# Alfio QuarteroniPolitecnico di Milano | Polimi · Department of Mathematics "Francesco Brioschi"

Alfio Quarteroni

Laurea in Mathematics, Laurea Honoris Causa in Naval Engineering

## About

929

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Introduction

## Publications

Publications (929)

We introduce Universal Solution Manifold Network (USM-Net), a surrogate model, based on Artificial Neural Networks (ANNs), which applies to differential problems whose solution depends on physical and geometrical parameters. We employ a mesh-less architecture, thus overcoming the limitations associated with image segmentation and mesh generation re...

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, a...

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 fu...

In this paper we propose a reduced order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two sub-problems with Dirichlet and Neumann interface conditions, respectively. After discretization by (e.g.) the...

In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically-based mathematical model, expressed by means of partial differential equations (PDEs), to carry out the task at hand. The goal is to...

This work dealt with the assessment of a computational tool to estimate the electrical activation in the left ventricle focusing on the latest electrically activated segment (LEAS) in patients with left bundle branch block and possible myocardial fibrosis. We considered the Eikonal-diffusion equation and to recover the electrical activation maps in...

We present a new model of human cardiac electromechanics for the left ventricle where electrophysiology is described by a Reaction–Eikonal model and which enables an off-line resolution of the reaction model, thus entailing a big saving of computational time. Subcellular dynamics is coupled with a model of tissue mechanics, which is in turn coupled...

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...

Purpose
Quantification of myocardial blood flow (MBF) and functional assessment of coronary artery disease (CAD) can be achieved through stress myocardial computed tomography perfusion (stress-CTP). This requires an additional scan after the resting coronary computed tomography angiography (cCTA) and administration of an intravenous stressor. This...

The numerical simulation of several virtual scenarios arising in cardiac mechanics poses a computational challenge that can be alleviated if traditional full-order models (FOMs) are replaced by reduced order models (ROMs). For example, in the case of problems involving a vector of input parameters related, e.g., to material coefficients, projection...

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 mes...

We propose a machine learning-based method to build a system of differential equations that approximates the dynamics of 3D electromechanical models for the human heart, accounting for the dependence on a set of parameters. Specifically, our method permits to create a reduced-order model (ROM), written as a system of Ordinary Differential Equations...

One of the major challenges of coupled problems is to manage nonconforming meshes at the interface between two models and/or domains, due to different numerical schemes or domains discretizations employed. Moreover, very often complex submodels depend on (e.g., physical or geometrical) parameters. Understanding how outputs of interest are affected...

Two crucial factors for accurate numerical simulations of cardiac electromechanics, which are also essential to reproduce the synchronous activity of the heart, are: (i) accounting for the interaction between the heart and the circulatory system that determines pressures and volumes loads in the heart chambers; (ii) reconstructing the muscular fibe...

Several epidemiological models have been proposed to study the evolution of COVID-19 pandemic. In this paper, we propose an extension of the SUIHTER model, to analyse the COVID-19 spreading in Italy, which accounts for the vaccination campaign and the presence of new variants when they become dominant. In particular, the specific features of the va...

Objectives
This study aimed to evaluate the progression of electrophysiological phenomena in a cohort of patients with paroxysmal atrial fibrillation (PAF) and persistent atrial fibrillation (PsAF).
Background
Electrical remodeling has been conjectured to determine atrial fibrillation (AF) progression.
Methods
High-density electroanatomic maps du...

In this paper we introduce the electromechanical mathematical model of the human heart. After deriving it from physical first principles, we discuss its mathematical properties and the way numerical methods can be set up to obtain numerical approximations of the (otherwise unachievable) mathematical solutions. The major challenges that we need to f...

In this paper we simulate the earthquake that hit the city of L’Aquila on the 6th of April 2009 using SPEED (SPectral Elements in Elastodynamics with Discontinuous Galerkin), an open-source code able to simulate the propagation of seismic waves in complex three-dimensional (3D) domains. Our model includes an accurate 3D reconstruction of the Quater...

Reducing the computational time required by high-fidelity, full order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. While FOMs, such as those based on the finite element method, provide valuable information of the cardiac mechanical functio...

We propose a novel mathematical and numerical model for cardiac electromechanics, wherein biophysically detailed core models describe the different physical processes concurring to the cardiac function. The core models, once suitably approximated, are coupled by a computationally efficient strategy. Our model is based on: (1) the combination of imp...

Modeling the whole cardiac function involves several complex multi-physics and multi-scale phenomena that are highly computationally demanding, which makes calling for simpler yet accurate, high-performance computational tools still a paramount challenge to be addressed. Despite all the efforts made by several research groups worldwide, no software...

Hypertrophic Cardiomyopathy (HCM) is a pathological condition characterized by an abnormal thickening of the myocardium. When affecting the medio-basal portion of the septum, it is named Hypertrophic Obstructive Cardiomyopathy (HOCM) because it induces a flow obstruction in the left ventricular outflow tract. In any type of HCM, the myocardial func...

Mechano-electric feedbacks (MEFs), which model how mechanical stimuli are transduced into electrical signals, have received sparse investigation by considering electromechanical simulations in simplified scenarios. In this paper, we study the effects of different MEFs modeling choices for myocardial deformation and nonselective stretch-activated ch...

We address numerical solvers for a poromechanics model particularly adapted for soft materials, as it generally respectsthermodynamics principles and energy balance. Considering the multi-physics nature of the problem, which involves solid andfluid species, interacting on the basis of mass balance and momentum conservation, we decide to adopt a sol...

We face a rigidity problem for the fractional $ p $-Laplace operator to extend to this new framework some tools useful for the linear case. It is known that $ (-\Delta)^s(1-|x|^{2})^s_+ $ and $ -\Delta_p(1-|x|^{\frac{p}{p-1}}) $ are constant functions in $ (-1, 1) $ for fixed $ p $ and $ s $. We evaluated $ (-\Delta_p)^s(1-|x|^{\frac{p}{p-1}})^s_+...

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 physiol...

Several epidemiological models have been proposed to study the evolution of COVID-19 pandemic. In this paper, we propose an extension of the SUIHTER model, first introduced in [Parolini et al, Proc R. Soc. A., 2021] to analyse the COVID-19 spreading in Italy, which accounts for the vaccination campaign and the presence of new variants when they bec...

Introduction
Electrogram (EGM) fractionation is often associated with diseased atrial tissue; however, mechanisms for fractionation occurring above an established threshold of 0.5 mV have never been characterized. We sought to investigate during sinus rhythm (SR) the mechanisms underlying bipolar EGM fractionation with high-density mapping in patie...

We face a rigidity problem for the fractional $p$-Laplace operator to extend to this new framework some tools useful for the linear case. It is known that $(-\Delta)^s(1-|x|^{2})^s_+$ and $-\Delta_p(1-|x|^{\frac{p}{p-1}})$ are constant functions in $(-1,1)$ for fixed $p$ and $s$. We evaluated $(-\Delta_p)^s(1-|x|^{\frac{p}{p-1}})^s_+$ proving that...

We construct an idealized computational model of the left human heart for the study of the blood flow dynamics in the left atrium and ventricle. We solve the Navier‐Stokes equations in the ALE formulation and we prescribe the left heart wall displacement based on physiological data; moreover, we consider the presence of both the mitral and aortic v...

Mechano-electric feedbacks (MEFs), which model how mechanical stimuli are transduced into electrical signals, have received sparse investigation by considering electromechanical simulations in simplified scenarios. In this paper, we study the effects of different MEFs modeling choices for myocardial deformation and nonselective stretch-activated ch...

We propose a machine learning-based method to build a system of differential equations that approximates the dynamics of 3D electromechanical models for the human heart, accounting for the dependence on a set of parameters. Specifically, our method permits to create a reduced-order model (ROM), written as a system of Ordinary Differential Equations...

We present a novel computational model for the numerical simulation of the blood flow in the human heart by focusing on 3D fluid dynamics of the left heart. With this aim, we employ the Navier-Stokes equations in an Arbitrary Lagrangian Eulerian formulation to account for the endocardium motion, and we model both the mitral and the aortic valves by...

This is the first chapter of a three-volume series dedicated to theory and application of Model Order Reduction (MOR). We motivate and introduce the basic concepts and notation, with reference to the two main cultural approaches to MOR: the system-theoretic approach employing state-space models and transfer function concepts (Volume 1), and the num...

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) for parametrized PDEs to speed up the solution of the aforementioned problems can be problemat...

Human-based computational models are a powerful tool that complements the experimental approaches and can improve our understanding of individual components
of the heart by integrating them into one system. This paper aims to couple and calibrate a human atrial electro-mechanical model to analyse the coupling effects and inotropic interventions on...

The COVID-19 epidemic is the latest in a long list of pandemics that have affected humankind in the last century. In this paper, we propose a novel mathematical epidemiological model named SUIHTER from the names of the seven compartments that it comprises: susceptible uninfected individuals ( S ), undetected (both asymptomatic and symptomatic) infe...

Two crucial factors for accurate numerical simulations of cardiac electromechanics, which are also essential to reproduce the synchronous activity of the heart, are: i) accounting for the interaction between the heart and the circulatory system that determines pressures and volumes loads in the heart chambers; ii) reconstructing the muscular fiber...

The results of numerical simulations of 3D cardiac electromechanical models are typically characterized by a long transient before reaching a periodic solution known as limit cycle. Since the only clinically relevant output is the one associated with such limit cycle, a long transient translates into a serious computational overhead. To accelerate...

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 t...

In the context of cardiac electrophysiology, we propose a novel computational approach to highlight and explain the long-debated mechanisms behind atrial fibrillation (AF) and to reliably numerically predict its induction and sustainment. A key role is played, in this respect, by a new way of setting a parametrization of electrophysiological mathem...

The results of numerical simulations of cardiac electromechanics are typically characterized by a long transient before reaching a periodic solution known as limit cycle. This yields a serious computational overhead, as the only clinically relevant output is associated with such limit cycle. To accelerate the convergence to the limit cycle, we prop...

We developed a novel patient-specific computational model for the numerical simulation of ventricular electromechanics in patients with ischemic cardiomyopathy (ICM). This model reproduces the activity both in sinus rhythm (SR) and in ventricular tachycardia (VT). The presence of scars, grey zones and non-remodeled regions of the myocardium is acco...

An analysis of the COVID-19 epidemic is proposed on the basis of the epiMOX dashboard (publicly accessible at https://www.epimox.polimi.it) that deals with data of the epidemic trends and outbreaks in Italy from late February 2020. Our analysis provides an immediate appreciation of the past epidemic development, together with its current trends by...

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 t...

We developed a novel patient-specific computational model for the numerical simulation of ventricular electromechanics in patients with ischemic cardiomyopathy (ICM). This model reproduces the activity both in sinus rhythm (SR) and in ventricular tachycardia (VT). The presence of scars, grey zones and non-remodeled regions of the myocardium is acco...

The importance of myocardial perfusion at the outset of cardiac disease remains largely understudied. To address this topic we present a mathematical model that considers the systemic circulation, the coronary vessels , the myocardium, and the interactions among these components. The core of the whole model is the description of the myocardium as a...