Analysis of cardiac signals using spatial filling index and time-frequency domain

BACKGROUND: Analysis of heart rate variation (HRV) has become a popular noninvasive tool for assessing the activities of the autonomic nervous system (ANS). HRV analysis is based on the concept that fast fluctuations may specifically reflect changes of sympathetic and vagal activity. It shows that the structure generating the signal is not simply linear, but also involves nonlinear contributions. These signals are essentially non-stationary; may contain indicators of current disease, or even warnings about impending diseases. The indicators may be present at all times or may occur at random in the time scale. However, to study and pinpoint abnormalities in voluminous data collected over several hours is strenuous and time consuming. METHODS: This paper presents the spatial filling index and time-frequency analysis of heart rate variability signal for disease identification. Renyi's entropy is evaluated for the signal in the Wigner-Ville and Continuous Wavelet Transformation (CWT) domain. RESULTS: This Renyi's entropy gives lower 'p' value for scalogram than Wigner-Ville distribution and also, the contours of scalogram visually show the features of the diseases. And in the time-frequency analysis, the Renyi's entropy gives better result for scalogram than the Wigner-Ville distribution. CONCLUSION: Spatial filling index and Renyi's entropy has distinct regions for various diseases with an accuracy of more than 95%

History-Dependent Excitability as a Single-Cell Substrate of Transient Memory for Information Discrimination

Neurons react differently to incoming stimuli depending upon their previous history of stimulation. This property can be considered as a single-cell substrate for transient memory, or context-dependent information processing: depending upon the current context that the neuron “sees” through the subset of the network impinging on it in the immediate past, the same synaptic event can evoke a postsynaptic spike or just a subthreshold depolarization. We propose a formal definition of History-Dependent Excitability (HDE) as a measure of the propensity to firing in any moment in time, linking the subthreshold history-dependent dynamics with spike generation. This definition allows the quantitative assessment of the intrinsic memory for different single-neuron dynamics and input statistics. We illustrate the concept of HDE by considering two general dynamical mechanisms: the passive behavior of an Integrate and Fire (IF) neuron, and the inductive behavior of a Generalized Integrate and Fire (GIF) neuron with subthreshold damped oscillations. This framework allows us to characterize the sensitivity of different model neurons to the detailed temporal structure of incoming stimuli. While a neuron with intrinsic oscillations discriminates equally well between input trains with the same or different frequency, a passive neuron discriminates better between inputs with different frequencies. This suggests that passive neurons are better suited to rate-based computation, while neurons with subthreshold oscillations are advantageous in a temporal coding scheme. We also address the influence of intrinsic properties in single-cell processing as a function of input statistics, and show that intrinsic oscillations enhance discrimination sensitivity at high input rates. Finally, we discuss how the recognition of these cell-specific discrimination properties might further our understanding of neuronal network computations and their relationships to the distribution and functional connectivity of different neuronal types

Calcium control of triphasic hippocampal STDP

Bush D, Jin Y. Calcium control of triphasic hippocampal STDP. Journal of Computational Neuroscience. 2012;33(3):495-514.Synaptic plasticity is believed to represent the neural correlate of mammalian learning and memory function. It has been demonstrated that changes in synaptic conductance can be induced by approximately synchronous pairings of pre- and post- synaptic action potentials delivered at low frequencies. It has also been established that NMDAr-dependent calcium influx into dendritic spines represents a critical signal for plasticity induction, and can account for this spike-timing dependent plasticity (STDP) as well as experimental data obtained using other stimulation protocols. However, subsequent empirical studies have delineated a more complex relationship between spike-timing, firing rate, stimulus duration and post-synaptic bursting in dictating changes in the conductance of hippocampal excitatory synapses. Here, we present a detailed biophysical model of single dendritic spines on a CA1 pyramidal neuron, describe the NMDAr-dependent calcium influx generated by different stimulation protocols, and construct a parsimonious model of calcium driven kinase and phosphatase dynamics that dictate the probability of stochastic transitions between binary synaptic weight states in a Markov model. We subsequently demonstrate that this approach can account for a range of empirical observations regarding the dynamics of synaptic plasticity induced by different stimulation protocols, under regimes of pharmacological blockade and metaplasticity. Finally, we highlight the strengths and weaknesses of this parsimonious, unified computational synaptic plasticity model, discuss differences between the properties of cortical and hippocampal plasticity highlighted by the experimental literature, and the manner in which further empirical and theoretical research might elucidate the cellular basis of mammalian learning and memory function

Nonlinear Dynamics Simulations of Microbial Ecological Processes: Model, Diagnostic Parameters of Deterministic Chaos, and Sensitivity Analysis

Modeling of ecological processes is demonstrated using a newly developed nonlinear dynamics model of microbial populations, consisting of a 4-variable system of coupled ordinary differential equations. The system also includes a modified version of the Monod kinetics equation. The model is designed to simulate the temporal behavior of a microbiological system containing a nutrient, two feeding microbes and a microbe predator. Three types of modeling scenarios were numerically simulated to assess the instability caused by (a) variations of the nutrient flux into the system, with fixed initial microbial concentrations and parameters, (b) variations in initial conditions, with fixed other parameters, and (c) variations in selected parameters. A modeling framework, using the high-level statistical computing languages MATLAB and R, was developed to conduct the time series analysis in the time domain and phase space. In the time domain, the Hurst exponent, the information measure–Shannon’s entropy, and the time delay of temporal oscillations of nutrient and microbe concentrations were calculated. In the phase domain, we calculated a set of diagnostic criteria of deterministic chaos: global and local embedding dimensions, correlation dimension, information dimension, and a spectrum of Lyapunov exponents. The time series data are used to plot the phase space attractors to express the dependence between the system’s state parameters, i.e., microbe concentrations, and pseudo-phase space attractors, in which the attractor axes are used to compare the observations from a single time series, which are separated by the time delay. Like classical Lorenz or Rossler systems of equations, which generate a deterministic chaotic behavior for a certain range of input parameters, the developed mathematical model generates a deterministic chaotic behavior for a particular set of input parameters. Even a slight variation of the system’s input data might result in vastly different predictions of the temporal oscillations of the system. As the nutrient influx increases, the system exhibits a sharp transition from a steady state to deterministic chaotic to quasi-periodic and again to steady state behavior. For small changes in initial conditions, resulting attractors are bounded (contrary to that of a random system), i.e., may represent a ‘sustainable state’ (i.e., resilience) of the ecological system

Controlling chemical chaos in the Belousov-Zhabotinsky oscillator

Chaos is ubiquitous in Nature and represents one of the most fascinating expressions of real world complexity. Depending on the specific context, the onset of chaotic behaviours can be undesirable, thus, controlling the mechanisms at the basis of chaotic dynamics represents a cutting-edge challenge in many areas, including cardiology, information processing, hydrodynamics and optics, to name a few. In this work we review our recent results showing how, in chemical reactions, the active interplay between a nonlinear kinetics and hydrodynamic instabilities can be exploited as a general mechanism to induce and control chemical chaos. To this end, we consider as a model system the Belousov-Zhabotinsky (BZ) reaction. Thanks to a chemo-hydrodynamic coupling, the reaction can undergo chaotic oscillations when carried out in batch conditions. Chaos appears and disappears by following Ruelle-Takens-Newhouse scenario both in the cerium- and ferroin-catalyzed BZ systems. Here, we present experimental evidence that the transition to chemical chaos can be directly controlled by tuning either kinetic or hydrodynamic parameters of the system. Experiments were simulated by using a reaction-diffusion-convection (RDC) model where the nonlinear reaction kinetics are coupled to the Navier-Stokes equations. Numerical solutions of the RDC model clearly indicate that natural convection can feedback on the spatio-temporal evolution of the concentration fields and, in turn, changes bulk oscillation patterns. Distinct bifurcations in the oscillation patterns are found when the Grashof numbers (governing the entity of convective flows into the system) and the diffusion coefficients of the chemical species are varied. The consumption of the initial reagents is also found to be a critical phenomenon able to modulate the strength of the RDC coupling and drive order-disorder transitions