Publications de Alfio Quarteroni

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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 wi ...

We present a model for mechanical activation of the cardiac tissue depending on the evolution of the transmembrane electrical potential and certain gating/ionic variables that are available in most of electrophysiological descriptions of the cardiac membra ...

In this work we introduce a new two-level preconditioner for the efficient solution of large scale linear systems arising from the discretization of parametrized PDEs. The proposed preconditioner combines in a multiplicative way a reduced basis solver, which plays the role of coarse component, and a "traditional" fine grid preconditioner, such as one-level Additive Schwarz, block Gauss-Seidel or block Jacobi preconditioners. The coarse component is built up on a new Multi Space Reduced Basis (MSRB) method t

Two different approaches are proposed to enhance the efficiency of the numerical resolution of optimal control problems governed by a linear advection-diffusion equation. In the framework of the Galerkin-Finite Element (FE) method, we adopt a novel a posteriori error estimate of the discretization error on the cost functional; this estimate is used in the course of a numerical adaptive strategy for the generation of efficient grids for the resolution of the optimal control problem. Moreover, we propose to s

In this paper a family of one-dimensional nonlinear systems which model the blood pulse propagation in compliant arteries is presented and investigated. They are obtained by averaging the Navier-Stokes equation on each section of an arterial vessel and using simplified models for the vessel compliance. Different differential operators arise depending on the simplifications made on the structural model. Starting from the most basic assumption of pure elastic instantaneous equilibrium, which provides a well-k

In this paper, we present a mathematical model able to simulate the cardiac function. We first describe the basic physical principles behind the mathematical equations, then we illustrate a few examples of application to problems of clinical relevance. ...

Cardiovascular diseases are the first cause of death in industrialized countries. It is now widely established that blood fluid dynamics and its interaction with the vascular wall play an essential role in the development and evolution of vascular pathologies. Mathematical modeling and numerical simulation are precious tools which may help to understand biomechanical phenomena in both physiological and pathological states and can lead to the development of new therapies or to assist physicians in clinical d

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 ...

We investigate multilevel Schwarz domain decomposition preconditioners, to efficiently solve linear systems arising from numerical discretizations of elliptic partial differential equations by the finite element method. In our analysis we deal with unstruc ...

In this paper, we consider Large Eddy Simulations (LES) for human stenotic carotids in presence of atheromasic plaque. It is well known that in such a pathological condition, transitional effects to turbulence may occur, with relevant clinical implications such as plaque rupture. The first aim of this work is to provide a way to define a Direct Numerical Simulation (DNS). In our context turbulence is not statistically homogeneous isotropic and stationary. We define mesh size and time step by considering the

In this paper, we propose a multi-fidelity approach for parameter estimation problems based on Physics-Informed Neural Networks (PINNs). The proposed methods apply to models expressed by linear or nonlinear differential equations, whose parameters need to ...

In this paper, we propose the mathematical and finite element analysis of a second-order partial differential equation endowed with a generalized Robin boundary condition which involves the Laplace--Beltrami operator by introducing a function space $H^1(\O ...

We consider the numerical approximation of geometric Partial Differential Equations (PDEs) defined on surfaces in the 3D space. In particular, we focus on the geometric PDEs deriving from the minimization of an energy functional by L2L2-gradient flow. We a ...

Cardiocirculatory mathematical models are valuable tools for investigating both physiological and pathological conditions of the circulatory system. To assess an individual's clinical condition, these models must be tailored through parameter calibration. ...

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential, that is the polarization/depola ...

The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to ...

In this paper we address an unresolved problem in the numerical modeling of cardiac electromechanics, that is the onset of numerical oscillations due to the dependence of force generation models on the fibers shortening velocity. A way to avoid numerical o ...

In the cardiovascular system, morphology and functionality are closely related. Altered flow conditions play an important role in the development of arterial disease. In turn, these flow conditions are modified by arterial wall changes. A detailed understanding of the local hemodynamic environment, the influence of wall modifications on flow patterns and the long-term adaptations of the vascular wall after surgical procedures can have useful clinical applications, especially in view of reconstruction and re

A fast computational framework is devised to the study of several configurations of patient-specific coronary artery by-pass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patient-specific medical images to fast

We consider a fluid–structure interaction (FSI) problem discretized by finite elements featuring two different grids that do not necessarily agree on the interface separating the computational domain of the fluid from the one of the structure. After identifying a master domain (the structural domain) and a slave domain (the fluid domain), we build up two radial basis function (RBF) inter-grid operators, one Π_fs from master to slave, and the other Π_sf from slave to master. Then, we enforce the kinematic co

Alfio Quarteroni

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The role of computational methods in cardiovascular medicine: a narrative review

Active strain and activation models in cardiac electromechanics

MATHICSE Technical Report : Multi space reduced basis preconditioners for large-scale parametrized PDEs

Numerical approximation of a control problem for advection-diffusion processes

One-dimensional models for blood flow in arteries

A mathematical model of the human heart

Efficient Solution of Fluid-Structure Interaction Problems in Computational Hemodynamics

A Geometric Multiscale Model For The Numerical Simulation Of Blood Flow In The Human Left Heart

Multilevel Schwarz methods for elliptic partial differential equations

MATHICSE Technical Report : Large Eddy simulations for blood fluid-dynamics in real stenotic carotids

Numerical Analysis - A physics-informed multi-fidelity approach for the estimation of differential equations parameters in low-data or large-noise regimes

Well-Posedness, Regularity, and Convergence Analysis of the Finite Element Approximation of a Generalized Robin Boundary Value Problem

Isogeometric Analysis of geometric partial differential equations

Two New Calibration Techniques of Lumped-Parameter Mathematical Models for the Cardiovascular System

Deep learning-based reduced order models in cardiac electrophysiology

Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries

An oscillation-free fully staggered algorithm for velocity-dependent active models of cardiac mechanics

Computational vascular fluid dynamics: problems, models and methods

MATHICSE Technical Report : A fast virtual surgery platform for many scenarios haemo-dynamics of patient-specific coronary artery bypass grafts

A Fluid–Structure Interaction Algorithm Using Radial Basis Function Interpolation Between Non-Conforming Interfaces