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A key factor governing the mechanical performance of the heart is the bidirectional coupling with the vascular system, where alterations in vascular properties modulate the pulsatile load imposed on the heart. Current models of cardiac electromechanics (EM) use simplified 0D representations of the vascular system when coupling to anatomically accurate 3D EM models is considered. However, these ignore important effects related to pulse wave transmission. Accounting for these effects requires 1D models, but a 3D-1D coupling remains challenging. In this work, we propose a novel, stable strategy to couple a 3D cardiac EM model to a 1D model of blood flow in the largest systemic arteries. For the first time, a personalised coupled 3D-1D model of left ventricle and arterial system is built and used in numerical benchmarks to demonstrate robustness and accuracy of our scheme over a range of time steps. Validation of the coupled model is performed by investigating the coupled system’s physiological response to variations in the arterial system affecting pulse wave propagation, comprising aortic stiffening, aortic stenosis or bifurcations causing wave reflections. Our first 3D-1D coupled model is shown to be efficient and robust, with negligible additional computational costs compared to 3D-0D models. We further demonstrate that the calibrated 3D-1D model produces simulated data that match with clinical data under baseline conditions, and that known physiological responses to alterations in vascular resistance and stiffness are correctly replicated. Thus, using our coupled 3D-1D model will be beneficial in modelling studies investigating wave propagation phenomena.

Personalized models of cardiac electrophysiology (EP) that match clinical observation with high fidelity, referred to as cardiac digital twins (CDTs), show promise as a tool for tailoring cardiac precision therapies. Building CDTs of cardiac EP relies on the ability of models to replicate the ventricular activation sequence under a broad range of conditions. Of pivotal importance is the His–Purkinje system (HPS) within the ventricles. Workflows for the generation and incorporation of HPS models are needed for use in cardiac digital twinning pipelines that aim to minimize the misfit between model predictions and clinical data such as the 12 lead electrocardiogram (ECG). We thus develop an automated two stage approach for HPS personalization. A fascicular-based model is first introduced that modulates the endocardial Purkinje network. Only emergent features of sites of earliest activation within the ventricular myocardium and a fast-conducting sub-endocardial layer are accounted for. It is then replaced by a topologically realistic Purkinje-based representation of the HPS. Feasibility of the approach is demonstrated. Equivalence between both HPS model representations is investigated by comparing activation patterns and 12 lead ECGs under both sinus rhythm and right-ventricular apical pacing. Predominant ECG morphology is preserved by both HPS models under sinus conditions, but elucidates differences during pacing. Supplementary Information The online version contains supplementary material available at 10.1007/s10439-021-02825-9.

Objective: In this study, we have used whole heart simulations parameterized with large animal experiments to validate three techniques (two from the literature and one novel) for estimating epicardial and volumetric conduction velocity (CV). Methods: We used an eikonal-based simulation model to generate ground truth activation sequences with prescribed CVs. Using the sampling density achieved experimentally we examined the accuracy with which we could reconstruct the wavefront, and then examined the robustness of three CV estimation techniques to reconstruction related error. We examined a triangulation-based, inverse-gradient-based, and streamline-based techniques for estimating CV cross the surface and within the volume of the heart. Results: The reconstructed activation times agreed closely with simulated values, with 50-70% of the volumetric nodes and 97-99% of the epicardial nodes were within 1 ms of the ground truth. We found close agreement between the CVs calculated using reconstructed versus ground truth activation times, with differences in the median estimated CV on the order of 3-5% volumetrically and 1-2% superficially, regardless of what technique was used. Conclusion: Our results indicate that the wavefront reconstruction and CV estimation techniques are accurate, allowing us to examine changes in propagation induced by experimental interventions such as acute ischemia, ectopic pacing, or drugs. Significance: We implemented, validated, and compared the performance of a number of CV estimation techniques. The CV estimation techniques implemented in this study produce accurate, high-resolution CV fields that can be used to study propagation in the heart experimentally and clinically.

Background and ObjectiveCardiac electrophysiology is a medical specialty with a long and rich tradition of computational modeling. Nevertheless, no community standard for cardiac electrophysiology simulation software has evolved yet. Here, we present theopenCARPsimulation environment as one solution that could foster the needs of large parts of this community.Methods and ResultsopenCARPand the Python-basedcarputilsframework allow developing and sharing simulation pipelines which automatein silicoexperiments including all modeling and simulation steps to increase reproducibility and productivity. The continuously expandingopenCARPuser community is supported by tailored infrastructure. Documentation and training material facilitate access to this complementary research tool for new users. After a brief historic review, this paper summarizes requirements for a high-usability electrophysiology simulator and describes howopenCARPfulfills them. We introduce theopenCARPmodeling workflow in a multi-scale example of atrial fibrillation simulations on single cell, tissue, organ and body level and finally outline future development potential.ConclusionAs an open simulator,openCARPcan advance the computational cardiac electrophysiology field by making state-of-the-art simulations accessible. In combination with thecarputilsframework, it offers a tailored software solution for the scientific community and contributes towards increasing use, transparency, standardization and reproducibility ofin silicoexperiments.

Introduction Acute myocardial ischemia occurs when coronary perfusion to the heart is inadequate, which can perturb the highly organized electrical activation of the heart and can result in adverse cardiac events including sudden cardiac death. Ischemia is known to influence the ST and repolarization phases of the ECG, but it also has a marked effect on propagation (QRS); however, studies investigating propagation during ischemia have been limited. Methods We estimated conduction velocity (CV) and ischemic stress prior to and throughout 20 episodes of experimentally induced ischemia in order to quantify the progression and correlation of volumetric conduction changes during ischemia. To estimate volumetric CV, we 1) reconstructed the activation wavefront; 2) calculated the elementwise gradient to approximate propagation direction; and 3) estimated conduction speed (CS) with an inverse-gradient technique. Results We found that acute ischemia induces significant conduction slowing, reducing the global median speed by 20 cm/s. We observed a biphasic response in CS (acceleration then deceleration) early in some ischemic episodes. Furthermore, we noted a high temporal correlation between ST-segment changes and CS slowing; however, when comparing these changes over space, we found only moderate correlation (corr. = 0.60). Discussion This study is the first to report volumetric CS changes (acceleration and slowing) during episodes of acute ischemia in the whole heart. We showed that while CS changes progress in a similar time course to ischemic stress (measured by ST-segment shifts), the spatial overlap is complex and variable, showing extreme conduction slowing both in and around regions experiencing severe ischemia.

His bundle pacing (HBP) and left bundle pacing (LBP) are novel delivery methods for cardiac resynchronisation therapy (CRT) for left bundle branch block (LBBB) patients. Septal flash (SF), an abnormal pre-ejection motion of the septum towards the left ventricle (LV) arising from dyssynchronous activation, has been shown in the past to be a robust and independent predictor for CRT response. Although small-cohort studies showed the feasibility and efficacy of HBP and LBP, the effects of HBP and LBP on septal motion have yet to be investigated. In this study, we used our four-chamber heart electro-mechanics simulation framework to determine whether HBP and LBP can correct for SF. We performed simulations in four four-chamber heart models. In synchronous and LBBB activation, simulated mean lateral septal movement from the right ventricle (RV) into the LV was -0.4±0.5mm and - 3.7±0.9mm (p

Computer models of cardiac electro-mechanics (EM) show promise as an effective means for the quantitative analysis of clinical data and, potentially, for predicting therapeutic responses. To realize such advanced applications methodological key challenges must be addressed. Enhanced computational efficiency and robustness is crucial to facilitate, within tractable time frames, model personalization, the simulation of prolonged observation periods under a broad range of conditions, and physiological completeness encompassing therapy-relevant mechanisms is needed to endow models with predictive capabilities beyond the mere replication of observations. Here, we introduce a universal feature-complete cardiac EM modeling framework that builds on a flexible method for coupling a 3D model of bi-ventricular EM to the physiologically comprehensive 0D CircAdapt model representing atrial mechanics and closed-loop circulation. A detailed mathematical description is given and efficiency, robustness, and accuracy of numerical scheme and solver implementation are evaluated. After parameterization and stabilization of the coupled 3D–0D model to a limit cycle under baseline conditions, the model’s ability to replicate physiological behaviors is demonstrated, by simulating the transient response to alterations in loading conditions and contractility, as induced by experimental protocols used for assessing systolic and diastolic ventricular properties. Mechanistic completeness and computational efficiency of this novel model render advanced applications geared towards predicting acute outcomes of EM therapies feasible., Graphic abstract

Computational models of the heart are increasingly being used in the development of devices, patient diagnosis and therapy guidance. While software techniques have been developed for simulating single hearts, there remain significant challenges in simulating cohorts of virtual hearts from multiple patients. To facilitate the development of new simulation and model analysis techniques by groups without direct access to medical data, image analysis techniques and meshing tools, we have created the first publicly available virtual cohort of twenty-four four-chamber hearts. Our cohort was built from heart failure patients, age 6714 years. We segmented four-chamber heart geometries from end-diastolic (ED) CT images and generated linear tetrahedral meshes with an average edge length of 1.10.2mm. Ventricular fibres were added in the ventricles with a rule-based method with an orientation of -60 and 80 at the epicardium and endocardium, respectively. We additionally refined the meshes to an average edge length of 0.390.10mm to show that all given meshes can be resampled to achieve an arbitrary desired resolution. We ran simulations for ventricular electrical activation and free mechanical contraction on all 1.1mm-resolution meshes to ensure that our meshes are suitable for electro-mechanical simulations. Simulations for electrical activation resulted in a total activation time of 14916ms. Free mechanical contractions gave an average left ventricular (LV) and right ventricular (RV) ejection fraction (EF) of 351% and 302%, respectively, and a LV and RV stroke volume (SV) of 9528mL and 6511mL, respectively. By making the cohort publicly available, we hope to facilitate large cohort computational studies and to promote the development of cardiac computational electro-mechanics for clinical applications. (VLID)5215097 Version of record

International audience; The pericardium affects cardiac motion by limiting epicardial displacement normal to the surface. In computational studies, it is important for the model to replicate realistic motion, as this affects the physiological fidelity of the model. Previous computational studies showed that accounting for the effect of the pericardium allows for a more realistic motion simulation. In this study, we describe the mechanism through which the pericardium causes improved cardiac motion. We simulated electrical activation and contraction of the ventricles on a four-chamber heart in the presence and absence of the effect of the pericardium. We simulated the mechanical constraints imposed by the pericardium by applying normal Robin boundary conditions on the ventricular epicardium. We defined a regional scaling of normal springs stiffness based on image-derived motion from CT images. The presence of the pericardium reduced the error between simulated and image-derived end-systolic configurations from 12.8±4.1 mm to 5.7±2.5 mm. First, the pericardium prevents the ventricles from spherising during isovolumic contraction, reducing the outward motion of the free walls normal to the surface and the upwards motion of the apex. Second, by restricting the inward motion of the free and apical walls of the ventricles the pericardium increases atrioventricular plane displacement by four folds during ejection. Our results provide a mechanistic explanation of the importance of the pericardium in physiological simulations of electromechanical cardiac function.

Computational fluid dynamics (CFD) models of blood flow in the left ventricle (LV) and aorta are important tools for analyzing the mechanistic links between myocardial deformation and flow patterns. Typically, the use of image-based kinematic CFD models prevails in applications such as predicting the acute response to interventions which alter LV afterload conditions. However, such models are limited in their ability to analyze any impacts upon LV load or key biomarkers known to be implicated in driving remodeling processes as LV function is not accounted for in a mechanistic sense. This study addresses these limitations by reporting on progress made toward a novel electro-mechano-fluidic (EMF) model that represents the entire physics of LV electromechanics (EM) based on first principles. A biophysically detailed finite element (FE) model of LV EM was coupled with a FE-based CFD solver for moving domains using an arbitrary Eulerian-Lagrangian (ALE) formulation. Two clinical cases of patients suffering from aortic coarctations (CoA) were built and parameterized based on clinical data under pre-treatment conditions. For one patient case simulations under post-treatment conditions after geometric repair of CoA by a virtual stenting procedure were compared against pre-treatment results. Numerical stability of the approach was demonstrated by analyzing mesh quality and solver performance under the significantly large deformations of the LV blood pool. Further, computational tractability and compatibility with clinical time scales were investigated by performing strong scaling benchmarks up to 1536 compute cores. The overall cost of the entire workflow for building, fitting and executing EMF simulations was comparable to those reported for image-based kinematic models, suggesting that EMF models show potential of evolving into a viable clinical research tool.

Aortic valve disease (AVD) causes pressure overload of the left ventricle (LV) which may trigger adverse remodeling and, eventually, precipitate progression towards heart failure (HF). A frequent therapy is transvenous aortic valve implant (TAVI) which aims at reducing the transvalvular pressure gradient. However, TAVI does not always reverse HF symptoms. We aim to develop personalized computer models of LV electromechanics (EM), suitable for predicting acute TAVI-induced changes in LV function and derive clinical markers such as internal heart power (IHP) which are believed to offer prognostic value of longer term outcomes. EM simulations of a heartbeat fitted to pre-treatment conditions were carried out and validated against complementary clinical data that were not used for model fitting. Based on the assumption of a reduced transvalvular pressure gradient < 20 mmHg, a change in characteristic impedance of the aorta was estimated to simulate post-treatment conditions. IHP computed for pre- and post-treatment conditions was compared against the image-based clinical estimation of these quantities. All in silico models replicated clinical markers within prescribed margins of accuracy. Model predictions of IHP were comparable to the clinically derived analog.

The equation of interest in this work is the Richards equation which describes the flow of water in a porous medium. Since the equation contains two nonlinearities, stable and efficient methods have to be developed. In Berninger (ph.D. thesis, Freie Universitat Berlin, 2008) a monotone multigrid method is considered in the case of a homogeneous soil. In the case of a heterogeneous soil, domain decomposition methods are discussed. In this work a different approach is considered. As already mentioned, the Richards equation contains two nonlinearities. In Berninger et al. (Comput Geosci 19(1):213-232, 2015) and Schreiber (Nichtuberlappende Gebietszerlegungsmethoden fur lineare und quasilineare (monotone und nichtmonotone) Probleme, Universitat Kassel, 2009) the so called Kirchhoff transformation is used to shift one nonlinearity from the domain to the boundary in the homogeneous setting. To carry this idea over to the heterogeneous case, a different formulation is needed to ensure compatibility with the Kirchhoff transformation. The Primal–Hybrid formulation is used to derive such a formulation. After applying local Kirchhoff transformations a coupled system of equations with one nonlinearity within the domain and nonlinear coupling conditions is derived. To approximate the solution, the mortar finite element method is applied.

Institut fur Numerische Mathematik, TU Graz, Steyrergasse 30, 8010 Graz, AustriaWe consider the transformation of quasilinear partial differential equations to a coupled system of linear equations, but withnonlinear transmission conditions on the interfaces. After deriving a variational formulation, we will discuss Mortar finiteelement discretization strategies and present a numerical example.

Introduction: Stenotic aortic valve disease (AS) causes pressure overload of the left ventricle (LV) that may trigger adverse remodeling and precipitate progression towards heart failure (HF). As myocardial energetics can be impaired during AS, LV wall stresses and biomechanical power provide a complementary view of LV performance that may aide in better assessing the state of disease. Objectives: Using a high-resolution electro-mechanical (EM) in silico model of the LV as a reference, we evaluated clinically feasible Laplace-based methods for assessing global LV wall stresses and biomechanical power. Methods: We used N = 4 in silico finite element (FE) EM models of LV and aorta of patients suffering from AS. All models were personalized with clinical data under pre-treatment conditions. LV wall stresses and biomechanical power were computed accurately from FE kinematic data and compared to Laplace-based estimation methods which were applied to the same FE model data. Results and Conclusion: Laplace estimates of LV wall stress are able to provide a rough approximation of global mean stress in the circumferential-longitudinal plane of the LV. However, according to FE results spatial heterogeneity of stresses in the LV wall is significant, leading to major discrepancies between local stresses and global mean stress. Assessment of mechanical power with Laplace methods is feasible, but these are inferior in accuracy compared to FE models. The accurate assessment of stress and power density distribution in the LV wall is only feasible based on patient-specific FE modeling., Comment: This research was supported by the grants F3210-N18 and I2760-B30 from the Austrian Science Fund (FWF), the EU grant CardioProof agreement 611232 and a BioTechMed award to GP. Additionally, this project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie Action H2020-MSCA-IF-2016 InsiliCardio, GA No. 750835