Scroll waves in isotropic excitable media : linear instabilities, bifurcations and restabilized states

Scroll waves are three-dimensional analogs of spiral waves. The linear stability spectrum of untwisted and twisted scroll waves is computed for a two-variable reaction-diffusion model of an excitable medium. Different bands of modes are seen to be unstable in different regions of parameter space. The corresponding bifurcations and bifurcated states are characterized by performing direct numerical simulations. In addition, computations of the adjoint linear stability operator eigenmodes are also performed and serve to obtain a number of matrix elements characterizing the long-wavelength deformations of scroll waves.Comment: 30 pages 16 figures, submitted to Phys. Rev.

The use of embolic protection device in the stenting of brachiocephalic arteries

Objective — to optimize the results of endovascular treatment of stenotic pathology of brachiocephalic arteries. Materials and methods. The results of surgical treatment of 112 patients, among whom there were 79 (70.5 %) men and 33 (29.5 %) women aged from 28 to 86 years with symptomatic stenotic lesions of brachiocephalic arteries treated in the neurosurgical department of the Zaporizhzhia regional hospital in the period from 2010 to 2018 were analyzed. Observations were divided into three groups depending on the localization of the defeat: internal carotid artery — 74 (66 %) cases (predominant stenosis of the mouth of the ICA (n = 71)), vertebral artery — 25 (22.4 %), a portion of the subclavian artery or brachiocephalic trunk — 13 (11.6 %). All patients underwent MRI of the brain in the preoperative period, as well as in 45 (40 %) cases of CTangiography. In all cases prior to surgery invasive angiography was performed with an assessment of the state and anatomy of the brachiocephalic and intracranial arteries, as well as the possibilities of collateral blood flow. Results. In the first group, which was conducted carotid stenting embolic protection device was used in 72 (97.2 %) cases. In the second group, distal protection device were used twice 2 (8 %) in the resolution of extended stenoses of the dominant vertebral artery mouth. In the third group, the distal protection device was used in 1 (7.7 %) case for stenting the critical extended stenosis of the brachiocephalic trunk with the transition to common carotid artery. Complications were noted in 9 observations. In one case there was a development of ischemic stroke, intraoperatively, in a patient with an echeloned lesion of the intracranial basin of a stenting internal carotid artery, probably against a background of hypotension of the stent developed during implantation. In 8 (7.1 %) cases the formation of the hematoma of the puncture site of the femoral artery was noted. Conclusions. The use of embolic protection device is mandatory in standard carotid stenting. The choice of method of protection depends on the severity of stenosis, as well as the individual features of collateral blood flow. When stenting subclavian artery, brachiocephalic trunk and vertebral artery, in some cases it is justified to use distal protection devices, the latter increases the safety of the operation

Lifetime enhancement of scroll rings by spatiotemporal fluctuations

The dynamics of three-dimensional scroll rings with spatiotemporal random excitability is investigated numerically using the FitzHugh-Nagumo model. Depending on the correlation time and length scales of the fluctuations, the lifetime of the ring filament is enlarged and a resonance effect between the time scale of the scroll ring and the time correlation of the noise is observed. Numerical results are interpreted in terms of a simplified stochastic model derived from the kinematical equations for three-dimensional excitable waves

Lifetime enhancement of scroll rings by spatiotemporal fluctuations

The dynamics of three-dimensional scroll rings with spatiotemporal random excitability is investigated numerically using the FitzHugh-Nagumo model. Depending on the correlation time and length scales of the fluctuations, the lifetime of the ring filament is enlarged and a resonance effect between the time scale of the scroll ring and the time correlation of the noise is observed. Numerical results are interpreted in terms of a simplified stochastic model derived from the kinematical equations for three-dimensional excitable waves