Biomedical subjects

Blas Echebarria

Publications and source records attributed to Blas Echebarria.

4 recordsLinked to original sources

PubMed2006

Nonequilibrium ribbon model of twisted scroll waves.

We formulate a reduced model to analyze the motion of the core of a twisted scroll wave. The model is first shown to provide a simple description of the onset and nonlinear evolution of the helical state appearing in the sproing bifurcation of scroll waves. It then serves to examine the experimentally studied case of a medium with spatially varying excitability. The model shows the role of sproing in this more complex setting and highlights the differences between the convective and absolute sproing instabilities.

DNA↗

PubMed2004

Quantitative phase-field model of alloy solidification.

We present a detailed derivation and thin interface analysis of a phase-field model that can accurately simulate microstructural pattern formation for low-speed directional solidification of a dilute binary alloy. This advance with respect to previous phase-field models is achieved by the addition of a phenomenological "antitrapping" solute current in the mass conservation relation [Phys. Rev. Lett. 87, 115701 (2001)]]. This antitrapping current counterbalances the physical, albeit artificially large, solute trapping effect generated when a mesoscopic interface thickness is used to simulate the interface evolution on experimental length and time scales. Furthermore, it provides additional freedom in the model to suppress other spurious effects that scale with this thickness when the diffusivity is unequal in solid and liquid [SIAM J. Appl. Math. 59, 2086 (1999)]], which include surface diffusion and a curvature correction to the Stefan condition. This freedom can also be exploited to make the kinetic undercooling of the interface arbitrarily small even for mesoscopic values of both the interface thickness and the phase-field relaxation time, as for the solidification of pure melts [Phys. Rev. E 53, R3017 (1996)]]. The performance of the model is demonstrated by calculating accurately within a phase-field approach the Mullins-Sekerka stability spectrum of a planar interface and nonlinear cellular shapes for realistic alloy parameters and growth conditions.

Journal Article↗

PubMed2002

Instability and spatiotemporal dynamics of alternans in paced cardiac tissue.

We derive an equation that governs the spatiotemporal dynamics of small amplitude alternans in paced cardiac tissue. We show that a pattern-forming linear instability leads to the spontaneous formation of stationary or traveling waves whose nodes divide the tissue into regions with opposite phase of oscillation of action potential duration. This instability is important because it creates dynamically a heterogeneous electrical substrate for the formation of conduction blocks and the induction of fibrillation if the tissue size exceeds a fraction of the pattern wavelength. We derive an analytical expression for this wavelength as a function of three basic length scales related to dispersion and intercellular electrical coupling.

Action Potentials↗

PubMed2002

Spatiotemporal control of cardiac alternans.

Electrical alternans are believed to be linked to the onset of life-threatening ventricular arrhythmias and sudden cardiac death. Recent studies have shown that alternans can be suppressed temporally by dynamic feedback control of the pacing interval. Here we investigate theoretically whether control can suppress alternans both temporally and spatially in homogeneous tissue paced at a single site. We first carry out ionic model simulations in a one-dimensional cable geometry which show that control is only effective up to a maximum cable length that decreases sharply away from the alternans bifurcation point. We then explain this finding by a linear stability analysis of an amplitude equation that describes the spatiotemporal evolution of alternans. This analysis reveals that control failure above a critical cable length is caused by the formation of standing wave patterns of alternans that are eigenfunctions of a forced Helmholtz equation, and therefore remarkably analogous to sound harmonics in an open pipe. We discuss the implications of these results for using control to suppress alternans in the human ventricles as well as to probe fundamental aspects of alternans morphogenesis. (c) 2002 American Institute of Physics.

Journal Article↗