Biophysics, 2007; 52(2):237-240.
Is monomorphic tachycardia indeed monomorphic?
A.V. Moskalenko*),
Yu. E. Elkin**) ***)
*)Institute for Theoretical & Experimental Biophysics RAS
**)Institute of Mathematical Problems of Biology RAS
***) Pushchino Branch of the Moscow State University
The dependence of some ECG characteristics on the excitation threshold was studied by mathematical modeling of cardiac arrhythmia in a 2D homogeneous excitable medium. It is shown that monomorphic tachycardias can arise both at elevated and at lowered excitability but the ECG characteristics in these cases are different.
Keywords:reentrant ventricular arrhythmia, excitable medium, spiral wave, ECG variability, mathematical modeling, normalized variability analysis
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MODEL AND METHODS
See as it was described elsewhere [Mathematical biology & bioinformatics, 2007; Chaos, Solitons and Fractals]
RESULTS
Evoking Monomorphic Tachycardia
At 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 V1(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 Tachycardia
At 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 V1 and V2: The first tends to zero and the second to a constant value. That is, an initially non-monomorphic 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 (right-hand panels in Fig.1). No such transition occurs at a > 0.180, V1 does not tend to zero and the tip trajectory is a two-period 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 Mode
At 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 Threshold
Figure 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.
DISCUSSION
Here 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 single-lead 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 ANI-method 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 V1 and V2.
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 two-period meander and the hypermeander [10, 11]. The gist of the phenomenon is that the tip trajectory is meander-like but the circular drift of the instant core slows down. This rotor mode is of self-contained interest and we plan to study it further.
REFERENCES
1. 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
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Fig.1. Monomorphic arrhythmias at various values of the parameter a. For each value of a, a group of four graphs is presented. In the group, the left upper panel shows ECG; the left lower panel presents the dynamics of the indices of variability V1(t) (thick line) and V2(t) (thin line); the right panel shows the model medium with a corresponding trajectory of the rotor tip. All the panels on the left have the same scale for abscissa, which represents the time in t.u. The ordinate for V1(t) is depicted on left side. The ordinate for V2(t) is depicted on right side. |
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Fig.2. Polymorphic arrhythmia. Notation is the same as the one in Fig. 1. This type of rotor behavior occurs at values of the parameter a greater than the values depicted on Fig.1. In these cases, the index V1(t) does not approximate zero, and the transient is not observed neither on the rotor tip trajectory nor in behavior of the indices V1(t) and V2(t). |
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Fig.3. Dependence of quasi-period (in t.u.) on the parameter a for monomorphic arrhythmias. |
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