The pinwheel experiment revisited: effects of cellular electrophysiological properties on vulnerability to cardiac reentry

The physics of heart rhythm disorders

The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.

Multimodal imaging shows fibrosis architecture and action potential dispersion are predictors of arrhythmic risk in spontaneous hypertensive rats

Hypertensive heart disease (HHD) increases risk of ventricular tachycardia (VT) and ventricular fibrillation (VF). The roles of structural vs. electrophysiological remodelling and age vs. disease progression are not fully understood. This cross-sectional study of cardiac alterations through HHD investigates mechanistic contributions to VT/VF risk. Risk was electrically assessed in Langendorff-perfused, spontaneously hypertensive rat hearts at 6, 12 and 18 months, and paced optical membrane voltage maps were acquired from the left ventricular (LV) free wall epicardium. Distributions of LV patchy fibrosis and 3D cellular architecture in representative anterior LV mid-wall regions were quantified from macroscopic and microscopic fluorescence images of optically cleared tissue. Imaging showed increased fibrosis from 6 months, particularly in the inner LV free wall. Myocyte cross-section increased at 12 months, while inter-myocyte connections reduced markedly with fibrosis. Conduction velocity decreased from 12 months, especially transverse to the myofibre direction, with rate-dependent anisotropy at 12 and 18 months, but not earlier. Action potential duration (APD) increased when clustered by age, as did APD dispersion at 12 and 18 months. Among 10 structural, functional and age variables, the most reliably linked were VT/VF risk, general LV fibrosis, a measure quantifying patchy fibrosis, and non-age clustered APD dispersion. VT/VF risk related to a quantified measure of patchy fibrosis, but age did not factor strongly. The findings are consistent with the notion that VT/VF risk is associated with rate-dependent repolarization heterogeneity caused by structural remodelling and reduced lateral electrical coupling between LV myocytes, providing a substrate for heterogeneous intramural activation as HHD progresses. KEY POINTS: There is heightened arrhythmic risk with progression of hypertensive heart disease. Risk is related to increasing left ventricular fibrosis, but the nature of this relationship has not been quantified. This study is a novel systematic characterization of changes in active electrical properties and fibrotic remodelling during progression of hypertensive heart disease in a well-established animal disease model. Arrhythmic risk is predicted by several left ventricular measures, in particular fibrosis quantity and structure, and epicardial action potential duration dispersion. Age alone is not a good predictor of risk. An improved understanding of links between arrhythmic risk and fibrotic architectures in progressive hypertensive heart disease aids better interpretation of late gadolinium-enhanced cardiac magnetic resonance imaging and electrical mapping signals.

Effect of anisotropy on ventricular vulnerability to unidirectional block and reentry by single premature stimulation during normal sinus rhythm in rat heart

Single high-intensity premature stimuli when applied to the ventricles during ventricular drive of an ectopic site, as in Winfree's "pinwheel experiment," usually induce reentry arrhythmias in the normal heart, while single low-intensity stimuli barely do. Yet ventricular arrhythmia vulnerability during normal sinus rhythm remains largely unexplored. With a view to define the role of anisotropy on ventricular vulnerability to unidirectional conduction block and reentry, we revisited the pinwheel experiment with reduced constraints in the in situ rat heart. New features included single premature stimulation during normal sinus rhythm, stimulation and unipolar potential mapping from the same high-resolution epicardial electrode array, and progressive increase in stimulation strength and prematurity from diastolic threshold until arrhythmia induction. Measurements were performed with 1-ms cathodal stimuli at multiple test sites (n = 26) in seven rats. Stimulus-induced virtual electrode polarization during sinus beat recovery phase influenced premature ventricular responses. Specifically, gradual increase in stimulus strength and prematurity progressively induced make, break, and graded-response stimulation mechanisms. Hence unidirectional conduction block occurred as follows: 1) along fiber direction, on right and left ventricular free walls (n = 23), initiating figure-eight reentry (n = 17) and tachycardia (n = 12), and 2) across fiber direction, on lower interventricular septum (n = 3), initiating spiral wave reentry (n = 2) and tachycardia (n = 1). Critical time window (55.1 ± 4.7 ms, 68.2 ± 6.0 ms) and stimulus strength lower limit (4.9 ± 0.6 mA) defined vulnerability to reentry. A novel finding of this study was that ventricular tachycardia evolves and is maintained by episodes of scroll-like wave and focal activation couplets. We also found that single low-intensity premature stimuli can induce repetitive ventricular response (n = 13) characterized by focal activations.NEW & NOTEWORTHY We performed ventricular cathodal point stimulation during sinus rhythm by progressively increasing stimulus strength and prematurity. Virtual electrode polarization and recovery gradient progressively induced make, break, and graded-response stimulation mechanisms. Unidirectional conduction block occurred along or across fiber direction, initiating figure-eight or spiral wave reentry, respectively, and tachycardia sustained by scroll wave and focal activations.

Nonlinear and Stochastic Dynamics in the Heart

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

Computational approaches to understand cardiac electrophysiology and arrhythmias

Cardiac rhythms arise from electrical activity generated by precisely timed opening and closing of ion channels in individual cardiac myocytes. These impulses spread throughout the cardiac muscle to manifest as electrical waves in the whole heart. Regularity of electrical waves is critically important since they signal the heart muscle to contract, driving the primary function of the heart to act as a pump and deliver blood to the brain and vital organs. When electrical activity goes awry during a cardiac arrhythmia, the pump does not function, the brain does not receive oxygenated blood, and death ensues. For more than 50 years, mathematically based models of cardiac electrical activity have been used to improve understanding of basic mechanisms of normal and abnormal cardiac electrical function. Computer-based modeling approaches to understand cardiac activity are uniquely helpful because they allow for distillation of complex emergent behaviors into the key contributing components underlying them. Here we review the latest advances and novel concepts in the field as they relate to understanding the complex interplay between electrical, mechanical, structural, and genetic mechanisms during arrhythmia development at the level of ion channels, cells, and tissues. We also discuss the latest computational approaches to guiding arrhythmia therapy.

Predictive value of electrical restitution in hypokalemia-induced ventricular arrhythmogenicity

The ventricular action potential (AP) shortens exponentially upon a progressive reduction of the preceding diastolic interval. Steep electrical restitution slopes have been shown to promote wavebreaks, thus contributing to electrical instability. The present study was designed to assess the predictive value of electrical restitution in hypokalemia-induced arrhythmogenicity. We recorded monophasic APs and measured effective refractory periods (ERP) at distinct ventricular epicardial and endocardial sites and monitored volume-conducted ECG at baseline and after hypokalemic perfusion (2.5 mM K+ for 30 min) in isolated guinea pig heart preparations. The restitution of AP duration measured at 90% repolarization (APD90) was assessed after premature extrastimulus application at variable coupling stimulation intervals, and ERP restitution was assessed by measuring refractoriness over a wide range of pacing rates. Hypokalemia increased the amplitude of stimulation-evoked repolarization alternans and the inducibility of tachyarrhythmias and reduced ventricular fibrillation threshold. Nevertheless, these changes were associated with flattened rather than steepened APD90 restitution slopes and slowed restitution kinetics. In contrast, ERP restitution slopes were significantly increased in hypokalemic hearts. Although epicardial APD90 measured during steady-state pacing (S1-S1 = 250 ms) was prolonged in hypokalemic hearts, the left ventricular ERP was shortened. Consistently, the epicardial ERP measured at the shortest diastolic interval achieved upon a progressive increase in pacing rate was reduced in the hypokalemic left ventricle. In conclusion, this study highlights the superiority of ERP restitution at predicting increased arrhythmogenicity in the hypokalemic myocardium. The lack of predictive value of APD90 restitution is presumably related to different mode of changes in ventricular repolarization and refractoriness in a hypokalemic setting, whereby APD90 prolongation may be associated with shortened ERP.

Liberation of a pinned spiral wave by a single stimulus in excitable media

The unpinning of a spiral wave from an anatomic obstacle by the application of a single stimulus near the core of the rotating wave was studied experimentally in a cell culture of cardiomyocyte monolayers as well as by computer simulations. It is shown that, with suitable positioning and timing, a single stimulus is sufficient for the successful unpinning of a pinned spiral wave. Successful unpinning is achieved when two conditions are fulfilled: (1) The stimulus is delivered in the vulnerable window of the rotating wave, and (2) the stimulus is delivered in a spatial zone in proximity to the obstacle, where the shape of the zone is defined by the phase of the anchored spiral wave. Two different scenarios for successful unpinning are discussed, which are distinguished by the distance to the stimuli applied to the obstacle.