Localization bias and spatial resolution of adaptive and non-adaptive spatial filters for MEG source reconstruction

Abstract

This paper discusses the location bias and the spatial resolution in the reconstruction of a single dipole source by various spatial filtering techniques used for neuromagnetic imaging. We first analyze the location bias for several representative adaptive and non-adaptive spatial filters using their resolution kernels. This analysis theoretically validates previously reported empirical findings that standardized low-resolution electromagnetic tomography (sLORETA) has no location bias. We also find that the minimum-variance spatial filter does exhibit bias in the reconstructed location of a single source, but that this bias is eliminated by using the normalized lead field. We then focus on the comparison of sLORETA and the lead-field normalized minimum-variance spatial filter, and analyze the effect of noise on source location bias. We find that the signal-to-noise ratio (SNR) in the measurements determines whether the sLORETA reconstruction has source location bias, while the lead-field normalized minimum-variance spatial filter has no location bias even in the presence of noise. Finally, we compare the spatial resolution for sLORETA and the minimum-variance filter, and show that the minimum-variance filter attains much higher resolution than sLORETA does. The results of these analyses are validated by numerical experiments as well as by reconstructions based on two sets of evoked magnetic responses.

Fig. 1

The coordinate system used in the numerical experiments. The coordinate origin was set at the center of the sensor coil located at the center of the array. The plane at x = 0 cm is shown. The circle indicates the boundary of the sphere used for the forward calculations. The center of the sphere was set to (0, 0, −12).

Fig. 2

The plot of the square of the resolution kernel ℛ(r, r₁)² on the plane x = 0. The point source is located at (0, −1.5, −6) cm. The contour plots in the left-hand side from top to bottom, respectively, show the results of the minimum-norm filter, the lead-field normalized minimum-norm filter, and the weight-normalized minimum-norm filter. The plots in the right-hand side from the top to the bottom, respectively, show the results of sLORETA, the minimum-variance filter, and the lead-field normalized minimum-variance filter. The cross mark × indicates the source location. Each contour map is normalized by its maximum value and contains the same number of contour lines.

Fig. 3

The results of the experiments regarding the effects of noise on location bias. (a) Results of point-source reconstruction from sLORETA and (b) those from the lead-field normalized minimum-variance filter. The point source is located at (0, −1.5, −6) cm. The contour plots from top to bottom, respectively, show the results for the input SNR α equal to 8M, 4M, and M. The cross mark × indicates the source location. Each contour map is normalized by its maximum value and contains the same number of contour lines.

Fig. 4

The plot of the point-spread function (the normalized resolution kernel) in the horizontal (y) direction. The three solid lines indicate the spread-function of the minimum-variance filter for the cases of α = 8M, α = 4M, and α = M. The broken line indicates the point-spread function of sLORETA. The point source was assumed to exist at (0, 0, −6), and the abscissa expresses the distance from the source location in the y direction.

Fig. 5

The averaged somatosensory response obtained using a 160-channel whole head sensor array (MEGVISION, Yokogawa Electric Corp, Tokyo, Japan) with an electric stimulus. The stimulus was delivered to the right median nerve at the subject’s wrist with a 250-ms interstimulus interval. An epoch was digitized at 10 kHz sampling frequency and a total of 10,000 epochs were averaged. The recorded epochs were filtered with a bandpass filter of 3–300 Hz bandwidth.

Fig. 6

(a) The reconstructed source-magnitude map at latencies of 15.5, 16.5, and 18.5 ms obtained using sLORETA. (b) The reconstructed source-magnitude map obtained using the lead-field normalized minimum-variance filter at the same latencies. The maximum intensity projections of the reconstructed three-dimensional current density onto the axial, coronal, and sagittal planes are shown in the right, middle and left panels, respectively. The letters L and R show the left and right hemisphere, respectively. The circles depicting a human head indicate the projections of the sphere used in the forward calculations. Each contour map is normalized by its maximum value, and contains the same number of contour lines. The color of the contour lines shows the relative intensity indicated by the color bar.

Fig. 7

The average evoked magnetic responses recorded with simultaneously applied auditory and somatosensory stimuli using the 37-channel Magnes™ magnetometer. The auditory stimulus was a 1000 Hz pure tone with a 200-ms duration; it was applied to the subject’s right ear. The somatosensory stimulus was a 30-ms duration tactile pulse (17 psi) delivered to the distal segment of the right index finger. The data was acquired at a sampling frequency of 1 kHz and averaged for 256 epochs. An on-line bandpass filter with a bandwidth from 1 to 400 Hz was used and no post-processing digital filter was applied.

Fig. 8

(a) The reconstructed source-magnitude map at latencies of 60, 120, and 180 ms obtained using sLORETA. (b) The reconstructed source-magnitude map obtained using the lead-field normalized minimum-variance filter at the same latencies. The maximum intensity projections of the three-dimensional current density reconstruction onto the axial, coronal, and sagittal planes are shown in the right, middle and left panels, respectively. The letters L and R show the left and right hemisphere, respectively. The circles depicting a human head indicate the projections of the sphere used in the forward calculations. Each contour map is normalized by its maximum value, and contains the same number of contour lines. The color of the contour lines shows the relative intensity indicated by the color bar.