The experimental and clinical possibilities for studying cardiac arrhythmias in human ventricular myocardium are very limited. Therefore, the use of alternative methods such as computer simulations is of great importance. In this article we introduce a mathematical model of the action potential of human ventricular cells that, while including a high level of electrophysiological detail, is computationally cost-effective enough to be applied in large-scale spatial simulations for the study of reentrant arrhythmias. The model is based on recent experimental data on most of the major ionic currents: the fast sodium, L-type calcium, transient outward, rapid and slow delayed rectifier, and inward rectifier currents. The model includes a basic calcium dynamics, allowing for the realistic modeling of calcium transients, calcium current inactivation, and the contraction staircase. We are able to reproduce human epicardial, endocardial, and M cell action potentials and show that differences can be explained by differences in the transient outward and slow delayed rectifier currents. Our model reproduces the experimentally observed data on action potential duration restitution, which is an important characteristic for reentrant arrhythmias. The conduction velocity restitution of our model is broader than in other models and agrees better with available data. Finally, we model the dynamics of spiral wave rotation in a two-dimensional sheet of human ventricular tissue and show that the spiral wave follows a complex meandering pattern and has a period of 265 ms. We conclude that the proposed model reproduces a variety of electrophysiological behaviors and provides a basis for studies of reentrant arrhythmias in human ventricular tissue.

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Early development of ionic models for cardiac myocytes, from the pioneering modification of the Hodgkin-Huxley giant squid axon model by Noble to the iconic DiFrancesco-Noble model integrating voltage-gated ionic currents, ion pumps and exchangers, Ca 2C sequestration and Ca 2C -induced Ca 2C release, provided a general description for a mammalian Purkinje fibre (PF) and the framework for modern cardiac models. In the past two decades, development has focused on tissue-specific models with an emphasis on the sino-atrial (SA) node, atria and ventricles, while the PFs have largely been neglected. However, achieving the ultimate goal of creating a virtual human heart will require detailed models of all distinctive regions of the cardiac conduction system, including the PFs, which play an important role in conducting cardiac excitation and ensuring the synchronized timing and sequencing of ventricular contraction. In this paper, we present details of our newly developed model for the human PF cell including validation against experimental data. Ionic mechanisms underlying the heterogeneity between the PF and ventricular action potentials in humans and other species are analysed. The newly developed PF cell model adds a new member to the family of human cardiac cell models developed previously for the SA node, atrial and ventricular cells, which can be incorporated into an anatomical model of the human heart with details of its electrophysiological heterogeneity and anatomical complexity.

Since the Principle of Biological Relativity was formulated and developed there have been many implementations in a wide range of biological fields. The purpose of this article is to assess the status of the applications of the principle and to clarify some misunderstandings. The principle requires circular causality between levels of organization. But the forms of causality are also necessarily different. They contribute in asymmetric ways. Upward causation can be represented by the differential or similar equations describing the mechanics of lower level processes. Downward causation is then best represented as determining initial and boundary conditions. The questions tackled in this article are: (1) where and when do these boundaries exist? and (2) how do they convey the influences between levels? We show that not all boundary conditions arise from higher-level organization. It is important to distinguish those that do from those that don’t. Both forms play functional roles in organisms, particularly in their responses to novel challenges. The forms of causation also change according to the levels concerned. These principles are illustrated with specific examples.

Effects of cardiac mechanical heterogeneity on the electrical function of the heart are difficult to assess experimentally, yet they pose a serious (patho-)physiological challenge. Here, we present an in silico study of the effects of mechanical heterogeneity on action potential duration (APD) in mechanically interacting muscle regions and consequent effects on the dispersion of repolarization, a well-established determinant of cardiac arrhythmogenesis. Using a novel mathematical description of ventricular electromechanical activity (virtual muscle), we first assessed how differences in intrinsic contractile properties affect the electrical behavior of cardiac muscle representations. In spite of identical electrophysiological model descriptions in virtual muscle samples, faster muscle models show shorter APD than their slower counterparts. This is a consequence of Ca 2+-mediated feedback from mechanical to electrical activity in the individual muscle models. This mechano-electric feedback (MEF) is, of course, significantly more complex in native cardiac tissue, as the heterogeneous muscle elements interact both mechanically and electrically. Cardiac mechanical heterogeneity, in its most reduced form, can be represented by a duplex consisting of two mechanically interacting muscle segments. Our in silico model of heterogeneous myocardium therefore consists of two individual virtual muscles that are mechanically interconnected in-series to form a virtual heterogeneous duplex. During isometric contraction of the duplex (i.e. at constant external length), internal mechanical interactions affect Ca 2+ handling and APD of muscle elements, resulting in an increased dispersion of repolarization beyond the intrinsic APD differences. Duplex electromechanical activity is strongly affected by the activation sequence of its elements. Late activation of the faster (subepicardial type) duplex element, postponed by time-lags that correspond to normal transmural activation delays, optimizes duplex contractility and smoothes out intrinsic APD differences, thereby reducing dispersion in repolarization. This smoothing effect is not observed upon delayed activation of the slower (subendocardial type) duplex element. In both settings, changes in repolarization timing follow a nonlinear dependence of APD on activation delay. Furthermore, asynchronous activation of identical elements in a homogeneous duplex causes an impairment of contractile function and increases dispersion of repolarization. This suggests that the normal electrical activation sequence in the heart requires matching mechanical and electrical heterogeneity for optimal cardiac performance. On the subcellular level, our results suggest that mechanical modulation of Ca 2+ handling is a key mechanism of MEF in heterogeneous myocardium, which contributes to the matching of local mechanical and/or electrical activity to global hemodynamic demand.