Mechanism of the Frank–Starling law—A simulation study with a novel cardiac muscle contraction model that includes titin and troponin I

An idealized human cardiomyocyte finite element model for studying the interaction between the cross-bridge state and cell mechanical response. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2023;2023:1-5. [PMID: 38082753 DOI: 10.1109/embc40787.2023.10341055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

The mechanical state of cardiomyocyte is directly related to the structure and function of internal sarcomeres. In the field of computational cardiac mechanics, attempts to establish models of human cardiomyocyte with a detailed representation of sarcomere cross-bridge (XB) are rare. In this study, we established a computational model for a cardiomyocyte with idealized geometry while containing a representative sarcomere composed of thick filament, thin filament, titin filament, and Z-disc. The formation of XB with passive tension in the model was simulated with the finite element (FE) method, and stochastic FE analyses were further carried out in conjunction with six sigma analysis to explore the interaction between the S1 power stroke and the twitch mechanics of cardiomyocyte. The proposed modeling method may help us better understand the working state of cardiomyocyte, and offer a potential means for exploring the cell-level mechanisms of cardiac diseases.

Computational modeling of electromechanical coupling in human cardiomyocyte applied to study hypertrophic cardiomyopathy and its drug response

BACKGROUND AND OBJECTIVE

Knowledge of electromechanical coupling in cardiomyocyte and how it is influenced by various pathophysiological factors is fundamental to understanding the pathogenesis of myocardial disease and its response to medication, which is however hard to be thoroughly addressed by clinical/experimental studies due to technical limitations. At this point, computational modeling offers an alternative approach. The main objective of the study was to develop a computational model capable of simulating the process of electromechanical coupling and quantifying the roles of various factors in play in the human left ventricular cardiomyocyte.

METHODS

A new electrophysiological model was firstly built by combining several existing electrophysiological models and incorporating the mechanism of electrophysiological homeostasis, which was subsequently coupled to models representing the cross-bridge dynamics and active force generation during excitation-contraction coupling and the passive mechanical properties of cardiomyocyte to yield an integrative electromechanical model. Model parameters were calibrated or optimized based on a large amount of experimental data. The resulting model was applied to delineate the characteristics of electromechanical coupling and explore underlying determinant factors in hypertrophic cardiomyopathy (HCM) cardiomyocyte, as well as quantify their changes in response to different medications.

RESULTS

Model predictions captured the major electromechanical characteristics of cardiomyocyte under both normal physiological and HCM conditions. In comparison with normal cardiomyocyte, HCM cardiomyocyte suffered from systemic changes in both electrophysiological and mechanical variables. Numerical simulations of drug response revealed that Mavacamten and Metoprolol could both reduce the active contractility and alleviate calcium overload but had marked differential influences on many other electromechanical variables, which theoretically explained why the two drugs have differential therapeutic effects. In addition, our numerical experiments demonstrated the important role of compensatory ion transport in maintaining electrophysiological homeostasis and regulating cytoplasmic volume.

CONCLUSIONS

A sophisticated computational model has the advantage of providing quantitative and integrative insights for understanding the pathogenesis and drug responses of HCM or other myocardial diseases at the level of cardiomyocyte, and hence may contribute as a useful complement to clinical/experimental studies. The model may also be coupled to tissue- or organ-level models to strengthen the physiological implications of macro-scale numerical simulations.

Ventricular Dysfunction in Obese and Nonobese Rats with Metabolic Syndrome

Obesity and dyslipidemias are both signs of metabolic syndrome, usually associated with ventricular arrhythmias. Here, we tried to identify cardiac electrical alteration and biomarkers in nonobese rats with metabolic syndrome (MetS), and these findings might lead to more lethal arrhythmias than obese animals. The MetS model was developed in Wistar rats with high-sucrose diet (20%), and after twenty-eight weeks were obtained two subgroups: obese (OMetS) and nonobese (NOMetS). The electrocardiogram was used to measure the ventricular arrhythmias and changes in the heart rate variability. Also, we measured ventricular hypertrophy and its relationship with electrical activity alterations of both ventricles, using micro-electrode and voltage clamp techniques. Also, we observed alterations in the contraction force of ventricles where a transducer was used to record mechanical and electrical papillary muscle, simultaneously. Despite both subgroups presenting long QT syndrome (0.66 ± 0.05 and 0.66 ± 0.07 ms with respect to the control 0.55 ± 0.1 ms), the changes in the heart rate variability were present only in OMetS, while the NOMetS subgroup presented changes in QT interval variability (NOMetS SD = 1.8, SD2 = 2.8; SD1/SD2 = 0.75). Also, the NOMetS revealed tachycardia (10%; p < 0.05) with changes in action potential duration (63% in the right papillary and 50% in the left papillary) in the ventricular papillary which are correlated with certain alterations in the potassium currents and the force of contraction. The OMetS showed an increase in action potential duration and the force of contraction in both ventricles, which are explained as bradycardia. Our results revealed lethal arrhythmias in both MetS subgroups, irrespectively of the presence of obesity. Consequently, the NOMetS showed mechanical-electrical alterations regarding ventricle hypertrophy that should be at the NOMetS, leading to an increase of CV mortality.

The use of Ca-transient to evaluate Ca2+ utilization by myofilaments in living cardiac muscle

The kinetics of Ca2+ interaction with myofilaments is an important determinant of the preload-dependent effects on myocardial contractility (the Frank-Starling Mechanism). However, the direct evaluation of this interaction in intact tissue is limited. To overcome this issue, the method of difference curve was proposed, which implements the subtraction of the referent Ca-transient (measured in non-stretched muscle) from the Ca-transients measured at different preloads. This method was tested on the cardiac trabeculae of healthy (CONT) and monocrotaline-treated rats (MCT), subjected to force-length protocol with simultaneous measurement of isometric twitch and Ca-transient. The difference curve had two components, C2 and C3, which are distinct in their directions and, as hypothesized, may reflect mainly the kinetics of Ca2+ utilization by and release from myofilaments, respectively. Both the components were quantitatively evaluated by their amplitude, integral magnitude and time-to-peak. The C3 component in either CONT or MCT was significantly higher in its amplitude/integral magnitude vs the C2 component, at any preload (P < .05). The time-to-peak value was preload-dependent only for the C3 component. There were tight relationships between the above characteristics of C2/C3 components and the characteristics of isometric tension (peak value, time-to-peak and the maximal rates of rise/decline) in CONT and MCT muscles. The C3 component was highly consistent with tension relaxation (Ca2+ release from myofilaments), but the C2 component was partially consistent with tension development (Ca2+ utilization by myofilaments). The novel method of the analysis of Ca-transients can be utilized for indirect evaluation of Ca2+ interaction with myofilaments in healthy and diseased myocardium.

Force-dependent recruitment from myosin OFF-state increases end-systolic pressure-volume relationship in left ventricle

Finite element (FE) modeling is becoming increasingly prevalent in the world of cardiac mechanics; however, many existing FE models are phenomenological and thus do not capture cellular-level mechanics. This work implements a cellular-level contraction scheme into an existing nonlinear FE code to model ventricular contraction. Specifically, this contraction model incorporates three myosin states: OFF-, ON-, and an attached force-generating state. It has been speculated that force-dependent transitions from the OFF- to ON-state may contribute to length-dependent activation at the cellular level. The current work investigates the contribution of force-dependent recruitment out of the OFF-state to ventricular-level function, specifically the Frank-Starling relationship, as seen through the end-systolic pressure-volume relationship (ESPVR). Five FE models were constructed using geometries of rat left ventricles obtained via cardiac magnetic resonance imaging. FE simulations were conducted to optimize parameters for the cellular contraction model such that the differences between FE predicted ventricular pressures for the models and experimentally measured pressures were minimized. The models were further validated by comparing FE predicted end-systolic strain to experimentally measured strain. Simulations mimicking vena cava occlusion generated descending pressure volume loops from which ESPVRs were calculated. In simulations with the inclusion of the OFF-state, using a force-dependent transition to the ON-state, the ESPVR calculated was steeper than in simulations excluding the OFF-state. Furthermore, the ESPVR was also steeper when compared to models that included the OFF-state without a force-dependent transition. This suggests that the force-dependent recruitment of thick filament heads from the OFF-state at the cellular level contributes to the Frank-Starling relationship observed at the organ level.

Mathematical model for β1-adrenergic regulation of the mouse ventricular myocyte contraction

The β1-adrenergic regulation of cardiac myocyte contraction plays an important role in regulating heart function. Activation of this system leads to an increased heart rate and stronger myocyte contraction. However, chronic stimulation of the β1-adrenergic signaling system can lead to cardiac hypertrophy and heart failure. To understand the mechanisms of action of β1-adrenoceptors, a mathematical model of cardiac myocyte contraction that includes the β1-adrenergic system was developed and studied. The model was able to simulate major experimental protocols for measurements of steady-state force-calcium relationships, cross-bridge release rate and force development rate, force-velocity relationship, and force redevelopment rate. It also reproduced quite well frequency and isoproterenol dependencies for intracellular Ca2+ concentration ([Ca2+]i) transients, total contraction force, and sarcomere shortening. The mathematical model suggested the mechanisms of increased contraction force and myocyte shortening on stimulation of β1-adrenergic receptors is due to phosphorylation of troponin I and myosin-binding protein C and increased [Ca2+]i transient resulting from activation of the β1-adrenergic signaling system. The model was used to simulate work-loop contractions and estimate the power during the cardiac cycle as well as the effects of 4-aminopyridine and tedisamil on the myocyte contraction. The developed mathematical model can be used further for simulations of contraction of ventricular myocytes from genetically modified mice and myocytes from mice with chronic cardiac diseases.

NEW & NOTEWORTHY A new mathematical model of mouse ventricular myocyte contraction that includes the β1-adrenergic system was developed. The model simulated major experimental protocols for myocyte contraction and predicted the effects of 4-aminopyridine and tedisamil on the myocyte contraction. The model also allowed for simulations of work-loop contractions and estimation of the power during the cardiac cycle.

Evaluation of a Novel Finite Element Model of Active Contraction in the Heart

Finite element (FE) modeling is becoming a widely used approach for the investigation of global heart function. In the present study, a novel model of cellular-level systolic contraction, which includes both length- and velocity-dependence, was implemented into a 3D non-linear FE code. To validate this new FE implementation, an optimization procedure was used to determine the contractile parameters, associated with sarcomeric function, by comparing FE-predicted pressure and strain to experimental measures collected with magnetic resonance imaging and catheterization in the ventricles of five healthy rats. The pressure-volume relationship generated by the FE models matched well with the experimental data. Additionally, the regional distribution of end-systolic strains and circumferential-longitudinal shear angle exhibited good agreement with experimental results overall, with the main deviation occurring in the septal region. Moreover, the FE model predicted a heterogeneous distribution of sarcomere re-lengthening after ventricular ejection, which is consistent with previous in vivo studies. In conclusion, the new FE active contraction model was able to predict the global performance and regional mechanical behaviors of the LV during the entire cardiac cycle. By including more accurate cellular-level mechanisms, this model could provide a better representation of the LV and enhance cardiac research related to both systolic and diastolic dysfunction.

A Spatially Detailed Model of Isometric Contraction Based on Competitive Binding of Troponin I Explains Cooperative Interactions between Tropomyosin and Crossbridges

Biophysical models of cardiac tension development provide a succinct representation of our understanding of force generation in the heart. The link between protein kinetics and interactions that gives rise to high cooperativity is not yet fully explained from experiments or previous biophysical models. We propose a biophysical ODE-based representation of cross-bridge (XB), tropomyosin and troponin within a contractile regulatory unit (RU) to investigate the mechanisms behind cooperative activation, as well as the role of cooperativity in dynamic tension generation across different species. The model includes cooperative interactions between regulatory units (RU-RU), between crossbridges (XB-XB), as well more complex interactions between crossbridges and regulatory units (XB-RU interactions). For the steady-state force-calcium relationship, our framework predicts that: (1) XB-RU effects are key in shifting the half-activation value of the force-calcium relationship towards lower [Ca²⁺], but have only small effects on cooperativity. (2) XB-XB effects approximately double the duty ratio of myosin, but do not significantly affect cooperativity. (3) RU-RU effects derived from the long-range action of tropomyosin are a major factor in cooperative activation, with each additional unblocked RU increasing the rate of additional RU’s unblocking. (4) Myosin affinity for short (1–4 RU) unblocked stretches of actin of is very low, and the resulting suppression of force at low [Ca²⁺] is a major contributor in the biphasic force-calcium relationship. We also reproduce isometric tension development across mouse, rat and human at physiological temperature and pacing rate, and conclude that species differences require only changes in myosin affinity and troponin I/troponin C affinity. Furthermore, we show that the calcium dependence of the rate of tension redevelopment k_tr is explained by transient blocking of RU’s by a temporary decrease in XB-RU effects.

Force generation in cardiac muscle cells is driven by changes in calcium concentration. Relatively small changes in the calcium concentration over the course of a heart beat lead to the large changes in force required to fully contract and relax the heart. This is known as ‘cooperative activation’, and involves a complex interaction of several proteins involved in contraction. Current computer models which reproduce force generation often do not represent these processes explicitly, and stochastic approaches that do tend to require large amounts of computational power to solve, which limit the range of investigations in which they can be used. We have created an new computational model that captures the underlying physiological processes in more detail, and is more efficient than stochastic approaches, while still being able to run a large range of simulations. The model is able to explain the biological processes leading to the cooperative activation of muscle. In addition, the model reproduces how this cooperative activation translates to normal muscle function to generate force from changes in calcium across three different species.

A mathematical model of the mouse ventricular myocyte contraction

Mathematical models of cardiac function at the cellular level include three major components, such as electrical activity, Ca²⁺ dynamics, and cellular shortening. We developed a model for mouse ventricular myocyte contraction which is based on our previously published comprehensive models of action potential and Ca²⁺ handling mechanisms. The model was verified with extensive experimental data on mouse myocyte contraction at room temperature. In the model, we implemented variable sarcomere length and indirect modulation of the tropomyosin transition rates by Ca²⁺ and troponin. The resulting model described well steady-state force-calcium relationships, dependence of the contraction force on the sarcomere length, time course of the contraction force and myocyte shortening, frequency dependence of the contraction force and cellular contraction, and experimentally measured derivatives of the myocyte length variation. We emphasized the importance of the inclusion of variable sarcomere length into a model for ventricular myocyte contraction. Differences in contraction force and cell shortening for epicardial and endocardial ventricular myocytes were investigated. Model applicability for the experimental studies and model limitations were discussed.

Cardiac electromechanical models: from cell to organ

The heart is a multiphysics and multiscale system that has driven the development of the most sophisticated mathematical models at the frontiers of computational physiology and medicine. This review focuses on electromechanical (EM) models of the heart from the molecular level of myofilaments to anatomical models of the organ. Because of the coupling in terms of function and emergent behaviors at each level of biological hierarchy, separation of behaviors at a given scale is difficult. Here, a separation is drawn at the cell level so that the first half addresses subcellular/single-cell models and the second half addresses organ models. At the subcellular level, myofilament models represent actin–myosin interaction and Ca-based activation. The discussion of specific models emphasizes the roles of cooperative mechanisms and sarcomere length dependence of contraction force, considered to be the cellular basis of the Frank–Starling law. A model of electrophysiology and Ca handling can be coupled to a myofilament model to produce an EM cell model, and representative examples are summarized to provide an overview of the progression of the field. The second half of the review covers organ-level models that require solution of the electrical component as a reaction–diffusion system and the mechanical component, in which active tension generated by the myocytes produces deformation of the organ as described by the equations of continuum mechanics. As outlined in the review, different organ-level models have chosen to use different ionic and myofilament models depending on the specific application; this choice has been largely dictated by compromises between model complexity and computational tractability. The review also addresses application areas of EM models such as cardiac resynchronization therapy and the role of mechano-electric coupling in arrhythmias and defibrillation.

Cardiac cell modelling: observations from the heart of the cardiac physiome project

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field.

Computational modeling of cardiac disease: potential for personalized medicine

Cardiovascular diseases are leading causes of death, reduce life quality and consume almost half a trillion dollars in healthcare expenses in the USA alone. Cardiac modeling and simulation technologies hold promise as important tools to improve cardiac care and are already in use to elucidate the fundamental mechanisms of cardiac physiology and pathophysiology. However, the emphasis has been on simulating average or exemplar cases. This report describes two classes of cardiac modeling efforts. First, electrophysiological models of channelopathies simulate the altered electrical activity that is thought to promote arrhythmias. Second, electromechanical models attempt to capture both the electrophysiological and mechanical aspects of heart function. One goal of the community is to develop models with sufficient patient customization to assist in personalized treatment planning. Some model aspects can be customized with existing data collection techniques to more closely represent individual patients while other model aspects will likely remain based on generic data. Despite important challenges, cardiac models hold promise to be important enablers of personalized medicine.

Simulation of steady state and transient cardiac muscle response experiments with a Huxley-based contraction model

A cardiac muscle model is presented with the purpose of representing a wide range of mechanical experiments at constant and transient Ca(2+) concentration. Modifications of a previous model were: weak and power attached crossbridge states, a troponin system involving three consecutive regulatory troponin-tropomyosin units acting together in Ca(2+) kinetics and detachment constants depending on crossbridge length. This model improved cooperativity (Hill coefficient close to 4) and the force-velocity relationship, and incorporated the representation of the four phases of muscle response to length and force steps, isotonic shortening and isosarcometric contractions, preserving previous satisfactory results. Moreover, experimentally reported effects, such as length dependence on Ca(2+) affinity, the decreased cooperativity at higher Ca(2+) concentrations, temperature effects on the stiffness-frequency relationship and the isometric internal shortening due to series elasticity, were obtained. In conclusion, the model is more comprehensive than a previous version because it is able to represent a wider variety of steady state experiments, the mechanical variables in twitches can be adequately related to intracellular Ca(2+), and all the simulations were performed with the same set of parameters.

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.

The cross-bridge dynamics during ventricular contraction predicted by coupling the cardiac cell model with a circulation model

The force-velocity (F-V) relationship of filament sliding is traditionally used to define the inotropic condition of striated muscles. A simple circulation model combined with the Laplace heart was developed to get a deeper insight into the relationship between the F-V characteristics and the cardiac ventricular inotropy. The circulation model consists of a preload and an afterload compartments. The linear F-V relationship for filament sliding in the NL model (Negroni and Lascano 1996) was replaced by the exponential F-V relation observed by Piazzesi et al. (2002). We also modified the NL model to a hybrid model to benefit from the Ca(2+) cooperativity described by the Robinson model (Robinson et al. 2002). The model was validated by determining the diastolic ventricular pressure-volume relationship of the Laplace heart and the F-V relation of the new hybrid model. The computed parameters of the cardiac cycle agreed well with the physiological data. Computational results showed that the cross-bridge elongation (h in the NL model) temporally undershot the equilibrium h(c) during the ejection period and overshot it during the rapid refilling phase. Thereby the time course of ejection and refilling was retarded. In a simulation where the velocity of the mobile myosin head (dX/dt) was varied, the systolic peak pressure of the ventricle varied from a minimum value at dX/dt = 0 to a saturating value obtained with a constant h(c), providing in silico evidence for a functional impact of the cross-bridge sliding rate on the ventricular inotropy.