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.

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 [Formula: see text] 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 [Formula: see text] models with a typical hydrate and gas signature. Models of S-wave velocity [Formula: see text] containing a hydrate signature can only be reconstructed when the parameter distribution of [Formula: see text] is already well-known. When we add noise to the modeled data to simulate field-data conditions, it prevents the reconstruction of [Formula: see text] completely, justifying the application of an acoustic approach. We invert for [Formula: see text] 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 [Formula: see text] 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.

Over the last decades, computational models have been applied in in-silico simulations of the heart biomechanics. These models depend on input parameters. In particular, four parameters are needed for the constitutive law of Guccione 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 relationship. 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=7.1and bft=12A. In general, this approach allows to identify optimized parameters for a constitutive law, for a patient-specific heart geometry. 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.

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 associated 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 contrast 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 pathological 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 models 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 reduction 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 accurate diagnosis of HCM.

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.

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 T ref and three orthotropic activation parameters (K ss , K sn and K nn). 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 T ref and K nn while K ss 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 • .

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 approximation 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 reduced 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.

Background: The human heart is a masterpiece of the highest complexity coordinating multi-physics aspects on a multi-scale range. Thus, modeling the cardiac function in silico 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.Methods and Results: 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.Conclusion: 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.