Nonlinear dynamics of two-dimensional cardiac action potential duration mapping model with memory.

The aim of this work is the analysis of the nonlinear dynamics of two-dimensional mapping model of cardiac action potential duration (2D-map APD) with memory derived from one dimensional map (1D-map). Action potential duration (APD) restitution, which relates APD to the preceding diastolic interval (DI), is a useful tool for predicting cardiac arrhythmias. For a constant rate of stimulation the short action potential during alternans is followed by a longer DI and inversely. It has been suggested that these differences in DI are responsible for the occurrence and maintenance of APD alternans. We focus our attention on the observed bifurcations produced by a change in the stimulation period and a fixed value of a particular parameter in the model. This parameter provides new information about the dynamics of the APD with memory, such as the occurrence of bistabilities not previously described in the literature, as well as the fact that synchronization rhythms occur in different ways and in a new fashion as the stimulation frequency increases. Moreover, we show that this model is flexible enough as to accurately reflect the chaotic dynamics properties of the APD: we have highlighted the fractal structure of the strange attractor of the 2D-map APD, and we have characterized chaos by tools such as the calculation of the Lyapunov exponents, the fractal dimension and the Kolmogorov entropy, with the next objective of refining the study of the nonlinear dynamics of the duration of the action potential and to apply methods of controlling chaos.

Parameters analysis of FitzHugh-Nagumo model for a reliable simulation.

Derived from the pioneer ionic Hodgkin-Huxley model and due to its simplicity and richness from a point view of nonlinear dynamics, the FitzHugh-Nagumo model (FHN) is one of the most successful simplified neuron / cardiac cell model. There exist many variations of the original FHN model. Though these FHN type models help to enrich the dynamics of the FHN model, the parameters used in these models are often in biased conditions. The related results would be questionable. So, in this study, the aim is to find the parameter thresholds for one of the commonly used FHN model in order to provide a better simulation environment. The results showed at first that inappropriate time step and integration tolerance in numerical solution of FHN model can give some biased results which would make some publications questionable. Then the thresholds of parameters α, γ and ε are presented. α controls the global dynamics of FHN. α > 0, the cell is in refractory mode; α <; 0, the cell is excitable. ε controls the main morphology of the action potential generated and has a relation with the period (P = 3.065 × αα,γ(-0.8275)+ 4.397). To show oscillations of relaxation with FHN, ε should be smaller than 0.0085. 7 influences barely action potential, it showed linear relationship with the period and duration of action potential. Even though α <; 0.1, ε <; 0.0085, there is no definite threshold for γ, smaller values are recommended.

A mixed FES/EMG system for real time analysis of muscular fatigue.

In this article, we present a functional electrical stimulator allowing the extraction in real time of M-wave characteristics from resulting EMG recodings in order to quantify muscle fatigue. This system is composed of three parts. A Labview software managing the stimulation output and electromyogram (EMG) input signal, a hardware part amplifying the output and input signal and a link between the two previous parts which is made up from input/output module (NIdaq USB 6251). In order to characterize the fatigue level, the Continuous Wavelet Transform is applied yielding a local maxima detection. The fatigue is represented on a scale from 0 for a fine shaped muscle to 100 for a very tired muscle. Premilary results are given.

Spiking dynamics of interacting oscillatory neurons.

Spiking sequences emerging from dynamical interaction in a pair of oscillatory neurons are investigated theoretically and experimentally. The model comprises two unidirectionally coupled FitzHugh-Nagumo units with modified excitability (MFHN). The first (master) unit exhibits a periodic spike sequence with a certain frequency. The second (slave) unit is in its excitable mode and responds on the input signal with a complex (chaotic) spike trains. We analyze the dynamic mechanisms underlying different response behavior depending on interaction strength. Spiking phase maps describing the response dynamics are obtained. Complex phase locking and chaotic sequences are investigated. We show how the response spike trains can be effectively controlled by the interaction parameter and discuss the problem of neuronal information encoding.