Fig 1.
Source space for the Utah array.
A. Schematic drawing of a piece of cortex enclosing the rectangular source space (black rectangle) and the Utah electrode array (red line). B. Close-up of the source space and Utah array. The array is located 1 mm under the pial surface. C. Two discretizations of the (intra-laminar) source space (left panel: high-resolution, right panel: low-resolution). Black dots and red circles denote the centers of source voxels and locations of the recording electrodes, respectively. In the high-resolution source space, each cortical slice contains 61 × 61 voxels with intra-laminar lengths of 100 μm. In the low-resolution source space, each cortical slice contains 18 × 18 voxels with intra-laminar lengths of 400 μm. The high and low resolution source spaces comprise 31 cortical slice, each 100 μm thick.
Table 1.
Linear distributed methods considered in this study.
First column: abbreviations of the methods’ names: (W)MNE = (weighted) minimum norm estimate, LORETA = low resolution electrical tomography, LORETA* = LORETA without weighting. Second column: corresponding prior structure on the intra-laminar CSD covariance matrix. W denotes a weighting matrix and Δ denotes the two-dimensional discrete Laplacian operator.
Table 2.
Free parameters and their values.
Listed are the free parameters, their symbols, units, and the two values they take on (Value 1 and Value 2).
Fig 2.
Simulation of evoked current source densities.
A. Inter-laminar current source density (CSD) component modeled by superficial (left) or deep (right) dipolar profiles. Deep and superficial are with respect to the electrode array, which is located at a depth of 1 mm (red line). Zero mm corresponds to the pial surface. B. Two (independent) realizations of simulated intra-laminar CSD components corresponding to local (left column) and global (right column) activations. Red and blue correspond to current sources (depolarization) and current sinks (hyperpolarization), respectively. Black dots denote the electrode locations (400 μm inter-electrode spacing).
Fig 3.
Limitations of the two-dimensional CSD method.
Bar plots of the average reconstruction errors for the (numerical) CSD method (yellow) and the MNE inverse method (green) and under each of the four CSD configurations. Errors were obtained by averaging over 500 independent realizations.
Fig 4.
Sensitivity of the Utah leadfield matrix.
A. Sensitivity profile of the leadfields along three intra-laminar (horizontal) slices at different cortical depths (left: 1 mm, middle: 1.4 mm, right: 1.8 mm). The Utah array is located at a depth of 1 mm. B. Sensitivity profile of the leadfields along three vertical slices at different lateral locations (left: through the center of the array and on the electrode line, middle: through the center of the array and off the electrode line, right: 200 μm lateral to the array). In all panels, the same color-scaling has been applied so that the sensitivities can be directly compared. Green and red correspond to low and high values, respectively. Black dots in A and B denote the electrodes of the 10 × 10 Utah electrode array (400 μm inter-electrode spacing).
Fig 5.
Proximity bias in high-resolution LFP imaging.
A. Reconstruction errors averaged over 100 independently generated evoked responses for each of the inverse methods. Intra-laminar spatial width of the responses was set to 0.45 mm, measurement noise was set to zero, and the responses were confined to the intra-laminar slice containing the electrode array. B. Single realization of a simulated evoked response (showing only the part that is covered by the electrode array). C. Reconstructions of the response in B. using the different inverse methods (MNE, WMNE, LORETA*, LORETA, dSPM, and sLORETA).
Fig 6.
Performance of the imaging methods.
A. Mean reconstruction errors for the four inverse methods (MNE (blue), WMNE (red), LORETA (green), and LORETA* (black)) as a function of noise-level and for each of the four combinations of simulated currents (superficial/deep and local/global). Noise-levels are 1, 5, 10, 15, and 20%. The mean errors were obtained by averaging over 500 realizations. B. Same format as in A. but displaying the error standard deviations instead of their means. In A and B, the solid lines correspond to the case of no mismatch in the a priori inter-laminar current profiles. The dashed lines correspond to the case of a mismatch in the a priori inter-laminar current profiles (see text).
Fig 7.
Effects of re-referencing the data.
Differences in mean reconstruction errors obtained using the average-reference montage and the single-wire montage for the four inverse methods (MNE (blue), WMNE (red), LORETA (green), and LORETA* (black)) as a function of noise-level and for each of the four combinations of simulated currents (superficial/deep and local/global). Noise-levels are 1, 5, 10, 15, and 20%. The mean errors were obtained by averaging over 500 realizations.
Fig 8.
Evoked potentials in macaque primary visual cortex.
A. Multiplot of the visually evoked potentials (VEPs) recorded at the 64 electrodes of the Utah array. Time ranges from 200 ms pre-stimulus to 500 ms post-stimulus. B. Close-up of the VEP at the lower-left corner of the electrode array (red trace in A). Time is relative to stimulus onset. The peaks selected for analysis is indicated by P1 and has a latency of 63 ms. C. Topographic map of P1. All potentials are relative to the single-wire reference.
Fig 9.
A. A priori inter-laminar CSD profile using in the inversion of P1. The profile is modeled by a dipolar generator of length 0.4 mm and is located 1.2 mm below the (modeled) pial surface. The horizontal red line indicates the depth of electrode plane. B. Reconstructed CSDs underlying P1 obtained using MNE (left), LORETA (middle), and the (numerical) CSD method (right). Blue and red correspond to superficial and deep generators, respectively.