Biophysically detailed mathematical models of multiscale cardiac active mechanics

Novel Gain-of-Function Mutation in the Kv11.1 Channel Found in the Patient with Brugada Syndrome and Mild QTc Shortening

Brugada syndrome (BrS) is an inherited disease characterized by right precordial ST-segment elevation in the right precordial leads on electrocardiograms (ECG), and high risk of life-threatening ventricular arrhythmia and sudden cardiac death (SCD). Mutations in the responsible genes have not been fully characterized in the BrS patients, except for the SCN5A gene. We identified a new genetic variant, c.1189C>T (p.R397C), in the KCNH2 gene in the asymptomatic male proband diagnosed with BrS and mild QTc shortening. We hypothesize that this variant could alter IKr-current and may be causative for the rare non-SCN5A-related form of BrS. To assess its pathogenicity, we performed patch-clamp analysis on IKr reconstituted with this KCNH2 mutation in the Chinese hamster ovary cells and compared the phenotype with the wild type. It appeared that the R397C mutation does not affect the IKr density, but facilitates activation, hampers inactivation of the hERG channels, and increases magnitude of the window current suggesting that the p.R397C is a gain-of-function mutation. In silico modeling demonstrated that this missense mutation potentially leads to the shortening of action potential in the heart.

Simulating impaired left ventricular-arterial coupling in aging and disease: a systematic review

Aortic stenosis, hypertension, and left ventricular hypertrophy often coexist in the elderly, causing a detrimental mismatch in coupling between the heart and vasculature known as ventricular-vascular (VA) coupling. Impaired left VA coupling, a critical aspect of cardiovascular dysfunction in aging and disease, poses significant challenges for optimal cardiovascular performance. This systematic review aims to assess the impact of simulating and studying this coupling through computational models. By conducting a comprehensive analysis of 34 relevant articles obtained from esteemed databases such as Web of Science, Scopus, and PubMed until July 14, 2022, we explore various modeling techniques and simulation approaches employed to unravel the complex mechanisms underlying this impairment. Our review highlights the essential role of computational models in providing detailed insights beyond clinical observations, enabling a deeper understanding of the cardiovascular system. By elucidating the existing models of the heart (3D, 2D, and 0D), cardiac valves, and blood vessels (3D, 1D, and 0D), as well as discussing mechanical boundary conditions, model parameterization and validation, coupling approaches, computer resources and diverse applications, we establish a comprehensive overview of the field. The descriptions as well as the pros and cons on the choices of different dimensionality in heart, valve, and circulation are provided. Crucially, we emphasize the significance of evaluating heart-vessel interaction in pathological conditions and propose future research directions, such as the development of fully coupled personalized multidimensional models, integration of deep learning techniques, and comprehensive assessment of confounding effects on biomarkers.

Modeling isovolumetric phases in cardiac flows by an Augmented Resistive Immersed Implicit Surface method

A major challenge in the computational fluid dynamics modeling of the heart function is the simulation of isovolumetric phases when the hemodynamics problem is driven by a prescribed boundary displacement. During such phases, both atrioventricular and semilunar valves are closed: consequently, the ventricular pressure may not be uniquely defined, and spurious oscillations may arise in numerical simulations. These oscillations can strongly affect valve dynamics models driven by the blood flow, making unlikely to recovering physiological dynamics. Hence, prescribed opening and closing times are usually employed, or the isovolumetric phases are neglected altogether. In this article, we propose a suitable modification of the Resistive Immersed Implicit Surface (RIIS) method (Fedele et al., Biomech Model Mechanobiol 2017, 16, 1779-1803) by introducing a reaction term to correctly capture the pressure transients during isovolumetric phases. The method, that we call Augmented RIIS (ARIIS) method, extends the previously proposed ARIS method (This et al., Int J Numer Methods Biomed Eng 2020, 36, e3223) to the case of a mesh which is not body-fitted to the valves. We test the proposed method on two different benchmark problems, including a new simplified problem that retains all the characteristics of a heart cycle. We apply the ARIIS method to a fluid dynamics simulation of a realistic left heart geometry, and we show that ARIIS allows to correctly simulate isovolumetric phases, differently from standard RIIS method. Finally, we demonstrate that by the new method the cardiac valves can open and close without prescribing any opening/closing times.

Mathematical modeling of active contraction of the human cardiac myocyte: A review

Background and objective

In this present research paper, a mathematical model has been developed to study myocyte contraction in the human cardiac muscle, using the Land model. Different parts of the human heart with a focus on the composition of the myocyte cells have been explored numerically to enabling us to determine the interaction of various parameters in the heart muscle. The main objective of the work is to direct the study of the Land model, which has been exploited to simulate the contraction of real human myocytes.

Methods

Mathematical models has been developed based on the Hill model and Huxley model. Myocyte contraction for different scenarios, such as in isometric tension and isotonic tension have been studied.

Results

It is found that increase in stretch, the peak active tension increases, in line with well-established length-dependent tension generation. Five parameters are selected: [Ca2+]T50, Tref, TRPN50, β0, and β1, which have been varied in between the range of -50%-100%, to examine the isometric effects of each parameter on the behavior of the tension developed in the intact myocyte cells, with the most sensitive parameter being [Ca2+]T50.

Conclusion

In conclusion, it is found that the Land model provides a good platform for the analysis of the active contraction of the human cardiac myocyte.

A comprehensive mathematical model for cardiac perfusion

The aim of this paper is to introduce a new mathematical model that simulates myocardial blood perfusion that accounts for multiscale and multiphysics features. Our model incorporates cardiac electrophysiology, active and passive mechanics, hemodynamics, valve modeling, and a multicompartment Darcy model of perfusion. We consider a fully coupled electromechanical model of the left heart that provides input for a fully coupled Navier-Stokes-Darcy Model for myocardial perfusion. The fluid dynamics problem is modeled in a left heart geometry that includes large epicardial coronaries, while the multicompartment Darcy model is set in a biventricular myocardium. Using a realistic and detailed cardiac geometry, our simulations demonstrate the biophysical fidelity of our model in describing cardiac perfusion. Specifically, we successfully validate the model reliability by comparing in-silico coronary flow rates and average myocardial blood flow with clinically established values ranges reported in relevant literature. Additionally, we investigate the impact of a regurgitant aortic valve on myocardial perfusion, and our results indicate a reduction in myocardial perfusion due to blood flow taken away by the left ventricle during diastole. To the best of our knowledge, our work represents the first instance where electromechanics, hemodynamics, and perfusion are integrated into a single computational framework.

A detailed mathematical model of the human atrial cardiomyocyte: integration of electrophysiology and cardiomechanics

Mechano-electric regulations (MER) play an important role in the maintenance of cardiac performance. Mechano-calcium and mechano-electric feedback (MCF and MEF) pathways adjust the cardiomyocyte contractile force according to mechanical perturbations and affects electro-mechanical coupling. MER integrates all these regulations in one unit resulting in a complex phenomenon. Computational modelling is a useful tool to accelerate the mechanistic understanding of complex experimental phenomena. We have developed a novel model that integrates the MER loop for human atrial cardiomyocytes with proper consideration of feedforward and feedback pathways. The model couples a modified version of the action potential (AP) Koivumäki model with the contraction model by Quarteroni group. The model simulates iso-sarcometric and isometric twitches and the feedback effects on AP and Ca2+ -handling. The model showed a biphasic response of Ca2+ transient (CaT) peak to increasing pacing rates and highlights the possible mechanisms involved. The model has shown a shift of the threshold for AP and CaT alternans from 4.6 to 4 Hz under post-operative atrial fibrillation, induced by depressed SERCA activity. The alternans incidence was dependent on a chain of mechanisms including RyRs availability time, MCF coupling, CaMKII phosphorylation, and the stretch levels. As a result, the model predicted a 10% slowdown of conduction velocity for a 20% stretch, suggesting a role of stretch in creation of substrate formation for atrial fibrillation. Overall, we conclude that the developed model provides a physiological CaT followed by a physiological twitch. This model can open pathways for the future studies of human atrial electromechanics. KEY POINTS: With the availability of human atrial cellular data, interest in atrial-specific model integration has been enhanced. We have developed a detailed mathematical model of human atrial cardiomyocytes including the mechano-electric regulatory loop. The model has gone through calibration and evaluation phases against a wide collection of available human in-vitro data. The usefulness of the model for analysing clinical problems has been preliminaryly tested by simulating the increased incidence of Ca2+ transient and action potential alternans at high rates in post-operative atrial fibrillation condition. The model determines the possible role of mechano-electric feedback in alternans incidence, which can increase vulnerability to atrial arrhythmias by varying stretch levels. We found that our physiologically accurate description of Ca2+ handling can reproduce many experimental phenomena and can help to gain insights into the underlying pathophysiological mechanisms.

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.

Fast and robust parameter estimation with uncertainty quantification for the cardiac function

BACKGROUND AND OBJECTIVES

Parameter estimation and uncertainty quantification are crucial in computational cardiology, as they enable the construction of digital twins that faithfully replicate the behavior of physical patients. Many model parameters regarding cardiac electromechanics and cardiovascular hemodynamics need to be robustly fitted by starting from a few, possibly non-invasive, noisy observations. Moreover, short execution times and a small amount of computational resources are required for the effective clinical translation.

METHODS

In the framework of Bayesian statistics, we combine Maximum a Posteriori estimation and Hamiltonian Monte Carlo to find an approximation of model parameters and their posterior distributions. Fast simulations and minimal memory requirements are achieved by using an accurate and geometry-specific Artificial Neural Network surrogate model for the cardiac function, matrix-free methods, automatic differentiation and automatic vectorization. Furthermore, we account for the surrogate modeling error and measurement error.

RESULTS

We perform three different in silico test cases, ranging from the ventricular function to the entire cardiocirculatory system, involving whole-heart mechanics, arterial and venous hemodynamics. By employing a single central processing unit on a standard laptop, we attain highly accurate estimations for all model parameters in short computational times. Furthermore, we obtain posterior distributions that contain the true values inside the 90% credibility regions.

CONCLUSIONS

Many model parameters regarding the entire cardiovascular system can be fastly and robustly identified with minimal hardware requirements. This can be achieved when a small amount of non-invasive data is available and when high levels of signal-to-noise ratio are present in the quantities of interest. With these features, our approach meets the requirements for clinical exploitation, while being compliant with Green Computing practices.

A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart

We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our model accounts for the major feedback effects among the different processes that characterize the heart function, including electro-mechanical and mechano-electrical feedback as well as force-strain and force-velocity relationships. Moreover, it provides a three-dimensional representation of both the cardiac muscle and the hemodynamics, coupled in a fluid-structure interaction (FSI) model. By leveraging the multiphysics nature of the problem, we discretize it in time with a segregated electrophysiology-force generation-FSI approach, allowing for efficiency and flexibility in the numerical solution. We employ a monolithic approach for the numerical discretization of the FSI problem. We use finite elements for the spatial discretization of partial differential equations. We carry out a numerical simulation on a realistic human left heart model, obtaining results that are qualitatively and quantitatively in agreement with physiological ranges and medical images.

Computational Modeling on Drugs Effects for Left Ventricle in Cardiomyopathy Disease

Cardiomyopathy is associated with structural and functional abnormalities of the ventricular myocardium and can be classified in two major groups: hypertrophic (HCM) and dilated (DCM) cardiomyopathy. Computational modeling and drug design approaches can speed up the drug discovery and significantly reduce expenses aiming to improve the treatment of cardiomyopathy. In the SILICOFCM project, a multiscale platform is developed using coupled macro- and microsimulation through finite element (FE) modeling of fluid-structure interactions (FSI) and molecular drug interactions with the cardiac cells. FSI was used for modeling the left ventricle (LV) with a nonlinear material model of the heart wall. Simulations of the drugs' influence on the electro-mechanics LV coupling were separated in two scenarios, defined by the principal action of specific drugs. We examined the effects of Disopyramide and Dygoxin which modulate Ca2+ transients (first scenario), and Mavacamten and 2-deoxy adenosine triphosphate (dATP) which affect changes of kinetic parameters (second scenario). Changes of pressures, displacements, and velocity distributions, as well as pressure-volume (P-V) loops in the LV models of HCM and DCM patients were presented. Additionally, the results obtained from the SILICOFCM Risk Stratification Tool and PAK software for high-risk HCM patients closely followed the clinical observations. This approach can give much more information on risk prediction of cardiac disease to specific patients and better insight into estimated effects of drug therapy, leading to improved patient monitoring and treatment.

Varying thin filament activation in the framework of the Huxley'57 model

Muscle contraction is triggered by the activation of the actin sites of the thin filament by calcium ions. It results that the thin filament activation level varies over time. Moreover, this activation process is also used as a regulation mechanism of the developed force. Our objective is to build a model of varying actin site activation level within the classical Huxley'57 two-state framework. This new model is obtained as an enhancement of a previously proposed formulation of the varying thick filament activation within the same framework. We assume that the state of an actin site depends on whether it is activated and whether it forms a cross-bridge with the associated myosin head, which results in four possible states. The transitions between the actin site states are controlled by the global actin sites activation level and the dynamics of these transitions is coupled with the attachment-detachment process. A preliminary calibration of the model with experimental twitch contraction data obtained at varying sarcomere lengths is performed.

Tools for studying and modulating (cardiac muscle) cell mechanics and mechanosensing across the scales

Cardiomyocytes generate force for the contraction of the heart to pump blood into the lungs and body. At the same time, they are exquisitely tuned to the mechanical environment and react to e.g. changes in cell and extracellular matrix stiffness or altered stretching due to reduced ejection fraction in heart disease, by adapting their cytoskeleton, force generation and cell mechanics. Both mechanical sensing and cell mechanical adaptations are multiscale processes. Receptor interactions with the extracellular matrix at the nanoscale will lead to clustering of receptors and modification of the cytoskeleton. This in turn alters mechanosensing, force generation, cell and nuclear stiffness and viscoelasticity at the microscale. Further, this affects cell shape, orientation, maturation and tissue integration at the microscale to macroscale. A variety of tools have been developed and adapted to measure cardiomyocyte receptor-ligand interactions and forces or mechanics at the different ranges, resulting in a wealth of new information about cardiomyocyte mechanobiology. Here, we take stock at the different tools for exploring cardiomyocyte mechanosensing and cell mechanics at the different scales from the nanoscale to microscale and macroscale.

A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation

In a multiscale simulation of a beating heart, the very large difference in the time scales between rapid stochastic conformational changes of contractile proteins and deterministic macroscopic outcomes, such as the ventricular pressure and volume, have hampered the implementation of an efficient coupling algorithm for the two scales. Furthermore, the consideration of dynamic changes of muscle stiffness caused by the cross-bridge activity of motor proteins have not been well established in continuum mechanics. To overcome these issues, we propose a multiple time step scheme called the multiple step active stiffness integration scheme (MusAsi) for the coupling of Monte Carlo (MC) multiple steps and an implicit finite element (FE) time integration step. The method focuses on the active tension stiffness matrix, where the active tension derivatives concerning the current displacements in the FE model are correctly integrated into the total stiffness matrix to avoid instability. A sensitivity analysis of the number of samples used in the MC model and the combination of time step sizes confirmed the accuracy and robustness of MusAsi, and we concluded that the combination of a 1.25 ms FE time step and 0.005 ms MC multiple steps using a few hundred motor proteins in each finite element was appropriate in the tradeoff between accuracy and computational time. Furthermore, for a biventricular FE model consisting of 45,000 tetrahedral elements, one heartbeat could be computed within 1.5 h using 320 cores of a conventional parallel computer system. These results support the practicality of MusAsi for uses in both the basic research of the relationship between molecular mechanisms and cardiac outputs, and clinical applications of perioperative prediction.

Accelerating the convergence to a limit cycle in 3D cardiac electromechanical simulations through a data-driven 0D emulator

The results of numerical simulations of cardiac electromechanics are typically characterized by a long transient before reaching a periodic solution known as limit cycle. This yields a serious computational overhead, as the only clinically relevant output is associated with such limit cycle. To accelerate the convergence to the limit cycle, we propose a strategy based on a surrogate model, wherein the computationally demanding 3D components are replaced by a 0D emulator, built through an automated data-driven algorithm on the basis of pressure-volume transients of as few as three heartbeats simulated with the 3D model. The 0D emulator, consisting of a time-dependent pressure-volume relationship, can provide the 3D model with an initial guess, such that in just two heartbeats a solution is reached that is as close to the limit cycle as the one obtained after more than 20 heartbeats with the 3D model. The 0D emulator is also recommended in many-query settings (e.g. when performing sensitivity analysis, parameter estimation and uncertainty quantification), that call for the repeated solution of the model for different values of the parameters. Indeed, the construction of the emulator does not have to be repeated when the parameters of the circulation model it is coupled with vary. Finally, should the parameters of the 3D electromechanical model vary as well, we propose a parametric emulator, obtained by interpolation of emulators constructed for given values of the parameters. This paper is accompanied by a Python library implementing the proposed algorithm, open to integration with existing cardiac solvers.

Modeling the cardiac response to hemodynamic changes associated with COVID-19: a computational study

Emerging studies address how COVID-19 infection can impact the human cardiovascular system. This relates particularly to the development of myocardial injury, acute coronary syndrome, myocarditis, arrhythmia, and heart failure. Prospective treatment approach is advised for these patients. To study the interplay between local changes (reduced contractility), global variables (peripheral resistances, heart rate) and the cardiac function, we considered a lumped parameters computational model of the cardiovascular system and a three-dimensional multiphysics model of cardiac electromechanics. Our mathematical model allows to simulate the systemic and pulmonary circulations, the four cardiac valves and the four heart chambers, through equations describing the underlying physical processes. By the assessment of conventionally relevant parameters of cardiac function obtained through our numerical simulations, we propose a computational model to effectively reveal the interactions between the cardiac and pulmonary functions in virtual subjects with normal and impaired cardiac function at baseline affected by mild or severe COVID-19.

Polygonal surface processing and mesh generation tools for the numerical simulation of the cardiac function

In order to simulate the cardiac function for a patient-specific geometry, the generation of the computational mesh is crucially important. In practice, the input is typically a set of unprocessed polygonal surfaces coming either from a template geometry or from medical images. These surfaces need ad-hoc processing to be suitable for a volumetric mesh generation. In this work we propose a set of new algorithms and tools aiming to facilitate the mesh generation process. In particular, we focus on different aspects of a cardiac mesh generation pipeline: (1) specific polygonal surface processing for cardiac geometries, like connection of different heart chambers or segmentation outputs; (2) generation of accurate boundary tags; (3) definition of mesh-size functions dependent on relevant geometric quantities; (4) processing and connecting together several volumetric meshes. The new algorithms-implemented in the open-source software vmtk-can be combined with each other allowing the creation of personalized pipelines, that can be optimized for each cardiac geometry or for each aspect of the cardiac function to be modeled. Thanks to these features, the proposed tools can significantly speed-up the mesh generation process for a large range of cardiac applications, from single-chamber single-physics simulations to multi-chambers multi-physics simulations. We detail all the proposed algorithms motivating them in the cardiac context and we highlight their flexibility by showing different examples of cardiac mesh generation pipelines.

Multiscale modeling of twitch contractions in cardiac trabeculae

Understanding the dynamics of a cardiac muscle twitch contraction is complex because it requires a detailed understanding of the kinetic processes of the Ca2+ transient, thin-filament activation, and the myosin-actin cross-bridge chemomechanical cycle. Each of these steps has been well defined individually, but understanding how all three of the processes operate in combination is a far more complex problem. Computational modeling has the potential to provide detailed insight into each of these processes, how the dynamics of each process affect the complexity of contractile behavior, and how perturbations such as mutations in sarcomere proteins affect the complex interactions of all of these processes. The mechanisms involved in relaxation of tension during a cardiac twitch have been particularly difficult to discern due to nonhomogeneous sarcomere lengthening during relaxation. Here we use the multiscale MUSICO platform to model rat trabecular twitches. Validation of computational models is dependent on being able to simulate different experimental datasets, but there has been a paucity of data that can provide all of the required parameters in a single experiment, such as simultaneous measurements of force, intracellular Ca2+ transients, and sarcomere length dynamics. In this study, we used data from different studies collected under similar experimental conditions to provide information for all the required parameters. Our simulations established that twitches either in an isometric sarcomere or in fixed-length, multiple-sarcomere trabeculae replicate the experimental observations if models incorporate a length-tension relationship for the nonlinear series elasticity of muscle preparations and a scheme for thick-filament regulation. The thick-filament regulation assumes an off state in which myosin heads are parked onto the thick-filament backbone and are unable to interact with actin, a state analogous to the super-relaxed state. Including these two mechanisms provided simulations that accurately predict twitch contractions over a range of different conditions.

Biophysically detailed mathematical models of multiscale cardiac active mechanics

We propose four novel mathematical models, describing the microscopic mechanisms of force generation in the cardiac muscle tissue, which are suitable for multiscale numerical simulations of cardiac electromechanics. Such models are based on a biophysically accurate representation of the regulatory and contractile proteins in the sarcomeres. Our models, unlike most of the sarcomere dynamics models that are available in the literature and that feature a comparable richness of detail, do not require the time-consuming Monte Carlo method for their numerical approximation. Conversely, the models that we propose only require the solution of a system of PDEs and/or ODEs (the most reduced of the four only involving 20 ODEs), thus entailing a significant computational efficiency. By focusing on the two models that feature the best trade-off between detail of description and identifiability of parameters, we propose a pipeline to calibrate such parameters starting from experimental measurements available in literature. Thanks to this pipeline, we calibrate these models for room-temperature rat and for body-temperature human cells. We show, by means of numerical simulations, that the proposed models correctly predict the main features of force generation, including the steady-state force-calcium and force-length relationships, the length-dependent prolongation of twitches and increase of peak force, the force-velocity relationship. Moreover, they correctly reproduce the Frank-Starling effect, when employed in multiscale 3D numerical simulation of cardiac electromechanics.

Active Force Generation in Cardiac Muscle Cells: Mathematical Modeling and Numerical Simulation of the Actin-Myosin Interaction

Cardiac in silico numerical simulations are based on mathematical models describing the physical processes involved in the heart function. In this review paper, we critically survey biophysically-detailed mathematical models describing the subcellular mechanisms behind the generation of active force, that is the process by which the chemical energy of ATP (adenosine triphosphate) is transformed into mechanical work, thus making the muscle tissue contract. While presenting these models, that feature different levels of biophysical detail, we analyze the trade-off between the accuracy in the description of the subcellular mechanisms and the number of parameters that need to be estimated from experiments. Then, we focus on a generalized version of the classic Huxley model, built on the basis of models available in the literature, that is able to reproduce the main experimental characterizations associated to the time scales typical of a heartbeat-such as the force-velocity relationship and the tissue stiffness in response to small steps-featuring only four independent parameters. Finally, we show how those parameters can be calibrated starting from macroscopic measurements available from experiments.