Specific resistivity of the cerebral cortex and white matter

The recording radius and spatial selectivity of an extracellular probe are important for interpreting neurophysiological recordings but are rarely measured. Moreover, an analysis of the recording biophysics of multisite probes (e.g., tetrodes) can provide for source characterization and localization of spiking single units, but this capability has remained largely unexploited. Here we address both issues quantitatively. Advancing a tetrode (Ϸ40-m contact separation, tetrahedral geometry) in 5-to 10-m steps, we repeatedly recorded extracellular action potentials (EAPs) of single neurons in the visual cortex. Using measured spatial variation of EAPs, the tetrodes' measured geometry, and a volume conductor model of the cortical tissue, we solved the inverse problem of estimating the location and the size of the equivalent dipole model of the spike generator associated with each neuron. Half of the 61 visual neurons were localized within a radius of Ϸ100 m and 95% within Ϸ130 m around the tetrode tip (i.e., a large fraction was much further than previously thought). Because of the combined angular sensitivity of the tetrode's leads, location uncertainty was less than one-half the cell's distance. We quantified the spatial dependence of the probability of cell isolation, the isolated fraction, and the dependence of the recording radius on probe size and equivalent dipole size. We also reconstructed the spatial configuration of sets of simultaneously recorded neurons to demonstrate the potential use of 3D dipole localization for functional anatomy. Finally, we found that the dipole moment vector, surprisingly, tended to point toward the probe, leading to the interpretation that the equivalent dipole represents a "local lobe" of the dendritic arbor. recording radius; extracellular action potential; multisite recording; inverse problem; equivalent dipole; lead field theory MULTICONTACT RECORDINGS HAVE HIGH YIELD (Blanche et al. 2005;Csicsvari et al. 2003;Eckhorn and Thomas 1993;Gray et al. 1995;McNaughton et al. 1983) (Buzsaki and Kandel 1998;Drake et al. 1988;Henze et al. 2000) show, the shape and size of the extracellular action potential (EAP) waveform depends on the relative position of cell and probe. Thus, these recordings carry spatial information about spike sources that is not available in single electrode records. However, this spatial information is typically not exploited, because extracting it requires solution of an inverse problem, deducing the position and the size of the current source of a spiking neuron from measurements of its EAP at multiple locations.Here, we solve this inverse problem by modeling the spiking neuron with a single current dipole. The choice of a dipole model rests on reasoning presented in detail in a companion paper and its supplemental material (Mechler and Victor 2011). Briefly, although the membrane currents of a spiking neuron constitute a genuinely distributed current source, the resulting extracellular field is well approximated by that of a dipole beyond a minimum distance a...

Section: Volume Conductor Model Of Brain Tissuementioning

confidence: 87%

Three-dimensional localization of neurons in cortical tetrode recordings

Mechler

Victor

Ohiorhenuan

et al. 2011

“…However, we believe that previous methods proposed in the literature to estimate the microscopic conductivity profile in the cerebral cortex (Hoeltzell and Dykes 1979;Li et al 1968;Logothetis et al 2007;Ranck Jr 1963) possess at least one of the following drawbacks: 1) a priori assumptions of global homogeneity in the tissue while estimating the local conductivity value; 2) a lack of adequate boundary conditions on the surface, limiting the brain and surrounding tissues; 3) errors in determining the relative positions of microelectrodes and the boundaries delimiting different cortical layers; and 4) large intermicroelectrode distances compared with the thickness of cortical layers. Furthermore, in previous studies, multielectrode arrays for both current injection and electric potential observations were not used and the curvature of the cortical sheet was ignored.…”

Section: Introductionmentioning

confidence: 98%

“…To that end, they not only modified the previous techniques introduced by Schwann (1963) to measure conductivity profiles in vivo, i.e., the four-electrode method, but also used a previous theoretical result by Rush (1962) to model the global effect of anisotropy on the observable electric fields. Li et al (1968) used the four-electrode method to estimate the electrical resistance of the cerebral cortex and white matter at the level of the suprasylvian gyrus in 42 cats. By using a similar methodology, Hoeltzell and Dykes (1979) were the first to present consistent experimental evidence of anisotropies in the somatosensory cortices of cats, a result that in combination with the frequency independent conductivity values found a few years earlier by Ranck Jr (1963) in the cerebral cortices of rabbits would set the basis for any microscopic forward generative model of the genesis of LFP in this major brain tissue.…”

Section: Introductionmentioning

confidence: 99%

An Evaluation of the Conductivity Profile in the Somatosensory Barrel Cortex of Wistar Rats

Goto

Hatanaka

Ogawa

et al. 2010

Microelectrode arrays used to record local field potentials from the brain are being built with increasingly more spatial resolution, ranging from the initially developed laminar arrays to those with planar and three-dimensional (3D) formats. In parallel with such development in recording techniques, current source density (CSD) analyses have recently been expanded up to the continuous-3D form. Unfortunately, the effect of the conductivity profile on the CSD analysis performed with contemporary microelectrode arrays has not yet been evaluated and most of the studies assumed it was homogeneous and isotropic. In this study, we measured the conductivity profile in the somatosensory barrel cortex of Wistar rats. To that end, we combined multisite electrophysiological data recorded with a homemade assembly of silicon-based probes and a nonlinear least-squares algorithm that implicitly assumed that the cerebral cortex of rodents could be locally approximated as a layered anisotropic spherical volume conductor. The eccentricity of the six cortical layers in the somatosensory barrel cortex was evaluated from postmortem histological images. We provided evidence for the local spherical character of the entire barrels field, with concentric cortical layers. We found significant laminar dependencies in the conductivity values with radial/tangential anisotropies. These results were in agreement with the layer-dependent orientations of myelinated axons, but hardly related to densities of cells. Finally, we demonstrated through simulations that ignoring the real conductivity profile in the somatosensory barrel cortex of rats caused considerable errors in the CSD reconstruction, with pronounced effects on the continuous-3D form and charge-unbalanced CSD. We concluded that the conductivity profile must be included in future developments of CSD analysis, especially for rodents.

“…This author found voltage gradient along the cortical laminas of up to 400 -450 V/mm. Taking into account these observations and timely estimations of the cortical conductivity (e.g., rabbits: 2.73-3.62 mS/cm, Ranck 1963; cats: 1.66 -1.96 mS/cm, Li et al 1968), it was possible through the use of the methodology proposed by Humphrey (1968) to obtain ranges (100 -250 nA/mm 2 ) for the typical transcortical current densities (Freeman 1975;Pollen 1969), which remain valid to this day (Baillet et al 2001). The strengths and spatial extensions of cortical dipoles were in agreement with estimations obtained from EEG and MEG data (10 -100 nA·m: Bowyer et al 1999;Cohen and Cuffin 1983;Chapman et al 1984;Jones et al 2007Jones et al , 2009).…”

mentioning

confidence: 99%

Pitfalls in the dipolar model for the neocortical EEG sources

Riera

Ogawa

Goto

et al. 2012

111

For about six decades, primary current sources of the electroencephalogram (EEG) have been assumed dipolar in nature. In this study, we used electrophysiological recordings from anesthetized Wistar rats undergoing repeated whisker deflections to revise the biophysical foundations of the EEG dipolar model. In a first experiment, we performed threedimensional recordings of extracellular potentials from a large portion of the barrel field to estimate intracortical multipolar moments generated either by single spiking neurons (i.e., pyramidal cells, PC; spiny stellate cells, SS) or by populations of them while experiencing synchronized postsynaptic potentials. As expected, backpropagating spikes along PC dendrites caused dipolar field components larger in the direction perpendicular to the cortical surface (49.7 Ϯ 22.0 nA·mm). In agreement with the fact that SS cells have "close-field" configurations, their dipolar moment at any direction was negligible. Surprisingly, monopolar field components were detectable both at the level of single units (i.e., Ϫ11.7 Ϯ 3.4 nA for PC) and at the mesoscopic level of mixed neuronal populations receiving extended synaptic inputs within either a cortical column (Ϫ0.44 Ϯ 0.20 A) or a 2.5-m 3 -voxel volume (Ϫ3.32 Ϯ 1.20 A). To evaluate the relationship between the macroscopically defined EEG equivalent dipole and the mesoscopic intracortical multipolar moments, we performed concurrent recordings of high-resolution skull EEG and laminar local field potentials. From this second experiment, we estimated the time-varying EEG equivalent dipole for the entire barrel field using either a multiple dipole fitting or a distributed type of EEG inverse solution. We demonstrated that mesoscopic multipolar components are altogether absorbed by any equivalent dipole in both types of inverse solutions. We conclude that the primary current sources of the EEG in the neocortex of rodents are not precisely represented by a single equivalent dipole and that the existence of monopolar components must be also considered at the mesoscopic level.electroencephalogram; neocortex; multipolar current sources; inverse problem THE DIPOLAR MODEL, used by generations of neuroscientists to represent the current sources of the electroencephalogram (EEG) in humans (Niedermeyer and Lopes da Silva 1987; Nunez and Srinivansan 2006;Plonsey 1969;Walter and Walter 1949), has roots in early interpretations by Adrian and Matthews (1934) about the origin of the Berger rhythm (i.e., the alpha rhythm). These authors suggested that the cortical electric potentials formerly observed by Berger (1929) were caused by electrical sources close to the brain surface with a polarity inversion in the axis perpendicular to it. The existence of dipole-like field distributions with axes parallel to the cortical surface was later suggested by Beevers (1944), with confirmations for the kappa rhythm (Kennedy et al. 1948) and the epileptic focal seizures (Gumnit and Takahashi 1965). This model, which eventually gained popularity in many other eme...