Features of the Left Ventricular Functional Geometry in Patients with Myocardial Diseases with Varying Degrees of Systolic Dysfunction.

We revealed some features of the left ventricular functional geometry in patients with myocardial diseases with different degrees of left ventricular systolic dysfunction. A negative correlation was found between the spatio-temporal heterogeneity of the kinetics of the left ventricular wall during systole and ejection fraction in normal heart and in systolic dysfunction. The differences in the quantitative characteristics of the functional geometry between patients and normal subjects and between different groups of patients depended on the severityof left-ventricular systolic dysfunction. In particular, spatial heterogeneity index that characterizes heterogeneity of systolic movement of the wall segments and end-systolic Fourier shape-power index characterizing complexity of the left ventricle shape during systole differed significantly in the examined groups of patients and have the greatest diagnostic power.

[Modeling of disturbances in electrical and mechanical function of cardiomyocytes under acute ischemia].

The effect of acute myocardial ischemia on the electrical and mechanical function of cardiomyocytes was studied in the framework of a mathematical model of a single cardiomyocyte. Acute ischemia consequences were simulated via a combination of two factors--a reduction of intracellular ATP concentration and an increase in extracellular potassium concentration, which affect the kinetics of ATP-sensitive potassium current and other potassium currents. In accord with experimental data, ischemic models produce action potential shortening and diastolic depolarization, which reduce contractile, ability of cardiomyocytes, Utilizing a 'difference-current integral' approach, we assessed quantitative contribution of ionic currents to changes in the action potential generation during ischemic injuries. It has been shown that an increase in the amplitude of inward rectifier potassium current I(K1) with increased extracellular potassium concentration has most essential contribution to the changes in the action potential duration under ischemia.

[Electromechanical coupling in cardiomyocytes from transmural layers of guinea pig left ventricle].

The electrical and mechanical activity of heart ventricle cardiomyocytes is known to vary depending on the spatial location of cells in the wall, in particular, transmurally from the sub-endocardial layer to the sub-epicardial one. To investigate intracellular mechanisms of the functional heterogeneity of cardiomyocytes we developed mathematical models of the electromechanical coupling in cardiomyocytes from different transmural layers across the left ventricle (LV) wall of guinea pig. It is shown that the mechanisms of both direct linkages and feedback in the electromechanical coupling contribute to differences in both the shape and duration of action potential, and speed characteristics of contraction between isolated cardiac myocytes from the sub-endocardial and sub-epicardial layers.

[Contribution of cooperative mechanisms of the thin filament activation to the myocardium contractile function. Assessment by a mathematical model].

We applied a mathematical model to compare the contributions to the myocardium mechanical activity of two a priori feasible variants of the cooperative effect of myosin cross-bridges on the calcium activation of sarcomere thin filaments. One of these variants implies that cross-bridge cooperative influence on the troponin C affinity to calcium is localized within the same functional cluster A7TmTn where the cross-bridge is attached. The second variant is based on the assumption that cross-bridges may affect the affinity of troponin C to calcium in other functional clusters A7TmTn as well (so that the nearer to the cross-bridge a cluster lies, the stronger the cross-bridge affects the affinity of CaTnC complex in this cluster). Each of these two variants and its contribution to the active mechanical performance of the heart muscle during the contraction-relaxation cycle were alternatively assessed in the model. It was found that only the second variant correctly simulates the mechanical activity of the muscle. Thus, the modeling suggests that just this variant of the cooperativity seems to be more feasible.

[Modeling of mechanoelectric coupling in cardiomyocytes in norm and pathology].

We developed mathematical models of the electromechanical function of cardiomyocytes and the simplest mechanically heterogeneous myocardial systems, muscle duplexes. By means of these models we studied the contribution of mechanoelectric feedbacks to the contractile activity of the myocardium in norm and pathology. In particular, we simulated and clarified the effects of mechanical conditions on both the form and the duration of the action potential during contractions. From this standpoint different kinds of myocardium mechanical heterogeneity were analyzed. As we have established, the latter can play both a positive and a negative role, depending on the distribution of mechanical nonuniformity and the sequence of activation of heterogeneous myocardium system elements. By means of the same models, we studied the contribution of mechanical factors to the arrhythmogenicity in the case of the cardiomyocyte calcium overload caused by the attenuation of the sodium-potassium pump and outlined the ways for correcting the contractile function in these disturbances.

[The role of nonspecific troponin in kinetics of intracellular calcium in cardiomyocytes]. / Rol' nespetsificheskogo troponina v kinetike vnutrikletochnogo kal'tsiia v kardiomitsitakh.

According to literature data nonspecific troponin TnC2 binds calcium in cardiac myocytes slowly and does not influence calcium transient. Therefore TnC2 often was not taken into consideration in models of the intracellular calcium kinetics. The mathematical model of the intracellular Ca(2+)-binding system we developed includes TnC2 as a ligand. Rate constants accepted for the complexation of Ca2+ by intracellular ligands give good agreement of the theoretical data with observed physiological ones. We compared the results of numerical experiments on this model with similar results obtained on the other model where TnC2 had been ignored. Some essential differences were revealed. In the model without TnC2 the fraction of calcium binding to specific troponin TnC1 always is smaller than the fraction of Ca2+ bound to the other ligands together. In our model TnC1 fraction (it regulates the mechanical response of muscle) is bigger that means more effective Ca(2+)-binding during activation of contractile proteins. The results above show that within the frame of our model the constants taken for Ca(2+)-binding ligands are more substantiate.

[The theory of regulation of the contraction force of the heart muscle]. / K teorii reguliatsii sily sokrashchenii serdechnoi myshtsy.

A model of rhythmoinotropic phenomena in the heart muscle is elaborated. Kinetics of calcium flowing in intracellular pools of cardiomyocytes is described by differential equations. Dimensionless values (portions) serve as equation coefficients. They determine calcium kinetics in the pools and finally its amount is liberated into the myoplasm during stimulation. Proceeding from physiological considerations for portions there are given laws connecting portion values with intervals between stimuli. S-pool introduced into the model is principally new, it permits quantitative description of the effects of postextrasystolic potentiation and paired stimulation. Introduction of S-pool into the model changes the commonly accepted concept of calcium recirculation in the pools, and apparently, makes it possible for the first time to model all the results obtained on isolated myocardium of warm-blooded animals.

[Mathematical model of a generalized calcium buffer in cardiac muscle cells]. / Matematicheskaia model' obobshchennogo kal'tsievogo bufera v kletakh serdechnoi myshtsy.

The problem of reduction of the earlier model for the calcium buffer system of cardiomyocytes was solved. A simpler model of generalized buffer, was obtained, which reproduces the behavior of the initial system in typical situations. To identify the parameters of the equations of the generalized buffer, recursive algorithms of filtration were developed. The model consists of two equations, which describe separately the fast and slow components of the buffer system. It is shown that the error of the generalized buffer model relative to the initial model of the calcium buffer system does not exceed 10% in a wide range of Ca2+ transients. The introduction of the generalized buffer into the model of mechanochemical coupling provides a more realistic description of a decrease in free calcium concentration. The new model adequately describes all mechanical events simulated by the initial model. In terms of the model, the effect of the slow component of the generalized buffer in a single contraction-relaxation cycle was studied. It was shown that the presence of the slow component leads to a marked decrease in the amplitude of contraction and increase in relaxation time.

[Experimental-theoretical study of the force-interval relationship in the developing chicken myocardium]. / Eksperimental'no-teoreticheskoe issledovanie sviazi interval-sila v razvivaiushchemsia miokarde tsyplenka.

The force-interval relationship was studied on myocardium preparations from chick embryos and hatched chickens. It is shown that the force-interval relationships of myocardium change during ontogenesis. A negative staircase (a decrease in the isometric force with increasing stimulation rate) in the chick embryo myocardium and a positive steady-state relationship in hatched stage myocardium were revealed. Changes in the force after switching from one stimulation frequency to another, the effects of poststimulation potentiation, as well as responses to the introduction of pauses and extrasystols at a constant stimulation rate were recorded. All the effects observed in the transient processes in preparations from hatched stage myocardium were more pronounced than in embryo myocardium. Our previous mathematical model of calcium recirculation in cardiomyocytes was adapted for simulating the main features of force-interval relationships in embryonal and relatively developed myocardium. The main source of regulatory calcium in the model of hatched stage myocardium is sarcoplasmic reticulum. In the model of embryo myocardium, it was postulated, based on data available in literature, that the main regulator of contractile response of the muscle is calcium that enters cardiomyocytes from extracellular medium. To describe force-interval relationships, by this model, the decreasing dependence of the entry of extracellular calcium on the intervals between stimuli was introduced.

[Mechanism of postextrasystolic potentiation of the myocardium]. / K mekhanizmu postékstrasistolicheskoi potentsiatsii v serdechnoi myshtse.

Combined effects of poststimulation and postextrasystolic potentiation (PESP) were studied in the rat papillary muscles. The constant PESP augmentation of isometric force triggered by extrasystolic stimulus was shown for 2-8 poststimulatory potentiated contractions. The PESP was not dependent upon the Ca2+ concentration within the 0.5-1.2 mM range. The findings corroborate the postulate that the PESP in cardiomyocytes is associated with special Ca2+ store which is triggered by two APs: regular and extrasystolic ones.

[Mathematical modelling in physiology].

The article illustrates the method of mathematical modelling in physiology as a unique tool to study physiological processes. A number of demonstrated examples appear as a result of long-term experience in mathematical modelling of electrical and mechanical phenomena in the heart muscle. These examples are presented here to show that the modelling provides insight into mechanisms underlying these phenomena and is capable to predict new ones that were previously unknown. While potentialities of the mathematical modelling are analyzed with regard to the myocardium, they are quite universal to deal with any physiological processes.

[Spatio-temporal heterogeneity of human left ventricle contractions in norm and under ischemic heart disease].

2D-ultrasonic images of the left ventricle are analyzed and spatio-temporal heterogeneity of regional wall motion is characterized quantitatively in norm and in ischemic heart disease. Negative correlation between regional heterogeneity and global ejection fraction is revealed. Regional heterogeneity is shown to increase significantly in a group of patients as compared to healthy people. Role of apex in ventricular pump function is specified. Diagnostic indicator of regional wall motion abnormality is suggested. The data allow one to challenge a new paradigm of morpho-functional organization of heart based on the functional heterogeneity of modules (segments) that compose ventricular wall and differ in biomechanical characteristics and timing of both electrical and mechanical activation.

[Mathematical models for the study of electromechanical and mechanoelectrical coupling in the myocardium].

Mathematical models have been developed to describe interactions of electrical, mechanical and chemical processes in cardiomyocytes. The models simulate wide range of experimental data on excitation-contraction coupling and, more importantly, on mechanoelectric feedback in heart muscle. The model results clearly show that mechano-dependence of intracellular calcium handling due to cooperative effects of contractile proteins activation plays a key role in cardiac mechanoelectric coupling. At the same time, mechanosensitive currents can also contribute to action potential responses to mechanical perturbations. Using this model to study the heterogeneous myocardium we have shown that temporal and functional electromechanical heterogeneity of coupled cardiomyocytes can essentially determine the myocardium contractility. Optimization of the electromechanical function of contractile system emerges from the fine coordination between the activation sequence of cardiomyocytes, their local electromechanical properties and the mechanical interaction during contraction.

[Mechanisms of electromechanical function disturbances in cardiomyocytes overloaded with calcium. The theoretical study].

Arrhythmias and mechanical disturbances are simulated in a mathematical model of cardiomyocyte electromechanical activity. The simulated pattern is similar to that observed for acute heart failure associated with calcium overloading of myocardium cells. Special attention was paid to the calcium overloading resulting from the reduced Na+,K+ pump activity. In the framework of the model, it was shown that mechanical factors could promote arrhythmia initiation when the pump activity reduced. Different approaches to electrical and mechanical function restoration during acute heart failure associated with calcium overloading were suggested and analyzed in the model.

[Contraction-relaxation dynamics and mechanical restitution in the developing myocardium of the chick embryo]. / Dinamika tsikla sokrashchenie-rasslablenie i mekhanicheskaia restitutsiia v razvivaiushchemsia miokarde émbriona tsyplenka.

Parameters of the contraction-relaxation cycle and mechanical restitution (MR) were assessed in isolated ventricular preparations of 3- and 4-day chick embryos (EM) and posthatched (PH) chicks. Ryanodine reduced the relaxation rate in the EM but increased it in the PH chicks. It also suppressed a rest-induced potentiation and the MR in all the preparations. Low Na superfusion significantly suppressed the relaxation and decreased the rest potentiation in the myocardial preparations all ages. The findings substantiate existence of a sarcolemmal Ca pool which participates in regulation of twitch parameters and Ca outflux via the Na-Ca exchange.