TY - JOUR
AU - Herreras,, Oscar
AB - Abstract Brain field potentials (FPs) can reach far from their sources, making difficult to know which waves come from where. We show that modern algorithms efficiently segregate the local and remote contributions to cortical FPs by recovering the generator-specific spatial voltage profiles. We investigated experimentally and numerically the local and remote origin of FPs in different cortical areas in anesthetized rats. All cortices examined show significant state, layer, and region dependent contribution of remote activity, while the voltage profiles help identify their subcortical or remote cortical origin. Co-activation of different cortical modules can be discriminated by the distinctive spatial features of the corresponding profiles. All frequency bands contain remote activity, thus influencing the FP time course, in cases drastically. The reach of different FP patterns is boosted by spatial coherence and curved geometry of the sources. For instance, slow cortical oscillations reached the entire brain, while hippocampal theta reached only some portions of the cortex. In anterior cortices, most alpha oscillations have a remote origin, while in the visual cortex the remote theta and gamma even surpass the local contribution. The quantitative approach to local and distant FP contributions helps to refine functional connectivity among cortical regions, and their relation to behavior. cortex, field potential, slow cortical oscillations, spatial discrimination, volume-conduction Introduction Multiple neuronal populations are co-activated when performing distinct tasks due to the functional specialization of brain areas and the organization of neural networks. Part of this activity contributes to electric field potentials (FPs), which have helped establish the role of different brain regions. FPs can extend far beyond their sites of origin due to volume-conduction (V-C) (Lorente de Nó 1947), a phenomenon that facilitates the remote monitoring of neuronal activity, such as in electroencephalograms (EEGs) recorded at the scalp. However, an important drawback is that these recordings are difficult to interpret as they involve a mix of activities originating at different sites, a problem that also affects the interpretation of intracranial recordings (Elul 1971; Gloor 1985; Herreras 2016). Indeed, while it is widely believed that EEGs have a cortical origin, there is no systematic study on the origin of cortical FPs themselves. Cortical areas receive a number of extrinsic inputs, and they also have numerous inter-areal and intracolumnar synaptic connections (Levitt and Lund 2002), which anticipates a complex blend of FPs produced by currents generated near the recording site, as well as V-C from adjacent and distant cortices. In addition, some subcortical structures like the hippocampus also produce large FPs and thus, there may be extensive mutual contamination that will affect different areas individually. This situation compromises the identification of the structures activated in functional studies and the reliability of using parameters such as the power of frequency bands, which is actually a blend of individual waves that cannot be reasonably assigned to any specific synaptic pathway (Herreras 2016). During the last decade, the so-called spatial reach of FPs has become a matter of intense debate. In the cortex, V-C is suspected to affect a number of issues, such as the site of origin of certain FP oscillations, the different spatial coverage of sensory-driven FPs and spikes, the mutual distortion of FPs between contiguous areas, or the lamina-specific behavior of FPs (Krupa et al. 2004; Belitski et al. 2008; Gieselmann and Thiele 2008; Katzner et al. 2009; Denker et al. 2011; Eggermont et al. 2011; Kajikawa and Schroeder 2011; Liu et al. 2015; Parabucki and Lampl 2017). Thus, it is important to determine whether the waves recorded at a specific site originate close to or far from the electrodes. To address this question, different strategies have been used to explore the origin of event-related potentials, oscillatory patterns, and evoked potentials, including the chemical or optogenetic modulation of specific neurons or activities, signal treatment such as current-source density (CSD) analysis, the selection of spatially coherent FP fluctuations, or computational approaches (Łęski et al. 2013; Herreras et al. 2015). The effectiveness of these approaches relies not so much on the capability of eliminating V-C, but rather, on their ability to simplify the blend of sources so as to avoid the mutual cancellation of currents and potentials that vary at different sites (Herreras 2016). While estimating the reach of a FP requires knowledge of the location and extension of the source, the local and remote origin of the currents contributing to a group of recordings can be disclosed by retrieving the respective spatial voltage profiles, which is readily achieved by applying blind source separation techniques to multisite intracranial recordings (de Cheveigné et al. 2013; Benito et al. 2014; Głąbska et al. 2014; Makarova et al. 2011; Martín-Vázquez et al. 2013, 2016; Whitmore and Lin 2016). The anatomical stability of these voltage profiles and the high spatial resolution provided by modern silicon probes have proved to perform optimally in the hippocampus (Benito et al. 2014, 2016). The time course of the separated generators can be used as a proxy for a given pathway-to-population’s activity, and based on the presence of maxima or of a nonzero linear shape, their voltage profiles reveal which is local and which is not, respectively (Herreras et al. 2015). Here we use multiple linear recordings from several cortices and nearby structures in anesthetized rats to unravel the mutual V-C contributions in a quantitative manner. In addition, we have exploited the V-C FPs by tracking them to their origins. We also use large-scale feed-forward mathematical models of the cortical mantle and the hippocampal formation to explore some essential features that are not attainable in experiments, such as the effect of interregional cortical coherence (synchronization) and the macroscopic curvature on the spatial reach of FPs. We show that different cortical areas receive a large V-C contribution, in a state, region, and layer-dependent manner. All frequency bands that characterize cortical FPs receive activity from other cortices and subcortical structures, mainly from the hippocampus. In summary, the heterogeneous origin of cortical FPs can be quantitatively approached by spatial discrimination. Materials and Methods Experimental Procedures All experiments were performed in accordance with EU (2010/63/UE), Spanish (RD 53/2013), and local (Autonomous Community of Madrid, Order 4/8/1988) regulations regarding the use of laboratory animals, and the experimental protocols were approved by the Research Committee of the Cajal Institute. Adult Wistar rats were anesthetized with urethane (1.5 g/kg, i.p.) and placed in a stereotaxic device. Surgical and stereotaxic procedures were performed as described previously (Canals et al. 2005). In different experiments, concentric stimulating electrodes were placed in the soma layer of the CA3b region to activate the Schaffer input to CA1, in the alveus to antidromically activate the same population, and in the lateral posterolateral thalamic nucleus (LPL) to activate thalamo-cortical inputs to the V2 cortex. Up to 64 simultaneous recordings were obtained with 2 linear silicon probes (32 sites, 100 μm intersite distance) from Atlas Neuroengineering (Leuven, Belgium) or Neuronexus (Ann Arbor, MI). The probes were stereotaxically placed in several cortical areas (in mm): the V2 cortex (AP: −4.4; L: 2.6), the forelimb somatosensory (S1) cortex (AP: −0.7; L: 3.9), and the M1 motor cortex (AP: 2.9; L: 2.6). Typically, the recording arrays spanned the cortical layers and sections of the underlying structures, among others the striatum, thalamus, and hippocampus. In some experiments, the M1 probe was lowered with a 10° anterior tilt to follow the main cell axis and to reach more distant subcortical sites. Probes were soaked in DiI before insertion (Molecular Probes, Invitrogen, Carlsbad, CA) to assess their location post-mortem in histological sections. A silver chloride wire implanted under the skin of the neck served as a reference for recordings. Signals were amplified and acquired using MultiChannel System (Reutlingen, Germany), or Open Ephys hardware and software at a 50 kHz sampling rate. We used histological and electrophysiological criteria to identify cortical and hippocampal strata, such as the reversal polarity for slow cortical oscillations (SCOs) at ~400 μm from the pial surface in M1 and S1 cortices, the maximum of the population spike in evoked potentials, and the spontaneous cell firing to determine the position of cell layers in the CA1 and DG. Deep structures were only approached by DiI marks. To discriminate the local FP components of the cortex from the volume-conducted contributions from other regions, experiments were carried out with the cortex silenced by delivery of lidocaine (0.4%) from a small pool at the pial surface. The pool was established with a 2 mm wide silicone ring glued to the skull surrounding a 1.5 mm hole drilled in the bone. Lidocaine was preferred to muscimol as it affects excitatory and inhibitory synapses and the associated intrinsic currents similarly. Passive diffusion was evident from the gradual top-down abolition of cortical FPs and spike activity, as well as that of evoked thalamo-cortical potentials. We checked for the possible expansion of the drug into the hippocampus by monitoring the antidromic CA1 population spikes elicited by alvear stimulation, immediately adjacent to the corpus callosum. Complete blockade of cortical activity in the cortical tissue surrounding the recording array was obtained within 40–60 min. We tested the subcortical reach of cortically coherent sources using a roving pipette recording in 0.5 mm steps along multiple trajectories up to 7 mm below the cortical surface and reaching deep structures, while a fixed pipette remained in the cortex or the hippocampus to assess the constancy of the electrographic state. Similar experiments were performed using linear arrays lowered in successive steps of 1.5 mm, enabling a 1.6 mm overlap of sites at successive stations. At the end of each experiment, the animals were perfused with PBS followed by paraformaldehyde (4%) through the abdominal aorta, and sagittal brain sections (100 μm) were then stained with bis-benzimide and the electrode position was assessed by fluorescence microscopy. Forward Models of Field Potentials General Design In order to estimate the spatial reach and magnitude of the electrical fields in a volume conductor, the geometry of the sources of current must be fully described. The sources that conform a dipolar distribution raise the largest fields, while quadrupolar and 2n-polar sources raise smaller or negligible FPs. Accordingly, the essential geometrical elements that must be defined are the morphology of the neurons, the architecture of the population and the subcellular distribution of the inputs (Makarova et al. 2011; Fernández-Ruiz et al. 2013; Herreras et al. 2015; Martín-Vázquez et al. 2016). To accomplish complementary purposes we used 2 different modeling strategies. The first was a multicellular aggregate of compartmental units of realistic morphology endowed with Hodgkin–Huxley (H–H) dynamics (e.g., Ibarz et al. 2006; Lindén et al. 2011; Makarova et al. 2011) and the second was a finite element method (FEM) (Fernández-Ruiz et al. 2013). Compartmental H–H models were employed to synthesize multisynaptic FPs from mixtures of inputs to specific subcellular domains that interact naturally within cells. In this approach, the input consists of a series of instants when synaptic channels are activated, and the temporal envelope of the transmembrane currents is computed from the channel kinetics. The FEM model skips this step and uses current sources with predefined spatial dimensions, locations in the volume, and temporal dynamics. Thus, it is best suited to explore the role of macroscopic factors, such as the effect of tissue heterogeneities and anisotropy. Compartmental H–H Models Blocks of tissue with a realistic 3D cytoarchitecture were organized into 3 contiguous structures, the cortex, the hippocampal CA1, and the Dentate Gyrus (DG). The experiments indicated that the latter 2 are the structures that contribute most of the remote activity to cortical sites. In each structure, we modeled only cell types with an appropriate morphology that might contribute to FPs (Lindén et al. 2011; Makarova et al. 2011; Herreras et al. 2015), which were the followings: PCs in the CA1, granule cells (GCs) in the DG, and layer-V PCs in the cortex. Polymorphic neurons were excluded as sources of extracellular currents, yet the output of some subtypes was simulated as they provide synaptic inputs to principal cells that drive large FPs (Benito et al. 2014). Layer II–III PCs contribute much less to FPs (Lindén et al. 2011) and they were therefore not considered in this study. This simplification allowed the computational resources to center on the contribution of remote hippocampal sources to the cortex rather than reproducing local cortical FP generators. FPs were estimated by distance weighted addition of all the compartmental currents obtained in a model neuron for each of the regions and/or patterns of temporal activation, and the activation of a block of tissue was achieved by replicating the currents through a system of spatial coordinates that represented all the compartments and neurons (Makarova et al. 2011; Martín-Vázquez et al. 2016). The blend of local and V-C activities in different cortical regions was simulated through distinct temporal activation of different blocks of cortical or hippocampal tissue (see below). Thus, model neurons were not synaptically connected and the dynamics of activation was established by the user as predefined sequences of afferent spikes activating synaptic currents in dendritic compartments that together produced FP time-envelopes akin to the experimental patterns observed in each structure. The transmembrane currents were calculated using the GENESIS simulator applying an exponential Euler method (Bower and Beeman 1998). We used 2 different spatial resolutions to achieve the coarse and fine representations of the model FPs. To describe the macroscopic reach of the FPs, a cubic grid (100 μm) was used to establish the spatial points where the transmembrane currents were integrated. These were large enough to collect the parts of the 3D voltage shell required for experimental comparison, in some cases as large as the entire cortical mantle, and they are represented in sagittal or coronal sections of the rat’s brain. Spatial contour plots of the FPs were built at a specific time-instant (snapshots), while the dynamic variations were represented in video format. Also, linear profiles were represented at 50 μm resolution in the center of the populations to enable the spatial profiles to be compared with those obtained in experiments. The contribution of the CA1 and DG currents to cortical sites was estimated for each of the pathways activated, alone or in combination. Although simulating distant contributions to cortical FPs does not require explicit modeling of cortical cells (only the extracellular space is required), we also modeled the cortex and simulated the main local source in order to get an insight into cortical V-C contributions to other structures. The conductivity of the tissue was set as 0.33 S/m, as reported in vivo (López-Aguado et al. 2001), and the calculations of the FPs were programmed in MATLAB. In this model, we did not include the effects of tissue heterogeneity and anisotropy that may be introduced by ventricles and axon bundles, or any frequency dependent properties of the medium (Bédard et al. 2004; Herreras 2016). The magnitude of possible errors was investigated by the FEM approach (see below). The Cortical Model We simulated about the 2 anterior thirds of the cortical mantle in one hemisphere. For simplicity, we used 6 planar blocks of identical thickness and cell density that were assembled at certain angles to reproduce macroscopic curvatures. The equivalent cortical zones in the rat brain were the followings: from V2 to the front end (anteroposterior) and downwards up to the olfactory bulb; all mediolateral cortices from the midline; and from V2 to the entorhinal cortex in a dorso-ventral direction. The cortex contained 2673,108 identical layer-V PCs arranged in a palisade-like manner, and with a cell density of 62 cells in a 50 × 50 lattice. The somata were scattered over 500 μm in the main cell axis (layer-V). Morphological data for the prototype layer-V PC unit was obtained from Romand et al. (2011), using 239 compartments representing the soma and the basal and apical dendritic trees. In earlier studies, we checked that other features were averaged out in the population and that they had negligible impact on the spatial configuration of the FPs in the hippocampus, such as the rotation of the main cell axis, the fanning angle of the basal tree or the orientation of secondary dendrites (Martín-Vázquez et al. 2016). We, therefore, assumed macroscopic averaging in the cortex as well. The electrotonic parameters and subcellular distribution of active channels parameters and kinetics were as reported previously (Migliore and Shepherd 2002; Hay et al. 2011). Briefly, the apical tree was made of a single 790 μm long dendrite with a tapering diameter (4.5–1.4 μm), 6 oblique dendrites, and an apical tuft extending 400 μm parallel to the outer “pial” border. The basal tree extended 350 × 500 μm in the plane parallel to the cortical surface. The passive properties Cm and Rm were the followings: 1 μF/cm2 and 5 Ωm2 for the soma and the proximal 25 and 100 μm of the basal and apical trees, and 2 μF/cm2 and 2.5 Ωm2 for all other dendritic compartments. Ra was 1Ωm. The model included 7 types of ion conductances to reproduce the active somato-dendritic properties (gNa, gCaHgCaT, gKM, gKDR, gKA, gKC). We simulated the 2 main electrographic patterns in the cortex, the SCO and the activated states. For the SCOs we used an excitatory input of the non-NMDA type to layer-V PC dendrites (from 600 μm into the apical trunk to 200 μm into the basal tree, except the soma and the surrounding 50 μm). These bands were fine-tuned so they fit the experimental source/sink spatial profiles (Chauvette et al. 2010). Note that the synaptic or intrinsic nature of the currents (Reimann et al. 2013) is not relevant for our purposes, rather the density and spatial distribution of the net electric charge in the extracellular space has to be carefully fitted. To simulate varying input from different assemblies of the same neuron population (putatively the thalamo-cortical neurons), we used a multithread global input made up of 12 different uncorrelated temporal patterns. These were set as random series of pulses with one uninterrupted input (baseline input) at a mean frequency of 40 Hz and gmax = 1 nS), while the other 11 inputs were activated under a common on-off pattern (the on phase lasted 300–500 ms per second) so as to reproduce the reported duration of the UP/DOWN states (Destexhe et al. 1999; Chauvette et al. 2011). The frequency of inputs ranged from 2 to 64 Hz, up to a maximum of 240 Hz in total, and the gmax ranged from 0.2 to 0.6 nS. According to the literature, SCOs are synchronous over large cortical regions (Destexhe et al. 1999) and thus, in some runs, they were activated synchronously throughout the cortical blocks, whereas coherent modules of different size were investigated in others. In this study, we did not simulate their dynamic spatial behavior (i.e., moving waves) (Chauvette et al. 2010). The activated cortical state was simulated using both excitatory and inhibitory inputs distributed in the same somato-dendritic bands, and we mimicked the topological activation of discrete cortical modules sized 0.5 × 0.5 mm in the center of each planar section (6 in total). For activation, we combined 6 excitatory and 6 inhibitory inputs: Glu, 20–72 Hz with a combined maximum limited to 200 Hz; gmax, 2–2.6 nS in 5 inputs and another at 6 nS; GABA, 8–30 Hz with a maximum limited to 70 Hz, and gmax at 8–28 nS in 5 inputs plus another of 40 nS. These inputs were uncorrelated in all cases. The CA1 Model The CA1 was constructed as 4 blocks of tissue with a constant width of 2 mm and jointly extending through 6.7 mm, assembled into a C-like structure that reproduced the curved septo-temporal axis. The assembly was tilted 45 degrees over the sagittal plane (temporal end out) to account for the mediolateral displacement. For simplicity, the rotation over the anteroposterior axis was not implemented (the temporal end laid beneath the septal one). It contained 232,502 CA1 PC units arranged in a palisade-like manner with a cell density of 54 units in a 50 × 50 μm lattice. The morphology, electrotonic parameters, and the subcellular distribution of active channels in the PC model were as reported earlier (Varona et al. 2000; Makarova et al. 2011; Martín-Vázquez et al. 2013, 2016). The model included 13 types of ion channels with an optimized subcellular distribution to simulate active somato-dendritic properties (Herreras 1990; Johnston et al. 1996; Canals et al. 2005; Ibarz et al. 2006; Makarova et al. 2011). In the subthreshold regime of synaptic inputs explored here, there was only a minor contribution of active properties to CA1 FP generators (Ibarz et al. 2006; Makarova et al. 2011; Martín-Vázquez et al. 2013, 2016). We simulated the main pathways that render sizable FPs in the CA1, namely the Schaffer-Commissural (Sch-Comm) excitatory input, and a mixture of excitatory and inhibitory inputs to the distal apical dendrites (Makarova et al. 2011; Benito et al. 2014, 2016). Schaffer and Comm inputs fully overlapped in the basal dendrites (50–250 μm from the soma) and they partially overlapped in the apical tree (150–250 μm and 200–400 μm from the soma for Comm and Sch inputs, respectively). The density of the synaptic conductance was set to replicate the relative density of the axon terminals. By default we used a gmax of 16.7 nS and 35.9 nS for the Comm and Sch inputs, respectively, below the threshold for local dendritic spikes when distributed over a sufficiently large dendritic surface (Ibarz et al. 2006), and a basal-to-apical conductance density ratio of 2:1 for the Comm and 1:4.5 for the Sch inputs. To mimic the timing of ipsi- and contralateral CA3 inputs to the CA1, the 2 inputs were activated nearly synchronously by series of pair-wise Sch and Comm excitatory gamma waves with bilateral random jitter <2 ms (Benito et al. 2014). The intensity of the individual waves varied, reproducing realistic gamma sequences (Fernández-Ruiz et al. 2012; Benito et al. 2016). Theta activity was simulated as a single inhibitory generator in the distal apical dendrites that reproduces well the spatial profiles in anesthetized preparations (Buzsáki et al. 1986; Brankačk et al. 1993), displaying a maximum toward the hippocampal fissure and a polarity reversal in the stratum radiatum near the cell body layer. Dentate Gyrus Model A 2 × 2 mm block was used to simulate the antero-dorsal portion of the DG, as we centered the study on this cortical quadrant. It was built as a C-folded sheet of GC units formed by 5 planar blocks extending over 3.7 mm and containing an aggregate of 128,685 morphologically identical GC units, with a cell density of 100 neurons in a 50 × 50 μm antero-lateral lattice (Fernández-Ruiz et al. 2013). The main FP generators modeled were the excitatory inputs from the lateral and medial perforant pathways (LPP, MPP) and a basket cell perisomatic inhibition, which jointly account for most (>95%) of the FP variance in the DG (Benito et al. 2014). The folded arrangement of this structure is particularly relevant as it produces giant FPs in the interposed hilar region that are volume-conducted from granule cell sites (Fernández-Ruiz et al. 2013). Excitatory and inhibitory synaptic inputs of the non-NMDA (τ = 2 ms), and GABAA types (τ = 30 ms) were used to mimic the LPP and MPP inputs, and perisomatic inhibition, respectively, and they were distributed throughout the soma and/or dendritic compartments matching the anatomical synaptic territories. Thus, LPP and MPP activated the outer and the middle third compartments of the dendritic arbor of GC units, respectively, while inhibition was only set at the soma. The synaptic conductances (4–12 nS and 30–60 nS for Glu and GABAA inputs, respectively) were activated at varying intensity in predetermined temporal sequences, irregular, periodic, or mixed. The FEM Model FEM allows explicit modeling of the geometry and the dielectric properties of the extracellular space. Here we used it to explore the electric field distortions caused by the presence of brain structures with different electric permittivity, such as the corpus callosum and the ventricle, as these may be relevant for estimating V-C far away from cortico-hippocampal sources. The volumetric character of FEM current sources allows the electrical currents produced by multiple synchronously activated neurons to be compiled in several block-like current generators. A 3D FEM model of a medial portion of a rat brain hemisphere was constructed using COMSOL Multiphysics software (COMSOL, Inc., Burlington, MA). We used the physical dimensions of the different modeled structures from the rat brain atlas (AP 4.56 mm: Paxinos and Watson, 2007) (Supplementary Fig. S1). The model included cellular portions representing the dimensions and curvatures of the layer-V pyramidal cell population of the cortex (4 mm wide), the pyramidal cell population of the hippocampal CA1 region, and the granule cell population of the DG (2.5 mm), all enclosed in a surrounding volume of the extracellular space equivalent to 20 × 20 × 20 mm (H, W, L), which minimizes the distortion of field curves in the region of interest (Fernández-Ruiz et al. 2013). In addition, we built a curved structure that represented the corpus callosum (4 mm) and another that represented a portion of the lateral ventricle (3 mm). The simulations sought to explore the distortion of V-C caused by the presence of these heterogeneities during activation of a single pathway in the cortex or the hippocampus, which were modeled as laminar dipolar sources. For the sake of simplicity, we represented the cellular portion as 2 stacked blocks of current sources and sinks accounting for subcellular “population” domains with outward and inward transmembrane currents. Single or multiple cortical blocks of different size were used to reproduce different extensions of the cortical sources and the curvature, thus mimicking the broadly synchronous cortical SCO state or the fragmented activation in cortical activated states. For simplicity, the curvatures of the CA1 and the DG were implemented in only one direction that served well the main objective. We used Dirichlet boundary conditions on the surface enclosing the volume and imposed charge conservation inside. A tetrahedral adaptive mesh of the highest resolution (smallest size: 30 μm) was used to ensure the correct resolution of field equations in the curved compartments. Signal Analysis Current-Source Density (CSD) One approach to discriminate local contributions to FPs is the use of CSD (Lorente de Nó 1947; Mitzdorf 1985). Assuming constant conductivity of the extracellular space σ we have: CSD = –σΔu, where u(t,x,y,z) is the electric potential and ∆ is the Laplace operator. For linear probes with M recording sites (usually M = 32), we used a 1D approach that calculates the CSD from the voltage distribution along the cells axis (Herreras 1990): CSDm(t)=−σh2(um−1(t)−2um(t)+um+1(t)) where um(t) is the FP recorded at the mth site and h is the intersite distance. We only used the CSD as a fast check for the visualization of the presence/absence of currents in a certain region, while to explore the reach of FPs and the origin of the remote contributions, it is best to explore the spatial profiles themselves on ICA-separated components that maintain both the local and remote values. Spatial Discrimination of Electric Fields by Independent Component Analysis (ICA) of the Real and Modeled FPs The performance and interpretation of ICA-separated components are largely dependent on the nature and characteristics of the signals (Bell and Sejnowski 1995; Stone et al. 2002). An ICA is routinely used to elucidate functional connectivity in multisite scalp EEG recordings or in fMRI (Onton et al. 2006; Rogers et al. 2019). The application of an ICA to intracranial FPs is much more informative as linear multielectrodes arrays may be situated to span the volume occupied by the sources themselves. Indeed, they can even resolve the different voltage shells produced by synaptic inputs arriving at the same cell population as long as they do not completely overlap in the same dendritic territory (Makarov et al. 2010; Benito et al. 2014). We routinely chose algorithms that optimize spatial coherence in the segregated components, which complies with the principle of charge conservation and the instantaneous character of the electrical fields. The algorithm renders the time course of the activity of the different pathways and neuron populations, and it also provides their relative power. This information together with anatomical data can be used to find the location, polarity and additional geometrical features of the source (Makarov et al. 2010), albeit with a number of restrictions (Herreras et al. 2015). In this study, we employed the kernel density ICA algorithm (KDICA) (Chen 2006) that was customarily implemented in Matlab. Recorded FP signals um(t) are considered as the weighted sum of the activities of N neuronal sources or FP-generators: um(t)=∑n=1NVmnsn(t),m=1,2,..,M where (Vmn) is the mixing matrix composed of the so-called voltage loadings or the spatial weights of N FP-generators on M electrodes and sn(t) is the time course of the nth FP-generator. Thus, the raw FP observed at the mth electrode tip is a linear mixture of the electrical activity of several independent FP-generators. Using um(t) the ICA finds both the (Vmn) and sn(t). The joint group of spatial weights (Vmn) is ordered into instant depth profiles of the voltage according to electrode position. Such curves can be compared to the spatial profiles of the standard evoked potentials of specific pathways when available (Korovaichuk et al. 2010; Benito et al. 2014). Although a single profile is insufficient to reconstruct the entire 3D voltage shell, it provides critical information to determine the local or remote location of the source by the curved or flat trend along the recording track, respectively (Herreras et al. 2015) (see Results). The time-course of a FP-generator sn(t) can be considered as a postsynaptic temporal convolution of spike output in an afferent population (i.e., afferent spike trains), as shown experimentally for the CA3–CA1 pathway (Fernández-Ruiz et al. 2012) and numerically for a variety of inputs (Makarova et al. 2011; Martín-Vázquez et al. 2013, 2016). Thus, evoked potentials are captured selectively in the temporal envelope of a FP generator with a matching spatial profile, which provides a means to identify the pathway and the target population generating the currents. The mathematical validation and practical limitations of this approach, as well as the possible causes leading to faulty separation and some of the possible workarounds have been thoroughly investigated using realistic modeling (Makarova et al. 2011; Martín-Vázquez et al. 2013, 2016). Once extracted, each FP-generator can be analyzed independently in the time or the frequency domains or used to re-construct virtual FPs produced by one or a desired blend of generators. As found earlier (Makarov et al. 2010), the linear samples of 3D voltage gradients reflected in the spatial profiles of FP generators remain stable within and across animals, whereas their landmarks (maxima or zero crossings) were matched to anatomical boundaries using electrophysiological correlates (unit firing in cell body layers and evoked potential profiles) and verified histologically (Benito et al. 2014). Such profiles are accurate to the subcellular level in monolayered structures, while they are less informative in glomerular structures in which they reproduce the joint field distribution of the activated populations (Makarova et al. 2014). In some cases, the cues for spatial interpretation have to be sought in the macroscopic arrangement of the structure, such as the layer folding (Fernández-Ruiz et al. 2013), or in the overall shape of the cortical mantle, although the presence of coherent activity in nearby structures also affects the spatial landmarks of FPs through volume-conduction (Martín-Vázquez et al. 2016). Specific Technical Considerations of the ICA Applied to Cortico-hippocampal FP Profiles Usually, a few ICA components exhibit significant variance and distinct spatial distributions (4–7 out of a possible 32, a maximum defined by the number of electrodes) (Korovaichuk et al. 2010; Benito et al. 2014). This permits further optimization by pre-processing FPs before performing the ICA by reducing the dimensions through a principal component analysis (PCA), efficiently diminishing weak noisy generators (Makarova et al. 2011). The PCA also stabilizes and accelerates the subsequent convergence of the ICA (Makarov et al. 2010). The optimal choice of PCA components is 2–3 more than those that attained significant variance in the ICA. We routinely disregard the ICA components with a total compound variance below 1% (i.e., always keeping 99% of the original FP variance), unless their spatial and temporal accuracy can be ensured through other means. The performance of the ICA may differ somewhat depending on the temporal structure of the FPs and the degree of spatial overlap of the original sources. In ordered structures, the different synaptic pathways contacting a single homogeneous population of neurons generate spatially distinct FPs that can be reliably separated, as in the hippocampus (Herreras et al. 2015). Typically, maintaining the 6–8 main PCA components optimizes the ICA’s performance in recordings spanning the dorsal CA1 and the DG (Benito et al. 2016). In the cortex, the temporal structure of the signals is rather different. For an initial search of the more stable components, we carried out a more parsimonious scrutiny of selected PCA components (Łęski et al. 2010; Makarov et al. 2010) (Supplementary Fig. S2). Spatial and temporal features of the signals deserve consideration. Using the ICA, the frequent co-activation of sources in different structures may cause incomplete separation when they present a similar temporal course. While it is possible that 2 structures receive a common synaptic input from the same population of origin, it is more likely that the co-activation results from network operation of multiple populations at different sites. Such a situation appeared here in the FP epochs displaying different but timed slow oscillations in the V2 cortex and hippocampus (e.g., Fig. 1B). The spatial distribution of the FP generators concerned may display maxima in the 2 structures depending on the degree of temporal overlap, although one can be easily appreciated as an inherited hump on the characteristic distribution of the other (for example, the spatial profile of the SCO component in Fig. 1B). In such cases, the otherwise linear tail of the voltage away from a source in one structure gets distorted in the other, which hinders the quantification of its V-C contribution there. In addition, the temporal course may convey some error, although it may be optimized by re-analyzing the same epoch after splitting the recording sites into 2 separated matrices, one for each structure. Consequently, according to the objective of this study, the FP epochs should be selected when co-activation is strong or reduced. Figure 1. Open in new tabDownload slide Separation of FPs into local and volume-conducted (remote) activities through spatial voltage gradients. (A) Laminar profile of a Schaffer evoked potential (EP) superimposed on the corresponding current-source density (CSD) map spanning the V2 cortex, the hippocampal CA1 and the Dentate Gyrus (DG). Horizontal dashed lines mark the CA1 boundaries. Clusters of the sources and sinks of current and voltage maxima are restricted to the regions of origin (CA1 and CA3), while a V-C positive wave extended into the cortex (arrowheads). (B) Extraction of spatially coherent ICA components or FP generators (colored traces) from a sample epoch of FPs (upper traces) recorded with a linear array across the V2 cortex and the CA1/DG. The color coded plots shown below depict the time course of separated FP generators, the spatial distribution of which (relative power along recording sites) is on the right (voltage (V)-profiles). The maximum indicates the region of origin and the non-zero flat voltage “tails” (asterisk) reflect the V-C potentials recorded in adjacent structures (the cortex). FP generators are labeled according to their origin as SCO (slow cortical wave), CIII (cortical layer III), Sch (CA1 Schaffer), L-M (CA1 st. lacunosum-moleculare), DG and Rem (remote unknown). Instances of the FP generators are superimposed on the FPs to facilitate their visual matching. Color code is maintained in color figures. (C) The segregation of independent components through the ICA allows their subsequent reconstruction into 2 sets of virtual FPs, local cortical (blue traces) and remote (purple traces). Faint color traces belong to extra-cortical recording sites (the striatum in this example across the M1 cortex). The corresponding CSD maps show similar spatiotemporal clusters of sources and sinks for raw FPs and the FPs reconstructed from cortical generators (blue and brown V-profiles), while the reconstructed remote FPs had no associated currents, in agreement with their linear spatial distribution (purple). FP generators, but not CSD maps, enable the grouped or individual quantification of local and remote dynamics in different cortical layers. (D) Simultaneous temporal envelopes of the power in local cortical FP generators and the V-C potentials entered from remote regions. p.a.u. and n.a.u., proportional and normalized arbitrary units; e#, electrode number (only every other channel is shown). Figure 1. Open in new tabDownload slide Separation of FPs into local and volume-conducted (remote) activities through spatial voltage gradients. (A) Laminar profile of a Schaffer evoked potential (EP) superimposed on the corresponding current-source density (CSD) map spanning the V2 cortex, the hippocampal CA1 and the Dentate Gyrus (DG). Horizontal dashed lines mark the CA1 boundaries. Clusters of the sources and sinks of current and voltage maxima are restricted to the regions of origin (CA1 and CA3), while a V-C positive wave extended into the cortex (arrowheads). (B) Extraction of spatially coherent ICA components or FP generators (colored traces) from a sample epoch of FPs (upper traces) recorded with a linear array across the V2 cortex and the CA1/DG. The color coded plots shown below depict the time course of separated FP generators, the spatial distribution of which (relative power along recording sites) is on the right (voltage (V)-profiles). The maximum indicates the region of origin and the non-zero flat voltage “tails” (asterisk) reflect the V-C potentials recorded in adjacent structures (the cortex). FP generators are labeled according to their origin as SCO (slow cortical wave), CIII (cortical layer III), Sch (CA1 Schaffer), L-M (CA1 st. lacunosum-moleculare), DG and Rem (remote unknown). Instances of the FP generators are superimposed on the FPs to facilitate their visual matching. Color code is maintained in color figures. (C) The segregation of independent components through the ICA allows their subsequent reconstruction into 2 sets of virtual FPs, local cortical (blue traces) and remote (purple traces). Faint color traces belong to extra-cortical recording sites (the striatum in this example across the M1 cortex). The corresponding CSD maps show similar spatiotemporal clusters of sources and sinks for raw FPs and the FPs reconstructed from cortical generators (blue and brown V-profiles), while the reconstructed remote FPs had no associated currents, in agreement with their linear spatial distribution (purple). FP generators, but not CSD maps, enable the grouped or individual quantification of local and remote dynamics in different cortical layers. (D) Simultaneous temporal envelopes of the power in local cortical FP generators and the V-C potentials entered from remote regions. p.a.u. and n.a.u., proportional and normalized arbitrary units; e#, electrode number (only every other channel is shown). An additional consideration is related to the markedly different electrographic patterns displayed by the cortex (SCOs/activated states) and the hippocampus (theta/irregular activity). Ideally, the statistical properties of the mixture should remain constant throughout the epoch for ICA usage, which is violated in cases when the epoch contains different electrographic states. In such cases, unstable, duplicated and hybrid generators may appear (Makarova et al. 2011; Herreras et al. 2015). Typically, these explain a small fraction of the total variance and they can be discarded given that the associated error in strong generators is negligible. However, if they gather a significant share of variance the error may indeed affect the fine temporal resolution of the true generators. To minimize this problem, we analyzed epochs with a homogeneous electrographic state. Statistics and Correlations Data Collection In experiments, we used 21 rats in total. Experimental groups contained at least 3 animals. FPs were recorded simultaneously from 32 or 64 recording sites at 20 kHz sampling rate and stored for further offline data analysis. The obtained results were averaged over all rats in each group. Software All statistical analyses and data treatment were performed in MATLAB® by using the Statistics and Machine Learning Toolbox. The ICA was performed by using the LFPsource® software running in MATLAB environment and freely available at http://www.mat.ucm.es/~vmakarov/downloads.php. For detailed description and examples, see Herreras et al. (2015). Descriptive Statistics All data are presented either as the mean ± SEM or the median ± the median absolute deviation (MAD) if the distribution deviated significantly from normal. In order to check for normality we used the Kolmogorov–Smirnov test. Individual data points and mean values are shown for all graphs in all figures. Hypothesis Testing We used either one-way ANOVA or the non-parametric Wilcoxon signed rank test (with 5% level of significance). The effect size r for the Wilcoxon signed rank test was computed as r=z/N ⁠, where z is the z-score value for the T parameter and N is the number of samples. Independent Component Analysis It is implemented as part of the LFPsource® software and uses the fast kernel density method (Chen 2006) with prior data conditioning. Raw FPs (an epoch with 32 or 64 channels) go through PCA and 1% of the data variance containing noisy signals is eliminated. This yields an appropriate dimension reduction. Then, ICA of the reduced data set is applied. Grouping of spatial distributions from similar generators was achieved by evaluating the distance measure. The sample sizes were similar to those reported in previous publications using the ICA for the segregation of FP generators and their quantification (Fernández-Ruiz et al. 2012; Benito et al. 2014, 2016; Martín-Vázquez et al. 2013, 2016). Estimation of Amplitude in Slow Cortical Oscillations The amplitude of SCOs was evaluated through estimation of the corresponding voltage distribution by building a histogram with an automatic bin width adjustment. The difference between peaks in the higher and lower ends of the bimodal distributions was taken as the estimate of the average amplitude. Spectral Analysis The occurrence of oscillatory bouts in specific frequency bands of raw FPs was detected through wavelet spectrograms. The threshold was set to twice the standard deviation of the mean value in the period analyzed. We estimated the power spectral density of the temporal activation of FP generators (periodogram) and then computed the signal power in different frequency bands: 0.5–3 Hz (δ), 3–8 Hz (θ), 8–20 Hz (α), and 20–80 Hz (low-γ). Power of FP Generators The time evolution of the power of a FP-generator (in mV2) was calculated by P(t)=∫H(t−τ)v2(τ)dτ,H(x)={1/Δifx∈[−Δ/2,Δ/2]0,otherwise where v(t) is the virtual FP at the electrode with maximal power and Δ is the length of averaging. The overall mean power is then defined by setting Δ equal to the complete time interval. Results In this paper we use the term local strictly to refer to the FP contribution by neuronal currents originated near the electrodes, since local and distant sources of current both contribute to FPs. Overview of the Separation of FPs into Local and Remote Activities Through Spatial Voltage Gradients We set out to reveal local and remote (V-C) contributions to spontaneous FPs recorded in the cortex as discriminated by their distinct spatial voltage profiles. One such distribution for a simple source is the evoked CA3 input (Schaffer) to the hippocampal CA1 region (Fig. 1A). In this example, the sink/source groups of current and the voltage maxima remained circumscribed to the CA1/3 sites where the neurons were activated, while a positive voltage wave extended across the volume into the overlying secondary visual cortex (V2) with a smooth linear decay and no associated currents (i.e., a remote wave that contaminated the cortical recordings: Fig. 1A, arrowheads). Two different types of remote cortical sources will be explored here, those from cortical sites outside of the recorded area and those from subcortical structures. During spontaneous multisource activity, the FP-generating structures contaminated each other (see Video 1) and the discrimination of genuine cortical waves from remote ones required the efficient separation of the co-activated sources to access the respective voltage profiles. This separation was achieved through an independent component analysis (ICA), which distinguished components that in most cases reflected pathway-specific generators or a small group of pathways with identical spatial distributions (Herreras et al. 2015). In cortical recordings, remote contributions reached all sites with a similar strength across the width of the cortex, and the corresponding voltage profiles were smooth and linear (Figs. 1B,C). It can be assumed that the FP generators displaying non-zero linear voltage profiles agglutinate all the activities generated by remote sites, some of which could be tracked to their origin by moving the recording probe in successive steps until a maximum appeared in the other structure. For example, the combined analysis of FPs recorded in the V2 cortex and the hippocampus (Fig. 1B) returned several hippocampal and cortical generators with local maxima, some of which had non-zero linear parts in the adjacent structure (asterisk). Occasionally, a voltage profile showed a maximum in 2 structures, indicating a certain degree of coherence between their activities (e.g., Fig. 1B, blue profile; see also Martín-Vázquez et al. 2016). In an example of the analysis of an FP epoch recorded through the motor cortex (M1; Fig. 1C), the ICA returned several generators, 2 of which displayed cortical maxima (voltage profiles in blue and brown) while the other was linear and continued steadily into subcortical regions (purple). The contribution to FPs by either one or by a desired group of generators can be reconstructed (Fig. 1C, 2 left lower panels). Hence, the time-course, power evolution (Fig. 1D), and frequency features of grouped local and remote sources could be explored and their relative contributions evaluated. This constitutes a major advantage over the CSD approach that cannot separate local sources and that obviates V-C dynamics (Fig. 1C, right panels). A great deal of the situations and features explored in this paper are agglutinated and can be easily appreciated in video of large-scale FP modeling across a brain hemisphere (Videos S1 and S2). The Blockade of Local Activity Reveals V-C Contributions to Cortical FPs Experimental evidence of V-C activity reaching cortical sites was revealed by silencing local activity through the delivery of lidocaine to the pial surface (Fig. 2A). In these experiments, we chose an anesthetic plane in which the animals typically displayed short SCOs (also known as delta activity or Up/Down states). This approach enabled a sensory-driven (tail pinch) transition to the activated state, allowing the effect of cortical lidocaine on 2 electrographic states to be compared. The activated state displayed irregular activity in the cortex and theta rhythm in the hippocampus. The extension of the drug into the cortex was assessed by selective blockade of thalamo-cortical but not hippocampal (alveus to CA1) evoked potentials (Fig. 2B). The fading of cortical evoked and spontaneous FP activity stabilized after 40–60 min, although cortical FPs did not disappear completely. Figure 2. Open in new tabDownload slide The blockade of local cortical activity reveals volume-conducted contributions to cortical FPs. (A) Schematic representation of the experimental setup to deliver lidocaine over the V2 cortex. (B) Control for drug extension by selective blockade of thalamo-cortical (Th-Cx) but not hippocampal antidromic evoked potentials (Alv-CA1). (C) Mean power of FPs across cortical layers before (brown) and after lidocaine (blue). (D) Amplitude histograms for estimating the amplitude of slow cortical oscillations (SCO) (net voltage between red arrows). (E,F) Sample epoch of raw FPs (black traces) and bi-dimensional spatial maps of pairwise CCs between cortical and hippocampal sites during SCOs (E) and theta (F) states, before (upper plots) and after lidocaine administration (lower plots). c–c, h–c, h–h stand for intra- and inter-structure zones of correlation. The time course of the L-M hippocampal generator is depicted by the green trace. The sign of the CC changed at the site of polarity reversal for the SCOs in cortical layer III, and for the hippocampal theta at the CA1 st. radiatum. The white dashed squares mark the strata originating these 2 activities. The spectral densities in the theta state are shown for the raw FP in cortical layer V (black), the hippocampal L-M generator (green), and the cortical SCO generator (blue). The red ovals mark the selective reduction of slow waves in the SCO generator and raw cortical FPs, while theta remained constant in both the cortex (arrows) and hippocampus. C,D,E correspond to a single animal: see population statistics in the text. Figure 2. Open in new tabDownload slide The blockade of local cortical activity reveals volume-conducted contributions to cortical FPs. (A) Schematic representation of the experimental setup to deliver lidocaine over the V2 cortex. (B) Control for drug extension by selective blockade of thalamo-cortical (Th-Cx) but not hippocampal antidromic evoked potentials (Alv-CA1). (C) Mean power of FPs across cortical layers before (brown) and after lidocaine (blue). (D) Amplitude histograms for estimating the amplitude of slow cortical oscillations (SCO) (net voltage between red arrows). (E,F) Sample epoch of raw FPs (black traces) and bi-dimensional spatial maps of pairwise CCs between cortical and hippocampal sites during SCOs (E) and theta (F) states, before (upper plots) and after lidocaine administration (lower plots). c–c, h–c, h–h stand for intra- and inter-structure zones of correlation. The time course of the L-M hippocampal generator is depicted by the green trace. The sign of the CC changed at the site of polarity reversal for the SCOs in cortical layer III, and for the hippocampal theta at the CA1 st. radiatum. The white dashed squares mark the strata originating these 2 activities. The spectral densities in the theta state are shown for the raw FP in cortical layer V (black), the hippocampal L-M generator (green), and the cortical SCO generator (blue). The red ovals mark the selective reduction of slow waves in the SCO generator and raw cortical FPs, while theta remained constant in both the cortex (arrows) and hippocampus. C,D,E correspond to a single animal: see population statistics in the text. The reduction of the FP magnitude was more pronounced in cortical layers that exhibited the largest FPs in control conditions (Fig. 2C), from 0.009 ± 0.004 mV2 in layers II–III and 0.056 ± 0.036 mV2 in layer V to 0.006 ± 0.001 mV2 and 0.012 ± 0.004 mV2 after exposure to lidocaine (median ± median absolute deviation, MAD, of 110 and 140 observations from n = 4 animals in layers II–III and 5 animals in layer V), estimated over 10 s epochs when the cortex displayed SCOs (T = 1197, P = 3.5e−4, r = 0.34, and T = 2484, P = 3.7e−13, r = 0.61, respectively, Wilcoxon signed rank test). Since the mean variance may be influenced by any instability in the temporal features of the SCOs (Bernardi et al. 2018), we also measured the difference in the mean amplitude between the UP and DOWN states through the amplitude histograms obtained in layers V and VI in 3 animals in which SCOs were regular enough yielding bimodal amplitude distributions (Fig. 2D). These were 0.45 ± 0.14 and 0.34 ± 0.07 mV in control conditions and 0.1 ± 0.03 and 0.16 ± 0.06 mV after exposure to lidocaine, respectively (median ± MAD of 45 observations; T = 1020, P = 1.44e−8, r = 0.6 and T = 962, P = 5.02e−7, r = 0.53), reflecting a 78% and 53% reduction. In addition, the diminished SCOs lost the characteristic spatial landmarks, i.e., the peak maximum in layer V and the polarity reversal at layer II/III (Fig. 2E and Supplementary Fig. S3), which already suggested a distant origin out of the treated volume. As expected, the CSD analysis revealed a complete absence of current sinks and sources in the cortex (not shown) indicating that all FP activity had reached there through volume-conduction. We also measured the power of FPs recorded in the stratum lacunosum-moleculare (L-M) of the CA1 region before and after lidocaine was delivered to the overlying V2 cortex. There was no significant effect either during the SCO or theta states (SCO state: 0.045 ± 0.009 mV2 vs. 0.054 ± 0.011 mV2, median ± MAD of 96 observations in n = 5 animals, T = 690, P = 0.29, r = 0.11; theta state: 0.058 ± 0.01 mV2 vs. 0.055 ± 0.008 mV2, 85 observations from n = 5 animals, T = 437, P = 0.51, r = 0.11). In order to test for possible distant effects of lidocaine, a recording probe was placed in 2 animals in the M1 cortex in addition to V2. We observed a small reduction of the mean power in one of them, whereas the depth profiles and landmarks of SCOs remained unchanged (see Supplementary Fig. S3). The Cortex Exports or Imports Volume-Conducted Activity in Different Electrographic States The cortex and hippocampus both produce large FPs and they contribute V-C activity to each other (Fig. 1B). In a first approach, this was studied through a single linear array spanning V2 and the dorsal part of the hippocampus and the Dentate Gyrus (DG). The dominant direction of the V-C activity between these structures can be visualized by plotting all pair-wise cross-correlations of the FPs simultaneously recorded with the linear array onto a spatial matrix, which provided spatial and anatomical perspective (Pearson’s lineal coefficients: CC, cross-correlation maps in Fig. 2E,F). Due to the instantaneity of electric fields, values close to 1 or −1 most likely arise from the same dipolar voltage shell, regardless of whether the sites are close or distant, while intermediate values of CC indicate the presence of several uncorrelated activities. We found that the strongest FP sources define the main origin and the target structures of the V-C activity. Thus, during SCOs under control conditions (Fig. 2E), the cortex-hippocampus correlation zone reproduced the intracortical pattern of correlation, in turn dominated by the SCO dipole, indicating a dominance of V-C activity from the cortex to the hippocampus. After cortical blockade (lower panels), the SCOs disappeared and the remaining cortical activity was still highly correlated internally, and with the hippocampus. Similar results were found in 5 animals (Supplementary Fig. S3). For instance, the CC between a pair of sites in the cortex and the hippocampus (asterisks) was 0.61 ± 0.11 in control vs. 0.37 ± 0.15 after lidocaine, respectively (the data are the median ± MAD obtained from 108 observations in n = 5 animals, each 15 s long; Wilcoxon signed rank test, T = 1419, P = 4.7e−10, r = 0.6). The moderate reduction was due to the still present hippocampal activity that also spread to the cortex. That is, the CC was biased by self-correlation of the SCO voltage recorded at the 2 sites. By contrast, the gross direction of the V-C activity reversed during cortical activated state (hippocampal theta: Fig. 2F andSupplementary Fig. S3) and the intracortical CCs reproduced intra-hippocampal correlations that were dominated by the theta dipole in CA1. The regularity and large amplitude of the theta rhythm allowed a direct visualization of its extension into the V2 cortex (Fig. 2F). In this case, the CC increased notably despite the lidocaine blockade of cortical activity (0.65 ± 0.12 vs. 0.82 ± 0.04, respectively; median of 80 observations in n = 5 animals; T = 0, P = 8.3e−6, r = 0.7). The loss of local but not V-C activity in the cortex was also appreciated in the drastic reduction of the slow (<2 Hz) components in the power spectra of the main cortical SCO generator (Fig. 2F: red circle in blue trace), while the theta band (~4 Hz) persisted in the raw FP recorded in cortical layer V (black trace) that reached there from the hippocampus. Indeed, the theta activity was captured by a CA1 FP generator in the stratum lacunosum-moleculare (L-M: green traces below FPs in Figs. 2E,F, and Supplementary Fig. S3) (Benito et al. 2014). State and Regional Dependence of Local and Remote Cortical Generators We examined the FP generators in 3 cortical regions (M1, the somatosensory S1 cortex, and V2; Fig. 3A) in 2 electrographic states defined by the presence of SCOs or hippocampal theta. All cortices displayed a reduced number of 8–9 components with a distinct spatial distribution. For quantification, we selected only those that appeared consistently in 60 s epochs and that contributed to most of the variance (see Fig. 3B and Supplementary Fig. S2). An experiment illustrating the characteristic voltage profiles of the main FP generators is shown in Fig. 3C, and the population data for the V2 cortex is shown in Fig. 3D. In the SCO state, the ICA may return 2 or 3 broad generators that strongly overlap across cortical layers and thus, we clustered them into one and termed it the SCO generator (Fig. 3C, voltage profile in blue). Presumably, this generator may still group several independent generators that are highly coherent in the SCO state. This generator exhibited a maximum in layer V and a reversal of polarity at ~400 μm below the pial surface. Two other well defined FP generators were found in all cortices, one with a maximum in layer III, ~250 μm above the peak of the SCO termed as C-III (Fig. 3C, V-profiles in brown), which was mostly active at the start and end of the SCOs (Fig. 1B), and another with a flat distribution (traces in purple). In the different cortical areas, this non-zero linear generator may display SCO activity, alpha oscillations, low-gamma or a ~2 Hz oscillatory activity consisting of small sawtooth-like irregular waves (note that multiple remote sources enter to all electrodes in a distant recording probe with proportional power and cannot be separated by the ICA: see below). It was particularly noticeable that SCOs dominated the linear generator preferentially in the most frontal cortex examined (M1), and they were coherent with local SCOs (Supplementary Fig. S4A). We hypothesized that this is an effect of the strong curvature in the frontal cortices and it was examined by the mathematical model (see Supplementary Fig. S3B and below). Figure 3. Open in new tabDownload slide State and regional dependence of local and remote cortical generators. (A) Schematic representation of recording arrays in the M1, S1 and V2 cortices. (B) Pretreatment of signals using a “peeling” method for the initial selection of components used for the ICA. The k index represents the number of principal components maintained in the FP matrix and the ICs are the number of components obtained by a subsequent ICA. See Supplementary Fig. S2. (C) The voltage profiles of the main FP generators are depicted in solid lines (SCO in blue, CIII in brown, and remote flat in purple), and those less stable are in dotted lines. Blue arrowheads point to the center of layer V. Note in the stable components how they retain their anatomical landmarks in the different cortices (the narrowing of the FP generators in the V2 cortex corresponding to the reduced width). The insets show the relative variance each generator contributed to the raw FPs. During the cortical activated state, some FP generators remained but other new ones appeared that were highly unstable over time. Data are from an illustrative experiment. (D) Population data of voltage profiles for found generators in the V2 cortex in the SCO state. Thin and thick traces correspond to individual animals and the mean inter-animal profile (mean ± SEM). The profiles were aligned by the SCO reversal site in each animal (n = 5–7), and they were sorted by hierarchical clustering. (E) Relative contribution and spectral content of local and remote cortical generators. The mean power was plotted for raw FPs in 3 cortical layers (II, III, and V), for the M1, S1, and V2 cortices, while only layer V was plotted for the remote contribution (purple circles). Empty and solid circles represent Individual animal values and population data (mean ± SEM). Figure 3. Open in new tabDownload slide State and regional dependence of local and remote cortical generators. (A) Schematic representation of recording arrays in the M1, S1 and V2 cortices. (B) Pretreatment of signals using a “peeling” method for the initial selection of components used for the ICA. The k index represents the number of principal components maintained in the FP matrix and the ICs are the number of components obtained by a subsequent ICA. See Supplementary Fig. S2. (C) The voltage profiles of the main FP generators are depicted in solid lines (SCO in blue, CIII in brown, and remote flat in purple), and those less stable are in dotted lines. Blue arrowheads point to the center of layer V. Note in the stable components how they retain their anatomical landmarks in the different cortices (the narrowing of the FP generators in the V2 cortex corresponding to the reduced width). The insets show the relative variance each generator contributed to the raw FPs. During the cortical activated state, some FP generators remained but other new ones appeared that were highly unstable over time. Data are from an illustrative experiment. (D) Population data of voltage profiles for found generators in the V2 cortex in the SCO state. Thin and thick traces correspond to individual animals and the mean inter-animal profile (mean ± SEM). The profiles were aligned by the SCO reversal site in each animal (n = 5–7), and they were sorted by hierarchical clustering. (E) Relative contribution and spectral content of local and remote cortical generators. The mean power was plotted for raw FPs in 3 cortical layers (II, III, and V), for the M1, S1, and V2 cortices, while only layer V was plotted for the remote contribution (purple circles). Empty and solid circles represent Individual animal values and population data (mean ± SEM). The combined analysis of FPs in the cortex and hippocampus (Fig. 1B) may return multiple non-zero linear parts across the cortical width, and they were segregated by the ICA as they hung from different hippocampal generators. On the contrary, in cortical-only recordings, such linear parts could not be disentangled and they remained unified in a single linear generator (e.g., Supplementary Fig. S4A). One exception was found in the V2 cortex, which returned an additional generator with a profile that increased in power in the deep cortical layers (Fig. 3D, green traces) immediately above the hippocampus. This generator could be tracked to the st. L-M of the hippocampal CA1 upon lowering the recording probe, and it was identified as the L-M (theta) generator (asterisk in Fig. 1B and green traces in Fig. 2E). Some of the generators that displayed cortical maxima in the SCO state were also detected in the activated cortical state, albeit with a much reduced variance (Fig. 3C). However, a variable number of additional generators appeared in different epochs (dotted profiles), suggesting that synaptic pathways co-activate less markedly than during the SCO state. Indeed, the mean variances were not quantified because of their instability. Relative Contribution and Spectral Content of Local and Remote Cortical Generators To quantify the relative contribution of local and remote generators to different cortical layers and regions, we reconstructed the virtual FPs produced by each type (i.e., local generators were summed into one) and the mean variance was then estimated in 60 s epochs during the SCO state. The proportion of the remote contribution was stronger in cortical layers I–III, as these produced small local FPs (e.g., Fig. 2C; but see below). Taking the sum of local and remote power as a reference, the remote contribution to layer II was 29 ± 11% in the M1 cortex, 22 ± 9% in the S1 cortex, and 24 ± 12% in the V2 cortex (measured ~200 μm under the pia; n = 5 animals). By contrast, at the site of polarity reversal of the SCOs, the relative contributions were 65 ± 14%, 58 ± 12%, and 64 ± 15%, and they were 14 ± 8%, 14 ± 10% and 13 ± 7% in layer V (~1 mm below where the SCOs were maximal). Since power is dominated by low frequency activity, we also quantified the contribution of local and remote generators to specific frequency bands predefined to contain the most characteristic cortical oscillations: SCOs, theta, alpha, and low-gamma activity (60 s epochs per animal; n = 5; Fig. 3E). In general, the remote generators contributed markedly to the power in all frequency bands, cortices, and layers. In the SCO band (delta: 0.1–3 Hz), the remote contribution to cortical layer V was weak (0.007–0.02 mV2) and it was significantly smaller than the local contribution in the M1 (ANOVA: F(1,9) = 22, P = 0.0015) and V2 cortices (F(1,9) = 16, P = 0.0036). Remote and local generators contributed similar amounts to the theta band (3–8 Hz), whereas in the alpha (8–20 Hz) and the low-gamma (20–80 Hz) frequency bands, the remote generators contributed to cortical FPs similarly or more strongly than local ones (alpha range, 8 × 10−4 to 15 × 10−4 mV2; low-gamma, 3.3 × 10−4 to 7.5 × 10−4 mV2) and they were only significantly larger in the V2 cortex (alpha, F(1,9) = 6, P = 0.04; low-gamma, F(1,9) = 14, P = 0.005). The temporal course of the activity within different frequency bands was not addressed explicitly (see examples in Fig. 4 and Supplementary Fig. S4), but we found significant inconsistencies between customary activities and the canonic frequency band they are normally assigned to. For instance, SCOs normally run on delta activity (1–2 Hz), but in some epochs, this cortical generator displayed genuine theta oscillations that were consistently shorter (100–200 ms) and conformed small strings of cortical theta (Fig. 4A). However, theta oscillations may also appear in some cortices due to volume-conduction from the hippocampus (e.g., the V2 shown in Fig. 2E). Also, the mutual V-C between generators in 2 structures displaying waves of similar duration led to notable changes in the time-course of recorded FPs. Notably, theta waves independently generated in the cortex (short SCOs) and hippocampus may summate, annihilate, or undergo varying phase shift in different recording sites depending on the respective phases in origin (Fig. 4A). Thus, the cross-contamination between local and remote contributions made the time courses of raw FPs to significantly deviate from their local contributions. Figure 4. Open in new tabDownload slide Temporal details of local and remote cortical generators and some interactions. (A) The mutual volume-conduction of theta waves between the V2 cortex and hippocampus severely distorts the FPs in both regions. Hippocampal theta waves are generated in the st. L-M of the CA1 region (green FP traces and L-M generator), and the cortex may also produce waves of similar duration (blue FP traces) that belong to the SCO generator (trace and V-profile in blue). These 2 FP generators extend significant V-C activity into the adjacent structure, and the relative power and polarity varies with the site of recording (ovals in the V-profiles to the right). In this epoch, theta appeared to alternate between the cortex and hippocampus (ovals in raw FPs), and the wavelet spectra detected intermittent theta activity in the CA1 st. L-M (arrowheads). However, this was not clear in the L-M generator that displayed rather steady theta amplitude (green trace). The discrepancy is explained by the joint effect of the amplitude, polarity, and specific phases of individual cortical and hippocampal waves that varied in different moments (3 cases are outlined in different colors in the enlarged fragment below. The green boxes mark when theta developed only in the hippocampus: polarity reversal at the st. pyramidale/radiatum border, and all cortical theta is V-C from the hippocampus (red oval). The blue box marks instances when both the cortex and the hippocampus develop theta waves that are in phase: no polarity reversal due to dominant V-C cortical waves that overcome hippocampal ones. The beige box marks when cortical and hippocampal waves were in anti-phase: V-C cortical waves subtract the local hippocampal ones in the st. L-M and almost completely annihilated, while they are preserved in the cortex. (B) Volume-conducted and genuine types of alpha oscillations in the M1 cortex. Some bouts displayed similar power across all layers (purple oval) that indicated a remote origin, while local bouts displayed marked gradients and cortical maxima (green oval). These 2 spatial patterns segregated into 2 different FP generators (color traces below). (C) Local and remote gamma generators in the cortex. The traces correspond to simultaneous recordings across the M1 cortex (e1–32) and the V2/CA1/DG (e33–64), bandpass filtered (20–100 Hz) to highlight the gamma activity. Bouts of gamma activity were not coherent in these cortices, and may appear in the upper or the lower halves of the cortex (red and blue ovals, respectively). Note the drifting phase in the superficial layers (black dashed lines). Gamma waves also appeared with a similar amplitude across the cortical width and they continued into subcortical zones (purple oval), which were, therefore, considered to be of remote origin. The V-profiles of the respective FP generators are shown to the left. For reference, the V-profiles of the main SCO and C-III cortical generators are also shown. Figure 4. Open in new tabDownload slide Temporal details of local and remote cortical generators and some interactions. (A) The mutual volume-conduction of theta waves between the V2 cortex and hippocampus severely distorts the FPs in both regions. Hippocampal theta waves are generated in the st. L-M of the CA1 region (green FP traces and L-M generator), and the cortex may also produce waves of similar duration (blue FP traces) that belong to the SCO generator (trace and V-profile in blue). These 2 FP generators extend significant V-C activity into the adjacent structure, and the relative power and polarity varies with the site of recording (ovals in the V-profiles to the right). In this epoch, theta appeared to alternate between the cortex and hippocampus (ovals in raw FPs), and the wavelet spectra detected intermittent theta activity in the CA1 st. L-M (arrowheads). However, this was not clear in the L-M generator that displayed rather steady theta amplitude (green trace). The discrepancy is explained by the joint effect of the amplitude, polarity, and specific phases of individual cortical and hippocampal waves that varied in different moments (3 cases are outlined in different colors in the enlarged fragment below. The green boxes mark when theta developed only in the hippocampus: polarity reversal at the st. pyramidale/radiatum border, and all cortical theta is V-C from the hippocampus (red oval). The blue box marks instances when both the cortex and the hippocampus develop theta waves that are in phase: no polarity reversal due to dominant V-C cortical waves that overcome hippocampal ones. The beige box marks when cortical and hippocampal waves were in anti-phase: V-C cortical waves subtract the local hippocampal ones in the st. L-M and almost completely annihilated, while they are preserved in the cortex. (B) Volume-conducted and genuine types of alpha oscillations in the M1 cortex. Some bouts displayed similar power across all layers (purple oval) that indicated a remote origin, while local bouts displayed marked gradients and cortical maxima (green oval). These 2 spatial patterns segregated into 2 different FP generators (color traces below). (C) Local and remote gamma generators in the cortex. The traces correspond to simultaneous recordings across the M1 cortex (e1–32) and the V2/CA1/DG (e33–64), bandpass filtered (20–100 Hz) to highlight the gamma activity. Bouts of gamma activity were not coherent in these cortices, and may appear in the upper or the lower halves of the cortex (red and blue ovals, respectively). Note the drifting phase in the superficial layers (black dashed lines). Gamma waves also appeared with a similar amplitude across the cortical width and they continued into subcortical zones (purple oval), which were, therefore, considered to be of remote origin. The V-profiles of the respective FP generators are shown to the left. For reference, the V-profiles of the main SCO and C-III cortical generators are also shown. In the alpha band, we found that remote contribution to cortical FPs was dominant and consisted of short bouts of a few (3–8) waves of uniform amplitude across the cortical layers (Fig. 4B, purple oval), occasionally clustering over long periods (20–60 s). Genuine cortical bouts of activity (with cortical maxima) were even less frequent (Fig. 4B, green oval). Local cortical gamma activity appeared as short bouts of regular oscillations during the UP state of SCO waves, and they typically segregated into 2 foci centered in the upper and lower halves of the cortex (Fig. 4C). The strings of gamma waves were not coherent across different cortices. Small waves spanning all cortical layers contributed to the remote gamma activity, exhibiting a variable temporal pattern and often representing a background contribution that constituted most of the low-gamma power in the V2 cortex (7.5 × 10–4 mV2 compared to 1.1 × 10–4 mV2 by local generators). The Extended and Curved Shape of the Cortical Mantle Boosts the Reach of FPs One of the principal factors promoting the buildup of extracellular currents (hence the V-C activity) is the extent of spatial coherence (i.e., the size of the source; Nunez and Srinivasan 2006). Since the coherence between FPs in 2 different cortices may vary due to the different pattern of activation of synaptic inputs in different areas and cortical layers, we measured the coherence on a FP generator, which by contrast to raw FPs, they have proportional values in all layers. We chose the SCO generator for its stability and easy identification in different cortices. The CC between the M1 and V2 cortices in the SCO state was high and it dropped dramatically in the activated state (0.78 ± 0.12 vs. 0.16 ± 0.12, respectively; median ± MAD of 30 and 24 observations in n = 5 and n = 4 animals; data over 10 s epochs; all correlations were statistically significant; Wilcoxon signed rank test: T = 280, P = 2.04e−4, r = 0.48). Hence, there appeared to be extended interregional synchronization of this cortical generator in the SCO state that nearly disappeared in the activated state when the participating inputs are functionally regionalized. The strong coherence of SCOs in different cortical regions offers a unique opportunity to explore how a large curved structure spreads V-C potentials over the whole brain. According to biophysical tenets, curved populations produce a clustering of V-C currents on the concave side, leading to larger FPs than in planar structures (Woodbury 1960; Fernández-Ruiz et al. 2013). We explored to what extent the macroscopic curvatures of the cortical mantle and the hippocampus may affect the reach of their activities through V-C. We first estimated the cortical coherence of SCOs between distant cortical areas in experiments by using a stationary pipette in layer V of V2 and another traversing across the striatum up to the rhinal fissure (Fig. 5A). The amplitude of the SCOs decreased smoothly with a slight drop when the moving pipette traversed the striatum, and the CC between sites in layer V of V2 and any other along the track remained high (e.g., 0.72 ± 0.12, mean ± SEM between V2 and the insular cortices; 8 observations from n = 3 animals). Such a strong correlation reflects the prominent temporal synchronization of SCOs across distant cortices, fulfilling the criteria necessary for the mutual amplifying summation of V-C currents in curved structures. Figure 5. Open in new tabDownload slide Coherence of SCOs across the curved cortical mantle boosts volume-conduction into subcortical sites. (A) Sample recordings (raw traces) and CC (lower plot) between SCOs recorded in the V2 cortex (black) and along an oblique trajectory from the V2 to the insular cortex (gray). Individual (thin) and mean ± SEM of 8 profiles in n = 3 animals (thick). (B) Slow cortical oscillation amplitude in subcortical sites using 2 linear arrays recording simultaneously along 2 parallel trajectories across multiple brain structures. SCOs reduced only moderately in subcortical sites far from their origin (upper traces). The lower plot illustrates the individual (empty circles) and mean value (filled circles) estimated from n = 3 animals (2–3 tracks per animal). Higher values in the st. L-M of the CA1 correspond to local delta activity different from SCOs. The symbols represent the successive recording stations. Figure 5. Open in new tabDownload slide Coherence of SCOs across the curved cortical mantle boosts volume-conduction into subcortical sites. (A) Sample recordings (raw traces) and CC (lower plot) between SCOs recorded in the V2 cortex (black) and along an oblique trajectory from the V2 to the insular cortex (gray). Individual (thin) and mean ± SEM of 8 profiles in n = 3 animals (thick). (B) Slow cortical oscillation amplitude in subcortical sites using 2 linear arrays recording simultaneously along 2 parallel trajectories across multiple brain structures. SCOs reduced only moderately in subcortical sites far from their origin (upper traces). The lower plot illustrates the individual (empty circles) and mean value (filled circles) estimated from n = 3 animals (2–3 tracks per animal). Higher values in the st. L-M of the CA1 correspond to local delta activity different from SCOs. The symbols represent the successive recording stations. We also estimated the amplitude of SCOs volume-conducted to subcortical sites across the brain using 2 parallel arrays moving along vertical tracks from the V2 and M1 cortices down to 7 mm below the surface (Fig. 5B). The peak amplitude was located in layer V of both areas reaching 1.25 ± 0.14 and 0.99 ± 0.05 mV (mean ± SEM in layer V of the M1 and V2 cortices, respectively), dropping smoothly to 0.57 ± 0.15 and 0.48 ± 0.06 mV in the lower parts of the brain. Brain structures as distant as the substantia nigra and the nucleus accumbens displayed V-C SCOs of similar amplitude although the waveforms differed somewhat, probably due to the influence of different cortical regions (CC, 0.79 ± 0.03, estimated over 60 s epochs in n = 3 animal; all correlations were statistically significant, P = 0). One exception was found in the stratum L-M of the CA1, which typically displayed delta activity of its own (Benito et al. 2014) in the same epochs as the cortex (see amplitude at position 3 mm in Fig. 5B). Such delta activity reflected inputs from the perforant pathway to the CA1/DG (Benito et al. 2014), and while it may appear with high coherence with that in the cortex it may also be totally disengaged from it. Notably, subcortical SCOs differed from the cortical ones in that they lost the abrupt start and end voltage deflections and they became sawtooth-like (see traces at position 6 mm in Fig. 5B), suggesting incomplete coherence of the start/end timings of SCOs (hence volume averaging) from multiple cortical areas. In addition, subcortical SCOs never displayed any associated current in a CSD analysis, corresponding closely to the flat profiles obtained by the ICA (not shown). In order to gain a quantitative view of how the V-C activity from extended (SCOs) or fragmented (activated state) cortical modules invaded different parts of the brain, we set up a large-scale model of the cortical mantle that reproduced about two-thirds of the anterior part of one hemisphere (>2.5 million layer V PCs; Fig. 6A, see Methods). The curved shape was mimicked by 6 planar blocks 3-dimensionally arranged at the appropriate angles (Fig. 6A, top panels, see Methods). The entire CA1 population of PCs was also included to simulate theta activity and the V-C potentials into the cortex and other structures. The voltage was plotted as series of mediolateral cuts of the entire brain at an instant when the simulated activities attained maximum voltage (Fig. 6A, plots on the right), while the temporal variations in a sagittal section are described in video (Videos S1 and S2). The simulations corresponded to coherent activation over different cortical expanses, which ranged from small cortical modules (0.5 mm wide) mimicking the activated cortical state (upper row), to the entire cortical mantle mimicking the SCO state (third row). For simplicity, the posterior cortices were excluded as they were found to have a rich local repertoire of FP activity in pilot experiments that deserve in depth scrutiny. The effect of reducing or enlarging coherence closely fitted the experimental measurements and explained the recordings of SCOs throughout the brain. Moreover, the hippocampal theta rhythm (bottom row) produced strong V-C FPs that affected a limited portion of subcortical structures that were mostly contained at the concave side of its curved shape (thalamus). They also spread rather selectively to the overlying dorsal and posterior cortices, again as recorded experimentally (compare Figs. 6C,D). Figure 6. Open in new tabDownload slide Spatial reach of FPs across brain structures obtained with a large-scale tridimensional model of the cortex and hippocampus (A) or a finite element approach (B). (A) The model represents about two-thirds of the anterior part of a cortical hemisphere, excluding the posterior cortices (faint portion of the image). The cortical mantle was built using 6 planar blocks at appropriate angles to simulate the curvature. Serial representations of the sagittal cuts represent the spatial voltage gradients across the entire brain for different modes of cortical and hippocampal activation. The structures drawn are only for reference and they were obtained from atlas sections at the marked lateral positions. The time instant plotted is depicted by the red lines in the sample FP model trace on the right. The black and green traces correspond to a cortical and a deep recording site (marked in the central panel of the upper series). The active cortex was simulated by activating 2 independent 0.5 mm wide cortical modules with excitatory gamma oscillations. Note the dipolar distribution of the associated FPs that decayed rapidly away from the source neurons. The second and third rows illustrate extended coherent activation over the dorsal cortex (planar configuration) and all 6 cortical blocks mimicking the curved cortical mantle. In the latter case, the decay in the more distant part of the brain was to about half the amplitude in the origin, as found in the experiments. The lower row shows the spatial distribution of the dipolar voltage recorded across the brain during hippocampal theta rhythm, simulated by synaptic input to the st. L-M of the CA1 PCs. Sizable V-C theta waves were only recorded in the V2 cortex overlying the hippocampus, while prominent theta voltages also expand within the concave side of the macroscopic C-shape, extending into the thalamus and nearby structures. Scale color bar: ±0.15 mV (first row) and ±0.6 mV (other rows). (B) A FEM model of a 4 mm portion of one hemisphere that included the corresponding portions of the corpus callosum and the ventricle. This model lacks the frontal cortices implemented in A (see Supplementary Fig. S1). Only the values at the central slab are shown. Note similar values for FPs at distant sites of the cortex as in A. (C,D) Model and experimental FPs of theta activity recorded in different parts of the brain showing similar decays of theta amplitude with distance. FPs were represented after AC-coupling to reproduce the experimental conditions (see Videos S1 and S2 for a comparison with DC-coupled FPs). Figure 6. Open in new tabDownload slide Spatial reach of FPs across brain structures obtained with a large-scale tridimensional model of the cortex and hippocampus (A) or a finite element approach (B). (A) The model represents about two-thirds of the anterior part of a cortical hemisphere, excluding the posterior cortices (faint portion of the image). The cortical mantle was built using 6 planar blocks at appropriate angles to simulate the curvature. Serial representations of the sagittal cuts represent the spatial voltage gradients across the entire brain for different modes of cortical and hippocampal activation. The structures drawn are only for reference and they were obtained from atlas sections at the marked lateral positions. The time instant plotted is depicted by the red lines in the sample FP model trace on the right. The black and green traces correspond to a cortical and a deep recording site (marked in the central panel of the upper series). The active cortex was simulated by activating 2 independent 0.5 mm wide cortical modules with excitatory gamma oscillations. Note the dipolar distribution of the associated FPs that decayed rapidly away from the source neurons. The second and third rows illustrate extended coherent activation over the dorsal cortex (planar configuration) and all 6 cortical blocks mimicking the curved cortical mantle. In the latter case, the decay in the more distant part of the brain was to about half the amplitude in the origin, as found in the experiments. The lower row shows the spatial distribution of the dipolar voltage recorded across the brain during hippocampal theta rhythm, simulated by synaptic input to the st. L-M of the CA1 PCs. Sizable V-C theta waves were only recorded in the V2 cortex overlying the hippocampus, while prominent theta voltages also expand within the concave side of the macroscopic C-shape, extending into the thalamus and nearby structures. Scale color bar: ±0.15 mV (first row) and ±0.6 mV (other rows). (B) A FEM model of a 4 mm portion of one hemisphere that included the corresponding portions of the corpus callosum and the ventricle. This model lacks the frontal cortices implemented in A (see Supplementary Fig. S1). Only the values at the central slab are shown. Note similar values for FPs at distant sites of the cortex as in A. (C,D) Model and experimental FPs of theta activity recorded in different parts of the brain showing similar decays of theta amplitude with distance. FPs were represented after AC-coupling to reproduce the experimental conditions (see Videos S1 and S2 for a comparison with DC-coupled FPs). We also explored the distortion of V-C produced by tissue heterogeneities and anisotropy using the FEM model (see Methods). The most relevant structures were the corpus callosum and the ventricle (see Supplementary Fig. S1). In general, they had a mild to negligible effect depending on the spatial extent and shape of the source, and the distances between sources, heterogeneities, and recording sites. For instance, a reduction of the FP generated by cortical sources was found inside the corpus callosum on account of the higher resistivity, although the effect waned with distance to recording sites. Also, the larger was the cortical source the smaller was the reduction of the FP at distant sites produced by heterogeneities near the sources (see details in Supplementary Fig. S1). Similar trend was found for the V-C of subcortical FPs into the cortex. Anisotropy in the corpus callosum (1:9 in the direction of the fibers) and the ventricle had negligible effects. Therefore, except for sites in the vicinity of the corpus callosum the V-C of widely synchronous SCOs was efficiently estimated by the H–H compartmental model that did not consider tissue heterogeneities (e.g., compare Figs. 6A,B). Local and Distant Coherent Contributions to Cortical FPs can be Discriminated in FP Generators So far, we have shown that a multisite linear sample of raw FPs is sufficient to disclose the local and remote contributions, and to estimate their frequency and power features. Experimental evidence of V-C contribution from distant generators was derived from blocking local cortical activity (Fig. 2). Interestingly, we found that the gradual reduction in the bell-shaped portion of the SCO generator (Fig. 7A, arrowhead in blue solid curve; see also Supplementary Fig. S3) unveiled an underlying quasi-linear part (blue dashed trace). This drug-resistant linear component of the SCO generator should therefore arise from regions not affected by the drug. A hippocampal origin for this linear portion is unlikely since hippocampal generators maintained their landmarks, including the linear portion in the cortex (Fig. 7A, asterisk in green traces), and their activities differed significantly. Thus, we hypothesized that the curved and the linear parts of the SCO’s voltage profile are due to coherent activity in cortical regions close to and at a certain distance from the recording probe, respectively. Figure 7. Open in new tabDownload slide Computational study of the buildup, spatial reach and disentangling of local and distant cortical contributions to FP voltage profiles. (A) Experimental V-profiles of the cortical SCO (solid blue) and the hippocampal L-M generators (solid green). The peak maximum and zero crossing of the SCO generator (arrows) disappeared after lidocaine blockade in the cortex (dashed traces), revealing an underlying flat component (blue asterisk). This was not originated in the hippocampus, which generators maintained their local maxima and flat voltage tails in the cortex (green asterisk). (B–E) Feed-forward realistic model simulating large portions of the candidate structures to enter V-C potentials to the cortex (B): the cortex itself (green), the hippocampal CA1 (purple) and the DG (red). The cortical slab and the hippocampal sheets mark the cell body layers of modeled neuron aggregates. Linear profiles of modeled FPs integrating activities from all neuron aggregates (C) were analyzed as for real FPs in control conditions (D), and (E) after removal of local cortical activity (cylinder in B). The laminar profile of the FP mean power is shown to the left, and the ICA segregation of the pathway-specific FP generators to the right. Note the disappearance of the cortical maximum of the SCO generator that uncovered a flat component (blue arrows). (F–H) Further exploration on the origin of flat cortical components through a cortical-only model with blockade of increasing size around the electrode (Ø: 0, 0.1, 0.2, 0.5, 0.75, 1, and 2 mm). Only distant contributions of layer V PCs were allowed (red arrowheads). The V-profiles (G) showed a gradual reduction in the cortical maxima with displacement of the peak value (horizontal dashes), and they revealed a flat component (dark to light blue profiles). The blue and red arrowheads mark the cortical and subcortical sites plotted in H, respectively. Note that subcortical recordings were poorly affected by removing sensible portions of cortical activity due to equalization of the distances of remaining cortical currents to all the electrodes. (I–K) The effect of increasing the extension of an activated cortical slab (width: 0.5 and 1–6 mm). (J) The V-profiles barely displace the maxima (horizontal dashes) as the nearby contribution is already maximized for the smaller slab. (K) The local FP peak amplitude (blue plot) saturates at cortical sites ~2 mm wide while it still increased at subcortical sites (red plot). For comparison, the black profile corresponds to a more comprehensive model incorporating larger cortical models and curvature (Fig. 6A). The small arrows indicate an offset-like effect caused by the almost equal contribution of distant neurons and cortices to a given recording site. (L-N) Contribution of different cortical modules of the same size (barrel cortex-like) with independent activation (Isyn: temporal patterns of synaptic conductances in layer V PCs) to a linear array of FPs in one of them (recoding is in the blue module). The lower plots (L) depict the FPs recorded in cortical layers III and V of the blue module contributed by each of 3 modules when activated in isolation (1–3→rec). (M) The integrated FP profile (upper traces) and the ICA components obtained from it (lower traces) are shown along with the relative variance. The contribution of cortical modules of increasing size (and distance) is shown in (N). For modules of 0.5 mm wide and larger, the distant contribution becomes negligible. The percentage contribution of local and remote modules is shown in the lower plots. (O) Exploration of FP contribution by cortical modules of different size. The V-profiles of the FP generators reveal distinctive spatial features of the contribution by the local module (blue profile) even when it contributed less than adjacent or distant modules. Figure 7. Open in new tabDownload slide Computational study of the buildup, spatial reach and disentangling of local and distant cortical contributions to FP voltage profiles. (A) Experimental V-profiles of the cortical SCO (solid blue) and the hippocampal L-M generators (solid green). The peak maximum and zero crossing of the SCO generator (arrows) disappeared after lidocaine blockade in the cortex (dashed traces), revealing an underlying flat component (blue asterisk). This was not originated in the hippocampus, which generators maintained their local maxima and flat voltage tails in the cortex (green asterisk). (B–E) Feed-forward realistic model simulating large portions of the candidate structures to enter V-C potentials to the cortex (B): the cortex itself (green), the hippocampal CA1 (purple) and the DG (red). The cortical slab and the hippocampal sheets mark the cell body layers of modeled neuron aggregates. Linear profiles of modeled FPs integrating activities from all neuron aggregates (C) were analyzed as for real FPs in control conditions (D), and (E) after removal of local cortical activity (cylinder in B). The laminar profile of the FP mean power is shown to the left, and the ICA segregation of the pathway-specific FP generators to the right. Note the disappearance of the cortical maximum of the SCO generator that uncovered a flat component (blue arrows). (F–H) Further exploration on the origin of flat cortical components through a cortical-only model with blockade of increasing size around the electrode (Ø: 0, 0.1, 0.2, 0.5, 0.75, 1, and 2 mm). Only distant contributions of layer V PCs were allowed (red arrowheads). The V-profiles (G) showed a gradual reduction in the cortical maxima with displacement of the peak value (horizontal dashes), and they revealed a flat component (dark to light blue profiles). The blue and red arrowheads mark the cortical and subcortical sites plotted in H, respectively. Note that subcortical recordings were poorly affected by removing sensible portions of cortical activity due to equalization of the distances of remaining cortical currents to all the electrodes. (I–K) The effect of increasing the extension of an activated cortical slab (width: 0.5 and 1–6 mm). (J) The V-profiles barely displace the maxima (horizontal dashes) as the nearby contribution is already maximized for the smaller slab. (K) The local FP peak amplitude (blue plot) saturates at cortical sites ~2 mm wide while it still increased at subcortical sites (red plot). For comparison, the black profile corresponds to a more comprehensive model incorporating larger cortical models and curvature (Fig. 6A). The small arrows indicate an offset-like effect caused by the almost equal contribution of distant neurons and cortices to a given recording site. (L-N) Contribution of different cortical modules of the same size (barrel cortex-like) with independent activation (Isyn: temporal patterns of synaptic conductances in layer V PCs) to a linear array of FPs in one of them (recoding is in the blue module). The lower plots (L) depict the FPs recorded in cortical layers III and V of the blue module contributed by each of 3 modules when activated in isolation (1–3→rec). (M) The integrated FP profile (upper traces) and the ICA components obtained from it (lower traces) are shown along with the relative variance. The contribution of cortical modules of increasing size (and distance) is shown in (N). For modules of 0.5 mm wide and larger, the distant contribution becomes negligible. The percentage contribution of local and remote modules is shown in the lower plots. (O) Exploration of FP contribution by cortical modules of different size. The V-profiles of the FP generators reveal distinctive spatial features of the contribution by the local module (blue profile) even when it contributed less than adjacent or distant modules. To explore this hypothesis, we built a realistic feed-forward compartmental model mimicking the experiments with cortical blockade. The model simulated FPs along a V2-like recording track in a multistructure conglomerate of the relevant neuron populations, the dorsal cortex (a 6 × 6 mm slab), the entire CA1 field, and a dorsal slab of the DG (2 × 2 mm) (Fig. 7B). This allowed V-C to integrate the SCO-like activation in cortical layer V pyramidal cell (PC) neurons, and other pathway-specific temporal patterns in the hippocampus (delta, theta, gamma, or irregular; for details see Methods). The model FPs obtained displayed a characteristic laminar profile with several maxima (Fig. 7C), corresponding to the active sites of the modeled synaptic sources (except in the DG, which was maximal in the hilus due to layer folding (Fernández-Ruiz et al. 2013). The ICA was highly effective in separating the pathway-specific FPs (Fig. 7D, IC’s V-prof). Each generator had voltage maxima in the source regions and a smooth almost-linear decay that reached adjacent structures, albeit at different rates (compare Figs 7D and 1B). The remote voltage raised in the hippocampus by the SCO generator was particularly large and it remained virtually unabated when the local cortical currents above it were removed in a 2 mm wide concentric cylinder (Fig. 7E), as estimated following lidocaine blockade in experiments. Note that neither in experiments nor in models the lidocaine-unveiled linear component of the SCO generator incorporated into any other linear component in the cortex, as these remained individualized by the presence of distant maxima in a group of recording electrodes at hippocampal sites. To further explore the cortical origin of the non-zero linear portions in cortical FP generators, we performed another series of simulations using cortical-only slabs with coherent activation all throughout. Neuronal activity was removed in cylinders of increasing diameter centered at the recording track, which allowed the contribution of nearby cortical regions to be estimated (Fig. 7F). The bell-shaped maxima in the center of the slab weakened as the inactivated area widened (darkest blue curve in Fig. 7G), and it finally degenerated into a quasi-linear distribution (lightest blue curve). The bell-shaped potentials were contributed by neurons located within 0.7 mm from the recording probes, while those at longer distances entered a quasi-linear potential through V-C that provoked an offset-like shift of the entire voltage profile. In addition, we also found that the more distant the active neurons, the further the peak voltage moves away from the activated dendritic domain toward deeper layers. Indeed, it may even shift to a subcortical position (dashes in Fig. 7G), as also observed experimentally (Fig. 7A). Moreover, the polarity reversal shifted toward the upper layers (Fig. 7G, oval). These effects can be explained by the neuron’s asymmetrical geometry. In cortical sites, the voltage declined rapidly as more cells were inactivated surrounding the recording track, while subcortical sites showed near constant amplitude (Fig. 7H). This highlights the principal contribution of cells near to the recording to the bell-shaped voltage maxima, while more distant cells contribute almost the same voltage to all electrodes, even to those lying outside the cortex. Spatial Profiles of Noncoherent Cortico-Cortical V-C FPs Vary with the Distance and the Size of the Sources By contrast to the wide spatial coherence of SCOs, we found that in the activated cortical state the FPs that exhibited a cortical maximum dropped rapidly at the subcortical sites, which along the small CC between distant cortices found in this state indicate a reduced extension of V-C FPs generated by fragmented cortical sources (e.g., Frostig et al. 2008). Given the highly anatomical and functional modular organization of the cortex, it has been considered essential to determine how far away from an activated cortical area the FPs produced are sizable (Łęski et al. 2013). We investigated this with an emphasis on the particular features of local and V-C spatial voltage profiles that may help their discrimination. We first quantified the voltage profiles induced by neurons situated at increasing distances from the recording site by cortical slabs of increasing size (Fig. 7I: from 0.5 mm to 6 mm) in which all PCs received identical SCO-like activation (Fig. 7J, blue traces). The FP amplitude inside the cortex (green surface) barely grew for slabs larger than 2 mm (~90% of the voltage was attained in a 6 × 6 mm slab). However, the FP amplitudes were proportionally larger at subcortical sites (Fig. 7K), revealing again the contribution of neurons distant from the recording site and the role of extended coherent activity on the V-C at a distance. Overall the voltage profiles were modified by an offset-like effect (all electrodes received a similar contribution), which was best appreciated at subcortical sites (Fig. 7J, curved arrow). Along with results shown in Fig. 7G, this suggests that the peak site may vary as a trade-off between the proportion of active cells near and far from the electrode, which should be minded when searching for spatial landmarks of FP events and oscillations. We then explored how much voltage could be attributed to the cortical sources at a distance from the electrodes in situations mimicking reduced cortical coherence (small cortical modules), a frequent situation during states of cortical activation in awaken animals. For the sake of simplicity, we modeled the regular geometry of the barrel cortex and simulated 3 contiguous 0.5 mm wide modules (Fig. 7L). Each module was activated by an input signal with a different temporal pattern but of similar amplitude in the same cell domains (i.e., only 1 synaptic SCO-like input: Isyn in Fig. 7L). This approach facilitates the identification of ICA components obtained from the model FPs as the distinct activities favored the segregation of spatial modules to ICA components. As expected, most of the FP voltage was contributed by the local source (traces 1→rec in Fig. 7L), while the adjacent module contributed FPs that were ~10% of the amplitude at their origin (2→rec) and which were negligible in the more distant module (3→rec). The ICA returned 2 components that could be easily discerned by their voltage profiles (Fig. 7M), one containing the activity of the local (recorded) module, and the other the summed activity of the adjacent modules (i.e., volume-conducted). We expanded the simulation to test the V-C and ICA efficiency in modules of different size (hence, also at a different distance to the recording site). The relative laminar power each module contributed through the V-C was evident in the recorded module (Fig. 7N, top panel). While the contributions of the local and the adjacent modules were quantitatively similar for very small modules (0.1 mm wide), these diverged rapidly as the modules increased in size (lower panel). Thus, V-C contamination is negligible starting from 0.5 mm for modules of similar size. However, real cortical areas have a varied geometry and they lie different distances to each other, therefore specific cases should be modeled accordingly. Such geometrical variety makes it possible that local and distant generators obtained through the ICA of FPs in a single recording track might not be recognized solely by their relative power. Thus, we explored features of the voltage profiles in some modules of heterogeneous size, and we found that the activity in the recorded (local) module can be well isolated and identified by the ICA. An extreme case of recording through a very narrow module (0.2 mm wide) with 2 large (1 mm) modules next to it is plotted in Fig. 7O. Even if the contribution of the adjacent module was larger than that of the local one, the voltage profiles for the local module displayed a distinctive inflection in layer VI (arrow in the V-profile), which was absent in the other components irrespective of their relative contribution. Discussion Volume-conducted potentials are inherent to neuronal activity in the brain and they are widely considered as a source of contamination in local FPs. We have shown that a laminar profile of spontaneous FPs across the cortical width is sufficient to appraise local and remote contributions quantitatively, turning V-C potentials into an important source of information on the network’s dynamics. This is achieved through spatial discrimination techniques without a priori knowledge on the spatial reach and composition of the sources. We report that all cortices receive a significant amount of V-C activity in all frequency bands, and this may even prevail over local contributions. These remote contributions originate from adjacent cortices and subcortical structures, mainly the hippocampus, and the relative weight of local and remote contributions is state, region, and layer dependent. Thus, their segregation is a must for the unequivocal identification of the structures involved in FP generation. The model confirms that the power of the V-C contribution depends not only on the distance but also, on the extension of the area activated in the origin. These competing factors do not allow the location of remote sources to be identified solely by the power, yet they can be tracked down by exploring the brain with one or several arrays and disentangling the sources through spatial discrimination. This is routinely employed to define zones of correlated activity in surface EEGs or in fMRI data (Onton et al. 2006; Rogers et al. 2019), and it is beginning to gain use also for intracraneal FP recordings (for review, see Herreras et al. 2015). The approach adopted here was formerly optimized for intracranial FP recordings in the hippocampus (Makarov et al. 2010), and conceptually implemented as for artifact removal (Castellanos and Makarov 2006), i.e., signals with similar power in all electrodes are originated far from them. Traditionally, V-C potentials are considered to be a contaminant and the standard method to get rid of them is through CSD analysis (Mitzdorf 1985; Gratiy et al. 2017), which works efficiently for evoked potentials but poorly for spontaneous multisource potentials (Brankačk et al. 1993; Martín-Vázquez et al. 2013). Earlier we discussed the main drawbacks of applying CSD to spontaneous FPs, which are mostly derived from the loss of the baseline in AC-coupled recordings, and the inability to separate the co-activated sources that offset each other. Thus, except for the absence of remote potentials, the CSD time course suffers from similar problems as raw FPs (Martín-Vázquez et al. 2013; Herreras et al. 2015). By contrast, spatial discrimination does not reject V-C contributions but rather, it segregates the sources and enables their local or remote identification through the shape of the respective spatial voltage profile. Importantly, here we were able to use the time courses of V-C FPs to quantitatively estimate the share of local and remote contributions to a cortical recording site without exploring across different cortical areas. This was possible because the temporal fluctuations of the FP produced by a coherent source are proportional at any site, regardless of the amplitude. Thus, although we cannot rule out a contribution from extracranial sources to V-C potentials (e.g., muscle activity) (Whitmore and Lin 2016), some FP events and oscillations are readily identified as of neuronal origin by previous reports, and we use their dynamics to find the structure of origin by simply moving the linear arrays around until the particular pattern finds a maximum. FPs reveal population and network activity and they are contributed mainly by synaptic and intrinsic currents (Elul 1971), and these may be excitatory as well as inhibitory (Benito et al. 2014; Teleńczuk et al. 2017). In addition, only a few anatomical pathways, and target neurons have the appropriate architecture to promote the buildup of net electrical currents in the extracellular space (Lorente de Nó 1947; Lindén et al. 2011; Herreras et al. 2015; Martín-Vázquez et al. 2016). Thus, FPs reflect the activity of only a fraction of local networks and extrinsic connections in a neuronal structure. For instance, studies in the hippocampus report a significant contribution to FPs by 6–7 pathways (Benito et al. 2014, 2016), while anatomical connections largely exceed this number. It has been shown in modeling studies that pathways making widespread contacts on individual cells and the poor axialization of dendritic trees reduce the possibilities of raising FPs, no matter how intense and synchronous the activation (Lorente de Nó 1947; Lindén et al. 2011; Herreras et al. 2015). The cortex has also a large number of synaptic pathways that may raise extracellular currents, while in the present study we have disclosed only 3–4 distinct FP generators in different areas during the dominant slow wave state that is common under anesthesia (Chauvette et al. 2011). Of these, only 2 are genuine local cortical generators with maxima in layers III and V, and the latter (the SCO generator) makes up most of the variance. At first, we may consider that the cytoarchitecture of the cortex is less suitable than that of the hippocampus to disentangle FPs using spatial discrimination. Thus, despite the large number of extrinsic and local cortical connections, many of them have a patchy topography (Levitt and Lund 2002) that is not favorable to the clustering of extracellular currents over large areas. In contrast to the hippocampus, cell alignment in the cortex is less regular. Functional factors may also limit the segregation of FP generators. Thus, during SCOs, the intracolumnar and cortico-cortical synaptic connections both follow an on-off pattern by which they all become active and silent in a coordinated manner (Destexhe et al. 1999; Volgushev et al. 2006; Chauvette et al. 2011; Reyes-Puerta et al. 2016; Capone et al. 2017). Such temporal coherence is a serious handicap for spatial discrimination algorithms that work more efficiently when there is little coherence among co-activated pathways (Makarova et al. 2011). Indeed, a less restrictive use of FP treatment with a PCA prior to ICA led to decomposition of the SCO component into 2–3 smaller ones. Also, more local FP generators were found during the activated state in which the functional segregation of different intracolumnar segments (Kaas 2012) reduces their coherence and facilitates their spatial discrimination. In this context, epoch selection helped disclose additional FP generators, such as the intracortical alpha or gamma generators, whose contribution to the total variance is very weak. It seems clear that the FP generators identified during the activated state should be used by carefully matching the cortical regions recorded to the behavioral/cognitive tasks in which they participate (Martín-Vázquez et al. 2018). In addition, it is long-known that the spectral features of EEG and intracranial FPs are strongly altered by anesthesia in different species including man (Leung and Vanderwolf 1980; Boly et al. 2012; Krishnan et al. 2016), and they affect the 2 principal structures producing FPs, the cortex and hippocampus. Changes in the power and frequency content of these mesoscopic activities denote the engagement of different networks and the anatomical pathways that form them, the activity of some of which can be efficiently segregated in FP generators (Herreras et al. 2015). Thus, the different relative power of cortical FP generators found in this study in different cortical states reflects the varying degree of ongoing activity through thalamocortical or intracortical synaptic pathways, as classically observed in unitary recordings (Fox et al. 1986; Aguilar and Castro-Alamancos 2005; Sakata and Harris 2012; Olcese et al. 2016). However, FPs and spikes may show notable functional discrepancies on account of their nature (population or single cell) and spatial scales (see Herreras 2016 for discussion and examples). Further studies are needed to identify the origin and the target populations for each cortical FP generator. Consequently, the varying proportion of remote and local contributions in cortical areas may arise by the different distance to active parts of remote structures, by their own variable engagement in specific functional states related to behavioral/cognitive tasks or global modes of operation (default or sensory driven), or by functional regional differences in the cortex. Hence, the reported values in this study should not be generalized to other animal states or conditions that should be individually considered. Strong intracolumnar coherence helped achieve the main objective of the present study, the segregation of local and V-C contributions to cortical FPs. The origin of FP generators in sites far from the recording was assessed by the nonzero linear spatial distribution of the power that characterizes distant sources, the absence of source/sink associated currents in CSD analysis, and their resistance to blockade of local cortical activity with lidocaine. The interpretation of linear components is not trivial though, as they may contain activity from one or multiple distant cortical and subcortical sources. It is important to always consider the relative size of the coherent source and its position relative to recording. The V-C contributions originated in cortical areas are easily discriminated: those arising in a cortical area functionally different from the recorded one come up in a different FP component as they have different time courses (noncoherent), whereas those from neurons in the same functional area (i.e., coherent) but at a certain distance from the recording (>0.5 mm according to model estimations) produce an offset-like (linear) shift of the local FP generator and do not segregate and mix with other remote sources. In turn, the discrimination of subcortical and far cortical contributions can be made by the presence or absence of a maximum in another part of the brain, which requires additional exploration that may be guided by the presence of characteristic FP oscillations and patterns. Model calculations also show that V-C cortical potentials recorded at subcortical sites are increasingly contributed by neurons outside the recording track, since the distance to the recording equalizes. This may also explain across-animal variability in the spatial landmarks and the amplitude of SCOs or other oscillatory patterns and FP events upon localized damage produced by intracranial electrodes. Volume conduction acts as a sort of common reference that confuses the estimates of any correlations between structures (Fein et al. 1988; Whitmore and Lin 2016; Palva et al. 2018), such as the CC. We showed it may also increase by unmasking the self-correlation of V-C potentials recorded at 2 sites upon the reduction of local activity. On a microscopic spatial scale (a few hundred microns), V-C potentials strongly influence the time course and the amplitude of widely used indices of neural activity, such as the evoked population spikes and synaptic field potentials (Varona et al. 2000). On a macroscopic spatial scale (centimeters), besides the well-known EEG that is essentially a V-C signal, there is ample literature regarding the somatosensory evoked potentials elicited by peripheral nerve stimulation centimeters away from the source in different parts of the body or brain (Cracco and Cracco 1976; Kimura et al. 1984). On the mesoscopic spatial scale (hundreds of microns to a few centimeters) addressed in this study, V-C activity is responsible for the buildup of giant FPs in concave parts of folded structures (Fernández-Ruiz et al. 2013), the modification of spatial landmarks associated to some pathway-specific FPs (Haegens et al. 2015; Martín-Vázquez et al. 2016), and the recording of FP waves and oscillatory patterns in distant structures (Lalla et al. 2017; Parabucki and Lampl 2018; Whitmore and Lin 2016). The latter is a major source of experimental inconsistency and unexplained electrophysiological relationships in the literature, such as the distinct feature selectivity reported for FPs or spikes (Gail et al. 2004; Nielsen et al. 2006), the layer-dependent spread of FPs (Xing et al. 2009), and the confusing scenario regarding the reliability of gamma oscillations introduced by distant sources or the mutual interference between nearby ones (Carmichael et al. 2017; Whitmore and Lin 2016). It is clear that a rough estimation of the FP power, whether in raw samples or in frequency bands, is subjected to a considerable error due to large V-C contributions, which in certain layers and regions can surpass the power of local sources. Indeed, changes in power may also reflect changes in nearby cortices and even in remote structures that spread V-C potentials to the recorded site. This is particularly relevant for customary gamma and alpha frequency bands that are widely studied in the cortex and also have a large contribution from subcortical structures. We found that all the cortices studied here receive significant amount of V-C activity and we highlight some due to their relevance in electrophysiological studies. For example, some sites in strongly curved portions of the cortical mantle may receive V-C SCO activity that blends into their own. As inferred from the model, V-C SCOs presumably originate from nearby cortices that lie at an angle. This may confuse observations of layer specificity and amplitude estimation when relating FPs to spikes or to behavior in the frontal cortical sites, and possibly also in lateral cortices. Such a modality of FP distortion in curved structures was previously reported for V-C potentials from the CA3 to CA1 hippocampal regions that jointly form a curved structure (Fernández-Ruiz et al. 2013). We also found that the global curved shape of the cortical mantle produces a strong clustering of V-C potentials that occupy about the entire brain during synchronous oscillations such as SCOs. This constitutes a strong source of contamination for FP recordings almost anywhere in the brain, and hence it demands careful placement of reference electrodes and efficient methods to separate local from V-C potentials, such as the spatial discrimination technique. Since these effects stem from the specific geometry and size of the sources, an interesting question is how they depend on the size of the brain. In simulations (Makarova and Herreras, unpublished) we scaled the cortex twice as large as in the rat, while maintaining the density of neurons, and we found very similar values of the FP amplitude and V-C potentials as in the rat. However, this situation is only applicable to species with lisencephalic cortex, while most mammals have strongly convoluted cortices in which gyri and sulci strongly modify the geometry and the relative position and orientation of active sources. Besides, different electrical properties of brain compartments (white matter, gray matter, ventricles) may play a more significant role in the spread of V-C potentials than we found here in the more regular rat brain, as detailed human brain models suggest (Wolters et al. 2006; Güllmar et al. 2010). Another significant observation is that the hippocampal theta activity is V-C specifically to the cortices near the hippocampus (e.g., V2), as well as to thalamic and other midbrain structures, and the model predicts that it will also extend into the lateral and posterior cortices. Most of these have been confirmed in the literature and we show here that they appear in FP generators with non-zero flat profiles and no associated CSD currents. Many more regions have been reported to contain theta modulation of cell spiking (Colom et al. 1988; Pedemonte et al. 1996), which sets a highly confusing scenario when establishing functional relationships between structures. For instance, we observed some genuine bouts of local theta waves in the M1 and V2 cortices that turned out to be short SCOs paced at a theta frequency but unrelated to hippocampal ones. In particular, since the V2 cortex enter a strong V-C in the hippocampus, theta waves there may be annihilated, or in the least dramatic of cases their phase may be strongly altered. Thus, changes in amplitude, waveform, or phase of theta waves in raw FPs can be expected, which introduces an error when they are used as temporal reference, e.g., in cross-frequency coupling studies or in relation to behavior. Also, it may be expected that the units in V2 cortex display a phase relationship to theta waves in some epochs depending on whether these are V-C from the hippocampus or generated locally. Another example that illustrates the confusion brought about by neglecting V-C FPs is the observation of the marked presence of bouts of alpha oscillations, particularly in anterior cortices. Although network oscillations such as these can be associated to certain behavioral manifestations, their actual site of origin is in many cases inferred by the often unproved assumption that they belong to the site where they are recorded from. FP relations to single cell activity recorded in the same electrodes are often interpreted as causal while they neglect the different nature, geometry and spatial scales (Elul 1971; Herreras 2016). Indeed, the mean power of frequency bands is widely used to infer changes in functional connectivity or pathology. Alpha oscillations are important to interpret attentional suppression in working memory and they may also reveal dysfunction associated to schizophrenia (Steriade 1997; Foxe and Snyder 2011; Haegens et al. 2015). Unfortunately, most studies use scalp or few intracranial recordings that are generally insufficient to ascertain the local or remote origin of recorded activities. Ongoing studies in our lab to find the origin of these cortically recorded remote oscillations indicate that structured bouts of FP oscillations with a frequency signature should be used whenever possible rather than the mean power of frequency bands, since the later may contain multiple contributions from different sites and they will display different values on different cortices. Presumably, the contamination of cortical FPs by remotely originated activity varies in different species according to the size, location and distance of the contaminating structures. This possibility does exist in the primate brain. For instance, in areas of the monkey cortex similar to those studied here, cortical alpha activity displayed sensitivity to the position of the reference electrode (Haegens et al. 2015), which indicates a contribution by remote sources. As we found here, alpha bouts coexist in the same electrode and cortical region whose local or remote origin can only be discriminated through the laminar voltage gradients contained in FP generators. All in all, these considerations call for a reappraisal of earlier FP studies that have not considered V-C contributions from remote sites. Concluding Remarks Classically, it has proven difficult to quantify mutual FP contamination between adjacent cortices or from subcortical structures. We show here that spatial discrimination analysis overcomes 2 major problems, the spatial blending of multiple sources and the unknown spatial reach of FPs. Through the spatial profile of segregated FP generators we discriminated which is local and which is not and we could establish substantial remote contributions to cortical FPs that may now be precisely quantified. Finally, it is worth considering that FPs originating in subcortical structures that contaminate cortical recordings might also be detected at the scalp. Therefore, customary EEGs may reflect subcortical dynamics to a larger extent than previously thought, an intriguing possibility that demands careful further examination. Footnotes We thank S. Hernández-Recio and V.J. López-Madrona for continuous discussion, and M. Sefton at BiomedRed for editorial support. The authors acknowledge the support of the Ministry of Economy and Competitiveness of Spain (Grants BFU2013-41533R and SAF2016-80100-R to O.H., FIS2017-82900-P to V.A.M., and BES-2014-071052 to D.T). Conflict of Interest: None declared. References Aguilar JR , Castro-Alamancos MA . 2005 . Spatiotemporal gating of sensory inputs in thalamus during quiescent and activated states . J Neurosci . 25 : 10990 – 11002 . Google Scholar Crossref Search ADS PubMed WorldCat Bédard C , Kröger H , Destexhe A . 2004 . 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TI - Local and Volume-Conducted Contributions to Cortical Field Potentials
JF - Cerebral Cortex
DO - 10.1093/cercor/bhz061
DA - 2019-12-17
UR - https://www.deepdyve.com/lp/oxford-university-press/local-and-volume-conducted-contributions-to-cortical-field-potentials-G0L0ny1qZ0
SP - 5234
VL - 29
IS - 12
DP - DeepDyve
ER -