arXiv subjects

Alfio Quarteroni

Publications and source records attributed to Alfio Quarteroni.

At least 37 records · Page 2Linked to original sources

arXiv2023

lifex-ep: a robust and efficient software for cardiac electrophysiology simulations

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.

math.NA↗

arXiv2023

Real-time whole-heart electromechanical simulations using Latent Neural Ordinary Differential Equations

Cardiac digital twins provide a physics and physiology informed framework to deliver predictive and personalized medicine. However, high-fidelity multi-scale cardiac models remain a barrier to adoption due to their extensive computational costs and the high number of model evaluations needed for patient-specific personalization. Artificial Intelligence-based methods can make the creation of fast and accurate whole-heart digital twins feasible. In this work, we use Latent Neural Ordinary Differential Equations (LNODEs) to learn the temporal pressure-volume dynamics of a heart failure patient. Our surrogate model based on LNODEs is trained from 400 3D-0D whole-heart closed-loop electromechanical simulations while accounting for 43 model parameters, describing single cell through to whole organ and cardiovascular hemodynamics. The trained LNODEs provides a compact and efficient representation of the 3D-0D model in a latent space by means of a feedforward fully-connected Artificial Neural Network that retains 3 hidden layers with 13 neurons per layer and allows for 300x real-time numerical simulations of the cardiac function on a single processor of a standard laptop. This surrogate model is employed to perform global sensitivity analysis and robust parameter estimation with uncertainty quantification in 3 hours of computations, still on a single processor. We match pressure and volume time traces unseen by the LNODEs during the training phase and we calibrate 4 to 11 model parameters while also providing their posterior distribution. This paper introduces the most advanced surrogate model of cardiac function available in the literature and opens new important venues for parameter calibration in cardiac digital twins.

math.NA↗

arXiv2023

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: application to cardiac electromechanics

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.

math.NA↗

arXiv2023

A mathematical model to assess the effects of COVID-19 on the cardiocirculatory system

Impaired cardiac function has been described as a frequent complication of COVID-19-related pneumonia. To investigate possible underlying mechanisms, we represented the cardiovascular system by means of a lumped-parameter 0D mathematical model. The model was calibrated using clinical data, recorded in 58 patients hospitalized for COVID-19-related pneumonia, to make it patient-specific and to compute model outputs of clinical interest related to the cardiocirculatory system. We assessed, for each patient with a successful calibration, the statistical reliability of model outputs estimating the uncertainty intervals. Then, we performed a statistical analysis to compare healthy ranges and mean values (over patients) of reliable model outputs to determine which were significantly altered in COVID-19-related pneumonia. Our results showed significant increases in right ventricular systolic pressure, diastolic and mean pulmonary arterial pressure, and capillary wedge pressure. Instead, physical quantities related to the systemic circulation were not significantly altered. Remarkably, statistical analyses made on raw clinical data, without the support of a mathematical model, were unable to detect the effects of COVID-19-related pneumonia, thus suggesting that the use of a calibrated 0D mathematical model to describe the cardiocirculatory system is an effective tool to investigate the impairments of the cardiocirculatory system associated with COVID-19.

math.NA↗

arXiv2023

Latent Dynamics Networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes

Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to yield predictions through the numerical approximation of high-dimensional systems of differential equations, thus calling for large-scale parallel computing platforms and requiring large computational costs. Data-driven approaches, instead, enable the description of systems evolution in low-dimensional latent spaces, by leveraging dimensionality reduction and deep learning algorithms. We propose a novel architecture, named Latent Dynamics Network (LDNet), which is able to discover low-dimensional intrinsic dynamics of possibly non-Markovian dynamical systems, thus predicting the time evolution of space-dependent fields in response to external inputs. Unlike popular approaches, in which the latent representation of the solution manifold is learned by means of auto-encoders that map a high-dimensional discretization of the system state into itself, LDNets automatically discover a low-dimensional manifold while learning the latent dynamics, without ever operating in the high-dimensional space. Furthermore, LDNets are meshless algorithms that do not reconstruct the output on a predetermined grid of points, but rather at any point of the domain, thus enabling weight-sharing across query-points. These features make LDNets lightweight and easy-to-train, with excellent accuracy and generalization properties, even in time-extrapolation regimes. We validate our method on several test cases and we show that, for a challenging highly-nonlinear problem, LDNets outperform state-of-the-art methods in terms of accuracy (normalized error 5 times smaller), by employing a dramatically smaller number of trainable parameters (more than 10 times fewer).

cs.LG↗

arXiv2023

A comprehensive mathematical model for cardiac perfusion

We present a novel mathematical model that simulates myocardial blood perfusion by embedding multiscale and multiphysics features. Our model incorporates cardiac electrophysiology, active and passive mechanics, hemodynamics, reduced valve modeling, and a multicompartment Darcy model of perfusion. We consider a fully coupled electromechanical model of the left heart that provides input for a fully coupled Navier-Stokes - Darcy Model for myocardial perfusion. The fluid dynamics problem is modeled in a left heart geometry that includes large epicardial coronaries, while the multicompartment Darcy model is set in a biventricular domain. Using a realistic and detailed cardiac geometry, our simulations demonstrate the accuracy of our model in describing cardiac perfusion, including myocardial blood flow maps. Additionally, we investigate the impact of a regurgitant aortic valve on myocardial perfusion, and our results indicate a reduction in myocardial perfusion due to blood flow taken away by the left ventricle during diastole. To the best of our knowledge, our work represents the first instance where electromechanics, hemodynamics, and perfusion are integrated into a single computational framework.

cs.CE↗

arXiv2023

A matrix-free high-order solver for the numerical solution of cardiac electrophysiology

We propose a matrix-free solver for the numerical solution of the cardiac electrophysiology model consisting of the monodomain nonlinear reaction-diffusion equation coupled with a system of ordinary differential equations for the ionic species. Our numerical approximation is based on the high-order Spectral Element Method (SEM) to achieve accurate numerical discretization while employing a much smaller number of Degrees of Freedom than first-order Finite Elements. We combine vectorization with sum-factorization, thus allowing for a very efficient use of high-order polynomials in a high performance computing framework. We validate the effectiveness of our matrix-free solver in a variety of applications and perform different electrophysiological simulations ranging from a simple slab of cardiac tissue to a realistic four-chamber heart geometry. We compare SEM to SEM with Numerical Integration (SEM-NI), showing that they provide comparable results in terms of accuracy and efficiency. In both cases, increasing the local polynomial degree $p$ leads to better numerical results and smaller computational times than reducing the mesh size $h$. We also implement a matrix-free Geometric Multigrid preconditioner that results in a comparable number of linear solver iterations with respect to a state-of-the-art matrix-based Algebraic Multigrid preconditioner. As a matter of fact, the matrix-free solver proposed here yields up to 45$\times$ speed-up with respect to a conventional matrix-based solver.

math.NA↗

arXiv2023

Let the paintings play

In this paper, we introduce a mathematical method to extract similarities between paintings and musical tracks. Our approach is based on the digitalization of both paintings and musical tracks by means of finite expansions in terms of orthogonal basis functions (with both Fourier and wavelet bases). The best fit between a specific painting and a sample of musical tracks from a given composer is achieved via an $L^2$ projection upon a finite-dimensional subspace. Several examples are provided for the analysis of a collection of works of art by the Italian artist Marcello Morandini. Finally, we have developed an original applet that implements the process above and which can be freely downloaded from the site https://github.com/pgerva/playing-paintings.git

cs.MM↗

arXiv2022

Optimized numerical solutions of SIRDVW multiage model controlling SARS-CoV-2 vaccine roll out: an application to the Italian scenario

In the context of SARS-CoV-2 pandemic, mathematical modelling has played a fundamental role for making forecasts, simulating scenarios and evaluating the impact of preventive political, social and pharmaceutical measures. Optimal control theory can be a useful tool based on solid mathematical bases to plan the vaccination campaign in the direction of eradicating the pandemic as fast as possible. The aim of this work is to explore the optimal prioritisation order for planning vaccination campaigns able to achieve specific goals, as the reduction of the amount of infected, deceased and hospitalized in a fixed time frame, among age classes. For this purpose, we introduce an age stratified SIR-like epidemic compartmental model settled in an abstract framework for modelling two-doses vaccination campaigns and conceived with the description of COVID19 disease. Overall, we formalize an optimal control framework adopting the model as state problem by acting on the administrations of vaccine-doses. An extensive campaign of numerical tests, featured in the Italian scenario and calibrated on available data from Dipartimento di Protezione Civile Italiana, shows that the presented framework can be a valuable tool to support the planning of vaccination campaigns minimizing specific goals.

math.OC↗

arXiv2022

An open tool based on lifex for myofibers generation in cardiac computational models

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 simulations in the scientific community has reached full maturity yet. In this work we present the first publicly released package of lifex, a high-performance Finite Element solver for multi-physics and multi-scale problems developed in the framework of the iHEART project. The goal of lifex is twofold. On the one side, it aims at making in silico experiments easily reproducible and accessible to a wide community of users, including those with a background in medicine or bio-engineering. On the other hand, as an academic research library lifex can be exploited by scientific computing experts to explore new mathematical models and numerical methods within a robust development framework. lifex has been developed with a modular structure and will be released bundled in different modules. The tool presented here proposes an innovative generator for myocardial fibers based on Laplace-Dirichlet Rule-Based Methods, which are the essential building blocks for modeling the electrophysiological, mechanical and electromechanical cardiac function, from single-chamber to whole-heart simulations. This report comes with an extensive technical and mathematical documentation to welcome new users to the core structure of a prototypical lifex application and to provide them with a possible approach to include the generated cardiac fibers into more sophisticated computational pipelines.

cs.MS↗

arXiv2022

Fast and robust parameter estimation with uncertainty quantification for the cardiac function

Parameter estimation and uncertainty quantification are crucial in computational cardiology, as they enable the construction of digital twins that faithfully replicate the behavior of physical patients. Robust and efficient mathematical methods must be designed to fit many model parameters starting from a few, possibly non-invasive, noisy observations. Moreover, the effective clinical translation requires short execution times and a small amount of computational resources. In the framework of Bayesian statistics, we combine Maximum a Posteriori estimation and Hamiltonian Monte Carlo to find an approximation of model parameters and their posterior distributions. To reduce the computational effort, we employ an accurate Artificial Neural Network surrogate of 3D cardiac electromechanics model coupled with a 0D cardiocirculatory model. Fast simulations and minimal memory requirements are achieved by using matrix-free methods, automatic differentiation and automatic vectorization. Furthermore, we account for the surrogate modeling error and measurement error. We perform three different in silico test cases, ranging from the ventricular function to the entire cardiovascular system, involving whole-heart mechanics, arterial and venous circulation. The proposed method is robust when high levels of signal-to-noise ratio are present in the quantities of interest in combination with a random initialization of the model parameters in suitable intervals. As a matter of fact, by employing a single central processing unit on a standard laptop and a few hours of computations, we attain small relative errors for all model parameters and we estimate posterior distributions that contain the true values inside the 90% credibility regions. With these benefits, our approach meets the requirements for clinical exploitation, while being compliant with Green Computing practices.

math.NA↗

arXiv2022

A stable loosely-coupled scheme for cardiac electro-fluid-structure interaction

We present a loosely coupled scheme for the numerical simulation of the cardiac electro-fluid-structure interaction problem, whose solution is typically computationally intensive due to the need to suitably treat the coupling of the different submodels. Our scheme relies on a segregated treatment of the subproblems, in particular on an explicit Robin-Neumann algorithm for the fluid-structure interaction, aiming at reducing the computational burden of numerical simulations. The results, both in an ideal and a realistic cardiac setting, show that the proposed scheme is stable at the regimes typical of cardiac simulations. From a comparison with a scheme with implicit fluid-structure interaction, it emerges that, while conservation properties are not fully preserved, computational times significantly benefit from the explicit scheme. Overall, the explicit discretization represents a good trade-off between accuracy and cost, and is a valuable alternative to implicit schemes for fast large-scale simulations.

math.NA↗

arXiv2022

Modeling isovolumetric phases in cardiac flows by an Augmented Resistive Immersed Implicit Surface Method

A major challenge in the computational fluid dynamics modeling of the heart function is the simulation of isovolumetric phases when the hemodynamics problem is driven by a prescribed boundary displacement. During such phases, both atrioventricular and semilunar valves are closed: consequently, the ventricular pressure may not be uniquely defined, and spurious oscillations may arise in numerical simulations. In this paper, we propose a suitable modification of the Resistive Immersed Implicit Surface (RIIS) method (Fedele et al., 2017) by introducing a reaction term to correctly capture the pressure transients during isovolumetric phases. The method, that we call Augmented RIIS (ARIIS) method, extends the previously proposed ARIS method (This et al., 2020) to the case of a mesh which is not body-fitted to the valves. We test the proposed method on two different benchmark problems, including a new simplified problem that retains all the characteristics of a heart cycle. We apply the ARIIS method to a fluid dynamics simulation of a realistic left heart geometry, and we show that ARIIS allows to correctly simulate isovolumetric phases, differently from standard RIIS method.

math.NA↗

arXiv2022

A mathematical model that integrates cardiac electrophysiology, mechanics and fluid dynamics: application to the human left heart

We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our model accounts for the major feedback effects among the different processes that characterize the heart function, including electro-mechanical and mechano-electrical feedback as well as force-strain and force-velocity relationships. Moreover, it provides a three-dimensional representation of both the cardiac muscle and the hemodynamics, coupled in a fluid-structure interaction (FSI) model. By leveraging the multiphysics nature of the problem, we discretize it in time with a segregated electrophysiology-force generation-FSI approach, allowing for efficiency and flexibility in the numerical solution. We employ a monolithic approach for the numerical discretization of the FSI problem. We use finite elements for the spatial discretization of those partial differential equations that contribute to the model. We carry out a numerical simulation on a realistic human left heart model, obtaining results that are qualitatively and quantitatively in agreement with physiological ranges and medical images.

math.NA↗

arXiv2022

A comprehensive and biophysically detailed computational model of the whole human heart electromechanics

While ventricular electromechanics is extensively studied, four-chamber heart models have only been addressed recently; most of these works however neglect atrial contraction. Indeed, as atria are characterized by a complex physiology influenced by the ventricular function, developing computational models able to capture the physiological atrial function and atrioventricular interaction is very challenging. In this paper, we propose a biophysically detailed electromechanical model of the whole human heart that considers both atrial and ventricular contraction. Our model includes: i) an anatomically accurate whole-heart geometry; ii) a comprehensive myocardial fiber architecture; iii) a biophysically detailed microscale model for the active force generation; iv) a 0D closed-loop model of the circulatory system; v) the fundamental interactions among the different core models; vi) specific constitutive laws and model parameters for each cardiac region. Concerning the numerical discretization, we propose an efficient segregated-intergrid-staggered scheme and we employ recently developed stabilization techniques that are crucial to obtain a stable formulation in a four-chamber scenario. We are able to reproduce the healthy cardiac function for all the heart chambers, in terms of pressure-volume loops, time evolution of pressures, volumes and fluxes, and three-dimensional cardiac deformation, with unprecedented matching (to the best of our knowledge) with the expected physiology. We also show the importance of considering atrial contraction, fibers-stretch-rate feedback and suitable stabilization techniques, by comparing the results obtained with and without these features in the model. The proposed model represents the state-of-the-art electromechanical model of the iHEART ERC project and is a fundamental step toward the building of physics-based digital twins of the human heart.

math.NA↗

arXiv2022

Hemodynamics of the heart's left atrium based on a Variational Multiscale-LES numerical method

In this paper, we investigate the hemodynamics of a left atrium (LA) by proposing a computational model suitable to provide physically meaningful fluid dynamics indications and detailed blood flow characterization. In particular, we consider the incompressible Navier-Stokes equations in Arbitrary Lagrangian Eulerian (ALE) formulation to deal with the LA domain under prescribed motion. A Variational Multiscale (VMS) method is adopted to obtain a stable formulation of the Navier-Stokes equations discretized by means of the Finite Element method and to account for turbulence modeling based on Large Eddy Simulation (LES). The aim of this paper is twofold: on one hand to improve the general understanding of blood flow in the human LA in normal conditions; on the other, to analyse the effects of the turbulence VMS-LES method on a situation of blood flow which is neither laminar, nor fully turbulent, but rather transitional as in LA. Our results suggest that if relatively coarse meshes are adopted, the additional stabilization terms introduced by the VMS-LES method allow to better predict transitional effects and cycle-to-cycle blood flow variations than the standard SUPG stabilization method.

physics.flu-dyn↗

arXiv2022

A geometric multiscale model for the numerical simulation of blood flow in the human left heart

We present a new computational model for the numerical simulation of blood flow in the human left heart. To this aim, we use the Navier-Stokes equations in an Arbitrary Lagrangian Eulerian formulation to account for the endocardium motion and we model the cardiac valves by means of the Resistive Immersed Implicit Surface method. To impose a physiological displacement of the domain boundary, we use a 3D cardiac electromechanical model of the left ventricle coupled to a lumped-parameter (0D) closed-loop model of the remaining circulation. We thus obtain a one-way coupled electromechanics-fluid dynamics model in the left ventricle. To extend the left ventricle motion to the endocardium of the left atrium and to that of the ascending aorta, we introduce a preprocessing procedure according to which an harmonic extension of the left ventricle displacement is combined with the motion of the left atrium based on the 0D model. To better match the 3D cardiac fluid flow with the external blood circulation, we couple the 3D Navier-Stokes equations to the 0D circulation model, obtaining a multiscale coupled 3D-0D fluid dynamics model that we solve via a segregated numerical scheme. We carry out numerical simulations for a healthy left heart and we validate our model by showing that meaningful hemodynamic indicators are correctly reproduced.

math.NA↗

arXiv2022

Universal Solution Manifold Networks (USM-Nets): non-intrusive mesh-free surrogate models for problems in variable domains

We introduce Universal Solution Manifold Network (USM-Net), a novel surrogate model, based on Artificial Neural Networks (ANNs), which applies to differential problems whose solution depends on physical and geometrical parameters. Our method employs a mesh-less architecture, thus overcoming the limitations associated with image segmentation and mesh generation required by traditional discretization methods. Indeed, we encode geometrical variability through scalar landmarks, such as coordinates of points of interest. In biomedical applications, these landmarks can be inexpensively processed from clinical images. Our approach is non-intrusive and modular, as we select a data-driven loss function. The latter can also be modified by considering additional constraints, thus leveraging available physical knowledge. Our approach can also accommodate a universal coordinate system, which supports the USM-Net in learning the correspondence between points belonging to different geometries, boosting prediction accuracy on unobserved geometries. Finally, we present two numerical test cases in computational fluid dynamics involving variable Reynolds numbers as well as computational domains of variable shape. The results show that our method allows for inexpensive but accurate approximations of velocity and pressure, avoiding computationally expensive image segmentation, mesh generation, or re-training for every new instance of physical parameters and shape of the domain.

math.NA↗