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 1238 prodotti
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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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09/2024 - 25/01/2024
Leimer Saglio, C. B.: Pagani, S.; Corti, M.; Antonietti, P. F.
A high-order discontinuous Galerkin method for the numerical modeling of epileptic seizures | Abstract | | Epilepsy is a clinical neurological disorder characterized by recurrent and spontaneous seizures consisting of abnormal high-frequency electrical activity in the brain.
In this condition, the transmembrane potential dynamics are characterized by rapid and sharp wavefronts traveling along the heterogeneous and anisotropic conduction pathways of the brain.
This work employs the monodomain model, coupled with specific neuronal ionic models characterizing ion concentration dynamics, to mathematically describe brain tissue electrophysiology in grey and white matter at the organ scale. This multiscale model is discretized in space with the high-order discontinuous Galerkin method on polygonal and polyhedral grids (PolyDG) and advanced in time with a Crank-Nicolson scheme. This ensures, on the one hand, efficient and accurate simulations of the high-frequency electrical activity that is responsible for epileptic seizure and, on the other hand, keeps reasonably low the computational costs by a suitable combination of high-order approximations and agglomerated polytopal meshes.
We numerically investigate synthetic test cases on a two-dimensional heterogeneous squared domain discretized with a polygonal grid, and on a two-dimensional brainstem in a sagittal plane with an agglomerated polygonal grid that takes full advantage of the flexibility of the PolyDG approximation of the semidiscrete formulation. Finally, we provide a theoretical analysis of stability and an a-priori convergence analysis for a simplified mathematical problem. |
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05/2024 - 24/01/2024
Conti, P.; Gobat, G.; Fresca, S.; Manzoni, A.; Frangi, A.
Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions | Abstract | | Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state solutions of PDEs for multiple combinations of control parameters and initial conditions. Therefore, constructing efficient reduced order models (ROMs) that enable accurate but fast predictions, while retaining the dynamical characteristics of the physical phenomenon as parameters vary, is of paramount importance. In this work, a data-driven, non-intrusive framework which combines ROM construction with reduced dynamics identification, is presented. Starting from a limited amount of full order solutions, the proposed approach leverages autoencoder neural networks with parametric sparse identification of nonlinear dynamics (SINDy) to construct a low-dimensional dynamical model. This model can be queried to efficiently compute full-time solutions at new parameter instances, as well as directly fed to continuation algorithms. These aim at tracking the evolution of periodic steady-state responses as functions of system parameters, avoiding the computation of the transient phase, and allowing to detect instabilities and bifurcations. Featuring an explicit and parametrized modeling of the reduced dynamics, the proposed data-driven framework presents remarkable capabilities to generalize with respect to both time and parameters. Applications to structural mechanics and fluid dynamics problems illustrate the effectiveness and accuracy of the proposed method. |
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06/2024 - 24/01/2024
Antonietti, P.F., Bonetti, S., Botti, M., Corti, M., Fumagalli, I., Mazzieri, I.
lymph: discontinuous poLYtopal methods for Multi-PHysics differential problems | Abstract | | We present the library lymph for the finite element numerical discretization of coupled multi-physics problems. lymph is a Matlab library for the discretization of partial differential equations based on high-order discontinuous Galerkin methods on polytopal grids (PolyDG) for spatial discretization coupled with suitable finite-difference time marching schemes. The objective of the paper is to introduce the library by describing it in terms of installation, input/output data, and code structure, highlighting -- when necessary -- key implementation aspects related to the method. A user guide, proceeding step-by-step in the implementation and solution of a Poisson problem, is also provided. In the last part of the paper, we show the results obtained for several differential problems, namely the Poisson problem, the heat equation, and the elastodynamics system. Through these examples, we show the convergence properties and highlight some of the main features of the proposed method, i.e. geometric flexibility, high-order accuracy, and robustness with respect to heterogeneous physical parameters. |
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