$$

which is exactly our original processing algorithm. CSS is then derived from this expression according to the outline in the “Methods” section. Our method can thus be seen as a tweaked version of an orthogonal projection to a zeroth order Wiener filter using gradiometer data as the corrupted signal and magnetometer data as target process.

CSS Further Explained

Figure 9 shows a graphic illustration of CSS. For a more detailed outline, see the pseudocode presented in Fig. 2 and the “CSS Method Theory” section.

Fig. 9

Illustration of CSS. ${{G}}_{{i}}$ and ${{M}}_{{i}}$ are the signals from gradiometer and magnetometer channel ${i}$, respectively. The vectors ${{U}}_{{i}=1,\dots ,204}$ are the gradiometer data represented in a new basis, arranged in descending order according to how well they correlate with the magnetometer data. ${\widehat{{S}}}_{{d}}$ is the estimate of subcortical sensor space signal based on the magnetometer data

In Detail, How Did We Apply CSS on the ASSR Data?

In summary, CSS was used in the following way on the ASSR data;

• 1. Average the gradiometer and magnetometer data over epochs

• 2. Orthonormalize the averaged gradiometer and magnetometer data

• 3. Cross-correlate the orthonormalized, averaged magnetometer data with the orthonormalized, averaged gradiometer data

• 4. Singular value decompose (SVD) the cross-correlation matrix

• 5. Find projection vectors $U$ by multiplying the averaged orthonormalized gradiometer data matrix with the left-sided singular vectors in the SVD of the cross-correlation matrix

• 6. Pick the top r rows of $U$, these are the projection vectors to be removed from the magnetometer/EEG data

• 7. For each epoch, project out the projection vectors from the magnetometer or EEG data