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(abstracts and reprints available - click on links)
Detection of repolarization alternans with an implantable cardioverter defibrillator lead in a porcine modelAnil Maybhate, Steven C. Hao, Sei Iwai, Jae Ung Lee, Amit B. Guttigoli, Kenneth M. Stein, Bruce B. Lerman, and David J. Christini Abstract Mechanistic links have been suggested between repolarization alternans (RPA) and the onset of ventricular tachycardia (VT) and/or fibrillation. Endocardial detection of RPA may therefore be an important step in future device-based treatments of arrhythmias. Here we investigate if RPA could be detected during acute ischemia using an implantable cardioverter defibrillator (ICD) lead (tip to distal coil) located in the right ventricular apex. In 18 pigs, the right coronary (n=10) or left anterior descending coronary (n=8) artery was occluded for 10 min using a balloon catheter, followed by reperfusion for 30 min, and re-occlusion for 30 min. RPA magnitude, computed using the Modified Moving Average (MMA) method, showed a sharp increase in all 18 animals, from a mean baseline level of 1.9+/-1.3 mV to 3.0+/-1.3 mV during first occlusion (p<0.001). RPA magnitude showed a prominent increase in 10 animals during re-occlusion, from a mean baseline level of 1.7+/-1.0 mV to 3.3+/-1.5 mV (p<0.001). The protocol was terminated during the first two stages of occlusion and reperfusion for the remaining 8 animals due to the occurrence of ventricular fibrillation (VF). These results confirm that RPA increases under ischemic conditions and that it is possible to detect and track RPA dynamics with an ICD lead that is positioned in a clinically realistic location. Such an approach may be useful in formulating improved arrhythmia detection and control algorithms.
to be Published in IEEE Transactions on Biomedical Engineering (2005).
Functional reentrant waves propagate outwardly in cardiac tissueYunfan Gong and David J. Christini Abstract The dynamical nature of cardiac arrhythmias has been investigated for decades by researchers from a wide range of disciplines. One long-standing unsettled issue involves whether the mechanism of functional reentry should be described by the "leading-circle" hypothesis or the "spiral-wave" hypothesis, which rely on inward and outward wave propagation, respectively. To address this issue, we investigated two-dimensional FitzHugh-Nagumo type models and found that inwardly propagating waves could occur in the spontaneous oscillatory mode, but not the excitable mode. However, such spontaneous oscillatory behavior is characterized by small-amplitude, sinusoidal oscillations that are fundamentally different from the stimulus-driven, excitable behavior of cardiac myocytes. This finding suggests that inward wave propagation, which is posited by the leading-circle hypothesis for the purpose of maintaining functional reentry, is unlikely to occur in cardiac tissue.
Published in Physics Letters A, 331, pp. 209-216 (2004).
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Adaptive diastolic interval control of cardiac action potential duration alternansPeter N. Jordan and David J. Christini Abstract Introduction: Recent experimental and computational studies have shown that beat-to-beat alternation in action potential duration can trigger cardiac reentry, suggesting that such "alternans" is a mechanistic precursor to arrhythmias. Given such a link, termination of alternans may help prevent the onset of arrhythmias. To this end, recent efforts have shown that chaos control methods can modulate the timing of electrical stimulation to eliminate alternans. Methods and Results: We have developed an alternative control method founded entirely in cardiac electrophysiology (rather than borrowing techniques from the control of physical systems as with existing control techniques). Using computer simulations, we show that this method, which exploits the rate-dependent behavior of cardiac tissue, can be used to control alternans (and higher-order) rhythms, and is robust to drift and noise. When applied to individual model cells exhibiting alternans, the algorithm converges to the period-1 rhythm over as wide, and in some cases a wider, range of feedback proportionality constant values relative to existing methods. Control success comparable to existing methods is achieved when the algorithm is applied to a simulated one-dimensional Purkinje fiber exhibiting alternans. Conclusion: We have developed a method that adaptively controls the timing of electrical stimulation to rapidly eliminate action potential duration alternans in cardiac tissue. This control method may prove valuable in future arrhythmia prevention therapies.
Published in Journal of Cardiovascular Electrophysiology, 15, pp. 1177-1185 (2004).
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Click to download an Editorial Comment on our paper: PDF (63 kB).
Time course and predictors of autonomic dysfunction after ablation of the slow atrioventricular nodal pathwaySteven M. Markowitz, David J. Christini, Kenneth M. Stein, Suneet Mittal, Sei Iwai, David J. Slotwiner, Bruce B. Lerman Abstract Withdrawal of parasympathetic tone has been reported after ablation in the posteroseptal right atrium and has been attributed to injury of vagal efferent fibers. The purpose of this study was to assess the time course and predictors of autonomic dysfunction after slow pathway ablation. In 30 patients with AV nodal reentrant tachycardia, time- and frequency-domain measures of heart rate variability (HRV) were measured before, 30 minutes after, and 1 day after slow pathway ablation. There were significant reductions in mean RR interval (724 ± 163 vs 836 ± 164 ms, P < 0.05), SD of RR intervals (29 ± 17 vs 40 ± 18 ms, P < 0.05), root mean squared difference (15 ± 8 vs 29 ± 17 ms, P < 0.05), and high frequency power (4.1 ± 0.4 vs 4.5 ± 0.6 log10ms2, P < 0.05) 30 minutes after ablation. However, these parameters returned to baseline 1 day after ablation. Multivariate regression identified isoproterenol dose during the diagnostic study (P = 0.02) and radiofrequency duration (P = 0.02) as statistically significant predictors of heart rate change (R2= 0.45). These findings suggest that changes in autonomic tone after ablation in the posteroseptal right atrium are transitory and resolve within 1 day of the procedure. These short-term changes may be related to procedural variables rather than direct injury to vagal efferent fibers.
Published in Pacing and Clinical Electrophysiology, 27, pp. 1638-1643 (2004).
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Determining the effects of memory and action potential duration alternans on cardiac restitution using a constant-memory restitution protocolPeter N. Jordan and David J. Christini Abstract Restitution, the dependence of action potential duration (APD) on diastolic interval, may be causally linked to the vulnerability of cardiac tissue to certain types of arrhythmias. While a number of pacing protocols are commonly used to quantify the restitution relation, one of these, the dynamic protocol, may result in the occurrence of APD alternans. However, the effects of APD alternans, and the concomitant alternation in cardiac memory, on the restitution curve are currently not well understood. Alternans preceding a given action potential may cause that action potential to have a different duration from one preceded by action potentials of identical duration. This interaction of alternans and memory can result in a dynamic restitution curve that is not unique. To address this, we have developed a constant-memory restitution protocol that enables the experimenter or modeller to obtain unique, constant-memory restitution curves at all diastolic intervals. Using this protocol, we obtained unique restitution curves for two ionic models of the cardiac action potential in the absence of alternans at all diastolic intervals. A comparison of the unique constant-memory and non-unique dynamic restitution curves for the two models shows that the presence of alternans can significantly alter the shape of the restitution curve compared to when alternans is absent.
Published in Physiological Measurement, 25, pp. 1013-1024 (2004).
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Effect of beta adrenergic blockade on dynamic electrical restitution in vivoSteven C. Hao, David J. Christini, Kenneth M. Stein, Peter N. Jordan, Sei Iwai, Orville Bramwell, Steven M. Markowitz, Suneet Mittal, and Bruce B. Lerman Abstract The slope of the action potential duration (APD) restitution curve may be a significant determinant of the propensity to develop ventricular fibrillation, with steeper slopes associated with a more arrhythmogenic substrate. We hypothesized that one mechanism by which -blockers reduce sudden cardiac death is by flattening the APD restitution curve. Therefore, we investigated whether infusion of esmolol modulates the APD restitution curve in vivo. In 10 Yorkshire pigs, dynamic APD restitution curves were determined from measurements of APD at 90% repolarization with a monophasic action potential catheter positioned against the right ventricular septum during right ventricular apical pacing in the basal state and during infusion of esmolol. APD restitution curves were fitted to the three-parameter (a, b, c) exponential equation, APD = a·[1 - exp(-b·DI)] + c, where DI is the diastolic interval. Esmolol decreased the maximal APD slope, 0.68 ± 0.14 vs. 0.94 ± 0.24 (baseline), P = 0.002, and flattened the APD restitution curve at shorter DIs, 75 and 100 ms (P < 0.05). To compare the slopes of the APD restitution curves at similar steady states, slopes were also computed at points of intersection between the restitution curve and the lines representing pacing at a fixed cycle length (CL) of 200, 225, 250, 275, and 300 ms using the relationship CL = APD + DI. Esmolol decreased APD restitution slopes at CLs 200-275 ms (P < 0.05). Esmolol flattens the cardiac APD restitution curve in vivo, particularly at shorter CLs and DIs. This may represent a novel mechanism by which -blockers prevent sudden cardiac death.
Published in American Journal of Physiology, 287, pp. H390-H394 (2004).
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Antispiral waves in reaction-diffusion systemsYunfan Gong and David J Christini Abstract We report spontaneous antispiral wave formation in typical reaction-diffusion systems. Our findings qualitatively reproduce a series of phenomena recently observed in a Belousov-Zhabotinsky-type chemical reaction. We found that antispiral waves can occur only near the Hopf bifurcation, when the system is characterized by small amplitude oscillatory (as opposed to excitable) dynamics. For reaction-diffusion systems in the vicinity of the Hopf bifurcation, the specific conditions required for antispiral formation are established here through theoretical analyses and numerical simulations. Thus, this work provides a comprehensive description of the mechanisms underlying antispiral waves in reaction-diffusion systems.
Published in Physical Review Letters, 90, article 088302 (2003).
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A PRL Comment on our paper: PDF (56 kB).
Endocardial detection of repolarization alternansDavid J Christini, Kenneth M. Stein, Steven C. Hao, Steven M. Markowitz, Suneet Mittal, David J. Slotwiner, Sei Iwai, Mithilesh K. Das, and Bruce B. Lerman Abstract Repolarization alternans (RPA) is prognostic of sudden cardiac death and is thought to be mechanistically linked to the initiation of ventricular tachyarrhythmias. Thus, implantable cardiac device detection of RPA may be therapeutically valuable. Because alternans detection is currently limited to surface electrocardiograms, we investigated whether RPA could be measured using a single right-ventricular endocardial lead in humans. Such a location was chosen because it is consistent with the requirements for long-term implantable-device implementation. During diagnostic electrophysiological testing, 28 patients (23M, 5F; 61+/-15yr) were evaluated for surface T-wave alternans (TWA; the current "gold standard" for RPA detection) and endocardial RPA during 5 min of 550 ms right-atrial pacing. Power spectral analysis indicated that 11/28 patients had both surface TWA and endocardial RPA, 9/28 patients had neither, and 8/28 patients had discordant results (71% concordance; p=0.02). Importantly, unlike surface TWA alternans, endocardial RPA was detectable on a beat-to-beat basis. Given the putative mechanistic link between RPA and ventricular arrhythmias, beat-to-beat endocardial RPA detection might be of diagnostic or therapeutic utility.
Published in IEEE Transactions on Biomedical Engineering, 50, pp. 855-862 (2003).
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MinK-related peptide 2 modulates Kv2.1 and Kv3.1 potassium channels in mammalian brainZoe A. McCrossan, Anthony Lewis, Gianina Panaghie, Peter N. Jordan, David J. Christini, Daniel J. Lerner, and Geoffrey W. Abbott Abstract Delayed rectifier potassium current diversity and regulation are essential for signal processing and integration in neuronal circuits. Here, we investigated a neuronal role for MinK-related peptides (MiRPs), membrane-spanning modulatory subunits that generate phenotypic diversity in cardiac potassium channels. Native coimmunoprecipitation from rat brain membranes identified two novel potassium channel complexes, MiRP2-Kv2.1 and MiRP2-Kv3.1b. MiRP2 reduces the current density of both channels, slows Kv3.1b activation, and slows both activation and deactivation of Kv2.1. Altering native MiRP2 expression levels by RNAi gene silencing or cDNA transfection toggles the magnitude and kinetics of endogenous delayed rectifier currents in PC12 cells and hippocampal neurons. Computer simulations predict that the slower gating of Kv3.1b in complexes with MiRP2 will broaden action potentials and lower sustainable firing frequency. Thus, MiRP2, unlike other known neuronal subunits, provides a mechanism for influence over multiple delayed rectifier potassium currents in mammalian CNS via modulation of subunits from structurally and kinetically distinct subfamilies.
Published in Journal of Neuroscience, 50, pp. 8077-8091 (2003).
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Genetically engineered biologically based hemostatic bioassayLilong Tang, David J Christini, and Jay M Edelberg Abstract Real-time direct measures of hemostatic parameters in vivo are required for optimizing the dynamic delivery of coagulation modifying pharmacotherapies. Typical sensors of physiologic functions in vivo, however, have only a restricted array of sensory inputs, and thus limited capacity to monitor thrombotic and hemostatic activity. To overcome this limitation we have developed a genetically engineered excitable cell line that can be potentially used for an implantable thrombin biosensor. Specifically, we have generated stem cell-derived cardiac myocyte aggregates overexpressing the human thrombin receptor, protease activated receptor-1 (PAR-1), which exploit the inherent electropotential input-output relationship of the cells to detect local changes in thrombin activity. In vitro, the signaling activity of PAR-1 cardiac myocytes was highly responsive to thrombin, inducing a sixfold increase in intracellular cAMP as compared with a twofold increase in control cells. In vivo, the engineered myocytes also detected alterations in local coagulation potential. Specifically, PAR-1 engineered cells implanted in vivo detected local increases in thrombin with a doubling in chronotropic activity compared with a 50% increase in control aggregates. Overall these studies demonstrate the potential of genetic engineering to expand the physiologic signals recognized by excitable cells, and may facilitate the translation of this approach for the real-time monitoring of hemostatic function in vivo.
Published in Annals of Biomedical Engineering, 31, pp. 159-162 (2003).
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Termination of reentry in an inhomogeneous ring of model cardiac cellsSitabhra Sinha and David J Christini Abstract Reentrant waves propagating in a ring or annulus of excitable media are a model of the basic mechanism underlying a major class of irregular cardiac rhythms known as anatomical reentry. Such reentrant waves are terminated by rapid electrical stimulation (pacing) from an implantable device. Because the mechanisms of such termination are poorly understood, we study pacing of anatomical reentry in a one-dimensional ring of model cardiac cells. For realistic off-circuit pacing, our model-independent results suggest that circuit inhomogeneities, and the electrophysiological dynamical changes they introduce, may be essential for terminating reentry in some cases.
Published in Physical Review E, 66, article 061903 (2002).
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Mapping and control of complex cardiac arrhythmiasDavid J Christini and Leon Glass Abstract This article serves as an introduction to the Focus Issue on mapping and control of complex cardiac arrhythmias. We first introduce basic concepts of cardiac electrophysiology and describe the main clinical methods being used to treat arrhythmia. We then provide a brief summary of the main themes contained in the articles in this Focus Issue. In recent years there have been important advances in the ability to map the spread of excitation in intact hearts and in laboratory settings. This work has been combined with simulations that use increasingly realistic geometry and physiology. Waves of excitation and contraction in the heart do not always propagate with constant velocity but are often subject to instabilities that may lead to fluctuations in velocity and cycle time. Such instabilities are often treated best in the context of simple one or two dimensional geometries. An understanding of the mechanisms of propagation and wave stability is leading to the implementation of different stimulation protocols in an effort to modify or eliminate abnormal rhythms.
Published in Chaos, 12, pp. 732-739 (2002).
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Critical role of inhomogeneities in pacing termination of cardiac reentrySitabhra Sinha, Kenneth M. Stein, and David J Christini Abstract Reentry around non-conducting ventricular scar tissue, a cause of lethal arrhythmias, is typically treated by rapid electrical stimulation from an implantable cardioverter defibrillator. However, the dynamical mechanisms of termination (success and failure) are poorly understood. To elucidate such mechanisms, we study the dynamics of pacing in one- and two-dimensional models of anatomical reentry. In a crucial realistic difference from previous studies of such systems, we have placed the pacing site away from the reentry circuit. Our model-independent results suggest that with such off-circuit pacing, the existence of inhomogeneity in the reentry circuit is essential for successful termination of tachycardia. Considering the critical role of such inhomogeneities may lead to more effective pacing algorithms.
Published in Chaos, 12, pp. 893-902 (2002).
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Enhanced myocyte-based biosensing of the blood-borne signals regulating chronotropyJay M Edelberg, Jason T Jacobson, David S Gidseg, Lilong Tang, and David J Christini Abstract Biosensors play a critical role in the real-time determination of relevant functional physiological needs. However, typical in vivo biosensors only approximate endogenous function via the measurement of surrogate signals, and therefore may often lack a high degree of dynamic fidelity with physiologic requirements. To overcome this limitation we have developed an excitable tissue-based implantable biosensor approach exploiting the inherent electropotential input-output relationship of cardiac myocytes to measure the physiological regulatory inputs of chronotropic demand via the detection of blood-borne signals. Here we report the improvement of this application through the modulation of host-biosensor communication via the enhancement of vascularization of chronotropic complexes in mice. Moreover, in an effort to further improve translational applicability as well as molecular plasticity, we have advanced this approach by employing stem cell-derived cardiac myocyte aggregates in the place of whole cardiac tissue. Overall these studies demonstrate the potential of biologically-based biosensors to predict endogenous physiological dynamics and may facilitate the translation of this approach for in vivo monitoring.
Published in Journal of Applied Physiology, 92, pp. 581-585 (2002).
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Complex AV-nodal dynamics during ventricular-triggered atrial pacing in humansDavid J. Christini, Kenneth M. Stein, Steven M. Markowitz, Suneet Mittal, David J. Slotwiner, Sei Iwai, and Bruce B. Lerman Abstract In vitro experiments have shown that the complexity of atrioventricular nodal (AVN) conduction dynamics increases with heart rate. Although complex AVN dynamics (e.g., alternans) have been observed clinically, human AVN dynamics during rapid pacing have not been systematically investigated. We studied such dynamics during ventricular-triggered atrial pacing in 37 patients with normal AVN function (18 with dual AVN-pathway physiology, 19 without). Alternans, which always resulted from single-pathway conduction, occurred in 18 patients. In 16 patients (3 of whom also had alternans), quasi-sinusoidal AVN conduction oscillations occurred (mean frequency 0.02 Hz); such oscillations have not been reported previously. There were no significant differences in the dynamics for patients with or without dual AVN pathways. To illuminate the governing dynamical mechanism, a second atrial pacing trial was performed on 12 patients following autonomic blockade. Blockade facilitated alternans but inhibited oscillations. This study suggests that rapid AVN excitation in vivo can lead to autonomically-mediated AVN-conduction oscillations or single-pathway alternans that are a function of inherent nonlinear-dynamical AVN-tissue properties.
Published in American Journal of Physiology, 281,
pp. H865-H872 (2001).
Click to download a PDF reprint (215 kB).
Nonlinear-dynamical arrhythmia control in humansDavid J. Christini, Kenneth M. Stein, Steven M. Markowitz, Suneet Mittal, David J. Slotwiner, Mark A. Scheiner, Sei Iwai, and Bruce B. Lerman Abstract Nonlinear-dynamical control, also known as chaos control, has been used with great success to control a wide range of physical systems. Such techniques have been used to control the behavior of in vitro excitable biological tissue, suggesting their potential for clinical utility. However, the feasibility of using such techniques to control physiologic processes has not been demonstrated in humans. Here we show that nonlinear-dynamical control can modulate human cardiac electrophysiological dynamics by rapidly stabilizing an unstable target rhythm. Specifically, in 52/54 control attempts in 5 patients, we successfully terminated pacing-induced period-2 atrioventricular-nodal conduction alternans by stabilizing the underlying unstable steady-state conduction. This proof-of-concept demonstration shows that nonlinear-dynamical control techniques are clinically feasible, and provides a foundation for developing such techniques for more complex forms of clinical arrhythmia.
Published in Proceedings of the National Academy of Science,
98, pp. 5827-5832 (2001).
Click to download a PDF reprint (160 kB).
Real-Time Linux Dynamic Clamp: A fast and flexible way to construct virtual ion channels in living cellsAlan D. Dorval, David J. Christini, and John A. White Abstract We describe a system for real-time control of biological and other experiments. This device, based around the Real-Time Linux operating system, was tested specifically in the context of dynamic clamping, a demanding real-time task in which a computational system mimics the effects of nonlinear membrane conductances in living cells. The system is fast enough to represent dozens of nonlinear conductances in real time at clock rates well above 10 kHz. Conductances can be represented in deterministic form, or more accurately as discrete collections of stochastically gating ion channels. Tests were performed using a variety of complex models of nonlinear membrane mechanisms in excitable cells, including simulations of spatially extended excitable structures, and multiple interacting cells. Only in extreme cases does the computational load interfere with high-speed "hard" real-time processing (i.e., real-time processing that never falters). Freely available on the worldwide web, this experimental control system combines good performance, immense flexibility, low cost, and reasonable ease of use. It is easily adapted to any task involving real-time control, and excels in particular for applications requiring complex control algorithms that must operate at speeds over 1 kHz.
Published in Annals of Biomedical Engineering, 29,
pp. 897-907 (2001).
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Direct biologically-based biosensing of dynamic physiological functionDavid J. Christini, Jeff Walden, and Jay M. Edelberg Abstract Dynamic regulation of biological systems requires real-time assessment of relevant physiological needs. Biosensors, which transduce biological actions or reactions into signals amenable to processing, are well-suited for such monitoring. Typically, in vivo biosensors approximate physiological function via the measurement of surrogate signals. An alternative approach, presented here, would be to use biologically-based biosensors for the direct measurement of physiological activity via functional integration of relevant governing inputs. We show that an implanted excitable-tissue biosensor (excitable cardiac tissue) can be used as a real-time, integrated bioprocessor to analyze the complex inputs regulating a dynamic physiological variable (heart rate). This approach offers the potential for long-term biologically-tuned quantification of endogenous physiological function.
Published in American Journal of Physiology, 280,
pp. H2006-H2010 (2001).
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Restricted feedback control of one-dimensional mapsKevin Hall and David J. Christini Abstract Dynamical control of biological systems is often restricted by the practical constraint of unidirectional parameter perturbations. We show that such a restriction introduces surprising complexity to the stability of one-dimensional map systems and can actually improve controllability. We present experimental cardiac control results that support these analyses. Finally, we develop new control algorithms that exploit the structure of the restricted-control stability zones to automatically adapt the control feedback parameter and thereby achieve improved robustness to noise and drifting system parameters.
Published in Physical Review E, 63, article 046204 (2001).
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Adaptive estimation and control method for unstable periodic dynamics in spike trainsDavid J. Christini and Daniel T. Kaplan Abstract Dynamical control of excitable biological systems is often complicated by the difficult and unreliable task of pre-control identification of unstable periodic orbits (UPOs). Here we show that, for both chaotic and nonchaotic systems, UPOs can be located, and their dynamics characterized, during control. Tracking of system nonstationarities emerges naturally from this approach. Such a method is potentially valuable for the control of spike trains of excitable biological systems, for which pre-control UPO identification is often impractical and nonstationarities (natural or stimulation-induced) are common.
Published in Physical Review E, 61, pp. 5149-5153 (2000).
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The role of nonlinear dynamics in cardiac arrhythmia controlDavid J. Christini, Kenneth M. Stein, Steven M. Markowitz, Suneet Mittal, David J. Slotwiner, and Bruce B. Lerman Abstract The field of nonlinear dynamics has made important contributions towards a mechanistic understanding of cardiac arrhythmias. In recent years, many of these advancements have been in the area of arrhythmia control. In this paper, we will review the analytical, modeling, and experimental nonlinear dynamical arrhythmia control literature. We will focus on stimulation and pharmacological techniques that have been developed, and in some cases used in experiments, to control reentrant rhythms (including spiral and scroll waves) and fibrillation. Although such approaches currently have practical limitations, they offer hope that nonlinear dynamical control techniques will be clinically useful in the coming years.
Published in Heart Disease, 1 pp. 190-200 (1999).
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A practical real-time computing system for biomedical experiment interfaceDavid J. Christini, Kenneth M. Stein, Steven M. Markowitz, and Bruce B. Lerman Abstract Many biomedical experiments require a precisely-timed real-time computer interface. Because commonly used desktop operating systems are inherently non-real-time, real-time laboratory computer systems are often based on outdated DOS software or expensive proprietary real-time operating systems. Here we discuss a real-time computing system, based on the free RT-Linux operating system, which we have developed for adaptive pacing control in a clinical cardiac electrophysiology laboratory. This powerful, flexible, and inexpensive system demonstrates that RT-Linux is well-suited for real-time biomedical experiment interface. For a website with more detailed technical information and the open-source software click here.
Published in Annals of Biomedical Engineering, 27 pp. 180-186 (1999).
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Real-time experimental control of a system in its chaotic and nonchaotic regimesDavid J. Christini, Visarath In, Mark L. Spano, William L. Ditto, and James J. Collins Abstract Current model-independent control techniques are limited, from a practical standpoint, by their dependence on a pre-control learning stage. Here we use a real-time, adaptive, model-independent (RTAMI) feedback control technique to control an experimental system - a driven magnetoelastic ribbon - in its nonchaotic and chaotic regimes. We show that the RTAMI technique is capable of tracking and stabilizing higher-order unstable periodic orbits. These results demonstrate that the RTAMI technique is practical for on-the-fly (i.e., no learning stage) control of real-world dynamical systems.
Published in Physical Review E, 56, pp. R3749-R3752 (1997).
Click to download a PDF reprint (116kB).
Control of chaos in excitable physiological systems: A geometric analysisDavid J. Christini and James J. Collins Abstract Model-independent chaos control techniques are inherently well-suited for the control of physiological systems for which quantitative system models are unavailable. The proportional perturbation feedback (PPF) control paradigm, which uses electrical stimulation to perturb directly the controlled system variable (e.g., the interbeat or interspike interval), was developed for excitable physiological systems that do not have an easily accessible system parameter. We develop the stable manifold placement (SMP) technique, a PPF-type technique which is simpler and more robust than the original PPF control algorithm. We use the SMP technique to control a simple geometric model of a chaotic system in the neighborhood of an unstable periodic orbit (UPO). We show that while the SMP technique can control a chaotic system that has UPO dynamics which are characterized by one stable manifold and one unstable manifold, the success of the SMP technique is sensitive to UPO parameter estimation errors.
Published in CHAOS, 7, pp. 544-549 (1997).
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Real-time, adaptive, model-independent control of low-dimensional chaotic and nonchaotic dynamical systemsDavid J. Christini and James J. Collins Abstract Current model-independent control techniques are limited, from a practical standpoint, by their dependence on a pre-control learning stage. Here we develop a model-independent control technique, for chaotic and nonchaotic low-dimensional dynamical systems, that operates in real-time (i.e., it does not require a learning stage). We show that this technique is adaptive to system non-stationarities, robust to noise, and capable of stabilizing higher-order unstable periodic orbits. Because this technique is real-time, adaptive, and model-independent, it is practical for real-world systems.
Published in IEEE Transactions on Circuits and
Systems-I, 44, pp. 1027-1030 (1997).
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Dynamic control of cardiac alternansKevin Hall, David J. Christini, Maurice Tremblay James J. Collins, Leon Glass, and Jacques Billette Abstract A dynamic control technique was used to suppress a cardiac arrhythmia called an alternans rhythm in an isolated rabbit heart preparation. We demonstrate that our control algorithm adapts to drifting system parameters, making it particularly well-suited for the control of physiological rhythms. Control of cardiac alternans rhythms may have important clinical implications since they often precede serious cardiac arrhythmias and are a harbinger of sudden cardiac death.
Published in Physical Review Letters, 78,
pp. 4518-4521 (1997).
Click to download a PDF reprint (140 kB).
Experimental control of high-dimensional chaos: The driven double pendulumDavid J. Christini, James J. Collins, and Paul S. Linsay Abstract Chaos control techniques exploit the sensitivity of chaos to initial conditions by applying feedback perturbations to an accessible system parameter. Most methods apply only one perturbation per period, and are thus susceptible to control failure when applied to highly unstable systems. Here, we extend a recently developed model-independent, quasicontinuous chaos control technique to stabilize a high-dimensional chaotic system: the driven double pendulum.
Published in Physical Review E, 54, pp. 4824-4827 (1996). Click to download a PDF reprint (575 kB).
Using chaos control and tracking to suppress a pathological non-chaotic rhythm in a cardiac modelDavid J. Christini and James J. Collins Abstract Atrioventricular (AV) nodal alternans is a pathological cardiac condition characterized by a beat-to-beat alternation (period-2 rhythm) in AV nodal conduction time. Here we implement an AV nodal conduction model which undergoes a period-doubling bifurcation into alternans. We show that additive noise can be used to locate the unstable period-1 fixed point which underlies the alternans rhythm. We then use chaos control to suppress alternans by stabilizing the model about its unstable period-1 fixed point. We also show that the period-doubling bifurcation into alternans can be prevented by tracking the period-1 rhythm into its unstable regime. We demonstrate that these techniques are robust to imprecise measurements and experimental noise. Importantly, these methods require no knowledge of the underlying system equations. These novel findings suggest that chaos control and tracking may be useful for suppressing alternans in a clinical environment.
Published in Physical Review E, 53, pp. R49-R52 (1996).
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Using noise and chaos control to control non-chaotic systemsDavid J. Christini and James J. Collins Abstract Here we show that chaos control techniques can be used to stabilize unstable periodic orbits in a non-chaotic system provided additive noise can be utilized: (1) to determine the local dynamics of a chosen orbit, and (2) to move the system's trajectory into the neighborhood of the orbit so that control can be initiated. Using these techniques, we demonstrate that the qualitative dynamics of a non-chaotic system can be altered without using large controls or large parameter shifts. Unlike classical control methods, this approach requires no knowledge of the underlying system equations.
Published in Physical Review E, 52,
pp. 5806-5809 (1995).
Click to download a PDF reprint (359 kB).
Controlling non-chaotic neuronal noise using chaos control techniquesDavid J. Christini and James J. Collins Abstract Chaos control techniques have been used to control a wide variety of experimental systems, including physiological systems. Here chaos control, periodic pacing and anticontrol were applied to a noise-driven, non-chaotic neuronal model, and results similar to those recently reported for apparently chaotic, in vitro neuronal networks were obtained. Similar results were also produced when chaos control was applied to a simple stochastic system. These findings suggest that the aforementioned neuronal networks may not have been chaotic and that chaos control techniques can be applied to a wider range of experimental systems (e.g., stochastic systems) than previously thought.
Published in Physical Review Letters,
75, pp. 2782-2785 (1995).
Click to download a PDF reprint (110 kB).
Influence of autoregressive model parameter uncertainty on spectral estimates of heart rate dynamicsDavid J. Christini, Abhijit Kulkarni, Srikar Rao, Eric R. Stutman, Frederick M. Bennett, Jeffrey M. Hausdorff, Nancy Oriol, and Kenneth R. Lutchen Abstract Linear autoregressive (AR) model- based heart rate (HR) spectral analysis has been widely used to study heart rate dynamics. Due to system and measurement noise, the parameters of an AR model have intrinsic statistical uncertainty. In this study, we evaluate how this AR parameter uncertainty can translate to uncertainty in HR power spectra. HR time series, obtained from seven subjects in supine and standing positions, were fit to AR models by least squares minimization via singular value decomposition (SVD). Spectral uncertainty due to inexact parameter estimation was assessed through a Monte Carlo study in which the AR model parameters were varied randomly according to their Gaussian distributions. Histogram techniques were used to evaluate the distribution of 50,000 AR spectral estimates of each HR time series. These Monte Carlo uncertainties were found to exceed those predicted by previous theoretical approximations. It was determined that the uncertainty of AR heart rate spectral estimates, particularly the locations and magnitudes of spectral peaks, can often be large. The same Monte Carlo analysis was applied to synthetic AR time series and found levels of spectral uncertainty similar to that of the HR data, thus suggesting that the results of this study are not specific to experimental HR data. Therefore, AR spectra may be unreliable, and one must be careful in assigning pathophysiological origins to specific spectral features of any one spectrum.
Published in Annals of Biomedical Engineering,
23, pp. 127-134 (1995).
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Application of linear and nonlinear time series modeling to heart rate dynamics analysisDavid J. Christini, Frederick M. Bennett, Kenneth R. Lutchen, Hassan M. Ahmed, Jeffrey M. Hausdorff, and Nancy Oriol Abstract The linear autoregressive (AR) model is often used to investigate the pathophysiologic mechanisms controlling heart rate (HR) dynamics. This study implemented parametric models new to this field to determine if there exists a more appropriate HR dynamics modeling structure. The linear AR and autoregressive-moving average (ARMA) models, and the nonlinear polynomial autoregressive (PAR) and bilinear (BL) models were fit to instantaneous HR time series obtained from 9 subjects in the supine position. Model orders were determined by the Akaike Information Criteria (AIC). Model residual variance was used as the primary inter-model comparison criterion, with significance evaluated by a c2 distributed statistic. The BL model best represented the HR dynamics, as its residual variance was significantly (p < 0.05) smaller than that of the corresponding AR model for 9/9 data sets. In all cases the BL model had a smaller residual variance than either the ARMA or PAR models. The bilinear model was ineffective at data forecasting, however we show that this cannot reflect BL model validity because poor prediction is inherent to the BL model structure. The apparent superiority of the nonlinear bilinear model suggests that future heart rate dynamics studies should put greater emphasis on nonlinear analyses.
Published in IEEE Transactions on Biomedical
Engineering, 42, pp. 411-415 (1995).
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