Cardiac Electromechanics Research Articles

Simulation of cardiac electromechanics of a rat left ventricle

AbstractThis work presents the modelling and simulation of the cardiac electromechanics of a rat left ventricle (LV) under normal and pathological conditions. The 3D LV model is constructed from MRI images of a rat heart. The electrical wave propagates through the whole heart to trigger the mechanical contraction. Our coupled electromechanical problem is formulated based on the mono‐domain and the active stress approach. An implicit finite element‐based method is employed to monolithically solve the problem for the LV. The numerical results show significant differences in the electromechanical behaviour of the healthy and infarcted model.

GEMS: A Fully Integrated PETSc-Based Solver for Coupled Cardiac Electromechanics and Bidomain Simulations.

Cardiac contraction is coordinated by a wave of electrical excitation which propagates through the heart. Combined modeling of electrical and mechanical function of the heart provides the most comprehensive description of cardiac function and is one of the latest trends in cardiac research. The effective numerical modeling of cardiac electromechanics remains a challenge, due to the stiffness of the electrical equations and the global coupling in the mechanical problem. Here we present a short review of the inherent assumptions made when deriving the electromechanical equations, including a general representation for deformation-dependent conduction tensors obeying orthotropic symmetry, and then present an implicit-explicit time-stepping approach that is tailored to solving the cardiac mono- or bidomain equations coupled to electromechanics of the cardiac wall. Our approach allows to find numerical solutions of the electromechanics equations using stable and higher order time integration. Our methods are implemented in a monolithic finite element code GEMS (Ghent Electromechanics Solver) using the PETSc library that is inherently parallelized for use on high-performance computing infrastructure. We tested GEMS on standard benchmark computations and discuss further development of our software.

Influence of fiber connectivity in simulations of cardiac biomechanics.

Personalized computational simulations of the heart could open up new improved approaches to diagnosis and surgery assistance systems. While it is fully recognized that myocardial fiber orientation is central for the construction of realistic computational models of cardiac electromechanics, the role of its overall architecture and connectivity remains unclear. Morphological studies show that the distribution of cardiac muscular fibers at the basal ring connects epicardium and endocardium. However, computational models simplify their distribution and disregard the basal loop. This work explores the influence in computational simulations of fiber distribution at different short-axis cuts. We have used a highly parallelized computational solver to test different fiber models of ventricular muscular connectivity. We have considered two rule-based mathematical models and an own-designed method preserving basal connectivity as observed in experimental data. Simulated cardiac functional scores (rotation, torsion and longitudinal shortening) were compared to experimental healthy ranges using generalized models (rotation) and Mahalanobis distances (shortening, torsion). The probability of rotation was significantly lower for ruled-based models [95% CI (0.13, 0.20)] in comparison with experimental data [95% CI (0.23, 0.31)]. The Mahalanobis distance for experimental data was in the edge of the region enclosing 99% of the healthy population. Cardiac electromechanical simulations of the heart with fibers extracted from experimental data produce functional scores closer to healthy ranges than rule-based models disregarding architecture connectivity.

Microstructural Infarct Border Zone Remodeling in the Post-infarct Swine Heart Measured by Diffusion Tensor MRI.

Introduction: Computational models of the heart increasingly require detailed microstructural information to capture the impact of tissue remodeling on cardiac electromechanics in, for example, hearts with myocardial infarctions. Myocardial infarctions are surrounded by the infarct border zone (BZ), which is a site of electromechanical property transition. Magnetic resonance imaging (MRI) is an emerging method for characterizing microstructural remodeling and focal myocardial infarcts and the BZ can be identified with late gadolinium enhanced (LGE) MRI. Microstructural remodeling within the BZ, however, remains poorly characterized by MRI due, in part, to the fact that LGE and DT-MRI are not always available for the same heart. Diffusion tensor MRI (DT-MRI) can evaluate microstructural remodeling by quantifying the DT apparent diffusion coefficient (ADC, increased with decreased cellularity), fractional anisotropy (FA, decreased with increased fibrosis), and tissue mode (decreased with increased fiber disarray). The purpose of this work was to use LGE MRI in post-infarct porcine hearts (N = 7) to segment remote, BZ, and infarcted myocardium, thereby providing a basis to quantify microstructural remodeling in the BZ and infarcted regions using co-registered DT-MRI.Methods: Chronic porcine infarcts were created by balloon occlusion of the LCx. 6–8 weeks post-infarction, MRI contrast was administered, and the heart was potassium arrested, excised, and imaged with LGE MRI (0.33 × 0.33 × 0.33 mm) and co-registered DT-MRI (1 × 1 × 3 mm). Myocardium was segmented as remote, BZ, or infarct by LGE signal intensity thresholds. DT invariants were used to evaluate microstructural remodeling by quantifying ADC, FA, and tissue mode.Results: The BZ significantly remodeled compared to both infarct and remote myocardium. BZ demonstrated a significant decrease in cellularity (increased ADC), significant decrease in tissue organization (decreased FA), and a significant increase in fiber disarray (decreased tissue mode) relative to remote myocardium (all p < 0.05). Microstructural remodeling in the infarct was similar, but significantly larger in magnitude (all p < 0.05).Conclusion: DT-MRI can identify regions of significant microstructural remodeling in the BZ that are distinct from both remote and infarcted myocardium.

Influence of the KCNQ1 S140G Mutation on Human Ventricular Arrhythmogenesis and Pumping Performance: Simulation Study.

The KCNQ1 S140G mutation, which is involved in IKs current, affects atrial fibrillation. However, little is known about its effect on the mechanical behavior of the heart. Therefore, we assessed the influence of the KCNQ1 S140G mutation on ventricular electrophysiological stability and mechanical pumping performance using a multi-scale model of cardiac electromechanics. An image-based electromechanical model was used to assess the effect on electrical propagation and arrhythmogenesis of the KCNQ1 S140G mutation. In addition, it was used to compare the mechanical response under the wild-type (WT) and S140G mutation conditions. The intracellular calcium transient obtained from the electrophysiological model was applied as an input parameter to a mechanical model to implement excitation–contraction coupling. The IKs current equation was modified to account for expression of the KCNQ1 S140G mutation, and it included a scaling factor (ϕ) for mutant expressivity. The WT and S140G mutation conditions were compared at the single-cell and three-dimensional (3D) tissue levels. The action potential duration (APD) was reduced by 60% by the augmented IKs current under the S140G mutation condition, which resulted in shorter QT interval. This reduced the 3D sinus rhythm wavelength by 60% and the sustained re-entry by 56%. However, pumping efficiency of mutant ventricles was superior in sinus rhythm condition. In addition, the shortened wavelength in cardiac tissue allowed a re-entrant circuit to form and increased the probability of sustaining ventricular tachycardia and ventricular fibrillation. In contrast, under the WT condition, a normal wavelength (20.8 cm) was unlikely to initiate and sustain re-entry in the cardiac tissue. Subsequently, the S140G mutant ventricles developed a higher dominant frequency distribution range (2.0–5.3 Hz) than the WT condition (2.8–3.7 Hz). In addition, stroke volume of mutant ventricles was reduced by 65% in sustained re-entry compared to the WT condition. In conclusion, signs of the S140G mutation might be difficult to identify in sinus rhythm even though the mutant ventricles show shortened QT interval. This suggests that the KCNQ1 S140G mutation increases the risk of death by sudden cardiac arrest. In addition, the KCNQ1 S140G mutation can induce ventricular arrhythmia and lessen ventricular contractility under re-entrant conditions.

A monolithic algorithm for the simulation of cardiac electromechanics in the human left ventricle

In this paper, we propose a monolithic algorithm for the numerical solution of the electromechanics model of the left ventricle in the human heart. Our coupled model integrates the monodomain equation with the Bueno-Orovio minimal model for electrophysiology and the Holzapfel-Ogden constitutive law for the passive mechanics of the myocardium; a distinguishing feature of our electromechanics model is the use of the active strain formulation for muscle contraction, which we exploit -- for the first time in this context -- by means of a transmurally variable active strain formulation. We use the Finite Element method for space discretization and Backward Differentiation Formulas for time discretization, which we consider for both implicit and semi-implicit schemes. We compare and discuss the two schemes in terms of computational efficiency as the semi-implicit scheme poses significant restrictions on the timestep size due to stability considerations, while the implicit scheme yields instead a nonlinear problem, which we solve by means of the Newton method. Emphasis is laid on preconditioning strategy of the linear solver, which we perform by factorizing a block Gauss-Seidel preconditioner in combination with combination with parallel preconditioners for each of the single core models composing the integrated electromechanics model. We carry out several numerical simulations in the High Performance Computing framework for both idealized and patient-specific left ventricle geometries and meshes, which we obtain by segmenting medical MRI images. We produce personalized pressure-volume loops by means of the computational procedure, which we use to synthetically interpret and analyze the outputs of the electromechanics model.

Computational cardiology: the bidomain based modified Hill model incorporating viscous effects for cardiac defibrillation

Working mechanisms of the cardiac defibrillation are still in debate due to the limited experimental facilities and one-third of patients even do not respond to cardiac resynchronization therapy. With an aim to develop a milestone towards reaching the unrevealed mechanisms of the defibrillation phenomenon, we propose a bidomain based finite element formulation of cardiac electromechanics by taking into account the viscous effects that are disregarded by many researchers. To do so, the material is deemed as an electro-visco-active material and described by the modified Hill model (Cansiz et al. in Comput Methods Appl Mech Eng 315:434–466, 2017). On the numerical side, we utilize a staggered solution method, where the elliptic and parabolic part of the bidomain equations and the mechanical field are solved sequentially. The comparative simulations designate that the viscoelastic and elastic formulations lead to remarkably different outcomes upon an externally applied electric field to the myocardial tissue. Besides, the achieved framework requires significantly less computational time and memory compared to monolithic schemes without loss of stability for the presented examples.

Integrative and quantitive evaluation of the efficacy of his bundle related pacing in comparison with conventional right ventricular pacing: a meta-analysis

BackgroundLong-term RVP could bring adverse problems to cardiac electro-mechanics and result in inter- and intra-ventricular asynchrony, impaired labor force, and aggravation of cardiac function. HBRP including direct His bundle pacing and para-His bundle pacing was regarded as a novel physiological pacing pattern to avoid devastating cardiac function. This synthetic study was conducted to integratively and quantitatively evaluate the efficacy of His bundle related pacing (HBRP) in comparison with conventional right ventricular pacing (RVP).MethodsPublished studies on comparison of left ventricular ejection fraction (LVEF), left ventricular end diastolic volume (LVEDV), left ventricular end systolic volume (LVESV), New York Heart Association (NYHA) class, inter-ventricular asynchrony, and QRS duration, etc. between HBRP and RVP were collected and for meta-analysis.ResultsHBRP showed higher LVEF (WMD = 3.9%, 95% CI: 1.6% – 6.1%), lower NYHA class (WMD = −0.5, 95% CI: -0.7 – -0.3), WMD of LVESV = −0.1 ml, 95% CI: -3.0 – 2.8 ml), less inter-ventricular asynchrony (WMD = −13.2 ms, 95% CI: -16.4 – -10.0 ms), and shorter QRS duration for long-term (WMD = −36.9 ms, 95% CI: -40.0 – -33.8 ms), however, no significant difference of ventricular volume (WMDLVEDV = −2.4 ml, 95% CI: -5.0 – 0.2 ml; WMDLVESV = −0.1 ml, 95% CI: -3.0 – 2.8 ml) compared to RVP.ConclusionsThe efficacy of HBRP was firstly verified by meta-analysis to date. Compared with RVP, HBRP markedly preserve LVEF, NYHA class, and QRS duration. However, it seemed to have less effect on ventricular volume.

Heart Rate Modification of Cardiac Output Following Cardiac Surgery: The Importance of Cardiac Time Intervals.

Inadequate cardiac output is associated with a poor outcome following cardiac surgery and is generally modified by the use of positive inotropic agents, volume resuscitation, and pacing. Echocardiography-guided pacemaker optimization is used in the outpatient setting, using different variables including total isovolumic time and the Tei index. We sought to determine the acute impact of heart rate on cardiac electromechanics, cardiac output, and stroke volume in the perioperative setting. Observational study. Cardiothoracic adult intensive care department. Twenty-four sequential patients admitted after cardiac surgery. Patients with pacemaker set by the treating anesthesiologist using hemodynamic parameters in theatre, within 4 hours of returning to intensive care, they were reassessed using transthoracic echocardiography. A comprehensive baseline echocardiographic study was performed at the clinician set RR interval and at heart rates from 70 to 110 beats/min, in increments of 10 beats/min. Pearson correlation coefficients were used to assess relationships between the measurements. Cardiac output and cardiac index were increased significantly in 79% patients using echocardiography-guided pacemaker optimization (2.21 L/min [± 0.97] and 1.2 L/min/m [± 0.52]). The echocardiography-driven cardiac output optimization protocol led to a significant reduction of total isovolumic time with concurrent increase of cardiac output and cardiac index in the overall population (p < 0.001). There was no consistent correlation between changes in RR interval and stroke volume, cardiac output, or cardiac index in the overall population. A strong negative correlation was found between the left ventricular total isovolumic time and stroke volume, cardiac output, and cardiac index in all groups. Echocardiography-guided heart rate optimization results in a significant increase in cardiac output when compared with clinically derived pacing settings in the postoperative period. The optimal heart rate should be individualized for each patient, and total isovolumic time is the echocardiographic index with the highest sensitivity to determine the optimal hemodynamic profile.

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.

The importance of mechano-electrical feedback and inertia in cardiac electromechanics

In the past years, a number of cardiac electromechanics models have been developed to better understand the excitation–contraction behavior of the heart. However, there is no agreement on whether inertial forces play a role in this system. In this study, we assess the influence of mass in electromechanical simulations, using a fully coupled finite element model. We include the effect of mechano-electrical feedback via stretch activated currents. We compare five different models: electrophysiology, electromechanics, electromechanics with mechano-electrical feedback, electromechanics with mass, and electromechanics with mass and mechano-electrical feedback. We simulate normal conduction to study conduction velocity and spiral waves to study fibrillation. During normal conduction, mass in conjunction with mechano-electrical feedback increased the conduction velocity by 8.12% in comparison to the plain electrophysiology case. During the generation of a spiral wave, mass and mechano-electrical feedback generated secondary wavefronts, which were not present in any other model. These secondary wavefronts were initiated in tensile stretch regions that induced electrical currents. We expect that this study will help the research community to better understand the importance of mechano-electrical feedback and inertia in cardiac electromechanics.

Mathematical analysis of cardiac electromechanics with physiological ionic model

This paper is concerned with the mathematical analysis of a coupled elliptic-parabolic system modeling the interaction between the propagation of electric potential coupled with general physiological ionic models and subsequent deformation of the cardiac tissue. A prototype system belonging to this class is provided by the electromechanical bidomain model, which is frequently used to study and simulate electrophysiological waves in cardiac tissue. The coupling between muscle contraction, biochemical reactions and electric activity is introduced with a so-called active strain decomposition framework, where the material gradient of deformation is split into an active (electrophysiology-dependent) part and an elastic (passive) one. We prove existence of weak solutions to the underlying coupled electromechanical bidomain model under the assumption of linearized elastic behavior and a truncation of the updated nonlinear diffu-sivities. The proof of the existence result, which constitutes the main thrust of this paper, is proved by means of a non-degenerate approximation system, the Faedo-Galerkin method, and the compactness method.

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.

Optical Mapping of Cardiac Electromechanics

Cardiac biophysics rests on three fundamental pillars: energy production, electrical excitation, and mechanical work. Studies of cardiac metabolism, bioelectricity, and biomechanics have been very productive at all levels of reduced complexity, but especially at the levels of tissue, cell, and molecule. The three cardiac biophysical pillars work in concert and cannot be fully understood in isolation. However, available experimental methods are limited, restricting our ability to study them simultaneously.

Optical Mapping of Membrane Potential and Epicardial Deformation in Beating Hearts

Cardiac optical mapping uses potentiometric fluorescent dyes to image membrane potential (Vm). An important limitation of conventional optical mapping is that contraction is usually arrested pharmacologically to prevent motion artifacts from obscuring Vm signals. However, these agents may alter electrophysiology, and by abolishing contraction, also prevent optical mapping from being used to study coupling between electrical and mechanical function. Here, we present a method to simultaneously map Vm and epicardial contraction in the beating heart. Isolated perfused swine hearts were stained with di-4-ANEPPS and fiducial markers were glued to the epicardium for motion tracking. The heart was imaged at 750 Hz with a video camera. Fluorescence was excited with cyan or blue LEDs on alternating camera frames, thus providing a 375-Hz effective sampling rate. Marker tracking enabled the pixel(s) imaging any epicardial site within the marked region to be identified in each camera frame. Cyan- and blue-elicited fluorescence have different sensitivities to Vm, but other signal features, primarily motion artifacts, are common. Thus, taking the ratio of fluorescence emitted by a motion-tracked epicardial site in adjacent frames removes artifacts, leaving Vm (excitation ratiometry). Reconstructed Vm signals were validated by comparison to monophasic action potentials and to conventional optical mapping signals. Binocular imaging with additional video cameras enabled marker motion to be tracked in three dimensions. From these data, epicardial deformation during the cardiac cycle was quantified by computing finite strain fields. We show that the method can simultaneously map Vm and strain in a left-sided working heart preparation and can image changes in both electrical and mechanical function 5 min after the induction of regional ischemia. By allowing high-resolution optical mapping in the absence of electromechanical uncoupling agents, the method relieves a long-standing limitation of optical mapping and has potential to enhance new studies in coupled cardiac electromechanics.

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.

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.

Solvability analysis and numerical approximation of linearized cardiac electromechanics

This paper is concerned with the mathematical analysis of a coupled elliptic–parabolic system modeling the interaction between the propagation of electric potential and subsequent deformation of the cardiac tissue. The problem consists in a reaction–diffusion system governing the dynamics of ionic quantities, intra- and extra-cellular potentials, and the linearized elasticity equations are adopted to describe the motion of an incompressible material. The coupling between muscle contraction, biochemical reactions and electric activity is introduced with a so-called active strain decomposition framework, where the material gradient of deformation is split into an active (electrophysiology-dependent) part and an elastic (passive) one. Under the assumption of linearized elastic behavior and a truncation of the updated nonlinear diffusivities, we prove existence of weak solutions to the underlying coupled reaction–diffusion system and uniqueness of regular solutions. The proof of existence is based on a combination of parabolic regularization, the Faedo–Galerkin method, and the monotonicity-compactness method of Lions. A finite element formulation is also introduced, for which we establish existence of discrete solutions and show convergence to a weak solution of the original problem. We close with a numerical example illustrating the convergence of the method and some features of the model.