Riding a Spiral Wave: Numerical Simulation of Spiral Waves in a Co-Moving Frame of Reference

We describe an approach to numerical simulation of spiral waves dynamics of large spatial extent, using small computational grids.Comment: 15 pages, 14 figures, as accepted by Phys Rev E 2010/03/2

Dynamical mechanism of atrial fibrillation: a topological approach

While spiral wave breakup has been implicated in the emergence of atrial fibrillation, its role in maintaining this complex type of cardiac arrhythmia is less clear. We used the Karma model of cardiac excitation to investigate the dynamical mechanisms that sustain atrial fibrillation once it has been established. The results of our numerical study show that spatiotemporally chaotic dynamics in this regime can be described as a dynamical equilibrium between topologically distinct types of transitions that increase or decrease the number of wavelets, in general agreement with the multiple wavelets hypothesis. Surprisingly, we found that the process of continuous excitation waves breaking up into discontinuous pieces plays no role whatsoever in maintaining spatiotemporal complexity. Instead this complexity is maintained as a dynamical balance between wave coalescence -- a unique, previously unidentified, topological process that increases the number of wavelets -- and wave collapse -- a different topological process that decreases their number.Comment: 15 pages, 14 figure

Helicoidal instability of a scroll vortex in three-dimensional reaction-diffusion systems

We study the dynamics of scroll vortices in excitable reaction-diffusion systems analytically and numerically. We demonstrate that intrinsic three-dimensional instability of a straight scroll leads to the formation of helicoidal structures. This behavior originates from the competition between the scroll curvature and unstable core dynamics. We show that the obtained instability persists even beyond the meander core instability of two-dimensional spiral wave.Comment: 4 pages, 5 figures, revte

Сложность алгоритмов криптографической системы Эль–Гамаля и ихэффективность

Objective. - Electrical remodeling as well as atrial contractile dysfunction after the conversion of atrial fibrillation (AF) to sinus rhythm (SR) are mainly caused by a reduction of the inward L-type Ca2+ current (ICaL). We investigated whether the expression of L-type Ca2+-channel subunits was reduced in atrial myocardium of AF patients. Methods. - Right atrial appendages were obtained from patients undergoing coronary artery bypass graft surgery (CAD, n = 35) or mitral valve surgery (MVD, n = 37). Seventeen of the CAD patients and 18 of the MVD patients were in chronic (>3 months) AF, whereas the others were in SR. The protein expression of the L-type Ca2+-channel subunits {alpha}1C and {beta}2 was quantified by western blot analysis. Furthermore, we measured the density of dihydropyridine (DHP)-binding sites of the L-type Ca2+ channel using 3H-PN220-100 as radioligand. Results. - Surprisingly, the {alpha}1C and the {beta}2-subunit expression was not altered in atrial myocardium of AF patients. Also, the DHP-binding site density was unchanged. Conclusion. - The protein expression of the L-type Ca2+-channel subunits {alpha}1C or {beta}2 is not reduced in atrial myocardium of AF patients. Therefore, the reduced ICaL might be due to downregulation of other accessory subunits ({alpha}2{delta}), expression of aberrant subunits, changes in channel trafficking or alterations in channel function

Electrophysiological characteristics of permanent atrial fibrillation: insights from research models of cardiac remodeling

[EN] Atrial fibrillation (AF) results in a remodeling of the electrical and structural characteristics of the cardiac tissue which dramatically reduces the efficacy of pharmacological and catheter-based ablation therapies. Recent experimental and clinical results have demonstrated that the complexity of the fibrillatory process significantly differs in paroxysmal versus persistent AF; however, the lack of appropriate research models of remodeled atrial tissue precludes the elucidation of the underlying AF mechanisms and the identification of appropriated therapeutic targets. Here, we summarize the different research models used to date, highlighting the lessons learned from them and pointing to the new doors that should be open for the development of innovative treatments for AF.The authors were supported by grants from the Spanish Ministry of Science and Innovation (PLE2009-0152), the Instituto de Salud Carlos III (Ministry of Economy and Competitiveness, Spain: PI13-01882 and PI13-00903) the Red de Investigacion Cardiovacular (RIC) from Instituto de Salud Carlos III (Ministry of Economy and Competitiveness, Spain). F Atienza served on the advisory board of Medtronic and has received research funding from St. Jude Medical Spain. The authors have no other relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript apart from those disclosed.Climent, A.; Guillem Sánchez, MS.; Atienza Fernández, F.; Fernandez-Aviles, F. (2014). Electrophysiological characteristics of permanent atrial fibrillation: insights from research models of cardiac remodeling. Expert Review of Cardiovascular Therapy. 13(1):1-3. https://doi.org/10.1586/14779072.2015.986465S1313