When to include ECoG electrode properties in volume conduction models.

OBJECTIVE: Implantable electrodes, such as electrocorticography (ECoG) grids, are used to record brain activity in applications like brain computer interfaces. To improve the spatial sensitivity of ECoG grid recordings, electrode properties need to be better understood. Therefore, the goal of this study is to analyze the importance of including electrodes explicitly in volume conduction calculations. APPROACH: We investigated the influence of ECoG electrode properties on potentials in three geometries with three different electrode models. We performed our simulations with FEMfuns, a volume conduction modeling software toolbox based on the finite element method. MAIN RESULTS: The presence of the electrode alters the potential distribution by an amount that depends on its surface impedance, its distance from the source and the strength of the source. Our modeling results show that when ECoG electrodes are near the sources the potentials in the underlying tissue are more uniform than without electrodes. We show that the recorded potential can change up to a factor of 3, if no extended electrode model is used. In conclusion, when the distance between an electrode and the source is equal to or smaller than the size of the electrode, electrode effects cannot be disregarded. Furthermore, the potential distribution of the tissue under the electrode is affected up to depths equal to the radius of the electrode. SIGNIFICANCE: This paper shows the importance of explicitly including electrode properties in volume conduction models for accurately interpreting ECoG measurements.

FEMfuns: A Volume Conduction Modeling Pipeline that Includes Resistive, Capacitive or Dispersive Tissue and Electrodes.

Applications such as brain computer interfaces require recordings of relevant neuronal population activity with high precision, for example, with electrocorticography (ECoG) grids. In order to achieve this, both the placement of the electrode grid on the cortex and the electrode properties, such as the electrode size and material, need to be optimized. For this purpose, it is essential to have a reliable tool that is able to simulate the extracellular potential, i.e., to solve the so-called ECoG forward problem, and to incorporate the properties of the electrodes explicitly in the model. In this study, this need is addressed by introducing the first open-source pipeline, FEMfuns (finite element method for useful neuroscience simulations), that allows neuroscientists to solve the forward problem in a variety of different geometrical domains, including different types of source models and electrode properties, such as resistive and capacitive materials. FEMfuns is based on the finite element method (FEM) implemented in FEniCS and includes the geometry tessellation, several electrode-electrolyte implementations and adaptive refinement options. The Python code of the pipeline is available under the GNU General Public License version 3 at https://github.com/meronvermaas/FEMfuns . We tested our pipeline with several geometries and source configurations such as a dipolar source in a multi-layer sphere model and a five-compartment realistically-shaped head model. Furthermore, we describe the main scripts in the pipeline, illustrating its flexible and versatile use. Provided with a sufficiently fine tessellation, the numerical solution of the forward problem approximates the analytical solution. Furthermore, we show dispersive material and interface effects in line with previous literature. Our results indicate substantial capacitive and dispersive effects due to the electrode-electrolyte interface when using stimulating electrodes. The results demonstrate that the pipeline presented in this paper is an accurate and flexible tool to simulate signals generated on electrode grids by the spatiotemporal electrical activity patterns produced by sources and thereby allows the user to optimize grids for brain computer interfaces including exploration of alternative electrode materials/properties.

Separating burst from background spikes in multichannel neuronal recordings using return map analysis.

We propose a preprocessing method to separate coherent neuronal network activity, referred to as "bursts", from background spikes. High background activity in neuronal recordings reduces the effectiveness of currently available burst detection methods. For long-term, stationary recordings, burst and background spikes have a bimodal ISI distribution which makes it easy to select the threshold to separate burst and background spikes. Finite, nonstationary recordings lead to noisy ISIs for which the bimodality is not that clear. We introduce a preprocessing method to separate burst from background spikes to improve burst detection reliability because it efficiently uses both single and multichannel activity. The method is tested using a stochastic model constrained by data available in the literature and recordings from primary cortical neurons cultured on multielectrode arrays. The separation between burst and background spikes is obtained using the interspike interval return map. The cutoff threshold is the key parameter to separate the burst and background spikes. We compare two methods for selecting the threshold. The 2-step method, in which threshold selection is based on fixed heuristics. The iterative method, in which the optimal cutoff threshold is directly estimated from the data. The proposed preprocessing method significantly increases the reliability of several established burst detection algorithms, both for simulated and real recordings. The preprocessing method makes it possible to study the effects of diseases or pharmacological manipulations, because it can deal efficiently with nonstationarity in the data.

An analytical comparison of the information in sorted and non-sorted cosine-tuned spike activity.

Spike sorting is a technologically expensive component of the signal processing chain required to interpret population spike activity acquired in a neuromotor prosthesis. No systematic analysis of the value of spike sorting has been carried out, and little is known about the effects of spike sorting error on the ability of a brain-machine interface (BMI) to decode intended motor commands. We developed a theoretical framework to examine the effects of spike processing on the information available to a BMI decoder. We computed the mutual information in neural activity in a simplified model of directional cosine tuning to compare the effects of pooling activity from up to four neurons to the effects of sorting with varying amounts of spike error. The results showed that information in a small population of cosine-tuned neurons is maximized when the responses are sorted and there is diverse tuning of units, but information was affected little when pooling units with similar preferred directions. Spike error had adverse effects on information, such that non-sorted population activity had 79-92% of the information in its sorted counterpart for reasonable amounts of detection and sorting error and for units with moderate differences in preferred direction. This quantification of information loss associated with pooling units and with spike detection and sorting error will help to guide the engineering decisions in designing a BMI spike processing system.

Chaos-induced modulation of reliability boosts output firing rate in downstream cortical areas.

The reproducibility of neural spike train responses to an identical stimulus across different presentations (trials) has been studied extensively. Reliability, the degree of reproducibility of spike trains, was found to depend in part on the amplitude and frequency content of the stimulus [J. Hunter and J. Milton, J. Neurophysiol. 90, 387 (2003)]. The responses across different trials can sometimes be interpreted as the response of an ensemble of similar neurons to a single stimulus presentation. How does the reliability of the activity of neural ensembles affect information transmission between different cortical areas? We studied a model neural system consisting of two ensembles of neurons with Hodgkin-Huxley-type channels. The first ensemble was driven by an injected sinusoidal current that oscillated in the gamma-frequency range (40 Hz) and its output spike trains in turn drove the second ensemble by fast excitatory synaptic potentials with short term depression. We determined the relationship between the reliability of the first ensemble and the response of the second ensemble. In our paradigm the neurons in the first ensemble were initially in a chaotic state with unreliable and imprecise spike trains. The neurons became entrained to the oscillation and responded reliably when the stimulus power was increased by less than 10%. The firing rate of the first ensemble increased by 30%, whereas that of the second ensemble could increase by an order of magnitude. We also determined the response of the second ensemble when its input spike trains, which had non-Poisson statistics, were replaced by an equivalent ensemble of Poisson spike trains. The resulting output spike trains were significantly different from the original response, as assessed by the metric introduced by Victor and Purpura [J. Neurophysiol. 76, 1310 (1996)]. These results are a proof of principle that weak temporal modulations in the power of gamma-frequency oscillations in a given cortical area can strongly affect firing rate responses downstream by way of reliability in spite of rather modest changes in firing rate in the originating area.

Rapid temporal modulation of synchrony by competition in cortical interneuron networks.

The synchrony of neurons in extrastriate visual cortex is modulated by selective attention even when there are only small changes in firing rate (Fries, Reynolds, Rorie, & Desimone, 2001). We used Hodgkin-Huxley type models of cortical neurons to investigate the mechanism by which the degree of synchrony can be modulated independently of changes in firing rates. The synchrony of local networks of model cortical interneurons interacting through GABA(A) synapses was modulated on a fast timescale by selectively activating a fraction of the interneurons. The activated interneurons became rapidly synchronized and suppressed the activity of the other neurons in the network but only if the network was in a restricted range of balanced synaptic background activity. During stronger background activity, the network did not synchronize, and for weaker background activity, the network synchronized but did not return to an asynchronous state after synchronizing. The inhibitory output of the network blocked the activity of pyramidal neurons during asynchronous network activity, and during synchronous network activity, it enhanced the impact of the stimulus-related activity of pyramidal cells on receiving cortical areas (Salinas & Sejnowski, 2001). Synchrony by competition provides a mechanism for controlling synchrony with minor alterations in rate, which could be useful for information processing. Because traditional methods such as cross-correlation and the spike field coherence require several hundred milliseconds of recordings and cannot measure rapid changes in the degree of synchrony, we introduced a new method to detect rapid changes in the degree of coincidence and precision of spike timing.

Attractor reliability reveals deterministic structure in neuronal spike trains.

When periodic current is injected into an integrate-and-fire model neuron, the voltage as a function of time converges from different initial conditions to an attractor that produces reproducible sequences of spikes. The attractor reliability is a measure of the stability of spike trains against intrinsic noise and is quantified here as the inverse of the number of distinct spike trains obtained in response to repeated presentations of the same stimulus. High reliability characterizes neurons that can support a spike-time code, unlike neurons with discharges forming a renewal process (such as a Poisson process). These two classes of responses cannot be distinguished using measures based on the spike-time histogram, but they can be identified by the attractor dynamics of spike trains, as shown here using a new method for calculating the attractor reliability. We applied these methods to spike trains obtained from current injection into cortical neurons recorded in vitro. These spike trains did not form a renewal process and had a higher reliability compared to renewal-like processes with the same spike-time histogram.

Precision and reliability of periodically and quasiperiodically driven integrate-and-fire neurons.

Neurons in the brain communicate via trains of all-or-none electric events known as spikes. How the brain encodes information using spikes-the neural code-remains elusive. Here the robustness against noise of stimulus-induced neural spike trains is studied in terms of attractors and bifurcations. The dynamics of model neurons converges after a transient onto an attractor yielding a reproducible sequence of spike times. At a bifurcation point the spike times on the attractor change discontinuously when a parameter is varied. Reliability, the stability of the attractor against noise, is reduced when the neuron operates close to a bifurcation point. We determined using analytical spike-time maps the attractor and bifurcation structure of an integrate-and-fire model neuron driven by a periodic or a quasiperiodic piecewise constant current and investigated the stability of attractors against noise. The integrate-and-fire model neuron became mode locked to the periodic current with a rational winding number p/q and produced p spikes per q cycles. There were q attractors. p:q mode-locking regions formed Arnold tongues. In the model, reliability was the highest during 1:1 mode locking when there was only one attractor, as was also observed in recent experiments. The quasiperiodically driven neuron mode locked to either one of the two drive periods, or to a linear combination of both of them. Mode-locking regions were organized in Arnold tongues and reliability was again highest when there was only one attractor. These results show that neuronal reliability in response to the rhythmic drive generated by synchronized networks of neurons is profoundly influenced by the location of the Arnold tongues in parameter space.

Information transfer in entrained cortical neurons.

Cortical interneurons connected by gap junctions can provide a synchronized inhibitory drive that can entrain pyramidal cells. This was studied in a single-compartment Hodgkin-Huxley-type model neuron that was entrained by periodic inhibitory inputs with low jitter in the input spike times (i.e. high precision), and a variable but large number of presynaptic spikes on each cycle. During entrainment the Shannon entropy of the output spike times was reduced sharply compared with its value outside entrainment. Surprisingly, however, the information transfer as measured by the mutual information between the number of inhibitory inputs in a cycle and the phase lag of the subsequent output spike was significantly increased during entrainment. This increase was due to the reduced contribution of the internal correlations to the output variability. These theoretical predictions were supported by experimental recordings from the rat neocortex and hippocampus in vitro.