Non-reversibility outperforms functional connectivity in characterisation of brain states in MEG data.

Characterising brain states during tasks is common practice for many neuroscientific experiments using electrophysiological modalities such as electroencephalography (EEG) and magnetoencephalography (MEG). Brain states are often described in terms of oscillatory power and correlated brain activity, i.e. functional connectivity. It is, however, not unusual to observe weak task induced functional connectivity alterations in the presence of strong task induced power modulations using classical time-frequency representation of the data. Here, we propose that non-reversibility, or the temporal asymmetry in functional interactions, may be more sensitive to characterise task induced brain states than functional connectivity. As a second step, we explore causal mechanisms of non-reversibility in MEG data using whole brain computational models. We include working memory, motor, language tasks and resting-state data from participants of the Human Connectome Project (HCP). Non-reversibility is derived from the lagged amplitude envelope correlation (LAEC), and is based on asymmetry of the forward and reversed cross-correlations of the amplitude envelopes. Using random forests, we find that non-reversibility outperforms functional connectivity in the identification of task induced brain states. Non-reversibility shows especially better sensitivity to capture bottom-up gamma induced brain states across all tasks, but also alpha band associated brain states. Using whole brain computational models we find that asymmetry in the effective connectivity and axonal conduction delays play a major role in shaping non-reversibility across the brain. Our work paves the way for better sensitivity in characterising brain states during both bottom-up as well as top-down modulation in future neuroscientific experiments.

MIIND : A Model-Agnostic Simulator of Neural Populations.

MIIND is a software platform for easily and efficiently simulating the behaviour of interacting populations of point neurons governed by any 1D or 2D dynamical system. The simulator is entirely agnostic to the underlying neuron model of each population and provides an intuitive method for controlling the amount of noise which can significantly affect the overall behaviour. A network of populations can be set up quickly and easily using MIIND's XML-style simulation file format describing simulation parameters such as how populations interact, transmission delays, post-synaptic potentials, and what output to record. During simulation, a visual display of each population's state is provided for immediate feedback of the behaviour and population activity can be output to a file or passed to a Python script for further processing. The Python support also means that MIIND can be integrated into other software such as The Virtual Brain. MIIND's population density technique is a geometric and visual method for describing the activity of each neuron population which encourages a deep consideration of the dynamics of the neuron model and provides insight into how the behaviour of each population is affected by the behaviour of its neighbours in the network. For 1D neuron models, MIIND performs far better than direct simulation solutions for large populations. For 2D models, performance comparison is more nuanced but the population density approach still confers certain advantages over direct simulation. MIIND can be used to build neural systems that bridge the scales between an individual neuron model and a population network. This allows researchers to maintain a plausible path back from mesoscopic to microscopic scales while minimising the complexity of managing large numbers of interconnected neurons. In this paper, we introduce the MIIND system, its usage, and provide implementation details where appropriate.

Complex patterns of subcellular cardiac alternans.

Cardiac alternans, in which the membrane potential and the intracellular calcium concentration exhibit alternating durations and peak amplitudes at consecutive beats, constitute a precursor to fatal cardiac arrhythmia such as sudden cardiac death. A crucial question therefore concerns the onset of cardiac alternans. Typically, alternans are only reported when they are fully developed. Here, we present a modelling approach to explore recently discovered microscopic alternans, which represent one of the earliest manifestations of cardiac alternans. In this case, the regular periodic dynamics of the local intracellular calcium concentration is already unstable, while the whole-cell behaviour suggests a healthy cell state. In particular, we use our model to investigate the impact of calcium diffusion in both the cytosol and the sarcoplasmic reticulum on the formation of microscopic calcium alternans. We find that for dominant cytosolic coupling, calcium alternans emerge via the traditional period doubling bifurcation. In contrast, dominant luminal coupling leads to a novel route to calcium alternans through a saddle-node bifurcation at the network level. Combining semi-analytical and computational approaches, we compute areas of stability in parameter space and find that as we cross from stable to unstable regions, the emergent patterns of the intracellular calcium concentration change abruptly in a fashion that is highly dependent upon position along the stability boundary. Our results demonstrate that microscopic calcium alternans may possess a much richer dynamical repertoire than previously thought and further strengthen the role of luminal calcium in shaping cardiac calcium dynamics.

Computational geometry for modeling neural populations: From visualization to simulation.

The importance of a mesoscopic description level of the brain has now been well established. Rate based models are widely used, but have limitations. Recently, several extremely efficient population-level methods have been proposed that go beyond the characterization of a population in terms of a single variable. Here, we present a method for simulating neural populations based on two dimensional (2D) point spiking neuron models that defines the state of the population in terms of a density function over the neural state space. Our method differs in that we do not make the diffusion approximation, nor do we reduce the state space to a single dimension (1D). We do not hard code the neural model, but read in a grid describing its state space in the relevant simulation region. Novel models can be studied without even recompiling the code. The method is highly modular: variations of the deterministic neural dynamics and the stochastic process can be investigated independently. Currently, there is a trend to reduce complex high dimensional neuron models to 2D ones as they offer a rich dynamical repertoire that is not available in 1D, such as limit cycles. We will demonstrate that our method is ideally suited to investigate noise in such systems, replicating results obtained in the diffusion limit and generalizing them to a regime of large jumps. The joint probability density function is much more informative than 1D marginals, and we will argue that the study of 2D systems subject to noise is important complementary to 1D systems.

Population density equations for stochastic processes with memory kernels.

We present a method for solving population density equations (PDEs)--a mean-field technique describing homogeneous populations of uncoupled neurons-where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different disciplines that traditionally have had limited interaction: computational neuroscience and the theory of random networks. The method uses a geometric binning scheme, based on the method of characteristics, to capture the deterministic neurodynamics of the population, separating the deterministic and stochastic process cleanly. We can independently vary the choice of the deterministic model and the model for the stochastic process, leading to a highly modular numerical solution strategy. We demonstrate this by replacing the master equation implicit in many formulations of the PDE formalism by a generalization called the generalized Montroll-Weiss equation-a recent result from random network theory-describing a random walker subject to transitions realized by a non-Markovian process. We demonstrate the method for leaky- and quadratic-integrate and fire neurons subject to spike trains with Poisson and gamma-distributed interspike intervals. We are able to model jump responses for both models accurately to both excitatory and inhibitory input under the assumption that all inputs are generated by one renewal process.

Noise-induced synchronization, desynchronization, and clustering in globally coupled nonidentical oscillators.

We study ensembles of globally coupled, nonidentical phase oscillators subject to correlated noise, and we identify several important factors that cause noise and coupling to synchronize or desynchronize a system. By introducing noise in various ways, we find an estimate for the onset of synchrony of a system in terms of the coupling strength, noise strength, and width of the frequency distribution of its natural oscillations. We also demonstrate that noise alone can be sufficient to synchronize nonidentical oscillators. However, this synchrony depends on the first Fourier mode of a phase-sensitivity function, through which we introduce common noise into the system. We show that higher Fourier modes can cause desynchronization due to clustering effects, and that this can reinforce clustering caused by different forms of coupling. Finally, we discuss the effects of noise on an ensemble in which antiferromagnetic coupling causes oscillators to form two clusters in the absence of noise.

Dispersal and noise: various modes of synchrony in ecological oscillators.

We use the theory of noise-induced phase synchronization to analyze the effects of dispersal on the synchronization of a pair of predator-prey systems within a fluctuating environment (Moran effect). Assuming that each isolated local population acts as a limit cycle oscillator in the deterministic limit, we use phase reduction and averaging methods to derive a Fokker-Planck equation describing the evolution of the probability density for pairwise phase differences between the oscillators. In the case of common environmental noise, the oscillators ultimately synchronize. However the approach to synchrony depends on whether or not dispersal in the absence of noise supports any stable asynchronous states. We also show how the combination of partially correlated noise with dispersal can lead to a multistable steady-state probability density.

Effects of demographic noise on the synchronization of a metapopulation in a fluctuating environment.

We use the theory of noise-induced phase synchronization to analyze the effects of demographic noise on the synchronization of a metapopulation of predator-prey systems within a fluctuating environment (Moran effect). Treating each local predator-prey population as a stochastic urn model, we derive a Langevin equation for the stochastic dynamics of the metapopulation. Assuming each local population acts as a limit cycle oscillator in the deterministic limit, we use phase reduction and averaging methods to derive the steady-state probability density for pairwise phase differences between oscillators, which is then used to determine the degree of synchronization of the metapopulation.

Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise.

We extend the theory of noise-induced phase synchronization to the case of a neural master equation describing the stochastic dynamics of an ensemble of uncoupled neuronal population oscillators with intrinsic and extrinsic noise. The master equation formulation of stochastic neurodynamics represents the state of each population by the number of currently active neurons, and the state transitions are chosen so that deterministic Wilson-Cowan rate equations are recovered in the mean-field limit. We apply phase reduction and averaging methods to a corresponding Langevin approximation of the master equation in order to determine how intrinsic noise disrupts synchronization of the population oscillators driven by a common extrinsic noise source. We illustrate our analysis by considering one of the simplest networks known to generate limit cycle oscillations at the population level, namely, a pair of mutually coupled excitatory (E) and inhibitory (I) subpopulations. We show how the combination of intrinsic independent noise and extrinsic common noise can lead to clustering of the population oscillators due to the multiplicative nature of both noise sources under the Langevin approximation. Finally, we show how a similar analysis can be carried out for another simple population model that exhibits limit cycle oscillations in the deterministic limit, namely, a recurrent excitatory network with synaptic depression; inclusion of synaptic depression into the neural master equation now generates a stochastic hybrid system.

Nonlinear waves in disordered diatomic granular chains.

We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin," so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: in low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatiotemporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for a transition between the two regimes. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves.