Kei-Ichi Ueda

Dynamics of traveling pulses in heterogeneous media.

One of the fundamental issues of pulse dynamics in dissipative systems is clarifying how the heterogeneity in the media influences the propagating manner. Heterogeneity is the most important and ubiquitous type of external perturbation. We focus on a class of one-dimensional traveling pulses, the associated parameters of which are close to drift and/or saddle-node bifurcations. The advantage in studying the dynamics in such a class is twofold: First, it gives us a perfect microcosm for the variety of outputs in a general setting when pulses encounter heterogeneities. Second, it allows us to reduce the original partial differential equation dynamics to a tractable finite-dimensional system. Such pulses are sensitive when they run into heterogeneities and show rich responses such as annihilation, pinning, splitting, rebound, as well as penetration. The reduced ordinary differential equations (ODEs) explain all these dynamics and the underlying bifurcational structure controlling the transitions among different dynamic regimes. It turns out that there are hidden ordered patterns associated with the critical points of ODEs that play a pivotal role in understanding the responses of the pulse; in fact, the depinning of pulses can be explained in terms of global bifurcations among those critical points. We focus mainly on a bump and periodic types of heterogeneity, however our approach is also applicable to general cases. It should be noted that there appears to be spatio-temporal chaos for a periodic type of heterogeneity when its period becomes comparable with the size of the pulse.

Arterial ketone body ratio as a prognostic indicator in acute heart failure.

The arterial ketone body ratio (AKBR), an established clinical tool that reflects hepatic mitochondrial oxidation-reduction potential, predicts the outcome of patients with shock and multiple organ failure and the postoperative outcome in patients who have undergone major liver or heart surgery. The purpose of this study was to determine the prognostic significance of AKBR in patients with acute heart failure. The subjects of this study were 52 patients with acute heart failure. The following parameters were analyzed after Cox univariate hazard analysis was performed: AKBR, plasma norepinephrine, left ventricular ejection fraction, cardiac index, pulmonary arterial wedge pressure, sex, age, human atrial natriuretic peptide, endothelin-1, and cholesterol. The follow-up period was 30 weeks with cardiac death as the end point. Stepwise multivariate proportional hazard analysis revealed that AKBR was the most significant predictor of death, followed by norepinephrine and human atrial natriuretic peptide. Curve-fitting analysis revealed that the relationship between log (norepinephrine) and AKBR could best be described by two distinct lines, with their intersection at AKBR = 0.7 and norepinephrine = 418. With these results we conducted Kaplan-Meier analysis for AKBR > or = 0.7 and AKBR <0.7. The survival rate in patients with AKBR > or = 0.7 was 100%, whereas that in patients with AKBR <0.7 was 15% (p < 0.0001, log-rank analysis). These results indicate that AKBR is a novel independent predictor of death in heart failure.

Breathing Scattors in Dissipative Systems

Scattering process between traveling breathers (TBs) is studied for the complex Ginzburg-Landau equations (CGLE) with a parametric forcing term. The phase-dependency of the input-output relation can be explained from the scattors viewpoint. In this note, we especially focus on the issue for the asymmetric head-on collisions, i.e., the phases of two colliding TBs are different.

Information Exchange between Moving Particles and Defects

Pulse wave is one of the main careers of information and the effect of heterogeneity of the media in which it propagates is of great importance for the understanding of signaling processes in biological and chemical systems. A typical one dimensional heterogeneity is a spatially localized bump or dent, which creates associated defects in the media. To know the behaviors of pulse in such media is equivalent to study the collision process between the pulse and the defect. A variety of outputs are observed depending on the height and width of the bump such as rebound, pinning, oscillatory motion as well as penetration. A remarkable thing is that PDE dynamics can be reduced to finite dimensional one near a drift bifurcation and the defects become equilibrium points of the reduced ODEs. The basin of each equilibrium point and the switching among those basins explain all the outputs after collision with the defects. We employ a three-component reaction-diffusion system of one-activator-two-inhibitor type to illustrate these issues.