Simulation of mechanoelectrical coupling in cardiomyocytes under normal and abnormal conditions

Mathematical models of the electromechanical function of cardiomyocytes and muscle duplexes, the simplest mechanically inhomogeneous myocardial systems, are developed. Using these models, the contribution of mechanoelectrical feedbacks to the contractive activity of the myocardium in normal and abnormal conditions is studied. In particular, the influence of the mechanical conditions of contraction on the shape and duration of the action potentials is reproduced and interpreted. In this context, different types of mechanical heterogeneity of the myocardium are analyzed. It is established that this heterogeneity can play a positive or negative role depending on the distribution of heterogeneous properties and on the order the elements of the system are activated. Using the same models, the contribution of mechanical factors to arrhythmogenesis under calcium overload of cardiomyocytes due to the weakening of the sodium-potassium pump is studied. Methods for correction of the contractive activity of cardiomyocytes in the case of such abnormalities are outlined.     

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.     

Electromechanical heterogeneity of the myocardium

Herein we discuss modem data showing that ventricle's working myocardium is highly heterogeneous. Significant transmural differences in electrophysiological and biomechanical properties of cardiomyocytes are reviewed. The reviewed evidence of myocardial heterogeneity constitutes the basis for modem assessment of segmental kinetics of different regions in intact heart. We used muscle duplexes as condensed models of a heterogeneous myocardial system. Experimental data, presented here were obtained both in biological duplexes formed by isolated myocardial preparations and in mathematical models of muscle duplexes. We showed that specific functional heterogeneity of cardiomyocytes, related to their excitation sequence, allowed the myocardium to optimise its contractile function and smooth dispersion of repolarisation.     

Mechano-electric interactions in heterogeneous myocardium: development of fundamental experimental and theoretical models

The heart is structurally and functionally a highly non-homogenous organ, yet its main function as a pump can only be achieved by the co-ordinated contraction of millions of ventricular cells. This apparent contradiction gives rise to the hypothesis that ‘well-organised’ inhomogeneity may be a pre-requisite for normal cardiac function. Here, we present a set of novel experimental and theoretical tools for the study of this concept. Heterogeneity, in its most condensed form, can be simulated using two individually controlled, mechanically interacting elements (duplex). We have developed and characterised three different types of duplexes: (i) biological duplex, consisting of two individually perfused biological samples (like thin papillary muscles or a trabeculae), (ii) virtual duplex, made-up of two interacting mathematical models of cardiac muscle, and (iii) hybrid duplex, containing a biological sample that interacts in real-time with a virtual muscle. In all three duplex types, in-series or in-parallel mechanical interaction of elements can be studied during externally isotonic, externally isometric, and auxotonic modes of contraction and relaxation. Duplex models, therefore, mimic (patho-)physiological mechano-electric interactions in heterogeneous myocardium at the multicellular level, and in an environment that allows one to control mechanical, electrical and pharmacological parameters. Results obtained using the duplex method show that: (i) contractile elements in heterogeneous myocardium are not ‘independent’ generators of tension/shortening, as their ino- and lusitropic characteristics change dynamically during mechanical interaction—potentially matching microscopic contractility to macroscopic demand, (ii) mechanical heterogeneity contributes differently to action potential duration (APD) changes, depending on whether mechanical coupling of elements is in-parallel or in-series, which may play a role in mechanical tuning of distant tissue regions, (iii) electro-mechanical activity of mechanically interacting contractile elements is affected by their activation sequence, which may optimise myocardial performance by smoothing intrinsic differences in APD. In conclusion, we present a novel set of tools for the experimental and theoretical investigation of cardiac mechano-electric interactions in healthy and/or diseased heterogeneous myocardium, which allows for the testing of previously inaccessible concepts.     

Cooperativity in mechano-calcium feedbacks in the myocardium: Some conceptual discrepancies and overcoming inconsistency within the framework of a mathematical model

Mechano-calcium feedbacks that provide fine tuning of electrical and calcium activation of the heart muscle to mechanical conditions of contractions are an important element of electromechanical coupling as a key mechanism of the autoregulation of the contractile activity of the myocardium. A large quantity of experimental and theoretical evidence supports the cooperative dependence of the calcium-troponin complex kinetics on the cross-bridge concentration as a principal mechanism that underlies the mechano-calcium feedback in the intact myocardium. At the same time, experiments performed using skinned myocardial preparations have demonstrated that mechanical conditions significantly affected only the calcium sensitivity of the Ca²⁺–force relationship rather than its Hill coefficient of cooperativity. These data make some investigators doubt the contribution of cooperativity to the mechano-calcium feedbacks. To overcome these arising discrepancies, we propose an improved conception of cooperativity that reveals the extent of intensity differently in the steady state and in transitional processes. The proposed conception enables us to reproduce and explain both the mechanodependence of calcium activation in the intact myocardium and the results with skinned muscle within the framework of a mathematical model.     

Engineered early embryonic cardiac tissue retains proliferative and contractile properties of developing embryonic myocardium

Embryonic myocardium has a high rate of cell proliferation and regulates cellular proliferation, contractile function, and myocardial architecture in response to changes in external mechanical loads. However, the small and complex three-dimensional (3D) structure of the embryonic myocardium limits our ability to directly investigate detailed relationships between mechanical load, contractile function, and cardiomyocyte proliferation. We developed a novel 3D engineered early embryonic cardiac tissue (EEECT) from early embryonic ventricular cells to test the hypothesis that EEECT retains the proliferative and contractile properties of embryonic myocardium. We combined freshly isolated White Leghorn chicken embryonic ventricular cells at Hamburger-Hamilton (HH) stage 31 (day 7 of a 46-stage, 21-day incubation period), collagen type I, and matrix factors to construct cylindrical-shaped EEECTs. We studied tissue architecture, cell proliferation patterns, and contractile function. We then generated engineered fetal cardiac tissue (EFCT) from HH stage 40 (day 14) fetal ventricular cells for direct comparison with EEECT. Tissue architecture was similar in EEECT and EFCT. EEECT maintained high cell proliferation patterns by culture day 12, whereas EFCT decreased cell proliferation rate by culture day 9 (P < 0.05). EEECT increased active contractile force from culture day 7 to day 12. The culture day 12 EEECT contractile response to the beta-adrenergic stimulation was less than culture day 9 EFCT (P < 0.05). Cyclic mechanical stretch stimulation induced myocardial hyperplasia in EEECT. Results indicate that EEECT retains the proliferative and contractile properties of developing embryonic myocardium and shows potential as a robust in vitro model of developing embryonic myocardium.     

Evidence for the existence of a functional helical myocardial band

Characterization of local and global contractile activities in the myocardium is essential for a better understanding of cardiac form and function. The spatial distribution of regions that contribute the most to cardiac function plays an important role in defining the pumping parameters of the myocardium like ejection fraction and dynamic aspects such as twisting and untwisting. In general, myocardium shortening, tangent to the wall, and ventricular wall thickening are important parameters that characterize the regional contribution within the myocardium to the global function of the heart. We have calculated these parameters using myocardium displacement fields, which were captured through the displacement-encoding with stimulated echoes (DENSE) MRI technique in three volunteers. High spatial resolution of the acquired data revealed transmural changes of thickening and tangential shortening with high fidelity in beating hearts. By filtering myocardium regions that showed a tangential shortening index of <0.23, we were able to identify the complete or a portion of a macrostructure composed of connected regions in the form of a helical bundle within the left ventricle mass. In this study, we present a representative case that shows the complete morphology of a helical myocardial band as well as two other cases that present ascending and descending portions of the helical myocardial band. Our observation of a helical functional band based on dynamics is in agreement with diffusion tensor MRI observations and gross dissection studies in the arrested heart.     

Effect of Adaptation to Graduated Physical Exercises on the Function of the Rat Myocardium

On isolated hearts obtained from control rats and rats subjected to regular physical exercises (forced swimming) during 6 weeks, we studied the contractile activity of the heart, resistance of the myocardium to ischemia/reperfusion-induced injuries, as well as the dependence of the developed and end-diastolic pressures in the aortic ventricle (AV) on the strain of the myocardium (by means of a dosed increase in the volume of a polyethylene reservoir inserted into the ventricle). It was demonstrated that adaptation to regular graduated physical exercises exerts a positive effect on the functional state of the AV myocardium and its contractile function. This was manifested in intensification of the contractile activity of the myocardium, a decrease in its oxygen “job cost,” and an increase in the resistance to injuries induced by ischemia-reperfusion. In addition, regular physical trainings led to an increase in the resistance of the AV myocardium to the strain. In trained rats, the plateau of the Frank–Starling plot was significantly greater than that in control animals, while the rigidity of the AV myocardium was significantly lower. Neirofiziologiya/Neurophysiology, Vol. 41, No. 1, pp. 41–47, January–February, 2009.     

Simultaneous orientation and cellular force measurements in adult cardiac myocytes using three-dimensional polymeric microstructures

A number of techniques have been developed to monitor contractile function in isolated cardiac myocytes. While invaluable observations have been gained from these methodologies in understanding the contractile processes of the heart, they are invariably limited by their in vitro conditions. The present challenge is to develop innovative assays to mimic the in vivo milieu so as to allow a more physiological assessment of cardiac myocyte contractile forces. Here we demonstrate the use of a silicone elastomer, poly(dimethylsiloxane) (PDMS), to simultaneously orient adult cardiac myocytes in primary culture and measure the cellular forces in a three-dimensional substrate. The realignment of adult cardiac myocytes in long-term culture (7 days) was achieved due to directional reassembly of the myofibrils along the parallel polymeric sidewalls. The cellular mechanical forces were recorded in situ by observing the deformation of the micropillars embedded in the substrate. By coupling the cellular mechanical force measurements with on-chip cell orientation, this novel assay is expected to provide a means of a more physiological assessment of single cardiac myocyte contractile function and may facilitate the future development of in vitro assembled functional cardiac tissue.     

Heterogeneity Profoundly Alters Emergent Stress Fields in Constrained Multicellular Systems

Stress fields emerging from the transfer of forces between cells within multicellular systems are increasingly being recognized as major determinants of cell fate. Current analytical and numerical models used for the calculation of stresses within cell monolayers assume homogeneous contractile and mechanical cellular properties; however, cell behavior varies by region within constrained tissues. Here, we show the impact of heterogeneous cell properties on resulting stress fields that guide cell phenotype and apoptosis. Using circular micropatterns, we measured biophysical metrics associated with cell mechanical stresses. We then computed cell-layer stress distributions using finite element contraction models and monolayer stress microscopy. In agreement with previous studies, cell spread area, alignment, and traction forces increase, whereas apoptotic activity decreases, from the center of cell layers to the edge. The distribution of these metrics clearly indicates low cell stress in central regions and high cell stress at the periphery of the patterns. However, the opposite trend is predicted by computational models when homogeneous contractile and mechanical properties are assumed. In our model, utilizing heterogeneous cell-layer contractility and elastic moduli values based on experimentally measured biophysical parameters, we calculate low cell stress in central areas and high anisotropic stresses in peripheral regions, consistent with the biometrics. These results clearly demonstrate that common assumptions of uniformity in cell contractility and stiffness break down in postconfluence confined multicellular systems. This work highlights the importance of incorporating regional variations in cell mechanical properties when estimating emergent stress fields from collective cell behavior.     

Protein mechanics: a route from structure to function

In order to better understand the mechanical properties of proteins, we have developed simulation tools which enable these properties to be analysed on a residue-by-residue basis. Although these calculations are relatively expensive with all-atom protein models, good results can be obtained much faster using coarse-grained approaches. The results show that proteins are surprisingly heterogeneous from a mechanical point of view and that functionally important residues often exhibit unusual mechanical behaviour. This finding offers a novel means for detecting functional sites and also potentially provides a route for understanding the links between structure and function in more general terms.     

Protein mechanics: a route from structure to function

In order to better understand the mechanical properties of proteins, we have developed simulation tools which enable these properties to be analysed on a residue-by-residue basis. Although these calculations are relatively expensive with all-atom protein models, good results can be obtained much faster using coarse-grained approaches. The results show that proteins are surprisingly heterogeneous from a mechanical point of view and that functionally important residues often exhibit unusual mechanical behaviour. This finding offers a novel means for detecting functional sites and also potentially provides a route for understanding the links between structure and function in more general terms.     

Lengthening-contractions in isolated myocardium impact force development and worsen cardiac contractile function in the mdx mouse model of muscular dystrophy

Lengthening-contractions exert eccentric stress on myofibers in normal myocardium. In congestive heart failure caused by a variety of diseases, the impact of lengthening-contractions of myocardium likely becomes more prevalent and severe. The present study introduces a method to investigate the role of stretching imposed by repetitive lengthening-contractions in myocardium under near-physiological conditions. By exerting various stretch-release ramps while the muscle is contracting, consecutive lengthening-contractions and their potential detrimental effect on cardiac function can be studied. We tested our model and hypothesis in age-matched (young and adult) mdx and wild-type mouse right ventricular trabeculae. These linear and ultrathin muscles possess all major cardiac cell types, and their contractile behavior very closely mimics that of the whole myocardium. In the first group of experiments, 10 lengthening-contractions at various magnitudes of stretch were performed in trabeculae from 10-wk-old mdx and wild-type mice. In the second group, 100 lengthening-contractions at various magnitudes were conducted in trabeculae from 10- and 20-wk-old mice. The peak isometric active developed tension (F(dev), in mN/mm(2)) and kinetic parameters time to peak tension (TTP, in ms) and time from peak tension to half-relaxation (RT50, in ms) were measured. Our results indicate lengthening-contractions significantly impact contractile behavior, and that dystrophin-deficient myocardium in mdx mice is significantly more susceptible to these damaging lengthening-contractions. The results indicate that lengthening-contractions in intact myocardium can be used in vitro to study this emerging contributor to cardiomyopathy.     

Time-dependent changes of the susceptibility of cardiac contractile function to hypoxia-reoxygenation after myocardial infarction in rats

In this study we analyzed the susceptibility of contractile function of the myocardium to hypoxia-reoxygenation after infarction. For this purpose, the contractility of isolated papillary muscles from rats was studied at high oxygen tension (pO₂ 80 kPa) and during hypoxia (pO₂ 3 kPa) with subsequent reoxygenation at variable intervals between 15 h and 9 weeks after permanent ligation of the left coronary artery. Hypoxic exposure reduced the contractile performance of the preparations to a similar extent in both groups. Notably, the contractility and, in particular, the relaxation rates recovered more completely from hypoxia in the hypertrophied myocardium of rats with coronary artery ligation than in sham-operated (SO) animals. The recovery of contractile function was improved maximally between 6 and 9 weeks after myocardial infarction (MI). The lower sensitivity of the (post)ischemic myocardium to hypoxia-reoxygenation correlated with enhanced left ventricular glutathione peroxidase (GSH-Px) activity (15 h to 9 weeks post-MI) and 2–3-fold increased expression levels (15 h to 6 weeks post-MI) of the 72 kDa heat shock protein (HSP72) in the papillary muscles. These findings suggest that the greater antioxidant potential and, possibly, stimulation of HSPs contribute to the sustained tolerance of the myocardium to hypoxia-reoxygenation injury after infarction.     

Cardiac remodeling in fish: strategies to maintain heart function during temperature Change

Rainbow trout remain active in waters that seasonally change between 4°C and 20°C. To explore how these fish are able to maintain cardiac function over this temperature range we characterized changes in cardiac morphology, contractile function, and the expression of contractile proteins in trout following acclimation to 4°C (cold), 12°C (control), and 17°C (warm). The relative ventricular mass (RVM) of the cold acclimated male fish was significantly greater than that of males in the control group. In addition, the compact myocardium of the cold acclimated male hearts was thinner compared to controls while the amount of spongy myocardium was found to have increased. Cold acclimation also caused an increase in connective tissue content, as well as muscle bundle area in the spongy myocardium of the male fish. Conversely, warm acclimation of male fish caused an increase in the thickness of the compact myocardium and a decrease in the amount of spongy myocardium. There was also a decrease in connective tissue content in both myocardial layers. In contrast, there was no change in the RVM or connective tissue content in the hearts of female trout with warm or cold acclimation. Cold acclimation also caused a 50% increase in the maximal rate of cardiac AM Mg(2+)-ATPase but did not influence the Ca(2+) sensitivity of this enzyme. To identify a mechanism for this change we utilized two-dimensional difference gel electrophoresis to characterize changes in the cardiac contractile proteins. Cold acclimation caused subtle changes in the phosphorylation state of the slow skeletal isoform of troponin T found in the heart, as well as of myosin binding protein C. These results demonstrate that acclimation of trout to warm and cold temperatures has opposing effects on cardiac morphology and tissue composition and that this results in distinct warm and cold cardiac phenotypes.     

Mechanisms of self-regulation of myocardial contractile function during hypokinesia and muscle training

This article analyzes the literature devoted to the role of the myocardial contractile apparatus in the regulation of cardiac pump function during hypokinesia, moderate and excessive physical exercises. These data indicate that moderate exercises increase the role of myocardial contractile apparatus, thereby efficiency of cardiac and extracardiac mechanisms for its regulation increase. Excessive loads increase adrenergic inotropic effects on the myocardium in combination with a reduction of the contribution of its contractile apparatus in a common set of regulatory influences on cardiac pump function. Weakening of self regulation mechanisms is typical for the regime of hypokinesia also. However, in the latter case the enhancement of adrenergic inotropic effects is absent.     

Adaptive changes in sections of the myocardium of experimental animals undergoing physical loading of a static nature

Adaptation of the parts of myocardium of 18 white rats to the physical static loadings during two months have been studied by means of morphometric and histological methods. Physical loadings cause hyperfunction and hypertrophy of all chambers of the heart with a predominant hypertrophy of the right ventricle, right auricle and dilatation of these cavities. The heterogeneous changes of the myocardium were found on the organic level.     

Tropaphen in experimental drug therapy of cor pulmonale]

The influence of alpha-adrenoblocking drug tropaphen on cardio- and haemodynamics under experimental lung-heart failure was studied in dogs. The findings suggest effectiveness of tropaphen administration in such pathology shown by a decrease of lung hypertension and heart overload, significant increase of the contractile activity and relaxation properties of myocardium of both ventricles and in cardiac pump function optimization.     

Disorders of myocardial contraction and cardiomyocyte ultrastructure after emotional stress

By means of physiological, electron microscopical and histochemical methods, changes in intensity of mechanisms participating in calcium transport and the cations localization in cardiomyocytes have been studied, the changes resulted from an emotional-painful stress. After the stress, the contractile function of the rat isolated heart becomes more dependent on calcium concentration in the perfusate. As demonstrate combined electron microscopical and histochemical methods and, first of all, determination of calcium antimonate in the cardiomyocytes, together with increased cardiac function, an elevated amount of calcium localized in sarcoplasm of cardiomyocytes is observed, especially in the subsarcolemmic area. The data obtained demonstrate that the membrane mechanisms of calcium transport are injured and calcium content in the sarcoplasm is increased; that can play a definite role in the development of focal lesions in the myocardium at a stress.     

An integrated inverse model-experimental approach to determine soft tissue three-dimensional constitutive parameters: application to post-infarcted myocardium

Knowledge of the complete three-dimensional (3D) mechanical behavior of soft tissues is essential in understanding their pathophysiology and in developing novel therapies. Despite significant progress made in experimentation and modeling, a complete approach for the full characterization of soft tissue 3D behavior remains elusive. A major challenge is the complex architecture of soft tissues, such as myocardium, which endows them with strongly anisotropic and heterogeneous mechanical properties. Available experimental approaches for quantifying the 3D mechanical behavior of myocardium are limited to preselected planar biaxial and 3D cuboidal shear tests. These approaches fall short in pursuing a model-driven approach that operates over the full kinematic space. To address these limitations, we took the following approach. First, based on a kinematical analysis and using a given strain energy density function (SEDF), we obtained an optimal set of displacement paths based on the full 3D deformation gradient tensor. We then applied this optimal set to obtain novel experimental data from a 1-cm cube of post-infarcted left ventricular myocardium. Next, we developed an inverse finite element (FE) simulation of the experimental configuration embedded in a parameter optimization scheme for estimation of the SEDF parameters. Notable features of this approach include: (i) enhanced determinability and predictive capability of the estimated parameters following an optimal design of experiments, (ii) accurate simulation of the experimental setup and transmural variation of local fiber directions in the FE environment, and (iii) application of all displacement paths to a single specimen to minimize testing time so that tissue viability could be maintained. Our results indicated that, in contrast to the common approach of conducting preselected tests and choosing an SEDF a posteriori, the optimal design of experiments, integrated with a chosen SEDF and full 3D kinematics, leads to a more robust characterization of the mechanical behavior of myocardium and higher predictive capabilities of the SEDF. The methodology proposed and demonstrated herein will ultimately provide a means to reliably predict tissue-level behaviors, thus facilitating organ-level simulations for efficient diagnosis and evaluation of potential treatments. While applied to myocardium, such developments are also applicable to characterization of other types of soft tissues.