D Yu

Characterizing nonlinearity in ventricular fibrillation

The authors apply techniques from nonlinear dynamical systems theory to determine whether Ventricular Fibrillation (VF) comes from a stochastic, or a more complex nonlinear process. Using electrocardiographic (ECG) data from seven pigs during ventricular fibrillation the authors apply various surrogate data techniques to test the observed data against a series of hypotheses. Standard linear surrogate techniques demonstrate that VF is inconsistent with data generated by a monotonic nonlinear transformation of a linearly filtered noise source. Nonlinear modeling methods show that VF is consistent with the output of a system exhibiting a stable periodic orbit and small scale high dimensional structure (either noise or chaos).

Linear and nonlinear characteristics of ECG signals produced by simulations of ventricular tachyarrhythmias

The aim of this study was to compare pseudo-ECGs produced by different configurations of re-entry in a computational model. We initiated single, double and multiple re-entrant waves in a cuboid with Fitz-Hugh Nagumo excitability. We estimated one component of the pseudo-ECG, and applied linear time-frequency and nonlinear dimensional analysis. The pseudo-ECG produced by a single re-entrant wave was periodic, whereas that produced by a double re-entrant wave was quasiperiodic with slow changes in both frequency content and amplitude. The dimension of these time series was around 1 and 3 respectively. The time-frequency distribution of the pseudo-ECG produced by multiple re-entrant waves was more complex with rapid changes in frequency and amplitude, and the dimension of the pseudo-ECG time series was around 4. Thus different configurations of re-entrant wave are associated with qualitatively and quantitatively different pseudo-ECG time series.

Nonlinear analysis of human ECG during sinus rhythm and arrhythmia

Using a new data collection facility we have recorded spontaneous episodes of VF (and other arrhythmia) in human subjects. We apply correlation dimension analysis and linear and nonlinear surrogate techniques to these data sets. We conclude that human VF is distinct from linearly filtered noise, but not distinct from a noise driven nonlinear system. The correlation dimension estimate from spontaneous VF is between 5 and 8. Furthermore, we show that the temporal complexity (dimensionality) during VF is higher than that observed during VT (4-5) and that during sinus rhythm (3-4). Finally, the characteristic shape of dimension curves obtained during sinus rhythm and arrhythmia are clearly distinct. These results are consistent with those obtained from animal experiments and with computational simulations of spiral wave break-up.

Pattern formation in a laser system: spontaneous and hard excitation phenomena

We present a study on pattern formation in an optically pumped three-level laser system. In a pump parameter region below the pattern-forming bifurca-tion, the system admits travelling solitary pulse solutions in one-dimensional space and rotating spiral waves in two-dimensional space under hard excitations. The pattern forming process and geometry are analysed and numerically simulated, the two showing a good qualitative agreement. When the control parameters are set beyond the bifurcation point, spontaneous emergence of spatiotemporal patterns is observed from an initially uniform background, evolving to rolls, dislocations and turbulence through a defect-mediated turbulence scenario.