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

Effects of cardiac growth on electrical dyssynchrony in the single ventricle patient

Single ventricle patients, including those with hypoplastic left heart syndrome (HLHS), typically undergo three palliative heart surgeries culminating in the Fontan procedure. HLHS is associated with high rates of morbidity and mortality, and many patients develop arrhythmias, electrical dyssynchrony, and eventually ventricular failure. However, the correlation between ventricular enlargement and electrical dysfunction in HLHS physiology remains poorly understood. Here we characterize the relationship between growth and electrophysiology in HLHS using computational modeling. We integrate a personalized finite element model, a volumetric growth model, and a personalized electrophysiology model to perform controlled in silico experiments. We show that right ventricle enlargement negatively affects QRS duration and interventricular dyssynchrony. Conversely, left ventricle enlargement can partially compensate for this dyssynchrony. These findings have potential implications on our understanding of the origins of electrical dyssynchrony and, ultimately, the treatment of HLHS patients.

Assessing Post-TAVR Cardiac Conduction Abnormalities Risk Using a Digital Twin of a Beating Heart

Transcatheter aortic valve replacement (TAVR) has rapidly displaced surgical aortic valve replacement (SAVR). However, certain post-TAVR complications persist, with cardiac conduction abnormalities (CCA) being one of the major ones. The elevated pressure exerted by the TAVR stent onto the conduction fibers situated between the aortic annulus and the His bundle, in proximity to the atrioventricular (AV) node, may disrupt the cardiac conduction leading to the emergence of CCA. In his study, an in-silico framework was developed to assess the CCA risk, incorporating the effect of a dynamic beating heart and pre-procedural parameters such as implantation depth and preexisting cardiac asynchrony in the new onset of post-TAVR CCA. A self-expandable TAVR device deployment was simulated inside an electro-mechanically coupled beating heart model in five patient scenarios, including three implantation depths, and two preexisting cardiac asynchronies: (i) a right bundle branch block (RBBB) and (ii) a left bundle branch block (LBBB). Subsequently, several biomechanical parameters were analyzed to assess the post-TAVR CCA risk. The results manifested a lower cumulative contact pressure on the conduction fibers following TAVR for aortic deployment (0.018 MPa) compared to baseline (0.29 MPa) and ventricular deployment (0.52 MPa). Notably, the preexisting RBBB demonstrated a higher cumulative contact pressure (0.34 MPa) compared to the baseline and preexisting LBBB (0.25 MPa). Deeper implantation and preexisting RBBB cause higher stresses and contact pressure on the conduction fibers leading to an increased risk of post-TAVR CCA. Conversely, implantation above the MS landmark and preexisting LBBB reduces the risk.

Differential effects of mechano-electric feedback mechanisms on whole-heart activation, repolarization, and tension

The human heart is subject to highly variable amounts of strain during day-to-day activities and needs to adapt to a wide range of physiological demands. This adaptation is driven by an autoregulatory loop that includes both electrical and the mechanical components. In particular, mechanical forces are known to feed back into the cardiac electrophysiology system, which can result in pro- and anti-arrhythmic effects. Despite the widespread use of computational modelling and simulation for cardiac electrophysiology research, the majority of in silico experiments ignore this mechano-electric feedback entirely due to the high computational cost associated with solving cardiac mechanics. In this study, we therefore use an electromechanically coupled whole-heart model to investigate the differential and combined effects of electromechanical feedback mechanisms with a focus on their physiological relevance during sinus rhythm. In particular, we consider troponin-bound calcium, the effect of deformation on the tissue diffusion tensor, and stretch-activated channels. We found that activation of the myocardium was only significantly affected when including deformation into the diffusion term of the monodomain equation. Repolarization, on the other hand, was influenced by both troponin-bound calcium and stretch-activated channels and resulted in steeper repolarization gradients in the atria. The latter also caused afterdepolarizations in the atria. Due to its central role for tension development, calcium bound to troponin affected stroke volume and pressure. In conclusion, we found that mechano-electric feedback changes activation and repolarization patterns throughout the heart during sinus rhythm and lead to a markedly more heterogeneous electrophysiological substrate. KEY POINTS: The electrophysiological and mechanical function of the heart are tightly interrelated by excitation-contraction coupling (ECC) in the forward direction and mechano-electric feedback (MEF) in the reverse direction. While ECC is considered in many state-of-the-art computational models of cardiac electromechanics, less is known about the effect of different MEF mechanisms. Accounting for calcium bound to troponin increases stroke volume and delays repolarization. Geometry-mediated MEF leads to more heterogeneous activation and repolarization with steeper gradients. Both effects combine in an additive way. Non-selective stretch-activated channels as an additional MEF mechanism lead to heterogeneous diastolic transmembrane voltage, higher developed tension and delayed repolarization or afterdepolarizations in highly stretched parts of the atria. The differential and combined effects of these three MEF mechanisms during sinus rhythm activation in a human four-chamber heart model may have implications for arrhythmogenesis, both in terms of substrate (repolarization gradients) and triggers (ectopy).

Machine learning modeling of lung mechanics: Assessing the variability and propagation of uncertainty in respiratory-system compliance and airway resistance

BACKGROUND AND OBJECTIVE

Traditional assessment of patient response in mechanical ventilation relies on respiratory-system compliance and airway resistance. Clinical evidence has shown high variability in these parameters, highlighting the difficulty of predicting them before the start of ventilation therapy. This motivates the creation of computational models that can connect structural and tissue features with lung mechanics. In this work, we leverage machine learning (ML) techniques to construct predictive lung function models informed by non-linear finite element simulations, and use them to investigate the propagation of uncertainty in the lung mechanical response.

METHODS

We revisit a continuum poromechanical formulation of the lungs suitable for determining patient response. Based on this framework, we create high-fidelity finite element models of human lungs from medical images. We also develop a low-fidelity model based on an idealized sphere geometry. We then use these models to train and validate three ML architectures: single-fidelity and multi-fidelity Gaussian process regression, and artificial neural networks. We use the best predictive ML model to further study the sensitivity of lung response to variations in tissue structural parameters and boundary conditions via sensitivity analysis and forward uncertainty quantification. Codes are available for download at https://github.com/comp-medicine-uc/ML-lung-mechanics-UQ RESULTS: The low-fidelity model delivers a lung response very close to that predicted by high-fidelity simulations and at a fraction of the computational time. Regarding the trained ML models, the multi-fidelity GP model consistently delivers better accuracy than the single-fidelity GP and neural network models in estimating respiratory-system compliance and resistance (R2∼0.99). In terms of computational efficiency, our ML model delivers a massive speed-up of ∼970,000× with respect to high-fidelity simulations. Regarding lung function, we observed an almost matched and non-linear behavior between specific structural parameters and chest wall stiffness with compliance. Also, we observed a strong modulation of airways resistance with tissue permeability.

CONCLUSIONS

Our findings unveil the relevance of specific lung tissue parameters and boundary conditions in the respiratory-system response. Furthermore, we highlight the advantages of adopting a multi-fidelity ML approach that combines data from different levels to yield accurate and efficient estimates of clinical mechanical markers. We envision that the methods presented here can open the way to the development of predictive ML models of the lung response that can inform clinical decisions.

Effect of strain-dependent conduction slowing on the re-entry formation and maintenance in cardiac muscle: 2D computer simulation

The effect of mechano-electrical feedback on re-entry formation and maintenance was studied using a model of myocardial electromechanics that accounts for two components of myocardial conductivity and delayed strain-dependent changes in membrane capacitance that causes a conduction slowing. Two scenarios were simulated in 2D numerical experiments: (i) propagation of an excitation-contraction wave beyond the edge of a nonconductive nonexcitable obstacle; (ii) circulation of a re-entry wave around a nonconductive nonexcitable obstacle. The simulations demonstrated that the delayed strain-dependent deceleration of the conduction waves promotes the detachment of the excitation-contraction waves from the sharp edge of an elongated obstacle and modulates the re-entry waves rotating around a compact obstacle. The data show that the mechano-electrical feedback, together with an increase in the stimulation frequency and an increase in the excitation threshold, is an arrhythmogenic factor that must be taken into account when analyzing the possibility of the re-entry formation.

Transmural fibre orientations based on Laplace-Dirichlet-Rule-Based-Methods and their influence on human heart simulations

It is well known that the orthotropic tissue structure decisively influences the mechanical and electrical properties of the heart. Numerous approaches to compute the orthotropic tissue structure in computational heart models have been developed in the past decades. In this study, we investigate to what extent different Laplace-Dirichlet-Rule-Based-Methods (LDRBMs) influence the local orthotropic tissue structure and thus the electromechanical behaviour of the subsequent cardiac simulation. In detail, we are utilising three Laplace-Dirichlet-Rule-Based-Methods and compare: (i) the local myofibre orientation; (ii) important global characteristics (ejection fraction, peak pressure, apex shortening, myocardial volume reduction, fractional wall thickening); (iii) local characteristics (active fibre stress, fibre strain). We observe that the orthotropic tissue structures for the three LDRBMs show significant differences in the local myofibre orientation. The global characteristics myocardial volume reduction and peak pressure are rather insensitive to a change in local myofibre orientation, while the ejection fraction is moderately influenced by the different LDRBMs. Moreover, the apical shortening and fractional wall thickening exhibit a sensitive behaviour to a change in the local myofibre orientation. The highest sensitivity can be observed for the local characteristics.

Computational cardiac physiology for new modelers: Origins, foundations, and future

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

How viscous is the beating heart?: Insights from a computational study

Understanding tissue rheology is critical to accurately model the human heart. While the elastic properties of cardiac tissue have been extensively studied, its viscous properties remain an issue of ongoing debate. Here we adopt a viscoelastic version of the classical Holzapfel Ogden model to study the viscous timescales of human cardiac tissue. We perform a series of simulations and explore stress-relaxation curves, pressure-volume loops, strain profiles, and ventricular wall strains for varying viscosity parameters. We show that the time window for model calibration strongly influences the parameter identification. Using a four-chamber human heart model, we observe that, during the physiologically relevant time scales of the cardiac cycle, viscous relaxation has a negligible effect on the overall behavior of the heart. While viscosity could have important consequences in pathological conditions with compromised contraction or relaxation properties, we conclude that, for simulations within the physiological range of a human heart beat, we can reasonably approximate the human heart as hyperelastic.

Computational modelling of mechano-electric feedback and its arrhythmogenic effects in human ventricular models

The current study aims to investigate the role of mechano-electric feedback (MEF) in healthy cardiac cycles and in cardiac arrhythmia using human ventricular models. The numerical formulation of stretch-activated channels (SACs) in terms of the fibre stretch of the myocardium is incorporated into the modified Hill model that describes the myocardium as an electro-visco-active material. Additionally, we propose models of SACs formulated in terms of the rate of stretch along fibre direction and the stretch along sheet direction. We analyze the effect of the three different models for SACs and different material properties on the regular cycles by using electrocardiogram and volume-time curves, and show that the each model of SACs has regionally different influences on the heart model. Moreover, we simulate 'commotio cordis' and 'precordial thump' and demonstrate that MEF plays a major role in the occurrence of fibrillation and defibrillation in the absence of the structural cardiac damage. Furthermore, we study the role of MEF in premature ventricular contraction when the blood pressure is disturbed.

A Fully-Coupled Electro-Mechanical Whole-Heart Computational Model: Influence of Cardiac Contraction on the ECG

The ECG is one of the most commonly used non-invasive tools to gain insights into the electrical functioning of the heart. It has been crucial as a foundation in the creation and validation of in silico models describing the underlying electrophysiological processes. However, so far, the contraction of the heart and its influences on the ECG have mainly been overlooked in in silico models. As the heart contracts and moves, so do the electrical sources within the heart responsible for the signal on the body surface, thus potentially altering the ECG. To illuminate these aspects, we developed a human 4-chamber electro-mechanically coupled whole heart in silico model and embedded it within a torso model. Our model faithfully reproduces measured 12-lead ECG traces, circulatory characteristics, as well as physiological ventricular rotation and atrioventricular valve plane displacement. We compare our dynamic model to three non-deforming ones in terms of standard clinically used ECG leads (Einthoven and Wilson) and body surface potential maps (BSPM). The non-deforming models consider the heart at its ventricular end-diastatic, end-diastolic and end-systolic states. The standard leads show negligible differences during P-Wave and QRS-Complex, yet during T-Wave the leads closest to the heart show prominent differences in amplitude. When looking at the BSPM, there are no notable differences during the P-Wave, but effects of cardiac motion can be observed already during the QRS-Complex, increasing further during the T-Wave. We conclude that for the modeling of activation (P-Wave/QRS-Complex), the associated effort of simulating a complete electro-mechanical approach is not worth the computational cost. But when looking at ventricular repolarization (T-Wave) in standard leads as well as BSPM, there are areas where the signal can be influenced by cardiac motion of the heart to an extent that should not be ignored.

Computationally efficient model of myocardial electromechanics for multiscale simulations

A model of myocardial electromechanics is suggested. It combines modified and simplified versions of previously published models of cardiac electrophysiology, excitation-contraction coupling, and mechanics. The mechano-calcium and mechano-electrical feedbacks, including the strain-dependence of the propagation velocity of the action potential, are also accounted for. The model reproduces changes in the twitch amplitude and Ca2+-transients upon changes in muscle strain including the slow response. The model also reproduces the Bowditch effect and changes in the twitch amplitude and duration upon changes in the interstimulus interval, including accelerated relaxation at high stimulation frequency. Special efforts were taken to reduce the stiffness of the differential equations of the model. As a result, the equations can be integrated numerically with a relatively high time step making the model suitable for multiscale simulation of the human heart and allowing one to study the impact of myocardial mechanics on arrhythmias.

A numerical study on the effects of spatial and temporal discretization in cardiac electrophysiology

Millions of degrees of freedom are often required to accurately represent the electrophysiology of the myocardium due to the presence of discretization effects. This study seeks to explore the influence of temporal and spatial discretization on the simulation of cardiac electrophysiology in conjunction with changes in modeling choices. Several finite element analyses are performed to examine how discretization affects solution time, conduction velocity and electrical excitation. Discretization effects are considered along with changes in the electrophysiology model and solution approach. Two action potential models are considered: the Aliev-Panfilov model and the ten Tusscher-Noble-Noble-Panfilov model. The solution approaches consist of two time integration schemes and different treatments for solving the local system of ordinary differential equations. The efficiency and stability of the calculation approaches are demonstrated to be dependent on the action potential model. The dependency of the conduction velocity on the element size and time step is shown to be different for changes in material parameters. Finally, the discrepancies between the wave propagation in coarse and fine meshes are analyzed based on the temporal evolution of the transmembrane potential at a node and its neighboring Gauss points. Insight obtained from this study can be used to suggest new methods to improve the efficiency of simulations in cardiac electrophysiology.

Precision medicine in human heart modeling : Perspectives, challenges, and opportunities

Precision medicine is a new frontier in healthcare that uses scientific methods to customize medical treatment to the individual genes, anatomy, physiology, and lifestyle of each person. In cardiovascular health, precision medicine has emerged as a promising paradigm to enable cost-effective solutions that improve quality of life and reduce mortality rates. However, the exact role in precision medicine for human heart modeling has not yet been fully explored. Here, we discuss the challenges and opportunities for personalized human heart simulations, from diagnosis to device design, treatment planning, and prognosis. With a view toward personalization, we map out the history of anatomic, physical, and constitutive human heart models throughout the past three decades. We illustrate recent human heart modeling in electrophysiology, cardiac mechanics, and fluid dynamics and highlight clinically relevant applications of these models for drug development, pacing lead failure, heart failure, ventricular assist devices, edge-to-edge repair, and annuloplasty. With a view toward translational medicine, we provide a clinical perspective on virtual imaging trials and a regulatory perspective on medical device innovation. We show that precision medicine in human heart modeling does not necessarily require a fully personalized, high-resolution whole heart model with an entire personalized medical history. Instead, we advocate for creating personalized models out of population-based libraries with geometric, biological, physical, and clinical information by morphing between clinical data and medical histories from cohorts of patients using machine learning. We anticipate that this perspective will shape the path toward introducing human heart simulations into precision medicine with the ultimate goals to facilitate clinical decision making, guide treatment planning, and accelerate device design.

In-silico study of the cardiac arrhythmogenic potential of biomaterial injection therapy

Biomaterial injection is a novel therapy to treat ischemic heart failure (HF) that has shown to reduce remodeling and restore cardiac function in recent preclinical studies. While the effect of biomaterial injection in reducing mechanical wall stress has been recently demonstrated, the influence of biomaterials on the electrical behavior of treated hearts has not been elucidated. In this work, we developed computational models of swine hearts to study the electrophysiological vulnerability associated with biomaterial injection therapy. The propagation of action potentials on realistic biventricular geometries was simulated by numerically solving the monodomain electrophysiology equations on anatomically-detailed models of normal, HF untreated, and HF treated hearts. Heart geometries were constructed from high-resolution magnetic resonance images (MRI) where the healthy, peri-infarcted, infarcted and gel regions were identified, and the orientation of cardiac fibers was informed from diffusion-tensor MRI. Regional restitution properties in each case were evaluated by constructing a probability density function of the action potential duration (APD) at different cycle lengths. A comparative analysis of the ventricular fibrillation (VF) dynamics for every heart was carried out by measuring the number of filaments formed after wave braking. Our results suggest that biomaterial injection therapy does not affect the regional dispersion of repolarization when comparing untreated and treated failing hearts. Further, we found that the treated failing heart is more prone to sustain VF than the normal heart, and is at least as susceptible to sustained VF as the untreated failing heart. Moreover, we show that the main features of VF dynamics in a treated failing heart are not affected by the level of electrical conductivity of the biogel injectates. This work represents a novel proof-of-concept study demonstrating the feasibility of computer simulations of the heart in understanding the arrhythmic behavior in novel therapies for HF.

Biological cells and coupled electro-mechanical effects: The role of organelles, microtubules, and nonlocal contributions

Biological cells are exposed to a variety of mechanical loads throughout their life cycles that eventually play an important role in a wide range of cellular processes. The understanding of cell mechanics under the application of external stimuli is important for capturing the nuances of physiological and pathological events. Such critical knowledge will play an increasingly vital role in modern medical therapies such as tissue engineering and regenerative medicine, as well as in the development of new remedial treatments. At present, it is well known that the biological molecules exhibit piezoelectric properties that are of great interest for medical applications ranging from sensing to surgery. In the current study, a coupled electro-mechanical model of a biological cell has been developed to better understand the complex behaviour of biological cells subjected to piezoelectric and flexoelectric properties of their constituent organelles under the application of external forces. Importantly, a more accurate modelling paradigm has been presented to capture the nonlocal flexoelectric effect in addition to the linear piezoelectric effect based on the finite element method. Major cellular organelles considered in the developed computational model of the biological cell are the nucleus, mitochondria, microtubules, cell membrane and cytoplasm. The effects of variations in the applied forces on the intrinsic piezoelectric and flexoelectric contributions to the electro-elastic response have been systematically investigated along with accounting for the variation in the coupling coefficients. In addition, the effect of mechanical degradation of the cytoskeleton on the electro-elastic response has also been quantified. The present studies suggest that flexoelectricity could be a dominant electro-elastic coupling phenomenon, exhibiting electric fields that are four orders of magnitude higher than those generated by piezoelectric effects alone. Further, the output of the coupled electro-mechanical model is significantly dependent on the variation of flexoelectric coefficients. We have found that the mechanical degradation of the cytoskeleton results in the enhancement of both the piezo and flexoelectric responses associated with electro-mechanical coupling. In general, our study provides a framework for more accurate quantification of the mechanical/electrical transduction within the biological cells that can be critical for capturing the complex mechanisms at cellular length scales.

Cardiac Mechano-Electric Coupling: Acute Effects of Mechanical Stimulation on Heart Rate and Rhythm

The heart is vital for biological function in almost all chordates, including humans. It beats continually throughout our life, supplying the body with oxygen and nutrients while removing waste products. If it stops, so does life. The heartbeat involves precise coordination of the activity of billions of individual cells, as well as their swift and well-coordinated adaption to changes in physiological demand. Much of the vital control of cardiac function occurs at the level of individual cardiac muscle cells, including acute beat-by-beat feedback from the local mechanical environment to electrical activity (as opposed to longer term changes in gene expression and functional or structural remodeling). This process is known as mechano-electric coupling (MEC). In the current review, we present evidence for, and implications of, MEC in health and disease in human; summarize our understanding of MEC effects gained from whole animal, organ, tissue, and cell studies; identify potential molecular mediators of MEC responses; and demonstrate the power of computational modeling in developing a more comprehensive understanding of ‟what makes the heart tick.ˮ.

An orthotropic electro-viscoelastic model for the heart with stress-assisted diffusion

We propose and analyse the properties of a new class of models for the electromechanics of cardiac tissue. The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law, for both active stress and active strain formulations of active mechanics, coupled with a four-variable phenomenological model for human cardiac cell electrophysiology, which produces an accurate description of the action potential. The conductivities in the model of electric propagation are modified according to stress, inducing an additional degree of nonlinearity and anisotropy in the coupling mechanisms, and the activation model assumes a simplified stretch-calcium interaction generating active tension or active strain. The influence of the new terms in the electromechanical model is evaluated through a sensitivity analysis, and we provide numerical validation through a set of computational tests using a novel mixed-primal finite element scheme.

Sensitivity analysis of a strongly-coupled human-based electromechanical cardiac model: Effect of mechanical parameters on physiologically relevant biomarkers

The human heart beats as a result of multiscale nonlinear dynamics coupling subcellular to whole organ processes, achieving electrophysiologically-driven mechanical contraction. Computational cardiac modelling and simulation have achieved a great degree of maturity, both in terms of mathematical models of underlying biophysical processes and the development of simulation software. In this study, we present the detailed description of a human-based physiologically-based, and fully-coupled ventricular electromechanical modelling and simulation framework, and a sensitivity analysis focused on its mechanical properties. The biophysical detail of the model, from ionic to whole-organ, is crucial to enable future simulations of disease and drug action. Key novelties include the coupling of state-of-the-art human-based electrophysiology membrane kinetics, excitation-contraction and active contraction models, and the incorporation of a pre-stress model to allow for pre-stressing and pre-loading the ventricles in a dynamical regime. Through high performance computing simulations, we demonstrate that 50% to 200% - 1000% variations in key parameters result in changes in clinically-relevant mechanical biomarkers ranging from diseased to healthy values in clinical studies. Furthermore mechanical biomarkers are primarily affected by only one or two parameters. Specifically, ejection fraction is dominated by the scaling parameter of the active tension model and its scaling parameter in the normal direction ( k ort 2 ); the end systolic pressure is dominated by the pressure at which the ejection phase is triggered ( P ej ) and the compliance of the Windkessel fluid model ( C ); and the longitudinal fractional shortening is dominated by the fibre angle ( ϕ ) and k ort 2 . The wall thickening does not seem to be clearly dominated by any of the considered input parameters. In summary, this study presents in detail the description and implementation of a human-based coupled electromechanical modelling and simulation framework, and a high performance computing study on the sensitivity of mechanical biomarkers to key model parameters. The tools and knowledge generated enable future investigations into disease and drug action on human ventricles.

Computational prediction of the effect of D172N KCNJ2 mutation on ventricular pumping during sinus rhythm and reentry

The understanding of cardiac arrhythmia under genetic mutations has grown in interest among researchers. Previous studies focused on the effect of the D172N mutation on electrophysiological behavior. In this study, we analyzed not only the electrophysiological activity but also the mechanical responses during normal sinus rhythm and reentry conditions by using computational modeling. We simulated four different ventricular conditions including normal case of ten Tusscher model 2006 (TTM), wild-type (WT), heterozygous (WT/D172N), and homozygous D172N mutation. The 2D simulation result (in wire-shaped mesh) showed the WT/D172N and D172N mutation shortened the action potential duration by 14%, and by 23%, respectively. The 3D electrophysiological simulation results showed that the electrical wavelength between TTM and WT conditions were identical. Under sinus rhythm condition, the WT/D172N and D172N reduced the pumping efficacy with a lower left ventricle (LV) and aortic pressures, stroke volume, ejection fraction, and cardiac output. Under the reentry conditions, the WT condition has a small probability of reentry. However, in the event of reentry, WT has shown the most severe condition. Furthermore, we found that the position of the rotor or the scroll wave substantially influenced the ventricular pumping efficacy during arrhythmia. If the rotor stays in the LV, it will cause very poor pumping performance. Graphical Abstract A model of a ventricular electromechanical system. This whole model was established to observe the effect of D172N KCNJ2 mutation on ventricular pumping behavior during sinus rhythm and reentry conditions. The model consists of two components; electrical component and mechanical component. The electrophysiological model based on ten Tusscher et al. with the IK1 D172N KCNJ2 mutation, and the myofilament dynamic (cross-bridge) model based on Rice et al. study. The 3D electrical component is a ventricular geometry based on MRI which composed of nodes representing single-cell with electrophysiological activation. The 3D ventricular mechanic is a finite element mesh composed of single-cells myofilament dynamic model. Both components were coupled with Ca2+ concentration. We used Gaussian points for the calcium interpolation from the electrical mesh to the mechanical mesh.

Interaction of the Mechano-Electrical Feedback With Passive Mechanical Models on a 3D Rat Left Ventricle: A Computational Study

In this paper, we are investigating the interaction between different passive material models and the mechano-electrical feedback (MEF) in cardiac modeling. Various types of passive mechanical laws (nearly incompressible/compressible, polynomial/exponential-type, transversally isotropic/orthotropic material models) are integrated in a fully coupled electromechanical model in order to study their specific influence on the overall MEF behavior. Our computational model is based on a three-dimensional (3D) geometry of a healthy rat left ventricle reconstructed from magnetic resonance imaging (MRI). The electromechanically coupled problem is solved using a fully implicit finite element-based approach. The effects of different passive material models on the MEF are studied with the help of numerical examples. It turns out that there is a significant difference between the behavior of the MEF for compressible and incompressible material models. Numerical results for the incompressible models exhibit that a change in the electrophysiology can be observed such that the transmembrane potential (TP) is unable to reach the resting state in the repolarization phase, and this leads to non-zero relaxation deformations. The most significant and strongest effects of the MEF on the rat cardiac muscle response are observed for the exponential passive material law.

Predicting critical drug concentrations and torsadogenic risk using a multiscale exposure-response simulator

Torsades de pointes is a serious side effect of many drugs that can trigger sudden cardiac death, even in patients with structurally normal hearts. Torsadogenic risk has traditionally been correlated with the blockage of a specific potassium channel and a prolonged recovery period in the electrocardiogram. However, the precise mechanisms by which single channel block translates into heart rhythm disorders remain incompletely understood. Here we establish a multiscale exposure-response simulator that converts block-concentration characteristics from single cell recordings into three-dimensional excitation profiles and electrocardiograms to rapidly assess torsadogenic risk. For the drug dofetilide, we characterize the QT interval and heart rate at different drug concentrations and identify the critical concentration at the onset of torsades de pointes: For dofetilide concentrations of 2x, 3x, and 4x, as multiples of the free plasma concentration Cmax = 2.1 nM, the QT interval increased by +62.0%, +71.2%, and +82.3% compared to baseline, and the heart rate changed by -21.7%, -23.3%, and +88.3%. The last number indicates that, at the critical concentration of 4x, the heart spontaneously developed an episode of a torsades-like arrhythmia. Strikingly, this critical drug concentration is higher than the concentration estimated from early afterdepolarizations in single cells and lower than in one-dimensional cable models. Our results highlight the importance of whole heart modeling and explain, at least in part, why current regulatory paradigms often fail to accurately quantify the pro-arrhythmic potential of a drug. Our exposure-response simulator could provide a more mechanistic assessment of pro-arrhythmic risk and help establish science-based guidelines to reduce rhythm disorders, design safer drugs, and accelerate drug development.

Using machine learning to characterize heart failure across the scales

Heart failure is a progressive chronic condition in which the heart undergoes detrimental changes in structure and function across multiple scales in time and space. Multiscale models of cardiac growth can provide a patient-specific window into the progression of heart failure and guide personalized treatment planning. Yet, the predictive potential of cardiac growth models remains poorly understood. Here, we quantify predictive power of a stretch-driven growth model using a chronic porcine heart failure model, subject-specific multiscale simulation, and machine learning techniques. We combine hierarchical modeling, Bayesian inference, and Gaussian process regression to quantify the uncertainty of our experimental measurements during an 8-week long study of volume overload in six pigs. We then propagate the experimental uncertainties from the organ scale through our computational growth model and quantify the agreement between experimentally measured and computationally predicted alterations on the cellular scale. Our study suggests that stretch is the major stimulus for myocyte lengthening and demonstrates that a stretch-driven growth model alone can explain [Formula: see text] of the observed changes in myocyte morphology. We anticipate that our approach will allow us to design, calibrate, and validate a new generation of multiscale cardiac growth models to explore the interplay of various subcellular-, cellular-, and organ-level contributors to heart failure. Using machine learning in heart failure research has the potential to combine information from different sources, subjects, and scales to provide a more holistic picture of the failing heart and point toward new treatment strategies.

A Contemporary Look at Biomechanical Models of Myocardium

Understanding and predicting the mechanical behavior of myocardium under healthy and pathophysiological conditions are vital to developing novel cardiac therapies and promoting personalized interventions. Within the past 30 years, various constitutive models have been proposed for the passive mechanical behavior of myocardium. These models cover a broad range of mathematical forms, microstructural observations, and specific test conditions to which they are fitted. We present a critical review of these models, covering both phenomenological and structural approaches, and their relations to the underlying structure and function of myocardium. We further explore the experimental and numerical techniques used to identify the model parameters. Next, we provide a brief overview of continuum-level electromechanical models of myocardium, with a focus on the methods used to integrate the active and passive components of myocardial behavior. We conclude by pointing to future directions in the areas of optimal form as well as new approaches for constitutive modeling of myocardium.

Machine learning in drug development: Characterizing the effect of 30 drugs on the QT interval using Gaussian process regression, sensitivity analysis, and uncertainty quantification

Prolonged QT intervals are a major risk factor for ventricular arrhythmias and a leading cause of sudden cardiac death. Various drugs are known to trigger QT interval prolongation and increase the proarrhythmic potential. Yet, how precisely the action of drugs on the cellular level translates into QT interval prolongation on the whole organ level remains insufficiently understood. Here we use machine learning techniques to systematically characterize the effect of 30 common drugs on the QT interval. We combine information from high fidelity three-dimensional human heart simulations with low fidelity one-dimensional cable simulations to build a surrogate model for the QT interval using multi-fidelity Gaussian process regression. Once trained and cross-validated, we apply our surrogate model to perform sensitivity analysis and uncertainty quantification. Our sensitivity analysis suggests that compounds that block the rapid delayed rectifier potassium current I Kr have the greatest prolonging effect of the QT interval, and that blocking the L-type calcium current I CaL and late sodium current I NaL shortens the QT interval. Our uncertainty quantification allows us to propagate the experimental variability from individual block-concentration measurements into the QT interval and reveals that QT interval uncertainty is mainly driven by the variability in I Kr block. In a final validation study, we demonstrate an excellent agreement between our predicted QT interval changes and the changes observed in a randomized clinical trial for the drugs dofetilide, quinidine, ranolazine, and verapamil. We anticipate that both the machine learning methods and the results of this study will have great potential in the efficient development of safer drugs.

A rule-based method to model myocardial fiber orientation in cardiac biventricular geometries with outflow tracts

Rule-based methods are often used for assigning fiber orientation to cardiac anatomical models. However, existing methods have been developed using data mostly from the left ventricle. As a consequence, fiber information obtained from rule-based methods often does not match histological data in other areas of the heart such as the right ventricle, having a negative impact in cardiac simulations beyond the left ventricle. In this work, we present a rule-based method where fiber orientation is separately modeled in each ventricle following observations from histology. This allows to create detailed fiber orientation in specific regions such as the endocardium of the right ventricle, the interventricular septum, and the outflow tracts. We also carried out electrophysiological simulations involving these structures and with different fiber configurations. In particular, we built a modeling pipeline for creating patient-specific volumetric meshes of biventricular geometries, including the outflow tracts, and subsequently simulate the electrical wavefront propagation in outflow tract ventricular arrhythmias with different origins for the ectopic focus. The resulting simulations with the proposed rule-based method showed a very good agreement with clinical parameters such as the 10 ms isochrone ratio in a cohort of nine patients suffering from this type of arrhythmia. The developed modeling pipeline confirms its potential for an in silico identification of the site of origin in outflow tract ventricular arrhythmias before clinical intervention.

Competing Mechanisms of Stress-Assisted Diffusivity and Stretch-Activated Currents in Cardiac Electromechanics

We numerically investigate the role of mechanical stress in modifying the conductivity properties of cardiac tissue, and also assess the impact of these effects in the solutions generated by computational models for cardiac electromechanics. We follow the recent theoretical framework from Cherubini et al. (2017), proposed in the context of general reaction-diffusion-mechanics systems emerging from multiphysics continuum mechanics and finite elasticity. In the present study, the adapted models are compared against preliminary experimental data of pig right ventricle fluorescence optical mapping. These data contribute to the characterization of the observed inhomogeneity and anisotropy properties that result from mechanical deformation. Our novel approach simultaneously incorporates two mechanisms for mechano-electric feedback (MEF): stretch-activated currents (SAC) and stress-assisted diffusion (SAD); and we also identify their influence into the nonlinear spatiotemporal dynamics. It is found that (i) only specific combinations of the two MEF effects allow proper conduction velocity measurement; (ii) expected heterogeneities and anisotropies are obtained via the novel stress-assisted diffusion mechanisms; (iii) spiral wave meandering and drifting is highly mediated by the applied mechanical loading. We provide an analysis of the intrinsic structure of the nonlinear coupling mechanisms using computational tests conducted with finite element methods. In particular, we compare static and dynamic deformation regimes in the onset of cardiac arrhythmias and address other potential biomedical applications.

Semi-implicit Non-conforming Finite-Element Schemes for Cardiac Electrophysiology: A Framework for Mesh-Coarsening Heart Simulations

The field of computational cardiology has steadily progressed toward reliable and accurate simulations of the heart, showing great potential in clinical applications such as the optimization of cardiac interventions and the study of pro-arrhythmic effects of drugs in humans, among others. However, the computational effort demanded by in-silico studies of the heart remains challenging, highlighting the need of novel numerical methods that can improve the efficiency of simulations while targeting an acceptable accuracy. In this work, we propose a semi-implicit non-conforming finite-element scheme (SINCFES) suitable for cardiac electrophysiology simulations. The accuracy and efficiency of the proposed scheme are assessed by means of numerical simulations of the electrical excitation and propagation in regular and biventricular geometries. We show that the SINCFES allows for coarse-mesh simulations that reduce the computation time when compared to fine-mesh models while delivering wavefront shapes and conduction velocities that are more accurate than those predicted by traditional finite-element formulations based on the same coarse mesh, thus improving the accuracy-efficiency trade-off of cardiac simulations.

Mechanical perturbation control of cardiac alternans

Cardiac alternans is a disturbance in heart rhythm that is linked to the onset of lethal cardiac arrhythmias. Mechanical perturbation control has been recently used to suppress alternans in cardiac tissue of relevant size. In this control strategy, cardiac tissue mechanics are perturbed via active tension generated by the heart's electrical activity, which alters the tissue's electric wave profile through mechanoelectric coupling. We analyze the effects of mechanical perturbation on the dynamics of a map model that couples the membrane voltage and active tension systems at the cellular level. Therefore, a two-dimensional iterative map of the heart beat-to-beat dynamics is introduced, and a stability analysis of the system of coupled maps is performed in the presence of a mechanical perturbation algorithm. To this end, a bidirectional coupling between the membrane voltage and active tension systems in a single cardiac cell is provided, and a discrete form of the proposed control algorithm, that can be incorporated in the coupled maps, is derived. In addition, a realistic electromechanical model of cardiac tissue is employed to explore the feasibility of suppressing alternans at cellular and tissue levels. Electrical activity is represented in two detailed ionic models, the Luo-Rudy 1 and the Fox models, while two active contractile tension models, namely a smooth variant of the Nash-Panfilov model and the Niederer-Hunter-Smith model, are used to represent mechanical activity in the heart. The Mooney-Rivlin passive elasticity model is employed to describe passive mechanical behavior of the myocardium.

Interpreting Activation Mapping of Atrial Fibrillation: A Hybrid Computational/Physiological Study

Atrial fibrillation is the most common rhythm disorder of the heart associated with a rapid and irregular beating of the upper chambers. Activation mapping remains the gold standard to diagnose and interpret atrial fibrillation. However, fibrillatory activation maps are highly sensitive to far-field effects, and often disagree with other optical mapping modalities. Here we show that computational modeling can identify spurious non-local components of atrial fibrillation electrograms and improve activation mapping. We motivate our approach with a cohort of patients with potential drivers of persistent atrial fibrillation. In a computational study using a monodomain Maleckar model, we demonstrate that in organized rhythms, electrograms successfully track local activation, whereas in atrial fibrillation, electrograms are sensitive to spiral wave distance and number, spiral tip trajectories, and effects of fibrosis. In a clinical study, we analyzed n = 15 patients with persistent atrial fibrillation that was terminated by limited ablation. In five cases, traditional activation maps revealed a spiral wave at sites of termination; in ten cases, electrogram timings were ambiguous and activation maps showed incomplete reentry. By adjusting electrogram timing through computational modeling, we found rotational activation, which was undetectable with conventional methods. Our results demonstrate that computational modeling can identify non-local deflections to improve activation mapping and explain how and where ablation can terminate persistent atrial fibrillation. Our hybrid computational/physiological approach has the potential to optimize map-guided ablation and improve ablation therapy in atrial fibrillation.

Predicting the cardiac toxicity of drugs using a novel multiscale exposure-response simulator

A common but serious side effect of many drugs is torsades de pointes, a rhythm disorder that can have fatal consequences. Torsadogenic risk has traditionally been associated with blockage of a specific potassium channel and an increased recovery period in the electrocardiogram. However, the mechanisms that trigger torsades de pointes remain incompletely understood. Here we establish a computational model to explore how drug-induced effects propagate from the single channel, via the single cell, to the whole heart level. Our mechanistic exposure-response simulator translates block-concentration characteristics for arbitrary drugs into three-dimensional excitation profiles and electrocardiogram recordings to rapidly assess torsadogenic risk. For the drug of dofetilide, we show that this risk is highly dose-dependent: at a concentration of 1x, QT prolongation is 55% but the heart maintains its regular sinus rhythm; at 5.7x, QT prolongation is 102% and the heart spontaneously transitions into torsades de points; at 30x, QT prolongation is 132% and the heart adapts a quasi-depolarized state with numerous rapidly flickering local excitations. Our simulations suggest that neither potassium channel blockage nor QT interval prolongation alone trigger torsades de pointes. The underlying mechanism predicted by our model is early afterdepolarization, which translates into pronounced U waves in the electrocardiogram, a signature that is correctly predicted by our model. Beyond the risk assessment of existing drugs, our exposure-response simulator can become a powerful tool to optimize the co-administration of drugs and, ultimately, guide the design of new drugs toward reducing life threatening drug-induced rhythm disorders in the heart.

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.

A note on stress-driven anisotropic diffusion and its role in active deformable media

We introduce a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to employ diffusion tensors directly influenced by the coupling with mechanical stress. The proposed generalised reaction-diffusion-mechanics model reveals that initially isotropic and homogeneous diffusion tensors turn into inhomogeneous and anisotropic quantities due to the intrinsic structure of the nonlinear coupling. We study the physical properties leading to these effects, and investigate mathematical conditions for its occurrence. Together, the mathematical model and the numerical results obtained using a mixed-primal finite element method, clearly support relevant consequences of stress-driven diffusion into anisotropy patterns, drifting, and conduction velocity of the resulting excitation waves. Our findings also indicate the applicability of this novel approach in the description of mechano-electric feedback in actively deforming bio-materials such as the cardiac tissue.