Trine Krogh-Madsen

Effects of electrical and structural remodeling on atrial fibrillation maintenance: A simulation study

Atrial fibrillation, a common cardiac arrhythmia, often progresses unfavourably: in patients with long-term atrial fibrillation, fibrillatory episodes are typically of increased duration and frequency of occurrence relative to healthy controls. This is due to electrical, structural, and contractile remodeling processes. We investigated mechanisms of how electrical and structural remodeling contribute to perpetuation of simulated atrial fibrillation, using a mathematical model of the human atrial action potential incorporated into an anatomically realistic three-dimensional structural model of the human atria. Electrical and structural remodeling both shortened the atrial wavelength - electrical remodeling primarily through a decrease in action potential duration, while structural remodeling primarily slowed conduction. The decrease in wavelength correlates with an increase in the average duration of atrial fibrillation/flutter episodes. The dependence of reentry duration on wavelength was the same for electrical vs. structural remodeling. However, the dynamics during atrial reentry varied between electrical, structural, and combined electrical and structural remodeling in several ways, including: (i) with structural remodeling there were more occurrences of fragmented wavefronts and hence more filaments than during electrical remodeling; (ii) dominant waves anchored around different anatomical obstacles in electrical vs. structural remodeling; (iii) dominant waves were often not anchored in combined electrical and structural remodeling. We conclude that, in simulated atrial fibrillation, the wavelength dependence of reentry duration is similar for electrical and structural remodeling, despite major differences in overall dynamics, including maximal number of filaments, wave fragmentation, restitution properties, and whether dominant waves are anchored to anatomical obstacles or spiralling freely.

Nonlinear dynamics in cardiology.

The dynamics of many cardiac arrhythmias, as well as the nature of transitions between different heart rhythms, have long been considered evidence of nonlinear phenomena playing a direct role in cardiac arrhythmogenesis. In most types of cardiac disease, the pathology develops slowly and gradually, often over many years. In contrast, arrhythmias often occur suddenly. In nonlinear systems, sudden changes in qualitative dynamics can, counterintuitively, result from a gradual change in a system parameter-this is known as a bifurcation. Here, we review how nonlinearities in cardiac electrophysiology influence normal and abnormal rhythms and how bifurcations change the dynamics. In particular, we focus on the many recent developments in computational modeling at the cellular level that are focused on intracellular calcium dynamics. We discuss two areas where recent experimental and modeling work has suggested the importance of nonlinearities in calcium dynamics: repolarization alternans and pacemaker cell automaticity.

Cell-specific cardiac electrophysiology models.

The traditional cardiac model-building paradigm involves constructing a composite model using data collected from many cells. Equations are derived for each relevant cellular component (e.g., ion channel, exchanger) independently. After the equations for all components are combined to form the composite model, a subset of parameters is tuned, often arbitrarily and by hand, until the model output matches a target objective, such as an action potential. Unfortunately, such models often fail to accurately simulate behavior that is dynamically dissimilar (e.g., arrhythmia) to the simple target objective to which the model was fit. In this study, we develop a new approach in which data are collected via a series of complex electrophysiology protocols from single cardiac myocytes and then used to tune model parameters via a parallel fitting method known as a genetic algorithm (GA). The dynamical complexity of the electrophysiological data, which can only be fit by an automated method such as a GA, leads to more accurately parameterized models that can simulate rich cardiac dynamics. The feasibility of the method is first validated computationally, after which it is used to develop models of isolated guinea pig ventricular myocytes that simulate the electrophysiological dynamics significantly better than does a standard guinea pig model. In addition to improving model fidelity generally, this approach can be used to generate a cell-specific model. By so doing, the approach may be useful in applications ranging from studying the implications of cell-to-cell variability to the prediction of intersubject differences in response to pharmacological treatment.

Kcne2 deletion creates a multisystem syndrome predisposing to sudden cardiac death.

Background—Sudden cardiac death (SCD) is the leading global cause of mortality, exhibiting increased incidence in patients with diabetes mellitus. Ion channel gene perturbations provide a well-established ventricular arrhythmogenic substrate for SCD. However, most arrhythmia-susceptibility genes, including the KCNE2 K+ channel &bgr; subunit, are expressed in multiple tissues, suggesting potential multiplex SCD substrates. Methods and Results—Using whole-transcript transcriptomics, we uncovered cardiac angiotensinogen upregulation and remodeling of cardiac angiotensinogen interaction networks in P21 Kcne2–/– mouse pups and adrenal remodeling consistent with metabolic syndrome in adult Kcne2–/– mice. This led to the discovery that Kcne2 disruption causes multiple acknowledged SCD substrates of extracardiac origin: diabetes mellitus, hypercholesterolemia, hyperkalemia, anemia, and elevated angiotensin II. Kcne2 deletion was also a prerequisite for aging-dependent QT prolongation, ventricular fibrillation and SCD immediately after transient ischemia, and fasting-dependent hypoglycemia, myocardial ischemia, and AV block. Conclusions—Disruption of a single, widely expressed arrhythmia-susceptibility gene can generate a multisystem syndrome comprising manifold electric and systemic substrates and triggers of SCD. This paradigm is expected to apply to other arrhythmia-susceptibility genes, the majority of which encode ubiquitously expressed ion channel subunits or regulatory proteins.

Improving cardiomyocyte model fidelity and utility via dynamic electrophysiology protocols and optimization algorithms

Mathematical models of cardiac electrophysiology are instrumental in determining mechanisms of cardiac arrhythmias. However, the foundation of a realistic multiscale heart model is only as strong as the underlying cell model. While there have been myriad advances in the improvement of cellular‐level models, the identification of model parameters, such as ion channel conductances and rate constants, remains a challenging problem. The primary limitations to this process include: (1) such parameters are usually estimated from data recorded using standard electrophysiology voltage‐clamp protocols that have not been developed with model building in mind, and (2) model parameters are typically tuned manually to subjectively match a desired output. Over the last decade, methods aimed at overcoming these disadvantages have emerged. These approaches include the use of optimization or fitting tools for parameter estimation and incorporating more extensive data for output matching. Here, we review recent advances in parameter estimation for cardiomyocyte models, focusing on the use of more complex electrophysiology protocols and global search heuristics. We also discuss future applications of such parameter identification, including development of cell‐specific and patient‐specific mathematical models to investigate arrhythmia mechanisms and predict therapy strategies.

Rapid Genetic Algorithm Optimization of a Mouse Computational Model: Benefits for Anthropomorphization of Neonatal Mouse Cardiomyocytes

While the mouse presents an invaluable experimental model organism in biology, its usefulness in cardiac arrhythmia research is limited in some aspects due to major electrophysiological differences between murine and human action potentials (APs). As previously described, these species-specific traits can be partly overcome by application of a cell-type transforming clamp (CTC) to anthropomorphize the murine cardiac AP. CTC is a hybrid experimental-computational dynamic clamp technique, in which a computationally calculated time-dependent current is inserted into a cell in real-time, to compensate for the differences between sarcolemmal currents of that cell (e.g., murine) and the desired species (e.g., human). For effective CTC performance, mismatch between the measured cell and a mathematical model used to mimic the measured AP must be minimal. We have developed a genetic algorithm (GA) approach that rapidly tunes a mathematical model to reproduce the AP of the murine cardiac myocyte under study. Compared to a prior implementation that used a template-based model selection approach, we show that GA optimization to a cell-specific model results in a much better recapitulation of the desired AP morphology with CTC. This improvement was more pronounced when anthropomorphizing neonatal mouse cardiomyocytes to human-like APs than to guinea pig APs. CTC may be useful for a wide range of applications, from screening effects of pharmaceutical compounds on ion channel activity, to exploring variations in the mouse or human genome. Rapid GA optimization of a cell-specific mathematical model improves CTC performance and may therefore expand the applicability and usage of the CTC technique.

Phase Resetting Neural Oscillators: Topological Theory Versus the RealWorld

Biological oscillations, despite their vast range of periodicities, can be described mathematically by stable limit cycles. Therefore, a general theory characterizing the effects of perturbations applied to such limit cycles allows predictions of qualitative features of a particular oscillation subject to perturbation. In this chapter, we summarize this topological approach and discuss ways in which the theory breaks down, mainly for neuronal and cardiac oscillators. In particular, we describe experimental and computational studies that demonstrate apparent discontinuities in the response to perturbations, and others where there is not a rapid return to the limit cycle following a perturbation. Finally, we discuss differences between the topological and the excitability-type descriptions of neuronal oscillators.

Differential roles of two delayed rectifier potassium currents in regulation of ventricular action potential duration and arrhythmia susceptibility

Arrhythmias result from disruptions to cardiac electrical activity, although the factors that control cellular action potentials are incompletely understood. We combined mathematical modelling with experiments in heart cells from guinea pigs to determine how cellular electrical activity is regulated. A mismatch between modelling predictions and the experimental results allowed us to construct an improved, more predictive mathematical model. The balance between two particular potassium currents dictates how heart cells respond to perturbations and their susceptibility to arrhythmias.

Voltage and calcium dynamics both underlie cellular alternans in cardiac myocytes.

Cardiac alternans, a putative trigger event for cardiac reentry, is a beat-to-beat alternation in membrane potential and calcium transient. Alternans was originally attributed to instabilities in transmembrane ion channel dynamics (i.e., the voltage mechanism). As of this writing, the predominant view is that instabilities in subcellular calcium handling are the main underlying mechanism. That being said, because the voltage and calcium systems are bidirectionally coupled, theoretical studies have suggested that both mechanisms can contribute. To date, to our knowledge, no experimental evidence of such a dual role within the same cell has been reported. Here, a combined electrophysiological and calcium imaging approach was developed and used to illuminate the contributions of voltage and calcium dynamics to alternans. An experimentally feasible protocol, quantification of subcellular calcium alternans and restitution slope during cycle-length ramping alternans control, was designed and validated. This approach allows simultaneous illumination of the contributions of voltage and calcium-driven instability to total cellular instability as a function of cycle-length. Application of this protocol in in vitro guinea-pig left-ventricular myocytes demonstrated that both voltage- and calcium-driven instabilities underlie alternans, and that the relative contributions of the two systems change as a function of pacing rate.

Computational Approaches to Understanding the Role of Fibroblast-Myocyte Interactions in Cardiac Arrhythmogenesis

The adult heart is composed of a dense network of cardiomyocytes surrounded by nonmyocytes, the most abundant of which are cardiac fibroblasts. Several cardiac diseases, such as myocardial infarction or dilated cardiomyopathy, are associated with an increased density of fibroblasts, that is, fibrosis. Fibroblasts play a significant role in the development of electrical and mechanical dysfunction of the heart; however the underlying mechanisms are only partially understood. One widely studied mechanism suggests that fibroblasts produce excess extracellular matrix, resulting in collagenous septa. These collagenous septa slow propagation, cause zig-zag conduction paths, and decouple cardiomyocytes resulting in a substrate for arrhythmia. Another emerging mechanism suggests that fibroblasts promote arrhythmogenesis through direct electrical interactions with cardiomyocytes via gap junctions. Due to the challenges of investigating fibroblast-myocyte coupling in native cardiac tissue, computational modeling and in vitro experiments have facilitated the investigation into the mechanisms underlying fibroblast-mediated changes in cardiomyocyte action potential morphology, conduction velocity, spontaneous excitability, and vulnerability to reentry. In this paper, we summarize the major findings of the existing computational studies investigating the implications of fibroblast-myocyte interactions in the normal and diseased heart. We then present investigations from our group into the potential role of voltage-dependent gap junctions in fibroblast-myocyte interactions.