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:

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:

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.