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 1268 prodotti
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54/2022 - 11/08/2022
Bucelli, M.; Zingaro, A.; Africa, P. C.; Fumagalli, I.; Dede', L.; Quarteroni, A.
A mathematical model that integrates cardiac electrophysiology, mechanics and fluid dynamics: application to the human left heart | Abstract | | We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our model accounts for the major feedback effects among the different processes that characterize the heart function, including electro-mechanical and mechano-electrical feedback as well as force-strain and force-velocity relationships. Moreover, it provides a three-dimensional representation of both the cardiac muscle and the hemodynamics, coupled in a fluid-structure interaction (FSI) model. By leveraging the multiphysics nature of the problem, we discretize it in time with a segregated electrophysiology-force generation-FSI approach, allowing for efficiency and flexibility in the numerical solution. We employ a monolithic approach for the numerical discretization of the FSI problem. We use finite elements for the spatial discretization of those partial differential equations that contribute to the model. We carry out a numerical simulation on a realistic human left heart model, obtaining results that are qualitatively and quantitatively in agreement with physiological ranges and medical images. |
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53/2022 - 28/07/2022
Antonietti, P.F; Cauzzi, C.; Mazzieri, I.; Melas L.; Stupazzini, M.
Numerical simulation of the Athens 1999 earthquake including simplified models of the Acropolis and the Parthenon: initial results and outlook | Abstract | | In this work we present a preliminary study of the seismic response of the Acropolis and of the Parthenon of Athens to the 1999 Mw 5.9 earthquake. The three-dimensional numerical model includes the surface topography of the Attica region, the seismogenic fault, and the most important geological units in the metropolitan area of Athens: the Acropolis hill and the Parthenon. The multiscale numerical model, designed in order to correctly propagate seismic waves up to $5Hz$, is solved through a discontinuous Galerkin spectral element method implemented in the open source library SPEED (speed.mox.polimi.it).
Numerical results show the effectiveness of this approach and highlight new challenges for dynamic soil-structure interaction problems at the regional scale. |
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52/2022 - 28/07/2022
Fedele, M.; Piersanti, R.; Regazzoni, F.; Salvador, M.; Africa, P. C.; Bucelli, M.; Zingaro, A.; Dede', L.; Quarteroni, A.
A comprehensive and biophysically detailed computational model of the whole human heart electromechanics | Abstract | | While ventricular electromechanics is extensively studied in both physiological and pathological conditions, 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 anatomy and a physiology that is strongly influenced by the ventricular function, developing computational models able to capture the physiological atrial function and atrioventricular interaction is very challenging. In this paper, we propose a biophysically detailed electromechanical model of the whole human heart that considers both atrial and ventricular contraction. Our model includes: i) an anatomically accurate whole-heart geometry; ii) a comprehensive myocardial fiber architecture; iii) a biophysically detailed microscale model for the active force generation; iv) a 0D closed-loop model of the circulatory system, fully-coupled with the mechanical model of the heart; v) the fundamental interactions among the different textit{core models}, such as the mechano-electric feedback or the fibers-stretch and fibers-stretch-rate feedbacks; vi) specific constitutive laws and model parameters for each cardiac region. Concerning the numerical discretization, we propose an efficient segregated-intergrid-staggered scheme and we employ recently developed stabilization techniques - regarding the circulation and the fibers-stretch-rate feedback - that are crucial to obtain a stable formulation in a four-chamber scenario. We are able to reproduce the healthy cardiac function for all the heart chambers, in terms of pressure-volume loops, time evolution of pressures, volumes and fluxes, and three-dimensional cardiac deformation, with unprecedented matching (to the best of our knowledge) with the expected physiology. We also show the importance of considering atrial contraction, fibers-stretch-rate feedback and suitable stabilization techniques, by comparing the results obtained with and without these features in the model. The proposed model represents the state-of-the-art electromechanical model of the iHEART ERC project - an Integrated Heart Model for the Simulation of the Cardiac Function - and is a fundamental step toward the building of physics-based digital twins of the human heart. |
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51/2022 - 28/07/2022
Losapio, D.; Scotti, A.
Local Embedded Discrete Fracture Model (LEDFM) | Abstract | | The study of flow in fractured porous media is a key ingredient for many geoscience applications, such as reservoir management and geothermal energy production. Modelling and simulation of these highly heterogeneous and geometrically complex systems require the adoption of non-standard numerical schemes. The Embedded Discrete Fracture Model (EDFM) is a simple and effective way to account for fractures with coarse and regular grids, but it suffers from some limitations: it assumes a linear pressure distribution around fractures, which holds true only far from the tips and fracture intersections, and it can be employed for highly permeable fractures only. In this paper we propose an improvement of EDFM which aims at overcoming these limitations computing an improved coupling between fractures and the surrounding porous medium by a) relaxing the linear pressure
distribution assumption, b) accounting for impermeable fractures modifying near-fracture transmissibilities. These results are achieved by solving different types of local problems with a fine conforming grid, and computing new transmissibilities (for connections between fractures and the surrounding porous medium and those through the porous medium itself near to the fractures). Such local problems are inspired from numerical upscaling techniques present in the literature. The new method is called Local Embedded Discrete Fracture Model (LEDFM) and the results obtained from several numerical tests confirm the aforementioned improvements. |
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50/2022 - 28/07/2022
Elías, A.; Jiménez, R.; Paganoni, A.M.; Sangalli, L.M.
Integrated Depths for Partially Observed Functional Data | Abstract | | Partially observed functional data are frequently encountered in applications and are the object of an increasing interest by the literature. We here address the problem of measuring the centrality of a datum in a partially observed functional sample. We propose an integrated functional depth for partially observed functional data, dealing with the very challenging case where partial observability can occur systematically on any observation of the functional dataset. In particular, differently f rom m any techniques f or partially observed functional data, we do not request that some functional datum is fully observed, nor we require that a common domain exist, where all of the functional data are recorded. Because of this, our proposal can also be used in those frequent situations where reconstructions methods and other techniques for partially observed functional data are inapplicable. By means of simulation studies, we demonstrate the very good performances the proposed depth on finite samples. Our proposal enables the use of benchmark methods based on depths, originally introduced for fully observed data, in the case of partially observed functional data. This include the functional boxplot, the outliergram and the depth vs depth classifiers. We illustrate our proposal on two case studies, the first concerning a problem of outlier detection in German electricity supply functions, the second regarding a classification problem with data obtained from medical imaging. |
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49/2022 - 18/07/2022
Botti, M.; Fumagalli, A.; Scotti, A.
Uncertainty quantification for mineral precipitation and dissolution in fractured porous media | Abstract | | In this work, we present an uncertainty quantification analysis to determine the influence and importance of some physical parameters in a reactive transport model in fractured porous media. An accurate description of flow and transport in the fractures is key to obtain reliable simulations, however,
fractures geometry and physical characteristics pose several challenges from both the modeling and implementation side. We adopt a mixed-dimensional approximation, where fractures and their intersections are represented as objects of lower dimension. To simplify the presentation, we consider only two
chemical species: one solute, transported by water, and one precipitate attached to the solid skeleton. A global sensitivity analysis to uncertain input data is performed exploiting the Polynomial Chaos expansion along with spectral projection methods on sparse grids. |
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48/2022 - 18/07/2022
Gregorio, C.; Barbati, G.; Ieva, F.
A wavelet-mixed landmark survival model for the effect of short-term oscillations in longitudinal biomarker’s profiles | Abstract | | Statistical methods to study the association between a longitudinal biomarker and the risk of death are very relevant for the long-term monitoring of frail subjects. In this context, sudden crises can cause the biomarker to undergo very abrupt changes. Although these oscillations are typically short-term, they often contain relevant prognostic information for the survival endpoint of interest. We propose a method that couples a linear mixed-model with a wavelet smoothing to extract both the long-term component and the short-term oscillations from the individual longitudinal biomarker profiles. We then use them as predictors in a landmark survival model to study their dynamic association with the risk of death. To illustrate the method, we use the clinical application which motivated our work, i.e., the monitoring of potassium in Heart Failure patients. The dataset consists of real-world data coming from the integration of Administrative Health Records with Outpatient and Inpatient Clinic E-chart. Our method not only allows us to identify the short-term oscillations but also reveals their prognostic role in predicting the risk of death, according to their duration and, demonstrating the importance of including such short-term oscillations into the modeling. Compared to standard landmark analyses and joint models, the proposed method achieves higher predictive performances. In the context of the potassium monitoring, our analysis has important clinical implications since it allows us to derive a dynamic score that can be used in clinical practice to assess the risk related to an observed patient's potassium trajectory. |
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47/2022 - 18/07/2022
Botti, M.; Di Pietro, D.A.; Salah, M.
A serendipity fully discrete div-div complex on polygonal meshes | Abstract | | In this work we address the reduction of face degrees of freedom (DOFs) for discrete elasticity complexes. Specifically, using serendipity techniques, we develop a reduced version of a recently introduced two-dimensional complex arising from traces of the three-dimensional elasticity complex. The keystone of the reduction process is a new estimate of symmetric tensor-valued polynomial fields in terms of boundary values, completed with suitable projections of internal values for higher degrees. We prove an extensive set of new results for the original complex and show that the reduced complex has the same homological and analytical properties as the original one. This paper also contains an appendix with proofs of general Poincar'e--Korn-type inequalities for hybrid fields. |
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