Electromechanical models of the ventricles

Computational modeling has traditionally played an important role in dissecting the mechanisms for cardiac dysfunction. Ventricular electromechanical models, likely the most sophisticated virtual organs to date, integrate detailed information across the spatial scales of cardiac electrophysiology and mechanics and are capable of capturing the emergent behavior and the interaction between electrical activation and mechanical contraction of the heart. The goal of this review is to provide an overview of the latest advancements in multiscale electromechanical modeling of the ventricles. We first detail the general framework of multiscale ventricular electromechanical modeling and describe the state of the art in computational techniques and experimental validation approaches. The powerful utility of ventricular electromechanical models in providing a better understanding of cardiac function is then demonstrated by reviewing the latest insights obtained by these models, focusing primarily on the mechanisms by which mechanoelectric coupling contributes to ventricular arrythmogenesis, the relationship between electrical activation and mechanical contraction in the normal heart, and the mechanisms of mechanical dyssynchrony and resynchronization in the failing heart. Computational modeling of cardiac electromechanics will continue to complement basic science research and clinical cardiology and holds promise to become an important clinical tool aiding the diagnosis and treatment of cardiac disease.     

Effect of bundle branch block on cardiac output: a whole heart simulation study

The heart is an electrically controlled fluid pump which operates by mechanical contraction. Whole heart modelling is a computationally daunting task which must incorporate several subsystems: mechanical, electrical, and fluidic. Numerous feedback mechanisms on many levels, and operating at different scales, exist to finely control behaviour. Understanding these interactions is necessary to understand heart operation, as well as pathologies and therapies. A review of the components in such a model is given. The authors then present a framework for their electro-mechano-fluidic whole heart model based on cable methods. The model incorporates atria and ventricles, and has functioning valves with papillary muscles. The effect of altered propagation due to left and right bundle branch block on cardiac output is examined using the cable-based model. Results are compared to clinically observed phenomena. Good agreement was obtained, but tighter coupling of mechanical and electrical events is needed to fully account for behaviour. Cable-based models offer an alternative to continuum models.     

Coupled pacing improves cardiac efficiency during acute atrial fibrillation with or without cardiac dysfunction

Coupled pacing (CP), a method for controlling ventricular rate during atrial fibrillation (AF), consists of a single electrical stimulation applied to the ventricles after each spontaneous activation. CP results in a mechanical contraction rate approximately one-half the rate during AF. Paired stimulation in which two electrical stimuli are delivered to the ventricles has also been proposed as a therapy for heart failure. Although paired stimulation enhances contractility, it greatly increases energy consumption. The primary hypothesis of the present study is that CP improves cardiac function during acute AF without a similar increase in energy consumption because of the reduced rate of ventricular contractions. In a canine model, CP was applied during four stages: sinus rhythm (SR), acute AF, cardiac dysfunction (CD), and AF in the presence of cardiac dysfunction. The rate of ventricular contraction decreased in all four stages as the result of CP. In addition, we determined the changes in external cardiac work, myocardial oxygen consumption, and myocardial efficiency in the each of four stages. CP partially reversed the effects of AF and CD on external cardiac work, whereas myocardial oxygen consumption increased only moderately. In all stages but SR, CP increased myocardial efficiency because of the marked increases in cardiac work compared with the moderate increases in total energy consumed. Thus this pacing therapy may be a viable therapy for patients with concurrent atrial fibrillation and heart failure.     

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 coupling in cardiomyocytes from transmural layers of guinea pig left ventricle

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

Simulation of the contraction of the ventricles in a human heart model including atria and pericardium

During the contraction of the ventricles, the ventricles interact with the atria as well as with the pericardium and the surrounding tissue in which the heart is embedded. The atria are stretched, and the atrioventricular plane moves toward the apex. The atrioventricular plane displacement (AVPD) is considered to be a major contributor to the ventricular function, and a reduced AVPD is strongly related to heart failure. At the same time, the epicardium slides almost frictionlessly on the pericardium with permanent contact. Although the interaction between the ventricles, the atria and the pericardium plays an important role for the deformation of the heart, this aspect is usually not considered in computational models. In this work, we present an electromechanical model of the heart, which takes into account the interaction between ventricles, pericardium and atria and allows to reproduce the AVPD. To solve the contact problem of epicardium and pericardium, a contact handling algorithm based on penalty formulation was developed, which ensures frictionless and permanent contact. Two simulations of the ventricular contraction were conducted, one with contact handling of pericardium and heart and one without. In the simulation with contact handling, the atria were stretched during the contraction of the ventricles, while, due to the permanent contact with the pericardium, their volume increased. In contrast to that, in the simulations without pericardium, the atria were also stretched, but the change in the atrial volume was much smaller. Furthermore, the pericardium reduced the radial contraction of the ventricles and at the same time increased the AVPD.     

Patient-specific modeling of dyssynchronous heart failure: A case study

The development and clinical use of patient-specific models of the heart is now a feasible goal. Models have the potential to aid in diagnosis and support decision-making in clinical cardiology. Several groups are now working on developing multi-scale models of the heart for understanding therapeutic mechanisms and better predicting clinical outcomes of interventions such as cardiac resynchronization therapy. Here we describe the methodology for generating a patient-specific model of the failing heart with a myocardial infarct and left ventricular bundle branch block. We discuss some of the remaining challenges in developing reliable patient-specific models of cardiac electromechanical activity, and identify some of the main areas for focusing future research efforts. Key challenges include: efficiently generating accurate patient-specific geometric meshes and mapping regional myofiber architecture to them; modeling electrical activation patterns based on cellular alterations in human heart failure, and estimating regional tissue conductivities based on clinically available electrocardiographic recordings; estimating unloaded ventricular reference geometry and material properties for biomechanical simulations; and parameterizing systemic models of circulatory dynamics from available hemodynamic measurements.     

It's all in the timing: Modeling isovolumic contraction through development and disease with a dynamic dual electromechanical bioreactor system

This commentary discusses the rationale behind our recently reported work entitled “Mimicking isovolumic contraction with combined electromechanical stimulation improves the development of engineered cardiac constructs,” introduces new data supporting our hypothesis, and discusses future applications of our bioreactor system. The ability to stimulate engineered cardiac tissue in a bioreactor system that combines both electrical and mechanical stimulation offers a unique opportunity to simulate the appropriate dynamics between stretch and contraction and model isovolumic contraction in vitro. Our previous study demonstrated that combined electromechanical stimulation that simulated the timing of isovolumic contraction in healthy tissue improved force generation via increased contractile and calcium handling protein expression and improved hypertrophic pathway activation. In new data presented here, we further demonstrate that modification of the timing between electrical and mechanical stimulation to mimic a non-physiological process negatively impacts the functionality of the engineered constructs. We close by exploring the various disease states that have altered timing between the electrical and mechanical stimulation signals as potential future directions for the use of this system.     

Distribution of Electromechanical Delay in the Heart: Insights from a Three-Dimensional Electromechanical Model

In the intact heart, the distribution of electromechanical delay (EMD), the time interval between local depolarization and myocyte shortening onset, depends on the loading conditions. The distribution of EMD throughout the heart remains, however, unknown because current experimental techniques are unable to evaluate three-dimensional cardiac electromechanical behavior. The goal of this study was to determine the three-dimensional EMD distributions in the intact ventricles for sinus rhythm (SR) and epicardial pacing (EP) by using a new, to our knowledge, electromechanical model of the rabbit ventricles that incorporates a biophysical representation of myofilament dynamics. Furthermore, we aimed to ascertain the mechanisms that underlie the specific three-dimensional EMD distributions. The results revealed that under both conditions, the three-dimensional EMD distribution is nonuniform. During SR, EMD is longer at the epicardium than at the endocardium, and is greater near the base than at the apex. After EP, the three-dimensional EMD distribution is markedly different; it also changes with the pacing rate. For both SR and EP, late-depolarized regions were characterized with significant myofiber prestretch caused by the contraction of the early-depolarized regions. This prestretch delays myofiber-shortening onset, and results in a longer EMD, giving rise to heterogeneous three-dimensional EMD distributions.     

Electromechanical model of excitable tissue to study reentrant cardiac arrhythmias

We introduce the concept of a contracting excitable medium that is capable of conducting non-linear waves of excitation that in turn initiate contraction. Furthermore, these kinematic deformations have a feedback effect on the excitation properties of the medium. Electrical characteristics resemble basic models of cardiac excitation that have been used to successfully study mechanisms of reentrant cardiac arrhythmias in electrophysiology. We present a computational framework that employs electromechanical and mechanoelectric feedback to couple a three-variable FitzHugh–Nagumo-type excitation-tension model to the non-linear stress equilibrium equations, which govern large deformation hyperelasticity. Numerically, the coupled electromechanical model combines a finite difference method approach to integrate the excitation equations, with a Galerkin finite element method to solve the equations governing tissue mechanics. We present example computations demonstrating various effects of contraction on stationary rotating spiral waves and spiral wave break. We show that tissue mechanics significantly contributes to the dynamics of electrical propagation, and that a coupled electromechanical approach should be pursued in future electrophysiological modelling studies.     

Comparison of the electromechanical responsiveness of alpha-1-adrenoceptor stimulation in ventricles of normal and cardiomyopathic hamsters

Alterations in alpha(1)-adrenoceptor (alpha(1)AR) density and related signal transduction proteins were reported in cardiomyopathic hearts in the failing stage. The electromechanical modification of alpha(1)-adrenergic stimulation in the failing heart is unclear. The present study compares the alpha(1)AR-stimulated electromechanical response in failing ventricles of genetically cardiomyopathic BIO 14.6 hamsters (280-320 days old) with that in age-matched normal Syrian hamsters. The action potential was recorded with a conventional microelectrode technique, and twitch force was measured with a transducer. In the presence of propranolol, phenylephrine increased the contraction and prolonged the action potential duration (APD) to similar values in ventricles of both strains, despite a prolonged basal APD in cardiomyopathic ventricles. The positive inotropism stimulated by phenylephrine was inhibited by staurosporine, and was potentiated by 4 beta-phorbol-12,13-dibutyrate (PDBu) in both strains. The maximum positive inotropic effect of phenylephrine in PDBu-treated ventricles of normal hamsters was significantly greater than that in BIO 14.6 hamsters. The effects of phenylephrine on the ventricular force-frequency relationship and on the mechanical restitution in both normal and BIO 14.6 strain hamsters were examined. The uniform negative force-frequency relationship and the altered mechanical restitution reveal a defect of intracellular Ca(2+) handling in cardiomyopathic BIO 14.6 hamsters. alpha(1)-Adrenergic modulation cannot convert the defective properties in the model of the failing heart. Nevertheless, phenylephrine decreased post-rest potentiation in short rest periods, and enhanced post-rest decay after longer resting periods. The results indicate that alpha(1)-adrenergic action enhances a gradual loss of Ca(2+) from the sarcoplasmic reticulum, although its action in prolonging the APD can indirectly increase the influx of Ca(2+).     

Fast Simulation of Mechanical Heterogeneity in the Electrically Asynchronous Heart Using the MultiPatch Module

Cardiac electrical asynchrony occurs as a result of cardiac pacing or conduction disorders such as left bundle-branch block (LBBB). Electrically asynchronous activation causes myocardial contraction heterogeneity that can be detrimental for cardiac function. Computational models provide a tool for understanding pathological consequences of dyssynchronous contraction. Simulations of mechanical dyssynchrony within the heart are typically performed using the finite element method, whose computational intensity may present an obstacle to clinical deployment of patient-specific models. We present an alternative based on the CircAdapt lumped-parameter model of the heart and circulatory system, called the MultiPatch module. Cardiac walls are subdivided into an arbitrary number of patches of homogeneous tissue. Tissue properties and activation time can differ between patches. All patches within a wall share a common wall tension and curvature. Consequently, spatial location within the wall is not required to calculate deformation in a patch. We test the hypothesis that activation time is more important than tissue location for determining mechanical deformation in asynchronous hearts. We perform simulations representing an experimental study of myocardial deformation induced by ventricular pacing, and a patient with LBBB and heart failure using endocardial recordings of electrical activation, wall volumes, and end-diastolic volumes. Direct comparison between simulated and experimental strain patterns shows both qualitative and quantitative agreement between model fibre strain and experimental circumferential strain in terms of shortening and rebound stretch during ejection. Local myofibre strain in the patient simulation shows qualitative agreement with circumferential strain patterns observed in the patient using tagged MRI. We conclude that the MultiPatch module produces realistic regional deformation patterns in the asynchronous heart and that activation time is more important than tissue location within a wall for determining myocardial deformation. The CircAdapt model is therefore capable of fast and realistic simulations of dyssynchronous myocardial deformation embedded within the closed-loop cardiovascular system.     

Proteome map of the normal murine ventricular myocardium

Cardiovascular disease is the leading cause of morbidity and mortality in developed countries. The underlying mechanisms involved in cardiac dysfunction and heart failure are poorly understood. In this study, 2-DE was utilised to map, for the first time, proteins of normal, nonfailing mouse ventricular tissues to form a basis for future comparative analysis of mouse models with cardiovascular disorders. Proteins were obtained from ventricles of C57BL6 mice, aged 18 wk, and separated by 2-DE. A total of 150 protein spots, corresponding to 77 distinct proteins, were identified by MALDI-TOF MS. The proteins identified in mouse ventricles covered a wide range of biological processes (e.g. cell cycle, muscle contraction and signal transduction), with the majority of proteins contributing to cardiomyocyte energetics and cell structure. This 2-D gel map of mouse myocardial proteins will be an invaluable tool in proteomic research for the detection of protein changes and identifying cardiac biomarkers of cardiovascular disease.     

Qualitative modeling of mechanoelectrical feedback in a ventricular cell

Mechanical changes in the heart muscle can influence its electrical properties through a process called mechanoelectrical feedback (MEF). This feedback can operate via changes in calcium dynamics during the cross-bridge cycle or via mechanosensitive (stretch-activated) channels. We present a four-variable ordinary differential equation (ODE) system that caricatures the electrical and mechanical activity of a ventricular cell and their mutual interactions. A three-variable excitable system with restitution properties of the FitzHugh-Nagumo type is coupled to a fourth equation which describes changes in cell length during a lightly loaded contraction. The resulting four-variable system models MEF in a cell and can be incorporated into spatially distributed models for mechanoelectric behavior during wave propagation in the cardiac tissue.     

A Tissue-Level Electromechanical Model of the Left Ventricle: Application to the Analysis of Intraventricular Pressure

The ventricular pressure profile is characteristic of the cardiac contraction progress and is useful to evaluate the cardiac performance. In this contribution, a tissue-level electromechanical model of the left ventricle is proposed, to assist the interpretation of left ventricular pressure waveforms. The left ventricle has been modeled as an ellipsoid composed of twelve mechano-hydraulic sub-systems. The asynchronous contraction of these twelve myocardial segments has been represented in order to reproduce a realistic pressure profiles. To take into account the different energy domains involved, the tissue-level scale and to facilitate the building of a modular model, multiple formalisms have been used: Bond Graph formalism for the mechano-hydraulic aspects and cellular automata for the electrical activation. An experimental protocol has been defined to acquire ventricular pressure signals from three pigs, with different afterload conditions. Evolutionary Algorithms have been used to identify the model parameters in order to minimize the error between experimental and simulated ventricular pressure signals. Simulation results show that the model is able to reproduce experimental ventricular pressure. In addition, electro-mechanical activation times have been determined in the identification process. For example, the maximum electrical activation time is reached, respectively, 96.5, 139.3 and 131.5 ms for the first, second, and third pigs. These preliminary results are encouraging for the application of the model on non-invasive data like ECG, arterial pressure or myocardial strain.     

Personalized Computer Simulation of Diastolic Function in Heart Failure

The search for a parameter representing left ventricular relaxation from non-invasive and invasive diagnostic tools has been extensive, since heart failure (HF) with preserved ejection fraction (HF-pEF) is a global health problem. We explore here the feasibility using patient-specific cardiac computer modeling to capture diastolic parameters in patients suffering from different degrees of systolic HF. Fifty eight patients with idiopathic dilated cardiomyopathy have undergone thorough clinical evaluation, including cardiac magnetic resonance imaging (MRI), heart catheterization, echocardiography, and cardiac biomarker assessment. A previously-introduced framework for creating multi-scale patient-specific cardiac models has been applied on all these patients. Novel parameters, such as global stiffness factor and maximum left ventricular active stress, representing cardiac active and passive tissue properties have been computed for all patients. Invasive pressure measurements from heart catheterization were then used to evaluate ventricular relaxation using the time constant of isovolumic relaxation Tau (s). Parameters from heart catheterization and the multi-scale model have been evaluated and compared to patient clinical presentation. The model parameter global stiffness factor, representing diastolic passive tissue properties, is correlated signif-icantly across the patient population with s. This study shows that multi-modal cardiac models can successfully capture diastolic (dys) function, a prerequisite for future clinical trials on HF-pEF.     

Efficient characterization of inhomogeneity in contraction strain pattern

Cardiac dyssynchrony often accompanies patients with heart failure (HF) and can lead to an increase in mortality rate. Cardiac resynchronization therapy (CRT) has been shown to provide substantial benefits to the HF population with ventricular dyssynchrony; however, there still exists a group of patients who do not respond to this treatment. In order to better understand patient response to CRT, it is necessary to quantitatively characterize both electrical and mechanical dyssynchrony. The quantification of mechanical dyssynchrony via characterization of contraction strain field inhomogeneity is the focus of this modeling investigation. Raw data from a 3D finite element (FE) model were received from Roy Kerckhoffs et al. and analyzed in MATLAB. The FE model consisted of canine left and right ventricles coupled to a closed circulation with the effects of the pericardium acting as a pressure on the epicardial surface. For each of three simulations (normal synchronous, SYNC, right ventricular apical pacing, RVA, and left ventricular free wall pacing, LVFW) the Gauss point locations and values were used to generate lookup tables (LUTs) with each entry representing a location in the heart. In essence, we employed piecewise cubic interpolation to generate a fine point cloud (LUTs) from a course point cloud (Gauss points). Strain was calculated in the fiber direction and was then displayed in multiple ways to better characterize strain inhomogeneity. By plotting average strain and standard deviation over time, the point of maximum contraction and the point of maximal inhomogeneity were found for each simulation. Strain values were organized into seven strain bins to show operative strain ranges and extent of inhomogeneity throughout the heart wall. In order to visualize strain propagation, magnitude, and inhomogeneity over time, we created 2D area maps displaying strain over the entire cardiac cycle. To visualize spatial strain distribution at the time point of maximum inhomogeneity, a 3D point cloud was created for each simulation, and a CURE index was calculated. We found that both the RVA and LFVW simulations took longer to reach maximum contraction than the SYNC simulation, while also exhibiting larger disparities in strain values during contraction. Strain in the hoop direction was also analyzed and was found to be similar to the fiber strain results. It was found that our method of analyzing contraction strain pattern yielded more detailed spacial and temporal information about fiber strain in the heart over the cardiac cycle than the more conventional CURE index method. We also observed that our method of strain binning aids in visualization of the strain fields, and in particular, the separation of the mass points into separate images associated with each strain bin allows the strain pattern to be explicitly compartmentalized.     

Myocardial segment-specific model generation for simulating the electrical action of the heart

Background  

Computer models of the electrical and mechanical actions of the heart, solved on geometrically realistic domains, are becoming an increasingly useful scientific tool. Construction of these models requires detailed measurement of the microstructural features which impact on the function of the heart. Currently a few generic cardiac models are in use for a wide range of simulation problems, and contributions to publicly accessible databases of cardiac structures, on which models can be solved, remain rare. This paper presents to-date the largest database of porcine left ventricular segment microstructural architecture, for use in both electrical and mechanical simulation.