Localization of single-cell current sources based on extracellular potential patterns: the spike CSD method

Discovering optimal features for neuron-type identification from extracellular recordings

Advancements in multichannel recordings of single-unit activity (SUA) in vivo present an opportunity to discover novel features of spatially-varying extracellularly-recorded action potentials (EAPs) that are useful for identifying neuron-types. Traditional approaches to classifying neuron-types often rely on computing EAP waveform features based on conventions of single-channel recordings and thus inherit their limitations. However, spatiotemporal EAP waveforms are the product of signals from underlying current sources being mixed within the extracellular space. We introduce a machine learning approach to demix the underlying sources of spatiotemporal EAP waveforms. Using biophysically realistic computational models, we simulate EAP waveforms and characterize them by the relative prevalence of these sources, which we use as features for identifying the neuron-types corresponding to recorded single units. These EAP sources have distinct spatial and multi-resolution temporal patterns that are robust to various sampling biases. EAP sources also are shared across many neuron-types, are predictive of gross morphological features, and expose underlying morphological domains. We then organize known neuron-types into a hierarchy of latent morpho-electrophysiological types based on differences in the source prevalences, which provides a multi-level classification scheme. We validate the robustness, accuracy, and interpretations of our demixing approach by analyzing simulated EAPs from morphologically detailed models with classification and clustering methods. This simulation-based approach provides a machine learning strategy for neuron-type identification.

Seeing beyond the spikes: reconstructing the complete spatiotemporal membrane potential distribution from paired intra- and extracellular recordings

Although electrophysiologists have been recording intracellular neural activity routinely ever since the ground-breaking work of Hodgkin and Huxley, and extracellular multichannel electrodes have also been used frequently and extensively, a practical experimental method to track changes in membrane potential along a complete single neuron is still lacking. Instead of obtaining multiple intracellular measurements on the same neuron, we propose an alternative method by combining single-channel somatic patch-clamp and multichannel extracellular potential recordings. In this work, we show that it is possible to reconstruct the complete spatiotemporal distribution of the membrane potential of a single neuron with the spatial resolution of an extracellular probe during action potential generation. Moreover, the reconstruction of the membrane potential allows us to distinguish between the two major but previously hidden components of the current source density (CSD) distribution: the resistive and the capacitive currents. This distinction provides a clue to the clear interpretation of the CSD analysis, because the resistive component corresponds to transmembrane ionic currents (all the synaptic, voltage-sensitive and passive currents), whereas capacitive currents are considered to be the main contributors of counter-currents. We validate our model-based reconstruction approach on simulations and demonstrate its application to experimental data obtained in vitro via paired extracellular and intracellular recordings from a single pyramidal cell of the rat hippocampus. In perspective, the estimation of the spatial distribution of resistive membrane currents makes it possible to distiguish between active and passive sinks and sources of the CSD map and the localization of the synaptic input currents, which make the neuron fire. KEY POINTS: A new computational method is introduced to calculate the unbiased current source density distribution on a single neuron with known morphology. The relationship between extracellular and intracellular electric potential is determined via mathematical formalism, and a new reconstruction method is applied to reveal the full spatiotemporal distribution of the membrane potential and the resistive and capacitive current components. The new reconstruction method was validated on simulations. Simultaneous and colocalized whole-cell patch-clamp and multichannel silicon probe recordings were performed from the same pyramidal neuron in the rat hippocampal CA1 region, in vitro. The method was applied in experimental measurements and returned precise and distinctive characteristics of various intracellular phenomena, such as action potential generation, signal back-propagation and the initial dendritic depolarization preceding the somatic action potential.

A Proof-of-Concept Numerical Ising Machine for Neural Spike Localization

Identifying the physical locations of neurons based on the spike waveforms captured by multiple recording channels, namely spike localization, can potentially enhance spike sorting accuracy. This study proposes a new method for spike localization, where the problem is first described as a nonconvex optimization problem and then the optimization is attempted heuristically via a numerical Ising solver. The paper first presents a quadratic unconstrained binary optimization (QUBO) formulation of spike localization. Then, a MATLAB solver simulating an Ising machine is written to solve the QUBO. The proposed method is evaluated on a 2D toy problem consisting of two electrodes and a single spike event, where the neuron location search is conducted in three different regions placed at increasing distances from the electrodes. The results indicate that the neuron can be accurately identified when in one of the nearest nodes to the electrodes, whereas the accuracy decreases to 87.5% and 75% as the search region distance increases. The study for the first time formulates the spike localization problem as a QUBO and demonstrates the feasibility of solving the resultant non-convex optimization problem heuristically using an Ising machine.Clinical Relevance- High channel-count implantable neural monitoring systems allow tracking large brain regions at the cost of increased data volumes to transmit and power dissipation. The new spike localization approach presented can potentially decrease the data volume and power consumption by enabling high accuracy spike localization at the implantable system.

Cross Laminar Traveling Components of Field Potentials due to Volume Conduction of Non-Traveling Neuronal Activity in Macaque Sensory Cortices

Field potentials (FPs) reflect neuronal activities in the brain, and often exhibit traveling peaks across recording sites. While traveling FPs are interpreted as propagation of neuronal activity, not all studies directly reveal such propagating patterns of neuronal activation. Neuronal activity is associated with transmembrane currents that form dipoles and produce negative and positive fields. Thereby, FP components reverse polarity between those fields and have minimal amplitudes at the center of dipoles. Although their amplitudes could be smaller, FPs are never flat even around these reversals. What occurs around the reversal has not been addressed explicitly, although those are rationally in the middle of active neurons. We show that sensory FPs around the reversal appeared with peaks traveling across cortical laminae in macaque sensory cortices. Interestingly, analyses of current source density did not depict traveling patterns but lamina-delimited current sinks and sources. We simulated FPs produced by volume conduction of a simplified 2 dipoles' model mimicking sensory cortical laminar current source density components. While FPs generated by single dipoles followed the temporal patterns of the dipole moments without traveling peaks, FPs generated by concurrently active dipole moments appeared with traveling components in the vicinity of dipoles by superimposition of individually non-traveling FPs generated by single dipoles. These results indicate that not all traveling FP are generated by traveling neuronal activity, and that recording positions need to be taken into account to describe FP peak components around active neuronal populations.SIGNIFICANCE STATEMENT Field potentials (FPs) generated by neuronal activity in the brain occur with fields of opposite polarity. Likewise, in the cerebral cortices, they have mirror-imaged waveforms in upper and lower layers. We show that FPs appear like traveling across the cortical layers. Interestingly, the traveling FPs occur without traveling components of current source density, which represents transmembrane currents associated with neuronal activity. These seemingly odd findings are explained using current source density models of multiple dipoles. Concurrently active, non-traveling dipoles produce FPs as mixtures of FPs produced by individual dipoles, and result in traveling FP waveforms as the mixing ratio depends on the distances from those dipoles. The results suggest that not all traveling FP components are associated with propagating neuronal activity.

Do not waste your electrodes-principles of optimal electrode geometry for spike sorting

Objective. This study examines how the geometrical arrangement of electrodes influences spike sorting efficiency, and attempts to formalise principles for the design of electrode systems enabling optimal spike sorting performance.Approach. The clustering performance of KlustaKwik, a popular toolbox, was evaluated using semi-artificial multi-channel data, generated from a library of real spike waveforms recorded in the CA1 region of mouse Hippocampusin vivo.Main results. Based on spike sorting results under various channel configurations and signal levels, a simple model was established to describe the efficiency of different electrode geometries. Model parameters can be inferred from existing spike waveform recordings, which allowed quantifying both the cooperative effect between channels and the noise dependence of clustering performance.Significance. Based on the model, analytical and numerical results can be derived for the optimal spacing and arrangement of electrodes for one- and two-dimensional electrode systems, targeting specific brain areas.

A model integrating multiple processes of synchronization and coherence for information instantiation within a cortical area

What is the form of dynamic, e.g., sensory, information in the mammalian cortex? Information in the cortex is modeled as a coherence map of a mixed chimera state of synchronous, phasic, and disordered minicolumns. The theoretical model is built on neurophysiological evidence. Complex spatiotemporal information is instantiated through a system of interacting biological processes that generate a synchronized cortical area, a coherent aperture. Minicolumn elements are grouped in macrocolumns in an array analogous to a phased-array radar, modeled as an aperture, a "hole through which radiant energy flows." Coherence maps in a cortical area transform inputs from multiple sources into outputs to multiple targets, while reducing complexity and entropy. Coherent apertures can assume extremely large numbers of different information states as coherence maps, which can be communicated among apertures with corresponding very large bandwidths. The coherent aperture model incorporates considerable reported research, integrating five conceptually and mathematically independent processes: 1) a damped Kuramoto network model, 2) a pumped area field potential, 3) the gating of nearly coincident spikes, 4) the coherence of activity across cortical lamina, and 5) complex information formed through functions in macrocolumns. Biological processes and their interactions are described in equations and a functional circuit such that the mathematical pieces can be assembled the same way the neurophysiological ones are. The model can be conceptually convolved over the specifics of local cortical areas within and across species. A coherent aperture becomes a node in a graph of cortical areas with a corresponding distribution of information.

How does the presence of neural probes affect extracellular potentials?

OBJECTIVE

Mechanistic modeling of neurons is an essential component of computational neuroscience that enables scientists to simulate, explain, and explore neural activity. The conventional approach to simulation of extracellular neural recordings first computes transmembrane currents using the cable equation and then sums their contribution to model the extracellular potential. This two-step approach relies on the assumption that the extracellular space is an infinite and homogeneous conductive medium, while measurements are performed using neural probes. The main purpose of this paper is to assess to what extent the presence of the neural probes of varying shape and size impacts the extracellular field and how to correct for them.

APPROACH

We apply a detailed modeling framework allowing explicit representation of the neuron and the probe to study the effect of the probes and thereby estimate the effect of ignoring it. We use meshes with simplified neurons and different types of probe and compare the extracellular action potentials with and without the probe in the extracellular space. We then compare various solutions to account for the probes' presence and introduce an efficient probe correction method to include the probe effect in modeling of extracellular potentials.

MAIN RESULTS

Our computations show that microwires hardly influence the extracellular electric field and their effect can therefore be ignored. In contrast, multi-electrode arrays (MEAs) significantly affect the extracellular field by magnifying the recorded potential. While MEAs behave similarly to infinite insulated planes, we find that their effect strongly depends on the neuron-probe alignment and probe orientation.

SIGNIFICANCE

Ignoring the probe effect might be deleterious in some applications, such as neural localization and parameterization of neural models from extracellular recordings. Moreover, the presence of the probe can improve the interpretation of extracellular recordings, by providing a more accurate estimation of the extracellular potential generated by neuronal models.

Accurate signal-source localization in brain slices by means of high-density microelectrode arrays

Extracellular recordings by means of high-density microelectrode arrays (HD-MEAs) have become a powerful tool to resolve subcellular details of single neurons in active networks grown from dissociated cells. To extend the application of this technology to slice preparations, we developed models describing how extracellular signals, produced by neuronal cells in slices, are detected by microelectrode arrays. The models help to analyze and understand the electrical-potential landscape in an in vitro HD-MEA-recording scenario based on point-current sources. We employed two modeling schemes, (i) a simple analytical approach, based on the method of images (MoI), and (ii) an approach, based on finite-element methods (FEM). We compared and validated the models with large-scale, high-spatiotemporal-resolution recordings of slice preparations by means of HD-MEAs. We then developed a model-based localization algorithm and compared the performance of MoI and FEM models. Both models provided accurate localization results and a comparable and negligible systematic error, when the point source was in saline, a condition similar to cell-culture experiments. Moreover, the relative random error in the x-y-z-localization amounted only up to 4.3% for z-distances up to 200 μm from the HD-MEA surface. In tissue, the systematic errors of both, MoI and FEM models were significantly higher, and a pre-calibration was required. Nevertheless, the FEM values proved to be closer to the tissue experimental results, yielding 5.2 μm systematic mean error, compared to 22.0 μm obtained with MoI. These results suggest that the medium volume or "saline height", the brain slice thickness and anisotropy, and the location of the reference electrode, which were included in the FEM model, considerably affect the extracellular signal and localization performance, when the signal source is at larger distance to the array. After pre-calibration, the relative random error of the z-localization in tissue was only 3% for z-distances up to 200 μm. We then applied the model and related detailed understanding of extracellular recordings to achieve an electrically-guided navigation of a stimulating micropipette, solely based on the measured HD-MEA signals, and managed to target spontaneously active neurons in an acute brain slice for electroporation.

Localizing neuronal somata from Multi-Electrode Array in-vivo recordings using deep learning

With the latest development in the design and fabrication of high-density Multi-Electrode Arrays (MEA) for in-vivo neural recordings, the spatiotemporal information in the recorded signals allows for refined estimation of a neuron's location around the probe. In parallel, advances in computational models for neural activity enables simulation of recordings from neurons with detailed morphology. Our approach uses deep learning algorithms on a large set of such simulation data to extract the 3D position of the neuronal somata. Multi-compartment models from 13 different neural morphologies in layer 5 (L5) of the rat's neocortex are placed at random locations and with different alignments with respect to the MEA. The sodium trough and repolarisation peak images on the MEA serve as input features for a Convolutional Neural Network (CNN), which predicts the neural location robustly and with low error rates. The forward modeling/machine learning approach yields very accurate results for the different morphologies and is able to cope with different neuron alignments.

Combining biophysical modeling and deep learning for multielectrode array neuron localization and classification

Neural circuits typically consist of many different types of neurons, and one faces a challenge in disentangling their individual contributions in measured neural activity. Classification of cells into inhibitory and excitatory neurons and localization of neurons on the basis of extracellular recordings are frequently employed procedures. Current approaches, however, need a lot of human intervention, which makes them slow, biased, and unreliable. In light of recent advances in deep learning techniques and exploiting the availability of neuron models with quasi-realistic three-dimensional morphology and physiological properties, we present a framework for automatized and objective classification and localization of cells based on the spatiotemporal profiles of the extracellular action potentials recorded by multielectrode arrays. We train convolutional neural networks on simulated signals from a large set of cell models and show that our framework can predict the position of neurons with high accuracy, more precisely than current state-of-the-art methods. Our method is also able to classify whether a neuron is excitatory or inhibitory with very high accuracy, substantially improving on commonly used clustering techniques. Furthermore, our new method seems to have the potential to separate certain subtypes of excitatory and inhibitory neurons. The possibility of automatically localizing and classifying all neurons recorded with large high-density extracellular electrodes contributes to a more accurate and more reliable mapping of neural circuits. NEW & NOTEWORTHY We propose a novel approach to localize and classify neurons from their extracellularly recorded action potentials with a combination of biophysically detailed neuron models and deep learning techniques. Applied to simulated data, this new combination of forward modeling and machine learning yields higher performance compared with state-of-the-art localization and classification methods.

Revealing the distribution of transmembrane currents along the dendritic tree of a neuron from extracellular recordings

Revealing the current source distribution along the neuronal membrane is a key step on the way to understanding neural computations; however, the experimental and theoretical tools to achieve sufficient spatiotemporal resolution for the estimation remain to be established. Here, we address this problem using extracellularly recorded potentials with arbitrarily distributed electrodes for a neuron of known morphology. We use simulations of models with varying complexity to validate the proposed method and to give recommendations for experimental applications. The method is applied to in vitro data from rat hippocampus.

Validating silicon polytrodes with paired juxtacellular recordings: method and dataset

Cross-validating new methods for recording neural activity is necessary to accurately interpret and compare the signals they measure. Here we describe a procedure for precisely aligning two probes for in vivo "paired-recordings" such that the spiking activity of a single neuron is monitored with both a dense extracellular silicon polytrode and a juxtacellular micropipette. Our new method allows for efficient, reliable, and automated guidance of both probes to the same neural structure with micrometer resolution. We also describe a new dataset of paired-recordings, which is available online. We propose that our novel targeting system, and ever expanding cross-validation dataset, will be vital to the development of new algorithms for automatically detecting/sorting single-units, characterizing new electrode materials/designs, and resolving nagging questions regarding the origin and nature of extracellular neural signals.

Revealing neuronal function through microelectrode array recordings

Microelectrode arrays and microprobes have been widely utilized to measure neuronal activity, both in vitro and in vivo. The key advantage is the capability to record and stimulate neurons at multiple sites simultaneously. However, unlike the single-cell or single-channel resolution of intracellular recording, microelectrodes detect signals from all possible sources around every sensor. Here, we review the current understanding of microelectrode signals and the techniques for analyzing them. We introduce the ongoing advancements in microelectrode technology, with focus on achieving higher resolution and quality of recordings by means of monolithic integration with on-chip circuitry. We show how recent advanced microelectrode array measurement methods facilitate the understanding of single neurons as well as network function.

Generation of field potentials and modulation of their dynamics through volume integration of cortical activity

Field potentials (FPs) recorded within the brain, often called "local field potentials" (LFPs), are useful measures of net synaptic activity in a neuronal ensemble. However, due to volume conduction, FPs spread beyond regions of underlying synaptic activity, and thus an "LFP" signal may not accurately reflect the temporal patterns of synaptic activity in the immediately surrounding neuron population. To better understand the physiological processes reflected in FPs, we explored the relationship between the FP and its membrane current generators using current source density (CSD) analysis in conjunction with a volume conductor model. The model provides a quantitative description of the spatiotemporal summation of immediate local and more distant membrane currents to produce the FP. By applying the model to FPs in the macaque auditory cortex, we have investigated a critical issue that has broad implications for FP research. We have shown that FP responses in particular cortical layers are differentially susceptible to activity in other layers. Activity in the supragranular layers has the strongest contribution to FPs in other cortical layers, and infragranular FPs are most susceptible to contributions from other layers. To define the physiological processes generating FPs recorded in loci of relatively weak synaptic activity, strong effects produced by synaptic events in the vicinity have to be taken into account. While outlining limitations and caveats inherent to FP measurements, our results also suggest specific peak and frequency band components of FPs can be related to activity in specific cortical layers. These results may help improving the interpretability of FPs.