Mechano-electric heterogeneity of the myocardium as a paradigm of its function

Myocardial heterogeneity is well appreciated and widely documented, from sub-cellular to organ levels. This paper reviews significant achievements of the group, led by Professor Vladimir S. Markhasin, Russia, who was one of the pioneers in studying and interpreting the relevance of cardiac functional heterogeneity

The importance of mechanical conditions in the testing of excitation abnormalities in a population of electro-mechanical models of human ventricular cardiomyocytes

Background: Populations of in silico electrophysiological models of human cardiomyocytes represent natural variability in cell activity and are thoroughly calibrated and validated using experimental data from the human heart. The models have been shown to predict the effects of drugs and their pro-arrhythmic risks. However, excitation and contraction are known to be tightly coupled in the myocardium, with mechanical loads and stretching affecting both mechanics and excitation through mechanisms of mechano-calcium-electrical feedback. However, these couplings are not currently a focus of populations of cell models.Aim: We investigated the role of cardiomyocyte mechanical activity under different mechanical conditions in the generation, calibration, and validation of a population of electro-mechanical models of human cardiomyocytes.Methods: To generate a population, we assumed 11 input parameters of ionic currents and calcium dynamics in our recently developed TP + M model as varying within a wide range. A History matching algorithm was used to generate a non-implausible parameter space by calibrating the action potential and calcium transient biomarkers against experimental data and rejecting models with excitation abnormalities. The population was further calibrated using experimental data on human myocardial force characteristics and mechanical tests involving variations in preload and afterload. Models that passed the mechanical tests were validated with additional experimental data, including the effects of drugs with high or low pro-arrhythmic risk.Results: More than 10% of the models calibrated on electrophysiological data failed mechanical tests and were rejected from the population due to excitation abnormalities at reduced preload or afterload for cell contraction. The final population of accepted models yielded action potential, calcium transient, and force/shortening outputs consistent with experimental data. In agreement with experimental and clinical data, the models demonstrated a high frequency of excitation abnormalities in simulations of Dofetilide action on the ionic currents, in contrast to Verapamil. However, Verapamil showed a high frequency of failed contractions at high concentrations.Conclusion: Our results highlight the importance of considering mechanoelectric coupling in silico cardiomyocyte models. Mechanical tests allow a more thorough assessment of the effects of interventions on cardiac function, including drug testing

Mathematical model of the anatomy and fibre orientation field of the left ventricle of the heart

Background: One of the main factors affecting propagation of electrical waves and contraction in ventricles of the heart is anisotropy of cardiac tissue. Anisotropy is determined by orientation of myocardial fibres. Determining fibre orientation field and shape of the heart is important for anatomically accurate modelling of electrical and mechanical function of the heart. The aim of this paper is to introduce a theoretical rule-based model for anatomy and fibre orientation of the left ventricle (LV) of the heart and to compare it with experimental data. We suggest explicit analytical formulae that allow us to obtain the left ventricle form and its fibre direction field. The ventricle band concept of cardiac architecture given by Torrent-Guasp is chosen as the model postulate. Methods: In our approach, anisotropy of the heart is derived from some general principles. The LV is considered as a set of identical spiral surfaces, each of which can be produced from the other by rotation around one vertical axis. Each spiral surface is filled with non-intersecting curves which represent myocardial fibres. For model verification, we use experimental data on fibre orientation in human and canine hearts. Results: LV shape and anisotropy are represented by explicit analytical expressions in a curvilinear 3-D coordinate system. The derived fibre orientation field shows good qualitative agreement with experimental data. The model reveals the most thorough quantitative simulation of fibre angles at the LV middle zone. Conclusions: Our analysis shows that the band concept can generate realistic anisotropy of the LV. Our model shows good qualitative agreement between the simulated fibre orientation field and the experimental data on LV anisotropy, and the model can be used for various numerical simulations to study the effects of anisotropy on cardiac excitation and mechanical function

Mathematical modelling of the mechano-electric coupling in the human cardiomyocyte electrically connected with fibroblasts

Cardiac fibroblasts are interspersed within mammalian cardiac tissue. Fibroblasts are mechanically passive; however, they may communicate electrically with cardiomyocytes via gap junctions and thus affect the electrical and mechanical activity of myocytes. Several in-silico studies at both cellular (0D) and ventricular (3D) levels analysed the effects of fibroblasts on the myocardial electrical function. However, none of them addressed possible effects of fibroblast-myocyte electrical coupling to cardiomyocyte mechanical activity. In this paper, we propose a mathematical model for studying both electrical and mechanical responses of the human cardiomyocyte to its electrotonic interaction with cardiac fibroblasts. Our simulations have revealed that electrotonic interaction with fibroblasts affects not only the mechanical activity of the cardiomyocyte, comprising either moderate or significant reduction of contractility, but also the mechano-calcium and mechano-electric feedback loops, and all these effects are enhanced as the number of coupled fibroblasts is increased. Obtained results suggest that moderate values of the myocyte-fibroblast gap junction conductance (less than 1 nS) can be attributed to physiological conditions, contrasting to the higher values (2 nS and higher) proper rather for pathological situations (e.g. for infarct and/or border zones), since all mechanical indexes falls down dramatically in the case of such high conductance

Electrical wave propagation in an anisotropic model of the left ventricle based on analytical description of cardiac architecture.

We develop a numerical approach based on our recent analytical model of fiber structure in the left ventricle of the human heart. A special curvilinear coordinate system is proposed to analytically include realistic ventricular shape and myofiber directions. With this anatomical model, electrophysiological simulations can be performed on a rectangular coordinate grid. We apply our method to study the effect of fiber rotation and electrical anisotropy of cardiac tissue (i.e., the ratio of the conductivity coefficients along and across the myocardial fibers) on wave propagation using the ten Tusscher-Panfilov (2006) ionic model for human ventricular cells. We show that fiber rotation increases the speed of cardiac activation and attenuates the effects of anisotropy. Our results show that the fiber rotation in the heart is an important factor underlying cardiac excitation. We also study scroll wave dynamics in our model and show the drift of a scroll wave filament whose velocity depends non-monotonically on the fiber rotation angle; the period of scroll wave rotation decreases with an increase of the fiber rotation angle; an increase in anisotropy may cause the breakup of a scroll wave, similar to the mother rotor mechanism of ventricular fibrillation

Slow force response and auto-regulation of contractility in heterogeneous myocardium

Classically, the slow force response (SFR) of myocardium refers to slowly developing changes in cardiac muscle contractility induced by external mechanical stimuli, e.g. sustained stretch. We present evidence for an intra-myocardial SFR (SFRIM), caused by the internal mechanical interactions of muscle segments in heterogeneous myocardium. Here we study isometric contractions of a pair of end-to-end connected functionally heterogeneous cardiac muscles (an in-series muscle duplex). Duplex elements can be either biological muscles (BM), virtual muscles (VM), or a hybrid combination of BM and VM. The VM implements an Ekaterinburg-Oxford mathematical model accounting for the ionic and myofilament mechanisms of excitation-contraction coupling in cardiomyocytes. SFRIM is expressed in gradual changes in the overall duplex force and in the individual contractility of each muscle, induced by cyclic auxotonic deformations of coupled muscles. The muscle that undergoes predominant cyclic shortening shows force enhancement upon return to its isometric state in isolation, whereas average cyclic lengthening may decrease the individual muscle contractility. The mechanical responses are accompanied with slow and opposite changes in the shape and duration of both the action potential and Ca2+ transient in the cardiomyocytes of interacting muscles. Using the mathematical model we found that the contractility changes in interacting muscles follow the alterations in the sarcoplasmic reticulum loading in cardiomyocytes which result from the length-dependent Ca2+ activation of myofilaments and intracellular mechano-electrical feedback. The SFRIM phenomena unravel an important mechanism of cardiac functional auto-regulation applicable to the heart in norm and pathology, especially to hearts with severe electrical and/or mechanical dyssynchrony. © 2012 Elsevier Ltd

Progrès technique et inégalité

<p>The notation is the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0093617#pone-0093617-g004" target="_blank">Fig. 4</a>.</p

Scroll wave rotation period <i>T</i>, ms, as a function of total fiber rotation angle <i>α</i>, deg.

<p>Scroll wave rotation period <i>T</i>, ms, as a function of total fiber rotation angle <i>α</i>, deg.</p

Potential, mV, on the LV surface during scroll wave rotation (left) and tip trajectory for <i>D</i>₁∶<i>D</i>₂ = 1∶0.111 (red line) and for <i>D</i>₁∶<i>D</i>₂ = 1∶0.25 (black line) (right).

<p>The results are shown for model 2 (<i>γ</i>₀ = 0.2, <i>γ</i>₁ = 0.7, see text and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0093617#pone-0093617-t001" target="_blank">Table 1</a> for details).</p