State and parameter estimation of a neural mass model from electrophysiological signals during the status epilepticus

Design of Closed-Loop Control Schemes Based on the GA-PID and GA-RBF-PID Algorithms for Brain Dynamic Modulation

Neurostimulation can be used to modulate brain dynamics of patients with neuropsychiatric disorders to make abnormal neural oscillations restore to normal. The control schemes proposed on the bases of neural computational models can predict the mechanism of neural oscillations induced by neurostimulation, and then make clinical decisions that are suitable for the patient's condition to ensure better treatment outcomes. The present work proposes two closed-loop control schemes based on the improved incremental proportional integral derivative (PID) algorithms to modulate brain dynamics simulated by Wendling-type coupled neural mass models. The introduction of the genetic algorithm (GA) in traditional incremental PID algorithm aims to overcome the disadvantage that the selection of control parameters depends on the designer's experience, so as to ensure control accuracy. The introduction of the radial basis function (RBF) neural network aims to improve the dynamic performance and stability of the control scheme by adaptively adjusting control parameters. The simulation results show the high accuracy of the closed-loop control schemes based on GA-PID and GA-RBF-PID algorithms for modulation of brain dynamics, and also confirm the superiority of the scheme based on the GA-RBF-PID algorithm in terms of the dynamic performance and stability. This research of making hypotheses and predictions according to model data is expected to improve and perfect the equipment of early intervention and rehabilitation treatment for neuropsychiatric disorders in the biomedical engineering field.

Analysis of the neural mechanism of spectra decrease in MCI by a thalamo-cortical coupled neural mass model

Objective.In order to deeply understand the neurophysiological mechanism of the spectra decrease in mild cognitive impairment (MCI), this paper studies a new neural mass model, which can simulate various intracerebral electrophysiological activities.Approach. In this study, a thalamo-cortical coupled neural mass model (TCC-NMM) is proposed. The influences of the coupling coefficients and other key parameters on the model spectra are simulated. Then, the unscented Kalman filter (UKF) algorithm is used to reversely identify the parameters in the TCC-NMM. Furthermore, the TCC-NMM and UKF are combined to analyze the spectra reduction mechanism of electroencephalogram (EEG) signals in MCI patients. The independent sample t-test is carried out to statistical analyze the differences of the identified parameters between MCI and normal controls. The Pearson correlation analysis is used to analyze the intrinsic relationship between parameters and the scores of the comprehensive competence assessment scale.Main results.The simulation results show that the decreased cortical synaptic connectivity constantsC₁can result in spectra decrease of the TCC-NMM outputs. The real EEG analysis results show that the identified values of parameterC₁are significant lower in the MCI group than in control group in frontal and occipital areas and the parametersC₁are positively correlated with the Montreal Cognitive Assessment (MoCA) scores in the two areas. This consistency suggests that the cortical synaptic connectivity loss from pyramidal cells to excitatory interneurons (eIN) may be one of the neural mechanisms of EEG spectra decrease in MCI.Significance. (a) In this study, a new mathematical model TCCNMM based on anatomy and neurophysiology is proposed. (b) All key parameters in TCC-NMM are studied in detail through the forward and reverse analysis and the influence of these parameters on the output spectra of the model is pointed out. (c) The possible neural mechanism of the decreased spectra in MCI patients is pointed out by the joint analysis of simulation in forward with TCC-NMM and analysis of the actual EEG signals in reverse with UKF identification algorithm. (d) We find that the identified parameter C1 of MCI patients is significantly lower than that of the control group, which is consistent with the simulation analysis of TCC-NMM. So, we suggest that the decreased MCI alpha power spectrum is likely related to the cortical synaptic connection loss from pyramidal cells to eIN.

Development of Mechanistic Neural Mass (mNM) Models that Link Physiology to Mean-Field Dynamics

Brain rhythms emerge from the mean-field activity of networks of neurons. There have been many efforts to build mathematical and computational embodiments in the form of discrete cell-group activities-termed neural masses-to understand in particular the origins of evoked potentials, intrinsic patterns of activities such as theta, regulation of sleep, Parkinson's disease related dynamics, and mimic seizure dynamics. As originally utilized, standard neural masses convert input through a sigmoidal function to a firing rate, and firing rate through a synaptic alpha function to other masses. Here we define a process to build mechanistic neural masses (mNMs) as mean-field models of microscopic membrane-type (Hodgkin Huxley type) models of different neuron types that duplicate the stability, firing rate, and associated bifurcations as function of relevant slow variables - such as extracellular potassium - and synaptic current; and whose output is both firing rate and impact on the slow variables - such as transmembrane potassium flux. Small networks composed of just excitatory and inhibitory mNMs demonstrate expected dynamical states including firing, runaway excitation and depolarization block, and these transitions change in biologically observed ways with changes in extracellular potassium and excitatory-inhibitory balance.

Using Constrained Square-Root Cubature Kalman Filter for Quantifying the Severity of Epileptic Activities in Mice

(1) Background: Quantification of severity of epileptic activities, especially during electrical stimulation, is an unmet need for seizure control and evaluation of therapeutic efficacy. In this study, a parameter ratio derived from constrained square-root cubature Kalman filter (CSCKF) was formulated to quantify the excitability of local neural network and compared with three commonly used indicators, namely, band power, Teager energy operator, and sample entropy, to objectively determine their effectiveness in quantifying the severity of epileptiform discharges in mice. (2) Methods: A set of one normal and four types of epileptic EEGs was generated by a mathematical model. EEG data of epileptiform discharges during two types of electrical stimulation were recorded in 20 mice. Then, EEG segments of 5 s in length before, during and after the real and sham stimulation were collected. Both simulated and experimental data were used to compare the consistency and differences among the performance indicators. (3) Results: For the experimental data, the results of the four indicators were inconsistent during both types of electrical stimulation, although there was a trend that seizure severity changed with the indicators. For the simulated data, when the simulated EEG segments were used, the results of all four indicators were similar; however, this trend did not match the trend of excitability of the model network. In the model output which retained the DC component, except for the CSCKF parameter ratio, the results of the other three indicators were almost identical to those using the simulated EEG. For CSCKF, the parameter ratio faithfully reflected the excitability of the neural network. (4) Conclusion: For common EEG, CSCKF did not outperform other commonly used performance indicators. However, for EEG with a preserved DC component, CSCKF had the potential to quantify the excitability of the neural network and the associated severity of epileptiform discharges.

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.

A state observer for the computational network model of neural populations

A state observer plays a vital role in the design of state feedback neuromodulation schemes used to prevent and treat neurological or psychiatric disorders. This paper aims to design a state observer to reconstruct all unmeasured states of the computational network model of neural populations that replicates patterns seen on the electroencephalogram by using the model inputs and outputs, as the theoretical basis for designing state feedback neuromodulation clinical schemes. The feasibility problem of linear matrix inequality conditions, which is the most important one for observer design of the computational network model of neural populations, is solved by using the input-output stability theory and the Lurie system theory. The observer matrices of the designed observer are formed by the optimal solution of the linear matrix inequality conditions. An illustrative example shows that the observer can simultaneously reproduce internal state variables of normal and lesion populations of the computational network model of neural populations under the background of focal origin brain dysfunction, and the designed observer has certain robustness toward input uncertainty and measurement noise. To the best of our knowledge, no observers have previously been designed for the computational network model of neural populations. The design of state feedback neuromodulation schemes based on the computational network model of neural populations is a new direction in the field of computational neuroscience.

LncRNA TUG1 inhibits neuronal apoptosis in status epilepticus rats via targeting the miR-421/mTOR axis

Status epilepticus (SE) induces apoptosis of hippocampal neurons. However, the underlying mechanism in SE is not fully understood. Recently, lncRNA TUG1 is reported as a significant mediator in neuronal development. In present study, we aimed to investigate whether lncRNA TUG1 induces apoptosis of hippocampal neurons in SE rat models. TUG1 expression in serum of normal volunteers and SE patients, SE rats and neurons with epileptiform discharge was detected. SE rat model was established and intervened with TUG1 to evaluate hippocampal neuronal apoptosis. The experiments in vitro were further performed in neurons with epileptiform discharge to verify the effects of TUG1 on neuronal apoptosis of SE rats. The downstream mechanism of TUG1 was predicted and verified. miR-421 was intervened to perform the rescue experiments. Levels of oxidative stress and inflammation-related factors and mTOR pathway-related proteins in SE rats and hippocampal neurons were detected. TUG1 was highly expressed in serum of SE patients, SE rats and neurons with epileptiform discharge. Inhibition of TUG1 relieved pathological injury, oxidative stress and inflammation and reduced neuronal apoptosis in SE rats, which were further verified in hippocampal neurons. TUG1 upregulated TIMP2 expression by targeting miR-421. Overexpressed miR-421 inhibited hippocampal neuronal apoptosis. TUG1 knockout inactivated the mTOR pathway via the miR-421/TIMP2 axis to relieve neuronal apoptosis, oxidative stress and inflammation in SE rats and hippocampal neurons. Taken together, these findings showed that downregulation of lncRNA TUG1 inhibited apoptosis of hippocampal neurons in SE rats, and attenuated oxidative stress and inflammation damage through regulating the miR-421/mTOR axis.

The Bayesian Virtual Epileptic Patient: A probabilistic framework designed to infer the spatial map of epileptogenicity in a personalized large-scale brain model of epilepsy spread

Despite the importance and frequent use of Bayesian frameworks in brain network modeling for parameter inference and model prediction, the advanced sampling algorithms implemented in probabilistic programming languages to overcome the inference difficulties have received relatively little attention in this context. In this technical note, we propose a probabilistic framework, namely the Bayesian Virtual Epileptic Patient (BVEP), which relies on the fusion of structural data of individuals to infer the spatial map of epileptogenicity in a personalized large-scale brain model of epilepsy spread. To invert the individualized whole-brain model employed in this study, we use the recently developed algorithms known as No-U-Turn Sampler (NUTS) as well as Automatic Differentiation Variational Inference (ADVI). Our results indicate that NUTS and ADVI accurately estimate the degree of epileptogenicity of brain regions, therefore, the hypothetical brain areas responsible for the seizure initiation and propagation, while the convergence diagnostics and posterior behavior analysis validate the reliability of the estimations. Moreover, we illustrate the efficiency of the transformed non-centered parameters in comparison to centered form of parameterization. The Bayesian framework used in this work proposes an appropriate patient-specific strategy for estimating the epileptogenicity of the brain regions to improve outcome after epilepsy surgery.

Model-based robust suppression of epileptic seizures without sensory measurements

Uncontrolled seizures may lead to irreversible damages in the brain and various limitations in the patient's life. There exist experimental studies to stabilize the patient seizures. However, the experimental setups have many sensory devices to measure the dynamics of the brain cortex. These equipments prevent to produce small portable stabilizers for patients in everyday life. Recently, a comprehensive cortex model is introduced to apply model-based observers and controllers. However, this cortex model can be uncertain and have time-varying parameters. Therefore, in this paper, a robust Takagi-Sugeno (TS) controller and observer are designed to suppress the epileptic seizures without sensory measurements. The unavailable sensory measurements are provided by the designed nonlinear observer. The exponential convergence of the observer and controller is satisfied by the feedback parameter design using linear matrix inequalities. In addition, TS fuzzy observer-controller design has been compared with the conventional PID method in terms of control performance and design problem. The numerical computations show that the epileptic seizures are more effectively suppressed by the TS fuzzy observer-based controller under uncertain membrane potential dynamics.

Automated epileptic seizure detection based on break of excitation/inhibition balance

Physiological models are attractive for seizure detection, as their parameters are related to physiological meanings. We propose an algorithm to early detect epileptic seizures based on automatic estimation of average synaptic gains (excitatory Ae, slow and fast inhibitory B and G) by combining clinical data with a neural mass model. Three indices (Ae/B, Ae/G and Ae/(B + G)), all related to excitation/inhibition balance, were calculated and used as cues to detect seizures. A simple thresholding method was employed. We evaluated the algorithm against the manual scoring of a human expert on intracranial EEG samples from 23 patients suffering from different types of epilepsy. Best performance was achieved using Ae/(B + G) as a cue, i.e. excitation/(slow + fast) inhibition, on temporal lobe epilepsy (TLE) patients. A leave-one-out cross-validation showed that the algorithm achieved 92.98% sensitivity for TLE patients. The median false positive rate was 0.16 per hour, and median detection delay was 14.5 s. Of interest, the threshold values determined by a leave-one-out cross-validation did nearly not vary among TLE patients, suggesting a general excitation/inhibition balance baseline in TLE patients. The same approach could be used with other types of epilepsy by adapting the neural mass model to these types.

Seizure evolution can be characterized as path through synaptic gain space of a neural mass model

Physiologically based models could facilitate better understanding of mechanisms underlying epileptic seizures. In this paper, we attempt to reveal the dynamic evolution of intracranial EEG activity during epileptic seizures based on synaptic gain identification procedure of a neural mass model. The distribution of average excitatory, slow and fast inhibitory synaptic gain in the parameter space and their temporal evolution, i.e., the path through the model parameter space, were analyzed in thirty seizures from ten temporal lobe epileptic patients. Results showed that the synaptic gain values located roughly on a plane before seizure onset, dispersed during seizure and returned to the plane when seizure terminated. Cluster analysis was performed on seizure paths and demonstrated consistency in synaptic gain evolution across different seizures from the individual patient. Furthermore, two patient groups were identified, each one corresponding to a specific synaptic gain evolution in the parameter space during a seizure. Results were validated by a bootstrapping approach based on comparison with random paths. The differences in the path revealed variations in EEG dynamics for patients despite showing identical seizure onset pattern. Our approach may have the potential to classify the epileptic patients into subgroups based on different mechanisms revealed by subtle changes in synaptic gains and further enable more robust decisions regarding treatment strategy.

Toward Rigorous Parameterization of Underconstrained Neural Network Models Through Interactive Visualization and Steering of Connectivity Generation

Simulation models in many scientific fields can have non-unique solutions or unique solutions which can be difficult to find. Moreover, in evolving systems, unique final state solutions can be reached by multiple different trajectories. Neuroscience is no exception. Often, neural network models are subject to parameter fitting to obtain desirable output comparable to experimental data. Parameter fitting without sufficient constraints and a systematic exploration of the possible solution space can lead to conclusions valid only around local minima or around non-minima. To address this issue, we have developed an interactive tool for visualizing and steering parameters in neural network simulation models. In this work, we focus particularly on connectivity generation, since finding suitable connectivity configurations for neural network models constitutes a complex parameter search scenario. The development of the tool has been guided by several use cases-the tool allows researchers to steer the parameters of the connectivity generation during the simulation, thus quickly growing networks composed of multiple populations with a targeted mean activity. The flexibility of the software allows scientists to explore other connectivity and neuron variables apart from the ones presented as use cases. With this tool, we enable an interactive exploration of parameter spaces and a better understanding of neural network models and grapple with the crucial problem of non-unique network solutions and trajectories. In addition, we observe a reduction in turn around times for the assessment of these models, due to interactive visualization while the simulation is computed.

Dynamics underlying interictal to ictal transition in temporal lobe epilepsy: insights from a neural mass model

We propose an approach that combines a neural mass model and clinical intracranial electroencephalographic (iEEG) recordings to explore the potential pathophysiological mechanisms (at the neuronal population level) of ictogenesis. Thirty iEEG recordings from 10 temporal lobe epilepsy (TLE) patients around seizure onset were investigated. Physiologically meaningful parameters [average excitatory (A_e ), slow (B), and fast (G) inhibitory synaptic gain] were identified during interictal to ictal transition. Four ratios (A_e /G, A_e /B, A_e /(B + G), and B/G) were derived from these parameters, and their evolution over time was analyzed. The excitation/inhibition ratio increased around seizure onset and decreased before seizure offset, indicating the impairment and re-emergence of excitation/inhibition balance around seizure onset and before seizure offset, respectively. Moreover, the slow inhibition may have an earlier effect on excitation/inhibition imbalance. We confirm the decrease in excitation/inhibition ratio upon seizure termination in human temporal lobe epilepsy, as revealed by optogenetic approaches both in vivo in animal models and in vitro. The increase in excitation/inhibition ratio around seizure occurrence could be an indicator to detect seizures.

Differential temperature sensitivity of synaptic and firing processes in a neural mass model of epileptic discharges explains heterogeneous response of experimental epilepsy to focal brain cooling

Experiments with drug-induced epilepsy in rat brains and epileptic human brain region reveal that focal cooling can suppress epileptic discharges without affecting the brain's normal neurological function. Findings suggest a viable treatment for intractable epilepsy cases via an implantable cooling device. However, precise mechanisms by which cooling suppresses epileptic discharges are still not clearly understood. Cooling experiments in vitro presented evidence of reduction in neurotransmitter release from presynaptic terminals and loss of dendritic spines at post-synaptic terminals offering a possible synaptic mechanism. We show that termination of epileptic discharges is possible by introducing a homogeneous temperature factor in a neural mass model which attenuates the post-synaptic impulse responses of the neuronal populations. This result however may be expected since such attenuation leads to reduced post-synaptic potential and when the effect on inhibitory interneurons is less than on excitatory interneurons, frequency of firing of pyramidal cells is consequently reduced. While this is observed in cooling experiments in vitro, experiments in vivo exhibit persistent discharges during cooling but suppressed in magnitude. This leads us to conjecture that reduction in the frequency of discharges may be compensated through intrinsic excitability mechanisms. Such compensatory mechanism is modelled using a reciprocal temperature factor in the firing response function in the neural mass model. We demonstrate that the complete model can reproduce attenuation of both magnitude and frequency of epileptic discharges during cooling. The compensatory mechanism suggests that cooling lowers the average and the variance of the distribution of threshold potential of firing across the population. Bifurcation study with respect to the temperature parameters of the model reveals how heterogeneous response of epileptic discharges to cooling (termination or suppression only) is exhibited. Possibility of differential temperature effects on post-synaptic potential generation of different populations is also explored.

Hybrid Cubature Kalman filtering for identifying nonlinear models from sampled recording: Estimation of neuronal dynamics

Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF) have extended this efficient estimation property to nonlinear systems, and also to hybrid nonlinear problems where by the processes are continuous and the observations are discrete (continuous-discrete CD-CKF). Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. This paper investigates the performance of cubature filtering (CKF and CD-CKF) in two flagship problems arising in the field of neuroscience upon relating brain functionality to aggregate neurophysiological recordings: (i) estimation of the firing dynamics and the neural circuit model parameters from electric potentials (EP) observations, and (ii) estimation of the hemodynamic model parameters and the underlying neural drive from BOLD (fMRI) signals. First, in simulated neural circuit models, estimation accuracy was investigated under varying levels of observation noise (SNR), process noise structures, and observation sampling intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited better accuracy for a given SNR, sharp accuracy increase with higher SNR, and persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows only a mild deterioration for non-Gaussian process noise, specifically with Poisson noise, a commonly assumed form of background fluctuations in neuronal systems. Second, in simulated hemodynamic models, parametric estimates were consistently improved under CD-CKF. Critically, time-localization of the underlying neural drive, a determinant factor in fMRI-based functional connectivity studies, was significantly more accurate under CD-CKF. In conclusion, and with the CKF recently benchmarked against other advanced Bayesian techniques, the CD-CKF framework could provide significant gains in robustness and accuracy when estimating a variety of biological phenomena models where the underlying process dynamics unfold at time scales faster than those seen in collected measurements.