Minimum Information about a Cardiac Electrophysiology Experiment (MICEE): standardised reporting for model reproducibility, interoperability, and data sharing.

Cardiac experimental electrophysiology is in need of a well-defined Minimum Information Standard for recording, annotating, and reporting experimental data. As a step towards establishing this, we present a draft standard, called Minimum Information about a Cardiac Electrophysiology Experiment (MICEE). The ultimate goal is to develop a useful tool for cardiac electrophysiologists which facilitates and improves dissemination of the minimum information necessary for reproduction of cardiac electrophysiology research, allowing for easier comparison and utilisation of findings by others. It is hoped that this will enhance the integration of individual results into experimental, computational, and conceptual models. In its present form, this draft is intended for assessment and development by the research community. We invite the reader to join this effort, and, if deemed productive, implement the Minimum Information about a Cardiac Electrophysiology Experiment standard in their own work.

Microtopographical effects of natural scaffolding on cardiomyocyte function and arrhythmogenesis.

A natural myocardial patch for heart regeneration derived from porcine urinary bladder matrix (UBM) was previously reported to outperform synthetic materials (Dacron and expanded polytetrafluoroethylene (ePTFE)) used in current surgical treatments. UBM, an extracellular matrix prepared from urinary bladder, has intricate three-dimensional architecture with two distinct sides: the luminal side with a smoother surface relief; and the abluminal side with a fine mesh of nano- and microfibers. This study tested the ability of this natural scaffold to support functional cardiomyocyte networks, and probed how the local microtopography and composition of the two sides affects cell function. Cardiomyocytes isolated from neonatal rats were seeded in vitro to form cardiac tissue onto luminal (L) or abluminal (Ab) UBM. Immunocytochemistry of contractile cardiac proteins demonstrated growth of cardiomyocyte networks with mature morphology on either side of UBM, but greater cell compactness was seen in L. Fluorescence-based imaging techniques were used to measure dynamic changes in intracellular calcium concentration upon electrical stimulation of L and Ab-grown cells. Functional differences in cardiac tissue grown on the two sides manifested themselves in faster calcium recovery (p<0.04) and greater hysteresis (difference in response to increasing and decreasing pacing rates) for L vs Ab side (p<0.03). These results suggest that surface differences may be leveraged to engineer the desired cardiomyocyte responses and highlight the potential of natural scaffolds for fostering heart repair.

Modelling excitable cells using cycle-linear hybrid automata.

Cycle-linear hybrid automata (CLHAs), a new model of excitable cells that efficiently and accurately captures action-potential morphology and other typical excitable-cell characteristics such as refractoriness and restitution, is introduced. Hybrid automata combine discrete transition graphs with continuous dynamics and emerge in a natural way during the (piecewise) approximation process of any nonlinear system. CLHAs are a new form of hybrid automata that exhibit linear behaviour on a per-cycle basis but whose overall behaviour is appropriately nonlinear. To motivate the need for this modelling formalism, first it is shown how to recast two recently proposed models of excitable cells as hybrid automata: the piecewise-linear model of Biktashev and the nonlinear model of Fenton-Karma. Both of these models were designed to efficiently approximate excitable-cell behaviour. We then show that the CLHA closely mimics the behaviour of several classical highly nonlinear models of excitable cells, thereby retaining the simplicity of Biktashev's model without sacrificing the expressiveness of Fenton-Karma. CLHAs are not restricted to excitable cells; they can be used to capture the behaviour of a wide class of dynamic systems that exhibit some level of periodicity plus adaptation.

Efficient event-driven simulation of excitable hybrid automata.

We present an efficient, event-driven simulation framework for large-scale networks of excitable hybrid automata (EHA), a particular kind of hybrid automata that we use to model excitable cells. A key aspect of EHA is that they possess protected modes of operation in which they are non-responsive to external inputs. In such modes, our approach takes advantage of the analytical solution of the modes' linear differential equations to eliminate all integration steps, and therefore to dramatically reduce the amount of computation required. We first present a simple simulation framework for EHA based on a time-step integration method that follows naturally from our EHA models. We then present our event-driven simulation framework, where each cell has an associated event specifying both the type of processing next required for the cell and a time at which the processing must occur. A priority queue, specifically designed to reduce queueing overhead, maintains the correct ordering among events. This approach allows us to avoid handling certain cells for extended periods of time. Through a mode-by-mode case analysis, we demonstrate that our event-driven simulation procedure is at least as accurate as the time-step one. As experimental validation of the efficacy of the event-driven approach, we demonstrate a five-fold improvement in the simulation time required to produce spiral waves in a 400-x-400 cell array.

A cycle-linear approach to modeling action potentials.

We introduce cycle-linear hybrid automata (CLHA) and show how they can be used to efficiently model dynamical systems that exhibit nonlinear, pseudo-periodic behavior. CLHA are based on the observation that such systems cycle through a fixed set of operating modes, although the dynamics and duration of each cycle may depend on certain computational aspects of past cycles. CLHA are constructed around these modes such that the per-cycle, per-mode dynamics are given by a time-invariant linear system of equations; the parameters of the system are dependent on a deformation coefficient computed at the beginning of each cycle as a function of memory units. Viewed over time, CLHA generate a very intuitive, linear approximation of the entire phase space of the original, nonlinear system. We show how CLHA can be used to efficiently model the action potential of various types of excitable cells and their adaptation to pacing frequency.

Hybrid automata as a unifying framework for modeling excitable cells.

We propose hybrid automata (HA) as a unifying framework for computational models of excitable cells. HA, which combine discrete transition graphs with continuous dynamics, can be naturally used to obtain a piecewise, possibly linear, approximation of a nonlinear excitable-cell model. We first show how HA can be used to efficiently capture the action-potential morphology--as well as reproduce typical excitable-cell characteristics such as refractoriness and restitution--of the dynamic Luo-Rudy model of a guinea-pig ventricular myocyte. We then recast two well-known computational models, Biktashev's and Fenton-Karma, as HA without any loss of expressiveness. Given that HA possess an intuitive graphical representation and are supported by a rich mathematical theory and numerous analysis tools, we argue that they are well positioned as a computational model for biological processes.

Contact fluorescence imaging of reentry in monolayers of cultured neonatal rat ventricular myocytes.

INTRODUCTION: We present a novel contact fluorescence imaging (CFI) approach to monitor transmembrane potentials in monolayers of cultured neonatal rat ventricular cells. We apply CFI to demonstrate, for the first time, long-term recordings as well as electrical induction and termination of reentrant activity in this in vitro model. METHODS AND RESULTS: CFI was performed in confluent cell monolayers stained with di-8-ANEPPS. An anatomic obstacle (6 x 0.5 mm) was created in the center of the monolayers. Reentry was induced with a premature stimulus after pacing at 2 Hz (both via field stimulation). Seven sustained (>3 min) reentrant episodes, anchored to the anatomic obstacle, were observed in three monolayers. Field stimulation (30 V/cm) was applied to successfully terminate 6 of the 7 reentries. Analysis of reentrant activity showed similarities with anatomic reentry in tissue preparations, such as reduced conduction velocity around the core, variable conduction velocity along the reentrant pathway due to wavefront curvature effects, and field-induced activation at the obstacle borders leading to reentry termination (cardioversion). CONCLUSION: This study demonstrates the feasibility of CFI for macroscopic optical mapping of transmembrane potentials in a single layer of cultured cells. Our results suggest that the monolayer cell culture model is an attractive complement to tissue models of reentry and cardioversion.

Influence of the electric axis of stimulation on the induced transmembrane potentials in ellipsoidal bidomain heart.

This theoretical study was provoked by and designed to interpret, complement and extend the implications of recent experimental observations by Wikswo and Lin (PACE, 21:940, 1998) on the epicardial surface of rabbit hearts. Using a macroscopic bidomain representation of the cardiac structure and the finite element method, we model the response of the heart to uniform electric fields applied under different angles. To overcome intra- and interspecies differences in the geometric and structural characteristics of the cardiac muscle, the analysis is conducted for an idealized ellipsoidal heart. Although idealized, this heart model incorporates important structural features, i.e., fiber curvature, transmural fiber rotation, and unequal anisotropy for the intra- and extracellular domains. This study shows that regions of maximum polarization of opposite sign may develop along an axis, significantly deviating from the axis of the applied electric field. The polarization evoked inside the ventricular wall seems to be a major contributor to this phenomenon. Nonperiodic structural inhomogeneities on multicellular level (endocardial "trabeculation" in our model) result in local unaligned polarization dipoles weakening the magnitude of the global polarization dipole and reducing its deviation from the axis of stimulation. Our results might be helpful in improving current understanding of defibrillation mechanisms.

Patterns of and mechanisms for shock-induced polarization in the heart: a bidomain analysis.

This paper examines the combined action of cardiac fiber curvature and transmural fiber rotation in polarizing the myocardium under the conditions of a strong electrical shock. The study utilizes a three-dimensional finite element model and the continuous bidomain representation of cardiac tissue to model steady-state polarization resulting from a defibrillation-strength uniform applied field. Fiber architecture is incorporated in the model via the shape of the heart, an ellipsoid of variable ellipticity index, and via an analytical function, linear or nonlinear, describing the transmural fiber rotation. Analytical estimates and numerical results are provided for the location and shape of the "bulk" polarization (polarization away from the tissue boundaries) as a function of the fiber field, or more specifically, of the conductivity changes in axial and radial direction with respect to the applied electrical field lines. Polarization in the tissue "bulk" is shown to exist only under the condition of unequal anisotropy ratios in the extra- and intracellular spaces. Variations in heart geometry and, thus, fiber curvature, are found to lead to change in location of the zones of significant membrane polarization. The transmural fiber rotation function modulates the transmembrane potential profile in the radial direction. A higher gradient of the transmural transmembrane potential is observed in the presence of fiber rotation as compared to the no rotation case. The analysis presented here is a step forward in understanding the interaction between tissue structure and applied electric field in establishing the pattern of membrane polarization during the initial phase of the defibrillation shock.

Defibrillation efficacy of different electrode placements in a human thorax model.

The objective of this study was to measure the defibrillation threshold (DFT) associated with different electrode placements using a three-dimensional anatomically realistic finite element model of the human thorax. Coil electrodes (Endotak DSP, model 125, Guidant/CPI) were placed in the RV apex along the lateral wall (RV), withdrawn 10 mm away from the RV apex along the lateral wall (RVprox), in the RV apex along the anterior septum (RVseptal), and in the SVC. An active pulse generator (can) was placed in the subcutaneous prepectoral space. Five electrode configurations were studied: RV-->SVC, RVprox-->SVC, RVSEPTAL-->SVC, RV-->Can, and RV-->SVC + Can. DFTs are defined as the energy required to produce a potential gradient of at least 5 V/cm in 95% of the ventricular myocardium. DFTs for RV-->SVC, RVprox-->SVC, RVseptal-->SVC, RV-->Can, and RV-->SVC + Can were 10, 16, 7, 9, and 6 J, respectively. The DFTs measured at each configuration fell within one standard deviation of the mean DFTs reported in clinical studies using the Endotak leads. The relative changes in DFT among electrode configurations also compared favorably. This computer model allows measurements of DFT or other defibrillation parameters with several different electrode configurations saving time and cost of clinical studies.

Virtual electrode effects in transvenous defibrillation-modulation by structure and interface: evidence from bidomain simulations and optical mapping.

INTRODUCTION: Our goal in this combined modeling and experimental study was to gain insight into the transmembrane potential changes in defibrillation conditions, namely, when shocks are delivered by an implantable cardioverter defibrillator (ICD). Two hypotheses concerning the presence and characteristics of virtual electrode effects (VEE) during an ICD shock were tested numerically and experimentally: (H1) anisotropy-dependent VEE are induced over a considerable portion of the "bulk" myocardium; and (H2) surface (epicardial and endocardial) VEE are generated under special tissue bath conditions and are not fully anisotropy determined. METHODS AND RESULTS: Optical mapping was performed on Langendorff-perfused rabbit hearts (n = 4) stained with di-4-ANEPPS. Monophasic shocks were applied during the plateau phase of an action potential through a 9-mm long distal electrode in the right or left ventricle and a 6-cm proximal electrode positioned 3 cm posteriorly to the heart. We modeled the experiment using an ellipsoidal bidomain heart with transmural fiber rotation, placed in a perfusing bath, and subjected to defibrillation shocks delivered by an electrode configuration as described. Our numerical simulations demonstrated VEE occupying a significant portion of the myocardium in the conditions of unequal anisotropy ratios for the intra- and extracellular domains. Statistically significant differences in epicardial polarization patterns were predicted numerically and confirmed experimentally when the interface conditions varied. CONCLUSION: The present study concludes that VEE are present in transvenous defibrillation. They are shaped by the combined effect of cardiac tissue characteristics and interface conditions. Because of their size, VEE might contribute significantly to defibrillation outcome.