source model for generating RR intervals in atrial fibrillation and beyond
چکیده
Background: Realistic modeling of cardiac inter-beat (RR) intervals is highly desirable for basic research in cardiac electrophysiology, clinical management of heart diseases, and developing signal processing tools for ECG analysis. Methods: We present an open source computer model that is capable to generate realistic time series of RR intervals in both physiologic and pathologic conditions. Detailed model structure and the software implementation are described. Results: Examples are provided on how to use this model to generate RR intervals in atrial fibrillation with ventricular pacing, normal sinus rhythm with heart rate variability, and typical atrial flutter with atrioventricular block. The extensibility of the model is also discussed. Conclusion: The present computer model provides a unified platform wherein various types of ventricular rhythm can be simulated. The availability of this open source model promises to support and stimulate future studies. Background The variation of cardiac inter-beat (PP, RR or NN) intervals results from both rhythmic activity of the heart electrical source and the dynamic properties of the cardiac conduction pathway, both of which are under autonomic control. In normal sinus rhythm, the RR intervals are known to fluctuate at various time scales, a phenomenon known as heart rate variability, which has been extensively investigated to probe the autonomic nervous activity [1]. On the other hand, the abnormal cardiac rhythm, for example during atrial fibrillation (AF), has been thought to mainly result from disturbance in autonomic modulations of the electrophysiological properties of the atria and the atrioventricular (AV) node [2]. Hence, analysis of RR intervals may offer valuable insights into the mechanisms of arrhythmia genesis, maintenance, and termination. From the therapeutic perspective, characterization of the RR intervals can guide the development of novel strategies for cardiac rhythm management. For instance, many antiarrhythmic drugs are known to affect ventricular rhythm by modifying various electrical properties of the heart, including the automaticity, the conduction velocity, and the refractory period [3]. In another example, specially designed pacing protocols could be used for prevention, termination, or rate regularization of AF through implantation of artificial pacemakers [4]. Published: 2 March 2007 BioMedical Engineering OnLine 2007, 6:9 doi:10.1186/1475-925X-6-9 Received: 14 November 2006 Accepted: 2 March 2007 This article is available from: http://www.biomedical-engineering-online.com/content/6/1/9 © 2007 Lian et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Page 1 of 16 (page number not for citation purposes) BioMedical Engineering OnLine 2007, 6:9 http://www.biomedical-engineering-online.com/content/6/1/9 Consequently, time series analysis of RR intervals has been a research thrust in the field of biomedical engineering. Numerous techniques based on RR interval analysis have been developed in the past decades to assess the autonomic control of the cardiovascular system, to assist clinical diagnosis of cardiac disorders, to facilitate arrhythmia predication and risk stratification, and so on [5]. However, quantitative comparison of different analytic methods has been hindered by the heterogeneity of various data sources and the inherent noise and uncontrollability of real world recordings. Therefore, realistic modeling of RR intervals is highly desired to provide a unified platform wherein various algorithms can be evaluated. Despite the apparent scientific merits and clinical significance, there is a stark paucity of computer models to generate realistic time series of RR intervals. Although several RR interval generators had been created in response to the PhysioNet/Computers in Cardiology Challenge 2002 [6], all these models are limited to synthesizing sinus rhythm with simulated heart rate variability, yet not applicable to abnormal rhythms. Recently, a novel computer model, known as AF-VP, was developed by the authors to elucidate the effects of ventricular pacing (VP) on the ventricular rhythm in AF [7]. The kernel component of the model is the AV junction (AVJ), which is treated as a lumped structure with defined electrical properties mimicking those of individual AV nodal cells. As illustrated in Figure 1, the action potential of the AV nodal cells has five phases. The cell is depolarized (Phase 0) when its membrane potential crosses the depolarization threshold. Then the cell repolarizes (Phases 1–3) and returns to the resting potential (Phase 4). The refractory period, when no new action potential can be initiated, begins with Phase 0 and extends into Phase 3. The AV nodal cells can depolarize spontaneously due to gradual increase of the membrane potential in Phase 4. Such automaticity is usually suppressed by the higher firing rate of the sinus node in atrium, but may manifest in abnormal conditions, such as during sinus node dysfunction or the AV junctional tachycardia. It has been demonstrated that this AF-VP model could account for most known experimental observations in AF [7]. Of particular note is the plasticity of the model, that is, this model can be easily extended beyond AF, to simulate various types of RR intervals in both normal physiologic and pathologic conditions. In order to facilitate the use and further improvement of the AF-VP model, its software (written in ANSI/ISO C [see Additional file 1]) has Illustration of the action potential of the AV nodal cells Figu e 1 Illustration of the action potential of the AV nodal cells. Page 2 of 16 (page number not for citation purposes) BioMedical Engineering OnLine 2007, 6:9 http://www.biomedical-engineering-online.com/content/6/1/9 been made freely available on PhysioNet [8], an on-line forum for the dissemination and exchange of recorded and simulated biomedical signals and archives of open source software [9]. In this paper, we describe the software architecture of the AF-VP model. Examples are given on how to use this model to synthesize RR intervals for different rhythms, and the extensibility of the model is discussed. Methods Model structure Figure 2 illustrates how the AF-VP model is composed of four inter-connected components: the AF generator, the AV junction (AVJ), the ventricle, and the electrode used to record the electrical activity [7]. The AF generator outputs random AF impulses bombarding the AVJ. However, retrograde conducted waves escaping the AVJ can collide with an imminent AF impulse or reset the timing cycle of the AF generator. The AVJ fires when its membrane potential (Vm) reaches the depolarization threshold (VT). The activation of AVJ starts a refractory period, when the AVJ is refractory to any stimulation. At the end of refractory period, Vm returns to the resting potential (VR) and starts to rise in a linear manner. Each time an AF impulse hits the AVJ during Phase 4, Vm is increased by a discrete amount ΔV [10,11]. However, if the AVJ is invaded by a VP-induced retrograde wave during Phase 4, Vm is brought to VT directly. The firing of the AVJ generates an activation wave that starts an antegrade or retrograde AV delay (AVD), depending on the direction of activation. If the AVJ is retrograde activated while an antegrade wave has not finished its AVD or vice versa, a collision occurs, annihilating the activation waves in both directions. Both refractory period and conduction delay of the AVJ are dependent upon its recovery time, which is defined as the interval between the end of last AVJ refractory period and the current AVJ activation time. In addition, the electrotonic modulation of the AVJ refractory period by blocked impulses is also incorporated in the model [7]. After finishing the antegrade AVD, an activation wave is generated in the ventricle and starts the antegrade ventricular conduction. The delivery of VP also generates a retrograde activation wave in the ventricle toward the AVJ. When both antegrade and retrograde waves are present in the ventricle, a ventricular fusion beat manifests, causing the extinction of both waves. The electrode for recording this activity is assumed to be implanted in the ventricle and connected to a pacing device operating in demand mode. If an activation wave propagates to the electrode after an antegrade ventricular conduction delay, a ventricular sense (VS) occurs that inhibits the scheduled VP, whereas the timeout of the pacing interval triggers the VP. Software implementation Figure 3 shows the top-level flowchart of the simulation model. The software loads the model parameters from an external configuration file (see Appendix A for an example), and then initializes variables that include various timers and counters as being summarized in Tables 1, 2, respectively. The simulation runs at the programmed samSchematic drawing of the AF-VP model Figure 2 Schematic drawing of the AF-VP model. Page 3 of 16 (page number not for citation purposes) BioMedical Engineering OnLine 2007, 6:9 http://www.biomedical-engineering-online.com/content/6/1/9 pling frequency (with a default of 1000 Hz). At each sampling time, the model adjusts the timers and updates Vm (in a linearly increasing manner) if the AVJ is in Phase 4, and then handles possible event(s) as detailed below. The simulation continues until the desired number of cardiac beats (RR intervals) is generated or the simulation time runs out, when the model logs statistics and exits. The event handling routine is described in Figure 4. Sequentially, the model checks its timers to detect the following events and calls for respective services if any: ventricular fusion (VtrFusion), AF bombardment of AVJ (AnteHitAvj), retrograde invasion of AVJ (RetrHitAvj), ventricular sense (VtrSense), ventricular pace (VtrPace), antegrade AVD timeout (AnteEscAvj), and retrograde AVD timeout (RetrEscAvj). The model then checks the status of the AVJ. If the AVJ is in Phase 4 and Vm ≥ VT, then services are called for AVJ activation (ActivateAvj) and the initiation of the refractory period (StartAvjRef). On the other hand, if the AVJ is in refractory period, then no action is taken until its timeout, when a service is called to start the Phase 4 (StartAvjPh4). Ventricular fusion is detected when two opposite traveling waves in the ventricle meet, based on the ratios of active ventricle timers to the fixed ventricular conduction delays in both directions. The VtrFusion service (Figure 5) increases the ventricular fusion counter, and then stops both antegrade and retrograde ventricle timers. The AVJ is bombarded by an AF impulse at the end of an AF interval. The AnteHitAvj service (Figure 6) increments the AF counter, resets the AF generator and obtains the next AF interval. If the AVJ is in Phase 4, then Vm has a step increase of ΔV. Antegrade AVJ activation is flagged if Vm ≥ VT. On the other hand, if the AF impulse hits the AVJ during refractory period, then the AVJ refractory period is extended, simulating the electrotonic modulation effect of the concealed conduction. If there is a retrograde wave in the AVJ and the AF impulse has supra-threshold strength, then the retrograde AVJ timer is disabled (prevent retrograde conduction to atrium) and the AVJ fusion counter is incremented. Otherwise, an antegrade AV block is registered. The AVJ is invaded by a VP-induced retrograde wave when its timer completes the retrograde ventricular conduction delay. The RetrHitAvj service (Figure 7) first stops the retrograde ventricular timer. If the AVJ is in Phase 4 and Vm 2(default): VVI Example of simulated RR intervals in the presence of AF and VP Figure 15 Example of simulated RR intervals in the presence of AF and VP. Page 14 of 16 (page number not for citation purposes) BioMedical Engineering OnLine 2007, 6:9 http://www.biomedical-engineering-online.com/content/6/1/9 Page 15 of 16 (page number not for citation purposes) Example of simulated PP and RR intervals in sinus rhythm with heart rate variability Figure 16 Example of simulated PP and RR intervals in sinus rhythm with heart rate variability. Example of simulated RR intervals in the presence of atrial flutter and AV block Figure 17 Example of simulated RR intervals in the presence of atrial flutter and AV block. BioMedical Engineering OnLine 2007, 6:9 http://www.biomedical-engineering-online.com/content/6/1/9 Appendix B Various patterns of RR intervals can be generated using the present AF-VP model by modifying the configuration file described in Appendix A. For example, Figure 15 (AF rhythm and VP) is produced by simply replacing the default values of the following two parameters as: