In this article, we compare quantitatively the efficiency of three different protocols commonly used in commercial defibrillators. These are based on monophasic and both symmetric and asymmetric biphasic shocks. A numerical one-dimensional model of cardiac tissue using the bidomain formulation is used in order to test the different protocols. In particular, we performed a total of 4.8 Â 10 6 simulations by varying shock waveform, shock energy, initial conditions, and heterogeneity in internal electrical conductivity. Whenever the shock successfully removed the reentrant dynamics in the tissue, we classified the mechanism. The analysis of the numerical data shows that biphasic shocks are significantly more efficient (by about 25%) than the corresponding monophasic ones. We determine that the increase in efficiency of the biphasic shocks can be explained by the higher proportion of newly excited tissue through the mechanism of direct activation. In the present paper, we show how numerical simulations can be used to understand the efficiency of different defibrillation protocols. Fibrillation is a rapid, irregular electrical activity of the heart. This fatal medical condition is usually treated by the application of an external electric shock to the patient chest through external paddle electrodes. The shape of the electric waveforms that are usually applied are either monophasic or biphasic. This means that in the latter the polarity is switched at some point in the course of the application of the shock. Empirical observations suggest that biphasic shocks are more efficient than monophasic shocks in terminating fibrillation. In this paper, by using a simplified mathematical model of cardiac tissue, which, however, includes a realistic response of the cells to large electric fields, we confirm and explain this experimental observation. The model developed here could be used in subsequent studies in order to design and test more complex waveforms, which could be done systematically because the model is simple and not very computationally costly. The next goal is to find the optimal waveform that reduces the energy needed for defibrillatory shocks. This would be of great benefit for patients undergoing defibrillation by limiting the damage to the heart tissue caused by such a strong electric shock.

Chaotic properties of symmetrical two-dimensional stadium-like billiards with elliptical arcs are studied numerically and analytically. For the two-parameter truncated elliptical billiard the existence and linear stability of several lowest-order periodic orbits are investigated in the full parameter space. Poincaré plots are computed and used for evaluation of the degree of chaoticity with the box-counting method. The limit of the fully chaotic behavior is identified with circular arcs. Above this limit, for flattened elliptical arcs, mixed dynamics with numerous stable elliptic islands is present, similarly as in the elliptical stadium billiards. Below this limit the full chaos extends over the whole region of elongated shapes and the existing orbits are either unstable or neutral. This is conspicuously different from the behavior in the elliptical stadium billiards, where the chaotic region is strictly bounded from both sides. To examine the mechanism of this difference, a generalization to a novel three-parameter family of boundary shapes is proposed and suggested for further evaluation.

Defibrillation is the standard clinical treatment used to stop ventricular fibrillation. An electrical device delivers a controlled amount of electrical energy via a pair of electrodes in order to reestablish the normal heart rate. We propose a new technique that is a combination of biphasic shocks applied with a four-electrode system rather than the standard two-electrode system. We use a numerical model of a one-dimensional ring of cardiac tissue in order to test and evaluate the benefit of such a new technique. We compare three different shock protocols, namely, a monophasic and two types of biphasic shocks. The results obtained by using a four-electrode system are compared quantitatively with those obtained with the standard two-electrode system. We find that a huge reduction in defibrillation threshold is achieved with the four-electrode system. For the most efficient protocol (asymmetric biphasic), we obtain a reduction in excess of 80 % in the energy required for a defibrillation success rate of 90 %. The mechanisms of successful defibrillation are also analyzed. This reveals that the advantage of asymmetric biphasic shocks with four electrodes lies in the duration of the cathodal and anodal phase of the shock.

U suvremenom se hrvatskom jeziku pravi jednostavni niječni imperativi u pravilu tvore od nesvršenih glagola (Ne dirajte mi ravnicu!). U prvom slavenskom književnom jeziku, starocrkvenoslavenskom, niječni su se imperativi mogli tvoriti od svršenih glagola, pri čemu se u literaturi navodila djelomična podudarnost s grčkim jezikom, odnosno s grčkim konjunktivima prezenta i aorista. U radu se ispituje odnos svršenih i nesvršenih pravih niječnih imperativa u prvom hrvatskom književnom jeziku, hrvatskom crkvenoslavenskom, s posebnim naglaskom na odnos s latinskim jezikom predložaka. Komparativno korpusno istraživanje provedeno je na tekstu hrvatskoglagoljskoga II. beramskoga brevijara(15. st.). Analiza je podataka pokazala da se glagolski vid upotrebljava neovisno o latinskom predlošku. Osim toga, kvantitativni podaci sugeriraju da u hrvatskom crkvenoslavenskom razdoblju nije još došlo do zapaženijega potiskivanja uporabe svršenoga vida s pravim niječnim imperativima

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