Frequency-domain analysis of membrane polarization in two-compartment model neurons with weak alternating electric fields.

Transcranial alternating current stimulation (tACS) is widely used in studying brain functions and the treatment of neuropsychiatric diseases in a frequency-specific manner. However, how tACS works on neuronal activity has been poorly understood. In this paper, we use linear system analysis to investigate how weak alternating electric fields (EFs) affect the membrane polarization of neurons in the frequency domain. Two biophysically realistic conductance-based two-compartment models of cortical pyramidal neurons are developed to simulate subthreshold membrane polarization with weak alternating EFs. We linearize the original nonlinear models at the stable equilibrium points and further simplify them to the two- or three-dimensional linear systems. Thus, we calculate the transfer functions of the low-dimensional linear models to model neuronal polarization patterns. Based on the transfer functions, we compute the amplitude- and phase-frequency characteristics to describe the relationship between weak EFs and membrane polarization. We also computed the parameters (gain, zeros, and poles) and structures (the number of zeros and poles) of transfer functions to reveal how neuronal intrinsic properties affect the parameters and structure of transfer functions and thus the frequency-dependent membrane polarization with alternating EFs. We find that the amplitude and phase of membrane polarization both strongly depended on EF frequency, and these frequency responses are modulated by the intrinsic properties of neurons. The compartment geometry, internal coupling conductance, and ionic currents (except Ih) affect the frequency-dependent polarization by mainly changing the gain and pole of transfer functions. Larger gain contributes to larger amplitude-frequency characteristics. The closer the pole is to the imaginary axis, the lower phase-frequency characteristics. However, Ih changes the structure of transfer function in the dendrite by introducing a new pair of zero-pole points, which decrease the amplitude at low frequencies and thus lead to a visible resonance. These results highlight the effects of passive properties and active ion currents on subthreshold membrane polarization with alternating EFs in the frequency domain, which provide an explainable connection of how intrinsic properties of neurons modulate the neuronal input-output functions with weak EF stimulation.

Assessment of impaired consciousness using EEG-based connectivity features and convolutional neural networks.

Growing electroencephalogram (EEG) studies have linked the abnormities of functional brain networks with disorders of consciousness (DOC). However, due to network data's high-dimensional and non-Euclidean properties, it is difficult to exploit the brain connectivity information that can effectively detect the consciousness levels of DOC patients via deep learning. To take maximum advantage of network information in assessing impaired consciousness, we utilized the functional connectivity with convolutional neural network (CNN) and employed three rearrangement schemes to improve the evaluation performance of brain networks. In addition, the gradient-weighted class activation mapping (Grad-CAM) was adopted to visualize the classification contributions of connections among different areas. We demonstrated that the classification performance was significantly enhanced by applying network rearrangement techniques compared to those obtained by the original connectivity matrix (with an accuracy of 75.0%). The highest classification accuracy (87.2%) was achieved by rearranging the alpha network based on the anatomical regions. The inter-region connections (i.e., frontal-parietal and frontal-occipital connectivity) played dominant roles in the classification of patients with different consciousness states. The effectiveness of functional connectivity in revealing individual differences in brain activity was further validated by the correlation between behavioral performance and connections among specific regions. These findings suggest that our proposed assessment model could detect the residual consciousness of patients.

Individual Prediction of Electric Field Induced by Deep-Brain Magnetic Stimulation With CNN-Transformer.

Deep-brain Magnetic Stimulation (DMS) can improve the symptoms caused by Alzheimer's disease by inducing rhythmic electric field in the deep brain, and the induced electric field is rhythm-dependent. However, calculating the induced electric field requires building a voxel model of the brain for the stimulated object, which usually takes several hours. In order to obtain the rhythm-dependent electric field induced by DMS in real time, we adopt a CNN-Transformer model to predict it. A data set with a sample size of 7350 is established for the training and testing of the model. 10-fold cross validation is used to determine the optimal hyperparameters for training CNN-Transformer. The combination of 5-layer CNN and 6-layer Transformer is verified as the optimal combination of CNN-Transformer model. The experimental results show that the CNN-Transformer model can complete the prediction in 0.731s (CPU) or 0.042s (GPU), and the overall performance metrics of prediction can reach: MAE =0.0269, RMSE =0.0420, MAPE =4.61% and R2=0.9627. The prediction performance of the CNN-Transformer model for the hippocampal electric field is better than that of the brain grey matter electric field, and the stimulation rhythm has less influence on the model performance than the coil configuration. Taking the same dataset to train and test the separate CNN model and Transformer model, it is found that CNN-Transformer has better prediction performance than the separate CNN model and Transformer model in the task of predicting electric field induced by DMS.

Electric field effects on neuronal input-output relationship by regulating NMDA spikes.

Evidence shows that the dendritic polarization induced by weak electrical field (EF) can affect the neuronal input-output function via modulating dendritic integration of AMPA synapses, indicating that the supralinear dendritic integration of NMDA synapses can also be influenced by dendritic polarization. However, it remains unknown how dendritic polarization affects NMDA-type dendritic integration, and then contributes to neuronal input-output relationship. Here, we used a computational model of pyramidal neuron with inhomogeneous extracellular potentials to characterize the relationship among EF, dendritic integration, and somatic output. Basing on singular perturbation we analyzed the subthreshold dynamics of membrane potentials in response to NMDA synapses, and found that the equilibrium mapping of a fast subsystem can characterize the asymptotic subthreshold input-output (sI/O) relationship for EF-regulated supralinear dendritic integration, allowing us to predict the tendency of EF-regulated dendritic integration by showing the variation of equilibrium mapping under EF stimulation. EF-induced depolarization at distal dendrites receiving synapses plays a crucial role in shifting the steep change of sI/O left by facilitating dendritic NMDA spike generation and in decreasing the plateau of sI/O via reducing driving force. And more effective EF modulation appears at sparsely activated NMDA receptors compared with clustered synaptic inputs. During the action potential (AP) generation, the respective contribution of EF-regulated dendritic integration and EF-induced somatic polarization was identified to show their synergetic or antagonistic effect on AP generation, depending on neuronal excitability. These results provided insight in understanding the modulation effect of EF on neuronal computation, which is important for optimizing noninvasive brain stimulation. Supplementary Information: The online version contains supplementary material available at 10.1007/s11571-022-09922-y.

Frequency-dependent membrane polarization across neocortical cell types and subcellular elements by transcranial alternating current stimulation.

Objective.Transcranial alternating current stimulation (tACS) is a non-invasive brain stimulation technique that directly interacts with ongoing brain oscillations in a frequency-dependent manner. However, it remains largely unclear how the cellular effects of tACS vary between cell types and subcellular elements.Approach.In this study, we use a set of morphologically realistic models of neocortical neurons to simulate the cellular response to uniform oscillating electric fields (EFs). We systematically characterize the membrane polarization in the soma, axons, and dendrites with varying field directions, intensities, and frequencies.Main results.Pyramidal cells are more sensitive to axial EF that is roughly parallel to the cortical column, while interneurons are sensitive to axial EF and transverse EF that is tangent to the cortical surface. Membrane polarization in each subcellular element increases linearly with EF intensity, and its slope, i.e. polarization length, highly depends on the stimulation frequency. At each frequency, pyramidal cells are more polarized than interneurons. Axons usually experience the highest polarization, followed by the dendrites and soma. Moreover, a visible frequency resonance presents in the apical dendrites of pyramidal cells, while the other subcellular elements primarily exhibit low-pass filtering properties. In contrast, each subcellular element of interneurons exhibits complex frequency-dependent polarization. Polarization phase in each subcellular element of cortical neurons lags that of field and exhibits high-pass filtering properties. These results demonstrate that the membrane polarization is not only frequency-dependent, but also cell type- and subcellular element-specific. Through relating effective length and ion mechanism with polarization, we emphasize the crucial role of cell morphology and biophysics in determining the frequency-dependent membrane polarization.Significance.Our findings highlight the diverse polarization patterns across cell types as well as subcellular elements, which provide some insights into the tACS cellular effects and should be considered when understanding the neural spiking activity by tACS.

Large-Scale Bio-Inspired FPGA Models for Path Planning.

The hippocampus provides significant inspiration for spatial navigation and memory in both humans and animals. Constructing large-scale spiking neural network (SNN) models based on the biological neural systems is an important approach to comprehend the computational principles and cognitive function of the hippocampus. Such models are usually implemented on neuromorphic computing platforms, which often have limited computing resources that constrain the achievable scale of the network. This work introduces a series of digital design methods to realize a Field-Programmable Gate Array (FPGA) friendly SNN model. The methods include FPGA-friendly nonlinear calculation modules and a fixed-point design algorithm. A brain-inspired large-scale SNN of ∼21 k place cells for path planning is mapped on FPGA. The results show that the path planning tasks in different environments are finished in real-time and the firing activities of place cells are successfully reproduced. With these methods, the achievable network size on one FPGA chip is increased by 1595 times with higher resource usage efficiency and faster computation speed compared to the state-of-the-art.

State-dependent modulation of low-threshold-current-regulated dendritic Ca2+ response in thalamic reticular neurons with extracellular electric fields.

Deep brain stimulation (DBS) in thalamic reticular nucleus (TRN) neuron provides a novel treatment for drug-resistant epilepsy via the induced electrical field (EFs). However, the mechanisms underlying EF effects remain unclear. This paper investigated how EFs regulate low-threshold dendritic Ca2+ (dCa) response and thus contribute to the input-output relationship of TRN cell. Our results showed that EFs modulate firing modes differently in a neuronal state-dependent manner. At the depolarized state, EFs only regulate the spike timing of a somatic stimulus-evoked single action potential (AP) with less contribution in the regulation of dCa response but could induce the transition between a dendritic stimulus-evoked single AP and a tonic burst of APs via the moderate regulation of dCa response. At the hyperpolarized state, EFs have significant effects on the dCa response, which modulate the large dCa response-dependent burst discharge and even cause a transition from this type of burst discharge to a single AP with less dCa response. Moreover, EF effects on stimulation threshold of somatic spiking prominently depend on EF-regulated dCa responses and the onset time differences between the stimulus and EF give rise to the distinct effect in the EF regulation of dCa responses. Finally, the larger neuronal axial resistance tends to result in the dendritic stimulus-evoked dCa response independent of somatic state. Interestingly, in this case, the EF application could reproduce the similar somatic state-dependent dCa response to dendritic stimulus which occurs in the case of lower axial resistance. These results suggest that the influence of EF on neuronal activities depends on neuronal intrinsic properties, which provides insight into understanding how DBS in TRN neuron modulates epilepsy from the point of view of biophysics.

Aberrant temporal correlations of ongoing oscillations in disorders of consciousness on multiple time scales.

Changes in neural oscillation amplitude across states of consciousness has been widely reported, but little is known about the link between temporal dynamics of these oscillations on different time scales and consciousness levels. To address this question, we analyzed amplitude fluctuation of the oscillations extracted from spontaneous resting-state EEG recorded from the patients with disorders of consciousness (DOC) and healthy controls. Detrended fluctuation analysis (DFA) and measures of life-time and waiting-time were employed to characterize the temporal structure of EEG oscillations on long time scales (1-20 s) and short time scales (< 1 s), in groups with different consciousness states: patients in minimally conscious state (MCS), patients with unresponsive wakefulness syndrome (UWS) and healthy subjects. Results revealed increased DFA exponents that implies higher long-range temporal correlations (LRTC), especially in the central brain area in alpha and beta bands. On short time scales, declined bursts of oscillations were also observed. All the metrics exhibited lower individual variability in the UWS or MCS group, which may be attributed to the reduced spatial variability of oscillation dynamics. In addition, the temporal dynamics of EEG oscillations showed significant correlations with the behavioral responsiveness of patients. In summary, our findings shows that loss of consciousness is accompanied by alternation of temporal structure in neural oscillations on multiple time scales, and thus may help uncover the mechanism of underlying neuronal correlates of consciousness. Supplementary Information: The online version contains supplementary material available at 10.1007/s11571-022-09852-9.

Evolution of brain network dynamics in early Parkinson's disease with mild cognitive impairment.

How mild cognitive impairment (MCI) is instantiated in dynamically interacting and spatially distributed functional brain networks remains an unexplored mystery in early Parkinson's disease (PD). We applied a machine-learning technology based on personalized sliding-window algorithm to track continuously time-varying and overlapping subnetworks under the functional brain networks calculated form resting state electroencephalogram data within a sample of 33 early PD patients (13 early PD patients with MCI and 20 early PD patients without MCI). We decoded a set of subnetworks that captured surprisingly dynamically varying and integrated interactions among certain brain lobes. We observed that the master expressed subnetworks were particularly transient, and flexibly switching between high and low expression during integration into a dynamic brain network. This transience was particularly salient in a subnetwork predominantly linking temporal-parietal-occipital lobes, which decreases in both expression and flexibility in early PD patients with MCI and expresses their degree of cognitive impairment. Moreover, MCI induced a regularly interrupted, slow evolution of subnetworks in functional brain network dynamics in early PD at the individual level, and the dynamic expression characteristics of subnetworks also reflected the degree of cognitive impairment in patients with early PD. Collectively, these results provide novel and deeper insights regarding MCI-induced abnormal dynamical interaction and large-scale changes in functional brain network of early PD.

Capturing the Abnormal Brain Network Activity in Early Parkinsons Disease with Mild Cognitive Impairment based on Dynamic Functional Connectivity.

The early Parkinson's disease (PD) with mild cognitive impairment (ePD-MCI) is a typical non-motor symptom reflected by the brain dysfunction of PD, which can be well depicted by the dynamic characteristics of brain functional connectivity networks. The aim of this study is to determine the unclear dynamic changes in functional connectivity networks induced by MCI in early PD patients. In this paper, the electroencephalogram (EEG) of each subject was reconstructed into the dynamic functional connectivity networks with five frequency bands based on adaptive sliding window method. By evaluating the fluctuations of dynamic functional connectivity and the transition stability of functional network state in ePD-MCI patients compared with early PD without mild cognitive impairment patients, it was found that in the alpha band, the functional network stability of central region, right frontal, parietal, occipital, and left temporal lobes was abnormally increased, and the dynamic connectivity fluctuations in these regions were significantly decreased in ePD-MCI group. In the gamma band, ePD-MCI patients showed decreased functional network stability in the central, left frontal, and right temporal lobes, and active dynamic connectivity fluctuations in the left frontal, temporal, and parietal lobes. The aberrant duration of network state in ePD-MCI patients was significantly negatively correlated with cognitive function in the alpha band, which might pave the way to identify and predict cognitive impairment in early PD patients.

Presynaptic spike-driven plasticity based on eligibility trace for on-chip learning system.

Introduction: Recurrent spiking neural network (RSNN) performs excellently in spatio-temporal learning with backpropagation through time (BPTT) algorithm. But the requirement of computation and memory in BPTT makes it hard to realize an on-chip learning system based on RSNN. In this paper, we aim to realize a high-efficient RSNN learning system on field programmable gate array (FPGA). Methods: A presynaptic spike-driven plasticity architecture based on eligibility trace is implemented to reduce the resource consumption. The RSNN with leaky integrate-and-fire (LIF) and adaptive LIF (ALIF) models is implemented on FPGA based on presynaptic spike-driven architecture. In this architecture, the eligibility trace gated by a learning signal is used to optimize synaptic weights without unfolding the network through time. When a presynaptic spike occurs, the eligibility trace is calculated based on its latest timestamp and drives synapses to update their weights. Only the latest timestamps of presynaptic spikes are required to be stored in buffers to calculate eligibility traces. Results: We show the implementation of this architecture on FPGA and test it with two experiments. With the presynaptic spike-driven architecture, the resource consumptions, including look-up tables (LUTs) and registers, and dynamic power consumption of synaptic modules in the on-chip learning system are greatly reduced. The experiment results and compilation results show that the buffer size of the on-chip learning system is reduced and the RSNNs implemented on FPGA exhibit high efficiency in resources and energy while accurately solving tasks. Discussion: This study provides a solution to the problem of data congestion in the buffer of large-scale learning systems.

Highly efficient neuromorphic learning system of spiking neural network with multi-compartment leaky integrate-and-fire neurons.

A spiking neural network (SNN) is considered a high-performance learning system that matches the digital circuits and presents higher efficiency due to the architecture and computation of spiking neurons. While implementing a SNN on a field-programmable gate array (FPGA), the gradient back-propagation through layers consumes a surprising number of resources. In this paper, we aim to realize an efficient architecture of SNN on the FPGA to reduce resource and power consumption. The multi-compartment leaky integrate-and-fire (MLIF) model is used to convert spike trains to the plateau potential in dendrites. We accumulate the potential in the apical dendrite during the training period. The average of this accumulative result is the dendritic plateau potential and is used to guide the updates of synaptic weights. Based on this architecture, the SNN is implemented on FPGA efficiently. In the implementation of a neuromorphic learning system, the shift multiplier (shift MUL) module and piecewise linear (PWL) algorithm are used to replace multipliers and complex nonlinear functions to match the digital circuits. The neuromorphic learning system is constructed with resources on FPGA without dataflow between on-chip and off-chip memories. Our neuromorphic learning system performs with higher resource utilization and power efficiency than previous on-chip learning systems.

An EEG-based systematic explainable detection framework for probing and localizing abnormal patterns in Alzheimer's disease.

Objective.Electroencephalography (EEG) is a potential source of downstream biomarkers for the early diagnosis of Alzheimer's disease (AD) due to its low-cost, noninvasive, and portable advantages. Accurately detecting AD-induced patterns from EEG signals is essential for understanding AD-related neurodegeneration at the EEG level and further evaluating the risk of AD at an early stage. This paper proposes a deep learning-based, functional explanatory framework that probes AD abnormalities from short-sequence EEG data.Approach.The framework is a learning-based automatic detection system consisting of three encoding pathways that analyze EEG signals in frequency, complexity, and synchronous domains. We integrated the proposed EEG descriptors with the neural network components into one learning system to detect AD patterns. A transfer learning-based model was used to learn the deep representations, and a modified generative adversarial module was attached to the model to overcome feature sparsity. Furthermore, we utilized activation mapping to obtain the AD-related neurodegeneration at brain rhythm, dynamic complexity, and functional connectivity levels.Main results.The proposed framework can accurately (100%) detect AD patterns based on our raw EEG recordings without delicate preprocessing. Meanwhile, the system indicates that (a) the power of different brain rhythms exhibits abnormal in the frontal lobes of AD patients, and such abnormality spreads to central lobes in the alpha and beta rhythms, (b) the difference in nonlinear complexity varies with the temporal scales, and (c) all the connections of pair-wise brain regions except bilateral temporal connectivity are weak in AD patterns. The proposed method outperforms other related methods in detection performance.Significance.We provide a new method for revealing abnormalities and corresponding localizations in different feature domains of EEG from AD patients. This study is a significant foundation for our future work on identifying individuals at high risk of AD at an early stage.

Analysis of complexity and dynamic functional connectivity based on resting-state EEG in early Parkinson's disease patients with mild cognitive impairment.

To explore the abnormal brain activity of early Parkinson's disease with mild cognitive impairment (ePD-MCI) patients, the study analyzed the dynamic fluctuation of electroencephalogram (EEG) signals and the dynamic change of information communication between EEG signals of ePD-MCI patients. In this study, we recorded resting-state EEG signals of 30 ePD-MCI patients and 37 early Parkinson's disease without mild cognitive impairment (ePD-nMCI) patients. First, we analyzed the difference of the complexity of EEG signals between the two groups. And we found that the complexity in the ePD-MCI group was significantly higher than that in the ePD-nMCI group. Then, by analyzing the dynamic functional network (DFN) topology based on the optimal sliding-window, we found that the temporal correlation coefficients of ePD-MCI patients were lower in the delta and theta bands than those in the ePD-nMCI patients. The temporal characteristic path length of ePD-MCI patients in the alpha band was higher than that of ePD-nMCI patients. In the theta and alpha bands, the temporal small world degrees of ePD-MCI patients were lower than that of patients with ePD-nMCI. In addition, the functional connectivity strength of ePD-MCI patients affected by cognitive impairment was weaker than that of ePD-nMCI patients, and the stability of dynamic functional connectivity network was decreased. This finding may serve as a biomarker to identify ePD-MCI and contribute to the early intervention treatment of ePD-MCI.

Epileptic Seizure Detection Using Brain-Rhythmic Recurrence Biomarkers and ONASNet-Based Transfer Learning.

OBJECTIVE: The electroencephalogram (EEG) tool has great potential for real-time monitoring of abnormal brain activities, such as preictal and ictal seizures. Developing an EEG-based detection system for patients with epilepsy is vital for clinical management and targeted therapy. METHODS: This paper proposes a single-channel seizure detection system using brain-rhythmic recurrence biomarkers (BRRM) and an optimized model (ONASNet). BRRM is a direct mapping of the recurrence morphology of brain rhythms in phase space; it reflects the nonlinear dynamics of original EEG signals. The architecture of ONASNet is determined through a modified neural network searching strategy. Then, we exploited transfer learning to apply ONASNet to our EEG data. The combination of BRRM and ONASNet leverages the multiple channels of a neural network to extract features from different brain rhythms simultaneously. RESULTS: We evaluated the efficiency of BRRM-ONASNet on the real EEG recordings derived from Bonn University. In the experiments, different transfer-learning models (TLMs) are respectively constructed using ONASNet and seven well-known neural network structures (VGG16/VGG19/ResNet50/InceptionV3/DenseNet121/Xception/NASNet). Moreover, we compared those TLMs by model size, computing complexity, learning capability, and prediction latency. ONASNet outperforms other structures by strong learning capability, high stability, small model size, short latency, and less requirement of computing resources. Comparing BRRM-ONASNet with other existing methods, our work performs better than others with 100% accuracy under the identical dataset and same detection task. Contributions: The proposed method in this study, analyzing nonlinear features from phase-space representations using a deep neural network, provides new insights for EEG decoding. The successful application of this method in epileptic-seizure detection contributes to computationally medical assistance for epilepsy.

The passive properties of dendrites modulate the propagation of slowly-varying firing rate in feedforward networks.

The propagation of slowly-varying firing rates has been proved significant for the development of the central nervous system. Recent reports have shown that the membrane passive properties of dendrites play a key role in the computation of the single neuron, which is of great importance to the function of neural networks. However, it is still unclear how dendritic passive properties affect the ability of cortical networks to propagate slowly-varying spiking activity. Here, we use two-compartment biophysical models to construct multilayered feedforward neural networks (FFNs) to investigate how dendritic passive properties affect the propagation of the slow-varying inputs. In the two-compartment biophysical models, one compartment represents apical dendrites, and the other compartment describes the soma plus the axon initial segment. Area proportion occupied by somatic compartment and coupling conductance between dendritic and somatic compartments are abstracted to capture the dendritic passive properties. A time-varying signal is injected into the first layer of the FFNs and the fidelity of the signal during propagation is used to qualify the ability of the FFN to transmit wave-like signals. Numerical results reveal an optimal value of coupling conductance between dendritic and somatic compartments to maximize the fidelity of the initial spiking activity. An increase of the dendritic area enhances the initial firing rate of neurons in the first layer by increasing the response of neurons to slow-varying wave-like input, resulting in a delay of attenuation of the firing rate, thus promoting the transmission of signals in FFN. Using a mean-field approach, we examine that changes in area proportion occupied by somatic compartment and coupling conductance between dendritic and somatic compartment affect the signal propagation ability of the FFN by adjusting the input-output transform of a single neuron. With the participation of external noise, a wide range of initial firing rates maintains a unique representation during propagation, which ensures the reliable transmission of slow-varying signals in FFNs. These findings are helpful to understand how passive properties of dendrites participate in the propagation of slowly varying signals in the cerebellum.

Disrupted Control Architecture of Brain Network in Disorder of Consciousness.

The human brain controls various cognitive functions via the functional coordination of multiple brain regions in an efficient and robust way. However, the relationship between consciousness state and the control mode of brain networks is poorly explored. Using multi-channel EEG, the present study aimed to characterize the abnormal control architecture of functional brain networks in the patients with disorders of consciousness (DOC). Resting state EEG data were collected from 40 DOC patients with different consciousness levels and 24 healthy subjects. Functional brain networks were constructed in five different EEG frequency bands and the broadband in the source level. Subsequently, a control architecture framework based on the minimum dominating set was applied to investigate the of control mode of functional brain networks for the subjects with different conscious states. Results showed that regardless of the consciousness levels, the functional networks of human brain operate in a distributed and overlapping control architecture different from that of random networks. Compared to the healthy controls, the patients have a higher control cost manifested by more minimum dominating nodes and increased degree of distributed control, especially in the alpha band. The ability to withstand network attack for the control architecture is positive correlated with the consciousness levels. The distributed of control increased correlation levels with Coma Recovery Scale-Revised score and improved separation between unresponsive wakefulness syndrome and minimal consciousness state. These findings may benefit our understanding of consciousness and provide potential biomarkers for the assessment of consciousness levels.

Asymptotic Input-Output Relationship Predicts Electric Field Effect on Sublinear Dendritic Integration of AMPA Synapses.

An extracellular electric field (EF) induces transmembrane polarizations on extremely inhomogeneous spaces. Evidence shows that EF-induced somatic polarization in pyramidal cells can modulate the neuronal input-output (I/O) function. However, it remains unclear whether and how dendritic polarization participates in the dendritic integration and contributes to the neuronal I/O function. To this end, we built a computational model of a simplified pyramidal cell with multi-dendritic tufts, one dendritic trunk, and one soma to describe the interactions among EF, dendritic integration, and somatic output, in which the EFs were modeled by inserting inhomogeneous extracellular potentials. We aimed to establish the underlying relationship between dendritic polarization and dendritic integration by analyzing the dynamics of subthreshold membrane potentials in response to AMPA synapses in the presence of constant EFs. The model-based singular perturbation analysis showed that the equilibrium mapping of a fast subsystem can serve as the asymptotic subthreshold I/O relationship for sublinear dendritic integration. This allows us to predict the tendency of EF-mediated dendritic integration by showing how EF changes modify equilibrium mapping. EF-induced hyperpolarization of distal dendrites receiving synapses inputs was found to play a key role in facilitating the AMPA receptor-evoked excitatory postsynaptic potential (EPSP) by enhancing the driving force of synaptic inputs. A significantly higher efficacy of EF modulation effect on global AMPA-type dendritic integration was found compared with local AMPA-type dendritic integration. During the generation of an action potential (AP), the relative contribution of EF-modulated dendritic integration and EF-induced somatic polarization was determined to show their collaboration in promoting or inhibiting the somatic excitability, depending on the EF polarity. These findings are crucial for understanding the EF modulation effect on neuronal computation, which provides insight into the modulation mechanism of noninvasive brain modulation.

A Data Driven Experimental System for Individualized Brain Stimulation Design and Validation.

Deep brain stimulation (DBS) is an effective clinical treatment for epilepsy. However, the individualized setting and adaptive adjustment of DBS parameters are still facing great challenges. This paper investigates a data-driven hardware-in-the-loop (HIL) experimental system for closed-loop brain stimulation system individualized design and validation. The unscented Kalman filter (UKF) is utilized to estimate critical parameters of neural mass model (NMM) from the electroencephalogram recordings to reconstruct individual neural activity. Based on the reconstructed NMM, we build a digital signal processor (DSP) based virtual brain platform with real time scale and biological signal level scale. Then, the corresponding hardware parts of signal amplification detection and closed-loop controller are designed to form the HIL experimental system. Based on the designed experimental system, the proportional-integral controller for different individual NMM is designed and validated, which proves the effectiveness of the experimental system. This experimental system provides a platform to explore neural activity under brain stimulation and the effects of various closed-loop stimulation paradigms.

An Embedded Multi-Core Real-Time Simulation Platform of Basal Ganglia for Deep Brain Stimulation.

Closed-loop deep brain stimulation (DBS) paradigm is gaining tremendous favor due to its potential capability of further and more efficient improvements in neurological diseases. Preclinical validation of closed-loop controller is quite necessary in order to minimize injury risks of clinical trials to patients, which can greatly benefit from real-time computational models and thus potentially reduce research and development costs and time. Here we developed an embedded multi-core real-time simulation platform (EMC-RTP) for a biological-faithful computational network model of basal ganglia (BG). The single neuron model is implemented in a highly real-time manner using a reasonable simplification. A modular mapping architecture with hierarchical routing organization was constructed to mimic the pathological neural activities of BG observed in parkinsonian conditions. A closed-loop simulation testbed for DBS validation was then set up using a host computer as the DBS controller. The availability of EMC-RTP and the testbed system was validated by comparing the performance of open-loop and proportional-integral (PI) controllers. Our experimental results showed that the proposed EMC-RTP reproduces abnormal beta bursts of BG in parkinsonian conditions while meets requirements of both real-time and computational accuracy as well. Closed-loop DBS experiments using the EMC-RTP suggested that the platform could perform reasonable output under different kinds of DBS strategies, indicating the usability of the platform.