Generator localization by current source density (CSD): implications of volume conduction and field closure at intracranial and scalp resolutions.

Left. Volume conduction from a fixed point sink at 950 μm depth, 50 μm lateral offset, and source at 450 μm, 50 μm lateral offset, shown in two dimensions. The recording electrode axis corresponds to the path of a single recording contact as it is inserted into the conductive medium at different depths. This track is aligned 50 μm lateral to each of the two poles. Although the electrode can only sample the potential on this axis (i.e., lateral offset = 0), the source and sink yield predictable potentials throughout the medium. Isopotential contours are indicated for positive (nearer to source; <700 μm depth) and negative (nearer to sink; >700 μm depth) curves. These potentials are sampled at eight distinct equidistant depths (large dots on recording electrode axis at multiples of 200 μm), producing the potential profile on the right. Using the electrode at 600 μm depth as an example, the potential measured at the recording contact (circled positive potential) may be directly computed from Eq. 1 as the sum of contributions from the sink (I is negative; d = length of arrow from sink) and source (I is positive; d = length of smaller arrow from source) contributions. This simplistic model may be generalized to compute forward solutions from any number, area, or volume of known generators in (piecewise) homogeneous media.

Auditory click-evoked potentials (AEP) recorded from 16-channel multicontact stainless steel electrodes (25 μm diameter, 100 μm intercontact spacing; Barna, Arezzo and Vaughan, 1981) during a transcortical penetration through primary auditory cortex of the monkey (subcutaneous needle electrode recording reference anterior to contralateral ear; >200 trials/average), with a trajectory approximately orthogonal to the surface of the superior temporal plane (from Tenke et al., 1987). A. Cortical dipole. AEP waveforms at sequential depths below the ipsilateral frontal dura reveal a cortical dipole, with depths indicated at left. At a shallow depth of 5 mm, the auditory brainstem response (ABR), initial negativity (N), and dual positivity (P12, P24) are all visible (see inset; positive up). Although the surface-to-depth AEP inversion across the cortex is simple (compare waveforms at 20 mm and 26 mm), the inversion sequence is complex within the generating tissue. B. Concurrent multicontact AEP, CSD (3-point algorithm) and multiunit activity (MUA; 500–10,000 Hz bandpass, rectified) at intracortical sites surrounding the AEP inversion (22.3–24.0 mm). The activity pattern for the waveforms marked in gray at 23.3 mm and 23.4 mm is consistent with thalamocortical activation of layer IV. The early sink in layer IV and subsequent sinks in supragranular layers (23 and 22.9 mm) arise from distinct cellular populations, with open- and closed-field properties evident for each in the balance of concurrent sources.

Nose-referenced ERP [μV] and CSD [μV/m2] topographies for different EEG montages (71, 67, or 31 channels) at the peak latency of N1 evoked by different auditory stimuli (spherical spline interpolations using constants of m = 4 for flexibility, λ = 10−5 for smoothing, and 50 iterations; cf. Perrin et al., 1989). A. Brief binaural tones (40 ms; 1000 Hz) presented during a loudness-dependency paradigm (no behavioral response required) as a function of stimulus intensity (60–100 dB; N = 127; number of trials/condition, M = 85 ± 11). B. Frequent binaural (300 ms; 1000 Hz; 85 dB; pure tones; N = 98; number of trials/condition, M = 222 ± 25; data from Tenke et al., 2010) and dichotic (250 ms; 444 or 485 Hz; 72 dB; complex tones; N = 64; number of trials/condition, M = 120 ± 34; data from Tenke et al., 2008) nontargets presented during oddball tasks. C. Infrequent binaural nontargets (100–400 ms; 85 dB; environmental sounds; N = 98; number of trials/condition, M = 30 ± 6; data from Tenke et al., 2010).

Comparison of surface potentials and surface Laplacian for auditory ERPs (complex tones) to targets (right-hand button press) during an auditory oddball paradigm (N = 66; number of trials, M = 26.3 ±5.5; data from Kayser and Tenke, 2006a). A. ERP waveforms [μV] referenced to linked mastoids (LM; TP9/10) or nose tip (NR) and current source density (CSD) waveforms [μV/m2] at selected midline (Fz, Cz, Pz) and lateral (T8, C3, C4) sites. Perpendicular lines (orange) indicate peak latencies of prominent deflections in these ERP and/or CSD waveforms typically associated with distinct ERP components (e.g., N1, P2, N2, P3; negative up). B. Scalp field potential (LM, NR) and surface Laplacian (CSD) topographies (31-channel EEG montage; top view of scalp, nose at top; radial 2-D projection by linear extension of spherical spline interpolation [m = 2, no smoothing; cf. Perrin et al., 1989]) corresponding to the peak latencies (ERP components) indicated in A. Note the different scales for each component (symmetric for N1, temporal N1, and P2; optimized for range for N2, P3, and frontal response-related negativity [FRN]).

Dipole forward solution manually positioned to approximate unilateral current source density (CSD) topography of an auditory N1 (cf. Fig. 3). A. Dipole location, orientation, and nose-referenced topography (Dipole Simulator; Berg, 2006; time course is arbitrary). B. Corresponding surface potential (SP [μV]) and Laplacian (CSD [μV/m2]) topographies, with maximal sink at site C3, and corresponding source maximal over inferior temporal sites. C. This surface potential topography is similarly mapped using sLORETA (v2008-11-04; Pascual-Marqui, 2002), which yields an inverse solution that approximately matches the surface Laplacian.

Implications of spatial density and spline flexibility on CSD topography of auditory N1 to 100 dB tones shown in Fig. 3A. A. Nose-referenced ERP [μV] and CSD [μV/m2] topographies at N1 peak latency for different montage densities (71-channel and 30, 24, or 16-channel subsets; m = 4, λ = 10−5, 50 iterations for all CSD maps). B. CSD topographies at N1 peak latency (cf. 71-channel ERP topography in A), computed using different spline flexibilities (m = 2–5).

A, B. Coronal section through a bilateral cortical generator located deep or superficially within the longitudinal fissure (dotted line). Within each hemisphere, equivalent planar current sources (+) and sinks (−) are distributed according to the lamination of the tissue within each hemisphere, resulting in local dipolar configurations radial to the local cortical surface (i.e., tangential to the scalp). Although this geometry results in extensive local field potential cancellation between hemispheres, an uncancelled residual positivity remains at the dorsal midline (large plus sign at surface), with the corresponding negativities preserved diffusely across lateral sites (smaller minus signs). The uncancelled residual positivity at the dorsal midline is larger for the shallow than the deep generator, and the corresponding negativities are closer to the midline. C, D. Deep and shallow generators are simplified as a pair of symmetric dipoles in the midline cortex of left and right hemispheres, with isopotential lines shown for each on the dorsal surface of the scalp. E, F. Field potentials (temporal waveforms; positive down; spherical average reference estimate [cf. Berg, 2006]) at 19 selected sites resulting from the deep or shallow generator consist of a midline positivity accompanied by adjacent negativities. Compared to the deep generator, the shallow generator produces a more focal midline positivity, maximal at frontocentral sites, which is surrounded by negativities on the surface of the frontal lobe, whereas negative maxima are displaced to the lateral surface of the frontal lobe for the deep generator. G. Surface potentials (SP) and current source density (CSD) topographies for deep (row 1) and shallow (row 2) closed field generator models, displayed using spherical spline interpolation without smoothing (top view of scalp; nose at top; radial 2-D projection by linear extension; scalp positivities/sources shown in red, negativities/sinks in blue; scales optimized for pairwise comparisons of generator depth). The deep closed field CSD topography (framed) is also displayed using the ellipsoid interpolation model of BESA (right), showing that the lateral displacement of the sinks is simply and geometrically related to the location and orientation of the dipoles composing the generator. Corresponding SP and CSD topographies for deep (row 3) and shallow (row 4) open field generator models were created by eliminating the left hemisphere dipoles.

Inverse solutions for generator configurations modeled in Fig. 7. A. BESA single dipole fits. For the deep closed field (row 1), the dipole aligns with one of the sinks on the lateral surface, and thereby fails to represent the underlying intracranial generator. A midline radial dipole is identified for the superficial closed field (row 2), although it aligns at an implausible location (i.e., above the brain). These solutions are thereby inconsistent with radial dipole solutions fit reported for empirical data. In contrast, single dipoles are accurately localized for open fields (unilateral dipoles) at both deep (row 3) and superficial (row 4) locations. B. sLORETA source tomographies (v2008-11-04; Pascual-Marqui, 2002). For the deep closed field (row 1), the generator is localized to regions essentially identical to those identified for a superficial closed field (row 2). In contrast, the inverses for deep (row 3) and superficial (row 4) open fields suggest plausible generators.