Representation of time-varying nonlinear systems with time-varying principal dynamic modes

The futility of long-term predictions in bipolar disorder: mood fluctuations are the result of deterministic chaotic processes

BACKGROUND

Understanding the underlying architecture of mood regulation in bipolar disorder (BD) is important, as we are starting to conceptualize BD as a more complex disorder than one of recurring manic or depressive episodes. Nonlinear techniques are employed to understand and model the behavior of complex systems. Our aim was to assess the underlying nonlinear properties that account for mood and energy fluctuations in patients with BD; and to compare whether these processes were different in healthy controls (HC) and unaffected first-degree relatives (FDR). We used three different nonlinear techniques: Lyapunov exponent, detrended fluctuation analysis and fractal dimension to assess the underlying behavior of mood and energy fluctuations in all groups; and subsequently to assess whether these arise from different processes in each of these groups.

RESULTS

There was a positive, short-term autocorrelation for both mood and energy series in all three groups. In the mood series, the largest Lyapunov exponent was found in HC (1.84), compared to BD (1.63) and FDR (1.71) groups [F (2, 87) = 8.42, p < 0.005]. A post-hoc Tukey test showed that Lyapunov exponent in HC was significantly higher than both the BD (p = 0.003) and FDR groups (p = 0.03). Similarly, in the energy series, the largest Lyapunov exponent was found in HC (1.85), compared to BD (1.76) and FDR (1.67) [F (2, 87) = 11.02; p < 0.005]. There were no significant differences between groups for the detrended fluctuation analysis or fractal dimension.

CONCLUSIONS

The underlying nature of mood variability is in keeping with that of a chaotic system, which means that fluctuations are generated by deterministic nonlinear process(es) in HC, BD, and FDR. The value of this complex modeling lies in analyzing the nature of the processes involved in mood regulation. It also suggests that the window for episode prediction in BD will be inevitably short.

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 certain 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.

From Anxious to Reckless: A Control Systems Approach Unifies Prefrontal-Limbic Regulation Across the Spectrum of Threat Detection

Here we provide an integrative review of basic control circuits, and introduce techniques by which their regulation can be quantitatively measured using human neuroimaging. We illustrate the utility of the control systems approach using four human neuroimaging threat detection studies (N = 226), to which we applied circuit-wide analyses in order to identify the key mechanism underlying individual variation. In so doing, we build upon the canonical prefrontal-limbic control system to integrate circuit-wide influence from the inferior frontal gyrus (IFG). These were incorporated into a computational control systems model constrained by neuroanatomy and designed to replicate our experimental data. In this model, the IFG acts as an informational set point, gating signals between the primary prefrontal-limbic negative feedback loop and its cortical information-gathering loop. Along the cortical route, if the sensory cortex provides sufficient information to make a threat assessment, the signal passes to the ventromedial prefrontal cortex (vmPFC), whose threat-detection threshold subsequently modulates amygdala outputs. However, if signal outputs from the sensory cortex do not provide sufficient information during the first pass, the signal loops back to the sensory cortex, with each cycle providing increasingly fine-grained processing of sensory data. Simulations replicate IFG (chaotic) dynamics experimentally observed at both ends at the threat-detection spectrum. As such, they identify distinct types of IFG disconnection from the circuit, with associated clinical outcomes. If IFG thresholds are too high, the IFG and sensory cortex cycle for too long; in the meantime the coarse-grained (excitatory) pathway will dominate, biasing ambiguous stimuli as false positives. On the other hand, if cortical IFG thresholds are too low, the inhibitory pathway will suppress the amygdala without cycling back to the sensory cortex for much-needed fine-grained sensory cortical data, biasing ambiguous stimuli as false negatives. Thus, the control systems model provides a consistent mechanism for IFG regulation, capable of producing results consistent with our data for the full spectrum of threat-detection: from fearful to optimal to reckless. More generally, it illustrates how quantitative characterization of circuit dynamics can be used to unify a fundamental dimension across psychiatric affective symptoms, with implications for populations that range from anxiety disorders to addiction.

The autonomic effects of cardiopulmonary decompression sickness in swine using principal dynamic mode analysis

Methods to predict onset of cardiopulmonary (CP) decompression sickness (DCS) would be of great benefit to clinicians caring for stricken divers. Principal dynamic mode (PDM) analysis of the electrocardiogram has been shown to provide accurate separation of the sympathetic and parasympathetic tone dynamics. Nine swine (Sus scrofa) underwent a 15-h saturation dive at 184 kPa (60 ft. of saltwater) in a hyperbaric chamber followed by dropout decompression, whereas six swine, used as a control, underwent a 15-h saturation dive at 15 kPa (5 ft. of saltwater). Noninvasive electrocardiograms were recorded throughout the experiment and autonomic nervous system dynamics were evaluated by heart rate series analysis using power spectral density (PSD) and PDM methods. We observed a significant increase in the sympathetic and parasympathetic tones using the PDM method on average 20 min before DCS onset following a sudden induction of decompression. Parasympathetic activities remained elevated, but the sympathetic modulation was significantly reduced at onset of cutis and CP DCS signs, as reported by a trained observer. Similar nonsignificant observations occurred during PSD analysis. PDM observations contrast with previous work showing that neurological DCS resulted in a >50% reduction in both sympathetic and parasympathetic tone. Therefore, tracking dynamics of the parasympathetic tones via the PDM method may allow discrimination between CP DCS and neurological DCS, and this significant increase in parasympathetic tone has potential use as a marker for early diagnosis of CP DCS.

Online modeling with tunable RBF network

In this paper, we propose a novel online modeling algorithm for nonlinear and nonstationary systems using a radial basis function (RBF) neural network with a fixed number of hidden nodes. Each of the RBF basis functions has a tunable center vector and an adjustable diagonal covariance matrix. A multi-innovation recursive least square (MRLS) algorithm is applied to update the weights of RBF online, while the modeling performance is monitored. When the modeling residual of the RBF network becomes large in spite of the weight adaptation, a node identified as insignificant is replaced with a new node, for which the tunable center vector and diagonal covariance matrix are optimized using the quantum particle swarm optimization (QPSO) algorithm. The major contribution is to combine the MRLS weight adaptation and QPSO node structure optimization in an innovative way so that it can track well the local characteristic in the nonstationary system with a very sparse model. Simulation results show that the proposed algorithm has significantly better performance than existing approaches.

Spectral analysis for nonstationary and nonlinear systems: a discrete-time-model-based approach

A new frequency-domain analysis framework for nonlinear time-varying systems is introduced based on parametric time-varying nonlinear autoregressive with exogenous input models. It is shown how the time-varying effects can be mapped to the generalized frequency response functions (FRFs) to track nonlinear features in frequency, such as intermodulation and energy transfer effects. A new mapping to the nonlinear output FRF is also introduced. A simulated example and the application to intracranial electroencephalogram data are used to illustrate the theoretical results.

Tracking temporal evolution of nonlinear dynamics in hippocampus using time-varying volterra kernels

Hippocampus and other parts of the cortex are not stationary, but change as a function of time and experience. The goal of this study is to apply adaptive modeling techniques to the tracking of multiple-input, multiple-output (MIMO) nonlinear dynamics underlying spike train transformations across brain subregions, e.g. CA3 and CA1 of the hippocampus. A stochastic state point process adaptive filter will be used to track the temporal evolutions of both feedforward and feedback kernels in the natural flow of multiple behavioral events.

Nonstationary modeling of neural population dynamics

A stochastic state point-process adaptive filter was used to track the temporal evolution of several simulated nonlinear dynamical systems. The estimated Laguerre coefficients and Laguerre poles were used to reconstruct the feedforward and feedback kernels in the system. Simulations showed that the proposed method could track the actual underlying changes of nonlinear kernels using spike input and spike output information alone. The estimated models also converge quickly to the actual models after abrupt step changes in kernels. The proposed method can be used to track the functional input-output properties of neural systems as a result of learning, changes in context, aging or other factors in the natural flow of behavioral events.