| Calcium is considered to be the most important ion for the physiological function of heart, and plays a profound role in cardiac excitation, myocardium contraction, signal transduction, and gene expression et al. Calcium handling is generally accepted to be the key connection between cardiac electrophysiology and mechanics. At present, there are still numerous questions and controversies on precise mechanisms of cardiac calcium handling. Therefore, modeling of cardiac calcium handling by mathematic language and methods has theoretical value and application value in exploring inherent mechanics of cardiac handling and studying pathological mechanism in heart diseases. We analyzed properties of calcium cycling, and developed a microcosmic calcium handling model on sub-cellular level and a multi-scale coupled model in this paper. A new concept was incorporated in the model for the first time, which provided a powerful model support and theoretical analysis for mechanic research in heart diseased especially heart failure. Physiology of calcium handling in myocardial cells, modeling, simulation, and pathophysiologic mechanism study are involved in this paper. Our research work includes five parts as followed:(1) Review of progress of calcium handling mathematic models and corresponding theoretical knowledge.We reviewed the progress and classification of calcium handling mathematic models, and then introduced anatomical structure of myocytes, action potential, muscle contraction, and calcium handling in process of cardiac excitation-contraction coupling. Then we focused on local control theory of calcium cycling, the properties of calcium channel, as well as sarcoplasmic reticulum (SR) calcium store uptake and release. Finally we described the basic features and inherent mechanics of calcium release events including calcium sparks and waves.(2) The microcosmic calcium handling model on sub-cellular level.Based on cytoplasmic calcium reaction-diffusion system, a spatio-temporal two dimension calcium handling model on sub-cellular level was developed with more realistic geometry of a ventricular myocyte and absorbing boundary conditions. Then the model was applied to simulate sub-cellular calcium signals including calcium sparks and waves, and to analyze these calcium signals quantitatively. Moreover, the phenomena of abnormal calcium signals and disturbed calcium equilibrium in ventricular cells under pathological conditions were analyzed by this model. The simulation results showed that the unstability of RyR clusters and/or the increase of resting [Ca2+]i would contributed to occurrence of spontaneous Ca2+ waves, and accelerated propagation of Ca2+ waves, while the effects of SR Ca2+ leak and SR Ca2+ pump were smaller. These results suggest that the initiation and development of Ca2+ waves are regulated by multiple factors.(3) The effect of rogue RyRs on calcium dynamic in failing heart.We incorporated the concept of'rogue RyR' into the spatio-temporal two dimension calcium handling model, then to simulate the characteristics of calcium handling when SR calcium store was partially unloaded in heart failure. The simulation results showed that calcium release via rogue RyR channels increased visible calcium leak in diastolic myocytes; raised the probability of occurrence of spontaneous calcium waves when SR luminal calcium concentration was reduced; and elevated the propagation velocity of calcium waves. The conclusion was that rogue RyR had an important role in disturbing calcium equilibrium in failing heart. These phenomena could not be mimicked in other calcium model by altering the parameters of RyR clusters and other ionic channels. Therefore, our work provided a new concept involved in calcium handling, and contributed to comprehending the mechanism of calcium dysfuncion in failing heart.(4) The multi-scale coupled model.We developed a multi-scale coupled model from sub-cellular level to cellular level in ventricular cell. The model was used to simulate sub-cellular microcosmic calcium handling and global calcium transient as well as electrophysiological property, and the influence among those components. Taking advantage of this coupled model, we found that SR luminal calcium concentration could influence calcium handling on cellular and sub-cellular levels as well as membrane potential and other electrophysiological properties. Moreover, overloaded SR Ca2+ pool was prone to induce spontaneous Ca2+ waves, and consequently leads to DADs.(5) Arrhythmogenic effect of rogue RyRs in failing heart.We incorporated rogue RyR channels into the multi-scale coupled model and developed a heart failure model based on it, to simulate the effect of density of rogue RyRs on subcellular calcium release events and consequent changes of global calcium transient and cellular pathophysiology. The simulation results indicated that the existence of rogue RyRs would induce delayed afterdepolarizations (DADs) and triggered action potential in ventricular cells, and there is a tight relationship between these triggered activities and distribution of rogue RyRs in heart failure, which suggested an arrhythmogenic effect of rogue RyRs. |
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