Linear feedback control of spreading dynamics in stochastic nonlinear network models: epileptic seizures.

The development of models and approaches for controlling the spreading dynamics of epileptic seizures is an essential step towards new therapies for people with pharmacologically resistant epilepsy. Beyond resective neurosurgery, in which epileptogenic zones (EZs) are the target of surgery, closed-loop control based on intracranial electrical stimulation, applied at the very early stage of seizure evolution, has been the main alternative, e.g. the RNS system from NeuroPace (Mountain View, CA). In this approach the electrical stimulation is delivered to target brain areas after detection of seizure initiation in the EZ. Here, we examined, on model simulations, some of the closed-loop control aspects of the problem. Seizure dynamics and spread are typically modeled with highly nonlinear dynamics on complex brain networks. Despite the nonlinearity and complexity, currently available optimal feedback control approaches are mostly based on linear approximations. Alternative machine learning control approaches might require amounts of data beyond what is commonly available in the intended application. We thus examined how standard linear feedback control approaches perform when applied to nonlinear models of neural dynamics of seizure generation and spread. In particular, we considered patient-specific epileptor network models for seizure onset and spread. The models incorporate network connectivity derived from (diffusion MRI) white-matter tractography, have been shown to capture the qualitative dynamics of epileptic seizures and can be fit to patient data. For control, we considered simple linear quadratic Gaussian (LQG) regulators. The LQG control was based on a discrete-time state-space model derived from the linearization of the patient-specific epileptor network model around a stable fixed point in the regime of preictal dynamics. We show in simulations that LQG regulators acting on the EZ node during the initial seizure period tend to be unstable. The LQG solution for the control law in this case leads to global feedback to the EZ-node actuator. However, if the LQG solution is constrained to depend on only local feedback originating from the EZ node itself, the controller is stable. In this case, we demonstrate that localized LQG can easily terminate the seizure at the early stage and prevent spread. In the context of optimal feedback control based on linear approximations, our results point to the need for investigating in more detail feedback localization and additional relevant control targets beyond epileptogenic zones.

Ictal autonomic activity recorded via wearable-sensors plus machine learning can discriminate epileptic and psychogenic nonepileptic seizures.

Differentiating epileptic seizures (ES) and psychogenic nonepileptic seizures (PNES) is commonly based on electroencephalogram and concurrent video recordings (vEEG). Here, we demonstrate that these two types of seizures can be discriminated based on signals related to autonomic nervous system activity recorded via wearable sensors. We used Empatica E4 Wristband sensors worn on both arms in vEEG confirmed seizures, and machine learning methods to train classifiers, specifically, extreme gradient boosting (XGBoost). Classification performance achieved a predictive accuracy of 78 ± 1.5% on previously unseen data for whether a seizure was epileptic or psychogenic, which is 6 standard deviations above the baseline of 68% accuracy. Our dataset contained altogether 35 seizures from 18 patients out of which 8 patients had 13 convulsive seizures. Prediction of seizure type was based on simple features derived from the segments of autonomic activity measurements (electrodermal activity, body temperature, blood volume pulse, and heart rate) and forearm acceleration. Features related to heart rate and electrodermal activity were ranked as the top predictors in XGBoost classifiers. We found that patients with PNES had a higher ictal heart rate and electrodermal activity than patients with ES. In contrast to existing published studies of mainly convulsive seizures, our classifier focuses on autonomic signals to differentiate convulsive or nonconvulsive semiology ES from PNES. Our results show that autonomic activity recorded via wearable sensors provides promising signals for detection and discrimination of psychogenic and epileptic seizures, but more work is necessary to improve the predictive power of the model.

Stochastic point process models for multi-compartment dendritic-tree input-output transformations in spiking neurons.

We extend stochastic point-process generalized linear models (PPGLMs) to the estimation of input-output transformations in dendritic trees and their contribution to the generation of soma action potentials in multi-compartmental models of single neurons. We used simulations of a model enthorinal cortex pyramidal neuron, with known dentritic tree and soma spatial organization, including active compartments defined in terms of standard cable and standard Hodgkin-Huxley equations. Each dendritic compartment (391 total) was endowed with either excitatory (E) or inhibitory (I) synaptic inputs whose strength was randomly specified. We examined the cases of both homogeneous and inhomogeneous spatial distributions for E and I synaptic inputs. The times for synaptic inputs followed a Poisson process with different mean rate regimes varying from 50 to 600 inputs/s. The soma membrane potential received also a background noise in the form of an Ornstein-Uhlenbeck process. Our main findings are: (1) Power spectra of soma membrane potentials revealed subthreshold resonances at ~40 Hz and ~80 Hz; (2) The contribution of different dendritic compartments, under the examined input ranges and spatial distributions, depended not only of the dendrite-soma path distance, but also on the number of compartments in the dendritic segment. (3) Estimated conditional intensity functions (CIFs) with PPGLMs successfully predicted spiking activity based on given E-I input times; area under ROC curves computed on test data varied from 0.8 - 0.95. (4) The CIF models identified compartments and regions receiving E-I synaptic inputs; Estimated temporal filters were consistent with dendrite-soma path distances and input weights. We expect this type of PPGLMs to contribute to data-driven identification of input-output transformations in dentritic trees based on single-neuron Ca2+ and voltage indicator imaging data.

FPGA implementation of deep-learning recurrent neural networks with sub-millisecond real-time latency for BCI-decoding of large-scale neural sensors (104 nodes).

Advances in neurotechnology are expected to provide access to thousands of neural channel recordings including neuronal spiking, multiunit activity and local field potentials. In addition, recent studies have shown that deep learning, in particular recurrent neural networks (RNNs), provide promising approaches for decoding of large-scale neural data. These approaches involve computationally intensive algorithms with millions of parameters. In this context, an important challenge in the application of neural decoding to next generation brain-computer interfaces for complex human tasks is the development of low-latency real-time implementations. We demonstrate a Field-Programmable Gate Array (FPGA) implementation of Long Short-Term Memory (LSTM) RNNs for decoding 10,000 channels of neural data on a mobile lowpower embedded system platform called "NeuroCoder". We provide a proof of concept in the context of decoding 20dimensional spectrotemporal representation of spoken words from simulated 10,000 neural channels. In this particular case, the LSTM model included 4,042,420 parameters. In addition to providing multiple communication interfaces for the BCI system, the NeuroCoder platform can achieve sub-millisecond real-time latencies.

Decoding hindlimb kinematics from primate motor cortex using long short-term memory recurrent neural networks.

Recent machine learning techniques have become a powerful tool in a variety of tasks, including neural decoding. Deep neural networks, particularly recurrent models, leverage the temporal evolution of neural ensemble activity to decode complex movement and sensory signals. Using single-unit recordings from microelectrode arrays implanted in the leg area of primary motor cortex in non-human primates, we decode the positions and angles of hindlimb joints during a locomotion task using a long short-term memory (LSTM) network. The LSTM decoder improved decoding over traditional filtering methods, such as Wiener and Kalman filters. However, dramatic improvements over other machine learning (e.g. XGBoost) and latent state-space methods were not observed.

Human seizures couple across spatial scales through travelling wave dynamics.

Epilepsy-the propensity toward recurrent, unprovoked seizures-is a devastating disease affecting 65 million people worldwide. Understanding and treating this disease remains a challenge, as seizures manifest through mechanisms and features that span spatial and temporal scales. Here we address this challenge through the analysis and modelling of human brain voltage activity recorded simultaneously across microscopic and macroscopic spatial scales. We show that during seizure large-scale neural populations spanning centimetres of cortex coordinate with small neural groups spanning cortical columns, and provide evidence that rapidly propagating waves of activity underlie this increased inter-scale coupling. We develop a corresponding computational model to propose specific mechanisms-namely, the effects of an increased extracellular potassium concentration diffusing in space-that support the observed spatiotemporal dynamics. Understanding the multi-scale, spatiotemporal dynamics of human seizures-and connecting these dynamics to specific biological mechanisms-promises new insights to treat this devastating disease.

Reconstruction of hand movement trajectories from a dynamic ensemble of spiking motor cortical neurons.

One of the many challenges in long-term decoding from chronically implanted electrodes involves tracking changes in the firing properties of the neural ensemble while simultaneously reconstructing the desired signal. We provide an approach to this problem based on adaptive point process filtering. In particular, we construct a lock-step adaptive filter built upon stochastic models for: a) the receptive field parameters of individual neurons within the ensemble, b) the biological signal to be reconstructed, and c) the instantaneous likelihood of firing in each neuron given the current state of a) and b). We assessed the ability of this filter to maintain a good representation of movement information in a dynamic ensemble of primary motor neurons tuned to hand kinematics. We simulated a recording scenario for this ensemble, where neurons were continuously becoming lost to the recording device while recordings from other, previously unobserved neurons became available. We found that this adaptive decoding algorithm was able to maintain accurate estimates of hand direction, even after the entire neural population had been replaced multiple times, but that the hand velocity signal tended to degrade over long periods.

Evaluating causal relations in neural systems: granger causality, directed transfer function and statistical assessment of significance.

We consider the question of evaluating causal relations among neurobiological signals. In particular, we study the relation between the directed transfer function (DTF) and the well-accepted Granger causality, and show that DTF can be interpreted within the framework of Granger causality. In addition, we propose a method to assess the significance of causality measures. Finally, we demonstrate the applications of these measures to simulated data and actual neurobiological recordings.