Models Of Cardiac Electromechanics Research Articles

Computational analysis of the effect of mitral and aortic regurgitation on the function of ventricular assist devices using 3D cardiac electromechanical model

Valvular insufficiency affects cardiac responses and the pumping efficacy of left ventricular assist devices (LVADs) when patients undergo LVAD therapy. Knowledge of the effect of valvular regurgitation on the function of LVADs is important when treating heart failure patients. The goal of this study was to examine the effect of valvular regurgitation on the ventricular mechanics of a heart under LVAD treatment and the pumping efficacy of an LVAD using a computational model of the cardiovascular system. For this purpose, a 3D electromechanical model of failing ventricles in a human heart was coupled with a lumped-parameter model of valvular regurgitation and an LVAD-implanted vascular system. We used the computational model to predict cardiac responses with respect to the severity of valvular regurgitation in the presence of LVAD treatment. An LVAD could reduce left ventricle (LV) pressure (up to 34%) and end-diastolic ventricular volume (up to 80%) and maintain cardiac output at the estimated flow rate from the LVAD under the condition of mitral regurgitation (MR); however, the opposite would occur under the condition of aortic regurgitation (AR). Considering these physiological responses, we conclude that AR, and not MR, diminishes the pumping function of LVADs.

Multifidelity-CMA: a multifidelity approach for efficient personalisation of 3D cardiac electromechanical models.

Personalised computational models of the heart are of increasing interest for clinical applications due to their discriminative and predictive abilities. However, the simulation of a single heartbeat with a 3D cardiac electromechanical model can be long and computationally expensive, which makes some practical applications, such as the estimation of model parameters from clinical data (the personalisation), very slow. Here we introduce an original multifidelity approach between a 3D cardiac model and a simplified "0D" version of this model, which enables to get reliable (and extremely fast) approximations of the global behaviour of the 3D model using 0D simulations. We then use this multifidelity approximation to speed-up an efficient parameter estimation algorithm, leading to a fast and computationally efficient personalisation method of the 3D model. In particular, we show results on a cohort of 121 different heart geometries and measurements. Finally, an exploitable code of the 0D model with scripts to perform parameter estimation will be released to the community.

Uncertainty quantification of 2 models of cardiac electromechanics.

Computational models of the heart have reached a maturity level that render them useful for in silico studies of arrhythmia and other cardiac diseases. However, the translation to the clinic of cardiac simulations critically depends on demonstrating the accuracy, robustness, and reliability of the underlying computational models under the presence of uncertainties. In this work, we study for the first time the effect of parameter uncertainty on 2 state-of-the-art coupled models of excitation-contraction of cardiac tissue. To this end, we perform forward uncertainty propagation and sensitivity analyses to understand how variability in key maximal conductances affect selected quantities of interest, such as the action potential duration (APD90 ), maximum intracellular calcium concentration, cardiac stretch, and stress. Our results suggest a strong linear relationship between selected maximal conductances and quantities of interest for a variability in parameters up to 25%, which justifies the construction of linear response surfaces that are used to compute the empirical probability density functions of all the quantities of interest under study. For both electromechanical models analyzed, uncertainty in the material parameters associated to the passive mechanical response of cardiac tissue does not affect the duration of action potentials, neither the amplitude of intracellular calcium concentrations. Our results confirm the poor mechanoelectric feedback that classical models of cardiac electromechanics have, even under the presence of parameter uncertainty.

Analysis of lead placement optimization metrics in cardiac resynchronization therapy with computational modelling.

The efficacy of cardiac resynchronization therapy (CRT) is known to vary considerably with pacing location, however the most effective set of metrics by which to select the optimal pacing site is not yet well understood. Computational modelling offers a powerful methodology to comprehensively test the effect of pacing location in silico and investigate how to best optimize therapy using clinically available metrics for the individual patient. Personalized computational models of cardiac electromechanics were used to perform an in silico left ventricle (LV) pacing site optimization study as part of biventricular CRT in three patient cases. Maps of response to therapy according to changes in total activation time (ΔTAT) and acute haemodynamic response (AHR) were generated and compared with preclinical metrics of electrical function, strain, stress, and mechanical work to assess their suitability for selecting the optimal pacing site. In all three patients, response to therapy was highly sensitive to pacing location, with laterobasal locations being optimal. ΔTAT and AHR were found to be correlated (ρ < -0.80), as were AHR and the preclinical activation time at the pacing site (ρ ≥ 0.73), however pacing in the last activated site did not result in the optimal response to therapy in all cases. This computational modelling study supports pacing in laterobasal locations, optimizing pacing site by minimizing paced QRS duration and pacing in regions activated late at sinus rhythm. Results demonstrate information content is redundant using multiple preclinical metrics. Of significance, the correlation of AHR with ΔTAT indicates that minimization of QRSd is a promising metric for optimization of lead placement.

Infarct Localization From Myocardial Deformation: Prediction and Uncertainty Quantification by Regression From a Low-Dimensional Space.

Diagnosing and localizing myocardial infarct is crucial for early patient management and therapy planning. We propose a new method for predicting the location of myocardial infarct from local wall deformation, which has value for risk stratification from routine examinations such as (3D) echocardiography. The pipeline combines non-linear dimensionality reduction of deformation patterns and two multi-scale kernel regressions. Confidence in the diagnosis is assessed by a map of local uncertainties, which integrates plausible infarct locations generated from the space of reduced dimensionality. These concepts were tested on 500 synthetic cases generated from a realistic cardiac electromechanical model, and 108 pairs of 3D echocardiographic sequences and delayed-enhancement magnetic resonance images from real cases. Infarct prediction is made at a spatial resolution around 4 mm, more than 10 times smaller than the current diagnosis, made regionally. Our method is accurate, and significantly outperforms the clinically-used thresholding of the deformation patterns (on real data: sensitivity/specificity of 0.828/0.804, area under the curve: 0.909 versus 0.742 for the most predictive strain component). Uncertainty adds value to refine the diagnosis and eventually re-examine suspicious cases.

Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation.

Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which are not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate efficient scaling up to 1024, 4096 and 8192 compute cores which allowed the simulation of a single heart beat in 44.3, 87.8 and 235.3 minutes, respectively. The efficiency of the method allows fast simulation cycles without compromising anatomical or biophysical detail.

Bioelectrical effects of mechanical feedbacks in a strongly coupled cardiac electro-mechanical model

The aim of this work is to investigate by means of numerical simulations the effects of myocardial deformation due to muscle contraction on the bioelectrical activity of the cardiac tissue. The three-dimensional electro-mechanical model considered consists of the following four components: the quasi-static orthotropic finite elasticity equations for the deformation of the cardiac tissue; the active tension model for the intracellular calcium dynamics and cross-bridge binding; the orthotropic Bidomain model for the electrical current flow through the tissue; the membrane model of the cardiac myocyte, including stretch-activated currents (I SAC ). In order to properly take into account cardiac mechanical feedbacks, the electrical current flow is described in a strongly coupled framework by the Bidomain model on the deformed tissue. We then derive a novel formulation of the Bidomain model in the reference configuration, with complete mechanical feedbacks affecting not only the conductivity tensors but also a convective term depending on the velocity of the deformation. The numerical simulations are based on our finite element parallel solver, which employs both Multilevel Additive Schwarz preconditioners for the solution of linear systems arising from the discretization of the Bidomain equations and Newton–Krylov-Algebraic Multigrid methods for the solution of nonlinear systems arising from the discretization of the finite elasticity equations. The results have shown that: (i) the I SAC current prolongs action potential duration (APD) of about 10–15 ms; (ii) the inclusion into the model of both I SAC current and the convective term reduces the dispersion of repolarization of about 7% (from 139 to 129 ms) and increases the dispersion of APD about three times (from 13 to 45 ms). These effects indicate that mechanical feedbacks might influence arrhythmogenic mechanisms when combined with pathological substrates.

Image-Based Personalization of Cardiac Anatomy for Coupled Electromechanical Modeling.

Computational models of cardiac electromechanics (EM) are increasingly being applied to clinical problems, with patient-specific models being generated from high fidelity imaging and used to simulate patient physiology, pathophysiology and response to treatment. Current structured meshes are limited in their ability to fully represent the detailed anatomical data available from clinical images and capture complex and varied anatomy with limited geometric accuracy. In this paper, we review the state of the art in image-based personalization of cardiac anatomy for biophysically detailed, strongly coupled EM modeling, and present our own tools for the automatic building of anatomically and structurally accurate patient-specific models. Our method relies on using high resolution unstructured meshes for discretizing both physics, electrophysiology and mechanics, in combination with efficient, strongly scalable solvers necessary to deal with the computational load imposed by the large number of degrees of freedom of these meshes. These tools permit automated anatomical model generation and strongly coupled EM simulations at an unprecedented level of anatomical and biophysical detail.

A New MRI-Based Model of Heart Function with Coupled Hemodynamics and Application to Normal and Diseased Canine Left Ventricles.

A methodology for the simulation of heart function that combines an MRI-based model of cardiac electromechanics (CE) with a Navier–Stokes-based hemodynamics model is presented. The CE model consists of two coupled components that simulate the electrical and the mechanical functions of the heart. Accurate representations of ventricular geometry and fiber orientations are constructed from the structural magnetic resonance and the diffusion tensor MR images, respectively. The deformation of the ventricle obtained from the electromechanical model serves as input to the hemodynamics model in this one-way coupled approach via imposed kinematic wall velocity boundary conditions and at the same time, governs the blood flow into and out of the ventricular volume. The time-dependent endocardial surfaces are registered using a diffeomorphic mapping algorithm, while the intraventricular blood flow patterns are simulated using a sharp-interface immersed boundary method-based flow solver. The utility of the combined heart-function model is demonstrated by comparing the hemodynamic characteristics of a normal canine heart beating in sinus rhythm against that of the dyssynchronously beating failing heart. We also discuss the potential of coupled CE and hemodynamics models for various clinical applications.

A gap junction-based cardiac electromechanics model.

Action potential propagation in cardiac tissue is mainly governed by highly resistive gap junctions, which causes the tissue to behave as a network of active cell nodes interconnected by resistors. This property causes the action potential propagation to be less dependent on the level of mechanical deformation. This study proposes that the electrical conductivity in cardiac electromechanical simulations should be held fixed relative to the material frame, reproducing the dominant effect of intercellular gap junctions on the tissue electrical resistance instead of the more commonly employed spatial frame. Our simulations showed that the implementation of gap junction-based conductivity resulted in similar activation times at given material point, irrespective of the level of deformation. In contrast, the activation time of a given material point using spatial-based conductivity was dependent on the deformation experienced by the tissue. These findings have implication on more complex electromechanical simulations such as spiral wave since gap junction-based conductivity is independent of contraction, in contrast to spatial-based conductivity. Therefore, selection of the appropriate electrical conductivity assumption is highly crucial in electromechanics models of cardiac tissue.

Newton–Krylov-BDDC solvers for nonlinear cardiac mechanics

Abstract The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton–Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.

A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method.

Cardiac tissue is a syncytium of coupled cells with pronounced intrinsic discrete nature. Previous models of cardiac electromechanics often ignore such discrete properties and treat cardiac tissue as a continuous medium, which has fundamental limitations. In the present study, we introduce a 2D electromechanical model for human atrial tissue based on the discrete element method (DEM). In the model, single-cell dynamics are governed by strongly coupling the electrophysiological model of Courtemanche et al. to the myofilament model of Rice et al. with two-way feedbacks. Each cell is treated as a viscoelastic body, which is physically represented by a clump of nine particles. Cell aggregations are arranged so that the anisotropic nature of cardiac tissue due to fibre orientations can be modelled. Each cell is electrically coupled to neighbouring cells, allowing excitation waves to propagate through the tissue. Cell-to-cell mechanical interactions are modelled using a linear contact bond model in DEM. By coupling cardiac electrophysiology with mechanics via the intracellular Ca2+ concentration, the DEM model successfully simulates the conduction of cardiac electrical waves and the tissue's corresponding mechanical contractions. The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart.

OP-273 Computational Quantification of the Cardiac Energy Consumption during Intra-Aortic Balloon Pumping by Using a Cardiac Electromechanics model

To quantify the reduction in workload during intra-aortic balloon pump (IABP) therapy, indirect parameters are used, such as the mean arterial pressure during diastole, product of heart rate and peak systolic pressure, and pressure–volume area. Therefore, we investigated the cardiac energy consumption during IABP therapy using a cardiac electromechanics model. We incorporated an IABP function into a previously developed electromechanical model of the ventricle with a lumped model of the circulatory system and investigated the cardiac energy consumption at different IABP inflation volumes.

Cardiac Electrophysiological Activation Pattern Estimation From Images Using a Patient-Specific Database of Synthetic Image Sequences

While abnormal patterns of cardiac electrophysiological activation are at the origin of important cardiovascular diseases (e.g., arrhythmia, asynchrony), the only clinically available method to observe detailed left ventricular endocardial surface activation pattern is through invasive catheter mapping. However, this electrophysiological activation controls the onset of the mechanical contraction; therefore, important information about the electrophysiology could be deduced from the detailed observation of the resulting motion patterns. In this paper, we present the study of this inverse cardiac electrokinematic relationship. The objective is to predict the activation pattern knowing the cardiac motion from the analysis of cardiac image sequences. To achieve this, we propose to create a rich patient-specific database of synthetic time series of the cardiac images using simulations of a personalized cardiac electromechanical model, in order to study this complex relationship between electrical activity and kinematic patterns in the context of this specific patient. We use this database to train a machine-learning algorithm which estimates the depolarization times of each cardiac segment from global and regional kinematic descriptors based on displacements or strains and their derivatives. Finally, we use this learning to estimate the patient’s electrical activation times using the acquired clinical images. Experiments on the inverse electrokinematic learning are demonstrated on synthetic sequences and are evaluated on clinical data with promising results. The error calculated between our prediction and the invasive intracardiac mapping ground truth is relatively small (around 10 ms for ischemic patients and 20 ms for nonischemic patient). This approach suggests the possibility of noninvasive electrophysiological pattern estimation using cardiac motion imaging.

Personalization of a cardiac electromechanical model using reduced order unscented Kalman filtering from regional volumes

Patient-specific cardiac modeling can help in understanding pathophysiology and therapy planning. However it requires to combine functional and anatomical data in order to build accurate models and to personalize the model geometry, kinematics, electrophysiology and mechanics. Personalizing the electromechanical coupling from medical images is a challenging task. We use the Bestel-Clément-Sorine (BCS) electromechanical model of the heart, which provides reasonable accuracy with a reasonable number of parameters (14 for each ventricle) compared to the available clinical data at the organ level. We propose a personalization strategy from cine MRI data in two steps. We first estimate global parameters with an automatic calibration algorithm based on the Unscented Transform which allows to initialize the parameters while matching the volume and pressure curves. In a second step we locally personalize the contractilities of all AHA (American Heart Association) zones of the left ventricle using the reduced order unscented Kalman filtering on Regional Volumes. This personalization strategy was validated synthetically and tested successfully on eight healthy and three pathological cases.

Computational Challenges in Building Multi-Scale and Multi-Physics Models of Cardiac Electro-Mechanics

Article Computational Challenges in Building Multi-Scale and Multi-Physics Models of Cardiac Electro-Mechanics was published on September 7, 2013 in the journal Biomedical Engineering / Biomedizinische Technik (volume 58, issue SI-1-Track-N).

Computational Quantification of the Cardiac Energy Consumption during Intra-Aortic Balloon Pumping Using a Cardiac Electromechanics Model

To quantify the reduction in workload during intra-aortic balloon pump (IABP) therapy, indirect parameters are used, such as the mean arterial pressure during diastole, product of heart rate and peak systolic pressure, and pressure-volume area. Therefore, we investigated the cardiac energy consumption during IABP therapy using a cardiac electromechanics model. We incorporated an IABP function into a previously developed electromechanical model of the ventricle with a lumped model of the circulatory system and investigated the cardiac energy consumption at different IABP inflation volumes. When the IABP was used at inflation level 5, the cardiac output and stroke volume increased 11%, the ejection fraction increased 21%, the stroke work decreased 1%, the mean arterial pressure increased 10%, and the ATP consumption decreased 12%. These results show that although the ATP consumption is decreased significantly, stroke work is decreased only slightly, which indicates that the IABP helps the failed ventricle to pump blood efficiently.

Mechanical discoordination increases continuously after the onset of left bundle branch block despite constant electrical dyssynchrony in a computational model of cardiac electromechanics and growth

To test whether a functional growth law leads to asymmetric hypertrophy and associated changes in global and regional cardiac function when integrated with a computational model of left bundle branch block (LBBB). In recent studies, we proposed that cardiac myocytes grow longer when a threshold of maximum fibre strain is exceeded and grow thicker when the smallest maximum principal strain in the cellular cross-sectional plane exceeds a threshold. A non-linear cardiovascular model of the beating canine ventricles was combined with the cellular growth law. After inducing LBBB, the ventricles were allowed to adapt in shape over time in response to mechanical stimuli. When subjected to electrical dyssynchrony, the combined model of ventricular electromechanics, haemodynamics, and growth led to asymmetric hypertrophy with a faster increase of wall mass in the left ventricular (LV) free wall (FW) than the septum, increased LV end-diastolic and end-systolic volumes, and decreased LV ejection fraction. Systolic LV pressure decreased during the acute phase of LBBB and increased at later stages. The relative changes of these parameters were similar to those obtained experimentally. Most of the dilation was due to radial and axial fibre growth, and hence altered shape of the LVFW. Our previously proposed growth law reproduced measured dyssynchronously induced asymmetric hypertrophy and the associated functional changes, when combined with a computational model of the LBBB heart. The onset of LBBB leads to a step increase in LV mechanical discoordination that continues to increase as the heart remodels despite the constant electrical dyssynchrony.

Fast parameter calibration of a cardiac electromechanical model from medical images based on the unscented transform

Patient-specific cardiac modelling can help in understanding pathophysiology and predict therapy planning. However, it requires to personalize the model geometry, kinematics, electrophysiology and mechanics. Calibration aims at providing proper initial values of parameters before performing the personalization stage which involves solving an inverse problem. We propose a fast automatic calibration method of the mechanical parameters of a complete electromechanical model of the heart based on a sensitivity analysis and the Unscented Transform algorithm. A new implementation of the complete Bestel-Clement-Sorine (BCS) cardiac model is also proposed, in a modular and efficient framework. A complete sensitivity analysis is performed that reveals which observations on the volume evolution are significant to characterize the global behaviour of the myocardium. We show that the calibration method gives satisfying results by optimizing up to 5 parameters of the BCS model in only one iteration. This method was evaluated synthetically as well as on 7 volunteers with a mean relative error from the real data of 10 %. This calibration is designed to replace manual parameter estimation as well as initialization steps that precede automatic personalization algorithms based on images.

Interpreting genetic effects through models of cardiac electromechanics

Multiscale models of cardiac electromechanics are being increasingly focused on understanding how genetic variation and environment underpin multiple disease states. In this paper we review the current state of the art in both the development of specific models and the physiological insights they have produced. This growing research body includes the development of models for capturing the effects of changes in function in both single and multiple proteins in both specific expression systems and in vivo contexts. Finally, the potential for using this approach for ultimately predicting phenotypes from genetic sequence information is discussed.