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![a Representation of the multiscale cardiac muscle. b Anatomical dissection of myocardial fibers in ventricles (top) and atria (bottom). Images taken and readapted from [54–57]. Images were available either freely under a Creative Commons Attribution license or have been granted reuse permission by the copyright holder](publication/369974190/figure/fig2/AS:11431281144714633@1681352556413/a-Representation-of-the-multiscale-cardiac-muscle-b-Anatomical-dissection-of-myocardial.png)
a Representation of the multiscale cardiac muscle. b Anatomical dissection of myocardial fibers in ventricles (top) and atria (bottom). Images taken and readapted from [54–57]. Images were available either freely under a Creative Commons Attribution license or have been granted reuse permission by the copyright holder
Source publication
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Background:
Modeling the whole cardiac function involves the solution of several complex multi-physics and multi-scale models that are highly computationally demanding, which call for simpler yet accurate, high-performance computational tools. Despite the efforts made by several research groups, no software for whole-heart fully-coupled cardiac si...
Contexts in source publication
Context 1
... schematic representation of the multiscale myocardial fiber-structure is shown in Fig. 2. Ventricular muscular fibers are well-organized as two intertwined spirals wrapping the heart around, defining the characteristic myocardial helical structure [20,21]. Local orientation of myofibers is identified by their angle on the tangent plane and on the normal plane of the heart, called the helical and the sheet angles, ...Context 2
... in a regular pattern [18]. Indeed, myofibers in the atria are arranged in individual bundles running along different directions throughout the wall chambers [23,24]. Preferred orientation of myofibers in the human atria is characterized by multiple overlapping structures, which promote the formation of separate attached bundles [25], as shown in Fig. 2. The cardiac muscular fiber architecture is the backbone of a proper pumping function and has a strong influence on the electric signal propagation throughout the myocardium and also on the mechanical contraction of the muscle [26][27][28][29]. This motivates the need to accurately include fibers orientation in cardiac computational ...Citations
... (B) APDs across the ventricular wall, as measured in sheep. Adapted under Creative Commons license[4,227,277]. ...
... In a cylindrical reference domain with a structured solid grid, this can be easily facilitated with a cylindrical coordinate system. A radial coordinate can be defined in patient-specific geometries, e.g., by solving a diffusion problem commonly used in cardiac geometries [48]. ...
Equilibrated fluid-solid-growth (FSGe) is a fast, open source, three-dimensional (3D) computational platform for simulating interactions between instantaneous hemodynamics and long-term vessel wall adaptation through growth and remodeling (G&R). Such models are crucial for capturing adaptations in health and disease and following clinical interventions. In traditional G&R models, this feedback is modeled through highly simplified fluid models, neglecting local variations in blood pressure and wall shear stress (WSS). FSGe overcomes these inherent limitations by strongly coupling the 3D Navier-Stokes equations for blood flow with a 3D equilibrated constrained mixture model (CMMe) for vascular tissue G&R. CMMe allows one to predict long-term evolved mechanobiological equilibria from an original homeostatic state at a computational cost equivalent to that of a standard hyperelastic material model. In illustrative computational examples, we focus on the development of a stable aortic aneurysm in a mouse model to highlight key differences in growth patterns and fluid-solid feedback between FSGe and solid-only G&R models. We show that FSGe is especially important in blood vessels with asymmetric stimuli. Simulation results reveal greater local variation in fluid-derived WSS than in intramural stress (IMS). Thus, differences between FSGe and G&R models became more pronounced with the growing influence of WSS relative to pressure. Future applications in highly localized disease processes, such as for lesion formation in atherosclerosis, can now include spatial and temporal variations of WSS.
... All numerical methods presented here are available as open source within the core module of life x [1, 41], a library based on deal.II [5,6,21] for finite element simulations of the cardiac function [2][3][4]. ...
Multiphysics simulations frequently require transferring solution fields between subproblems with non-matching spatial discretizations, typically using interpolation techniques. Standard methods are usually based on measuring the closeness between points by means of the Euclidean distance, which does not account for curvature, cuts, cavities or other non-trivial geometrical or topological features of the domain. This may lead to spurious oscillations in the interpolant in proximity to these features. To overcome this issue, we propose a modification to rescaled localized radial basis function (RL-RBF) interpolation to account for the geometry of the interpolation domain, by yielding conformity and fidelity to geometrical and topological fieatures. The proposed method, referred to as RL-RBF-G, relies on measuring the geodesic distance between data points. RL-RBF-G removes all oscillations appearing in the RL-RBF interpolant, resulting in increased accuracy in domains with complex geometries. We demonstrate the effectiveness of RL-RBF-G interpolation through a convergence study in an idealized setting. Furthermore, we discuss the algorithmic aspects and the implementation of RL-RBF-G interpolation in a distributed-memory parallel framework, and present the results of a strong scalability test yielding nearly ideal results. Finally, we show the effectiveness of RL-RBF-G interpolation in multiphysics simulations by considering an application to a whole-heart cardiac electromecanics model.
... This facilitates the separate analysis of (i) the effects of myocardial deformation on EP propagation within the heart and, consequently, on the ECG, and (ii) of the impact of shifting the torso domain shape, and thus the position of the electrical sources in the body, according to the myocardial displacement. The proposed computational framework leverages high-performance computing to enable large-scale simulations, making use of the C++ finite element library life x [63,64,65]. ...
... We carry out EM and CFD simulations in life x [113,114,115,116] 2 , a high-performance C++ FE library developed within the iHEART project 3 , mainly focused on cardiac simulations and based on the deal.II finite element core [117,118,119]. ...
... Most of the simulations based on such models have been carried out in a high-performance computing environment, using the finite element software library life x (https://lifex.gitlab.io/) (99)(100)(101)(102). For the integration of clinical imaging data into the computational models, specific image-and surface-processing procedures have been devised and implemented based on VMTK (103,104), elastix (elastix.lumc.nl) ...
Background and Objective
Computational models of the cardiovascular system allow for a detailed and quantitative investigation of both physiological and pathological conditions, thanks to their ability to combine clinical—possibly patient-specific—data with physical knowledge of the processes underlying the heart function. These models have been increasingly employed in clinical practice to understand pathological mechanisms and their progression, design medical devices, support clinicians in improving therapies. Hinging upon a long-year experience in cardiovascular modeling, we have recently constructed a computational multi-physics and multi-scale integrated model of the heart for the investigation of its physiological function, the analysis of pathological conditions, and to support clinicians in both diagnosis and treatment planning. This narrative review aims to systematically discuss the role that such model had in addressing specific clinical questions, and how further impact of computational models on clinical practice are envisaged.
Methods
We developed computational models of the physical processes encompassed by the heart function (electrophysiology, electrical activation, force generation, mechanics, blood flow dynamics, valve dynamics, myocardial perfusion) and of their inherently strong coupling. To solve the equations of such models, we devised advanced numerical methods, implemented in a flexible and highly efficient software library. We also developed computational procedures for clinical data post-processing—like the reconstruction of the heart geometry and motion from diagnostic images—and for their integration into computational models.
Key Content and Findings
Our integrated computational model of the heart function provides non-invasive measures of indicators characterizing the heart function and dysfunctions, and sheds light on its underlying processes and their coupling. Moreover, thanks to the close collaboration with several clinical partners, we addressed specific clinical questions on pathological conditions, such as arrhythmias, ventricular dyssynchrony, hypertrophic cardiomyopathy, degeneration of prosthetic valves, and the way coronavirus disease 2019 (COVID-19) infection may affect the cardiac function. In multiple cases, we were also able to provide quantitative indications for treatment.
Conclusions
Computational models provide a quantitative and detailed tool to support clinicians in patient care, which can enhance the assessment of cardiac diseases, the prediction of the development of pathological conditions, and the planning of treatments and follow-up tests.
... Processing and meshing of Ω H and Ω T are carried out by means of the software library VMTK [64] and the open access Paraview software [65]. Solvers for the coupled model were implemented in the C++ library life x [66,67,68] based on the finite element core deal.II [69,70,71]. All the simulation are run at the CINECA high-performance computing center (Italy), employing 192 parallel processes on the GALILEO100 supercomputer 1 . ...
Computer-based simulations of non-invasive cardiac electrical outputs, such as electrocardiograms and body surface potential maps, usually entail severe computational costs due to the need of capturing fine-scale processes and to the complexity of the heart-torso morphology. In this work, we model cardiac electrical outputs by employing a coupled model consisting of a reaction-diffusion model - either the bidomain model or the most efficient pseudo-bidomain model - on the heart, and an elliptic model in the torso. We then solve the coupled problem with a segregated and staggered in-time numerical scheme, that allows for independent and infrequent solution in the torso region. To further reduce the computational load, main novelty of this work is in introduction of an interpolation method at the interface between the heart and torso domains, enabling the use of non-conforming meshes, and the numerical framework application to realistic cardiac and torso geometries. The reliability and efficiency of the proposed scheme is tested against the corresponding state-of-the-art bidomain-torso model. Furthermore, we explore the impact of torso spatial discretization and geometrical non-conformity on the model solution and the corresponding clinical outputs. The investigation of the interface interpolation method provides insights into the influence of torso spatial discretization and of the geometrical non-conformity on the simulation results and their clinical relevance.
... As part of the life x ecosystem, the software released in life x -ep has already been widely employed in combination with other modules for cardiac simulations (some of which publicly available: life x [13], life x -fiber [15] and life x -cfd [16], see also Fig. 1), including electrophysiology [17,18,19,20], mechanics [21,22,23], electromechanics [24,25,26,27], fluid dynamics [28,29,30,31,32,33,34,35], fluid-structure interaction [36], electro-mechano-fluid interaction [37,38] and myocardial perfusion [39,40]. This wide range of applications stands as a proof of the flexibility and usability of life x -ep. ...
... The solver also exhibits ideal scalability up to thousands of cores, as demonstrated in Section Strong scalability test, allowing to efficiently simulate large-scale scenarios. In addition to the numerical and programming features stemming from its foundation on life x , life x -ep offers two options for prescribing myocardial fibers, which can be either imported from a file or generated online taking advantage of the previous release life x -fiber [15], based on the Laplace-Dirichlet Rule-Based Methods (LDRBMs) presented in [17]. Moreover, it supports spatial heterogeneity in the choice of both models and physical coefficients, easily configurable through a convenient parameter file, without the need to access and modify the source code. ...
... The parameter file includes a dedicated section called Fiber generation, which serves the purpose of enabling the importing from a file of the myocardial fibers or the online generation of them on various geometry types, such as slabs, ventricles, and atria. To accomplish this, life x -ep incorporates the functionalities of its predecessor, life x -fiber [15], which utilizes the Laplace-Dirichlet Rule-Based Methods presented in [17]. This unique feature of life x -ep sets it apart from other existing software alternatives. ...
Simulating the cardiac function requires the numerical solution of multi-physics and multi-scale mathematical models. This underscores the need for streamlined, accurate, and high-performance computational tools. Despite the dedicated endeavors of various research teams, comprehensive and user-friendly software programs for cardiac simulations are still in the process of achieving full maturity within the scientific community. This work introduces lifex-ep, a publicly available software for numerical simulations of the electrophysiology activity of the cardiac muscle, under both physiological and pathological conditions. lifex-ep employs the monodomain equation to model the heart's electrical activity. It incorporates both phenomenological and second-generation ionic models. These models are discretized using the Finite Element method on tetrahedral or hexahedral meshes. Additionally, lifex-ep integrates the generation of myocardial fibers based on Laplace-Dirichlet Rule-Based Methods, previously released in Africa et al., 2023, within lifex-fiber. This paper provides a concise overview of the mathematical models and numerical methods underlying lifex-ep, along with comprehensive implementation details and instructions for users. lifex-ep features exceptional parallel speedup, scaling efficiently when using up to thousands of cores, and its implementation has been verified against an established benchmark problem for computational electrophysiology. We showcase the key features of lifex-ep through various idealized and realistic simulations. lifex-ep offers a user-friendly and flexible interface. lifex-ep provides easy access to cardiac electrophysiology simulations for a wide user community. It offers a computational tool that integrates models and accurate methods for simulating cardiac electrophysiology within a high-performance framework, while maintaining a user-friendly interface.
... All simulations discussed below are performed using life x , a C++ high-performance library for cardiac applications [68][69][70] based on the finite element core deal.II [39,71]. The RBF-F-SVD interpolation method is implemented in the life x core module, 2 available as open source under the GNU LGPLv3 license. ...
... All simulations discussed below are performed using life x , a C++ high-performance library for cardiac applications [1][2][3] based on the finite element core deal.II [6,7]. The computational domain is the left ventricle of the Zygote Heart Model [73], pre-processed using the techniques described in [22]. ...
The accurate robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. We present a novel method that combines rescaled localized Radial Basis Function (RBF) interpolation with Singular Value Decomposition (SVD) to preserve the positivity of the determinant of the deformation gradient tensor. The method involves decomposing the evaluations of the tensor at the quadrature nodes of the source mesh into rotation matrices and diagonal matrices of singular values; computing the RBF interpolation of the quaternion representation of rotation matrices and the singular value logarithms; reassembling the deformation gradient tensors at quadrature nodes of the destination mesh, to be used in the assembly of the electrophysiology model equations. The proposed method overcomes limitations of existing interpolation methods, including nested intergrid interpolation and RBF interpolation of the displacement field, that may lead to the loss of physical meaningfulness of the mathematical formulation and then to solver failures at the algebraic level, due to negative determinant values. The proposed method enables the transfer of solution variables between finite element spaces of different degrees and shapes and without stringent conformity requirements between different meshes, enhancing the flexibility and accuracy of electromechanical simulations. Numerical results confirm that the proposed method enables the transfer of the deformation gradient tensor, allowing to successfully run simulations in cases where existing methods fail. This work provides an efficient and robust method for the intergrid transfer of the deformation gradient tensor, enabling independent tailoring of mesh discretizations to the particular characteristics of the physical components concurring to the of the multiphysics model.
