Modelling and Analysis of Electrical Potentials Recorded in Microelectrode Arrays (MEAs)

A Multimodal Fitting Approach to Construct Single-Neuron Models With Patch Clamp and High-Density Microelectrode Arrays

In computational neuroscience, multicompartment models are among the most biophysically realistic representations of single neurons. Constructing such models usually involves the use of the patch-clamp technique to record somatic voltage signals under different experimental conditions. The experimental data are then used to fit the many parameters of the model. While patching of the soma is currently the gold-standard approach to build multicompartment models, several studies have also evidenced a richness of dynamics in dendritic and axonal sections. Recording from the soma alone makes it hard to observe and correctly parameterize the activity of nonsomatic compartments. In order to provide a richer set of data as input to multicompartment models, we here investigate the combination of somatic patch-clamp recordings with recordings of high-density microelectrode arrays (HD-MEAs). HD-MEAs enable the observation of extracellular potentials and neural activity of neuronal compartments at subcellular resolution. In this work, we introduce a novel framework to combine patch-clamp and HD-MEA data to construct multicompartment models. We first validate our method on a ground-truth model with known parameters and show that the use of features extracted from extracellular signals, in addition to intracellular ones, yields models enabling better fits than using intracellular features alone. We also demonstrate our procedure using experimental data by constructing cell models from in vitro cell cultures. The proposed multimodal fitting procedure has the potential to augment the modeling efforts of the computational neuroscience community and provide the field with neuronal models that are more realistic and can be better validated.

Improving morphological and functional properties of enteric neuronal networks in vitro using a novel upside-down culture approach

The enteric nervous system (ENS) comprises millions of neurons and glia embedded in the wall of the gastrointestinal tract. It not only controls important functions of the gut but also interacts with the immune system, gut microbiota, and the gut-brain axis, thereby playing a key role in the health and disease of the whole organism. Any disturbance of this intricate system is mirrored in an alteration of electrical functionality, making electrophysiological methods important tools for investigating ENS-related disorders. Microelectrode arrays (MEAs) provide an appropriate noninvasive approach to recording signals from multiple neurons or whole networks simultaneously. However, studying isolated cells of the ENS can be challenging, considering the limited time that these cells can be kept vital in vitro. Therefore, we developed an alternative approach cultivating cells on glass samples with spacers (fabricated by photolithography methods). The spacers allow the cells to grow upside down in a spatially confined environment while enabling acute consecutive recordings of multiple ENS cultures on the same MEA. Upside-down culture also shows beneficial effects on the growth and behavior of enteric neural cultures. The number of dead cells was significantly decreased, and neural networks showed a higher resemblance to the myenteric plexus ex vivo while producing more stable signals than cultures grown in the conventional way. Overall, our results indicate that the upside-down approach not only allows to investigate the impact of neurological diseases in vitro but could also offer insights into the growth and development of the ENS under conditions much closer to the in vivo environment.NEW & NOTEWORTHY In this study, we devised a novel approach for culturing and electrophysiological recording of the enteric nervous system using custom-made glass substrates with spacers. This allows to turn cultures of isolated myenteric plexus upside down, enhancing the use of the microelectrode array technique by allowing recording of multiple cultures consecutively using only one chip. In addition, upside-down culture led to significant improvements in the culture conditions, resulting in a more in vivo-like growth.

Local contribution to the somatosensory evoked potentials in rat's thalamus

Local Field Potential (LFP), despite its name, often reflects remote activity. Depending on the orientation and synchrony of their sources, both oscillations and more complex waves may passively spread in brain tissue over long distances and be falsely interpreted as local activity at such distant recording sites. Here we show that the whisker-evoked potentials in the thalamic nuclei are of local origin up to around 6 ms post stimulus, but the later (7-15 ms) wave is overshadowed by a negative component reaching from cortex. This component can be analytically removed and local thalamic LFP can be recovered reliably using Current Source Density analysis. We used model-based kernel CSD (kCSD) method which allowed us to study the contribution of local and distant currents to LFP from rat thalamic nuclei and barrel cortex recorded with multiple, non-linear and non-regular multichannel probes. Importantly, we verified that concurrent recordings from the cortex are not essential for reliable thalamic CSD estimation. The proposed framework can be used to analyze LFP from other brain areas and has consequences for general LFP interpretation and analysis.

kCSD-python, reliable current source density estimation with quality control

Interpretation of extracellular recordings can be challenging due to the long range of electric field. This challenge can be mitigated by estimating the current source density (CSD). Here we introduce kCSD-python, an open Python package implementing Kernel Current Source Density (kCSD) method and related tools to facilitate CSD analysis of experimental data and the interpretation of results. We show how to counter the limitations imposed by noise and assumptions in the method itself. kCSD-python allows CSD estimation for an arbitrary distribution of electrodes in 1D, 2D, and 3D, assuming distributions of sources in tissue, a slice, or in a single cell, and includes a range of diagnostic aids. We demonstrate its features in a Jupyter Notebook tutorial which illustrates a typical analytical workflow and main functionalities useful in validating analysis results.

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.

Adaptive octree meshes for simulation of extracellular electrophysiology

Objective.The interaction between neural tissues and artificial electrodes is crucial for understanding and advancing neuroscientific research and therapeutic applications. However, accurately modeling this space around the neurons rapidly increases the computational complexity of neural simulations.Approach.This study demonstrates a dynamically adaptive simulation method that greatly accelerates computation by adjusting spatial resolution of the simulation as needed. Use of an octree structure for the mesh, in combination with the admittance method for discretizing conductivity, provides both accurate approximation and ease of modification on-the-fly.Main results.In tests of both local field potential estimation and multi-electrode stimulation, dynamically adapted meshes achieve accuracy comparable to high-resolution static meshes in an order of magnitude less time.Significance.The proposed simulation pipeline improves model scalability, allowing greater detail with fewer computational resources. The implementation is available as an open-source Python module, providing flexibility and ease of reuse for the broader research community.

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.

An automated method for precise axon reconstruction from recordings of high-density micro-electrode arrays

Objective

Neurons communicate with each other by sending action potentials through their axons. The velocity of axonal signal propagation describes how fast electrical action potentials can travel. This velocity can be affected in a human brain by several pathologies, including multiple sclerosis, traumatic brain injury and channelopathies. High-density microelectrode arrays (HD-MEAs) provide unprecedented spatio-temporal resolution to extracellularly record neural electrical activity. The high density of the recording electrodes enables to image the activity of individual neurons down to subcellular resolution, which includes the propagation of axonal signals. However, axon reconstruction, to date, mainly relies on manual approaches to select the electrodes and channels that seemingly record the signals along a specific axon, while an automated approach to track multiple axonal branches in extracellular action-potential recordings is still missing.

Approach

In this article, we propose a fully automated approach to reconstruct axons from extracellular electrical-potential landscapes, so-called “electrical footprints” of neurons. After an initial electrode and channel selection, the proposed method first constructs a graph based on the voltage signal amplitudes and latencies. Then, the graph is interrogated to extract possible axonal branches. Finally, the axonal branches are pruned, and axonal action-potential propagation velocities are computed.

Main results

We first validate our method using simulated data from detailed reconstructions of neurons, showing that our approach is capable of accurately reconstructing axonal branches. We then apply the reconstruction algorithm to experimental recordings of HD-MEAs and show that it can be used to determine axonal morphologies and signal-propagation velocities at high throughput.

Significance

We introduce a fully automated method to reconstruct axonal branches and estimate axonal action-potential propagation velocities using HD-MEA recordings. Our method yields highly reliable and reproducible velocity estimations, which constitute an important electrophysiological feature of neuronal preparations.

Nonhomogeneous volume conduction effects affecting needle electromyography: an analytical and simulation study

Objective.Needle electromyography (EMG) is used to study the electrical behavior of myofiber properties in patients with neuromuscular disorders. However, due to the complexity of electrical potential spatial propagation in nonhomogeneous diseased muscle, a comprehensive understanding of volume conduction effects remains elusive. Here, we develop a framework to study the conduction effect of extracellular abnormalities and electrode positioning on extracellular local field potential (LFP) recordings.Methods.The framework describes the macroscopic conduction of electrical potential in an isotropic, nonhomogeneous (i.e. two tissue) model. Numerical and finite element model simulations are provided to study the conduction effect in prototypical monopolar EMG measurements.Results.LFPs recorded are influenced in amplitude, phase and duration by the electrode position in regards to the vicinity of tissue with different electrical properties.Conclusion.The framework reveals the influence of multiple mechanisms affecting LFPs including changes in the distance between the source-electrode and tissue electrical properties.Clinical significance.Our modeled predictions may lead to new ways for interpreting volume conduction effects on recorded EMG activity, for example in neuromuscular diseases that cause structural and compositional changes in muscle tissue. These change will manifest itself by changing the electric properties of the conductor media and will impact recorded potentials in the area of affected tissue.

A multimodal 3D neuro-microphysiological system with neurite-trapping microelectrodes

Three-dimensional cell technologies as pre-clinical models are emerging tools for mimicking the structural and functional complexity of the nervous system. The accurate exploration of phenotypes in engineered 3D neuronal cultures, however, demands morphological, molecular and especially functional measurements. Particularly crucial is measurement of electrical activity of individual neurons with millisecond resolution. Current techniques rely on customized electrophysiological recording set-ups, characterized by limited throughput and poor integration with other readout modalities. Here we describe a novel approach, using multiwell glass microfluidic microelectrode arrays, allowing non-invasive electrical recording from engineered 3D neural tissues. We demonstrate parallelized studies with reference compounds, calcium imaging and optogenetic stimulation. Additionally, we show how microplate compatibility allows automated handling and high-content analysis of human induced pluripotent stem cell-derived neurons. This microphysiological platform opens up new avenues for high-throughput studies on the functional, morphological and molecular details of neurological diseases and their potential treatment by therapeutic compounds.

Cross-population coupling of neural activity based on Gaussian process current source densities

Because local field potentials (LFPs) arise from multiple sources in different spatial locations, they do not easily reveal coordinated activity across neural populations on a trial-to-trial basis. As we show here, however, once disparate source signals are decoupled, their trial-to-trial fluctuations become more accessible, and cross-population correlations become more apparent. To decouple sources we introduce a general framework for estimation of current source densities (CSDs). In this framework, the set of LFPs result from noise being added to the transform of the CSD by a biophysical forward model, while the CSD is considered to be the sum of a zero-mean, stationary, spatiotemporal Gaussian process, having fast and slow components, and a mean function, which is the sum of multiple time-varying functions distributed across space, each varying across trials. We derived biophysical forward models relevant to the data we analyzed. In simulation studies this approach improved identification of source signals compared to existing CSD estimation methods. Using data recorded from primate auditory cortex, we analyzed trial-to-trial fluctuations in both steady-state and task-evoked signals. We found cortical layer-specific phase coupling between two probes and showed that the same analysis applied directly to LFPs did not recover these patterns. We also found task-evoked CSDs to be correlated across probes, at specific cortical depths. Using data from Neuropixels probes in mouse visual areas, we again found evidence for depth-specific phase coupling of primary visual cortex and lateromedial area based on the CSDs.

Using multielectrode arrays to investigate neurodegenerative effects of the amyloid-beta peptide

BACKGROUND

Multielectrode arrays are widely used to analyze the effects of potentially toxic compounds, as well as to evaluate neuroprotective agents upon the activity of neural networks in short- and long-term cultures. Multielectrode arrays provide a way of non-destructive analysis of spontaneous and evoked neuronal activity, allowing to model neurodegenerative diseases in vitro. Here, we provide an overview on how these devices are currently used in research on the amyloid-β peptide and its role in Alzheimer's disease, the most common neurodegenerative disorder.

MAIN BODY

Most of the studies analysed here indicate fast responses of neuronal cultures towards aggregated forms of amyloid-β, leading to increases of spike frequency and impairments of long-term potentiation. This in turn suggests that this peptide might play a crucial role in causing the typical neuronal dysfunction observed in patients with Alzheimer's disease.

CONCLUSIONS

Although the number of studies using multielectrode arrays to examine the effect of the amyloid-β peptide onto neural cultures or whole compartments is currently limited, they still show how this technique can be used to not only investigate the interneuronal communication in neural networks, but also making it possible to examine the effects onto synaptic currents. This makes multielectrode arrays a powerful tool in future research on neurodegenerative diseases.

A framework for modeling bioimpedance measurements of nonhomogeneous tissues: a theoretical and simulation study

Objective.Bioimpedance technology is experiencing an increased use to assess health in a wide range of new consumer, research and clinical applications. However, the interaction between tissues producing bioimpedance data is often unclear.Methods.This work provides a novel theoretical framework to model bioimpedance measurements of nonhomogeneous tissues. We consider five case studies to validate the usefulness of our approach against finite element model simulations.Results.Theoretical and FEM-simulated apparent resistance and reactance data were in good agreement, with a maximum relative errors <4% and <8%, respectively.Conclusion.The biophysics-driven framework developed provides compact analytical expressions to model nonhomogeneous bioimpedance measurements including multiple tissues with arbitrary shape and electrical properties. This work provides a new perspective to interpret nonhomogeneous bioimpedance measurements usingseries,parallel, andseries-parallelcircuit-like topology equivalents.Significance.Our framework is a new tool to better understand and describe complex nonhomogeneous biological measurements as, for example, cardiac, brain and respiratory applications using (non)invasive electrodes.

What we can and what we cannot see with extracellular multielectrodes

Extracellular recording is an accessible technique used in animals and humans to study the brain physiology and pathology. As the number of recording channels and their density grows it is natural to ask how much improvement the additional channels bring in and how we can optimally use the new capabilities for monitoring the brain. Here we show that for any given distribution of electrodes we can establish exactly what information about current sources in the brain can be recovered and what information is strictly unobservable. We demonstrate this in the general setting of previously proposed kernel Current Source Density method and illustrate it with simplified examples as well as using evoked potentials from the barrel cortex obtained with a Neuropixels probe and with compatible model data. We show that with conceptual separation of the estimation space from experimental setup one can recover sources not accessible to standard methods.

Every set of measurements is a window into reality rendering its incomplete or distorted picture. It is often difficult to relate the obtained representation of the world to underlying ground truth. Here we show, for brain electrophysiology, for arbitrary experimental setup (distribution of electrodes), and arbitrary analytical setup (function space of current source densities), that one can identify distributions of current sources which can be recovered precisely, and those which are invisible in the system. This shows what is and what is not observable in the studied system for a given setup, allows to improve the analysis results by modifying analytical setup, and facilitates interpretation of the measured sets of LFP, ECoG and EEG recordings. In particular we show that with conceptual separation of the estimation space from experimental setup one can recover source distributions not accessible to standard methods.

MEArec: A Fast and Customizable Testbench Simulator for Ground-truth Extracellular Spiking Activity

When recording neural activity from extracellular electrodes, both in vivo and in vitro, spike sorting is a required and very important processing step that allows for identification of single neurons’ activity. Spike sorting is a complex algorithmic procedure, and in recent years many groups have attempted to tackle this problem, resulting in numerous methods and software packages. However, validation of spike sorting techniques is complicated. It is an inherently unsupervised problem and it is hard to find universal metrics to evaluate performance. Simultaneous recordings that combine extracellular and patch-clamp or juxtacellular techniques can provide ground-truth data to evaluate spike sorting methods. However, their utility is limited by the fact that only a few cells can be measured at the same time. Simulated ground-truth recordings can provide a powerful alternative mean to rank the performance of spike sorters. We present here MEArec, a Python-based software which permits flexible and fast simulation of extracellular recordings. MEArec allows users to generate extracellular signals on various customizable electrode designs and can replicate various problematic aspects for spike sorting, such as bursting, spatio-temporal overlapping events, and drifts. We expect MEArec will provide a common testbench for spike sorting development and evaluation, in which spike sorting developers can rapidly generate and evaluate the performance of their algorithms.

Biophysically detailed forward modeling of the neural origin of EEG and MEG signals

Electroencephalography (EEG) and magnetoencephalography (MEG) are among the most important techniques for non-invasively studying cognition and disease in the human brain. These signals are known to originate from cortical neural activity, typically described in terms of current dipoles. While the link between cortical current dipoles and EEG/MEG signals is relatively well understood, surprisingly little is known about the link between different kinds of neural activity and the current dipoles themselves. Detailed biophysical modeling has played an important role in exploring the neural origin of intracranial electric signals, like extracellular spikes and local field potentials. However, this approach has not yet been taken full advantage of in the context of exploring the neural origin of the cortical current dipoles that are causing EEG/MEG signals. Here, we present a method for reducing arbitrary simulated neural activity to single current dipoles. We find that the method is applicable for calculating extracranial signals, but less suited for calculating intracranial electrocorticography (ECoG) signals. We demonstrate that this approach can serve as a powerful tool for investigating the neural origin of EEG/MEG signals. This is done through example studies of the single-neuron EEG contribution, the putative EEG contribution from calcium spikes, and from calculating EEG signals from large-scale neural network simulations. We also demonstrate how the simulated current dipoles can be used directly in combination with detailed head models, allowing for simulated EEG signals with an unprecedented level of biophysical details. In conclusion, this paper presents a framework for biophysically detailed modeling of EEG and MEG signals, which can be used to better our understanding of non-inasively measured neural activity in humans.

Adaptive virtual referencing for the extraction of extracellularly recorded action potentials in noisy environments

OBJECTIVE

Removal of common mode noise and artifacts from extracellularly measured action potentials, herein referred to as spikes, recorded with multi-electrode arrays (MEAs) which included severe noise and artifacts generated by an ultrahigh field (UHF) 16.4 Tesla magnetic resonance imaging (MRI) scanner.

APPROACH

An adaptive virtual referencing (AVR) algorithm is used to remove artifacts and thus enable extraction of neural spike signals from extracellular recordings in anesthetized rat brains. A 16-channel MEA with 150-micron inter-site spacing is used, and a virtual reference is created by spatially averaging the 16 signal channels which results in a reference signal without extracellular spiking activity while preserving common mode noise and artifacts. This virtual reference signal is then used as the input to an adaptive FIR filter which optimally scales and time-shifts the reference to each specific electrode site to remove the artifacts and noise.

MAIN RESULTS

By removing artifacts and reducing noise, the neural spikes at each electrode site can be well extracted, even from data originally recorded with a high noise floor due to electromagnetic interference and artifacts generated by a 16.4T MRI scanner. The AVR method enables many more spikes to be detected than would otherwise be possible. Further, the filtered spike waveforms can be well separated from each other using PCA feature extraction and semi-supervised k-means clustering. While data in a 16.4T MRI scanner contains significantly more noise and artifacts, the developed AVR method enables similar data quality to be extracted as recorded on benchtop experiments outside the MRI scanner.

SIGNIFICANCE

AVR of extracellular spike signals recorded with MEAs has not been previously reported and fills a technical need by enabling low-noise extracellular spike extraction in noisy and challenging environments such as UHF MRI that will enable further study of neuro-vascular coupling at UHF.

Impact of Brain Surface Boundary Conditions on Electrophysiology and Implications for Electrocorticography

Volume conduction of electrical potentials in the brain is highly influenced by the material properties and geometry of the tissue and recording devices implanted into the tissue. These effects are very large in EEG due to the volume conduction through the skull and scalp but are often neglected in intracranial electrophysiology. When considering penetrating electrodes deep in the brain, the assumption of an infinite and homogenous medium can be used when the sources are far enough from the brain surface and the electrodes to minimize the boundary effect. When the electrodes are recording from the brain's surface the effect of the boundary cannot be neglected, and the large surface area and commonly used insulating materials in surface electrode arrays may further increase the effect by altering the nature of the boundary in the immediate vicinity of the electrodes. This gives the experimenter some control over the spatial profiles of the potentials by appropriate design of the electrode arrays. We construct a simple three-layer model to describe the effect of material properties and geometry above the brain surface on the electric potentials and conduct empirical experiments to validate this model. A laminar electrode array is used to measure the effect of insulating and relatively conducting layers above the cortical surface by recording evoked potentials alternating between a dried surface and saline covering layer, respectively. Empirically, we find that an insulating boundary amplifies the potentials relative to conductive saline by about a factor of 4, and that the effect is not constrained to potentials that originate near the surface. The model is applied to predict the influence of array design and implantation procedure on the recording amplitude and spatial selectivity of the surface electrode arrays.

Fast simulation of extracellular action potential signatures based on a morphological filtering approximation

Simulating extracellular recordings of neuronal populations is an important and challenging task both for understanding the nature and relationships between extracellular field potentials at different scales, and for the validation of methodological tools for signal analysis such as spike detection and sorting algorithms. Detailed neuronal multicompartmental models with active or passive compartments are commonly used in this objective. Although using such realistic NEURON models could lead to realistic extracellular potentials, it may require a high computational burden making the simulation of large populations difficult without a workstation. We propose in this paper a novel method to simulate extracellular potentials of firing neurons, taking into account the NEURON geometry and the relative positions of the electrodes. The simulator takes the form of a linear geometry based filter that models the shape of an action potential by taking into account its generation in the cell body / axon hillock and its propagation along the axon. The validity of the approach for different NEURON morphologies is assessed. We demonstrate that our method is able to reproduce realistic extracellular action potentials in a given range of axon/dendrites surface ratio, with a time-efficient computational burden.

PyPNS: Multiscale Simulation of a Peripheral Nerve in Python

Bioelectronic Medicines that modulate the activity patterns on peripheral nerves have promise as a new way of treating diverse medical conditions from epilepsy to rheumatism. Progress in the field builds upon time consuming and expensive experiments in living organisms. To reduce experimentation load and allow for a faster, more detailed analysis of peripheral nerve stimulation and recording, computational models incorporating experimental insights will be of great help. We present a peripheral nerve simulator that combines biophysical axon models and numerically solved and idealised extracellular space models in one environment. We modelled the extracellular space as a three-dimensional resistive continuum governed by the electro-quasistatic approximation of the Maxwell equations. Potential distributions were precomputed in finite element models for different media (homogeneous, nerve in saline, nerve in cuff) and imported into our simulator. Axons, on the other hand, were modelled more abstractly as one-dimensional chains of compartments. Unmyelinated fibres were based on the Hodgkin-Huxley model; for myelinated fibres, we adapted the model proposed by McIntyre et al. in 2002 to smaller diameters. To obtain realistic axon shapes, an iterative algorithm positioned fibres along the nerve with a variable tortuosity fit to imaged trajectories. We validated our model with data from the stimulated rat vagus nerve. Simulation results predicted that tortuosity alters recorded signal shapes and increases stimulation thresholds. The model we developed can easily be adapted to different nerves, and may be of use for Bioelectronic Medicine research in the future.

Large-Scale, High-Resolution Microelectrode Arrays for Interrogation of Neurons and Networks

High-density microelectrode arrays (HD-MEAs) are increasingly being used for the observation and manipulation of neurons and networks in vitro. Large-scale electrode arrays allow for long-term extracellular recording of the electrical activity from thousands of neurons simultaneously. Beyond population activity, it has also become possible to extract information of single neurons at subcellular level (e.g., the propagation of action potentials along axons). In effect, HD-MEAs have become an electrical imaging platform for label-free extraction of the structure and activation of cells in cultures and tissues. The quality of HD-MEA data depends on the resolution of the electrode array and the signal-to-noise ratio. In this chapter, we begin with an introduction to HD-MEA signals. We provide an overview of the developments on complementary metal-oxide-semiconductor or CMOS-based HD-MEA technology. We also discuss the factors affecting the performance of HD-MEAs and the trending application requirements that drive the efforts for future devices. We conclude with an outlook on the potential of HD-MEAs for advancing basic neuroscience and drug discovery.

Bayesian Modelling of Induced Responses and Neuronal Rhythms

Neural rhythms or oscillations are ubiquitous in neuroimaging data. These spectral responses have been linked to several cognitive processes; including working memory, attention, perceptual binding and neuronal coordination. In this paper, we show how Bayesian methods can be used to finesse the ill-posed problem of reconstructing-and explaining-oscillatory responses. We offer an overview of recent developments in this field, focusing on (i) the use of MEG data and Empirical Bayes to build hierarchical models for group analyses-and the identification of important sources of inter-subject variability and (ii) the construction of novel dynamic causal models of intralaminar recordings to explain layer-specific activity. We hope to show that electrophysiological measurements contain much more spatial information than is often thought: on the one hand, the dynamic causal modelling of non-invasive (low spatial resolution) electrophysiology can afford sub-millimetre (hyper-acute) resolution that is limited only by the (spatial) complexity of the underlying (dynamic causal) forward model. On the other hand, invasive microelectrode recordings (that penetrate different cortical layers) can reveal laminar-specific responses and elucidate hierarchical message passing and information processing within and between cortical regions at a macroscopic scale. In short, the careful and biophysically grounded modelling of sparse data enables one to characterise the neuronal architectures generating oscillations in a remarkable detail.

ELFENN: A Generalized Platform for Modeling Ephaptic Coupling in Spiking Neuron Models

The transmembrane ionic currents that underlie changes in a cell's membrane potential give rise to electric fields in the extracellular space. In the context of brain activity, these electric fields form the basis for extracellularly recorded signals, such as multiunit activity, local field potentials and electroencephalograms. Understanding the underlying neuronal dynamics and localizing current sources using these signals is often challenging, and therefore effective computational modeling approaches are critical. Typically, the electric fields from neural activity are modeled in a post-hoc form, i.e., a traditional neuronal model is used to first generate the membrane currents, which in turn are then used to calculate the electric fields. When the conductivity of the extracellular space is high, the electric fields are weak, and therefore treating membrane currents and electric fields separately is justified. However, in brain regions of lower conductivity, extracellular fields can feed back and significantly influence the underlying transmembrane currents and dynamics of nearby neurons—this is often referred to as ephaptic coupling. The closed-loop nature of ephaptic coupling cannot be modeled using the post-hoc approaches implemented by existing software tools; instead, electric fields and neuronal dynamics must be solved simultaneously. To this end, we have developed a generalized modeling toolbox for studying ephaptic coupling in compartmental neuron models: E_LFENN (E_Lectric Field Effects in Neural Networks). In open loop conditions, we validate the separate components of E_LFENN for modeling membrane dynamics and associated field potentials against standard approaches (NEURON and LFPy). Unlike standard approaches however, E_LFENN enables the closed-loop condition to be modeled as well, in that the field potentials can feed back and influence membrane dynamics. As an example closed-loop case, we use E_LFENN to study phase-locking of action potentials generated by a population of axons running parallel in a bundle. Being able to efficiently explore ephaptic coupling from a computational perspective using tools, such as E_LFENN will allow us to better understand the physical basis of electric fields in the brain, as well as the conditions in which these fields may influence neuronal dynamics in general.

Optimal Electrode Size for Multi-Scale Extracellular-Potential Recording From Neuronal Assemblies

Advances in microfabrication technology have enabled the production of devices containing arrays of thousands of closely spaced recording electrodes, which afford subcellular resolution of electrical signals in neurons and neuronal networks. Rationalizing the electrode size and configuration in such arrays demands consideration of application-specific requirements and inherent features of the electrodes. Tradeoffs among size, spatial density, sensitivity, noise, attenuation, and other factors are inevitable. Although recording extracellular signals from neurons with planar metal electrodes is fairly well established, the effects of the electrode characteristics on the quality and utility of recorded signals, especially for small, densely packed electrodes, have yet to be fully characterized. Here, we present a combined experimental and computational approach to elucidating how electrode size, and size-dependent parameters, such as impedance, baseline noise, and transmission characteristics, influence recorded neuronal signals. Using arrays containing platinum electrodes of different sizes, we experimentally evaluated the electrode performance in the recording of local field potentials (LFPs) and extracellular action potentials (EAPs) from the following cell preparations: acute brain slices, dissociated cell cultures, and organotypic slice cultures. Moreover, we simulated the potential spatial decay of point-current sources to investigate signal averaging using known signal sources. We demonstrated that the noise and signal attenuation depend more on the electrode impedance than on electrode size, per se, especially for electrodes <10 μm in width or diameter to achieve high-spatial-resolution readout. By minimizing electrode impedance of small electrodes (<10 μm) via surface modification, we could maximize the signal-to-noise ratio to electrically visualize the propagation of axonal EAPs and to isolate single-unit spikes. Due to the large amplitude of LFP signals, recording quality was high and nearly independent of electrode size. These findings should be of value in configuring in vitro and in vivo microelectrode arrays for extracellular recordings with high spatial resolution in various applications.

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.

Multimodal Modeling of Neural Network Activity: Computing LFP, ECoG, EEG, and MEG Signals With LFPy 2.0

Recordings of extracellular electrical, and later also magnetic, brain signals have been the dominant technique for measuring brain activity for decades. The interpretation of such signals is however nontrivial, as the measured signals result from both local and distant neuronal activity. In volume-conductor theory the extracellular potentials can be calculated from a distance-weighted sum of contributions from transmembrane currents of neurons. Given the same transmembrane currents, the contributions to the magnetic field recorded both inside and outside the brain can also be computed. This allows for the development of computational tools implementing forward models grounded in the biophysics underlying electrical and magnetic measurement modalities. LFPy (LFPy.readthedocs.io) incorporated a well-established scheme for predicting extracellular potentials of individual neurons with arbitrary levels of biological detail. It relies on NEURON (neuron.yale.edu) to compute transmembrane currents of multicompartment neurons which is then used in combination with an electrostatic forward model. Its functionality is now extended to allow for modeling of networks of multicompartment neurons with concurrent calculations of extracellular potentials and current dipole moments. The current dipole moments are then, in combination with suitable volume-conductor head models, used to compute non-invasive measures of neuronal activity, like scalp potentials (electroencephalographic recordings; EEG) and magnetic fields outside the head (magnetoencephalographic recordings; MEG). One such built-in head model is the four-sphere head model incorporating the different electric conductivities of brain, cerebrospinal fluid, skull and scalp. We demonstrate the new functionality of the software by constructing a network of biophysically detailed multicompartment neuron models from the Neocortical Microcircuit Collaboration (NMC) Portal (bbp.epfl.ch/nmc-portal) with corresponding statistics of connections and synapses, and compute in vivo-like extracellular potentials (local field potentials, LFP; electrocorticographical signals, ECoG) and corresponding current dipole moments. From the current dipole moments we estimate corresponding EEG and MEG signals using the four-sphere head model. We also show strong scaling performance of LFPy with different numbers of message-passing interface (MPI) processes, and for different network sizes with different density of connections. The open-source software LFPy is equally suitable for execution on laptops and in parallel on high-performance computing (HPC) facilities and is publicly available on GitHub.com.

BioNet: A Python interface to NEURON for modeling large-scale networks

There is a significant interest in the neuroscience community in the development of large-scale network models that would integrate diverse sets of experimental data to help elucidate mechanisms underlying neuronal activity and computations. Although powerful numerical simulators (e.g., NEURON, NEST) exist, data-driven large-scale modeling remains challenging due to difficulties involved in setting up and running network simulations. We developed a high-level application programming interface (API) in Python that facilitates building large-scale biophysically detailed networks and simulating them with NEURON on parallel computer architecture. This tool, termed "BioNet", is designed to support a modular workflow whereby the description of a constructed model is saved as files that could be subsequently loaded for further refinement and/or simulation. The API supports both NEURON's built-in as well as user-defined models of cells and synapses. It is capable of simulating a variety of observables directly supported by NEURON (e.g., spikes, membrane voltage, intracellular [Ca++]), as well as plugging in modules for computing additional observables (e.g. extracellular potential). The high-level API platform obviates the time-consuming development of custom code for implementing individual models, and enables easy model sharing via standardized files. This tool will help refocus neuroscientists on addressing outstanding scientific questions rather than developing narrow-purpose modeling code.

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.

A biopotential optrode array: operation principles and simulations

We propose an optical electrode ’optrode’ sensor array for biopotential measurements. The transduction mechanism is based on deformed helix ferroelectric liquid crystals which realign, altering the optrode’s light reflectance properties, relative to applied potential fields of biological cells and tissue. A computational model of extracellular potential recording by the optrode including the electro-optical transduction mechanism is presented, using a combination of time-domain and frequency-domain finite element analysis. Simulations indicate that the device has appropriate temporal response to faithfully transduce neuronal spikes, and spatial resolution to capture impulse propagation along a single neuron. These simulations contribute to the development of multi-channel optrode arrays for spatio-temporal mapping of electric events in excitable biological tissue.

Unsupervised Spike Sorting for Large-Scale, High-Density Multielectrode Arrays

We present a method for automated spike sorting for recordings with high-density, large-scale multielectrode arrays. Exploiting the dense sampling of single neurons by multiple electrodes, an efficient, low-dimensional representation of detected spikes consisting of estimated spatial spike locations and dominant spike shape features is exploited for fast and reliable clustering into single units. Millions of events can be sorted in minutes, and the method is parallelized and scales better than quadratically with the number of detected spikes. Performance is demonstrated using recordings with a 4,096-channel array and validated using anatomical imaging, optogenetic stimulation, and model-based quality control. A comparison with semi-automated, shape-based spike sorting exposes significant limitations of conventional methods. Our approach demonstrates that it is feasible to reliably isolate the activity of up to thousands of neurons and that dense, multi-channel probes substantially aid reliable spike sorting.

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.

Effect of Morphologic Features of Neurons on the Extracellular Electric Potential: A Simulation Study Using Cable Theory and Electro-Quasi-Static Equations

Microelectrode arrays serve as an indispensable tool in electro-physiological research to study the electrical activity of neural cells, enabling measurements of single cell as well as network communication analysis. Recent experimental studies have reported that the neuronal geometry has an influence on electrical signaling and extracellular recordings. However, the corresponding mechanisms are not yet fully understood and require further investigation. Allowing systematic parameter studies, computational modeling provides the opportunity to examine the underlying effects that influence extracellular potentials. In this letter, we present an in silico single cell model to analyze the effect of geometrical variability on the extracellular electric potentials. We describe finite element models of a single neuron with varying geometric complexity in three-dimensional space. The electric potential generation of the neuron is modeled using Hodgkin-Huxley equations. The signal propagation is described with electro-quasi-static equations, and results are compared with corresponding cable equation descriptions. Our results show that both the geometric dimensions and the distribution of ion channels of a neuron are critical factors that significantly influence both the amplitude and shape of extracellular potentials.

Computational analysis of network activity and spatial reach of sharp wave-ripples

Network oscillations of different frequencies, durations and amplitudes are hypothesized to coordinate information processing and transfer across brain areas. Among these oscillations, hippocampal sharp wave-ripple complexes (SPW-Rs) are one of the most prominent. SPW-Rs occurring in the hippocampus are suggested to play essential roles in memory consolidation as well as information transfer to the neocortex. To-date, most of the knowledge about SPW-Rs comes from experimental studies averaging responses from neuronal populations monitored by conventional microelectrodes. In this work, we investigate spatiotemporal characteristics of SPW-Rs and how microelectrode size and distance influence SPW-R recordings using a biophysical model of hippocampus. We also explore contributions from neuronal spikes and synaptic potentials to SPW-Rs based on two different types of network activity. Our study suggests that neuronal spikes from pyramidal cells contribute significantly to ripples while high amplitude sharp waves mainly arise from synaptic activity. Our simulations on spatial reach of SPW-Rs show that the amplitudes of sharp waves and ripples exhibit a steep decrease with distance from the network and this effect is more prominent for smaller area electrodes. Furthermore, the amplitude of the signal decreases strongly with increasing electrode surface area as a result of averaging. The relative decrease is more pronounced when the recording electrode is closer to the source of the activity. Through simulations of field potentials across a high-density microelectrode array, we demonstrate the importance of finding the ideal spatial resolution for capturing SPW-Rs with great sensitivity. Our work provides insights on contributions from spikes and synaptic potentials to SPW-Rs and describes the effect of measurement configuration on LFPs to guide experimental studies towards improved SPW-R recordings.

Collection of Simulated Data from a Thalamocortical Network Model

A major challenge in experimental data analysis is the validation of analytical methods in a fully controlled scenario where the justification of the interpretation can be made directly and not just by plausibility. In some sciences, this could be a mathematical proof, yet biological systems usually do not satisfy assumptions of mathematical theorems. One solution is to use simulations of realistic models to generate ground truth data. In neuroscience, creating such data requires plausible models of neural activity, access to high performance computers, expertise and time to prepare and run the simulations, and to process the output. To facilitate such validation tests of analytical methods we provide rich data sets including intracellular voltage traces, transmembrane currents, morphologies, and spike times. Moreover, these data can be used to study the effects of different tissue models on the measurement. The data were generated using the largest publicly available multicompartmental model of thalamocortical network (Traub et al., Journal of Neurophysiology, 93(4), 2194–2232 (Traub et al. 2005)), with activity evoked by different thalamic stimuli.

Focal Local Field Potential Signature of the Single-Axon Monosynaptic Thalamocortical Connection

A resurgence has taken place in recent years in the use of the extracellularly recorded local field potential (LFP) to investigate neural network activity. To probe monosynaptic thalamic activation of cortical postsynaptic target cells, so called spike-trigger-averaged LFP (stLFP) signatures have been measured. In these experiments, the cortical LFP is measured by multielectrodes covering several cortical lamina and averaged on spontaneous spikes of thalamocortical (TC) cells. Using a well established forward-modeling scheme, we investigated the biophysical origin of this stLFP signature with simultaneous synaptic activation of cortical layer-4 neurons, mimicking the effect of a single afferent spike from a single TC neuron. Constrained by previously measured intracellular responses of the main postsynaptic target cell types and with biologically plausible assumptions regarding the spatial distribution of thalamic synaptic inputs into layer 4, the model predicted characteristic contributions to monosynaptic stLFP signatures both for the regular-spiking (RS) excitatory neurons and the fast-spiking (FS) inhibitory interneurons. In particular, the FS cells generated stLFP signatures of shorter temporal duration than the RS cells. Added together, a sum of the stLFP signatures of these two principal synaptic targets of TC cells were observed to resemble experimentally measured stLFP signatures. Outside the volume targeted by TC afferents, the resulting postsynaptic LFP signals were found to be sharply attenuated. This implies that such stLFP signatures provide a very local measure of TC synaptic activation, and that newly developed inverse current-source density (CSD)-estimation methods are needed for precise assessment of the underlying spatiotemporal CSD profiles.SIGNIFICANCE STATEMENT Despite its long history and prevalent use, the proper interpretation of the extracellularly recorded local field potential (LFP) is still not fully established. Here we investigate by biophysical modeling the origin of the focal LFP signature of the single-axon monosynaptic thalamocortical connection as measured by spike-trigger-averaging of cortical LFPs on spontaneous spikes of thalamocortical neurons. We find that this LFP signature is well accounted for by a model assuming thalamic projections to two cortical layer-4 cell populations: one excitatory (putatively regular-spiking cells) and one inhibitory (putatively fast-spiking cells). The LFP signature is observed to decay sharply outside the cortical region receiving the thalamocortical projection, implying that it indeed provides a very local measure of thalamocortical synaptic activation.

Analysis and Modeling of Subthreshold Neural Multi-Electrode Array Data by Statistical Field Theory

Multi-electrode arrays (MEA) are increasingly used to investigate spontaneous neuronal network activity. The recorded signals comprise several distinct components: Apart from artifacts without biological significance, one can distinguish between spikes (action potentials) and subthreshold fluctuations (local fields potentials). Here we aim to develop a theoretical model that allows for a compact and robust characterization of subthreshold fluctuations in terms of a Gaussian statistical field theory in two spatial and one temporal dimension. What is usually referred to as the driving noise in the context of statistical physics is here interpreted as a representation of the neural activity. Spatial and temporal correlations of this activity give valuable information about the connectivity in the neural tissue. We apply our methods on a dataset obtained from MEA-measurements in an acute hippocampal brain slice from a rat. Our main finding is that the empirical correlation functions indeed obey the logarithmic behavior that is a general feature of theoretical models of this kind. We also find a clear correlation between the activity and the occurrence of spikes. Another important insight is the importance of correctly separating out certain artifacts from the data before proceeding with the analysis.

Linking canonical microcircuits and neuronal activity: Dynamic causal modelling of laminar recordings

Neural models describe brain activity at different scales, ranging from single cells to whole brain networks. Here, we attempt to reconcile models operating at the microscopic (compartmental) and mesoscopic (neural mass) scales to analyse data from microelectrode recordings of intralaminar neural activity. Although these two classes of models operate at different scales, it is relatively straightforward to create neural mass models of ensemble activity that are equipped with priors obtained after fitting data generated by detailed microscopic models. This provides generative (forward) models of measured neuronal responses that retain construct validity in relation to compartmental models. We illustrate our approach using cross spectral responses obtained from V1 during a visual perception paradigm that involved optogenetic manipulation of the basal forebrain. We find that the resulting neural mass model can distinguish between activity in distinct cortical layers - both with and without optogenetic activation - and that cholinergic input appears to enhance (disinhibit) superficial layer activity relative to deep layers. This is particularly interesting from the perspective of predictive coding, where neuromodulators are thought to boost prediction errors that ascend the cortical hierarchy.

Impedance Spectrum in Cortical Tissue: Implications for Propagation of LFP Signals on the Microscopic Level

Brain research investigating electrical activity within neural tissue is producing an increasing amount of physiological data including local field potentials (LFPs) obtained via extracellular in vivo and in vitro recordings. In order to correctly interpret such electrophysiological data, it is vital to adequately understand the electrical properties of neural tissue itself. An ongoing controversy in the field of neuroscience is whether such frequency-dependent effects bias LFP recordings and affect the proper interpretation of the signal. On macroscopic scales and with large injected currents, previous studies have found various grades of frequency dependence of cortical tissue, ranging from negligible to strong, within the frequency band typically considered relevant for neuroscience (less than a few thousand hertz). Here, we performed a detailed investigation of the frequency dependence of the conductivity within cortical tissue at microscopic distances using small current amplitudes within the typical (neuro)physiological micrometer and sub-nanoampere range. We investigated the propagation of LFPs, induced by extracellular electrical current injections via patch-pipettes, in acute rat brain slice preparations containing the somatosensory cortex in vitro using multielectrode arrays. Based on our data, we determined the cortical tissue conductivity over a 100-fold increase in signal frequency (5-500 Hz). Our results imply at most very weak frequency-dependent effects within the frequency range of physiological LFPs. Using biophysical modeling, we estimated the impact of different putative impedance spectra. Our results indicate that frequency dependencies of the order measured here and in most other studies have negligible impact on the typical analysis and modeling of LFP signals from extracellular brain recordings.

Hybrid Scheme for Modeling Local Field Potentials from Point-Neuron Networks

With rapidly advancing multi-electrode recording technology, the local field potential (LFP) has again become a popular measure of neuronal activity in both research and clinical applications. Proper understanding of the LFP requires detailed mathematical modeling incorporating the anatomical and electrophysiological features of neurons near the recording electrode, as well as synaptic inputs from the entire network. Here we propose a hybrid modeling scheme combining efficient point-neuron network models with biophysical principles underlying LFP generation by real neurons. The LFP predictions rely on populations of network-equivalent multicompartment neuron models with layer-specific synaptic connectivity, can be used with an arbitrary number of point-neuron network populations, and allows for a full separation of simulated network dynamics and LFPs. We apply the scheme to a full-scale cortical network model for a ∼1 mm² patch of primary visual cortex, predict laminar LFPs for different network states, assess the relative LFP contribution from different laminar populations, and investigate effects of input correlations and neuron density on the LFP. The generic nature of the hybrid scheme and its public implementation in hybridLFPy form the basis for LFP predictions from other and larger point-neuron network models, as well as extensions of the current application with additional biological detail.

Visualization of electrical field of electrode using voltage-controlled fluorescence release

In this study we propose an approach to directly visualize electrical current distribution at the electrode-electrolyte interface of a biopotential electrode. High-speed fluorescent microscopic images are acquired when an electric potential is applied across the interface to trigger the release of fluorescent material from the surface of the electrode. These images are analyzed computationally to obtain the distribution of the electric field from the fluorescent intensity of each pixel. Our approach allows direct observation of microscopic electrical current distribution around the electrode. Experiments are conducted to validate the feasibility of the fluorescent imaging method.

Computational Modeling of Single Neuron Extracellular Electric Potentials and Network Local Field Potentials using LFPsim

Local Field Potentials (LFPs) are population signals generated by complex spatiotemporal interaction of current sources and dipoles. Mathematical computations of LFPs allow the study of circuit functions and dysfunctions via simulations. This paper introduces LFPsim, a NEURON-based tool for computing population LFP activity and single neuron extracellular potentials. LFPsim was developed to be used on existing cable compartmental neuron and network models. Point source, line source, and RC based filter approximations can be used to compute extracellular activity. As a demonstration of efficient implementation, we showcase LFPs from mathematical models of electrotonically compact cerebellum granule neurons and morphologically complex neurons of the neocortical column. LFPsim reproduced neocortical LFP at 8, 32, and 56 Hz via current injection, in vitro post-synaptic N_2a, N_2b waves and in vivo T-C waves in cerebellum granular layer. LFPsim also includes a simulation of multi-electrode array of LFPs in network populations to aid computational inference between biophysical activity in neural networks and corresponding multi-unit activity resulting in extracellular and evoked LFP signals.

1D Current Source Density (CSD) Estimation in Inverse Theory: A Unified Framework for Higher-Order Spectral Regularization of Quadrature and Expansion-Type CSD Methods

Estimation of current source density (CSD) from the low-frequency part of extracellular electric potential recordings is an unstable linear inverse problem. To make the estimation possible in an experimental setting where recordings are contaminated with noise, it is necessary to stabilize the inversion. Here we present a unified framework for zero- and higher-order singular-value-decomposition (SVD)-based spectral regularization of 1D (linear) CSD estimation from local field potentials. The framework is based on two general approaches commonly employed for solving inverse problems: quadrature and basis function expansion. We first show that both inverse CSD (iCSD) and kernel CSD (kCSD) fall into the category of basis function expansion methods. We then use these general categories to introduce two new estimation methods, quadrature CSD (qCSD), based on discretizing the CSD integral equation with a chosen quadrature rule, and representer CSD (rCSD), an even-determined basis function expansion method that uses the problem's data kernels (representers) as basis functions. To determine the best candidate methods to use in the analysis of experimental data, we compared the different methods on simulations under three regularization schemes (Tikhonov, tSVD, and dSVD), three regularization parameter selection methods (NCP, L-curve, and GCV), and seven different a priori spatial smoothness constraints on the CSD distribution. This resulted in a comparison of 531 estimation schemes. We evaluated the estimation schemes according to their source reconstruction accuracy by testing them using different simulated noise levels, lateral source diameters, and CSD depth profiles. We found that ranking schemes according to the average error over all tested conditions results in a reproducible ranking, where the top schemes are found to perform well in the majority of tested conditions. However, there is no single best estimation scheme that outperforms all others under all tested conditions. The unified framework we propose expands the set of available estimation methods, provides increased flexibility for 1D CSD estimation in noisy experimental conditions, and allows for a meaningful comparison between estimation schemes.

Aberrant Activity in Degenerated Retinas Revealed by Electrical Imaging

In this review, I present and discuss the current understanding of aberrant electrical activity found in the ganglion cell layer (GCL) of rod-degenerated (rd) mouse retinas. The reported electrophysiological properties revealed by electrical imaging using high-density microelectrode arrays can be subdivided between spiking activity originating from retinal ganglion cells (RGCs) and local field potentials (LFPs) reflecting strong trans-membrane currents within the GCL. RGCs in rd retinas show increased and rhythmic spiking compared to age-matched wild-type retinas. Fundamental spiking frequencies range from 5 to 15 Hz in various mouse models. The rhythmic RGC spiking is driven by a presynaptic network comprising AII amacrine and bipolar cells. In the healthy retina this rhythm-generating circuit is inhibited by photoreceptor input. A unique physiological feature of rd retinas is rhythmic LFP manifested as spatially-restricted low-frequency (5-15 Hz) voltage changes. Their spatiotemporal characterization revealed propagation and correlation with RGC spiking. LFPs rely on gap-junctional coupling and are shaped by glycinergic and by GABAergic transmission. The aberrant RGC spiking and LFPs provide a simple readout of the functionality of the remaining retinal circuitry which can be used in the development of improved vision restoration strategies.

Generalized Laminar Population Analysis (gLPA) for Interpretation of Multielectrode Data from Cortex

Laminar population analysis (LPA) is a method for analysis of electrical data recorded by linear multielectrodes passing through all lamina of cortex. Like principal components analysis (PCA) and independent components analysis (ICA), LPA offers a way to decompose the data into contributions from separate cortical populations. However, instead of using purely mathematical assumptions in the decomposition, LPA is based on physiological constraints, i.e., that the observed LFP (low-frequency part of signal) is driven by action-potential firing as observed in the MUA (multi-unit activity; high-frequency part of the signal). In the presently developed generalized laminar population analysis (gLPA) the set of basis functions accounting for the LFP data is extended compared to the original LPA, thus allowing for a better fit of the model to experimental data. This enhances the risk for overfitting, however, and we therefore tested various versions of gLPA on virtual LFP data in which we knew the ground truth. These synthetic data were generated by biophysical forward-modeling of electrical signals from network activity in the comprehensive, and well-known, thalamocortical network model developed by Traub and coworkers. The results for the Traub model imply that while the laminar components extracted by the original LPA method overall are in fair agreement with the ground-truth laminar components, the results may be improved by use of gLPA method with two (gLPA-2) or even three (gLPA-3) postsynaptic LFP kernels per laminar population.