arXiv subjects

Alberto Zingaro

Publications and source records attributed to Alberto Zingaro.

13 recordsLinked to original sources

arXiv2026

Physics-Informed Neural Networks for the High-Resolution Reconstruction of Flow Measurement Indicators in Fluid Dynamics

Accurate, spatially resolved flow field measurements are essential for the reliable assessment of hemodynamic quantities in cardiovascular research and clinical practice. Experimental techniques, such as 4D flow MRI, PIV, or Doppler ultrasound, often yield data that are sparse, noisy, or under-resolved, particularly near vessel walls and in regions of complex flow. This limits the fidelity of distributed or derived hemodynamic indicators such as the wall shear stress and the clinical utility of such measurements. To address these challenges, we propose a physics-informed neural network (PINN) framework that integrates the incompressible Navier-Stokes equations with velocity measurements coming from experimental flow field data. By embedding physical laws into data, PINN enhances the reconstruction of velocity fields, enables the estimation of unmeasured quantities such as pressure and wall shear stress, and improves the spatial resolution of hemodynamic indicators. We show the effectiveness of our approach using both in silico and experimental data. First, we apply our method to the FDA nozzle benchmark, leveraging both control particle image velocimetry (PIV) measurements and computational fluid dynamics (CFD) simulations. Next, we apply our method to the more complex case of blood flow in an aneurysm model, exploiting in vitro 4D flow MRI data. In both cases, the synergy between data-driven learning and physics-based regularization yields results that align more closely with ground truth observations than standard CFD or pure data-driven approaches. Our findings highlight the potential of PINNs to improve the fidelity of under-resolved flow field measurements and yield spatially resolved hemodynamic indicators.

math.NA↗

arXiv2024

A Multi-Component, Multi-Physics Computational Model for Solving Coupled Cardiac Electromechanics and Vascular Haemodynamics

The circulatory system, comprising the heart and blood vessels, is vital for nutrient transport, waste removal, and homeostasis. Traditional computational models often treat cardiac electromechanics and blood flow dynamics separately, overlooking the integrated nature of the system. This paper presents an innovative approach that couples a 3D electromechanical model of the heart with a 3D fluid mechanics model of vascular blood flow. Using a file-based partitioned coupling scheme, these models run independently while sharing essential data through intermediate files. We validate this approach using solvers developed by separate research groups, each targeting disparate dynamical scales employing distinct discretisation schemes, and implemented in different programming languages. Numerical simulations using idealised and realistic anatomies show that the coupling scheme is reliable and requires minimal additional computation time relative to advancing individual time steps in the heart and blood flow models. Notably, the coupled model predicts muscle displacement and aortic wall shear stress differently than the standalone models, highlighting the importance of coupling between cardiac and vascular dynamics in cardiovascular simulations. Moreover, we demonstrate the model's potential for medical applications by simulating the effects of myocardial scarring on downstream vascular flow. This study presents a paradigm case of how to build virtual human models and digital twins by productive collaboration between teams with complementary expertise.

physics.flu-dyn↗

arXiv2024

Advancing aortic stenosis assessment: validation of fluid-structure interaction models against 4D flow MRI data

Systematic in vivo validations of computational models of the aortic valve remain scarce, despite successful validation against in vitro data. Utilizing a combination of computed tomography and 4D flow magnetic resonance imaging data, we developed patient-specific fluid-structure interaction models of the aortic valve immersed in the aorta for five patients in the pre-transcatheter aortic valve replacement configuration. Incorporating also an in vitro setup of the valve, our computational models are subjected to rigorous validation against 4D flow measurements. Our results demonstrate the models' capacity to accurately replicate flow dynamics within established ranges of uncertainties mainly arising from 4D flow noise. In addition, we illustrate how computational models can serve as valuable cross-checks to reduce noise and erratic behaviour of in vivo data. This study represents a significant step towards integrating in silico technologies into real clinical contexts, providing a robust framework for improving aortic stenosis diagnosis and the design of next-generation aortic valve bioprostheses.

physics.flu-dyn↗

arXiv2024

An electromechanics-driven fluid dynamics model for the simulation of the whole human heart

We introduce a multiphysics and geometric multiscale computational model, suitable to describe the hemodynamics of the whole human heart, driven by a four-chamber electromechanical model. We first present a study on the calibration of the biophysically detailed RDQ20 activation model (Regazzoni et al., 2020) that is able to reproduce the physiological range of hemodynamic biomarkers. Then, we demonstrate that the ability of the force generation model to reproduce certain microscale mechanisms, such as the dependence of force on fiber shortening velocity, is crucial to capture the overall physiological mechanical and fluid dynamics macroscale behavior. This motivates the need for using multiscale models with high biophysical fidelity, even when the outputs of interest are relative to the macroscale. We show that the use of a high-fidelity electromechanical model, combined with a detailed calibration process, allows us to achieve remarkable biophysical fidelity in terms of both mechanical and hemodynamic quantities. Indeed, our electromechanical-driven CFD simulations - carried out on an anatomically accurate geometry of the whole heart - provide results that match the cardiac physiology both qualitatively (in terms of flow patterns) and quantitatively (when comparing in silico results with biomarkers acquired in vivo). We consider the pathological case of left bundle branch block, and we investigate the consequences that an electrical abnormality has on cardiac hemodynamics thanks to our multiphysics integrated model. The computational model that we propose can faithfully predict a delay and an increasing wall shear stress in the left ventricle in the pathological condition. The interaction of different physical processes in an integrated framework allows us to faithfully describe and model this pathology, by capturing and reproducing the intrinsic multiphysics nature of the human heart.

math.NA↗

arXiv2023

lifex-cfd: an open-source computational fluid dynamics solver for cardiovascular applications

Computational fluid dynamics (CFD) is an important tool for the simulation of the cardiovascular function and dysfunction. Due to the complexity of the anatomy, the transitional regime of blood flow in the heart, and the strong mutual influence between the flow and the physical processes involved in the heart function, the development of accurate and efficient CFD solvers for cardiovascular flows is still a challenging task. In this paper we present lifex-cfd, an open-source CFD solver for cardiovascular simulations based on the lifex finite element library, written in modern C++ and exploiting distributed memory parallelism. We model blood flow in both physiological and pathological conditions via the incompressible Navier-Stokes equations, accounting for moving cardiac valves, moving domains, and transition-to-turbulence regimes. In this paper, we provide an overview of the underlying mathematical formulation, numerical discretization, implementation details and examples on how to use lifex-cfd. We verify the code through rigorous convergence analyses, and we show its almost ideal parallel speedup. We demonstrate the accuracy and reliability of the numerical methods implemented through a series of idealized and patient-specific vascular and cardiac simulations, in different physiological flow regimes. The lifex-cfd source code is available under the LGPLv3 license, to ensure its accessibility and transparency to the scientific community, and to facilitate collaboration and further developments.

physics.flu-dyn↗

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↗

arXiv2022

Impact of Atrial Fibrillation on Left Atrium Haemodynamics: A Computational Fluid Dynamics Study

We analyze left atrium haemodynamics, highlighting differences among healthy individuals and patients affected by atrial fibrillation. The computational study is based on patient-specific geometries of the left atria to simulate blood flow dynamics. We devise a novel procedure aimed at recovering the boundary conditions for the 3D haemodynamics simulations, particularly useful in absence of specific ones provided by clinical measurements. With this aim, we introduce a parametric definition of the atria displacement, and we employ a closed-loop lumped parameter model of the whole cardiocirculatory system conveniently tuned on the basis of the patient characteristics. We evaluate a number of fluid dynamics indicators for the atrial haemodynamics, validating our numerical results in terms of several clinical measurements; we investigate the impact of geometrical and clinical features on the risk of thrombosis. To analyse the correlation of thrombus formation with atrial fibrillation, coherently with the medical evidence, we propose a novel indicator, which we call age stasis and that arises from the combination of Eulerian and Lagrangian quantities. This indicator identifies regions where the slow flow cannot rinse the chamber properly, accumulating stale blood particles and creating optimal conditions for clot formation.

physics.flu-dyn↗

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

A Machine Learning approach to enhance the SUPG stabilization method for advection-dominated differential problems

We propose using machine learning and artificial neural networks (ANNs) to enhance residual-based stabilization methods for advection-dominated differential problems. Specifically, in the context of the finite element method, we consider the streamline upwind Petrov-Galerkin (SUPG) stabilization method and we employ ANNs to optimally choose the stabilization parameter on which the method relies. We generate our dataset by solving optimization problems to find the optimal stabilization parameters that minimize the distances among the numerical and the exact solutions for different data of differential problem and the numerical settings of the finite element method, e.g., mesh size and polynomial degree. The dataset generated is used to train the ANN, and we used the latter ``online'' to predict the optimal stabilization parameter to be used in the SUPG method for any given numerical setting and problem data. We show, by means of 1D and 2D numerical tests for the advection-dominated differential problem, that our ANN approach yields more accurate solution than using the conventional stabilization parameter for the SUPG method.

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↗