Abstract:

Background: Computer models for simulating cardiac electrophysiology are valuable tools for research and clinical applications. Traditional reaction-diffusion (RD) models used for these purposes are computationally expensive. While eikonal models offer a faster alternative, they are not well-suited to study cardiac arrhythmias driven by reentrant activity. The present work extends the diffusion-reaction eikonal alternant model (DREAM), incorporating conduction velocity (CV) restitution for simulating complex cardiac arrhythmias. Methods: The DREAM modifies the fast iterative method to model cyclical behavior, dynamic boundary conditions, and frequency-dependent anisotropic CV. Additionally, the model alternates with an approximated RD model, using a detailed ionic model for the reaction term and a triple-Gaussian to approximate the diffusion term. The DREAM and monodomain models were compared, simulating reentries in 2D manifolds with different resolutions. Results: The DREAM produced similar results across all resolutions, while experiments with the monodomain model failed at lower resolutions. CV restitution curves obtained using the DREAM closely approximated those produced by the monodomain simulations. Reentry in 2D slabs yielded similar results in vulnerable window and mean reentry duration for low CV in both models. In the left atrium, most inducing points identified by the DREAM were also present in the high-resolution monodomain model. DREAM's reentry simulations on meshes with an average edge length of 1600$\mu$m were 40x faster than monodomain simulations at 200$\mu$m. Conclusion: This work establishes the mathematical foundation for using the accelerated DREAM simulation method for cardiac electrophysiology. Cardiac research applications are enabled by a publicly available implementation in the openCARP simulator.

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:

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:

Atrial fibrillation (AF) is the most common supra-ventricular tachycardia. Despite not fully understanding all mechanisms leading to AF, atrial dilation and thus cellular stretch are identified as risk factors. It is suspected that the influence of stretch-activated ion channels (SACs) on electrophysiological cellular properties connects atrial stretch and the pathogenesis of AF, among other contributing factors. Therefore, this work investigates the possible relationship between SACs and AF in silico. In addition, this also provides a better understanding of SACs in general. For this purpose, a model was implemented that distinguished between a K+-selective component and a non-selective component. Then conditions were identified that triggered stretch-induced action potentials (APs) on the cellular level and in coupled whole heart simulations. In the specific case of a constant stretch application at the cellular level, a problematic time-dependent depolarization of the transmembrane voltage was observed. This issue is not yet critically discussed in literature but was addressed to be able to perform whole heart simulations with a physiological atrial pre-stretch of λ ≈ 1.10 m/m. Adaptations of the channel conductances for the non-selective SAC current and the rectifying K+ current (IK1) were required to overcome the problem of excited states in continuously stretched cells. On the tissue level, a homogeneous distribution of SACs was considered in healthy as well as in pathological conditions on a whole heart geometry. In healthy tissue, the impact of SACs was varied to understand the effects of this channel type. This was done by scaling the sensitivity of the channel conductance towards stretch which led to ectopic beats for GSAC,NS ≥ 0.39 nS/pF. Pathological tissue conditions were simulated with GSAC,NS = 0.33 nS/pF to prevent spontaneous activity. Additionally, different aspects of cardiac remodeling were considered to represent tissue adaptations in the presence of AF. No ectopic activity was triggered with an ionic remodeling due to a faster repolarization mainly attributed to the adapted channel conductance of IK1. Only a reduction of the tissue conductivity in the myocardium of the atria to 40 % of the healthy conductivity initiated extrasystoles. Simulations of reduced basic cycle lengths showed unphysiological behavior and, therefore, revealed a lack of ability of the current simulation setup towards investigations using increased heart rates. In summary, the myocardium in cranial regions as well as close to the atrioventricular valves was identified as vulnerable towards triggering stretch-induced APs and causing conduction blocks that could lead to chaotic ectopic excitation propagations. Therefore, this simulation setup might be able to initiate AF if reentries are present additionally. To conclude, the amount and timing of atrial stretch were identified as equally important contributors to ectopic activity. Additionally, the simulations provide evidence to support the presumed connection between SACs and AF.

Abstract:

As direct activators of the contractile apparatus of cardiac myocytes, calcium ions have a strong impact on the tension development of the heart. Therefore, the standard procedure for modelling the electromechanical coupling is based on the transfer of the calcium transient from the cell model to the force model. As a consequence, the coupling of various models can lead to significantly different trajectories of active tension due to diverging implementations of calcium dynamics. As this phenomenon is not to be expected in a healthy human heart, the aim of this thesis was to generate standardized tension development in coupled force- and cell models for atria and ventricles. The ventricular cell models according to O’Hara et al. [1], Tomek et al. [2] and Ten Tusscher and Panfilov [3] as well as the atrial models following Courtemanche et al. [4], Koivumäki et al. [5] and Maleckar et al. [6] were considered. The calcium sensitivity of the parameters of the force models according to Land et al. [7, 8] were evaluated by means of a sensitivity analysis and categorized by their influence on the active tension. Based on the findings obtained, a parameter optimization of the Land models was developed. The results obtained showed that standardized tension developments could only be achieved when coupling selected models. For the cell model according to Courtemanche et al. and all considered cell models of the ventricle the optimization using constant stretches in the interval λ = [0.85, 1.2] gave convincing results with an error ≤ 50 %. The error refers to the average relative error of each considered characteristic of the active tension. With the use of time-variable stretches, the optimization did not yield satisfactory results so far, because only Courtemanche et al. was found to be robust to changes in stretch with an error of 40.4 %. It could also be concluded that calcium transients with unusual behavior hamper the parameter optimization. The limitations of the optimization were confirmed by tissue simulations. With the simu- lations an alternative method for the re-parameterization of the force models was also investigated. However, the considered scaling of the parameter Tref showed a second contrac- tion in the atrium and a maximum force of ≈ 320 kPa in the ventricle. Thus, the optimization based on single cells was still the better method for generating physiologically justified tension development. Furthermore, the implementations of the cell models according to Courtemanche et al. and O’Hara et al. were adapted to take into account the sarcomere length dependent calcium binding to Troponin C (TnC) described in Land et al. To re-determine the calciumsensitive parameters, parameter estimation methods were developed based on the previously designed optimization. It was shown that the simulated intracellular calcium concentration of the rescaled feedback systems, regarding varying sarcomere lengths, partly behave in reverse to experimental findings. This might be explained by the insufficiently detailed implementation of the cell models with respect to the calcium handling.