Itinerant Dynamics Research Articles

NHSMM-MAR-sdNC: A novel data-driven computational framework for state-dependent effective connectivity analysis

The brain exhibits intrinsic dynamics characterized by spontaneous spatiotemporal reorganization of neural activity or metastability, which is associated closely with functional integration and segregation. Compared to dynamic functional connectivity, state-dependent effective connectivity (i.e., dynamic effective connectivity) is more suitable for exploring the metastability as its ability to infer causalities between brain regions. However, methods for state-dependent effective connectivity are scarce and urgently needed. In this study, a novel data-driven computational framework, named NHSMM-MAR-sdNC integrating nonparametric hidden semi-Markov model combined with multivariate autoregressive model and state-dependent new causality, is proposed to investigate the state-dependent effective connectivity. The framework is not constrained by any biological assumptions. Furthermore, state number can be inferred from the observed data directly and the state duration distributions will be estimated explicitly rather than restricted by geometric form, which overcomes limitations of hidden Markov model. Experimental results of synthetic data show that the framework can identify the state number adaptively and the state-dependent causality networks accurately. The dynamics of state-related causality networks are also revealed by the new method on real-world resting-state fMRI data. Our method provides a new data-driven computational framework for identifying state-dependent effective connectivity, which will facilitate the identification and assessment of metastability and itinerant dynamics of the brain.

Itinerant complexity in networks of intrinsically bursting neurons.

Active neurons can be broadly classified by their intrinsic oscillation patterns into two classes characterized by spiking or bursting. Here, we show that networks of identical bursting neurons with inhibitory pulsatory coupling exhibit itinerant dynamics. Using the relative phases of bursts between neurons, we numerically demonstrate that the network exhibits endogenous transitions between multiple modes of transient synchrony. This is true even for bursts consisting of two spikes. In contrast, our simulations reveal that networks of identical singlet-spiking neurons do not exhibit such complexity. These results suggest a role for bursting dynamics in realizing itinerant complexity in neural circuits.

Deep Temporal Organization of fMRI Phase Synchrony Modes Promotes Large-Scale Disconnection in Schizophrenia.

Itinerant dynamics of the brain generates transient and recurrent spatiotemporal patterns in neuroimaging data. Characterizing metastable functional connectivity (FC) – particularly at rest and using functional magnetic resonance imaging (fMRI) – has shaped the field of dynamic functional connectivity (DFC). Mainstream DFC research relies on (sliding window) correlations to identify recurrent FC patterns. Recently, functional relevance of the instantaneous phase synchrony (IPS) of fMRI signals has been revealed using imaging studies and computational models. In the present paper, we identify the repertoire of whole-brain inter-network IPS states at rest. Moreover, we uncover a hierarchy in the temporal organization of IPS modes. We hypothesize that connectivity disorder in schizophrenia (SZ) is related to the (deep) temporal arrangement of large-scale IPS modes. Hence, we analyze resting-state fMRI data from 68 healthy controls (HC) and 51 SZ patients. Seven resting-state networks (and their sub-components) are identified using spatial independent component analysis. IPS is computed between subject-specific network time courses, using analytic signals. The resultant phase coupling patterns, across time and subjects, are clustered into eight IPS states. Statistical tests show that the relative expression and mean lifetime of certain IPS states have been altered in SZ. Namely, patients spend (45%) less time in a globally coherent state and a subcortical-centered state, and (40%) more time in states reflecting anticoupling within the cognitive control network, compared to the HC. Moreover, the transition profile (between states) reveals a deep temporal structure, shaping two metastates with distinct phase synchrony profiles. A metastate is a collection of states such that within-metastate transitions are more probable than across. Remarkably, metastate occupation balance is altered in SZ, in favor of the less synchronous metastate that promotes disconnection across networks. Furthermore, the trajectory of IPS patterns is less efficient, less smooth, and more restricted in SZ subjects, compared to the HC. Finally, a regression analysis confirms the diagnostic value of the defined IPS measures for SZ identification, highlighting the distinctive role of metastate proportion. Our results suggest that the proposed IPS features may be used for classification studies and for characterizing phase synchrony modes in other (clinical) populations.

Dynamic effective connectivity

Metastability is a key source of itinerant dynamics in the brain; namely, spontaneous spatiotemporal reorganization of neuronal activity. This itinerancy has been the focus of numerous dynamic functional connectivity (DFC) analyses – developed to characterize the formation and dissolution of distributed functional patterns over time, using resting state fMRI. However, aside from technical and practical controversies, these approaches cannot recover the neuronal mechanisms that underwrite itinerant (e.g., metastable) dynamics—due to their descriptive, model-free nature. We argue that effective connectivity (EC) analyses are more apt for investigating the neuronal basis of metastability. To this end, we appeal to biologically-grounded models (i.e., dynamic causal modelling, DCM) and dynamical systems theory (i.e., heteroclinic sequential dynamics) to create a probabilistic, generative model of haemodynamic fluctuations. This model generates trajectories in the parametric space of EC modes (i.e., states of connectivity) that characterize functional brain architectures. In brief, it extends an established spectral DCM, to generate functional connectivity data features that change over time. This foundational paper tries to establish the model’s face validity by simulating non-stationary fMRI time series and recovering key model parameters (i.e., transition probabilities among connectivity states and the parametric nature of these states) using variational Bayes. These data are further characterized using Bayesian model comparison (within and between subjects). Finally, we consider practical issues that attend applications and extensions of this scheme. Importantly, the scheme operates within a generic Bayesian framework – that can be adapted to study metastability and itinerant dynamics in any non-stationary time series.

Multistability in large scale models of brain activity

Rich spatiotemporal dynamical patterns, observed in the brain at rest, reveal several large-scale functional networks, presumably involved in different brain functions. In parallel, structural networks obtained by Diffusion Spectrum Imaging (connectome) identify several interconnected sub-networks that overlap with the functional networks [3]. Neural mass model simulations aim at developing realistic models of the brain activity. In particular, multiple attractors can be identified and spontaneous alternation between several brain states can be obtained [2]. The number and the organization of the fixed-point attractors strongly vary depending of the parameters used in the model. In order to provide a general view of connectome-based dynamical systems, we developed a simplified neural mass model inspired by the continuous Hopfield network [4], to which we add a stochastic component, and a dynamic threshold (eq.2) that prevents reaching the two trivial attractors of system (eq.1). τdxidt=-xi+∑j=1NWi,jφxj,γ,θ+σ2ηi(t) (1) τθdθdt=-θ+ΩN∑i=1Nφxi,γ,θ (2) φxi,γ,θ=121+tanhγxi-θ (3) where W is the N = 66 nodes human connectome [3], x is the node potential, φ is the node output, θ is the adaptive threshold, η(t) is a white noise and σ the diffusion parameter. Three main parameters (excitation strength ||W||, inhibition strength Ω and node excitability γ) are systematically varied in order to identify the fixed points attractors of the dynamics (Figure ​(Figure11). Figure 1 Number of attractors obtained for different (Ω, ||W||) couples with γ = 30. Attractor patterns isodensity lines are indicated in black The adaptive threshold plays the role of a global inhibition and allows stabilizing many attractors, where the Ω / ||W|| ratio controls the sparsity of the activity. Then multistable dynamical systems are obtained in a large region of the parameter space, allowing to identify many different attractor patterns. The number of attractors is found to increase with the value of gamma (node excitability), at the expense of their intrinsic stability. Itinerant dynamics is obtained when a significant noise level is introduced in the system. Then, several attractive patterns can be reached on a single trajectory, where the duration of the visit reflects the stability of the pattern. The simple dynamical system we have implemented allows exploring a large region of the parameters space, but is also capable of reproducing some aspects of the brain's spontaneous activity (switching between different attractors). The set of attractors we find in some regions of the parameters space share similarities with the different functional modes observed in the resting-state activity [1].

Connectivity and thought: The influence of semantic network structure in a neurodynamical model of thinking

Understanding cognition has been a central focus for psychologists, neuroscientists and philosophers for thousands of years, but many of its most fundamental processes remain very poorly understood. Chief among these is the process of thought itself: the spontaneous emergence of specific ideas within the stream of consciousness. It is widely accepted that ideas, both familiar and novel, arise from the combination of existing concepts. From this perspective, thought is an emergent attribute of memory, arising from the intrinsic dynamics of the neural substrate in which information is embedded. An important issue in any understanding of this process is the relationship between the emergence of conceptual combinations and the dynamics of the underlying neural networks. Virtually all theories of ideation hypothesize that ideas arise during the thought process through association, each one triggering the next through some type of linkage, e.g., structural analogy, semantic similarity, polysemy, etc. In particular, it has been suggested that the creativity of ideation in individuals reflects the qualitative structure of conceptual associations in their minds. Interestingly, psycholinguistic studies have shown that semantic networks across many languages have a particular type of structure with small-world, scale free connectivity. So far, however, these related insights have not been brought together, in part because there has been no explicitly neural model for the dynamics of spontaneous thought. Recently, we have developed such a model. Though simplistic and abstract, this model attempts to capture the most basic aspects of the process hypothesized by theoretical models within a neurodynamical framework. It represents semantic memory as a recurrent semantic neural network with itinerant dynamics. Conceptual combinations arise through this dynamics as co-active groups of neural units, and either dissolve quickly or persist for a time as emergent metastable attractors and are recognized consciously as ideas. The work presented in this paper describes this model in detail, and uses it to systematically study the relationship between the structure of conceptual associations in the neural substrate and the ideas arising from this system's dynamics. In particular, we consider how the small-world and scale-free characteristics influence the effectiveness of the thought process under several metrics, and show that networks with both attributes indeed provide significant advantages in generating unique conceptual combinations.

Competitive dynamics in the brain: Comment on “Information flow dynamics in the brain” by M.I. Rabinovich et al.

Rabinovich et al. [1] motivate the importance of itinerant and competitive dynamics when considering the brain as an information processing device [2,3]. They treat us to a rich series of insights afforded by a dynamical perspective that emphasizes metastability and winnerless competition. Their review pursues a compelling tradition of trying to understand neuronal activity in terms of attractor dynamics and how the resulting dynamics are coupled to the sensorium [4–11]. The authors start by making a key point — to properly understand neural processing one has to move beyond classical information theoretic approaches and look at the itinerant dynamics that underpin self-organization in nonequilibrium systems, like the brain, that maintain a steady state or homeostasis [6,11,12]. Rabinovich et al. cover many themes. I will focus on the broad implications for understanding brain function from the Helmholtzian perspective on the brain as an inference machine [12–14]. In this view, the brain tries to model its sensory exchanges with the world, where this modelling gives rise to perception and the selection of sensory evidence that we know as behavior. Winnerless competition and metastable dynamics are absolutely central to this notion, given the metastability of the world we are obliged to model. A nice example here is communication among conspecifics that has a deep hierarchical structure and a separation of temporal scales. One perspective, on this remarkable capacity of higher organisms, is that their brains contain the same central pattern generators or stable heteroclinic channels that are coupled through sensory exchanges. Rabinovich et al. look at this in terms of the binding of stable heteroclinic channels [15]. It is interesting to reflect on the nature of this binding in the context of language [16]. To cut a long story short, it is possible for the itinerant pattern generators in a speaker to entrain equivalent dynamics in a listener, if the listener uses his pattern generator to predict the behavior (i.e., speech) of the speaker. This leads naturally to a view of the brain in terms of predictive coding [17], where prediction errors bind metastable orbits in different brains and, indeed, hierarchical levels of a single brain [12]. The key thing here is that winnerless competition and competitive dynamics provide a model or prior beliefs about the unfolding world and therefore provide a basis for predicting our sensory impressions of that world [18]. Exactly the same perspective can be applied to action, where kinaesthetic or proprioceptive predictions produce movements through classical reflex arcs. Rabinovich et al. provide a beautiful example of this in the Mollusc Clione limacina. They consider the competitive dynamics between statocyst receptor neurons and how these provide command signals

Behavior of quantum entropies in polaronic systems

Quantum entropies and state distances are analyzed in polaronic systems with short range (Holstein model) and long range (Fr$\ddot{o}$hlich model) electron-phonon coupling. These quantities are extracted by a variational wave function which describes very accurately polaron systems with arbitrary size in all the relevant parameter regimes. With the use of quantum information tools, the crossover region from weak to strong coupling regime can be characterized with high precision. Then, the linear entropy is found to be very sensitive to the range of the electron-phonon coupling and the adiabatic ratio. Finally, the entanglement entropy is studied as a function of the system size pointing out that it not bounded, but scales as the logarithm of the size either for weak electron-phonon coupling or for short range interaction. This behavior is ascribed to the peculiar coupling induced by the single electron itinerant dynamics on the phonon subsystem.

Computational significance of transient dynamics in cortical networks

Neural responses are most often characterized in terms of the sets of environmental or internal conditions or stimuli with which their firing rate [corrected]increases or decreases are correlated [corrected] Their transient (nonstationary) temporal profiles of activity have received comparatively less attention. Similarly, the computational framework of attractor neural networks puts most emphasis on the representational or computational properties of the stable states of a neural system. Here we review a couple of neurophysiological observations and computational ideas that shift the focus to the transient dynamics of neural systems. We argue that there are many situations in which the transient neural behaviour, while hopping between different attractor states or moving along 'attractor ruins', carries most of the computational and/or behavioural significance, rather than the attractor states eventually reached. Such transients may be related to the computation of temporally precise predictions or the probabilistic transitions among choice options, accounting for Weber's law in decision-making tasks. Finally, we conclude with a more general perspective on the role of transient dynamics in the brain, promoting the view that brain activity is characterized by a high-dimensional chaotic ground state from which transient spatiotemporal patterns (metastable states) briefly emerge. Neural computation has to exploit the itinerant dynamics between these states.

Modeling birdsong learning with a chaotic Elman network

Among passerines, Bengali finches are known to sing extremely complex courtship songs with three hierarchical structures: namely, the element, the chunk, and the syntax. In this work, we theoretically studied the mechanism of the song of Bengali finches in aides to provide a dynamic view of the development of birdsong learning. We first constructed a model of the Elman network with chaotic neurons that successfully learned the supervisor signal defined by a simple finite-state syntax. Second, we focused on the process of individual-specific increases in the complexity of song syntax. We propose a new learning algorithm to produce the intrinsic diversification of song syntax without a supervisor on the basis of the itinerant dynamics of chaotic neural networks and the Hebbian learning rule. The emergence of novel syntax modifying the acquired syntax is demonstrated.

Chaotic itinerancy, temporal segmentation and spatio-temporal combinatorial codes

We study a deterministic dynamics with two time scales in a continuous state attractor network. To the usual (fast) relaxation dynamics towards point attractors (“patterns”) we add a slow coupling dynamics that makes the visited patterns lose stability, leading to an itinerant behavior in the form of punctuated equilibria. One finds that the transition frequency matrix for transitions between patterns shows non-trivial statistical properties in the chaotic itinerant regime. We show that mixture input patterns can be temporally segmented by the itinerant dynamics. The viability of a combinatorial spatio-temporal neural code is also demonstrated.

CIRCUIT IMPLEMENTATION AND DYNAMICS OF A TWO-DIMENSIONAL MOSFET NEURON MODEL

We propose a two-dimensional neuron model using metal-oxide-semiconductor field-effect-transistors (MOSFETs). It can be implemented with a compact circuitry. This is because we designed its phase portrait structure utilizing the curves native to the MOSFET circuitries. Bifurcation theory is applied to tune the characteristics of the circuitry. Biological neurons can be divided into two main classes based on their responses to sustained current stimuli: classes I and II. At the onset of firing, the firing frequency of class I neurons is asymptotically zero, while that of class II neurons is nonzero. It is generally accepted that classes I and II excitabilities are produced by a saddle-node bifurcation and a subcritical Hopf bifurcation, respectively. Class I* neurons, which belong to a subclass of class I, are characterized by a phase plane structure called a narrow channel. By changing a few circuit parameters, our circuitry can achieve class I without a narrow channel, class I*, and class II. The proposed circuitry is compatible with standard complementary metal-oxide-semiconductor (CMOS) processes. Hence, it can be easily implemented in an analog very-large-scale integrated (VLSI) circuit; further, large networks can be constructed by using this circuitry. We implemented and tested our circuitry, that was constructed using discrete components. We analyzed the responses to singlet, doublet, periodic pulses, and sustained current stimuli; further, we demonstrated that our circuitry inherited three critical properties of biological neurons: (a) the fundamental abilities of excitable cells, (b) neural excitability such as of classes I and II, and (c) an ability to generate chaotic responses to periodic pulse stimuli. We then applied the bifurcation theory to our circuitry and verified its mathematical structure using XPPAUT software. Furthermore, the simulation results on a gap junction (GJ)-coupled network comprising class I* neurons revealed the genesis of itinerant dynamics similar to that found by Fujii et al..

MOSFET implementation of class I* neurons coupled by gap junctions

We propose a two-dimensional class I* neuron circuit coupled by gap junctions (GJs) consisting of enhancement-type metal-oxide-semiconductor field-effect-trangistors (MOSFETs). It is shown that some neurons that belong to a subclass of class I, when coupled by GJs, exhibit extensive spatiotemporal chaos in some parameter regions. This subclass is called class I* and is characterized by a phase plane structure with a narrow channel. We can tune our circuit to be class I, I*, or II by changing the resistance values. We show PSpice simulation results for a circuit implemented with discrete elements. A GJ-coupled network consisting of 20 such neurons is shown to generate itinerant dynamics with spatiotemporal chaos similar to class I* GJ-couple systems. The circuitry is compatible with standard complementary metal-oxide semiconductor (CMOS) processes. Hence, it can be implemented in an analog very-large-scale integrated circuit (VLSI) and the construction of a relatively large network is possible.

Chaotic itinerancy needs embodied cognition to explain memory dynamics

Memory dynamics need both stable and unstable properties simultaneously. Hence memory dynamics cannot be simulated by chaotic itinerant dynamics alone, with no real world correspondence. Memory dynamics are constrained by both semantics and causalities in the embodied cognition.