Reconstructing cardiac electrical excitations from optical mapping recordings.

The reconstruction of electrical excitation patterns through the unobserved depth of the tissue is essential to realizing the potential of computational models in cardiac medicine. We have utilized experimental optical-mapping recordings of cardiac electrical excitation on the epicardial and endocardial surfaces of a canine ventricle as observations directing a local ensemble transform Kalman filter data assimilation scheme. We demonstrate that the inclusion of explicit information about the stimulation protocol can marginally improve the confidence of the ensemble reconstruction and the reliability of the assimilation over time. Likewise, we consider the efficacy of stochastic modeling additions to the assimilation scheme in the context of experimentally derived observation sets. Approximation error is addressed at both the observation and modeling stages through the uncertainty of observations and the specification of the model used in the assimilation ensemble. We find that perturbative modifications to the observations have marginal to deleterious effects on the accuracy and robustness of the state reconstruction. Furthermore, we find that incorporating additional information from the observations into the model itself (in the case of stimulus and stochastic currents) has a marginal improvement on the reconstruction accuracy over a fully autonomous model, while complicating the model itself and thus introducing potential for new types of model errors. That the inclusion of explicit modeling information has negligible to negative effects on the reconstruction implies the need for new avenues for optimization of data assimilation schemes applied to cardiac electrical excitation.

Key aspects for effective mathematical modelling of fractional-diffusion in cardiac electrophysiology: a quantitative study.

Microscopic structural features of cardiac tissue play a fundamental role in determining complex spatio-temporal excitation dynamics at the macroscopic level. Recent efforts have been devoted to the development of mathematical models accounting for non-local spatio-temporal coupling able to capture these complex dynamics without the need of resolving tissue heterogeneities down to the micro-scale. In this work, we analyse in detail several important aspects affecting the overall predictive power of these modelling tools and provide some guidelines for an effective use of space-fractional models of cardiac electrophysiology in practical applications. Through an extensive computational study in simplified computational domains, we highlight the robustness of models belonging to different categories, i.e., physiological and phenomenological descriptions, against the introduction of non-locality, and lay down the foundations for future research and model validation against experimental data. A modern genetic algorithm framework is used to investigate proper parameterisations of the considered models, and the crucial role played by the boundary assumptions in the considered settings is discussed. Several numerical results are provided to support our claims.

Creation and application of virtual patient cohorts of heart models.

Patient-specific cardiac models are now being used to guide therapies. The increased use of patient-specific cardiac simulations in clinical care will give rise to the development of virtual cohorts of cardiac models. These cohorts will allow cardiac simulations to capture and quantify inter-patient variability. However, the development of virtual cohorts of cardiac models will require the transformation of cardiac modelling from small numbers of bespoke models to robust and rapid workflows that can create large numbers of models. In this review, we describe the state of the art in virtual cohorts of cardiac models, the process of creating virtual cohorts of cardiac models, and how to generate the individual cohort member models, followed by a discussion of the potential and future applications of virtual cohorts of cardiac models. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Electromechanical vortex filaments during cardiac fibrillation.

The self-organized dynamics of vortex-like rotating waves, which are also known as scroll waves, are the basis of the formation of complex spatiotemporal patterns in many excitable chemical and biological systems. In the heart, filament-like phase singularities that are associated with three-dimensional scroll waves are considered to be the organizing centres of life-threatening cardiac arrhythmias. The mechanisms that underlie the onset, maintenance and control of electromechanical turbulence in the heart are inherently three-dimensional phenomena. However, it has not previously been possible to visualize the three-dimensional spatiotemporal dynamics of scroll waves inside cardiac tissues. Here we show that three-dimensional mechanical scroll waves and filament-like phase singularities can be observed deep inside the contracting heart wall using high-resolution four-dimensional ultrasound-based strain imaging. We found that mechanical phase singularities co-exist with electrical phase singularities during cardiac fibrillation. We investigated the dynamics of electrical and mechanical phase singularities by simultaneously measuring the membrane potential, intracellular calcium concentration and mechanical contractions of the heart. We show that cardiac fibrillation can be characterized using the three-dimensional spatiotemporal dynamics of mechanical phase singularities, which arise inside the fibrillating contracting ventricular wall. We demonstrate that electrical and mechanical phase singularities show complex interactions and we characterize their dynamics in terms of trajectories, topological charge and lifetime. We anticipate that our findings will provide novel perspectives for non-invasive diagnostic imaging and therapeutic applications.

Multi-band decomposition analysis: application to cardiac alternans as a function of temperature.

OBJECTIVE: It has long been known that variations in temperature can facilitate the development of cardiac arrhythmias. Here, we aim to quantify the effects of temperature on cardiac alternans properties. APPROACH: in this work, we use optical mapping recordings of canine ventricular epicardial preparations to demonstrate that hypothermia can promote the formation of alternans, which is an important precursor to potentially lethal arrhythmias like fibrillation. We then present a novel quantification of alternans properties for a broad range of cycle lengths under different thermal states. Specifically, we apply the recently developed multi-band-decomposition analysis (MBDA) in the context of cardiac action potential dynamics. MAIN RESULTS: We show that the MBDA offers several advantages compared with traditional analysis of action potential durations. First, MBDA allows a depiction and quantification of the magnitude of alternans at all threshold values simultaneously and thus offers more information about how alternans relates to the action potential morphology while also removing the necessity of choosing a single threshold value. Second, the MBDA technique offers simple ways for assessing action potential amplitude alternans. Finally, MBDA provides a quantification of signal quality without any additional processing. SIGNIFICANCE: We find that the MBDA technique shows promise in leading to a deeper understanding of cardiac alternans properties.

Reconstructing three-dimensional reentrant cardiac electrical wave dynamics using data assimilation.

For many years, reentrant scroll waves have been predicted and studied as an underlying mechanism for cardiac arrhythmias using numerical techniques, and high-resolution mapping studies using fluorescence recordings from the surfaces of cardiac tissue preparations have confirmed the presence of visible spiral waves. However, assessing the three-dimensional dynamics of these reentrant waves using experimental techniques has been limited to verifying stable scroll-wave dynamics in relatively thin preparations. We propose a different approach to recovering the three-dimensional dynamics of reentrant waves in the heart. By applying techniques commonly used in weather forecasting, we combine dual-surface observations from a particular experiment with predictions from a numerical model to reconstruct the full three-dimensional time series of the experiment. Here, we use model-generated surrogate observations from a numerical experiment to evaluate the performance of the ensemble Kalman filter in reconstructing such time series for a discordant alternans state in one spatial dimension and for scroll waves in three dimensions. We show that our approach is able to recover time series of both observed and unobserved variables matching the truth. Where nearby observations are available, the error is reduced below the synthetic observation error, with a smaller reduction with increased distance from observations. Our findings demonstrate that state reconstruction for spatiotemporally complex cardiac electrical dynamics is possible and will lead naturally to applications using real experimental data.

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.

Mechanisms for discordant alternans.

INTRODUCTION: Discordant alternans has the potential to produce larger alternans of the ECG T wave than concordant alternans, but its mechanism is unknown. METHODS AND RESULTS: We demonstrate by one- and two-dimensional simulation of action potential propagation models that discordant alternans can form spontaneously in spatially homogeneous tissue through one of two mechanisms, due to the interaction of conduction velocity and action potential duration restitution at high pacing frequencies or through the dispersion of diastolic interval produced by ectopic foci. In discordant alternans due to the first mechanism, the boundaries marking regions of alternans with opposite phase arise far from the stimulus site, move toward the stimulus site, and stabilize. Dynamic splitting of action potential duration restitution curves due to electrotonic coupling plays a crucial role in this stability. Larger tissues and faster pacing rates are conducive to multiple boundaries, and inhomogeneities of tissue properties facilitate or inhibit formation of boundaries. CONCLUSION: Spatial inhomogeneities of electrical restitution properties are not required to produce discordant alternans.

Alternans and the onset of ventricular fibrillation.

Ventricular fibrillation (VF) remains a major cause of death in the industrialized world. Alternans (a period-doubling bifurcation of cardiac electrical activity) have recently been causally linked to the progression from ventricular tachycardia (VT) to VF, a more spatiotemporally disorganized electrical activity. In this paper, we show how alternans and thus VT degenerate to chaos via multiple, specific dynamical routes, largely associated with spatial components of VF dynamics, explaining failures of many recently proposed antiarrhythmic drugs. Identification of dynamical mechanisms for the onset of VF should lead to the design of future experiments and consequently to more effective antiarrhythmic drugs.