Hybrid duplex: a novel method to study the contractile function of heterogeneous myocardium

Mechano-calcium and mechano-electric feedbacks in the human cardiomyocyte analyzed in a mathematical model

Experiments on animal hearts (rat, rabbit, guinea pig, etc.) have demonstrated that mechano-calcium feedback (MCF) and mechano-electric feedback (MEF) are very important for myocardial self-regulation because they adjust the cardiomyocyte contractile function to various mechanical loads and to mechanical interactions between heterogeneous myocardial segments in the ventricle walls. In in vitro experiments on these animals, MCF and MEF manifested themselves in several basic classical phenomena (e.g., load dependence, length dependence of isometric twitches, etc.), and in the respective responses of calcium transients and action potentials. However, it is extremely difficult to study simultaneously the electrical, calcium, and mechanical activities of the human heart muscle in vitro. Mathematical modeling is a useful tool for exploring these phenomena. We have developed a novel model to describe electromechanical coupling and mechano-electric feedbacks in the human cardiomyocyte. It combines the 'ten Tusscher-Panfilov' electrophysiological model of the human cardiomyocyte with our module of myocardium mechanical activity taken from the 'Ekaterinburg-Oxford' model and adjusted to human data. Using it, we simulated isometric and afterloaded twitches and effects of MCF and MEF on excitation-contraction coupling. MCF and MEF were found to affect significantly the duration of the calcium transient and action potential in the human cardiomyocyte model in response to both smaller afterloads as compared to bigger ones and various mechanical interventions applied during isometric and afterloaded twitches.

The phenomena of mechanical interaction of segments of hypertrophied myocardium

The main aims of adaptation mechanisms of heart contractility are to regulate the stroke volume and optimize the global heart function. These mechanisms manifest themselves in hearts of healthy animals and in hearts with severe hypertrophy in different ways. Severe right ventricle hypertrophy was induced by single treatment with monocrotaline. Young rats of both sexes were used to prevent influences of sex hormones on the development of right ventricular hypertrophy. Serial duplex method is used as a model of interaction of two ventricular wall segments. In serial duplex the muscles are in connection 'end-to-end' and subjected to mutual deformations during contractions. It is important to establish the fine-tuning phenomena and evaluate their expressiveness in healthy hearts and hearts with severe hypertrophy. Mild force transient processes occur on muscle connection to serial duplex and on muscle separation from duplex in all experimental groups. These transients manifest themselves as slow changes in the amplitude of muscle contraction from cycle to cycle. During the muscle interaction in the serial duplex, evident transient processes in the mutual amplitude of deformations in all experimental groups are observed. The greatest changes in the length occur in the relaxation phase of the contraction cycle. The loss of interaction between ventricular muscles of rats with severe heart hypertrophy is the most likely cause of an additional deterioration in the heart pumping function. New targets may occur for the recovery of contractility of hearts with severe hypertrophy.

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 cardiac muscle duplex as a method to study myocardial heterogeneity

This paper reviews the development and application of paired muscle preparations, called duplex, for the investigation of mechanisms and consequences of intra-myocardial electro-mechanical heterogeneity. We illustrate the utility of the underlying combined experimental and computational approach for conceptual development and integration of basic science insight with clinically relevant settings, using previously published and new data. Directions for further study are identified.

Approximate model of cooperative activation and crossbridge cycling in cardiac muscle using ordinary differential equations

We develop a point model of the cardiac myofilament (MF) to simulate a wide variety of experimental muscle characterizations including Force-Ca relations and twitches under isometric, isosarcometric, isotonic, and auxotonic conditions. Complex MF behaviors are difficult to model because spatial interactions cannot be directly implemented as ordinary differential equations. We therefore allow phenomenological approximations with careful consideration to the relationships with the underlying biophysical mechanisms. We describe new formulations that avoid mean-field approximations found in most existing MF models. To increase the scope and applicability of the model, we include length- and temperature-dependent effects that play important roles in MF responses. We have also included a representation of passive restoring forces to simulate isolated cell shortening protocols. Possessing both computational efficiency and the ability to simulate a wide variety of muscle responses, the MF representation is well suited for coupling to existing cardiac cell models of electrophysiology and Ca-handling mechanisms. To illustrate this suitability, the MF model is coupled to the Chicago rabbit cardiomyocyte model. The combined model generates realistic appearing action potentials, intracellular Ca transients, and cell shortening signals. The combined model also demonstrates that the feedback effects of force on Ca binding to troponin can modify the cytosolic Ca transient.

Force-length relations in isolated intact cardiomyocytes subjected to dynamic changes in mechanical load

We developed a dynamic force-length (FL) control system for single intact cardiomyocytes that uses a pair of compliant, computer-controlled, and piezo translator (PZT)-positioned carbon fibers (CF). CF are attached to opposite cell ends to afford dynamic and bidirectional control of the cell's mechanical environment. PZT and CF tip positions, as well as sarcomere length (SL), are simultaneously monitored in real time, and passive/active forces are calculated from CF bending. Cell force and length were dynamically adjusted by corresponding changes in PZT position, to achieve isometric, isotonic, or work-loop style contractions. Functionality of the technique was assessed by studying FL behavior of guinea pig intact cardiomyocytes. End-diastolic and end-systolic FL relations, obtained with varying preload and/or afterloads, were near linear, independent of the mode of contraction, and overlapping for the range of end-diastolic SLs tested (1.85-2.05 micro m). Instantaneous elastance curves, obtained from FL relation curves, showed an afterload-dependent decrease in time to peak elastance and slowed relaxation with both increased preload and afterload. The ability of the present system to independently and dynamically control preload, afterload, and transition between end-diastolic and end-systolic FL coordinates provides a valuable extension to the range of tools available for the study of single cardiomyocyte mechanics, to foster its interrelation with whole heart pathophysiology.

Activation sequence as a key factor in spatio-temporal optimization of myocardial function

Using one-dimensional models of myocardial tissue, implemented as chains of virtual ventricular muscle segments that are kinematically connected in series, we studied the role of the excitation sequence in spatio-temporal organization of cardiac function. Each model element was represented by a well-verified mathematical model of cardiac electro-mechanical activity. We found that homogeneous chains, consisting of identical elements, respond to non-simultaneous stimulation by generation of complex spatio-temporal heterogeneities in element deformation. These are accompanied by the establishment of marked gradients in local electro-mechanical properties of the elements (heterogeneity in action potential duration, Ca2+ transient characteristics and sarcoplasmic reticulum Ca2+ loading). In heterogeneous chains, composed of elements simulating fast and slow contracting cardiomyocytes from different transmural layers, we found that only activation sequences where stimulation of the slower elements preceded that of faster ones gave rise to optimization of the system's electro-mechanical function, which was confirmed experimentally. Based on the results obtained, we hypothesize that the sequence of activation of cardiomyocytes in different ventricular layers is one of the key factors of spatio-temporal organization of myocardium. Moreover, activation sequence and regional differences in intrinsic electro-mechanical properties of cardiac muscle must be matched in order to optimize myocardial function.

Effects of mechanosensitive ion channels on ventricular electrophysiology: experimental and theoretical models

The heart is an electrically driven mechanical pump, somewhat like an electric motor. Interestingly, like an electric motor in 'dynamo mode', the heart can also convert mechanical stimuli into electrical signals. This feedback from cardiac mechanics to electrical activity involves mechanosensitive ion channels, whose properties and pathophysiological relevance are reviewed in the context of experimental and theoretical modelling of ventricular beat-by-beat electromechanical function.