The heart utilizes electrical waves that normally spread in a coordinated manner to initiate a mechanical contraction, but in pathologic states, electrical wave propagation can be disrupted by pre-existing heterogeneous regions or by dynamic heterogeneities that develop as a consequence of rapid pacing and the nonlinear dynamics of the system. An important example of the latter that is often a precursor to life-threatening arrhythmias is electrical alternans, in which two successive paced beats elicit electrical responses (and thus mechanical responses) of different amplitudes and durations. Despite much attention, fundamental characteristics about alternans remain under-studied, and attempts to use electrical interventions to control alternans have not been successful on a global level. Our research aims to advance the understanding of cardiac alternans at the most basic level and to use this knowledge to implement improved schemes of electrical control using fundamental nonlinear dynamics principles. In particular, we will characterize the type of period-doubling bifurcation underlying electrical alternans, develop mathematical models to investigate the dynamical and biophysical mechanisms underlying alternans, and to implement and test novel control algorithms. Mathematical modeling and computer simulations in single-and multi-processor environments will be used in conjunction with experimental techniques, including microelectrodes, laser-scanning confocal microscopy, and optical mapping using fluorescence signals obtained with voltage-sensitive dyes in cardiac tissue. The proposed research will elucidate the nature of the period-doubling bifurcation to electrical alternans, quantify the roles of intracellular calcium dynamics and transmembrane voltage in the origin of alternans, and improve the understanding of global control algorithms in tissue. In the course of this project, graduate and undergraduate students will participate in this research and will benefit from an interdisciplinary environment. A key component of the project is to promote broad dissemination of information. The mathematical models and algorithms developed in this proposal will be made available free as stand alone codes and interactive Java applets via web sites. Results will be presented as well, with a special emphasis on interactive programs and animations for both scientists and the general public. Ultimately, this research may lead to improved treatments for life-threatening cardiac arrhythmias: by preventing alternans, the lethal cardiac arrhythmias that alternans can trigger also can be avoided. Furthermore, the improved understanding of electrical abnormalities and novel methods for controlling complex dynamics may translate to other related systems, including the brain and peripheral nervous system and other types of muscle.
Our main objective was to study the nonlinear dynamics of cardiac tissue as related to arrhythmias using mathematical modeling/computer simulation along with biological experiments. We focused particularly on using this knowledge to develop advanced algorithms to control or terminate complex cardiac dynamics, such as fibrillation. Our most significant result was the development of a novel low-energy defibrillation strategy that we hope will be brought to the clinic. Conventional defibrillation uses only a single high-voltage shock, but this shock, although highly successful at stopping the arrhythmia, can cause tissue damage and pain. In contrast, our new method delivers a short train of low-intensity electric pulses from field electrodes near the dominant frequency of the arrhythmia. We studied the relationship between the response of cardiac tissue to an electric field and the spatial distribution of heterogeneities in the coronary vascular structure. We showed that when a pulsed electric field is applied, these heterogeneities serve as sources for intramural electrical waves and demonstrated that the time required for full tissue depolarization followed a power law. The intramural wave nucleation sites form throughout the tissue, including near the cores of the spiral and scroll waves of electrical activity that drive complex fibrillatory dynamics. For atrial fibrillation, which is resistant to many clinical treatments, our method had a success rate of 93% using only 13% of the energy required for defibrillation by conventional means. Our in vitro experiments showed that defibrillation was accomplished by synchronization of the tissue, and we used this control strategy to terminate fibrillation in vivo at low energies. We also studied other methods for controlling complex cardiac dynamics in the context of alternans, which is a beat-to-beat alternation of the electrical response of cardiac tissue to stimulation despite an invariant stimulation period. Alternans is of interest because it has been identified as a frequent precursor of fibrillation. Although various methods for eliminating alternans by injecting weak external currents have been proposed, they have not performed sufficiently well to be considered for clinical use. We proposed a new that, in contrast to most previous approaches, includes information from the underlying model in order to increase its efficiency. We compared our approach’s performance with that of two other methods within a ring geometry using a single control electrode. We demonstrated that although the other methods were capable of suppressing alternans in some circumstances, our model-based method could suppress alternans more quickly using a smaller control current. We also analyzed the controllability and observability as the locations of the recording and control electrodes were varied. Our study showed that the loss of controllability caused the failure of a previously studied control approach at longer fiber lengths. We were able to describe how to choose the optimal locations for both electrodes as well as the timing of the feedback current. With a different approach, we were able to effectively double the length of fibers for which alternans could be suppressed compared to previous methods. Along with these research findings, our project aimed to provide interdisciplinary training for graduate and undergraduate students and to communicate our results broadly, including to the general public. Four graduate and two undergraduate students were trained in experimental and modeling techniques; these students came from disciplines including physiology, biomedical engineering, computer science, and software engineering and learned to integrate the approaches and techniques of multiple traditional disciplines to study cardiac dynamics using a different approach with a broad range of tools. We published nine articles in peer-reviewed journals, including one in the prestigious journal Nature. We organized several conference sessions and together with our student participants gave approximately 40 presentations about our work at conferences, workshops, invited seminars at universities, and other venues. To reach a broader audience, we reached out in different ways. For example, one of us gave a presentation on cardiac dynamics to an audience of 30-40 high school mathematics, physics, and computer science teachers at the Summer Mathematics Institute Teachers’ Workshop at Rochester Institute of Technology in June 2011. The talk was successful and engaged the interest of these teachers in understanding how mathematics could be used to study the heart. In addition, one of us appeared in a five-minute movie about applied mathematics, including a discussion of heart-related research, at the Rochester Institute of Technology. This movie was featured at the ICIAM conference in Vancouver in July 2011. Results from this award also were included in several university classes, including a class for science exploration majors (who must later choose a more specific major). Finally, we continue to make cardiac arrhythmia research accessible to researchers and the general public alike through our website, TheVirtualHeart.org, which provides information about the heart and arrhythmias through interactive Java applets and movies.
