Publications de Alfio Quarteroni

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Medicine is one of the branches of scientific research in which numerical simulation can give a great support. In particular, a well mature branch like computational fluid dynamics (CFD) can provide a substantial help for the understanding of several pathologies of the cardiovascular system. The local behavior of blood flow may affect substantially the on-rise of such pathologies: a remarkable instance is atherosclerosis, which is unfortunately largely widespread in Western Countries. An accurate fluid dyna

In this paper, we propose a full computational pipeline to simulate the hemodynamics in the aorta including the valve. Closed and open valve surfaces, as well as the lumen aorta, are reconstructed directly from medical images using new ad hoc algorithms, allowing a patient-specific simulation. The fluid dynamics problem that accounts from the movement of the valve is solved by a new 3D-0D fluid-structure interaction model in which the valve surface is implicitly represented through level set functions, yiel

Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty Quantification Variational AutoEncoders (UQ-VAE), a class of neural networks, approximate the posterior distribution mean and covariance of model parameters. This allows for both the estimation of the parameters and their uncertainty in relation to the observational data. In

In this paper, we propose a monolithic algorithm for the numerical solution of the electromechanics model of the left ventricle in the human heart. Our coupled model integrates the monodomain equation with the Bueno-Orovio minimal model for electrophysiolo ...

We are interested in the approximation of partial differential equations on domains decomposed into two (or several) subdomains featuring non-conforming interfaces. The non-conformity may be due to different meshes and/or different polynomial degrees used from the two sides, or even to a geometrical mismatch. Across each interface, one subdomain is identified as master and the other as slave. We consider Galerkin methods for the discretization (such as finite element or spectral element methods) that make u

The Fisher-Kolmogorov equation is a diffusion-reaction PDE that models the accumulation of prionic proteins, which are responsible for many different neurological disorders. The most important and studied misfolded protein in literature is the Amyloid-beta ...

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 ...

The numerical simulation of multiple scenarios easily becomes computationally prohibitive for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models (FOMs). Likewise, the use of traditional reduced order models (ROMs) ...

This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities – which are mainly related either to nonlin ...

High fidelity (HF) mathematical models describing the generation of active force in the cardiac muscle tissue typically feature a large number of state variables to capture the intrinsically complex underlying subcellular mechanisms. With the aim of drasti ...

We consider the numerical approximation of high order Partial Differential Equations (PDEs) defined on surfaces in the three dimensional space, with particular emphasis on closed surfaces. We consider computational domains that can be represented by B-spli ...

Transcatheter aortic valve implantation (TAVI) is a minimally invasive intervention for the treatment of severe aortic valve stenosis. The main cause of failure is the structural deterioration of the implanted prosthetic leaflets, possibly inducing a valvu ...

The author discusses the development of mathematical models for the flow of blood in the human circulatory system. By necessity, such a model of a living system must include several simplifications, ignore some factors, and make several assumptions. This is not a simple fluid flow problem with a routine application of Navier-Stoke equations. There are several chemical reactions going on, there is a coupling between the fluid flow and the motion of the vessel wall. Moreover, the material of the vessel is not

Background: 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 ...

The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

In this paper we present a numerical tool to simulate dynamics of stratified sedimentary basins, i.e. depressions on the Earth’s surface filled by sediments. The basins are usually complicated by crustal deformations and faulting of the sediments. The bala ...

In this paper, we study the blood flow dynamics in a three-dimensional (3D) idealized left ventricle of the human heart whose deformation is driven by muscle contraction and relaxation in coordination with the action of the mitral and aortic valves. We propose a simplified but realistic mathematical treatment of the valves function based on mixed time-varying boundary conditions (BCs) for the Navier-Stokes equations modeling the flow. These switching in time BCs, from natural to essential and viceversa, mod

The simulation of the physiological loading situation of arteries with moderate atherosclerotic plaque may provide additional indicators for medical doctors to estimate if the plaque is likely to rupture and if surgical intervention is required. In particular the transmural stresses are important in this context. They depend strongly on the mechanical response and thus, a predictive material model capturing all characteristics of the material behavior is required. Here, polyconvex strain energy functions ar

The numerical modeling of solutes absorption processes by the arterial wall is of paramount interest for the understanding of the relationships between the local features of blood flow, the nourishing of the inner arterial wall by the blood solutes, and the pathologies that can appear when this process is for some reason perturbed. In the present work, two models for the solutes dynamics are investigated. In the first model, which is essentially based on the one introduced by Rappitsch and Perktold (1996) a

In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algor ...

Alfio Quarteroni

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Modeling and simulation of blood flow problems

MATHICSE Technical Report : A patient-specific aortic valve model based on moving resistive immersed implicit surfaces

Improvements on uncertainty quantification with variational autoencoders

A monolithic algorithm for the simulation of cardiac electromechanics in the human left ventricle

MATHICSE Technical Report : INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutations of PDEs on subdomains featuring non-conforming interfaces

Uncertainty quantification for Fisher-Kolmogorov equation on graphs with application to patient-specific Alzheimer's disease

lifex-fiber: an open tool for myofibers generation in cardiac computational models

POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium

Model order reduction in fluid dynamics: challenges and perspectives

Machine learning of multiscale active force generation models for the efficient simulation of cardiac electromechanics

Isogeometric Analysis of high order Partial Differential Equations on surfaces

Fluid-structure interaction analysis of transcatheter aortic valve implantation

Mathematical modelling of the cardiovascular system

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

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

An ALE-based numerical technique for modeling sedimentary basin evolution featuring layer deformations and faults

MATHICSE Technical Report : A complex blood flow patterns in an idealized left ventricle: a numerical study

Aspects of Arterial Wall Simulations: Nonlinear Anisotropic Material Models and Fluid Structure Interaction

Mathematical and numerical modeling of solute dynamics in blood flow and arterial walls

Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization