Abstract:

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).

Abstract:

PURPOSE: Atrial fibrillation is one of the most frequent cardiac arrhythmias in the industrialized world and ablation therapy is the method of choice for many patients. However, ablation scars alter the electrophysiological activation and the mechanical behavior of the affected atria. Different ablation strategies with the aim to terminate atrial fibrillation and prevent its recurrence exist but their impact on the performance of the heart is often neglected. METHODS: In this work, we present a simulation study analyzing five commonly used ablation scar patterns and their combinations in the left atrium regarding their impact on the pumping function of the heart using an electromechanical whole-heart model. We analyzed how the altered atrial activation and increased stiffness due to the ablation scars affect atrial as well as ventricular contraction and relaxation. RESULTS: We found that systolic and diastolic function of the left atrium is impaired by ablation scars and that the reduction of atrial stroke volume of up to 11.43% depends linearly on the amount of inactivated tissue. Consequently, the end-diastolic volume of the left ventricle, and thus stroke volume, was reduced by up to 1.4 and 1.8%, respectively. During ventricular systole, left atrial pressure was increased by up to 20% due to changes in the atrial activation sequence and the stiffening of scar tissue. CONCLUSION: This study provides biomechanical evidence that atrial ablation has acute effects not only on atrial contraction but also on ventricular performance. Therefore, the position and extent of ablation scars is not only important for the termination of arrhythmias but is also determining long-term pumping efficiency. If confirmed in larger cohorts, these results have the potential to help tailoring ablation strategies towards minimal global cardiovascular impairment.

Abstract:

Cardiac resynchronization therapy is a valuable tool to restore left ventricular function in patients experiencing dyssynchronous ventricular activation. However, the non-responder rate is still as high as 40%. Recent studies suggest that left ventricular torsion or specifically the lack thereof might be a good predictor for the response of cardiac resynchronization therapy. Since left ventricular torsion is governed by the muscle fiber orientation and the heterogeneous electromechanical activation of the myocardium, understanding the relation between these components and the ability to measure them is vital. To analyze if locally altered electromechanical activation in heart failure patients affects left ventricular torsion, we conducted a simulation study on 27 personalized left ventricular models. Electroanatomical maps and late gadolinium enhanced magnetic resonance imaging data informed our in-silico model cohort. The angle of rotation was evaluated in every material point of the model and averaged values were used to classify the rotation as clockwise or counterclockwise in each segment and sector of the left ventricle. 88% of the patient models (n = 24) were classified as a wringing rotation and 12% (n = 3) as a rigid-body-type rotation. Comparison to classification based on in vivo rotational NOGA XP maps showed no correlation. Thus, isolated changes of the electromechanical activation sequence in the left ventricle are not sufficient to reproduce the rotation pattern changes observed in vivo and suggest that further patho-mechanisms are involved.

Abstract:

Mathematical models of the human heart are evolving to become a cornerstone of precision medicine and support clinical decision making by providing a powerful tool to understand the mechanisms underlying pathophysiological conditions. In this study, we present a detailed mathematical description of a fully coupled multi-scale model of the human heart, including electrophysiology, mechanics, and a closed-loop model of circulation. State-of-the-art models based on human physiology are used to describe membrane kinetics, excitation-contraction coupling and active tension generation in the atria and the ventricles. Furthermore, we highlight ways to adapt this framework to patient specific measurements to build digital twins. The validity of the model is demonstrated through simulations on a personalized whole heart geometry based on magnetic resonance imaging data of a healthy volunteer. Additionally, the fully coupled model was employed to evaluate the effects of a typical atrial ablation scar on the cardiovascular system. With this work, we provide an adaptable multi-scale model that allows a comprehensive personalization from ion channels to the organ level enabling digital twin modeling

Abstract:

We investigate the properties of static mechanical and dynamic electro-mechanical models for the deformation of the human heart. Numerically this is realized by a staggered scheme for the coupled partial/ordinary differential equation (PDE-ODE) system. First, we consider a static and purely mechanical benchmark configuration on a realistic geometry of the human ventricles. Using a penalty term for quasi-incompressibility, we test different parameters and mesh sizes and observe that this approach is not sufficient for lowest order conforming finite elements. Then, we compare the approaches of active stress and active strain for cardiac muscle contraction. Finally, we compare in a coupled anatomically realistic electro-mechanical model numerical Newmark damping with a visco-elastic model using Rayleigh damping. Nonphysiological oscillations can be better mitigated using viscosity.

Abstract:

Approximating the fast dynamics of depolarization waves in the human heart described by the monodomain model is numerically challenging. Splitting methods for the PDE-ODE coupling enable the computation with very fine space and time discretizations. Here, we compare different splitting approaches regarding convergence, accuracy, and efficiency. Simulations were performed for a benchmark problem with the Beeler-Reuter cell model on a truncated ellipsoid approximating the left ventricle including a localized stimulation. For this configuration, we provide a reference solution for the transmembrane potential. We found a semi-implicit approach with state variable interpolation to be the most efficient scheme. The results are transferred to a more physiological setup using a bi-ventricular domain with a complex external stimulation pattern to evaluate the accuracy of the activation time for different resolutions in space and time.

Abstract:

Background: Hypertrophic cardiomyopathy (HCM) is typically caused by mutations in sarcomeric genes leading to cardiomyocyte disarray, replacement fibrosis, impaired contractility, and elevated filling pressures. These varying tissue properties are associ- ated with certain strain patterns that may allow to establish a diagnosis by means of non-invasive imaging without the necessity of harmful myocardial biopsies or con- trast agent application. With a numerical study, we aim to answer: how the variability in each of these mechanisms contributes to altered mechanics of the left ventricle (LV) and if the deformation obtained in in-silico experiments is comparable to values reported from clinical measurements. Methods: We conducted an in-silico sensitivity study on physiological and pathologi- cal mechanisms potentially underlying the clinical HCM phenotype. The deformation of the four-chamber heart models was simulated using a finite-element mechanical solver with a sliding boundary condition to mimic the tissue surrounding the heart. Furthermore, a closed-loop circulatory model delivered the pressure values acting on the endocardium. Deformation measures and mechanical behavior of the heart mod- els were evaluated globally and regionally. Results: Hypertrophy of the LV affected the course of strain, strain rate, and wall thickening—the root-mean-squared difference of the wall thickening between control (mean thickness 10 mm) and hypertrophic geometries (17 mm) was >10%. A reduc- tion of active force development by 40% led to less overall deformation: maximal radial strain reduced from 26 to 21%. A fivefold increase in tissue stiffness caused a more homogeneous distribution of the strain values among 17 heart segments. Fiber disarray led to minor changes in the circumferential and radial strain. A combination of pathological mechanisms led to reduced and slower deformation of the LV and halved the longitudinal shortening of the LA. Conclusions: This study uses a computer model to determine the changes in LV deformation caused by pathological mechanisms that are presumed to underlay HCM. This knowledge can complement imaging-derived information to obtain a more accu- rate diagnosis of HCM.

Abstract:

The human heart is a masterpiece of the highest complexity coordinating multi-physics aspects on a multi-scale range. Thus, modeling the cardiac function to reproduce physiological characteristics and diseases remains challenging. Especially the complex simulation of the blood's hemodynamics and its interaction with the myocardial tissue requires a high accuracy of the underlying computational models and solvers. These demanding aspects make whole-heart fully-coupled simulations computationally highly expensive and call for simpler but still accurate models. While the mechanical deformation during the heart cycle drives the blood flow, less is known about the feedback of the blood flow onto the myocardial tissue. To solve the fluid-structure interaction problem, we suggest a cycle-to-cycle coupling of the structural deformation and the fluid dynamics. In a first step, the displacement of the endocardial wall in the mechanical simulation serves as a unidirectional boundary condition for the fluid simulation. After a complete heart cycle of fluid simulation, a spatially resolved pressure factor (PF) is extracted and returned to the next iteration of the solid mechanical simulation, closing the loop of the iterative coupling procedure. All simulations were performed on an individualized whole heart geometry. The effect of the sequential coupling was assessed by global measures such as the change in deformation and-as an example of diagnostically relevant information-the particle residence time. The mechanical displacement was up to 2 mm after the first iteration. In the second iteration, the deviation was in the sub-millimeter range, implying that already one iteration of the proposed cycle-to-cycle coupling is sufficient to converge to a coupled limit cycle. Cycle-to-cycle coupling between cardiac mechanics and fluid dynamics can be a promising approach to account for fluid-structure interaction with low computational effort. In an individualized healthy whole-heart model, one iteration sufficed to obtain converged and physiologically plausible results.

Abstract:

Lumped parameter models of the human circulatory sys-tem are able to reproduce major features and phases of human circulation. However, they often lack physiological detail regarding pressure and flow across the valves. To alleviate these shortcomings, we implement a model of heart valve dynamics based on Bernoulli's principle to account for the transvalvular pressure drop and extend it by smooth opening and closing of the valves. We evaluate the new model based on a simulation with healthy valves and explore the possibility of simulating heart valve diseases by considering a case of severe aortic stenosis. The model more faithfully reproduces pressure, volume, and flow in all four chambers and in particular across the valves. Most of the changes are related to the consideration of blood inertia. However, only by opening and closing the valves more slowly, it is possible to reproduce features connected to backflow. When reducing the maximum area ratio of the aortic valve to 10%, a pressure gradient of 77.2 mmHg during systole and a 20% reduction in stroke volume was observed in accordance with the AHA guidelines of severe aortic stenosis. To conclude, we were able to improve our existing OD circulation model in terms of physiological accuracy by replacing the diode-like valves with an easy to implement model of heart valve dynamics that is capable of simulating both healthy and pathological scenarios.

Abstract:

A variety of biophysical and phenomenological active tension models has been proposed during the last decade that show physiological behaviour on a cellular level. However, applying these models in a whole heart finite element simulation framework yields either unphysiological values of stress and strain or an insufficient deformation pattern compared to magnetic resonance imaging data. In this study, we evaluate how introducing an orthotropic active stress tensor affects the deformation pattern by conducting a sensitivity analysis regarding the active tension at resting length Tref and three orthotropic activation parameters (Kss, Ksn and Knn). Deformation of left ventricular contraction is evaluated on a truncated ellipsoid using four features: wall thickening (WT), longitudinal shortening (LS), torsion (Θ) and ejection fraction (EF). We show that EF, WT and LS are positively correlated with the parameters Tref and Knn while Kss reduces all of the four observed features. Introducing shear stress to the model has little to no effect on EF, WT and LS, although it reduces torsion by up to 3◦. We find that added stress in the normal direction can support healthy deformation patterns. However, the twisting motion, which has been shown to be important for cardiac function, reduces by up to 20◦.

Abstract:

In silico studies are often used to analyze mechanisms of cardiac arrhythmias. The electrophysiological cell models that are used to simulate the membrane potential in these studies range from highly detailed physiological models to simplistic phenomenological models. To effectively cover the middle ground between those cell models, we utilize the manifold boundary approxi- mation method (MBAM) to systematically reduce the widely used O’Hara-Rudy ventricular cell model (ORd) and investigate the influence of parametrization of the model as well as different strategies of choosing input quantities, further called quantities of interest (QoI). As a result of the reduction process, we present three re- duced model variants of the ORd model that only contain a fraction of the original model’s ionic currents resulting in a twofold speedup in computation times compared to the original model. We find that the reduced models show similar action potential duration restitution and repolarization rates. Additionally, we are able to initialize and observe stable spiral wave dynamics on a 3D tissue patch for 2 out of the 3 reduced models.

Abstract:

The restraining effect of the pericardium and surrounding tissues on the human heart is essential to reproduce physiological valve plane movement in simulations and can be modeled in different ways. In this study, we investigate five different approaches used in recent publications and apply them to the same whole heart geometry. Some approaches use Robin boundary conditions, others use a volumetric representation of the pericardium and solve a contact problem. These two strategies are combined with a smooth spatially varying scaling or a region-wise partitioning of the epicardial surface. In general, all simulations follow the same morphology regarding mitral valve displacement, tricuspid valve displacement and left ventricular twist. We show that – with the parameters used in the original papers – Robin boundary conditions are computationally more expensive and lead to smaller stroke volumes and less ventricular twist. Unrelated to this, simulations with a penalty scaling result in a less pronounced displacement of the tricuspid valve. In one of the investigated scenarios adipose tissue is modeled using a volumetric mesh and the Robin boundary conditions are applied on its outside surface. We conclude that this approach leads to similar results as a partitioning of the epicardial surface into two regions with different penalty parameters and therefore a volumetric representation of the adipose tissue is neither necessary nor practical.

Abstract:

Individualized computer models of the geometry of the human heart are often based on mag- netic resonance images (MRI) or computed tomography (CT) scans. The stress distribution in the imaged state cannot be measured but needs to be estimated from the segmented geometry, e.g. by an iterative algorithm. As the convergence of this algorithm depends on different geometrical conditions, we system- atically studied their influence. Beside various shape alterations, we investigated the chamber volume, as well as the effect of material parameters. We found a marked influence of passive material parameters: increasing the model stiffness by a factor of ten halved the residual norm in the first iteration. Flat and concave areas led to a reduced robustness and convergence rate of the unloading algorithm. With this study, the geometric effects and modeling aspects governing the unloading algorithm’s convergence are identified and can be used as a basis for further improvement.

Abstract:

Today a variety of models describe the physiological behavior of the heart on a cellular level. The intracellular calcium concentration plays an important role, since it is the main driver for the active contraction of the heart. Due to different implementations of the calcium dynamics, simulating cardiac electromechanics can lead to severely different behaviorsof the active tension when coupling the same tension model with different electrophysiological models. To handle these variations, we present an optimization tool that adapts the parameters of the most recent, human based tension model. The goal is to generate a physiologically valid tension development when coupled to an electrophysiological cellular model independent of the specifics of that model's calcium transient. In this work, we focus ona ventricular cell model. In order to identify the calcium-sensitive parameters, a sensitivity analysis of the tension model was carried out. In a further step, the cell model was adapted to reproduce the sarcomere length-dependent behavior of troponin C. With a maximum relative deviationof 20.3% per defined characteristic of the tension development, satisfactory results could be obtained for isometric twitch tension. Considering the length-dependent troponin handling, physiological behavior could be reproduced. In conclusion, we propose an algorithm to adapt the tension development model to any calcium transient input toachieve a physiologically valid active contraction on a cellular level. As a proof of concept, the algorithm is successfully applied to one of the most recent human ventricular cell models. This is an important step towards fullycoupled electromechanical heart models, which are a valuable tool in personalized health care

Abstract:

In order to be used in a clinical context, numerical simulation tools have to strike a balance between accuracy and low computational effort. For re- producing the pumping function of the human heart numerically, the physical domains of cardiac continuum mechanics and fluid dynamics have a significant relevance. In this context, fluid-structure interaction between the heart muscle and the blood flow is particularly important: Myocardial tension development and wall deformation drive the blood flow. However, the degree to which the blood flow has a retrograde effect on the cardiac mechanics in this multi-physics problem remains unclear up to now. To address this question, we implemented a cycle-to-cycle coupling based on a finite element model of a patient-specific whole heart geometry. The deforma- tion of the cardiac wall over one heart cycle was computed using our mechanical simulation framework. A closed loop circulatory system model as part of the simulation delivered the chamber pressures. The displacement of the endo- cardial surfaces and the pressure courses of one cycle were used as boundary conditions for the fluid solver. After solving the Navier-Stokes equations, the relative pressure was extracted for all endocardial wall elements from the three dimensional pressure field. These local pressure deviations were subsequently returned to the next iteration of the continuum mechanical simulation, thus closing the loop of the iterative coupling procedure. Following this sequential coupling approach, we simulated three iterations of mechanic and fluid simulations. To characterize the convergence, we evaluated the time course of the normalized pressure field as well as the euclidean distance between nodes of the mechanic simulation in subsequent iterations. For the left ventricle (LV), the maximal euclidean distance of all endocardial wall nodes was smaller than 2mm between the first and second iteration. The maximal distance between the second and third iteration was 70μm, thus the limit of necessary cycles was already reached after two iterations. In future work, this iterative coupling approach will have to prove its abil- ity to deliver physiologically accurate results also for diseased heart models. Altogether, the sequential coupling approach with its low computational effort delivered promising results for modeling fluid-structure interaction in cardiac simulations.

Abstract:

Over the last decades, computational models have been applied in in-silico simulations of the heart biomechan- ics. These models depend on input parameters. In particular, four parameters are needed for the constitutive law of Guc- cione et al., a model describing the stress-strain relation of the heart tissue. In the literature, we could find a wide range of values for these parameters. In this work, we propose an optimization framework which identifies the parameters of a constitutive law. This framework is based on experimental measurements conducted by Klotz et al.. They provide an end-diastolic pressure-volume relation- ship. We applied the proposed framework on one heart model and identified the following elastic parameters to optimally match the Klotz curve: 𝐶 = 313 Pa, 𝑏𝑓 = 17.8, 𝑏𝑡 = 7.1 and 𝑏𝑓𝑡 = 12.4. In general, this approach allows to identify optimized param- eters for a constitutive law, for a patient-specific heart geome- try. The use of optimized parameters will lead to physiological simulation results of the heart biomechanics and is therefore an important step towards applying computational models in clinical practice.

Abstract:

Mathematical models of the human heart are evolving to become a cornerstone of precision medicine and support clinical decision making by providing a powerful tool to understand the mechanisms underlying pathophysiological conditions.Due to the complexity of the heart, these models require a detailed description of physical processes that interact on different spatial and temporal scales ranging from nanometers to centimeters and from nanoseconds to seconds, respectively.From a mathematical perspective, this poses a variety of challenges such as developing robust numerical schemes for the solution of the model in space and time and parameter identification based on patient specific measurements.In this work, a detailed mathematical description of the electromechanically coupled multi-scale model of the human heart is presented, including the propagation of electrical excitation, large scale deformations, and a model of the circulatory system.Starting from state-of-the-art models of membrane kinetics and active force generation based on human physiology, an atrial and ventricular model of cardiac excitation-contraction coupling is developed and parameterized to match observations from single cell experiments.Furthermore, a segregated and staggered numerical scheme to solve the electromechanically coupled model of the whole heart is established based on already existing software and used to investigate the effects of mechano-electric feedback during sinus rhythm.The numerical results showed that mechano-electric feedback on the cellular level has an impact on the mechanical behavior of the heart due to changes in the active force generation by modulating the interaction between calcium and the binding units of troponin C.Including the effect of deformation on the diffusion of the electrical signal had no significant effect.To verify the different components of the modeling framework, specific problems are designed to cover the most important aspects of electrophysiology and mechanics.Additionally, these problems are used to assess how spatial and temporal discretization affect the numerical solution.The results show that spatial and temporal discretization of the electrophysiology problem dictate the limitations of numerical accuracy while the mechanics problem is more vulnerable to locking effects due to the choice of tetrahedral finite elements.The model is further used to investigate how a dispersion of fiber stress into the sheet and sheetnormal directions changes mechanical biomarkers of the left ventricle.In an idealized model of the left ventricle, additional stress in the sheetnormal direction promoted a more physiological contraction with respect to ejection fraction, longitudinal shortening, wall thickening, and rotation.However, numerical results using the whole heart model revealed contradicting results compared to the idealized left ventricle.In a second project, in vivo measurements of electromechanical parameters in 30 patients suffering from heart failure with reduced ejection fraction and left bundle branch block were integrated into the left ventricular model to shed light on the clinical hypothesis that local electromechanical alterations change the left ventricular rotation pattern.Simulation results could not verify this hypothesis and showed no correlation between the electromechanical parameters and rotation.Next, the impact of standard ablation strategies for the treatment of atrial fibrillation on cardiovascular performance is evaluated in a four-chamber heart model.Due to the scars in the left atrium, the electrical activation and stiffness of the myocardium was altered resulting in a reduction of atrial stroke volume that depends linearly on the amount of inactivated tissue.Additionally, atrial pressure was increased depending on the stiffness of the scar tissue and ventricular function was only affected slightly.Finally, pathological mechanisms related to heart failure in patients with dilated cardiomyopathy are introduced into the whole heart model one by one to differentiate their individual contribution.The numerical results showed that cellular remodeling, especially the one affecting electrophysiology, is mainly responsible for the poor mechanical activity of the heart in patients with dilated cardiomyopathy.Furthermore, structural remodeling and an increased stiffness of the myocardium as well as adaptations of the circulatory system were necessary to replicate in vivo observations.In conclusion, this work presents a numerical framework for the approximation of electromechanical whole heart models including the circulatory system.The framework was verified with the use of simple problem definitions, validated using magnetic resonance imaging data, and used to answer clinical questions that would otherwise be impossible to address in real world scenarios.