Нелинейные динамические модели и структурный анализ проводящей системы сердца : научное издание | Научно-инновационный портал СФУ

Нелинейные динамические модели и структурный анализ проводящей системы сердца : научное издание

Перевод названия: Nonlinear dynamic model and structural analysis of the cardiac conduction system

Тип публикации: статья из журнала

Год издания: 2012

Ключевые слова: автоволны, электрокардиосигнал, самоподобие, autowave, elektroсardiosignal, selforganization, pacemaker, conducting nervous system of the heart, nonlinear oscillators, soliton, fractal, scaling, пейсмейкер, проводящая нервная система сердца, нелинейные осцилляторы, солитон, фрактал, скейлинг

Аннотация: Для объяснения феноменов процессов, протекающих в биосистемах особенно актуален анализ их фрактальной структурной организации на основе автоволновых моделей. Interest in the problem of synchronization and rhythmogenesis in the sinus node has grown considerably in recent years, a large number of publications devoted to models of biological processes in a system of coupled nonlinear oscillators. Developed new mathematica models of electrical processes in the sinus node. However, these models do not explain how thousands of pacemaker cells synchronously through metabolism at the cellular level of tens of microns in size on the membrane thickness produce 8-10 nm potential in the tens of mV of cycling in the Hz range. In this sense, the theorem can clarify the Fermi – Pasta – Ulam (Theorem “return” or “cubic lattice” FPU) if we consider the automaticity of the pacemaker-based models of self-organizing ensemble of P-cells in the oscillatory regime, as a system connected by extracellular (interstitial) liquid nonlinear oscillators. The model of the pacemaker according to FPU-theorem presented in the form of cluster synchronization in a chain of self-oscillating elements “of a cubic lattice”. Theorem “return” FPU shows that any perturbation of the coupled system transformed into a set of self (self-similar) “allowed” states (modes) that determine the order of the system, generated a wave of excitement in the form of a soliton, the frequency is determined by the number of cell oscillators. Permanent pacemaker cells of chaotic oscillations is accompanied by a sequence of bifurcations of separatrices resulting in self-organization and development of fracrtal structures in the form of an n-dimensional torus, with a scale-invariant self-similarity, as the trajectory of the oscillators, according to a theorem of stability of the Kolmogorov-Arnold-Moser ratio of the frequencies which correspond to the Fibonacci series. In this capacity-building actions in pacemaker is due to the redistribution of energy in the spectrum of coupled oscillators in the side of the low-frequency modes as the number of oscillators. The structure of the nervous system can also be seen in the fractal structure of individual neurons in the structure of neural networks. The presence of dynamic chaos and 1/f-fluctuations in the data is determined by the morphological structure of th physiology of the nervous system of the heart in the form of a branching tree. Soliton excitation in the propagation of channel branching at each branch generates fluctuations in an inhomogeneous channel network, forming a range of ECS scaling with 1/f. The above model provides a basis to make axxumptions about the nature of the Pathology on the basis of spectral deviations from the law of 1/f. Pathology causing a local change in the spectral picture of ECS, which is observed on the verified records. Dips in the spectra of pacemaker patients with a diagnosis of “myocardial infarction” and diagnosed with “Block bundle-branch Gis” corresponds to the topology of neural networks.

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Издание

Журнал: Успехи современной радиоэлектроники

Выпуск журнала: 9

Номера страниц: 046-050

ISSN журнала: 20700784

Место издания: Москва

Издатель: Закрытое акционерное общество Издательство Радиотехника

Авторы

  • Алдонин Г.М. (Институт инженерной физики и радиоэлектроники, Сибирский федеральный университет (г. Красноярск))

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