Effect of transmurally heterogeneous myocyte excitation-contraction coupling on canine left ventricular electromechanics

Numerical evaluation of cardiac mechanical markers as estimators of the electrical activation time

Recent advances in the development of noninvasive cardiac imaging technologies have made it possible to measure longitudinal and circumferential strains at a high spatial resolution also at intramural level. Local mechanical activation times derived from these strains can be used as noninvasive estimates of electrical activation, in order to determine, eg, the origin of premature ectopic beats during focal arrhythmias or the pathway of reentrant circuits. The aim of this work is to assess the reliability of mechanical activation time markers derived from longitudinal and circumferential strains, denoted by AT_ell and AT_ecc , respectively, by means of three-dimensional cardiac electromechanical simulations. These markers are compared against the electrical activation time (AT_v ), computed from the action potential waveform, and the reference mechanical activation markers derived from the active tension and fiber strain waveforms, denoted by AT_ta and AT_eff , respectively. Our numerical simulations are based on a strongly coupled electromechanical model, including bidomain representation of the cardiac tissue, mechanoelectric (ie, stretch-activated channels) and geometric feedbacks, transversely isotropic strain energy function for the description of passive mechanics and detailed membrane and excitation-contraction coupling models. The results have shown that, during endocardial and epicardial ectopic stimulations, all the mechanical markers considered are highly correlated with AT_v , exhibiting correlation coefficients larger than 0.8. However, during multiple endocardial stimulations, mimicking the ventricular sinus rhythm, the mechanical markers are less correlated with the electrical activation time, because of the more complex resulting excitation sequence. Moreover, the inspection of the endocardial and epicardial isochrones has shown that the AT_ell and AT_ecc mechanical activation sequences reproduce only some qualitative features of the electrical activation sequence, such as the areas of early and late activation, but in some cases, they might yield wrong excitation sources and significantly different isochrones patterns.

Multiphysics computational modelling of the cardiac ventricles

Development of cardiac multiphysics models has progressed significantly over the decades and simulations combining multiple physics interactions have become increasingly common. In this review, we summarise the progress in this field focusing on various approaches of integrating ventricular structures. electrophysiological properties, myocardial mechanics, as well as incorporating blood hemodynamics and the circulatory system. Common coupling approaches are discussed and compared, including the advantages and shortcomings of each. Currently used strategies for patient-specific implementations are highlighted and potential future improvements considered.

A short history of the development of mathematical models of cardiac mechanics

Cardiac mechanics plays a crucial role in atrial and ventricular function, in the regulation of growth and remodelling, in the progression of disease, and the response to treatment. The spatial scale of the critical mechanisms ranges from nm (molecules) to cm (hearts) with the fastest events occurring in milliseconds (molecular events) and the slowest requiring months (growth and remodelling). Due to its complexity and importance, cardiac mechanics has been studied extensively both experimentally and through mathematical models and simulation. Models of cardiac mechanics evolved from seminal studies in skeletal muscle, and developed into cardiac specific, species specific, human specific and finally patient specific calculations. These models provide a formal framework to link multiple experimental assays recorded over nearly 100 years into a single unified representation of cardiac function. This review first provides a summary of the proteins, physiology and anatomy involved in the generation of cardiac pump function. We then describe the evolution of models of cardiac mechanics starting with the early theoretical frameworks describing the link between sarcomeres and muscle contraction, transitioning through myosin-level models to calcium-driven systems, and ending with whole heart patient-specific models.

Transmural cellular heterogeneity in myocardial electromechanics

Myocardial heterogeneity is an attribute of the normal heart. We have developed integrative models of cardiomyocytes from the subendocardial (ENDO) and subepicardial (EPI) ventricular regions that take into account experimental data on specific regional features of intracellular electromechanical coupling in the guinea pig heart. The models adequately simulate experimental data on the differences in the action potential and contraction between the ENDO and EPI cells. The modeling results predict that heterogeneity in the parameters of calcium handling and myofilament mechanics in isolated ENDO and EPI cardiomyocytes are essential to produce the differences in Ca2+ transients and contraction profiles via cooperative mechanisms of mechano-calcium-electric feedback and may further slightly modulate transmural differences in the electrical properties between the cells. Simulation results predict that ENDO cells have greater sensitivity to changes in the mechanical load than EPI cells. These data are important for understanding the behavior of cardiomyocytes in the intact heart.

Effect of Transmural Differences in Excitation-Contraction Delay and Contraction Velocity on Left Ventricle Isovolumic Contraction: A Simulation Study

Recent studies have shown that left ventricle (LV) exhibits considerable transmural differences in active mechanical properties induced by transmural differences in electrical activity, excitation-contraction coupling, and contractile properties of individual myocytes. It was shown that the time between electrical and mechanical activation of myocytes (electromechanical delay: EMD) decreases from subendocardium to subepicardium and, on the contrary, the myocyte shortening velocity (MSV) increases in the same direction. To investigate the physiological importance of this inhomogeneity, we developed a new finite element model of LV incorporating the observed transmural gradients in EMD and MSV. Comparative simulations with the model showed that when EMD or MSV or both were set constant across the LV wall, the LV contractility during isovolumic contraction (IVC) decreased significantly ((dp/dt)max⁡  was reduced by 2 to 38% and IVC was prolonged by 18 to 73%). This was accompanied by an increase of transmural differences in wall stress. These results suggest that the transmural differences in EMD and MSV play an important role in physiological contractility of LV by synchronising the contraction of individual layers of ventricular wall during the systole. Reduction or enhancement of these differences may therefore impair the function of LV and contribute to heart failure.

Regional effects of streptozotocin-induced diabetes on shortening and calcium transport in epicardial and endocardial myocytes from rat left ventricle

In the heart, the left ventricle pumps blood at higher pressure than the right ventricle. Within the left ventricle, the electromechanical properties of ventricular cardiac myocytes vary transmurally and this may be related to the gradients of stress and strain experienced in vivo across the ventricular wall. Diabetes is also associated with alterations in hemodynamic function. The aim of this study was to investigate shortening and Ca²⁺ transport in epicardial (EPI) and endocardial (ENDO) left ventricular myocytes in the streptozotocin (STZ)‐induced diabetic rat. Shortening, intracellular Ca²⁺ and L‐type Ca²⁺ current (I_Ca,L) were measured by video detection, fura‐2 microfluorimetry, and whole‐cell patch clamp techniques, respectively. Time to peak (TPK) shortening was prolonged to similar extents in ENDO and EPI myocytes from STZ‐treated rats compared to ENDO and EPI myocytes from controls. Time to half (THALF) relaxation of shortening was prolonged in ENDO myocytes from STZ‐treated rats compared to ENDO controls. TPK Ca²⁺ transient was prolonged in ENDO myocytes from STZ‐treated rats compared to ENDO controls. THALF decay of the Ca²⁺ transient was prolonged in ENDO myocytes from STZ‐treated rats compared to ENDO controls. Sarcoplasmic reticulum (SR) fractional release of Ca²⁺ was reduced in EPI myocytes from STZ‐treated rats compared to EPI controls. I_Ca,L activation, inactivation, and recovery from inactivation were not significantly altered in EPI and ENDO myocytes from STZ‐treated rats or controls. Regional differences in Ca²⁺ transport may partly underlie differences in ventricular myocyte shortening across the wall of the healthy and the STZ‐treated rat left ventricle.

Effects of cellular electromechanical coupling on functional heterogeneity in a one-dimensional tissue model of the myocardium

Based on the experimental evidence, we developed a one-dimensional (1D) model of heterogeneous myocardial tissue consisting of in-series connected cardiomyocytes from distant transmural regions using mathematical models of subendocardial and subepicardial cells. The regional deformation patterns produced by our 1D model are consistent with the transmural regional strain patterns obtained experimentally in the normal heart in vivo. The modelling results suggest that the mechanical load may essentially affect the transmural gradients in the electrical and mechanical properties of interacting myocytes within a tissue, thereby regulating global myocardial output.

Transmural gradients of myocardial structure and mechanics: Implications for fiber stress and strain in pressure overload

Although a truly complete understanding of whole heart activation, contraction, and deformation is well beyond our current reach, a significant amount of effort has been devoted to discovering and understanding the mechanisms by which myocardial structure determines cardiac function to better treat patients with cardiac disease. Several experimental studies have shown that transmural fiber strain is relatively uniform in both diastole and systole, in contrast to predictions from traditional mechanical theory. Similarly, mathematical models have largely predicted uniform fiber stress across the wall. The development of this uniform pattern of fiber stress and strain during filling and ejection is due to heterogeneous transmural distributions of several myocardial structures. This review summarizes these transmural gradients, their contributions to fiber mechanics, and the potential functional effects of their remodeling during pressure overload hypertrophy.

Multiscale Interactions in a 3D Model of the Contracting Ventricle

A biophysical detailed multiscale model of the myocardium is presented. The model was used to study the contribution of interrelated cellular mechanisms to global myocardial function. The multiscale model integrates cellular electrophysiology, excitation propagation dynamics and force development models into a geometrical fiber based model of the ventricle. The description of the cellular electrophysiology in this study was based on the Ten Tusscher-Noble-Noble-Panfilov heterogeneous model for human ventricular myocytes. A four-state model of the sarcomeric control of contraction developed by Negroni and Lascano was employed to model the intracellular mechanism of force generation. The propagation of electrical excitation was described by a reaction-diffusion equation. The 3D geometrical model of the ventricle, based on single fiber contraction was used as a platform for the evaluation of proposed models. The model represents the myocardium as an anatomically oriented array of contracting fibers with individual fiber parameters such as size, spatial location, orientation and mechanical properties. Moreover, the contracting ventricle model interacts with intraventricular blood elements linking the contractile elements to the heart's preload and afterload, thereby producing the corresponding pressure-volume loop. The results show that the multiscale ventricle model is capable of simulating mechanical contraction, pressure generation and load interactions as well as demonstrating the individual contribution of each ion current.

High-order finite element methods for cardiac monodomain simulations

Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori.

Towards causally cohesive genotype-phenotype modelling for characterization of the soft-tissue mechanics of the heart in normal and pathological geometries

A scientific understanding of individual variation is key to personalized medicine, integrating genotypic and phenotypic information via computational physiology. Genetic effects are often context-dependent, differing between genetic backgrounds or physiological states such as disease. Here, we analyse in silico genotype-phenotype maps (GP map) for a soft-tissue mechanics model of the passive inflation phase of the heartbeat, contrasting the effects of microstructural and other low-level parameters assumed to be genetically influenced, under normal, concentrically hypertrophic and eccentrically hypertrophic geometries. For a large number of parameter scenarios, representing mock genetic variation in low-level parameters, we computed phenotypes describing the deformation of the heart during inflation. The GP map was characterized by variance decompositions for each phenotype with respect to each parameter. As hypothesized, the concentric geometry allowed more low-level parameters to contribute to variation in shape phenotypes. In addition, the relative importance of overall stiffness and fibre stiffness differed between geometries. Otherwise, the GP map was largely similar for the different heart geometries, with little genetic interaction between the parameters included in this study. We argue that personalized medicine can benefit from a combination of causally cohesive genotype-phenotype modelling, and strategic phenotyping that captures effect modifiers not explicitly included in the mechanistic model.

Modelling the heart as a communication system

Electrical communication between cardiomyocytes can be perturbed during arrhythmia, but these perturbations are not captured by conventional electrocardiographic metrics. We developed a theoretical framework to quantify electrical communication using information theory metrics in two-dimensional cell lattice models of cardiac excitation propagation. The time series generated by each cell was coarse-grained to 1 when excited or 0 when resting. The Shannon entropy for each cell was calculated from the time series during four clinically important heart rhythms: normal heartbeat, anatomical reentry, spiral reentry and multiple reentry. We also used mutual information to perform spatial profiling of communication during these cardiac arrhythmias. We found that information sharing between cells was spatially heterogeneous. In addition, cardiac arrhythmia significantly impacted information sharing within the heart. Entropy localized the path of the drifting core of spiral reentry, which could be an optimal target of therapeutic ablation. We conclude that information theory metrics can quantitatively assess electrical communication among cardiomyocytes. The traditional concept of the heart as a functional syncytium sharing electrical information cannot predict altered entropy and information sharing during complex arrhythmia. Information theory metrics may find clinical application in the identification of rhythm-specific treatments which are currently unmet by traditional electrocardiographic techniques.

Effects of deformation on transmural dispersion of repolarization using in silico models of human left ventricular wedge

Mechanical deformation affects the electrical activity of the heart through multiple feedback loops. The purpose of this work is to study the effect of deformation on transmural dispersion of repolarization and on surface electrograms using an in silico human ventricular wedge. To achieve this purpose, we developed a strongly coupled electromechanical cell model by coupling a human left ventricle electrophysiology model and an active contraction model reparameterized for human cells. This model was then embedded in tissue simulations on the basis of bidomain equations and nonlinear solid mechanics. The coupled model was used to evaluate effects of mechanical deformation on important features of repolarization and electrograms. Our results indicate an increase in the T-wave amplitude of the surface electrograms in simulations that account for the effects of cardiac deformation. This increased T-wave amplitude can be explained by changes to the coupling between neighboring myocytes, also known as electrotonic effect. The thickening of the ventricular wall during repolarization contributes to the decoupling of cells in the transmural direction, enhancing action potential heterogeneity and increasing both transmural repolarization dispersion and T-wave amplitude of surface electrograms. The simulations suggest that a considerable percentage of the T-wave amplitude (15%) may be related to cardiac deformation.

A study on the relationship between electrical transmural heterogeneity and ventricular energetics

In this study, we use cardiovascular simulation to gain new insights on the correlation between electrical heterogeneity and ventricular energetics. Although there are numerous in vivo and in vitro studies on the electrical heterogeneity within the ventricular myocardium, not much attention has been directed to its correlation to cardiovascular mechanics, because of difficulties in simultaneously observing and analyzing multiple spatial scales (the cell, the organ, and the system). We performed simulations with two cardiovascular simulation models, one which uses different myocardial cell models for the epicardial, endocardial, and mid-myocardial cells, and another which uses a homogeneous model throughout the entire myocardium. The epicardial, endocardial, and midmyocardial cell models were created by parametrically tuning a homogenous cell model. From the cardiovascular simulation we obtained pressure-volume loops which were used to calculate cardiovascular energetic efficiency and myocardial contractility. We found that energetic efficiency is higher in the electrically heterogeneous model.

Mechanistic insight into prolonged electromechanical delay in dyssynchronous heart failure: a computational study

In addition to the left bundle branch block type of electrical activation, there are further remodeling aspects associated with dyssynchronous heart failure (HF) that affect the electromechanical behavior of the heart. Among the most important are altered ventricular structure (both geometry and fiber/sheet orientation), abnormal Ca(2+) handling, slowed conduction, and reduced wall stiffness. In dyssynchronous HF, the electromechanical delay (EMD), the time interval between local myocyte depolarization and myofiber shortening onset, is prolonged. However, the contributions of the four major HF remodeling aspects in extending EMD in the dyssynchronous failing heart remain unknown. The goal of this study was to determine the individual and combined contributions of HF-induced remodeling aspects to EMD prolongation. We used MRI-based models of dyssynchronous nonfailing and HF canine electromechanics and constructed additional models in which varying combinations of the four remodeling aspects were represented. A left bundle branch block electrical activation sequence was simulated in all models. The simulation results revealed that deranged Ca(2+) handling is the primary culprit in extending EMD in dyssynchronous HF, with the other aspects of remodeling contributing insignificantly. Mechanistically, we found that abnormal Ca(2+) handling in dyssynchronous HF slows myofiber shortening velocity at the early-activated septum and depresses both myofiber shortening and stretch rate at the late-activated lateral wall. These changes in myofiber dynamics delay the onset of myofiber shortening, thus giving rise to prolonged EMD in dyssynchronous HF.

Altered ventricular torsion and transmural patterns of myocyte relaxation precede heart failure in aging F344 rats

The purpose of this study was to identify and explain changes in ventricular and cellular function that contribute to aging-associated cardiovascular disease in aging F344 rats. Three groups of female F344 rats, aged 6, 18, and 22 mo, were studied. Echocardiographic measurements in isoflurane-anesthetized animals showed an increase in peak left ventricular torsion between the 6- and the 18-mo-old groups that was partially reversed in the 22-mo-old animals (P < 0.05). Epicardial, midmyocardial, and endocardial myocytes were subsequently isolated from the left ventricles of each group of rats. Unloaded sarcomere shortening and Ca(2+) transients were then measured in these cells (n = >75 cells for each of the nine age-region groups). The decay time of the Ca(2+) transient and the time required for 50% length relaxation both increased with age but not uniformly across the three regions (P < 0.02). Further analysis revealed a significant shift in the transmural distribution of these properties between 18 and 22 mo of age, with the largest changes occurring in epicardial myocytes. Computational modeling suggested that these changes were due in part to slower Ca(2+) dissociation from troponin in aging epicardial myocytes. Subsequent biochemical assays revealed a >50% reduction in troponin I phosphoprotein content in 22-mo-old epicardium relative to the other regions. These data suggest that between 18 and 22 mo of age (before the onset of heart failure), F344 rats display epicardial-specific myofilament-level modifications that 1) break from the progression observed between 6 and 18 mo and 2) coincide with aberrant patterns of cardiac torsion.

Improved discretisation and linearisation of active tension in strongly coupled cardiac electro-mechanics simulations

Mathematical models of cardiac electro-mechanics typically consist of three tightly coupled parts: systems of ordinary differential equations describing electro-chemical reactions and cross-bridge dynamics in the muscle cells, a system of partial differential equations modelling the propagation of the electrical activation through the tissue and a nonlinear elasticity problem describing the mechanical deformations of the heart muscle. The complexity of the mathematical model motivates numerical methods based on operator splitting, but simple explicit splitting schemes have been shown to give severe stability problems for realistic models of cardiac electro-mechanical coupling. The stability may be improved by adopting semi-implicit schemes, but these give rise to challenges in updating and linearising the active tension. In this paper we present an operator splitting framework for strongly coupled electro-mechanical simulations and discuss alternative strategies for updating and linearising the active stress component. Numerical experiments demonstrate considerable performance increases from an update method based on a generalised Rush-Larsen scheme and a consistent linearisation of active stress based on the first elasticity tensor.

At the heart of computational modelling

The link between experimental data and biophysically based mathematical models is key to computational simulation meeting its potential to provide physiological insight. However, despite the importance of this link, scrutiny and analysis of the processes by which models are parameterised from data are currently lacking. While this situation is common to many areas of physiological modelling, to provide a concrete context, we use examples drawn from detailed models of cardiac electro-mechanics. Using this biophysically detailed cohort of models we highlight the specific issues of model parameterization and propose this process can be separated into three stages: observation, fitting and validation. Finally, future research challenges and directions in this area are discussed.

Left-ventricular shape determines intramyocardial mechanical heterogeneity

Left-ventricular remodeling is considered to be an important mechanism of disease progression leading to mechanical dysfunction of the heart. However, the interaction between the physiological changes in the remodeling process and the associated mechanical dysfunction is still poorly understood. Clinically, it has been observed that the left ventricle often undergoes large shape changes, but the importance of left-ventricular shape as a contributing factor to alterations in mechanical function has not been clearly determined. Therefore, the interaction between left-ventricular shape and systolic mechanical function was examined in a computational finite-element study. Hereto, finite-element models were constructed with varying shapes, ranging from an elongated ellipsoid to a sphere. A realistic transmural gradient in fiber orientation was considered. The passive myocardium was described by an incompressible hyperelastic material law with transverse isotropic symmetry. Activation was governed by the eikonal-diffusion equation. Contraction was incorporated using a Hill model. For each shape, simulations were performed in which passive filling was followed by isovolumic contraction and ejection. It was found that the intramyocardial distributions of fiber stress, strain, and stroke work density were shape dependent. Ejection performance was reduced with increasing sphericity, which was regionally related to a reduction in the active fiber stress development, fiber shortening, and stroke work in the midwall and subepicardial region at the midheight level in the left-ventricular wall. Based on these results, we conclude that a significant interaction exists between left-ventricular shape and regional myofiber mechanics, but the importance for left-ventricular remodeling requires further investigation.

Clinical benefits of integrating cardiac and vascular models

INTRODUCTION

Recent advances in computational methods and medical imaging techniques have enabled non-invasive exploration of cardiovascular pathologies, from cardiac level to complex arterial networks. The potential of cardiac and vascular modeling in guiding and monitoring therapies could be further extended through the integration of the two systems.

AREAS COVERED

This review includes advances in methods for cardiac electromechanics and vascular flow simulations. The results of a literature search depicting the state of the art in cardiac and vascular modeling are reviewed. The paper goes on to address the benefits and challenges of combined cardiovascular modeling, highlighting the relevance of specific cardiovascular features and implementation. Various alternative approaches and insights on future directions are presented and analyzed with respect to their applicability to clinical practice.

EXPERT OPINION

The article has emerged from the exploration of currently available cardiac and vascular mathematical tools and their corresponding clinical application. The summarized analysis suggests that future efforts should be aimed at developing more accurate and patient-specific mathematical models integrating cardiac and vascular functions to enhance the knowledge of cardiovascular pathologies.

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.

Multi-scale computational models of familial hypertrophic cardiomyopathy: genotype to phenotype

Familial hypertrophic cardiomyopathy (FHC) is an inherited disorder affecting roughly one in 500 people. Its hallmark is abnormal thickening of the ventricular wall, leading to serious complications that include heart failure and sudden cardiac death. Treatment is complicated by variation in the severity, symptoms and risks for sudden death within the patient population. Nearly all of the genetic lesions associated with FHC occur in genes encoding sarcomeric proteins, indicating that defects in cardiac muscle contraction underlie the condition. Detailed biophysical data are increasingly available for computational analyses that could be used to predict heart phenotypes based on genotype. These models must integrate the dynamic processes occurring in cardiac cells with properties of myocardial tissue, heart geometry and haemodynamic load in order to predict strain and stress in the ventricular walls and overall pump function. Recent advances have increased the biophysical detail in these models at the myofilament level, which will allow properties of FHC-linked mutant proteins to be accurately represented in simulations of whole heart function. The short-term impact of these models will be detailed descriptions of contractile dysfunction and altered myocardial strain patterns at the earliest stages of the disease-predictions that could be validated in genetically modified animals. Long term, these multi-scale models have the potential to improve clinical management of FHC through genotype-based risk stratification and personalized therapy.

Torsion of the human left ventricle: experimental analysis and computational modeling

We set a twofold investigation: we assess left ventricular (LV) rotation and twist in the human heart through 3D-echocardiographic speckle tracking, and use representative experimental data as benchmark with respect to numerical results obtained by solving our mechanical model of the LV. We aim at new insight into the relationships between myocardial contraction patterns and the overall behavior at the scale of the whole organ. It is concluded that torsional rotation is sensitive to transmural gradients of contractility which is assumed linearly related to action potential duration (APD). Pressure-volume loops and other basic strain measures are not affected by these gradients. Therefore, realistic torsional behavior of human LV may indeed correspond to the electrophysiological and functional differences between endocardial and epicardial cells recently observed in non-failing hearts. Future investigations need now to integrate the mechanical model proposed here with minimal models of human ventricular APD to drive excitation-contraction coupling transmurally.

Models of cardiac electromechanics based on individual hearts imaging data: image-based electromechanical models of the heart

Current multi-scale computational models of ventricular electromechanics describe the full process of cardiac contraction on both the micro- and macro- scales including: the depolarization of cardiac cells, the release of calcium from intracellular stores, tension generation by cardiac myofilaments, and mechanical contraction of the whole heart. Such models are used to reveal basic mechanisms of cardiac contraction as well as the mechanisms of cardiac dysfunction in disease conditions. In this paper, we present a methodology to construct finite element electromechanical models of ventricular contraction with anatomically accurate ventricular geometry based on magnetic resonance and diffusion tensor magnetic resonance imaging of the heart. The electromechanical model couples detailed representations of the cardiac cell membrane, cardiac myofilament dynamics, electrical impulse propagation, ventricular contraction, and circulation to simulate the electrical and mechanical activity of the ventricles. The utility of the model is demonstrated in an example simulation of contraction during sinus rhythm using a model of the normal canine ventricles.

Whole-heart modeling: applications to cardiac electrophysiology and electromechanics

Recent developments in cardiac simulation have rendered the heart the most highly integrated example of a virtual organ. We are on the brink of a revolution in cardiac research, one in which computational modeling of proteins, cells, tissues, and the organ permit linking genomic and proteomic information to the integrated organ behavior, in the quest for a quantitative understanding of the functioning of the heart in health and disease. The goal of this review is to assess the existing state-of-the-art in whole-heart modeling and the plethora of its applications in cardiac research. General whole-heart modeling approaches are presented, and the applications of whole-heart models in cardiac electrophysiology and electromechanics research are reviewed. The article showcases the contributions that whole-heart modeling and simulation have made to our understanding of the functioning of the heart. A summary of the future developments envisioned for the field of cardiac simulation and modeling is also presented. Biophysically based computational modeling of the heart, applied to human heart physiology and the diagnosis and treatment of cardiac disease, has the potential to dramatically change 21st century cardiac research and the field of cardiology.

Integrative modeling of the cardiac ventricular myocyte

Cardiac electrophysiology is a discipline with a rich 50-year history of experimental research coupled with integrative modeling which has enabled us to achieve a quantitative understanding of the relationships between molecular function and the integrated behavior of the cardiac myocyte in health and disease. In this paper, we review the development of integrative computational models of the cardiac myocyte. We begin with a historical overview of key cardiac cell models that helped shape the field. We then narrow our focus to models of the cardiac ventricular myocyte and describe these models in the context of their subcellular functional systems including dynamic models of voltage-gated ion channels, mitochondrial energy production, ATP-dependent and electrogenic membrane transporters, intracellular Ca dynamics, mechanical contraction, and regulatory signal transduction pathways. We describe key advances and limitations of the models as well as point to new directions for future modeling research. WIREs Syst Biol Med 2011 3 392-413 DOI: 10.1002/wsbm.122

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.

Multi-scale modeling of excitation-contraction coupling in the normal and failing heart

Here we describe new computational models of cardiac electromechanics starting from the cellular scale and building to the tissue, organ and system scales. We summarize application to human genetic diseases (LQT1 and LQT3) and to modeling of congestive heart failure.

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.

Current progress in patient-specific modeling

We present a survey of recent advancements in the emerging field of patient-specific modeling (PSM). Researchers in this field are currently simulating a wide variety of tissue and organ dynamics to address challenges in various clinical domains. The majority of this research employs three-dimensional, image-based modeling techniques. Recent PSM publications mostly represent feasibility or preliminary validation studies on modeling technologies, and these systems will require further clinical validation and usability testing before they can become a standard of care. We anticipate that with further testing and research, PSM-derived technologies will eventually become valuable, versatile clinical tools.

Coupling multi-physics models to cardiac mechanics

We outline and review the mathematical framework for representing mechanical deformation and contraction of the cardiac ventricles, and how this behaviour integrates with other processes crucial for understanding and modelling heart function. Building on general conservation principles of space, mass and momentum, we introduce an arbitrary Eulerian-Lagrangian framework governing the behaviour of both fluid and solid components. Exploiting the natural alignment of cardiac mechanical properties with the tissue microstructure, finite deformation measures and myocardial constitutive relations are referred to embedded structural axes. Coupling approaches for solving this large deformation mechanics framework with three dimensional fluid flow, coronary hemodynamics and electrical activation are described. We also discuss the potential of cardiac mechanics modelling for clinical applications.