Discrete Model of Three Interacting Pacemakers Taking into Account the Time of Refractoriness as Applied to The Activity of Cardiac Fibrillation

Heart muscle (like any other muscle tissue) refers to the so-called excitable systems. Wave propagation in such systems is carried out by means of an energy source distributed in it. When a pulse is applied to such a system from the place of its application, a perturbation begins to propagate --the excitation wave: the incoming pulse is transmitted from the element to the element without damping sequentially. Usually, after excitation, each element is not able to immediately be excited again. As a rule, there is a certain “relaxation time”, called the refractory period, during which the element as it is restored. This leads, on the one hand, to an ordered spatial propagation of the excitation wave, and on the other hand, with frequent supply of pulses (or with a large period of refractoriness), some of them will be blocked. In the description of a number of excitable media often resort to the approximation of the original system a set of individual excitable elements, locally interacting with each other. Each such element is capable of being in one of three States --rest, excitation and refractoriness. From the state of rest, the element can go into an excited state, in which there will be a certain time. Then he goes into a state of refractoriness and only then again in a state of rest. Thus, the transition to the excited state is possible only from the state of rest. Although this model is a certain approximation, it very well reproduces the main phenomena in excitable media, including in the tissues of the heart. Suppose that there is a homogeneous excitable medium in which all elements have identical properties. Then the excitation frequency of all such elements will be the same. If some area of this environment to start periodically to perturb, in this region there is a source of concentrically radiating waves of excitement. Such a source is called a leading center or pejjsmeker. If an excitable medium is two or more pacemaker, the pejjsmeker less of the oscillation frequency with time is suppressed by pejjsmeker greater frequency. In other words, there is competition between pacemakers. Ideally, after a certain time, only one pacemaker will remain in the entire environment. In addition to pacemakers, in excitable media may appear other sources of excitation --spiral waves, which are “rotating” spiral. All spiral waves have the same frequency. Therefore, they always coexist with each other, but extinguish the leading center, which is a slower autowave source. In addition, spiral waves are the main type of elementary self-supporting structures in homogeneous excitable media. Like vortices in a superconductor or in superfluid helium, they are extremely stable. The appearance of several sources of excitation in the heart muscle is currently associated with dangerous disorders of the normal functioning of the heart --arrhythmia. With a large number of abnormal sources, fibrillation occurs. Let’s say that in some medium available only main and additional leading centres. Then even such a simple situation, depending on the frequency Abstract