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A new technique of ECG analysis and its application to evaluation of disorders during ventricular tachycardia
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Chaos, Solitons and Fractals 36 (2008) 66–72 www.elsevier.com/locate/chaos
A new technique of ECG analysis and its application to evaluation of disorders during ventricular tachycardia A.V. Moskalenko a
a,*
, A.V. Rusakov a, Yu.E. Elkin
b
Institute of Theoretical and Experimental Biophysics RAS, Institutskaya Street, 3, Pushchino 142290, Russia b Institute of Mathematical Problems of Biology RAS, Institutskaya Street, 4, Pushchino 142290, Russia Accepted 5 June 2006
Communicated by Prof. M.S. El Naschie
Abstract We propose a new technique of ECG analysis to characterize the properties of polymorphic ventricular arrhythmias, potentially life-threatening disorders of cardiac activation. The technique is based on extracting two indices from the ECG fragment. The result is a new detailed quantitative description of polymorphic ECGs. Our observations suggest that the proposed ECG processing algorithm provides information that supplements the traditional visual ECG analysis. The estimates of ECG variation in this study reveal some unexpected details of ventricular activation dynamics, which are possibly useful for diagnosing cardiac rhythm disturbances. Ó 2006 Elsevier Ltd. All rights reserved.
1. Introduction Ventricular arrhythmias are life-threatening disorders of cardiac excitation. Despite considerable progress in recent years, the pharmacological treatment of patients with ventricular fibrillation and polymorphic ventricular tachycardia is marginally effective. In accordance with the recent multicenter investigations (CAST, ESVEM, CASCADE, etc. [1,2]), treatment using antiarrhytmic drugs of all classes leads to positive results in 58.5% of cases. Such low treatment efficiency can be caused by inaccurate diagnostic differentiation of ventricular arrhythmias. It is expected that a more detailed diagnosis will lead to improved matching of treatment with the underlying arrhythmia. The most widely used clinical tool for assessing arrhythmias is the body surface ECG. In order to provide a more detailed quantitative description of polymorphic ventricular arrhythmia, we propose a new technique for ECG analysis, the ANI-method [5]. The ANI-method was tested with ECG data obtained both from in vitro experiments [3–5] and in numeric simulations [6]. The objective of this work was to characterize the properties of polymorphic ventricular arrhythmias in terms of the ANI-method. *
Corresponding author. E-mail address: [email protected] (A.V. Moskalenko). URL: http://www.avmoskalenko.ru/Eng/ (A.V. Moskalenko).
0960-0779/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2006.06.009
A.V. Moskalenko et al. / Chaos, Solitons and Fractals 36 (2008) 66–72
67
2. Materials and methods We studied pseudo electrocardiograms (pseudo-ECGs) obtained from in vitro studies of ventricular arrhythmias (‘‘physiological ECG’’) as well as from numerical simulations (‘‘numerical ECG’’). Each ‘‘physiological ECG’’ represented a time series constructed by weighted summation of separate electrograms obtained by multielectrode mapping of excitation propagation during an arrhythmia obtained from the isolated wall of the ground squirrel right ventricle. The experimental model and the procedure for constructing the pseudo-ECG were described in detail elsewhere [3,7]. For calculation of ‘‘numerical ECGs’’ we used the Aliev–Panfilov mathematical model of heart tissue [8]: ou ¼ Du kuðu aÞðu 1Þ uv; ot ov ¼ eðu; vÞðu kuðu a 1ÞÞ; ot lv eðu; vÞ ¼ e0 þ 1 : u þ l2 The parameters in the equations were adjusted [8] to accurately reflect cardiac tissue properties (k = 8.0; l1 = 0.2; l2 = 0.3; a = 0.15; e0 = 0.01). In our simulations, the parameter l2 was equal to 0.3 or 1.3, with the parameter a being varied from 0.12 to 0.19. Note that the parameter, a, specifies threshold of excitation. The simulations were carried out in 2D as well as 3D excitable media (128 elements along each dimension) with von Neumann boundary conditions. The details of 3D simulations and the procedure for constructing the pseudo-ECGs in the simulations were described in detail elsewhere [6]. Each pseudo-ECG was quantitatively evaluated by the ANI-method [5] in its current implementation (ANI-2003, [6]). Fig. 1 demonstrates successive steps of the ANI-2003 procedure, with the demonstration using an ‘‘artificial ECG’’ composed of two short real ECG segments. The procedure used for building the artificial ECGs was described in [5]. The ANI-2003 maps an ECG fragment onto two real indices (arbitrary units). The indices provide a quantitative representation of polymorphism, which is one of the qualitative ECG features of potentially life-threatening reentrant arrhythmias. Index V1 represents an average evaluation of the unlikeness of ECG segments inside the studied fragment and the index V2 is its variation. To calculate the indices, we compared an arbitrary segment of an electrocardiogram with another segment, which was considered to be a reference sample. The compared ECG segments were assumed to correspond to similar intervals of adjacent cycles of cardiac activation. We chose the segment length (sampling window width) to be comparable with the shortest width of the QRS of the biological species under studying under control conditions (normal sinus rhythm). The comparison procedure was carried out at each moment of time yielding the local characteristic of electrocardiographic variability (instant variability index I). This index was used to compare numerically segment i corresponding to the current position of the sampling window with the first segment most closely resembling segment i in the subsequent recording. The successive comparison results in the function, Ii (Fig. 1C). The V1i and V2i were produced from Ii. V1i is the average Ii inside some short interval (Fig. 1D), and V2i is V1i divided by the standard deviation of Ii inside the interval (Fig. 1E). For successive ECG fragments of fixed length, a sequence of the indices draws a trajectory in the index space (Fig. 1F) that is a 2D time series. The trajectory drawn in (V1i, V2i) index space enables one to visualize the detailed ECG dynamics. In the index space, regions of different polymorphism were identified. As shown in Fig. 2A–F, the indices increased when the number of transitions from one monomorphic fragment to another increased. Note that the artificial ECGs in the left column were assembled from the ECG samples of different types (Fig. 1A) while the artificial ECGs in the right column were assembled from the ECG samples of a single type changed in amplitude. The trajectory displacement was conditioned by the frequency of transitions between the ECG samples and depends, to a lesser extent, on the type of the ECG sample. Fig. 2G and 2H demonstrate that noise is characterized with significantly larger V2i than the ECGs recorded under conditions of fibrillation. The dependence of the trajectory location on ECG polymorphism defines a partial order in the (V1i, V2i) index space (Fig. 2). The result is a new detailed quantitative description of polymorphic ECGs. Note that one cannot know the number of transitions in a real ECGs recorded during polymorphic ventricular tachycardia or ventricular fibrillation, but one can use the ANI-method to estimate it. 2.1. Results and discussion The results of application of the ANI-2003 to ‘‘physiological ECGs’’ are shown on the Fig. 3. Fig. 3A–C demonstrates trajectory shifts in the (V1i, V2i)-space as arrhythmias appear more and more polymorphic. Panels D–F demon-
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Fig. 1. Successive steps of the ANI-2003 procedure. For the demonstration, an artificial ECG composed of two real ECG segments is used. (A) The ‘‘physiologic ECG’’ segments used for building artificial ECGs, (B) a fragment of artificial ECG and the corresponding (C) Ii, (D) V1i, (E) and V2i functions (arbitrary units). The fragment corresponds to 1000 ms, (F) Corresponding trajectory in the (V1i, V2i) index space. Insert in the upper right corner is the same ECG fragment.
strate cases with arrhythmia transition from one state to another. The encircled mark 1 indicates the most polymorphic ECG segments and the encircled mark 2 indicates less polymorphyc ECG segments. Note the differences in Fig. 3C and E examples. In both C and E, the pseudo-ECGs have no obvious visual transitions, but one can see that the case, E, has obvious transitions in the corresponding (V1i, V2i) plane. This transition
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Fig. 2. Demonstration of ANI-method adjustment using simple artificial ECGs. Axes are the same as in Fig. 1F. (A–F) Artificial ECGs, which were built with sewing together two ECG segments shown in Fig. 1A. The artificial ECGs contain different amount of transitions from one monomorphic fragment to another. The amount of transitions increases from top to bottom. All fragments correspond to 2000 ms, (G) noise recorded during physiological experiments. The fragment corresponds to 6000 ms, (H) regular impulses versus a background noise. The fragment corresponds to 6000 ms.
indicates that the arrhythmia state has been changed. Fig. 3F demonstrates an opposite case, in which visual ECG transition is clearly seen, but there is no transition in (V1i, V2i). These observations let us conclude that ECG trajectories in the (V1i, V2i)-space provide information that supplements traditional visual ECG analysis. It is expected that combined use of visual ECG analysis and ANI-2003 may enable one to improve assessment of underlying arrhythmia
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Fig. 3. ‘‘Physiological ECGs’’ and their trajectories in the (V1i, V2i) parameter plane. The ECG fragments shown correspond to 5000 ms. Axes are the same as in the Fig. 1F.
mechanisms. For an ECG amplitude decrease without pronounced changes of polymorphism (see Fig. 3F), we assume that one spiral wave orientation was altered, but there was not any significant change of regime of excitation spread. Such a conclusion follows from the fact that the presence of many spiral waves alters the ECG amplitude either by a change in the number of spiral waves or by synchronisation of the spiral waves. Considering that either arrhythmia mechanism leads to changes in ECG polymorphism, we assume that there are no essential changes in the mechanism of the arrhythmia displayed in case F. The results of application of the ANI-2003 to ‘‘numerical ECGs’’ are shown on the Fig. 4. Comparing the cases of monomorphic pseudo-ECGs in Figs. 3 and 4 one can find that the trajectories of the ‘‘physiological ECGs’’ and the trajectories of the ‘‘numerical ECGs’’ have significantly different locations, with the ECGs shape having no evident visual differences. For the cases of polymorphic pseudo-ECGs, analogous conclusions were drawn formerly [6]. It is interesting that the ‘‘numerical ECGs’’ are less ‘‘deterministic’’ than the ‘‘physiological ECGs’’ when polymorphic cases are distinguished with respect to the indices. But the ‘‘numerical ECGs’’ are more ‘‘deterministic’’ than the ‘‘physiological ECGs’’ in monomorphic cases. We explain these results in the following manner. In both our natural and numerical experiments, monomorphic arrhythmias were caused by 2D spiral waves. Therefore, it is reasonable that the ‘‘numerical ECGs’’ have no stochastic component and are estimated to be more regular. Concerning the polymorphic cases, the ‘‘physiological ECGs’’ were caused by 2D spiral waves only, whereas the ‘‘numerical ECGs’’ were caused by single 2D spiral waves (meander mode) as well as by complex 3D broken scroll waves. Therefore, it is most likely that all the arrhythmias caused by broken scrolls are more polymorphic than the arrhythmias caused by 2D spiral waves only. This hypothesis is confirmed by the observation that the ‘‘numerical ECGs’’ obtained in the 3D simulations without broken scrolls have the location in the (V1i, V2i)-space similar to the location of the ‘‘numerical ECGs’’ obtained in the 2D simulations with meandering spiral waves. In addition, it is significant that the polymorphic ‘‘physiological ECGs’’ have the location in the (V1i, V2i)-space similar to the location of the ‘‘numerical ECGs’’ obtained in the simulations without broken scrolls. This observation is consistent with other evidence that the thin wall of the right ventricle used in our natural experiments behaves as a 2D excitable medium.
A.V. Moskalenko et al. / Chaos, Solitons and Fractals 36 (2008) 66–72
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Fig. 4. ‘‘Numerical ECGs’’ simulated for 2D medium and their trajectories in the (V1i, V2i) parameter plane. The ECG fragments shown correspond to 5000 ms. Axes are the same as in the Fig. 1F. Upper row contains monomorphic ECGs, whereas lower row demonstrates polymorphic ones. For upper row, l1 is equal to 0.3, and a is equal to 0.15; 0.16; 0.17 from (A) to (C), respectively. For lower row, l1 is equal to 1.3, and a is equal to 0.16; 0.17; 0.18 from (D) to (F), respectively.
3. Conclusions In this study, we have shown that a novel technique for ECG analysis referred to as ANI-method could provide cardiologists with sensitive clinical tool for identifying life-threatening arrhythmias. The estimates derived from pseudo-ECGs in this study reveal some unexpected details of ventricular arrhythmia dynamics, which probably will be useful for diagnosis of cardiac rhythm disturbances. This study has demonstrated the feasibility of the ANI-method for quantitative distinction of ECGs during lifethreatening ventricular arrhythmias. Many of the phenomena found are not yet understood because of the complexity of heart activity during ventricular arrhythmias. Since the regime of circulation of excitation waves in myocardium is strongly determined by the state of the membrane ionic channels [9], further development of the ANI-method is suggested to turn the technique into new effective non-invasive procedure for evaluation of myocardial state. Further work will explore how reentrant and focal arrhythmias could be distinguished by their ECGs.
Acknowledgements We are thankful to Prof. C.F. Starmer for very useful discussion and linguistic advice.
References [1] Waldo AL, Henthorh RW, Carlson MD. A perspective on ventricular arrhythmias: patient assessment for therapy and outcome. Am J Cardiol 1990;65(4):30–5.
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[2] Fisher JD, Broadman RF, Kim SG, Ferrick KJ, Roth JA. VT/VF: 60/60 protection. Pace 1990;13(2):218–22. [3] Sarancha DYu, Medvinsky AB, Kukushkin NI, Sidorov VYu, Romashko DN, Burashnikov AYu, Moskalenko AV, Starmer CF. A system for the computer visualization of the propagation of excitation waves in the myocardium. Biophysics 1997;42(2):491–6. [4] Moskalenko AV, Medvinsky AB, Tikhonova IA, Sidorov VYu, Kukushkin NI, Starmer CF. Automatized working place for researcher on an example of the plant for multielectrode mapping of myocardium. Moscow: Progress-Tradition; 1999. p. 131–4. [5] Moskalenko AV, Kukushkin NI, Starmer CF, Deev AA, Kukushkina KN, Medvinsky AB. Quantitative analysis of variability of the electrocardiograms typical of polymorphic arrhythmias. Biophysics 2001;46(2):313–23. [6] Medvinsky AB, Rusakov AV, Moskalenko AV, Fedorov MV, Panfilov AV. The study of autowave mechanisms of electrocardiogram variability during high-frequency arrhythmias: the result of mathematical modelling. Biophysics 2003;48(2):303–12. [7] Kukushlin NI, Sidorov VYu, Medvinsky AB, Romashko DN, Burashnikov AYu, Baum OV, Sarancha DYu, Starmer CF. Slow excitation waves and mechanisms of polymorphic ventricular tachycardia in an experimental model: isolated walls of the right ventricles of the hearts of rabbit and ground squirrel. Biophysics 1998;43(6):995–1010. [8] Aliev RR, Panfilov AVA. simple two-variable model of cardiac excitation. Chaos, Solitons & Fractals 1996;7(3):293–301. [9] Efimov IR, Krinsky VI, Jalife J. Dynamics of rotating vortices in the Beeler–Reuter model of cardiac tissue. Chaos, Solitons & Fractals 1995;5:513–26.
Chaos, Solitons and Fractals 36 (2008) 66–72 www.elsevier.com/locate/chaos
A new technique of ECG analysis and its application to evaluation of disorders during ventricular tachycardia A.V. Moskalenko a
a,*
, A.V. Rusakov a, Yu.E. Elkin
b
Institute of Theoretical and Experimental Biophysics RAS, Institutskaya Street, 3, Pushchino 142290, Russia b Institute of Mathematical Problems of Biology RAS, Institutskaya Street, 4, Pushchino 142290, Russia Accepted 5 June 2006
Communicated by Prof. M.S. El Naschie
Abstract We propose a new technique of ECG analysis to characterize the properties of polymorphic ventricular arrhythmias, potentially life-threatening disorders of cardiac activation. The technique is based on extracting two indices from the ECG fragment. The result is a new detailed quantitative description of polymorphic ECGs. Our observations suggest that the proposed ECG processing algorithm provides information that supplements the traditional visual ECG analysis. The estimates of ECG variation in this study reveal some unexpected details of ventricular activation dynamics, which are possibly useful for diagnosing cardiac rhythm disturbances. Ó 2006 Elsevier Ltd. All rights reserved.
1. Introduction Ventricular arrhythmias are life-threatening disorders of cardiac excitation. Despite considerable progress in recent years, the pharmacological treatment of patients with ventricular fibrillation and polymorphic ventricular tachycardia is marginally effective. In accordance with the recent multicenter investigations (CAST, ESVEM, CASCADE, etc. [1,2]), treatment using antiarrhytmic drugs of all classes leads to positive results in 58.5% of cases. Such low treatment efficiency can be caused by inaccurate diagnostic differentiation of ventricular arrhythmias. It is expected that a more detailed diagnosis will lead to improved matching of treatment with the underlying arrhythmia. The most widely used clinical tool for assessing arrhythmias is the body surface ECG. In order to provide a more detailed quantitative description of polymorphic ventricular arrhythmia, we propose a new technique for ECG analysis, the ANI-method [5]. The ANI-method was tested with ECG data obtained both from in vitro experiments [3–5] and in numeric simulations [6]. The objective of this work was to characterize the properties of polymorphic ventricular arrhythmias in terms of the ANI-method. *
Corresponding author. E-mail address: [email protected] (A.V. Moskalenko). URL: http://www.avmoskalenko.ru/Eng/ (A.V. Moskalenko).
0960-0779/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2006.06.009
A.V. Moskalenko et al. / Chaos, Solitons and Fractals 36 (2008) 66–72
67
2. Materials and methods We studied pseudo electrocardiograms (pseudo-ECGs) obtained from in vitro studies of ventricular arrhythmias (‘‘physiological ECG’’) as well as from numerical simulations (‘‘numerical ECG’’). Each ‘‘physiological ECG’’ represented a time series constructed by weighted summation of separate electrograms obtained by multielectrode mapping of excitation propagation during an arrhythmia obtained from the isolated wall of the ground squirrel right ventricle. The experimental model and the procedure for constructing the pseudo-ECG were described in detail elsewhere [3,7]. For calculation of ‘‘numerical ECGs’’ we used the Aliev–Panfilov mathematical model of heart tissue [8]: ou ¼ Du kuðu aÞðu 1Þ uv; ot ov ¼ eðu; vÞðu kuðu a 1ÞÞ; ot lv eðu; vÞ ¼ e0 þ 1 : u þ l2 The parameters in the equations were adjusted [8] to accurately reflect cardiac tissue properties (k = 8.0; l1 = 0.2; l2 = 0.3; a = 0.15; e0 = 0.01). In our simulations, the parameter l2 was equal to 0.3 or 1.3, with the parameter a being varied from 0.12 to 0.19. Note that the parameter, a, specifies threshold of excitation. The simulations were carried out in 2D as well as 3D excitable media (128 elements along each dimension) with von Neumann boundary conditions. The details of 3D simulations and the procedure for constructing the pseudo-ECGs in the simulations were described in detail elsewhere [6]. Each pseudo-ECG was quantitatively evaluated by the ANI-method [5] in its current implementation (ANI-2003, [6]). Fig. 1 demonstrates successive steps of the ANI-2003 procedure, with the demonstration using an ‘‘artificial ECG’’ composed of two short real ECG segments. The procedure used for building the artificial ECGs was described in [5]. The ANI-2003 maps an ECG fragment onto two real indices (arbitrary units). The indices provide a quantitative representation of polymorphism, which is one of the qualitative ECG features of potentially life-threatening reentrant arrhythmias. Index V1 represents an average evaluation of the unlikeness of ECG segments inside the studied fragment and the index V2 is its variation. To calculate the indices, we compared an arbitrary segment of an electrocardiogram with another segment, which was considered to be a reference sample. The compared ECG segments were assumed to correspond to similar intervals of adjacent cycles of cardiac activation. We chose the segment length (sampling window width) to be comparable with the shortest width of the QRS of the biological species under studying under control conditions (normal sinus rhythm). The comparison procedure was carried out at each moment of time yielding the local characteristic of electrocardiographic variability (instant variability index I). This index was used to compare numerically segment i corresponding to the current position of the sampling window with the first segment most closely resembling segment i in the subsequent recording. The successive comparison results in the function, Ii (Fig. 1C). The V1i and V2i were produced from Ii. V1i is the average Ii inside some short interval (Fig. 1D), and V2i is V1i divided by the standard deviation of Ii inside the interval (Fig. 1E). For successive ECG fragments of fixed length, a sequence of the indices draws a trajectory in the index space (Fig. 1F) that is a 2D time series. The trajectory drawn in (V1i, V2i) index space enables one to visualize the detailed ECG dynamics. In the index space, regions of different polymorphism were identified. As shown in Fig. 2A–F, the indices increased when the number of transitions from one monomorphic fragment to another increased. Note that the artificial ECGs in the left column were assembled from the ECG samples of different types (Fig. 1A) while the artificial ECGs in the right column were assembled from the ECG samples of a single type changed in amplitude. The trajectory displacement was conditioned by the frequency of transitions between the ECG samples and depends, to a lesser extent, on the type of the ECG sample. Fig. 2G and 2H demonstrate that noise is characterized with significantly larger V2i than the ECGs recorded under conditions of fibrillation. The dependence of the trajectory location on ECG polymorphism defines a partial order in the (V1i, V2i) index space (Fig. 2). The result is a new detailed quantitative description of polymorphic ECGs. Note that one cannot know the number of transitions in a real ECGs recorded during polymorphic ventricular tachycardia or ventricular fibrillation, but one can use the ANI-method to estimate it. 2.1. Results and discussion The results of application of the ANI-2003 to ‘‘physiological ECGs’’ are shown on the Fig. 3. Fig. 3A–C demonstrates trajectory shifts in the (V1i, V2i)-space as arrhythmias appear more and more polymorphic. Panels D–F demon-
68
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Fig. 1. Successive steps of the ANI-2003 procedure. For the demonstration, an artificial ECG composed of two real ECG segments is used. (A) The ‘‘physiologic ECG’’ segments used for building artificial ECGs, (B) a fragment of artificial ECG and the corresponding (C) Ii, (D) V1i, (E) and V2i functions (arbitrary units). The fragment corresponds to 1000 ms, (F) Corresponding trajectory in the (V1i, V2i) index space. Insert in the upper right corner is the same ECG fragment.
strate cases with arrhythmia transition from one state to another. The encircled mark 1 indicates the most polymorphic ECG segments and the encircled mark 2 indicates less polymorphyc ECG segments. Note the differences in Fig. 3C and E examples. In both C and E, the pseudo-ECGs have no obvious visual transitions, but one can see that the case, E, has obvious transitions in the corresponding (V1i, V2i) plane. This transition
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Fig. 2. Demonstration of ANI-method adjustment using simple artificial ECGs. Axes are the same as in Fig. 1F. (A–F) Artificial ECGs, which were built with sewing together two ECG segments shown in Fig. 1A. The artificial ECGs contain different amount of transitions from one monomorphic fragment to another. The amount of transitions increases from top to bottom. All fragments correspond to 2000 ms, (G) noise recorded during physiological experiments. The fragment corresponds to 6000 ms, (H) regular impulses versus a background noise. The fragment corresponds to 6000 ms.
indicates that the arrhythmia state has been changed. Fig. 3F demonstrates an opposite case, in which visual ECG transition is clearly seen, but there is no transition in (V1i, V2i). These observations let us conclude that ECG trajectories in the (V1i, V2i)-space provide information that supplements traditional visual ECG analysis. It is expected that combined use of visual ECG analysis and ANI-2003 may enable one to improve assessment of underlying arrhythmia
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Fig. 3. ‘‘Physiological ECGs’’ and their trajectories in the (V1i, V2i) parameter plane. The ECG fragments shown correspond to 5000 ms. Axes are the same as in the Fig. 1F.
mechanisms. For an ECG amplitude decrease without pronounced changes of polymorphism (see Fig. 3F), we assume that one spiral wave orientation was altered, but there was not any significant change of regime of excitation spread. Such a conclusion follows from the fact that the presence of many spiral waves alters the ECG amplitude either by a change in the number of spiral waves or by synchronisation of the spiral waves. Considering that either arrhythmia mechanism leads to changes in ECG polymorphism, we assume that there are no essential changes in the mechanism of the arrhythmia displayed in case F. The results of application of the ANI-2003 to ‘‘numerical ECGs’’ are shown on the Fig. 4. Comparing the cases of monomorphic pseudo-ECGs in Figs. 3 and 4 one can find that the trajectories of the ‘‘physiological ECGs’’ and the trajectories of the ‘‘numerical ECGs’’ have significantly different locations, with the ECGs shape having no evident visual differences. For the cases of polymorphic pseudo-ECGs, analogous conclusions were drawn formerly [6]. It is interesting that the ‘‘numerical ECGs’’ are less ‘‘deterministic’’ than the ‘‘physiological ECGs’’ when polymorphic cases are distinguished with respect to the indices. But the ‘‘numerical ECGs’’ are more ‘‘deterministic’’ than the ‘‘physiological ECGs’’ in monomorphic cases. We explain these results in the following manner. In both our natural and numerical experiments, monomorphic arrhythmias were caused by 2D spiral waves. Therefore, it is reasonable that the ‘‘numerical ECGs’’ have no stochastic component and are estimated to be more regular. Concerning the polymorphic cases, the ‘‘physiological ECGs’’ were caused by 2D spiral waves only, whereas the ‘‘numerical ECGs’’ were caused by single 2D spiral waves (meander mode) as well as by complex 3D broken scroll waves. Therefore, it is most likely that all the arrhythmias caused by broken scrolls are more polymorphic than the arrhythmias caused by 2D spiral waves only. This hypothesis is confirmed by the observation that the ‘‘numerical ECGs’’ obtained in the 3D simulations without broken scrolls have the location in the (V1i, V2i)-space similar to the location of the ‘‘numerical ECGs’’ obtained in the 2D simulations with meandering spiral waves. In addition, it is significant that the polymorphic ‘‘physiological ECGs’’ have the location in the (V1i, V2i)-space similar to the location of the ‘‘numerical ECGs’’ obtained in the simulations without broken scrolls. This observation is consistent with other evidence that the thin wall of the right ventricle used in our natural experiments behaves as a 2D excitable medium.
A.V. Moskalenko et al. / Chaos, Solitons and Fractals 36 (2008) 66–72
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Fig. 4. ‘‘Numerical ECGs’’ simulated for 2D medium and their trajectories in the (V1i, V2i) parameter plane. The ECG fragments shown correspond to 5000 ms. Axes are the same as in the Fig. 1F. Upper row contains monomorphic ECGs, whereas lower row demonstrates polymorphic ones. For upper row, l1 is equal to 0.3, and a is equal to 0.15; 0.16; 0.17 from (A) to (C), respectively. For lower row, l1 is equal to 1.3, and a is equal to 0.16; 0.17; 0.18 from (D) to (F), respectively.
3. Conclusions In this study, we have shown that a novel technique for ECG analysis referred to as ANI-method could provide cardiologists with sensitive clinical tool for identifying life-threatening arrhythmias. The estimates derived from pseudo-ECGs in this study reveal some unexpected details of ventricular arrhythmia dynamics, which probably will be useful for diagnosis of cardiac rhythm disturbances. This study has demonstrated the feasibility of the ANI-method for quantitative distinction of ECGs during lifethreatening ventricular arrhythmias. Many of the phenomena found are not yet understood because of the complexity of heart activity during ventricular arrhythmias. Since the regime of circulation of excitation waves in myocardium is strongly determined by the state of the membrane ionic channels [9], further development of the ANI-method is suggested to turn the technique into new effective non-invasive procedure for evaluation of myocardial state. Further work will explore how reentrant and focal arrhythmias could be distinguished by their ECGs.
Acknowledgements We are thankful to Prof. C.F. Starmer for very useful discussion and linguistic advice.
References [1] Waldo AL, Henthorh RW, Carlson MD. A perspective on ventricular arrhythmias: patient assessment for therapy and outcome. Am J Cardiol 1990;65(4):30–5.
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