A spatial scale factor for electrophysiological models of myocardium

Depolarization of cardiac membrane potential synchronizes calcium sparks and waves in tissue

The diastolic membrane potential (Vm) can be hyperpolarized or depolarized by various factors such as hyperkalemia or hypokalemia in the long term, or by delayed afterdepolarizations in the short term. In this study, we investigate how Vm affects Ca sparks and waves. We use a physiologically detailed mathematical model to investigate individual factors that affect Ca spark generation and wave propagation. We focus on the voltage range of -90 ∼ -70 mV, which is just below the Vm for sodium channel activation. We find that Vm depolarization promotes Ca wave propagation and hyperpolarization prevents it. This finding is directly validated in voltage clamp experiments with Ca waves using isolated rat ventricular myocytes. Ca transport by the sodium-calcium exchanger (NCX) is determined by Vm as well as Na and Ca concentrations. Depolarized Vm reduces NCX-mediated efflux, elevating [Ca]i, and thus promoting Ca wave propagation. Moreover, depolarized Vm promotes spontaneous Ca releases that can cause initiation of multiple Ca waves. This indicates that during delayed afterdepolarizations, Ca release units (CRUs) interact with not just the immediately adjacent CRUs via Ca diffusion, but also further CRUs via fast (∼0.1 ms) changes in Vm mediated by the voltage and Ca-sensitive NCX. This may contribute significantly to synchronization of Ca waves among multiple cells in tissue.

Cardiac cellular coupling and the spread of early instabilities in intracellular Ca2+

Recent experimental and modeling studies demonstrate the fine spatial scale, complex nature, and independent contribution of Ca(2+) dynamics as a proarrhythmic factor in the heart. The mechanism of progression of cell-level Ca(2+) instabilities, known as alternans, to tissue-level arrhythmias is not well understood. Because gap junction coupling dictates cardiac syncytial properties, we set out to elucidate its role in the spatiotemporal evolution of Ca(2+) instabilities. We experimentally perturbed cellular coupling in cardiac syncytium in vitro. Coupling was quantified by fluorescence recovery after photobleaching, and related to function, including subtle fine-scale Ca(2+) alternans, captured by optical mapping. Conduction velocity and threshold for alternans monotonically increased with coupling. Lower coupling enhanced Ca(2+) alternans amplitude, but the spatial spread of early (<2 Hz) alternation was the greatest under intermediate (not low) coupling. This nonmonotonic relationship was closely matched by the percent of samples exhibiting large-scale alternans at higher pacing rates. Computer modeling corroborated these experimental findings for strong but not weak electromechanical (voltage-Ca(2+)) coupling, and offered mechanistic insight. In conclusion, using experimental and modeling approaches, we reveal a general mechanism for the spatial spread of subtle cellular Ca(2+) alternans that relies on a combination of gap-junctional and voltage-Ca(2+) coupling.

New index for categorising cardiac reentrant wave: in silico evaluation

Based on the similarity between a reentrant wave in cardiac tissue and a vortex in fluid dynamics, the authors hypothesised that a new non-dimensional index, like the Reynolds number in fluid dynamics, may play a critical role in categorising reentrant wave dynamics. Therefore the goal of the present study is to devise a new index to characterise electric wave conduction in cardiac tissue and examined whether this index can be used as a biomarker for categorising the reentrant wave pattern in cardiac tissue. Similar to the procedure used to derive the Reynolds number in fluid dynamics, the authors used a non-dimensionalisation technique to obtain the new index. Its usefulness was verified using a two-dimensional simulation model of electrical wave propagation in cardiac tissue. The simulation results showed that electrical waves in cardiac tissue move into an unstable region when the index exceeds a threshold value.

Models of cardiac tissue electrophysiology: progress, challenges and open questions

Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.

Macroscopic optical mapping of excitation in cardiac cell networks with ultra-high spatiotemporal resolution

Optical mapping of cardiac excitation using voltage- and calcium-sensitive dyes has allowed a unique view into excitation wave dynamics, and facilitated scientific discovery in the cardiovascular field. At the same time, the structural complexity of the native heart has prompted the design of simplified experimental models of cardiac tissue using cultured cell networks. Such reduced experimental models form a natural bridge between single cells and tissue/organ level experimental systems to validate and advance theoretical concepts of cardiac propagation and arrhythmias. Macroscopic mapping (over >1cm(2) areas) of transmembrane potentials and intracellular calcium in these cultured cardiomyocyte networks is a relatively new development and lags behind whole heart imaging due to technical challenges. In this paper, we review the state-of-the-art technology in the field, examine specific aspects of such measurements and outline a rational system design approach. Particular attention is given to recent developments of sensitive detectors allowing mapping with ultra-high spatiotemporal resolution (>5 megapixels/s). Their interfacing with computer platforms to match the high data throughput, unique for this new generation of detectors, is discussed here. This critical review is intended to guide basic science researchers in assembling optical mapping systems for optimized macroscopic imaging with high resolution in a cultured cell setting. The tools and analysis are not limited to cardiac preparations, but are applicable for dynamic fluorescence imaging in networks of any excitable media.

The sensitivity of the heart to static magnetic fields

Static magnetic fields induce flow potentials in arterial flows in and around the heart, that have been detected as distortions in the ECG. The resultant currents flowing through the myocardium could alter the rate or rhythm of the heart. No such changes have been seen in animal experiments, or with humans, in static fields up to 8 T. The possible effects of such currents induced by fields larger than 8 T on cardiac pacemaker rate, and arrhythmogenesis are reviewed, using virtual cardiac tissues-computational models of cardiac electrophysiology. Arrhythmogenesis can be by the initiation of ectopic beats, or by re-entry, whose probability of occurrence is increased by any increase in the electrical heterogeneity, in particular, the action potential duration heterogeneity of the ventricle. Focal ectopic activity would be readily detectable, but since re-entrant arrhythmias are very rare events, even a large increase in their probability of occurrence still leaves them unlikely to be observed. Both of these two arrhythmogenic mechanisms would show a steep sigmoidal, or threshold dependence on induced current intensity, with the threshold for increasing the vulnerability to re-entry less than the threshold for initiating activity. Failure to observe them at fields less than 8 T provides only a lower bound for any threshold for arrhythmogenesis.