Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1321 prodotti
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19/2024 - 22/02/2024
Torzoni, M.; Manzoni, A.; Mariani, S.
A multi-fidelity surrogate model for structural health monitoring exploiting model order reduction and artificial neural networks | Abstract | | Stochastic approaches to structural health monitoring (SHM) are often inevitably limited by computational constraints. For instance, for Markov chain Monte Carlo algorithms relying upon computationally expensive finite element models it is almost infeasible to sample the probability distribution of the structural state. To provide instead real-time procedures, this work proposes a non-intrusive surrogate modeling strategy, leveraging model order reduction and artificial neural networks. By relying upon a multi-fidelity (MF) framework, a composition of deep neural networks (DNNs) is devised to map damage and operational parameters onto time-dependent sensor recordings. Such an effective strategy is able to exploit datasets characterized by different fidelity levels without any prior assumption, allowing to blend a small high-fidelity (HF) dataset with a large low-fidelity (LF) dataset, ultimately alleviating the computational burden of supervised training while ensuring the accuracy of the approximated quantities of interest. The resulting surrogate model is made of an LF-DNN, which mimics sensor recordings in the undamaged condition, and of a long short-term memory HF-DNN, which adaptively refines the approximation with the effect of damage. An HF finite element model and an LF reduced order model are adopted offline to generate labeled training data of different fidelity, respectively in the presence or absence of a structural damage. Results relevant to an L-shaped cantilever beam and a portal frame railway bridge prove that the procedure efficiently provides remarkably accurate approximations, outperforming their single-fidelity counterparts. The capability of the MF-DNN to be exploited for SHM purposes is finally shown within an automated Bayesian procedure, aimed at updating the probability distribution of the structural state conditioned on sensor recordings, in the presence of operational variability and measurement noise. |
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17/2024 - 14/02/2024
Fois, M.; de Falco, C.; Formaggia, L.
A semi-conservative depth-averaged Material Point Method for fast flow-like landslides and mudflows | Abstract | | We present a two-dimensional semi-conservative variant of the depth averaged material point method (DAMPM) for modelling flow-like landslides. The mathematical model is given by the shallow water equations, derived from the depth-integration of the Navier-Stokes equations with the inclusion of an appropriate bed friction model and material rheology, namely Voellmy and the depth-integrated Bingham viscoplastic stress model, respectively. After assessing the accuracy and performance of the proposed numerical method by means of several idealised benchmarks, we test its behaviour in a realistic scenario. |
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16/2024 - 12/02/2024
Domanin D. A.; Pegoraro M.; Trimarchi S.; Domanin M.; Secchi P.
Persistence diagrams for exploring the shape variability of abdominal aortic aneurysms | Abstract | | Abdominal Aortic Aneurysm consists of a permanent dilation in the abodminal portion of the aorta and, along with its associated pathologies like calcifications and intraluminal thrombi, is one of the most important pathologies of the circulatory system. The shape of the aorta is among the primary drivers for these health issues, with particular reference to all the characteristics which affects the hemodynamics. Starting from the computed tomography angiography of a patient, we propose to summarize such information using tools derived from Topological Data Analysis, obtaining persistence diagrams which describe the irregularities of the lumen of the aorta. We showcase the effectiveness of such shape-related descriptors with a series of supervised and unsupervised case studies. |
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14/2024 - 09/02/2024
Zappon, E.; Salvador, M.; Piersanti, R.; Regazzoni, F.; Dede', L.; Quarteroni, A.
An integrated heart-torso electromechanical model for the simulation of electrophysiological outputs accounting for myocardial deformation | Abstract | | When generating in-silico clinical electrophysiological outputs, such as electrocardiograms (ECGs) and body surface potential maps (BSPMs), mathematical models have relied on single physics, i.e. of the cardiac electrophysiology (EP), neglecting the role of the heart motion. Since the heart is the most powerful source of electrical activity in the human body, its motion dynamically shifts the position of the principal electrical sources in the torso, influencing electrical potential distribution and potentially altering the EP outputs. In this work, we propose a computational model for the simulation of ECGs and BSPMs by coupling a cardiac electromechanical model with a model that simulates the propagation of the EP signal in the torso, thanks to a flexible numerical approach, that simulates the torso domain deformation induced by the myocardial displacement. Our model accounts for the major mechano-electrical feedbacks, along with unidirectional displacement and potential couplings from the heart to the surrounding body. For the numerical discretization, we employ a versatile intergrid transfer operator that allows for the use of different Finite Element spaces to be used in the cardiac and torso domains. Our numerical results are obtained on a realistic 3D biventricular-torso geometry, and cover both cases of sinus rhythm and ventricular tachycardia (VT), solving both the electromechanical-torso model in dynamical domains, and the classical electrophysiology-torso model in static domains. By comparing standard 12-lead ECG and BSPMs, we highlight the non-negligible effects of the myocardial contraction on the EP-outputs, especially in pathological conditions, such as the VT.
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15/2024 - 09/02/2024
Vaccaro, F.; Mauri, A.G.; Perotto, S.; Brivio, S.; Spiga, S.
Modeling and simulation of electrochemical and surface diffusion effects in filamentary cation-based resistive memory devices | Abstract | | Cation-based (or electrochemical) resistive memory devices are gaining increasing interest in neuromorphic applications due to their capability to emulate the dynamic behaviour of biological neurons and synapses. The utilization of such devices in neuromorphic systems necessitates a reliable physical model for the resistance switching mechanism, which is based on the formation and dissolution of a conductive filament in a thin dielectric layer, sandwiched between two metal electrodes.
We propose a comprehensive model to simulate the evolution of the filament geometry under the effect of both surface diffusion caused by curvature gradient and electromechanical stress, and mass injection due to electrodeposition of cations.
The model has been implemented in a C++ platform using a level-set approach based on a mixed finite element formulation, enriched by a mesh adaptation strategy to accurately and efficiently track the evolution of the filament shape.
The numerical scheme is initially validated on various benchmark case studies.
We then simulate the growth and self-dissolution of the filamentary geometry, incorporating an electrical model allowing a comparison with conventional cation-based memories. The simulations showcase filament formation under varying applied voltages and filament dissolution under different initial resistances. |
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12/2024 - 02/02/2024
Zingaro, A.; Ahmad, Z.; Kholmovski, E.; Sakata, K.; Dede', L.; Morris, A.K.; Quarteroni, A.; Trayanova, N.A.
A comprehensive stroke risk assessment by combining atrial computational fluid dynamics simulations and functional patient data | Abstract | | Stroke, a major global health concern often rooted in cardiac dynamics, demands precise risk evaluation for targeted intervention. Current risk models, like the CHA2DS2-VASc score, often lack the granularity required for personalized predictions. In this study, we present a nuanced and thorough stroke risk assessment by integrating functional insights from cardiac magnetic
resonance (CMR) with patient-specific computational fluid dynamics (CFD) simulations. Our cohort, evenly split between control and stroke groups, comprises eight patients. Utilizing CINE CMR, we compute kinematic features, revealing smaller left atrial volumes for stroke patients. The incorporation of patient-specific atrial displacement into our hemodynamic simulations unveils the influence of atrial compliance on the flow fields, emphasizing the importance of LA motion in CFD simulations and challenging the conventional rigid wall assumption in hemodynamics models. Standardizing hemodynamic features with functional metrics enhances the differentiation between stroke and control cases. While standalone assessments provide limited clarity, the synergistic fusion of CMR-derived functional data and patient-informed CFD simulations offers a personalized and mechanistic understanding, distinctly segregating stroke from control cases. Specifically, our investigation reveals a crucial clinical insight: normalizing hemodynamic features based on ejection fraction fails to differentiate between stroke and control patients. Differently, when normalized with stroke volume, a clear and clinically significant distinction emerges and this holds true for both the left atrium and its appendage, providing valuable implications for precise stroke risk assessment in clinical settings. This work introduces a novel framework for seamlessly integrating hemodynamic and functional metrics, laying the groundwork for improved predictive models, and highlighting the significance of motion-informed, personalized risk assessments. |
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11/2024 - 29/01/2024
Antonietti, P.F.; Corti, M.
Numerical modelling of protein misfolding in neurodegenerative diseases: a computational study | Abstract | | The spreading of misfolded proteins is a known hallmark in some neurodegenerative diseases, known as proteinopathies. A significant example is the tau protein, associated with many pathologies, such as Alzheimer's. In this work, we discuss and compare two different models for the mathematical modelling of protein misfolding, namely the heterodimer model and the Fisher-Kolmogorov model, as well as their numerical discretizations. We introduce a discontinuous Galerkin method on polygonal and polyhedral grids for space discretization to accurately simulate the wavefronts typically observed in the prionic spreading. Starting from the semidiscrete formulations, we use a Crank-Nicolson scheme to advance in time. Finally, we simulate the spreading of the misfolded tau protein in a two-dimensional brain slice in the sagittal plane with a polygonal agglomerated grid. The simulation is performed using both the presented models, and we compare the results and the differences deriving from the modelling choices. |
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10/2024 - 25/01/2024
Capuano E.; Regazzoni F.; Maines M.; Fornara S.; Locatelli V.; Catanzariti D.; Stella S.; Nobile F.; Del Greco M.; Vergara C.
Personalized Computational Electro-mechanics Simulations to Optimize Cardiac Resynchronization Therapy | Abstract | | In this study, we present a computational framework designed to evaluate virtual scenarios of Cardiac Resynchronization Therapy (CRT) and compare their effectiveness based on relevant clinical biomarkers. Our approach involves electro-mechanical numerical simulations calibrated, for patients with left bundle branch block, using data from Electro-Anatomical Mapping System (EAMS) measures, as well as ventricular pressures and volumes, both obtained pre-implantation. We validate the calibration by using EAMS data coming from right pacing conditions. Three patients with fibrosis and three without are considered to explore various conditions.
Our virtual scenarios consist of personalized numerical experiments, incorporating different positions of the left electrode along reconstructed epicardial veins; different locations of the right electrode; different ventriculo-ventricular delays. The aim is to offer a comprehensive tool capable of optimizing CRT efficiency for individual patients, by providing preliminary answers on optimal electrode placement and delay. |
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