Nonlinear System Identification of Neural Systems from Neurophysiological Signals

The human nervous system is one of the most complicated systems in nature. Complex nonlinear behaviours have been shown from the single neuron level to the system level. For decades, linear connectivity analysis methods, such as correlation, coherence and Granger causality, have been extensively used to assess the neural connectivities and input-output interconnections in neural systems. Recent studies indicate that these linear methods can only capture a small amount of neural activities and functional relationships, and therefore cannot describe neural behaviours in a precise or complete way. In this review, we highlight recent advances in nonlinear system identification of neural systems, corresponding time and frequency domain analysis, and novel neural connectivity measures based on nonlinear system identification techniques. We argue that nonlinear modelling and analysis are necessary to study neuronal processing and signal transfer in neural systems quantitatively. These approaches can hopefully provide new insights to advance our understanding of neurophysiological mechanisms underlying neural functions. These nonlinear approaches also have the potential to produce sensitive biomarkers to facilitate the development of precision diagnostic tools for evaluating neurological disorders and the effects of targeted intervention

Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons

Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data

Neural population coding: combining insights from microscopic and mass signals

Behavior relies on the distributed and coordinated activity of neural populations. Population activity can be measured using multi-neuron recordings and neuroimaging. Neural recordings reveal how the heterogeneity, sparseness, timing, and correlation of population activity shape information processing in local networks, whereas neuroimaging shows how long-range coupling and brain states impact on local activity and perception. To obtain an integrated perspective on neural information processing we need to combine knowledge from both levels of investigation. We review recent progress of how neural recordings, neuroimaging, and computational approaches begin to elucidate how interactions between local neural population activity and large-scale dynamics shape the structure and coding capacity of local information representations, make them state-dependent, and control distributed populations that collectively shape behavior

Information flow through a model of the C. elegans klinotaxis circuit

Understanding how information about external stimuli is transformed into behavior is one of the central goals of neuroscience. Here we characterize the information flow through a complete sensorimotor circuit: from stimulus, to sensory neurons, to interneurons, to motor neurons, to muscles, to motion. Specifically, we apply a recently developed framework for quantifying information flow to a previously published ensemble of models of salt klinotaxis in the nematode worm C. elegans. The models are grounded in the neuroanatomy and currently known neurophysiology of the worm. The unknown model parameters were optimized to reproduce the worm's behavior. Information flow analysis reveals several key principles underlying how the models operate: (1) Interneuron class AIY is responsible for integrating information about positive and negative changes in concentration, and exhibits a strong left/right information asymmetry. (2) Gap junctions play a crucial role in the transfer of information responsible for the information symmetry observed in interneuron class AIZ. (3) Neck motor neuron class SMB implements an information gating mechanism that underlies the circuit's state-dependent response. (4) The neck carries non-uniform distribution about changes in concentration. Thus, not all directions of movement are equally informative. Each of these findings corresponds to an experimental prediction that could be tested in the worm to greatly refine our understanding of the neural circuit underlying klinotaxis. Information flow analysis also allows us to explore how information flow relates to underlying electrophysiology. Despite large variations in the neural parameters of individual circuits, the overall information flow architecture circuit is remarkably consistent across the ensemble, suggesting that information flow analysis captures general principles of operation for the klinotaxis circuit

Efficiency characterization of a large neuronal network: a causal information approach

When inhibitory neurons constitute about 40% of neurons they could have an important antinociceptive role, as they would easily regulate the level of activity of other neurons. We consider a simple network of cortical spiking neurons with axonal conduction delays and spike timing dependent plasticity, representative of a cortical column or hypercolumn with large proportion of inhibitory neurons. Each neuron fires following a Hodgkin-Huxley like dynamics and it is interconnected randomly to other neurons. The network dynamics is investigated estimating Bandt and Pompe probability distribution function associated to the interspike intervals and taking different degrees of inter-connectivity across neurons. More specifically we take into account the fine temporal ``structures'' of the complex neuronal signals not just by using the probability distributions associated to the inter spike intervals, but instead considering much more subtle measures accounting for their causal information: the Shannon permutation entropy, Fisher permutation information and permutation statistical complexity. This allows us to investigate how the information of the system might saturate to a finite value as the degree of inter-connectivity across neurons grows, inferring the emergent dynamical properties of the system.Comment: 26 pages, 3 Figures; Physica A, in pres

Locally embedded presages of global network bursts

Spontaneous, synchronous bursting of neural population is a widely observed phenomenon in nervous networks, which is considered important for functions and dysfunctions of the brain. However, how the global synchrony across a large number of neurons emerges from an initially non-bursting network state is not fully understood. In this study, we develop a new state-space reconstruction method combined with high-resolution recordings of cultured neurons. This method extracts deterministic signatures of upcoming global bursts in "local" dynamics of individual neurons during non-bursting periods. We find that local information within a single-cell time series can compare with or even outperform the global mean field activity for predicting future global bursts. Moreover, the inter-cell variability in the burst predictability is found to reflect the network structure realized in the non-bursting periods. These findings demonstrate the deterministic mechanisms underlying the locally concentrated early-warnings of the global state transition in self-organized networks

Neuroplastic Changes Following Brain Ischemia and their Contribution to Stroke Recovery: Novel Approaches in Neurorehabilitation

Ischemic damage to the brain triggers substantial reorganization of spared areas and pathways, which is associated with limited, spontaneous restoration of function. A better understanding of this plastic remodeling is crucial to develop more effective strategies for stroke rehabilitation. In this review article, we discuss advances in the comprehension of post-stroke network reorganization in patients and animal models. We first focus on rodent studies that have shed light on the mechanisms underlying neuronal remodeling in the perilesional area and contralesional hemisphere after motor cortex infarcts. Analysis of electrophysiological data has demonstrated brain-wide alterations in functional connectivity in both hemispheres, well beyond the infarcted area. We then illustrate the potential use of non-invasive brain stimulation (NIBS) techniques to boost recovery. We finally discuss rehabilitative protocols based on robotic devices as a tool to promote endogenous plasticity and functional restoration