Electromechanics of paced left ventricle simulated by straightforward mathematical model: comparison with experiments

Simultaneous Widefield Voltage and Dye-Free Optical Mapping Quantifies Electromechanical Waves in Human Induced Pluripotent Stem Cell-Derived Cardiomyocytes

Coupled electromechanical waves define a heart's function in health and diseases. Optical mapping of electrical waves using fluorescent labels offers mechanistic insights into cardiac conduction abnormalities. Dye-free/label-free mapping of mechanical waves presents an attractive non-invasive alternative. In this study, we developed a simultaneous widefield voltage and interferometric dye-free optical imaging methodology that was used as follows: (1) to validate dye-free optical mapping for quantification of cardiac wave properties in human iPSC-cardiomyocytes (CMs); (2) to demonstrate low-cost optical mapping of electromechanical waves in hiPSC-CMs using recent near-infrared (NIR) voltage sensors and orders of magnitude cheaper miniature industrial CMOS cameras; (3) to uncover previously underexplored frequency- and space-varying parameters of cardiac electromechanical waves in hiPSC-CMs. We find similarity in the frequency-dependent responses of electrical (NIR fluorescence-imaged) and mechanical (dye-free-imaged) waves, with the latter being more sensitive to faster rates and showing steeper restitution and earlier appearance of wavefront tortuosity. During regular pacing, the dye-free-imaged conduction velocity and electrical wave velocity are correlated; both modalities are sensitive to pharmacological uncoupling and dependent on gap-junctional protein (connexins) determinants of wave propagation. We uncover the strong frequency dependence of the electromechanical delay (EMD) locally and globally in hiPSC-CMs on a rigid substrate. The presented framework and results offer new means to track the functional responses of hiPSC-CMs inexpensively and non-invasively for counteracting heart disease and aiding cardiotoxicity testing and drug development.

Optimization of cardiac resynchronization therapy based on a cardiac electromechanics-perfusion computational model

Cardiac resynchronization therapy (CRT) is an established treatment for left bundle branch block (LBBB) resulting in mechanical dyssynchrony. Approximately 1/3 of patients with CRT, however, are non-responders. To understand factors affecting CRT response, an electromechanics-perfusion computational model based on animal-specific left ventricular (LV) geometry and coronary vascular networks located in the septum and LV free wall is developed. The model considers contractility-flow and preload-activation time relationships, and is calibrated to simultaneously match the experimental measurements in terms of the LV pressure, volume waveforms and total coronary flow in the left anterior descending and left circumflex territories from 2 swine models under right atrium and right ventricular pacing. The model is then applied to investigate the responses of CRT indexed by peak LV pressure and (dP/dt)max at multiple pacing sites with different degrees of perfusion in the LV free wall. Without the presence of ischemia, the model predicts that basal-lateral endocardial region is the optimal pacing site that can best improve (dP/dt)max by 20%, and is associated with the shortest activation time. In the presence of ischemia, a non-ischemic region becomes the optimal pacing site when coronary flow in the ischemic region fell below 30% of its original value. Pacing at the ischemic region produces little response at that perfusion level. The optimal pacing site is associated with one that optimizes the LV activation time. These findings suggest that CRT response is affected by both pacing site and coronary perfusion, which may have clinical implication in improving CRT responder rates.

Transmural Distribution of Coronary Perfusion and Myocardial Work Density Due to Alterations in Ventricular Loading, Geometry and Contractility

Myocardial supply changes to accommodate the variation of myocardial demand across the heart wall to maintain normal cardiac function. A computational framework that couples the systemic circulation of a left ventricular (LV) finite element model and coronary perfusion in a closed loop is developed to investigate the transmural distribution of the myocardial demand (work density) and supply (perfusion) ratio. Calibrated and validated against measurements of LV mechanics and coronary perfusion, the model is applied to investigate changes in the transmural distribution of passive coronary perfusion, myocardial work density, and their ratio in response to changes in LV contractility, preload, afterload, wall thickness, and cavity volume. The model predicts the following: (1) Total passive coronary flow varies from a minimum value at the endocardium to a maximum value at the epicardium transmurally that is consistent with the transmural distribution of IMP; (2) Total passive coronary flow at different transmural locations is increased with an increase in either contractility, afterload, or preload of the LV, whereas is reduced with an increase in wall thickness or cavity volume; (3) Myocardial work density at different transmural locations is increased transmurally with an increase in either contractility, afterload, preload or cavity volume of the LV, but is reduced with an increase in wall thickness; (4) Myocardial work density-perfusion mismatch ratio at different transmural locations is increased with an increase in contractility, preload, wall thickness or cavity volume of the LV, and the ratio is higher at the endocardium than the epicardium. These results suggest that an increase in either contractility, preload, wall thickness, or cavity volume of the LV can increase the vulnerability of the subendocardial region to ischemia.

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.

Left ventricular dyssynchrony and post-systolic shortening in young bodybuilders using anabolic-androgenic steroids

Left ventricular (LV) remodeling, characterized by increased LV hypertrophy and depressed systolic and diastolic function, is observed in strength-trained athletes who use anabolic-androgenic steroids (AAS). Previous studies suggested a pathological remodeling with an increase in cardiac fibrosis in these athletes, which could promote intraventricular dyssynchrony. In this context, this study evaluated LV dyssynchrony in strength-trained athletes using AAS, hypothesizing that the use of AAS would lead to an increase in post-systolic shortening. Forty-four male subjects (aged 20-40 yr) were divided into three age-matched groups: strength-trained athletes using (users, n = 14) or not (nonusers, n = 15) AAS and healthy sedentary men (controls, n = 15). After completing a survey, each participant was assessed with two-dimensional (2D)-strain echocardiography. LV dyssynchrony was quantified using the standard deviation (SD) of the time to peak for longitudinal strain of the 18 LV-segments (from the apical 4, 3, and 2 chambers views), the longitudinal strain delay index (LSDI), and the segmental post-systolic index (PSI). Users showed mean AAS dosages of 564 ± 288 mg[Formula: see text]wk^-1 with a mean protocol duration of 12 ± 6 wk and a history of use of 4.7 ± 1.8 yr. They exhibited a greater LV mass index and depressed systolic and diastolic function when compared with both nonusers and controls. The decrease in LV strain in users was predominantly observed at the interventricular septum level (-16.9% ± 2.5% vs. -19.2% ± 1.8% and -19.0% ± 1.6% in users, nonusers, and controls, respectively, P < 0.01). Users showed higher SD than controls (43 ± 8 ms vs. 32 ± 5 ms, respectively, P < 0.01). The LSDI was significantly higher in users compared with both nonusers and controls (-23.4 ± 9.5 vs. -15.9 ± 9.3 and -9.8 ± 3.9, respectively, P < 0.01). PSI, calculated on the basal inferoseptal, basal anteroseptal, and basal inferolateral segments, were also greater in users compared with the two other groups. Our results reported an increase in LV dyssynchrony in young AAS users that brought new evidences of a pathologic cardiac remodeling in this specific population.NEW & NOTEWORTHY Illicit androgenic anabolic steroids (AAS) use is widespread, but data on LV dyssynchrony are lacking, although it could be increased by a higher prevalence of myocardial fibrosis reported in this population. In AAS users, the decrease in LV strain was predominantly observed in interventricular segments. All dyssynchrony indices were higher in AAS users and several segments exhibited post-systolic shortening. These results showed an association between AAS consumption, LV remodeling, and dyssynchrony.

Role of coronary flow regulation and cardiac-coronary coupling in mechanical dyssynchrony associated with right ventricular pacing

Mechanical dyssynchrony (MD) affects left ventricular (LV) mechanics and coronary perfusion. To understand the multifactorial effects of MD, we developed a computational model that bidirectionally couples the systemic circulation with the LV and coronary perfusion with flow regulation. In the model, coronary flow in the left anterior descending (LAD) and left circumflex (LCX) arteries affects the corresponding regional contractility based on a prescribed linear LV contractility-coronary flow relationship. The model is calibrated with experimental measurements of LV pressure and volume, as well as LAD and LCX flow rate waveforms acquired under regulated and fully dilated conditions from a swine under right atrial (RA) pacing. The calibrated model is applied to simulate MD. The model can simultaneously reproduce the reduction in mean LV pressure (39.3%), regulated flow (LAD: 7.9%; LCX: 1.9%), LAD passive flow (21.6%), and increase in LCX passive flow (15.9%). These changes are associated with right ventricular pacing compared with RA pacing measured in the same swine only when LV contractility is affected by flow alterations with a slope of 1.4 mmHg/mL² in a contractility-flow relationship. In sensitivity analyses, the model predicts that coronary flow reserve (CFR) decreases and increases in the LAD and LCX with increasing delay in LV free wall contraction. These findings suggest that asynchronous activation associated with MD impacts 1) the loading conditions that further affect the coronary flow, which may explain some of the changes in CFR, and 2) the coronary flow that reduces global contractility, which contributes to the reduction in LV pressure.NEW & NOTEWORTHY A computational model that couples the systemic circulation of the left ventricular (LV) and coronary perfusion with flow regulation is developed to study the effects of mechanical dyssynchrony. The delayed contraction in the LV free wall with respect to the septum has a significant effect on LV function and coronary flow reserve.

Modeling left ventricular dynamics with characteristic deformation modes

A computationally efficient method is described for simulating the dynamics of the left ventricle (LV) in three dimensions. LV motion is represented as a combination of a limited number of deformation modes, chosen to represent observed cardiac motions while conserving volume in the LV wall. The contribution of each mode to wall motion is determined by a corresponding time-dependent deformation variable. The principle of virtual work is applied to these deformation variables, yielding a system of ordinary differential equations for LV dynamics, including effects of muscle fiber orientations, active and passive stresses, and surface tractions. Passive stress is governed by a transversely isotropic elastic model. Active stress acts in the fiber direction and incorporates length-tension and force-velocity properties of cardiac muscle. Preload and afterload are represented by lumped vascular models. The variational equations and their numerical solutions are verified by comparison to analytic solutions of the strong form equations. Deformation modes are constructed using Fourier series with an arbitrary number of terms. Greater numbers of deformation modes increase deformable model resolution but at increased computational cost. Simulations of normal LV motion throughout the cardiac cycle are presented using models with 8, 23, or 46 deformation modes. Aggregate quantities that describe LV function vary little as the number of deformation modes is increased. Spatial distributions of stress and strain change as more deformation modes are included, but overall patterns are conserved. This approach yields three-dimensional simulations of the cardiac cycle on a clinically relevant time-scale.

Effects of mechanical feedback on the stability of cardiac scroll waves: A bidomain electro-mechanical simulation study

In this work, we investigate the influence of cardiac tissue deformation on re-entrant wave dynamics. We have developed a 3D strongly coupled electro-mechanical Bidomain model posed on an ideal monoventricular geometry, including fiber direction anisotropy and stretch-activated currents (SACs). The cardiac mechanical deformation influences the bioelectrical activity with two main mechanical feedback: (a) the geometric feedback (GEF) due to the presence of the deformation gradient in the diffusion coefficients and in a convective term depending on the deformation rate and (b) the mechano-electric feedback (MEF) due to SACs. Here, we investigate the relative contribution of these two factors with respect to scroll wave stability. We extend the previous works [Keldermann et al., Am. J. Physiol. Heart Circ. Physiol. 299, H134-H143 (2010) and Hu et al., PLoS One 8(4), e60287 (2013)] that were based on the Monodomain model and a simple non-selective linear SAC, while here we consider the full Bidomain model and both selective and non-selective components of SACs. Our simulation results show that the stability of cardiac scroll waves is influenced by MEF, which in case of low reversal potential of non-selective SACs might be responsible for the onset of ventricular fibrillation; GEF increases the scroll wave meandering but does not determine the scroll wave stability.

A two dimensional electromechanical model of a cardiomyocyte to assess intra-cellular regional mechanical heterogeneities

Experimental studies on isolated cardiomyocytes from different animal species and human hearts have demonstrated that there are regional differences in the Ca2+ release, Ca2+ decay and sarcomere deformation. Local deformation heterogeneities can occur due to a combination of factors: regional/local differences in Ca2+ release and/or re-uptake, intra-cellular material properties, sarcomere proteins and distribution of the intracellular organelles. To investigate the possible causes of these heterogeneities, we developed a two-dimensional finite-element electromechanical model of a cardiomyocyte that takes into account the experimentally measured local deformation and cytosolic [Ca2+] to locally define the different variables of the constitutive equations describing the electro/mechanical behaviour of the cell. Then, the model was individualised to three different rat cardiac cells. The local [Ca2+] transients were used to define the [Ca2+]-dependent activation functions. The cell-specific local Young's moduli were estimated by solving an inverse problem, minimizing the error between the measured and simulated local deformations along the longitudinal axis of the cell. We found that heterogeneities in the deformation during contraction were determined mainly by the local elasticity rather than the local amount of Ca2+, while in the relaxation phase deformation was mainly influenced by Ca2+ re-uptake. Our electromechanical model was able to successfully estimate the local elasticity along the longitudinal direction in three different cells. In conclusion, our proposed model seems to be a good approximation to assess the heterogeneous intracellular mechanical properties to help in the understanding of the underlying mechanisms of cardiomyocyte dysfunction.

Joint influence of transmural heterogeneities and wall deformation on cardiac bioelectrical activity: A simulation study

The aim of this work is to investigate, by means of numerical simulations, the influence of myocardial deformation due to muscle contraction and relaxation on the cardiac repolarization process in presence of transmural intrinsic action potential duration (APD) heterogeneities. The three-dimensional electromechanical model considered consists of the following four coupled components: the quasi-static transversely isotropic finite elasticity equations for the deformation of the cardiac tissue; the active tension model for the intracellular calcium dynamics and cross-bridge binding; the anisotropic Bidomain model for the electrical current flow through the deforming cardiac tissue; the membrane model of ventricular myocytes, including stretch-activated channels. The numerical simulations are based on our finite element parallel solver, which employs Multilevel Additive Schwarz preconditioners for the solution of the discretized Bidomain equations and Newton-Krylov methods for the solution of the discretized non-linear finite elasticity equations. Our findings show that: (i) the presence of intrinsic transmural cellular APD heterogeneities is not fully masked by electrotonic current flow or by the presence of the mechanical deformation; (ii) despite the presence of transmural APD heterogeneities, the recovery process follows the activation sequence and there is no significant transmural repolarization gradient; (iii) with or without transmural APD heterogeneities, epicardial electrograms always display the same wave shape and discordance between the polarity of QRS complex and T-wave; (iv) the main effects of the mechanical deformation are an increase of the dispersion of repolarization time and APD, when computed over the total cardiac domain and over the endo- and epicardial surfaces, while there is a slight decrease along the transmural direction.

The cardiac torsion as a sensitive index of heart pathology: A model study

The torsional behaviour of the heart (i.e. the mutual rotation of the cardiac base and apex) was proved to be sensitive to alterations of some cardiovascular parameters, i.e. preload, afterload and contractility. Moreover, pathologies which affect the fibers architecture and cardiac geometry were proved to alter the cardiac torsion pattern. For these reasons, cardiac torsion represents a sensitive index of ventricular performance. The aim of this work is to provide further insight into physiological and pathological alterations of the cardiac torsion by means of computational analyses, combining a structural model of the two ventricles with simple lumped parameter models of both the systemic and the pulmonary circulations. Starting from diagnostic images, a 3D anatomy based geometry of the two ventricles was reconstructed. The myocytes orientation in the ventricles was assigned according to literature data and the myocardium was modelled as an anisotropic hyperelastic material. Both the active and the passive phases of the cardiac cycle were modelled, and different clinical conditions were simulated. The results in terms of alterations of the cardiac torsion in the presence of pathologies are in agreement with experimental literature data. The use of a computational approach allowed the investigation of the stresses and strains in the ventricular wall as well as of the global hemodynamic parameters in the presence of the considered pathologies. Furthermore, the model outcomes highlight how for specific pathological conditions, an altered torsional pattern of the ventricles can be present, encouraging the use of the ventricular torsion in the clinical practice.

Computer Modelling for Better Diagnosis and Therapy of Patients by Cardiac Resynchronisation Therapy

Mathematical or computer models have become increasingly popular in biomedical science. Although they are a simplification of reality, computer models are able to link a multitude of processes to each other. In the fields of cardiac physiology and cardiology, models can be used to describe the combined activity of all ion channels (electrical models) or contraction-related processes (mechanical models) in potentially millions of cardiac cells. Electromechanical models go one step further by coupling electrical and mechanical processes and incorporating mechano-electrical feedback. The field of cardiac computer modelling is making rapid progress due to advances in research and the ever-increasing calculation power of computers. Computer models have helped to provide better understanding of disease mechanisms and treatment. The ultimate goal will be to create patient-specific models using diagnostic measurements from the individual patient. This paper gives a brief overview of computer models in the field of cardiology and mentions some scientific achievements and clinical applications, especially in relation to cardiac resynchronisation therapy (CRT).

Current concepts relating coronary flow, myocardial perfusion and metabolism in left bundle branch block and cardiac resynchronisation therapy

Cardiac resynchronisation therapy (CRT) improves mortality and symptoms in heart failure patients with electromechanically dyssynchronous ventricles. There is a 50% non-response rate and reproducible biomarkers to predict non-response have not been forthcoming. Therefore, there has been increasing interest in the pathophysiological effects of dyssynchrony particularly focusing on coronary flow, myocardial perfusion and metabolism. Studies suggest that dyssynchronous electrical activation effects coronary flow throughout the coronary vasculature from the epicardial arteries to the microvascular bed and that these changes can be corrected by CRT. The effect of both electrical and mechanical dyssynchrony on myocardial perfusion is unclear with some studies suggesting there is a reduction in septal perfusion whilst others propose that there is an increase in lateral perfusion. Better understanding of these effects offers the possibility for better prediction of non-response. CRT appears to improve homogeneity in myocardial perfusion where heterogeneity is described in the initial substrate. Novel approaches to the identification of non-responders via metabolic phenotyping both invasively and non-invasively have been encouraging. There remains a need for further research to clarify the interaction of coronary flow with perfusion and metabolism in patients who undergo CRT.

Myofiber prestretch magnitude determines regional systolic function during ectopic activation in the tachycardia-induced failing canine heart

Electrical dyssynchrony leads to prestretch in late-activated regions and alters the sequence of mechanical contraction, although prestretch and its mechanisms are not well defined in the failing heart. We hypothesized that in heart failure, fiber prestretch magnitude increases with the amount of early-activated tissue and results in increased end-systolic strains, possibly due to length-dependent muscle properties. In five failing dog hearts with scars, three-dimensional strains were measured at the anterolateral left ventricle (LV). Prestretch magnitude was varied via ventricular pacing at increasing distances from the measurement site and was found to increase with activation time at various wall depths. At the subepicardium, prestretch magnitude positively correlated with the amount of early-activated tissue. At the subendocardium, local end-systolic strains (fiber shortening, radial wall thickening) increased proportionally to prestretch magnitude, resulting in greater mean strain values in late-activated compared with early-activated tissue. Increased fiber strains at end systole were accompanied by increases in preejection fiber strain, shortening duration, and the onset of fiber relengthening, which were all positively correlated with local activation time. In a dog-specific computational failing heart model, removal of length and velocity dependence on active fiber stress generation, both separately and together, alter the correlations between local electrical activation time and timing of fiber strains but do not primarily account for these relationships.

A study of mechanical optimization strategy for cardiac resynchronization therapy based on an electromechanical model

An optimal electrode position and interventricular (VV) delay in cardiac resynchronization therapy (CRT) improves its success. However, the precise quantification of cardiac dyssynchrony and magnitude of resynchronization achieved by biventricular (BiV) pacing therapy with mechanical optimization strategies based on computational models remain scant. The maximum circumferential uniformity ratio estimate (CURE) was used here as mechanical optimization index, which was automatically computed for 6 different electrode positions based on a three-dimensional electromechanical canine model of heart failure (HF) caused by complete left bundle branch block (CLBBB). VV delay timing was adjusted accordingly. The heart excitation propagation was simulated with a monodomain model. The quantification of mechanical intra- and interventricular asynchrony was then investigated with eight-node isoparametric element method. The results showed that (i) the optimal pacing location from maximal CURE of 0.8516 was found at the left ventricle (LV) lateral wall near the equator site with a VV delay of 60 ms, in accordance with current clinical studies, (ii) compared with electrical optimization strategy of E_RMS, the LV synchronous contraction and the hemodynamics improved more with mechanical optimization strategy. Therefore, measures of mechanical dyssynchrony improve the sensitivity and specificity of predicting responders more. The model was subject to validation in future clinical studies.

A single strain-based growth law predicts concentric and eccentric cardiac growth during pressure and volume overload

Adult cardiac muscle adapts to mechanical changes in the environment by growth and remodeling (G&R) via a variety of mechanisms. Hypertrophy develops when the heart is subjected to chronic mechanical overload. In ventricular pressure overload (e.g. due to aortic stenosis) the heart typically reacts by concentric hypertrophic growth, characterized by wall thickening due to myocyte radial growth when sarcomeres are added in parallel. In ventricular volume overload, an increase in filling pressure (e.g. due to mitral regurgitation) leads to eccentric hypertrophy as myocytes grow axially by adding sarcomeres in series leading to ventricular cavity enlargement that is typically accompanied by some wall thickening. The specific biomechanical stimuli that stimulate different modes of ventricular hypertrophy are still poorly understood. In a recent study, based on in-vitro studies in micropatterned myocyte cell cultures subjected to stretch, we proposed that cardiac myocytes grow longer to maintain a preferred sarcomere length in response to increased fiber strain and grow thicker to maintain interfilament lattice spacing in response to increased cross-fiber strain. Here, we test whether this growth law is able to predict concentric and eccentric hypertrophy in response to aortic stenosis and mitral valve regurgitation, respectively, in a computational model of the adult canine heart coupled to a closed loop model of circulatory hemodynamics. A non-linear finite element model of the beating canine ventricles coupled to the circulation was used. After inducing valve alterations, the ventricles were allowed to adapt in shape in response to mechanical stimuli over time. The proposed growth law was able to reproduce major acute and chronic physiological responses (structural and functional) when integrated with comprehensive models of the pressure-overloaded and volume-overloaded canine heart, coupled to a closed-loop circulation. We conclude that strain-based biomechanical stimuli can drive cardiac growth, including wall thickening during pressure overload.

Modeling cardiac electromechanics and mechanoelectrical coupling in dyssynchronous and failing hearts: insight from adaptive computer models

Computer models have become more and more a research tool to obtain mechanistic insight in the effects of dyssynchrony and heart failure. Increasing computational power in combination with increasing amounts of experimental and clinical data enables the development of mathematical models that describe electrical and mechanical behavior of the heart. By combining models based on data at the molecular and cellular level with models that describe organ function, so-called multi-scale models are created that describe heart function at different length and time scales. In this review, we describe basic modules that can be identified in multi-scale models of cardiac electromechanics. These modules simulate ionic membrane currents, calcium handling, excitation-contraction coupling, action potential propagation, and cardiac mechanics and hemodynamics. In addition, we discuss adaptive modeling approaches that aim to address long-term effects of diseases and therapy on growth, changes in fiber orientation, ionic membrane currents, and calcium handling. Finally, we discuss the first developments in patient-specific modeling. While current models still have shortcomings, well-chosen applications show promising results on some ultimate goals: understanding mechanisms of dyssynchronous heart failure and tuning pacing strategy to a particular patient, even before starting the therapy.

Electromechanical feedback with reduced cellular connectivity alters electrical activity in an infarct injured left ventricle: a finite element model study

Myocardial infarction (MI) significantly alters the structure and function of the heart. As abnormal strain may drive heart failure and the generation of arrhythmias, we used computational methods to simulate a left ventricle with an MI over the course of a heartbeat to investigate strains and their potential implications to electrophysiology. We created a fully coupled finite element model of myocardial electromechanics consisting of a cellular physiological model, a bidomain electrical diffusion solver, and a nonlinear mechanics solver. A geometric mesh built from magnetic resonance imaging (MRI) measurements of an ovine left ventricle suffering from a surgically induced anteroapical infarct was used in the model, cycled through the cardiac loop of inflation, isovolumic contraction, ejection, and isovolumic relaxation. Stretch-activated currents were added as a mechanism of mechanoelectric feedback. Elevated fiber and cross fiber strains were observed in the area immediately adjacent to the aneurysm throughout the cardiac cycle, with a more dramatic increase in cross fiber strain than fiber strain. Stretch-activated channels decreased action potential (AP) dispersion in the remote myocardium while increasing it in the border zone. Decreases in electrical connectivity dramatically increased the changes in AP dispersion. The role of cross fiber strain in MI-injured hearts should be investigated more closely, since results indicate that these are more highly elevated than fiber strain in the border of the infarct. Decreases in connectivity may play an important role in the development of altered electrophysiology in the high-stretch regions of the heart.

Improvement in pump function with endocardial biventricular pacing increases with activation time at the left ventricular pacing site in failing canine hearts

Recently, attention has been focused on comparing left ventricular (LV) endocardial (ENDO) with epicardial (EPI) pacing for cardiac resynchronization therapy. However, the effects of ENDO and EPI lead placement at multiple sites have not been studied in failing hearts. We hypothesized that differences in the improvement of ventricular function due to ENDO vs. EPI pacing in dyssynchronous (DYSS) heart failure may depend on the position of the LV lead in relation to the original activation pattern. In six nonfailing and six failing dogs, electrical DYSS was created by atrioventricular sequential pacing of the right ventricular apex. ENDO was compared with EPI biventricular pacing at five LV sites. In failing hearts, increases in the maximum rate of LV pressure change (dP/dt; r = 0.64), ejection fraction (r = 0.49), and minimum dP/dt (r = 0.51), relative to DYSS, were positively correlated (P < 0.01) with activation time at the LV pacing site during ENDO but not EPI pacing. ENDO pacing at sites with longer activation delays led to greater improvements in hemodynamic parameters and was associated with an overall reduction in electrical DYSS compared with EPI pacing (P < 0.05). These findings were qualitatively similar for nonfailing hearts. Improvement in hemodynamic function increased with activation time at the LV pacing site during ENDO but not EPI pacing. At the anterolateral wall, end-systolic transmural function was greater with local ENDO compared with EPI pacing. ENDO pacing and intrinsic activation delay may have important implications for management of DYSS heart failure.

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.

Ventricular dilation and electrical dyssynchrony synergistically increase regional mechanical nonuniformity but not mechanical dyssynchrony: a computational model

BACKGROUND

Heart failure (HF) in combination with mechanical dyssynchrony is associated with a high mortality rate. To quantify contractile dysfunction in patients with HF, investigators have proposed several indices of mechanical dyssynchrony, including percentile range of time to peak shortening (WTpeak), circumferential uniformity ratio estimate (CURE), and internal stretch fraction (ISF). The goal of this study was to compare the sensitivity of these indices to 4 major abnormalities responsible for cardiac dysfunction in dyssynchronous HF: dilation, negative inotropy, negative lusitropy, and dyssynchronous activation.

METHODS AND RESULTS

All combinations of these 4 major abnormalities were included in 3D computational models of ventricular electromechanics. Compared with a nonfailing heart model, ventricles were dilated, inotropy was reduced, twitch duration was prolonged, and activation sequence was changed from normal to left bundle branch block. In the nonfailing heart, CURE, ISF, and WTpeak were 0.97+/-0.004, 0.010+/-0.002, and 78+/-1 milliseconds, respectively. With dilation alone, CURE decreased 2.0+/-0.07%, ISF increased 58+/-47%, and WTpeak increased 31+/-3%. With dyssynchronous activation alone, CURE decreased 15+/-0.6%, ISF increased 14-fold (+/-3), and WTpeak increased 121+/-4%. With the combination of dilation and dyssynchronous activation, CURE decreased 23+/-0.8%, ISF increased 20-fold (+/-5), and WTpeak increased 147+/-5%.

CONCLUSIONS

Dilation and left bundle branch block combined synergistically decreased regional cardiac function. CURE and ISF were sensitive to this combination, but WTpeak was not. CURE and ISF also reflected the relative nonuniform distribution of regional work better than WTpeak. These findings might explain why CURE and ISF are better predictors of reverse remodeling in cardiac resynchronization therapy.

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.

Global electrophysiological and hemodynamic assessment of ventricular pacing employing non-contact mapping

OBJECTIVE

Right ventricular (RV) pacing has been associated with abnormal cardiac electrical and mechanical dyssynchrony, resulting in impaired global and regional ventricular pump function. This study aimed to characterize the relative effects of pacing site on left ventricular (LV) activation patterns and associated hemodynamic performances.

METHODS

Acute pacing was performed in anesthetized swine (n=10) instrumented for RV and LV pressure, noncontact mapping (NCM) of endocardial unipolar electrograms, surface ECG, aortic flow, and sonomicrometry. Bipolar endocardial pacing leads were positioned in the right atrial appendage (RAA), RV apex (RVA), and RV outflow tract (RVOT), while bipolar epicardial leads were positioned on the LV-free wall (LVFW) and LV apex (LVA).

RESULTS

LVFW and RVA pacing induced the largest increase in intraventricular electrical dyssynchrony (IVED; 32.2+/-10 ms, 21.7+/-4.1 ms, respectively; both p<0.01), whereas pacing from all sites increased QRS and total endocardial LV activation durations (p<0.01). The largest impairment of LV and RV contractility (dP/dtmax) and relaxation (dP/dtmin) was observed during RVA pacing (p= ns). Synchronous electrical activation patterns were observed on NCM during RVOT and LVA pacing. LVFW pacing was the only site that significantly increased tau values as compared to RAA pacing (approximately 25%), whereas LVA pacing elicited only slight increases (approximately 1%).

CONCLUSIONS

In swine with preserved ventricular conduction, in vivo pacing of the RVOT and LVA was associated with preserved, physiologically similar electrical activation sequences and LV function relative to RAA pacing. In contrast, RVA pacing caused widespread electrical dyssynchrony of the LV and prolonged activation durations, thereby impairing associated cardiac performance. Such insights into alternate site cardiac pacing, which employed the combination of high-resolution electrical mapping with real-time hemodynamic assessments, may further increase acute and long-term benefits in patients requiring permanent pacemaker support.

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

The excitation-contraction coupling properties of cardiac myocytes isolated from different regions of the mammalian left ventricular wall have been shown to vary considerably, with uncertain effects on ventricular function. We embedded a cell-level excitation-contraction coupling model with region-dependent parameters within a simple finite element model of left ventricular geometry to study effects of electromechanical heterogeneity on local myocardial mechanics and global haemodynamics. This model was compared with one in which heterogeneous myocyte parameters were assigned randomly throughout the mesh while preserving the total amount of each cell subtype. The two models displayed nearly identical transmural patterns of fibre and cross-fibre strains at end-systole, but showed clear differences in fibre strains at earlier points during systole. Haemodynamic function, including peak left ventricular pressure, maximal rate of left ventricular pressure development and stroke volume, were essentially identical in the two models. These results suggest that in the intact ventricle heterogeneously distributed myocyte subtypes primarily impact local deformation of the myocardium, and that these effects are greatest during early systole.

Computational modeling of cardiac disease: potential for personalized medicine

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

Mechanical analysis of congestive heart failure caused by bundle branch block based on an electromechanical canine heart model

Asynchronous electrical activation, induced by bundle branch block (BBB), can cause reduced ventricular function. However, the effects of BBB on the mechanical function of heart are difficult to assess experimentally. Many heart models have been developed to investigate cardiac properties during BBB but have mainly focused on the electrophysiological properties. To date, the mechanical function of BBB has not been well investigated. Based on a three-dimensional electromechanical canine heart model, the mechanical properties of complete left and right bundle branch block (LBBB and RBBB) were simulated. The anatomical model as well as the fiber orientations of a dog heart was reconstructed from magnetic resonance imaging (MRI) and diffusion tensor MRI (DT-MRI). Using the solutions of reaction-diffusion equations and with a strategy of parallel computation, the asynchronous excitation propagation and intraventricular conduction in BBB was simulated. The mechanics of myocardial tissues were computed with time-, sarcomere length-dependent uniaxial active stress initiated at the time of depolarization. The quantification of mechanical intra- and interventricular asynchrony of BBB was then investigated using the finite-element method with an eight-node isoparametric element. The simulation results show that (1) there exists inter- and intraventricular systolic dyssynchrony during BBB; (2) RBBB may have more mechanical synchrony and better systolic function of the left ventricle (LV) than LBBB; (3) the ventricles always move toward the early-activated ventricle; and (4) the septum experiences higher stress than left and right ventricular free walls in BBB. The simulation results validate clinical and experimental recordings of heart deformation and provide regional quantitative estimates of ventricular wall strain and stress. The present work suggests that an electromechanical heart model, incorporating real geometry and fiber orientations, may be helpful for better understanding of the mechanical implications of congestive heart failure (CHF) caused by BBB.

Computational modeling for bedside application

Advances in computer power, novel diagnostic and therapeutic medical technologies, and an increasing knowledge of pathophysiology from gene to organ systems make it increasingly feasible to apply multiscale patient-specific modeling based on proven disease mechanisms. Such models may guide and predict the response to therapy in many areas of medicine. This is an exciting and relatively new approach, for which efficient methods and computational tools are of the utmost importance. Investigators have designed patient-specific models in almost all areas of human physiology. Not only will these models be useful in clinical settings to predict and optimize the outcome from surgery and non-interventional therapy, but they will also provide pathophysiologic insights from the cellular level to the organ system level. Models, therefore, will provide insight as to why specific interventions succeed or fail.

Effects of biventricular pacing and scar size in a computational model of the failing heart with left bundle branch block

OBJECTIVES

To study the impact of biventricular pacing (BiV) and scar size on left ventricular (LV) regional and global function using a detailed finite element model of three-dimensional electromechanics in the failing canine heart.

BACKGROUND

Cardiac resynchronization therapy (CRT) clinical trials have demonstrated that up to 30% of patients may be classified as non-responders. The presence of a scar appears to contribute to those that do not respond to CRT. A recent study in patients with myocardial scar showed that LV dyssynchrony was the sole independent predictor of reverse remodeling, and not scar location or size.

METHODS

Two activation sequences were simulated: left bundle branch block (LBBB) and acute simultaneous BiV (with leads in the left and right ventricle) in hearts with chronic scars of various sizes. The dependence of regional function (mean fiber ejection strain, variance of fiber isovolumic strain and fraction of tissue stretched during ejection) and global function (left ventricular dP/dt(max), ejection fraction, stroke work) on scar size and pacing protocol was tested.

RESULTS

Global function and regional function averaged over the whole LV during LBBB and BiV decreased as a function of scar size. In the non-scarred regions, however, regional function was largely independent of scar size for a fixed pacing site.

CONCLUSIONS

The model results suggest that uniformity of mechanical contraction in non-scarred regions in the failing heart during biventricular pacing is independent of scar size for a fixed pacing site.

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.

Cardiac resynchronization: insight from experimental and computational models

Cardiac resynchronization therapy (CRT) is a promising therapy for heart failure patients with a conduction disturbance, such as left bundle branch block. The aim of CRT is to resynchronize contraction between and within ventricles. However, about 30% of patients do not respond to this therapy. Therefore, a better understanding is needed for the relation between electrical and mechanical activation. In this paper, we focus on to what extent animal experiments and mathematical models can help in order to understand the pathophysiology of asynchrony to further improve CRT.

Multi-scale computational modelling in biology and physiology

Recent advances in biotechnology and the availability of ever more powerful computers have led to the formulation of increasingly complex models at all levels of biology. One of the main aims of systems biology is to couple these together to produce integrated models across multiple spatial scales and physical processes. In this review, we formulate a definition of multi-scale in terms of levels of biological organisation and describe the types of model that are found at each level. Key issues that arise in trying to formulate and solve multi-scale and multi-physics models are considered and examples of how these issues have been addressed are given for two of the more mature fields in computational biology: the molecular dynamics of ion channels and cardiac modelling. As even more complex models are developed over the coming few years, it will be necessary to develop new methods to model them (in particular in coupling across the interface between stochastic and deterministic processes) and new techniques will be required to compute their solutions efficiently on massively parallel computers. We outline how we envisage these developments occurring.

Mechanoelectric feedback leads to conduction slowing and block in acutely dilated atria: a modeling study of cardiac electromechanics

Atrial fibrillation, a common cardiac arrhythmia, is promoted by atrial dilatation. Acute atrial dilatation may play a role in atrial arrhythmogenesis through mechanoelectric feedback. In experimental studies, conduction slowing and block have been observed in acutely dilated atria. In the present study, the influence of the stretch-activated current ( Isac) on impulse propagation is investigated by means of computer simulations. Homogeneous and inhomogeneous atrial tissues are modeled by cardiac fibers composed of segments that are electrically and mechanically coupled. Active force is related to free Ca2+ concentration and sarcomere length. Simulations of homogeneous and inhomogeneous cardiac fibers have been performed to quantify the relation between conduction velocity and Isac under stretch. In our model, conduction slowing and block are related to the amount of stretch and are enhanced by contraction of early-activated segments. Conduction block can be unidirectional in an inhomogeneous fiber and is promoted by a shorter stimulation interval. Slowing of conduction is explained by inactivation of Na+ channels and a lower maximum upstroke velocity due to a depolarized resting membrane potential. Conduction block at shorter stimulation intervals is explained by a longer effective refractory period under stretch. Our observations are in agreement with experimental results and explain the large differences in intra-atrial conduction, as well as the increased inducibility of atrial fibrillation in acutely dilated atria.

Asynchrony of ventricular activation affects magnitude and timing of fiber stretch in late-activated regions of the canine heart

Abnormal electrical activation of the left ventricle results in mechanical dyssynchrony, which is in part characterized by early stretch of late-activated myofibers. To describe the pattern of deformation during "prestretch" and gain insight into its causes and sequelae, we implanted midwall and transmural arrays of radiopaque markers into the left ventricular anterolateral wall of open-chest, isoflurane-anesthetized, adult mongrel dogs. Biplane cineradiography (125 Hz) was used to determine the time course of two- and three-dimensional strains while pacing from a remote, posterior wall site. Strain maps were generated as a function of time. Electrical activation was assessed with bipolar electrodes. Posterior wall pacing generated prestretch at the measurement site, which peaked 44 ms after local electrical activation. Overall magnitudes and transmural gradients of strain were reduced when compared with passive inflation. Fiber stretch was larger at aortic valve opening compared with end diastole (P < 0.05). Fiber stretch at aortic valve opening was weakly but significantly correlated with local activation time (r(2) = 0.319, P < 0.001). With a short atrioventricular delay, fiber lengths were not significantly different at the time of aortic valve opening during ventricular pacing compared with atrial pacing. However, ejection strain did significantly increase (P < 0.05). We conclude that the majority of fiber stretch occurs after local electrical activation and mitral valve closure and is different from passive inflation. The increased shortening of these regions appears to be because of a reduced afterload rather than an effect of length-dependent activation in this preparation.

Coupling of a 3D finite element model of cardiac ventricular mechanics to lumped systems models of the systemic and pulmonic circulation

In this study we present a novel, robust method to couple finite element (FE) models of cardiac mechanics to systems models of the circulation (CIRC), independent of cardiac phase. For each time step through a cardiac cycle, left and right ventricular pressures were calculated using ventricular compliances from the FE and CIRC models. These pressures served as boundary conditions in the FE and CIRC models. In succeeding steps, pressures were updated to minimize cavity volume error (FE minus CIRC volume) using Newton iterations. Coupling was achieved when a predefined criterion for the volume error was satisfied. Initial conditions for the multi-scale model were obtained by replacing the FE model with a varying elastance model, which takes into account direct ventricular interactions. Applying the coupling, a novel multi-scale model of the canine cardiovascular system was developed. Global hemodynamics and regional mechanics were calculated for multiple beats in two separate simulations with a left ventricular ischemic region and pulmonary artery constriction, respectively. After the interventions, global hemodynamics changed due to direct and indirect ventricular interactions, in agreement with previously published experimental results. The coupling method allows for simulations of multiple cardiac cycles for normal and pathophysiology, encompassing levels from cell to system.

From in vivo to in silico biology and back

The massive acquisition of data in molecular and cellular biology has led to the renaissance of an old topic: simulations of biological systems. Simulations, increasingly paired with experiments, are being successfully and routinely used by computational biologists to understand and predict the quantitative behaviour of complex systems, and to drive new experiments. Nevertheless, many experimentalists still consider simulations an esoteric discipline only for initiates. Suspicion towards simulations should dissipate as the limitations and advantages of their application are better appreciated, opening the door to their permanent adoption in everyday research.