Biophysics, 2007; 52(2):237240. Is monomorphic tachycardia indeed monomorphic?
A.V. Moskalenko^{*)},
Yu. E. Elkin^{**) ***)}
<..> MODEL AND METHODSSee as it was described elsewhere [Mathematical biology & bioinformatics, 2007; Chaos, Solitons and Fractals] RESULTSEvoking Monomorphic TachycardiaAt all values of a from 0.090 to about 0.180 we obtain ECGs (Fig. 1) visually corresponding to monomorphic tachycardia; this is confirmed by the nearly zero values of V_{1}(t). At higher a, the movement of the spiral wave tip gives rise to a classical meander (Fig. 2), and the ECG resembles the one obtained in torsade de pointes [2, 3]. These results are not analyzed here. Spontaneous Evolution to Monomorphic TachycardiaAt a = 0.120 the wave practically from the very beginning rotates about a round core (Fig. 1), whereas at higher a this mode is attained only through a distinct transition process, which is clearly seen in the dynamics of V_{1} and V_{2}: The first tends to zero and the second to a constant value. That is, an initially nonmonomorphic arrhythmia evolves into a monomorphic one. Note that the higher the a (starting from ~0.145) the longer the transition process, which is especially vivid in the tip trajectory (righthand panels in Fig.1). No such transition occurs at a > 0.180, V_{1} does not tend to zero and the tip trajectory is a twoperiod meander (Fig. 2) throughout the observation period (8000 time units). At a < 0.145 the rotor becomes stable in two or three turns. The phenomenon of spontaneous deceleration of the rotor drift, with transition from a meander to steady rotation, has not been described heretofore. Change of the Rotation ModeAt a = 0.090 the tip trajectory is obviously ‘angular’ (Fig. 1 top); to a lesser extent this is also observed at a = 0.095. Scrutiny of the pattern reveals that it is a hypothrochoid. That is, in the interval 0.090 < a < 0.150 there is a change in the rotation mode with hypothrochoid/epitrochoid wave tip trajectories. Note that the hypothrochoid is not quite common as it lacks the usual petals [10, 11]. Dependence of the Quasiperiod on the Excitation ThresholdFigure 3 shows that the ECG quasiperiod monotonically increases with a, whereby the state of the 'virtual myocardium' (its excitability) can be characterized by the period in monomorphic tachycardia, and thus one can infer both the rotor tip trajectory and the deviation of a from its 'normal' value. DISCUSSIONHere we demonstrate the dependence of some ECG characteristics on the model parameter corresponding to the excitation threshold for the case of monomorphic reentrant arrhythmia in a homogeneous 2D excitable medium. In silico experiments for such arrhythmias show that with a singlelead ECG one can assess the state (excitability) of the medium; the ECG quasiperiod by itself provides information on the deviation from normal excitability. The authors of the model used here [9] state that normal excitability corresponds to a = 0.150. In the present work we have observed monomorphic tachycardia at this parameter value as well as at those higher and lower. The differences in ECGs reflect the different mechanisms of arrhythmia (reentry modes). This result appears to be quite important in the medical aspect. It indicates that reentrant monomorphic ventricular tachycardia may require different treatment depending on the sign of the deviation of excitability from the norm. Currently, physicians do not attempt to distinguish such cases. If further studies prove that these results can be extended to clinical ECGs, the refined diagnosis would allow a more expedient therapy. We also demonstrate the sensitivity of the ANImethod to transitory processes in the virtual myocardium in cases when the ECG instability is not visually apparent. In particular, a monomorphic ECG does not guarantee a stationary mode of excitation spread. Such regions of “hidden nonstationarity” can be distinguished from truly monomorphic ones by the variability indices V_{1} and V_{2}. Studying monomorphic tachycardia in the Aliev–Panfilov model, we discovered a new type of wave tip trajectory in a homogeneous medium. We call it a 'lacet' to emphasize its distinction from the twoperiod meander and the hypermeander [10, 11]. The gist of the phenomenon is that the tip trajectory is meanderlike but the circular drift of the instant core slows down. This rotor mode is of selfcontained interest and we plan to study it further. REFERENCES1. Unified Electrocardiographic Reports: Methodical Recommendations, Ed. by B. A. Sidorenko (GMU UDP, Moscow, 2005) [in Russian]. 2. N. I. Kukushkin and A. B. Medvinsky, Vestn. Aritmol. No. 35, 49 (2004). 3. D. M. Krikler, M. Perelman, and E. Rowland, in Cardiac Arrhythmias, Ed. by W. J. Mandel (JB Lippincott, Philadelphia, 1995; Meditsina, Moscow, 1996), Vol. 2, pp. 373–410 [in Russian]. 4. D. Noble, BioEssays 24, 1156 (2002). 5. E.J. Crampin, M. Halstead, P. Hunter, et al., Exp. Physiol. 89 (1), 1 (2003). 6. A. V. Moskalenko, N. I. Kukushkin, C. F. Starmer, et al., Biofizika 46, 319 (2001). 7. A.V. Moskalenko, A.V. Rusakov, and Yu.E. Elkin, Chaos, Solitons & Fractals (in press), DOI: 10.1016/j.chaos.2006.06.009. 8. A. B. Medvinsky, A. V. Rusakov, A. V. Moskalenko, M. V. Fedorov, and A. V. Panfilov, Biofizika 48, 314 (2003). 9. R. Aliev and A. Panfilov, Chaos, Solutions & Fractals 7 (3), 293 (1996). 10. A.T. Winfree, Chaos 1 (3), 303 (1991). 11. I. R. Efimov, V. I. Krinsky, and J. Jalife, Chaos, Solitons & Fractals 5 (3/4), 513 (1995). FIGURES
