Simulated Local Field Potentials Research Articles

Role of the volume conductor on simulations of local field potential recordings from deep brain stimulation electrodes.

Local field potential (LFP) recordings from deep brain stimulation (DBS) electrodes are commonly used in research analyses, and are beginning to be used in clinical practice. Computational models of DBS LFPs provide tools for investigating the biophysics and neural synchronization that underlie LFP signals. However, technical standards for DBS LFP model parameterization remain to be established. Therefore, the goal of this study was to evaluate the role of the volume conductor (VC) model complexity on simulated LFP signals in the subthalamic nucleus (STN). We created a detailed human head VC model that explicitly represented the inhomogeneity and anisotropy associated with 12 different tissue structures. This VC model represented our "gold standard" for technical detail and electrical realism. We then incrementally decreased the complexity of the VC model and quantified the impact on the simulated LFP recordings. Identical STN neural source activity was used when comparing the different VC model variants. Results Ignoring tissue anisotropy reduced the simulated LFP amplitude by ~12%, while eliminating soft tissue heterogeneity had a negligible effect on the recordings. Simplification of the VC model to consist of a single homogenous isotropic tissue medium with a conductivity of 0.215 S/m contributed an additional ~3% to the error. Highly detailed VC models do generate different results than simplified VC models. However, with errors in the range of ~15%, the use of a well-parameterized simple VC model is likely to be acceptable in most contexts for DBS LFP modeling.

Large-scale biophysically detailed model of somatosensory thalamocortical circuits in NetPyNE.

The primary somatosensory cortex (S1) of mammals is critically important in the perception of touch and related sensorimotor behaviors. In 2015, the Blue Brain Project (BBP) developed a groundbreaking rat S1 microcircuit simulation with over 31,000 neurons with 207 morpho-electrical neuron types, and 37 million synapses, incorporating anatomical and physiological information from a wide range of experimental studies. We have implemented this highly detailed and complex S1 model in NetPyNE, using the data available in the Neocortical Microcircuit Collaboration Portal. NetPyNE provides a Python high-level interface to NEURON and allows defining complicated multiscale models using an intuitive declarative standardized language. It also facilitates running parallel simulations, automates the optimization and exploration of parameters using supercomputers, and provides a wide range of built-in analysis functions. This will make the S1 model more accessible and simpler to scale, modify and extend in order to explore research questions or interconnect to other existing models. Despite some implementation differences, the NetPyNE model preserved the original cell morphologies, electrophysiological responses and spatial distribution for all 207 cell types; and the connectivity properties of all 1941 pathways, including synaptic dynamics and short-term plasticity (STP). The NetPyNE S1 simulations produced reasonable physiological firing rates and activity patterns across all populations. When STP was included, the network generated a 1 Hz oscillation comparable to the original model in vitro-like state. By then reducing the extracellular calcium concentration, the model reproduced the original S1 in vivo-like states with asynchronous activity. These results validate the original study using a new modeling tool. Simulated local field potentials (LFPs) exhibited realistic oscillatory patterns and features, including distance- and frequency-dependent attenuation. The model was extended by adding thalamic circuits, including 6 distinct thalamic populations with intrathalamic, thalamocortical (TC) and corticothalamic connectivity derived from experimental data. The thalamic model reproduced single known cell and circuit-level dynamics, including burst and tonic firing modes and oscillatory patterns, providing a more realistic input to cortex and enabling study of TC interactions. Overall, our work provides a widely accessible, data-driven and biophysically-detailed model of the somatosensory TC circuits that can be employed as a community tool for researchers to study neural dynamics, function and disease.

Levodopa-dependent differences in the non-oscillatory activity of the subthalamic nucleus.

The study of local field potentials (LFP) recorded from the basal ganglia of patients with movement disorders led to significant advancement in the understanding the pathophysiology of Parkinson's disease (PD). The possibility of investigating possible changes in the activity of the brain caused by the levodopa administration may provide a useful tool to evaluate the influence or the side-effects of the treatment from patient to patient. The analysis was carried out through a systematic analysis of the fractal component of the subthalamic local field potentials (STN-LFP) that may reveal, with respect to the classical power spectrum analysis, novel important information about the dynamic modulation caused by the drug intake. Indeed, so far, much of what is known about that is related to the presence of a spectral peak in the beta frequency band then attenuated after the levodopa administration. The nonlinear power-law exponent goes beyond this feature, exploring differences that reflect the fractal (scale-free) behavior of the PD brain dynamics. Here, in order to demonstrate that the presence or absence of the peak has no effect on the computation of the power-law exponent, we used simulated LFP recordings. After that, we performed the fractal analysis in shorts epochs of STN LFPs recordings ( N=24 patients, 12 females and 12 males) before and after Levodopa administration. We found no differences in the nonlinear power-law exponent for simulated data, reinforcing the idea that the parameter was not influenced by the attenuation of the hallmark peak for PD patients. As regard real LFP time series, we found that pharmacological treatment for PD differently altered LFP power of non-oscillatory activity, as well as changed the level of fractal exponent in specific frequency bands. Particularly we observed an increase of the fractal exponent in condition of post-levodopa with significant differences related to the response to levodopa in Parkinson's disease. Clinical Relevance- This study points out a potentially novel non-oscillatory biomarker which could reflect intrinsic properties of complex biological systems thus constituting a potential target parameter for novel and alternative neuroprosthetic applications.

Brain simulation augments machine-learning-based classification of dementia.

ABSTRACTIntroductionComputational brain network modeling using The Virtual Brain (TVB) simulation platform acts synergistically with machine learning (ML) and multi‐modal neuroimaging to reveal mechanisms and improve diagnostics in Alzheimer's disease (AD).MethodsWe enhance large‐scale whole‐brain simulation in TVB with a cause‐and‐effect model linking local amyloid beta (Aβ) positron emission tomography (PET) with altered excitability. We use PET and magnetic resonance imaging (MRI) data from 33 participants of the Alzheimer's Disease Neuroimaging Initiative (ADNI3) combined with frequency compositions of TVB‐simulated local field potentials (LFP) for ML classification.ResultsThe combination of empirical neuroimaging features and simulated LFPs significantly outperformed the classification accuracy of empirical data alone by about 10% (weighted F1‐score empirical 64.34% vs. combined 74.28%). Informative features showed high biological plausibility regarding the AD‐typical spatial distribution.DiscussionThe cause‐and‐effect implementation of local hyperexcitation caused by Aβ can improve the ML–driven classification of AD and demonstrates TVB's ability to decode information in empirical data using connectivity‐based brain simulation.

Canard solutions in neural mass models: consequences on critical regimes

Mathematical models at multiple temporal and spatial scales can unveil the fundamental mechanisms of critical transitions in brain activities. Neural mass models (NMMs) consider the average temporal dynamics of interconnected neuronal subpopulations without explicitly representing the underlying cellular activity. The mesoscopic level offered by the neural mass formulation has been used to model electroencephalographic (EEG) recordings and to investigate various cerebral mechanisms, such as the generation of physiological and pathological brain activities. In this work, we consider a NMM widely accepted in the context of epilepsy, which includes four interacting neuronal subpopulations with different synaptic kinetics. Due to the resulting three-time-scale structure, the model yields complex oscillations of relaxation and bursting types. By applying the principles of geometric singular perturbation theory, we unveil the existence of the canard solutions and detail how they organize the complex oscillations and excitability properties of the model. In particular, we show that boundaries between pathological epileptic discharges and physiological background activity are determined by the canard solutions. Finally we report the existence of canard-mediated small-amplitude frequency-specific oscillations in simulated local field potentials for decreased inhibition conditions. Interestingly, such oscillations are actually observed in intracerebral EEG signals recorded in epileptic patients during pre-ictal periods, close to seizure onsets.

Excitation and Inhibition Balance Underlying Epileptiform Activity.

The phenomenon of postictal generalized EEG suppression state (PGES) - a period with suppressed activity following seizure termination and has been found to be associated with sudden unexpected death in epilepsy - remains poorly understood. This article aims to examine the how the balance of excitation and inhibition (E/I balance) affect the dynamics of seizure and PGES. A network of 1000 Izhikevich model neurons was developed and only the strengths of synaptic connections were adjusted to recreate the dynamics observed in recordings of seizure and PGES from human patients. A rapid rise followed by a slow decay of dominant frequency was observed in iEEG recordings of ictal periods and reproduced in the simulated local field potential by changing the E/I balance of the model network. The rate of this dominant frequency evolution was quantified by a single measure, β, which was found to have a significant rank correlation with the duration of PGES in iEEG data and the rate of E/I balance shift in the model. Significance and Conclusion: (i) highlighting the importance of E/I balance in the dynamics of seizure and PGES; (ii) suggesting the measure, β, as a marker for PGES and the shift in E/I balance as a neural correlate for this marker.

Linking Molecular Pathways and Large-Scale Computational Modeling to Assess Candidate Disease Mechanisms and Pharmacodynamics in Alzheimer's Disease.

Introduction: While the prevalence of neurodegenerative diseases associated with dementia such as Alzheimer's disease (AD) increases, our knowledge on the underlying mechanisms, outcome predictors, or therapeutic targets is limited. In this work, we demonstrate how computational multi-scale brain modeling links phenomena of different scales and therefore identifies potential disease mechanisms leading the way to improved diagnostics and treatment.Methods: The Virtual Brain (TVB; thevirtualbrain.org) neuroinformatics platform allows standardized large-scale structural connectivity-based simulations of whole brain dynamics. We provide proof of concept for a novel approach that quantitatively links the effects of altered molecular pathways onto neuronal population dynamics. As a novelty, we connect chemical compounds measured with positron emission tomography (PET) with neural function in TVB addressing the phenomenon of hyperexcitability in AD related to the protein amyloid beta (Abeta). We construct personalized virtual brains based on an averaged healthy connectome and individual PET derived distributions of Abeta in patients with mild cognitive impairment (MCI, N = 8) and Alzheimer's Disease (AD, N = 10) and in age-matched healthy controls (HC, N = 15) using data from ADNI-3 data base (http://adni.loni.usc.edu). In the personalized virtual brains, individual Abeta burden modulates regional Excitation-Inhibition balance, leading to local hyperexcitation with high Abeta loads. We analyze simulated regional neural activity and electroencephalograms (EEG).Results: Known empirical alterations of EEG in patients with AD compared to HCs were reproduced by simulations. The virtual AD group showed slower frequencies in simulated local field potentials and EEG compared to MCI and HC groups. The heterogeneity of the Abeta load is crucial for the virtual EEG slowing which is absent for control models with homogeneous Abeta distributions. Slowing phenomena primarily affect the network hubs, independent of the spatial distribution of Abeta. Modeling the N-methyl-D-aspartate (NMDA) receptor antagonism of memantine in local population models, reveals potential functional reversibility of the observed large-scale alterations (reflected by EEG slowing) in virtual AD brains.Discussion: We demonstrate how TVB enables the simulation of systems effects caused by pathogenetic molecular candidate mechanisms in human virtual brains.

Reconstruction of post-synaptic potentials by reverse modeling of local field potentials

Objective. Among electrophysiological signals, local field potentials (LFPs) are extensively used to study brain activity, either in vivo or in vitro. LFPs are recorded with extracellular electrodes implanted in brain tissue. They reflect intermingled excitatory and inhibitory processes in neuronal assemblies. In cortical structures, LFPs mainly originate from the summation of post-synaptic potentials (PSPs), either excitatory (ePSPs) or inhibitory (iPSPs) generated at the level of pyramidal cells. The challenging issue, addressed in this paper, is to estimate, from a single extracellularly-recorded signal, both ePSP and iPSP components of the LFP. Approach. The proposed method is based on a model-based reverse engineering approach in which the measured LFP is fed into a physiologically-grounded neural mass model (mesoscopic level) to estimate the synaptic activity of a sub-population of pyramidal cells interacting with local GABAergic interneurons. Main results. The method was first validated using simulated LFPs for which excitatory and inhibitory components are known a priori and can thus serve as a ground truth. It was then evaluated on in vivo data (PTZ-induced seizures, rat; PTZ-induced excitability increase, mouse; epileptiform discharges, mouse) and on in clinico data (human seizures recorded with depth-EEG electrodes). Significance. Under these various conditions, results showed that the proposed reverse engineering method provides a reliable estimation of the average excitatory and inhibitory post-synaptic potentials originating of the measured LFPs. They also indicated that the method allows for monitoring of the excitation/inhibition ratio. The method has potential for multiple applications in neuroscience, typically when a dynamical tracking of local excitability changes is required.

A biologically plausible mechanism for neuronal coding organized by the phase of alpha oscillations

The visual system receives a wealth of sensory information of which only little is relevant for behaviour. We present a mechanism in which alpha oscillations serve to prioritize different components of visual information. By way of simulated neuronal networks, we show that inhibitory modulation in the alpha range (~ 10 Hz) can serve to temporally segment the visual information to prevent information overload. Coupled excitatory and inhibitory neurons generate a gamma rhythm in which information is segmented and sorted according to excitability in each alpha cycle. Further details are coded by distributed neuronal firing patterns within each gamma cycle. The network model produces coupling between alpha phase and gamma (40–100 Hz) amplitude in the simulated local field potential similar to that observed experimentally in human and animal recordings.

Modelling local field potential features during network gamma oscillations

While the physics of local field potential (LFP) generation are well-established, the complexity of neural network dynamics means that interpreting LFP measurements in terms of the underlying neural activity is very difficult [1]. Recent studies have therefore investigated forward models of the LFP: calculating the LFP due to known arrangements of neuronal current sources [1]. We use this approach to study the spatio-temporal features of the LFP recorded during persistent gamma-oscillations in vitro. The mechanism by which this activity regime is generated is well-known [2], and many multi-electrode array recordings are available that allow us to compare the spatio-temporal properties of the experimentally measured and simulated LFPs. For simplicity, we implemented a model of a neocortical slice containing only layer 2/3, using our VERTEX simulation tool. The model contained a gamma oscillation-generating region surrounded by regions that did not participate in the gamma oscillation (i.e. the neurons in these regions fired randomly). These enforced conditions allowed us to study the spatial profile of the LFP from differently sized gamma oscillation-generating patches, while minimising the number of variables we changed between simulations. Additionally, we could make observations about properties of the LFP during random activity in the network. We describe three key results from our simulations. Firstly, we found that perisomatic synaptic currents on pyramidal neurons resulting from basket interneuron firing dominate the LFP during gamma oscillations, in agreement with recent experimental results [3,4]. We predict that basket interneurons will also contribute the majority of the LFP signal during random, uncorrelated activity because of the location of their synapses at pyramidal neuron somas. This contribution is amplified during oscillatory activity because of increased basket cell synchrony relative to other neuron types. Secondly, we investigated how gamma-frequency power from a localised gammagenerating region in the model spread due to volume conduction. We found that the spatial spread of the oscillation in the LFP increased above and below the neurons’ somadepth, and depended on the level of the random surround activity. Finally, we investigated frequency scaling in the LFP power spectrum across space. We showed that LFPs at the level of the pyramidal cells’ apical dendrites exhibit a low-pass filtering effect (as predicted previously [5]), which is absent from LFPs recorded at the soma level because of the relative dominance and localisation of the basket cell input. We confirmed that this matched the frequency scaling in our comparison experimental data recorded in macaque neocortical slices, and, based on the frequency characteristics in our model, propose that the experimentally recorded LFP could contain contributions from spiking activity at frequencies down to, and perhaps below, 100 Hz.

Inferring network model from local field potentials

Experimental study of neural information processing requires simultaneous sampling of the activity of multiple cells over the network. One of the promising approaches relies on monitoring local field potentials (LFPs) by multi-electrode arrays that can span large brain regions (see Figure 1A,B). LFPs may contain firing activity of different cells and, more importantly, they capture synaptic activity produced by principal cells. Thus LFPs enclose extremely rich information on how principal cells integrate converging inputs coming from multiple neuronal populations. However, since synaptic currents mix in the extracellular volume, LFPs have complex spatiotemporal structure making them hard to be exploited. Recently we proposed a biophysical framework to identify and separate LFPs into so-called LFP-generators [1]. Here we discuss how this technique can be used to identify spatial characteristics and temporal patterns of main LFP-generators actuating in the rat hippocampus. The electrical activity of each generator is defined by the spatial distribution of synaptic terminals and the time course of synaptic currents initiated by spike trains sent by the corresponding presynaptic population. Remarkably some recognized pathways do not contribute notably to LFPs [2]. We localized synaptic inputs with subcellular accuracy and reconstructed time courses of main LFP-generators up to millisecond time scales. We were able to readout in parallel the pathway-specific presynaptic activity of projection cells in the entorhinal cortex and pyramidal cells in the ipsilateral and contralateral CA3. We also provide results on spatial extension of the generators. Then we use a computational multi-neuronal model (see Figure ​Figure1C)1C) that scales up single cell electrogenesis driven by several synaptic inputs to realistic aggregate LFPs. This approach relies on the fixed but distinct locations of synaptic inputs from different presynaptic populations obtained experimentally. We show that this approach reliably reproduces ongoing LFPs in the hippocampus (see Figure ​Figure1D).1D). Then simulated LFPs can be used for studying relationships between phases of LFP-generators and spike trains fired by presynaptic neurons (see Figure ​Figure1E).1E). We show that the phase-spike relations provide information on spatial location of axon terminals in contrast to extended opinion on phase spike locking. Figure 1 Inferring network dynamics from LFPs. A. Sketch of experimental setup. Multi-electrode spans CA1-CA3 region of the rat hippocampus. B. Experimental spontaneous LFPs. C. local circuit included in the model. D. Simulated LFPs. E. Phase-spike relations.

Local field potentials in the auditory brain stem described by idealized biophysically-based models of the medial superior olive

The medial superior olive (MSO) is one of the first stages in the mammalian auditory pathway to receive inputs from both ears. MSO neurons can act as exquisitely sensitive coincidence detectors and are able to detect interaural time differences with submillisecond precision [1]. Due to these specializations, the MSO is thought to play a critical role in spatial hearing [2]. A conspicuous feature of MSO electrophysiology is the presence of large, stimulus-evoked extracellular field potentials. These field potentials, known as the auditory neurophonic, have been observed since the earliest recordings from the auditory brain stem over half a century ago [3] and remain a topic of current interest [4]. The precise generators and functional consequences of the neurophonic remain largely unknown. We study these extracellular potentials in order to gain a new vantage point from which to advance both experimental and theoretical analyses of the MSO. We begin with the assumption that postsynaptic current flow in MSO neurons is the dominant generator of the brain stem auditory neurophonic. We use a biophysically-based computational model of MSO neurons to simulate membrane currents [5]. To model extracellular currents, we make two idealizations. First, since MSO inputs are frequency-selective and strongly phase-locked to tonal stimuli, we assume synaptic inputs are synchronous. Second, since MSO neurons have a distinctive bipolar morphology with cell bodies that are approximately aligned in a two-dimensional sheet, we assume there is spatial symmetry in the distribution of synaptic currents. These assumptions of synchrony and symmetry lead to reduced models that we use to analyze the generation of the neurophonic. We first show how monolateral excitatory input, when isolated on a single dendrite, creates an extracellular current sink near the site of excitation and a distributed current source along the remainder of the neuron. Simulated local field potentials share many qualitative features with published reports of the neurophonic. In particular, our model results are largely consistent with a classical description of the neurophonic as a dipole field generated by postsynaptic currents in MSO neurons [3,4]. The dipole theory makes no strong predictions about the dynamics of extracellular potentials, so we investigate how additional features of MSO activity – somatic inhibition, asymmetries between ipsilateral and contralateral inputs, subthreshold voltage-activated currents, bilateral inputs with varying delays – shape the evolution of the neurophonic. We conclude that an idealized model of MSO neurons with symmetric and synchronous inputs provides a useful tool for studying the neurophonic. Ongoing work seeks to relax these simplifying assumptions and to explore how local field potentials in the brain stem may influence the coincidence detection properties of MSO cells.

Ih modulates theta rhythm and synchrony in computer model of CA3

Although the contributions of different hippocampal cell classes to oscillatory activity has been studied, the intrinsic membrane mechanisms contributing to the oscillations and neuronal synchronization are not well understood. The hyperpolarization-activated cation (HCN) channel is a voltage-gated ion channel potentially implicated in epilepsy. Ih, the current produced by HCN channels, plays an important role in regulating neuronal excitability, particularly in hippocampal and neocortical pyramidal neurons. Changes in HCN conductance have been associated with epilepsy, manifesting as discharges with aberrant synchrony [1]. In this study we investigated the role of Ih in pacing network oscillations and synchronizing activity. We studied the effects of modulating both the Ih time-constant and the Ih conductance level in a biophysical computer model of the CA3 region of the hippocampus using the NEURON simulator. Some of the manipulations could be realized in-vitro with pharmacological manipulation via the Ih blocker, ZD7288. Our network consisted of 800 five-compartment pyramidal cells, 200 one-compartment basket cell interneurons, and 200 one-compartment oriens lacunosum-moleculare (O-LM) interneurons. All cells contained leak current, transient sodium current and delayed rectifier current. Additionally, pyramidal cells contained potassium type A current and pyramidal and OLM cells had Ih current. Cell classes were interconnected probabilistically with AMPA/NMDA, and two classes of GABAA synapses. The O-LM cells formed synapses on the distal dendrites of pyramidal cells, while the basket cells synapsed proximally on pyramidal and other basket cells. Pyramidal cells synapsed on both types of interneurons with AMPA/NMDA synapses. All synapses were bombarded with external Poisson inputs to generate network activity. We used Kendall’s tau correlation to measure the synchrony between pairs of pyramidal cells and performed FFT analysis on local field potentials generated by the pyramidal cells to measure rhythmic activity. At baseline, OLM cells fired preferentially at the theta frequency, causing periodic inhibition/disinhibition of pyramidal cells [2]. Although lowering the Ih conductance of pyramidal cell distal dendrites did not change average firing rates of pyramidal cells, the delay to pyramidal cell synchronization increased. Delayed synchronization was associated with a delay in the emergence of pyramidal interneuron network gamma (PING; in PING, pyramidal cells drive basket cells via AMPA/NMDA receptors and basket cells in turn inhibit the pyramidal cells through GABAergic synapses). This mechanism depends on stabilization via pyramidal cell synchronization. Analysis of the simulated local field potential spectral power showed that Ih conductance level correlated with the peak theta rhythm, from ~6.5 - 8.5 Hz. Our model demonstrates that changes in conductance of HCN channels can modulate hippocampal network rhythms and synchrony. These effects could be tested in-vivo and in-vitro, under neuromodulatory or pharmacological control. Our model also predicts that hippocampal networks may become more prone towards epilepsy with alterations in the level of HCN channel expression.

Synaptic activations of neuronal populations in the thalamocortical loop from LFP using kCSD and ICA

Local field potentials (LFP), the low-frequency part of the electric potential recorded extracellularly in the brain, is a well-established measure of neural activity at the population level. However, the origin and the nature of the LFP make it harder to interpret than other electrophysiological signals such as spikes. Two problems intertwine here: first, the extracellular field spreads over significant distances from the generating population; second, the recorded signal is typically a combination of contributions from several sources. The former problem is often addressed by reconstructing the underlying currents using Current Source Density (CSD) analysis. To solve the latter issue we have employed in the past the combination of CSD and Independent Component Analysis (ICA) [1]. Here we test the combination of CSD analysis [2] and ICA on simulated LFP data obtained from a computational model of a single thalamocortical column [3,4]. We test how the components obtained by analyzing the full LFP are related to the ‘building blocks’ of population activity, that is the specific synaptic activations of individual populations of neurons. We show which populations can possibly be recorded with a limited number of electrodes and in the presence of noise, and discuss the limitations of the approach and ways to improve the reconstructions.

A computational role for bistability and traveling waves in motor cortex

Adaptive changes in behavior require rapid changes in brain states yet the brain must also remain stable. We investigated two neural mechanisms for evoking rapid transitions between spatiotemporal synchronization patterns of beta oscillations (13–30 Hz) in motor cortex. Cortex was modeled as a sheet of neural oscillators that were spatially coupled using a center-surround connection topology. Manipulating the inhibitory surround was found to evoke reliable transitions between synchronous oscillation patterns and traveling waves. These transitions modulated the simulated local field potential in agreement with physiological observations in humans. Intermediate levels of surround inhibition were also found to produce bistable coupling topologies that supported both waves and synchrony. State-dependent perturbation between bistable states produced very rapid transitions but were less reliable. We surmise that motor cortex may thus employ state-dependent computation to achieve very rapid changes between bistable motor states when the demand for speed exceeds the demand for accuracy.

Characterizing Deep Brain Stimulation effects in computationally efficient neural network models

BackgroundRecent studies on the medical treatment of Parkinson's disease (PD) led to the introduction of the so called Deep Brain Stimulation (DBS) technique. This particular therapy allows to contrast actively the pathological activity of various Deep Brain structures, responsible for the well known PD symptoms. This technique, frequently joined to dopaminergic drugs administration, replaces the surgical interventions implemented to contrast the activity of specific brain nuclei, called Basal Ganglia (BG). This clinical protocol gave the possibility to analyse and inspect signals measured from the electrodes implanted into the deep brain regions. The analysis of these signals led to the possibility to study the PD as a specific case of dynamical synchronization in biological neural networks, with the advantage to apply the theoretical analysis developed in such scientific field to find efficient treatments to face with this important disease. Experimental results in fact show that the PD neurological diseases are characterized by a pathological signal synchronization in BG. Parkinsonian tremor, for example, is ascribed to be caused by neuron populations of the Thalamic and Striatal structures that undergo an abnormal synchronization. On the contrary, in normal conditions, the activity of the same neuron populations do not appear to be correlated and synchronized.ResultsTo study in details the effect of the stimulation signal on a pathological neural medium, efficient models of these neural structures were built, which are able to show, without any external input, the intrinsic properties of a pathological neural tissue, mimicking the BG synchronized dynamics.We start considering a model already introduced in the literature to investigate the effects of electrical stimulation on pathologically synchronized clusters of neurons. This model used Morris Lecar type neurons. This neuron model, although having a high level of biological plausibility, requires a large computational effort to simulate large scale networks. For this reason we considered a reduced order model, the Izhikevich one, which is computationally much lighter. The comparison between neural lattices built using both neuron models provided comparable results, both without traditional stimulation and in presence of all the stimulation protocols. This was a first result toward the study and simulation of the large scale neural networks involved in pathological dynamics.Using the reduced order model an inspection on the activity of two neural lattices was also carried out at the aim to analyze how the stimulation in one area could affect the dynamics in another area, like the usual medical treatment protocols require.The study of population dynamics that was carried out allowed us to investigate, through simulations, the positive effects of the stimulation signals in terms of desynchronization of the neural dynamics.ConclusionsThe results obtained constitute a significant added value to the analysis of synchronization and desynchronization effects due to neural stimulation. This work gives the opportunity to more efficiently study the effect of stimulation in large scale yet computationally efficient neural networks. Results were compared both with the other mathematical models, using Morris Lecar and Izhikevich neurons, and with simulated Local Field Potentials (LFP).

Closed-Loop Control of Deep Brain Stimulation: A Simulation Study

Deep brain stimulation (DBS) is an effective therapy to treat movement disorders including essential tremor, dystonia, and Parkinson's disease. Despite over a decade of clinical experience the mechanisms of DBS are still unclear, and this lack of understanding makes the selection of stimulation parameters quite challenging. The objective of this work was to develop a closed-loop control system that automatically adjusted the stimulation amplitude to reduce oscillatory neuronal activity, based on feedback of electrical signals recorded from the brain using the same electrode as implanted for stimulation. We simulated a population of 100 intrinsically active model neurons in the Vim thalamus, and the local field potentials (LFPs) generated by the population were used as the feedback (control) variable for closed loop control of DBS amplitude. Based on the correlation between the spectral content of the thalamic activity and tremor (Hua , 1998), (Lenz , 1988), we implemented an adaptive minimum variance controller to regulate the power spectrum of the simulated LFPs and restore the LFP power spectrum present under tremor conditions to a reference profile derived under tremor free conditions. The controller was based on a recursively identified autoregressive model (ARX) of the relationship between stimulation input and LFP output, and showed excellent performances in tracking the reference spectral features through selective changes in the theta (2-7 Hz), alpha (7-13 Hz), and beta (13-35 Hz) frequency ranges. Such changes reflected modifications in the firing patterns of the model neuronal population, and, differently from open-loop DBS, replaced the tremor-related pathological patterns with patterns similar to those simulated in tremor-free conditions. The closed-loop controller generated a LFP spectrum that approximated more closely the spectrum present in the tremor-free condition than did open loop fixed intensity stimulation and adapted to match the spectrum after a change in the neuronal oscillation frequency. This computational study suggests the feasibility of closed-loop control of DBS amplitude to regulate the spectrum of the local field potentials and thereby normalize the aberrant pattern of neuronal activity present in tremor.

Testing methodologies for the nonlinear analysis of causal relationships in neurovascular coupling

We investigated the use and implementation of a nonlinear methodology for establishing which changes in neurophysiological signals cause changes in the blood oxygenation level-dependent (BOLD) contrast measured in functional magnetic resonance imaging. Unlike previous analytical approaches, which used linear correlation to establish covariations between neural activity and BOLD, we propose a directed information-theoretic measure, the transfer entropy, which can elucidate even highly nonlinear causal relationships between neural activity and BOLD signal. In this study we investigated the practicality of such an analysis given the limited data samples that can be collected experimentally due to the low temporal resolution of BOLD signals. We implemented several algorithms for the estimation of transfer entropy and we tested their effectiveness using simulated local field potentials (LFPs) and BOLD data constructed to match the main statistical properties of real LFP and BOLD signals measured simultaneously in monkey primary visual cortex. We found that using the advanced methods of entropy estimation implemented and described here, a transfer entropy analysis of neurovascular coupling based on experimentally attainable data sets is feasible.

Analysis of Intracerebral EEG Recordings of Epileptic Spikes: Insights From a Neural Network Model

The pathophysiological interpretation of EEG signals recorded with depth electrodes [i.e., local field potentials (LFPs)] during interictal (between seizures) or ictal (during seizures) periods is fundamental in the presurgical evaluation of patients with drug-resistant epilepsy. Our objective was to explain specific shape features of interictal spikes in the hippocampus (observed in LFPs) in terms of cell- and network-related parameters of neuronal circuits that generate these events. We developed a neural network model based on "minimal" but biologically relevant neuron models interconnected through GABAergic and glutamatergic synapses that reproduce the main physiological features of the CA1 subfield. Simulated LFPs were obtained by solving the forward problem (dipole theory) from networks including a large number ( approximately 3000) of cells. Insertion of appropriate parameters allowed the model to simulate events that closely resemble actual epileptic spikes. Moreover, the shape of the early fast component ("spike'') and the late slow component ("negative wave'') was linked to the relative contribution of glutamatergic and GABAergic synaptic currents in pyramidal cells. In addition, the model provides insights about the sensitivity of electrode localization with respect to recorded tissue volume and about the relationship between the LFP and the intracellular activity of principal cells and interneurons represented in the network.

Sleep Homeostasis and Cortical Synchronization: II. A Local Field Potential Study of Sleep Slow Waves in the Rat

Sleep slow-wave activity (SWA, EEG power between 0.5 and 4.0 Hz) decreases homeostatically in the course of non-rapid eye movement sleep (NREM) sleep. According to a recent hypothesis, the homeostatic decrease of sleep SWA is due to a progressive decrease in the strength of corticocortical connections. This hypothesis was evaluated in a large-scale thalamocortical model, which showed that a decrease in synaptic strength, implemented through a reduction of postsynaptic currents, resulted in lower sleep SWA in simulated local field potentials (LFP). The decrease in SWA was associated with a decreased proportion of high-amplitude slow waves, a decreased slope of the slow waves, and an increase in the number of multipeak waves. Here we tested the model predictions by obtaining LFP recordings from the rat cerebral cortex and comparing conditions of high homeostatic sleep pressure (early sleep) and low homeostatic sleep pressure (late sleep). Intracortical LFP recordings during baseline sleep and after 6 hours of sleep deprivation. Basic sleep research laboratory. WKY adult male rats. N/A. Early sleep (sleep at the beginning of the major sleep phase, sleep immediately after sleep deprivation) was associated with (1) high SWA, (2) many large slow waves, (3) steep slope of slow waves, and (4) rare occurrence of multipeak waves. By contrast, late sleep (sleep at the end of the major sleep phase, sleep several hours after the end of sleep deprivation) was associated with (1) low SWA, (2) few high-amplitude slow waves, (3) reduced slope of slow waves, and (4) more frequent multipeak waves. In rats, changes in sleep SWA are associated with changes in the amplitude and slope of slow waves, and in the number of multi-peak waves. Such changes in slow-wave parameters are compatible with the hypothesis that average synaptic strength decreases in the course of sleep.