Quantification of transmembrane currents during action potential propagation in the heart

Heart-on-a-chip systems with tissue-specific functionalities for physiological, pathological, and pharmacological studies

Recent advances in heart-on-a-chip systems hold great promise to facilitate cardiac physiological, pathological, and pharmacological studies. This review focuses on the development of heart-on-a-chip systems with tissue-specific functionalities. For one thing, the strategies for developing cardiac microtissues on heart-on-a-chip systems that closely mimic the structures and behaviors of the native heart are analyzed, including the imitation of cardiac structural and functional characteristics. For another, the development of techniques for real-time monitoring of biophysical and biochemical signals from cardiac microtissues on heart-on-a-chip systems is introduced, incorporating cardiac electrophysiological signals, contractile activity, and biomarkers. Furthermore, the applications of heart-on-a-chip systems in intelligent cardiac studies are discussed regarding physiological/pathological research and pharmacological assessment. Finally, the future development of heart-on-a-chip toward a higher level of systematization, integration, and maturation is proposed.

Cardiac cells stimulated with an axial current-like waveform reproduce electrophysiological properties of tissue fibers

BACKGROUND AND OBJECTIVE

In silico electrophysiological models are generally validated by comparing simulated results with experimental data. When dealing with single-cell and tissue scales simultaneously, as occurs frequently during model development and calibration, the effects of inter-cellular coupling should be considered to ensure the trustworthiness of model predictions. The hypothesis of this paper is that the cell-tissue mismatch can be reduced by incorporating the effects of conduction into the single-cell stimulation current.

METHODS

Five different stimulation waveforms were applied to the human ventricular O'Hara-Rudy cell model. The waveforms included the commonly used monophasic and biphasic (symmetric and asymmetric) pulses, a triangular waveform and a newly proposed asymmetric waveform (stimulation A) that resembles the transmembrane current associated with AP conduction in tissue. A comparison between single-cell and fiber simulated results was established by computing the relative difference between the values of AP-derived properties at different scales, and by evaluating the differences in the contributions of ionic conductances to each evaluated property. As a proof of the benefit, we investigated multi-scale differences in the simulation of the effects induced by dofetilide, a selective I_Kr blocker with high torsadogenic risk, on ventricular repolarization at different pacing rates.

RESULTS

Out of the five tested stimulation waveforms, stimulation A produced the closest correspondence between cell and tissue simulations in terms of AP properties at steady-state and under dynamic pacing and of ionic contributors to those AP properties. Also, stimulation A reproduced the effects of dofetilide better than the other alternative waveforms, mirroring the 'beat-skipping' behavior observed at fast pacing rates in experiments with human tissue.

CONCLUSIONS

The proposed stimulation current waveform accounts for inter-cellular coupling effects by mimicking cell excitation during AP conduction. The proposed waveform improves the correspondence between simulation scales, which could improve the trustworthiness of single-cell simulations without adding computational cost.

Bidomain modeling of electrical and mechanical properties of cardiac tissue

Throughout the history of cardiac research, there has been a clear need to establish mathematical models to complement experimental studies. In an effort to create a more complete picture of cardiac phenomena, the bidomain model was established in the late 1970s to better understand pacing and defibrillation in the heart. This mathematical model has seen ongoing use in cardiac research, offering mechanistic insight that could not be obtained from experimental pursuits. Introduced from a historical perspective, the origins of the bidomain model are reviewed to provide a foundation for researchers new to the field and those conducting interdisciplinary research. The interplay of theory and experiment with the bidomain model is explored, and the contributions of this model to cardiac biophysics are critically evaluated. Also discussed is the mechanical bidomain model, which is employed to describe mechanotransduction. Current challenges and outstanding questions in the use of the bidomain model are addressed to give a forward-facing perspective of the model in future studies.

Excitability and propagation of the electrical impulse in Venus flytrap; a comparative electrophysiological study of unipolar electrograms with myocardial tissue

Mammalian heart cells and cells of leaves of Dionaea muscipula share the ability to generate propagated action potentials, because the excitable cells are electrically coupled. In the heart the propagated action potential causes synchronized contraction of the heart muscle after automatic generation of the impulse in the sinus node. In Dionaea propagation results in closure of the trap after activation of trigger hairs by an insect. The electrical activity can be recorded in the extracellular space as an extracellular electrogram, resulting from transmembrane currents. Although the underlying physiological mechanism that causes the electrogram is similar for heart and Dionaea cells, the contribution of the various ions to the transmembrane current is different. We recorded extracellular electrograms from Dionaea leaves and compared the recorded signals with those known from the heart. The morphology of the electrograms differed considerably. In comparison to activation in mammalian myocardium, electrograms of Dionaea are more temporally and spatially variable. Whereas electrograms in healthy myocardium recorded at some distance from the site of activation reveal a simple biphasic pattern, Dionaea activation showed positive, negative or biphasic deflections. Comparison of patch clamp data from plant cells and cardiomyocytes suggests a role of temperature and ion concentrations in extracellular space for the diversity of morphologies of the Dionaea electrograms.

A model for human action potential dynamics in vivo

Computational modeling based on experimental data remains an important component in cardiac electrophysiological research, especially because clinical data such as human action potential (AP) dynamics are scarce or limited by practical or ethical concerns. Such modeling has been used to develop and test a variety of mechanistic hypotheses, with the majority of these studies involving the rate dependence of AP duration (APD) including APD restitution and conduction velocity (CV). However, there is very little information regarding the complex dynamics at the boundary of repolarization (or refractoriness) and reexcitability. Here, we developed a "minimal" ionic model of the human AP, based on in vivo human monophasic AP (MAP) recordings obtained during clinical programmed electrical stimulation (PES) to address the progressive decrease in AP take-off potential (TOP) and associated CV slowing seen during three tightly spaced extrastimuli. Recent voltage-clamp data demonstrating the effect of intracellular calcium on sodium current availability were incorporated and were required to reproduce large (>15 mV) elevations in take-off potential and progressive encroachment. Introducing clinically observed APD gradients into the model enabled us to replicate the dynamic response to PES in patients leading to conduction block and reentry formation for the positive, but not the negative, APD gradient. Finally, we modeled the dynamics of reentry and show that spiral waves follow a meandering trajectory with a period of ~180 ms. We conclude that our model reproduces a variety of electrophysiological behavior including the response to sequential premature stimuli and provides a basis for studies of the initiation of reentry in human ventricular tissue.NEW & NOTEWORTHY This work presents a new model of the action potential of the human which reproduces the complex dynamics during premature stimulation in patients.

Effect of Heart Structure on Ventricular Fibrillation in the Rabbit: A Simulation Study

Ventricular fibrillation (VF) is a lethal condition that affects millions worldwide. The mechanism underlying VF is unstable reentrant electrical waves rotating around lines called filaments. These complex spatio-temporal patterns can be studied using both experimental and numerical methods. Computer simulations provide unique insights including high resolution dynamics throughout the heart and systematic control of quantities such as fiber orientation and cellular kinetics that are not feasible experimentally. Here we study filament dynamics using two bi-ventricular 3-D high-resolution rabbit heart geometries, one with detailed fine structure and another without fine structure. We studied filament dynamics using anisotropic and isotropic conductivities, and with four cellular action potential models with different recovery kinetics. Spiral wave dynamics observed in isotropic two-dimensional sheets were not predictive of the behavior in the whole heart. In 2-D the four cell models exhibited stable reentry, meandering spiral waves, and spiral-wave breakup. In the whole heart with fine structure, all simulation results exhibited complex dynamics reminiscent of fibrillation observed experimentally. In the whole heart without fine structure, anisotropy acted to destabilize filament dynamics although the number of filaments was reduced compared to the heart with structure. In addition, in isotropic hearts without structure the two cell models that exhibited meandering spiral waves in 2-D, stabilized into figure-of-eight surface patterns. We also studied the sensitivity of filament dynamics to computer system configuration and initial conditions. After large simulation times, different macroscopic results sometimes occurred across different system configurations, likely due to a lack of bitwise reproducibility. The study conclusions were insensitive to initial condition perturbations, however, the exact number of filaments over time and their trends were altered by these changes. In summary, we present the following new results. First, we provide a new cell model that resembles the surface patterns of VF in the rabbit heart both qualitatively and quantitatively. Second, filament dynamics in the whole heart cannot be predicted from spiral wave dynamics in 2-D and we identified anisotropy as one destabilizing factor. Third, the exact dynamics of filaments are sensitive to a variety of factors, so we suggest caution in their interpretation and their quantitative analyses.

New insights on the cardiac safety factor: Unraveling the relationship between conduction velocity and robustness of propagation

Cardiac conduction disturbances are linked with arrhythmia development. The concept of safety factor (SF) has been derived to describe the robustness of conduction, but the usefulness of this metric has been constrained by several limitations. For example, due to the difficulty of measuring the necessary input variables, SF calculations have only been applied to synthetic data. Moreover, quantitative validation of SF is lacking; specifically, the practical meaning of particular SF values is unclear, aside from the fact that propagation failure (i.e., conduction block) is characterized by SF < 1. This study aims to resolve these limitations for our previously published SF formulation and explore its relationship to relevant electrophysiological properties of cardiac tissue. First, HL-1 cardiomyocyte monolayers were grown on multi-electrode arrays and the robustness of propagation was estimated using extracellular potential recordings. SF values reconstructed purely from experimental data were largely between 1 and 5 (up to 89.1% of sites characterized). This range is consistent with values derived from synthetic data, proving that the formulation is sound and its applicability is not limited to analysis of computational models. Second, for simulations conducted in 1-, 2-, and 3-dimensional tissue blocks, we calculated true SF values at locations surrounding the site of current injection for sub- and supra-threshold stimuli and found that they differed from values estimated by our SF formulation by <10%. Finally, we examined SF dynamics under conditions relevant to arrhythmia development in order to provide physiological insight. Our analysis shows that reduced conduction velocity (Θ) caused by impaired intrinsic cell-scale excitability (e.g., due to sodium current a loss-of-function mutation) is associated with less robust conduction (i.e., lower SF); however, intriguingly, Θ variability resulting from modulation of tissue scale conductivity has no effect on SF. These findings are supported by analytic derivation of the relevant relationships from first principles. We conclude that our SF formulation, which can be applied to both experimental and synthetic data, produces values that vary linearly with the excess charge needed for propagation. SF calculations can provide insights helpful in understanding the initiation and perpetuation of cardiac arrhythmia.

Electromechanics of polarized cell growth

One of the most challenging questions in cell and developmental biology is how molecular signals are translated into mechanical forces that ultimately drive cell growth and motility. Despite an impressive body of literature demonstrating the importance of cytoskeletal and motor proteins as well as osmotic stresses for cell developmental mechanics, a host of dissenting evidence strongly suggests that these factors per se cannot explain growth mechanics even at the level of a single tip-growing cell. The present study addresses this issue by exploring fundamental interrelations between electrical and mechanical fields operating in cells. In the first instance, we employ a simplified but instructive model of a quiescent cell to demonstrate that even in a quasi-equilibrium state, ion transport processes are conditioned principally by mechanical tenets. Then we inquire into the electromechanical conjugacy in growing pollen tubes as biologically relevant and physically tractable developmental systems owing to their extensively characterized growth-associated ionic fluxes and strikingly polarized growth and morphology. A comprehensive analysis of the multifold stress pattern in the growing apices of pollen tubes suggests that tip-focused ionic fluxes passing through the polyelectrolyte-rich apical cytoplasm give rise to electrokinetic flows that actualize otherwise isotropic intracellular turgor into anisotropic stress field. The stress anisotropy can be then imparted from the apical cytoplasm to the abutting frontal cell wall to induce its local extension and directional cell growth. Converging lines of evidence explored in the concluding sections attest that tip-focused ionic fluxes and associated interfacial transport phenomena are not specific for pollen tubes but are also employed by a vast variety of algal, plant, fungal and animal cells, rendering their cytoplasmic stress fields essentially anisotropic and ultimately instrumental in cell shaping, growth and motility.

Organic Bioelectronics: Materials and Biocompatibility

Organic electronic materials have been considered for a wide-range of technological applications. More recently these organic (semi)conductors (encompassing both conducting and semi-conducting organic electronic materials) have received increasing attention as materials for bioelectronic applications. Biological tissues typically comprise soft, elastic, carbon-based macromolecules and polymers, and communication in these biological systems is usually mediated via mixed electronic and ionic conduction. In contrast to hard inorganic semiconductors, whose primary charge carriers are electrons and holes, organic (semi)conductors uniquely match the mechanical and conduction properties of biotic tissue. Here, we review the biocompatibility of organic electronic materials and their implementation in bioelectronic applications.

Validation and Trustworthiness of Multiscale Models of Cardiac Electrophysiology

Computational models of cardiac electrophysiology have a long history in basic science applications and device design and evaluation, but have significant potential for clinical applications in all areas of cardiovascular medicine, including functional imaging and mapping, drug safety evaluation, disease diagnosis, patient selection, and therapy optimisation or personalisation. For all stakeholders to be confident in model-based clinical decisions, cardiac electrophysiological (CEP) models must be demonstrated to be trustworthy and reliable. Credibility, that is, the belief in the predictive capability, of a computational model is primarily established by performing validation, in which model predictions are compared to experimental or clinical data. However, there are numerous challenges to performing validation for highly complex multi-scale physiological models such as CEP models. As a result, credibility of CEP model predictions is usually founded upon a wide range of distinct factors, including various types of validation results, underlying theory, evidence supporting model assumptions, evidence from model calibration, all at a variety of scales from ion channel to cell to organ. Consequently, it is often unclear, or a matter for debate, the extent to which a CEP model can be trusted for a given application. The aim of this article is to clarify potential rationale for the trustworthiness of CEP models by reviewing evidence that has been (or could be) presented to support their credibility. We specifically address the complexity and multi-scale nature of CEP models which makes traditional model evaluation difficult. In addition, we make explicit some of the credibility justification that we believe is implicitly embedded in the CEP modeling literature. Overall, we provide a fresh perspective to CEP model credibility, and build a depiction and categorisation of the wide-ranging body of credibility evidence for CEP models. This paper also represents a step toward the extension of model evaluation methodologies that are currently being developed by the medical device community, to physiological models.

Cardiac action potential repolarization revisited: early repolarization shows all-or-none behaviour

In healthy mammalian hearts the action potential (AP) waveform initiates and modulates each contraction, or heartbeat. As a result, AP height and duration are key physiological variables. In addition, rate-dependent changes in ventricular AP duration (APD), and variations in APD at a fixed heart rate are both reliable biomarkers of electrophysiological stability. Present guidelines for the likelihood that candidate drugs will increase arrhythmias rely on small changes in APD and Q-T intervals as criteria for safety pharmacology decisions. However, both of these measurements correspond to the final repolarization of the AP. Emerging clinical evidence draws attention to the early repolarization phase of the action potential (and the J-wave of the ECG) as an additional important biomarker for arrhythmogenesis. Here we provide a mechanistic background to this early repolarization syndrome by summarizing the evidence that both the initial depolarization and repolarization phases of the cardiac action potential can exhibit distinct time- and voltage-dependent thresholds, and also demonstrating that both can show regenerative all-or-none behaviour. An important consequence of this is that not all of the dynamics of action potential repolarization in human ventricle can be captured by data from single myocytes when these results are expressed as 'repolarization reserve'. For example, the complex pattern of cell-to-cell current flow that is responsible for AP conduction (propagation) within the mammalian myocardium can change APD and the Q-T interval of the electrocardiogram alter APD stability, and modulate responsiveness to pharmacological agents (such as Class III anti-arrhythmic drugs).

A Parsimonious Model of the Rabbit Action Potential Elucidates the Minimal Physiological Requirements for Alternans and Spiral Wave Breakup

Elucidating the underlying mechanisms of fatal cardiac arrhythmias requires a tight integration of electrophysiological experiments, models, and theory. Existing models of transmembrane action potential (AP) are complex (resulting in over parameterization) and varied (leading to dissimilar predictions). Thus, simpler models are needed to elucidate the "minimal physiological requirements" to reproduce significant observable phenomena using as few parameters as possible. Moreover, models have been derived from experimental studies from a variety of species under a range of environmental conditions (for example, all existing rabbit AP models incorporate a formulation of the rapid sodium current, INa, based on 30 year old data from chick embryo cell aggregates). Here we develop a simple "parsimonious" rabbit AP model that is mathematically identifiable (i.e., not over parameterized) by combining a novel Hodgkin-Huxley formulation of INa with a phenomenological model of repolarization similar to the voltage dependent, time-independent rectifying outward potassium current (IK). The model was calibrated using the following experimental data sets measured from the same species (rabbit) under physiological conditions: dynamic current-voltage (I-V) relationships during the AP upstroke; rapid recovery of AP excitability during the relative refractory period; and steady-state INa inactivation via voltage clamp. Simulations reproduced several important "emergent" phenomena including cellular alternans at rates > 250 bpm as observed in rabbit myocytes, reentrant spiral waves as observed on the surface of the rabbit heart, and spiral wave breakup. Model variants were studied which elucidated the minimal requirements for alternans and spiral wave break up, namely the kinetics of INa inactivation and the non-linear rectification of IK.The simplicity of the model, and the fact that its parameters have physiological meaning, make it ideal for engendering generalizable mechanistic insight and should provide a solid "building-block" to generate more detailed ionic models to represent complex rabbit electrophysiology.

Estimability Analysis and Optimal Design in Dynamic Multi-scale Models of Cardiac Electrophysiology

We present an applied approach to optimal experimental design and estimability analysis for mechanistic models of cardiac electrophysiology, by extending and improving on existing computational and graphical methods. These models are 'multi-scale' in the sense that the modeled phenomena occur over multiple spatio-temporal scales (e.g., single cell vs. whole heart). As a consequence, empirical observations of multi-scale phenomena often require multiple distinct experimental procedures. We discuss the use of conventional optimal design criteria (e.g., D-optimality) in combining experimental observations across multiple scales and multiple experimental modalities. In addition, we present an improved 'sensitivity plot' - a graphical assessment of parameter estimability - that overcomes a well-known limitation in this context. These techniques are demonstrated using a working Hodgkin-Huxley cell model and three simulated experimental procedures: single cell stimulation, action potential propagation, and voltage clamp. In light of these assessments, we discuss two model modifications that improve parameter estimability, and show that the choice of optimality criterion has a profound effect on the contribution of each experiment.

Filament Dynamics during Simulated Ventricular Fibrillation in a High-Resolution Rabbit Heart

The mechanisms underlying ventricular fibrillation (VF) are not well understood. The electrical activity on the heart surface during VF has been recorded extensively in the experimental setting and in some cases clinically; however, corresponding transmural activation patterns are prohibitively difficult to measure. In this paper, we use a high-resolution biventricular heart model to study three-dimensional electrical activity during fibrillation, focusing on the driving sources of VF: “filaments,” the organising centres of unstable reentrant scroll waves. We show, for the first time, specific 3D filament dynamics during simulated VF in a whole heart geometry that includes fine-scale anatomical structures. Our results suggest that transmural activity is much more complex than what would be expected from surface observations alone. We present examples of complex intramural activity, including filament breakup and reattachment, anchoring to the thin right ventricular apex; rapid transitions among various filament shapes; and filament lengths much greater than wall thickness. We also present evidence for anatomy playing a major role in VF development and coronary vessels and trabeculae influencing filament dynamics. Overall, our results indicate that intramural activity during simulated VF is extraordinarily complex and suggest that further investigation of 3D filaments is necessary to fully comprehend recorded surface patterns.

Influence of the Circulating Current on the Propagation of the Change in Membrane Potential

The propagation of the change in potential differences across liquid membranes from the potential-sending cell to the potential-receiving cell was investigated by use of a system combined with three liquid membrane cells, which were composed of two aqueous phases and a 1,2-dichloroethane solution phase. The ionic composition of one potential-sending cell (S) was identical to that of the receiving cell (Rec), and that of another potential-sending cell (Ap) was different from that of the Rec. When the connection of cell Rec was switched from cell S to cell Ap, the change in the membrane potential was caused by the circulating current. The greater the ratio of the interfacial area of the membrane of cell Ap to that of cell Rec, the faster the change in the membrane potential propagated from cell Ap to cell Rec.

Transmembrane current imaging in the heart during pacing and fibrillation

Recently, we described a method to quantify the time course of total transmembrane current (Im) and the relative role of its two components, a capacitive current (Ic) and a resistive current (Iion), corresponding to the cardiac action potential during stable propagation. That approach involved recording high-fidelity (200 kHz) transmembrane potential (Vm) signals with glass microelectrodes at one site using a spatiotemporal coordinate transformation via measured conduction velocity. Here we extend our method to compute these transmembrane currents during stable and unstable propagation from fluorescence signals of Vm at thousands of sites (3 kHz), thereby introducing transmembrane current imaging. In contrast to commonly used linear Laplacians of extracellular potential (Ve) to compute Im, we utilized nonlinear image processing to compute the required second spatial derivatives of Vm. We quantified the dynamic spatial patterns of current density of Im and Iion for both depolarization and repolarization during pacing (including nonplanar patterns) by calibrating data with the microelectrode signals. Compared to planar propagation, we found that the magnitude of Iion was significantly reduced at sites of wave collision during depolarization but not repolarization. Finally, we present uncalibrated dynamic patterns of Im during ventricular fibrillation and show that Im at singularity sites was monophasic and positive with a significant nonzero charge (Im integrated over 10 ms) in contrast with nonsingularity sites. Our approach should greatly enhance the understanding of the relative roles of functional (e.g., rate-dependent membrane dynamics and propagation patterns) and static spatial heterogeneities (e.g., spatial differences in tissue resistance) via recordings during normal and compromised propagation, including arrhythmias.