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.

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. image 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).

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.

Evidence for gas-hydrate occurrence in the Western Black Sea is found from seismic measurements revealing bottom-simulating reflectors (BSRs) of varying distinctness. From an ocean-bottom seismic data set, low-resolution traveltime-tomography models of P-wave velocity VP are constructed. They serve as input for acoustic full-waveform inversion (FWI), which we apply to derive high-resolution parameter models aiding the interpretation of the seismic data for potential hydrate and gas deposits. Synthetic tests indicate the applicability of the FWI approach to robustly reconstruct VP models with a typical hydrate and gas signature. Models of S-wave velocity VS containing a hydrate signature can only be reconstructed when the parameter distribution of VS is already well-known. When we add noise to the modeled data to simulate field-data conditions, it prevents the reconstruction of VS completely, justifying the application of an acoustic approach. We invert for VP models from field data of two parallel profiles of 14 km length with a distance of 1 km. Results indicate a characteristic velocity trend for hydrate and gas occurrence at BSR depth in the first of the analyzed profiles. We find no indications for gas accumulations below the BSR on the second profile and only weak indications for hydrate. These differences in the VP signature are consistent with the reflectivity behavior of the migrated seismic streamer data of both profiles in which a zone of high-reflectivity amplitudes is coincident with the potential gas zone derived from the FWI result. Calculating saturation estimates for the potential hydrate and gas zones yields values of up to 30% and 1.2%, respectively.

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.

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 hemodynamic performance of the heart has not been investigated thoroughly. 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 scar affect atrial as well as ventricular contraction and relaxation. 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. This study provides biomechanical evidence that atrial ablation has acute effects not only on atrial contraction but also on ventricular pumping function. Our results have the potential to help tailoring ablation strategies towards minimal global hemodynamic impairment.