MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1287 products
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32/2021 - 06/02/2021
Sangalli, L.M.
Spatial regression with partial differential equation regularization | Abstract | | This work gives an overview of an innovative class of methods for the analysis of spatial and of functional data observed over complicated two-dimensional domains. This class is based on regression with regularizing terms involving partial differential equations. The associated estimation problems are solved resorting to advanced numerical analysis techniques. The synergical interplay of approaches from statistics, applied mathematics and engineering endows the methods with important advantages with respect to the available techniques, and makes them able to accurately deal with data structures for which the classical techniques are unfit. Spatial regression with differential regularization is illustrated via applications to the analysis of eco-color doppler measurements of blood-flow velocity, and to functional magnetic resonance imaging signals associated with neural connectivity in the cerebral cortex. |
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31/2021 - 06/02/2021
Ferraccioli, F.; Arnone, E.; Finos, L.; Ramsay, J.O.; Sangalli, L.M.
Nonparametric density estimation over complicated domains | Abstract | | We propose a nonparametric method for density estimation over
(possibly complicated) spatial domains. The method combines a likelihood approach with a regularization based on a di fferential operator. We demonstrate the good inferential properties of the method.
Moreover, we develop an estimation procedure based on advanced numerical techniques, and in particular making use of finite elements.
This ensures high computational efficiency and enables great
flexibility. The proposed method efficiently deals with data scattered over regions having complicated shapes, featuring complex boundaries, sharp
concavities or holes. Moreover, it captures very well complicated signals having multiple modes with di fferent directions and intensities of anisotropy. We show the comparative advantages of the proposed approach over state of the art methods, in simulation studies and in an
application to the study of criminality in the city of Portland, Oregon. |
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30/2021 - 06/01/2021
Fumagalli, I.
A reduced 3D-0D FSI model of the aortic valve including leaflets curvature | Abstract | | In the present work, we propose a novel lumped-parameter model for
the description of the aortic valve dynamics, including elastic effects associated to the leaflets’ curvature. The introduction of a lumped-parameter model based on momentum balance entails an easier calibration of the parameter models, that are instead typically numerous in phenomenologicalbased models. This model is coupled with 3D Navier-Stokes equations describing the blood flow, where the valve surface is represented by a resistive method, and valve leaflets velocity is taken into consideration.
The resulting reduced fluid-structure interaction problem has a computational cost that is comparable with the solution of a prescribed-motion fluid dynamics problem. A SUPG-PSPG stabilized finite element scheme is adopted for the discretization of the coupled problem, and the computational results show the suitability of the system in representing the leaflets motion, the blood flow in the ascending aorta, and the pressure jump across the leaflets. |
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29/2021 - 06/01/2021
Fumagalli, I.; Vitullo, P.; Scrofani, R.; Vergara, C.
Image-based computational hemodynamics analysis of systolic obstruction in hypertrophic cardiomyopathy | Abstract | | Hypertrophic Cardiomyopathy (HCM) is a pathological condition characterized by an abnormal thickening of the myocardium. When it affects the medio-basal portion of the septum, it is named Hypertrophic Obstructive Cardiomyopathy because it induces a flow obstruction in the left ventricle outflow tract, which may compromise the cardiac function and possibly lead to cardiac death.
In this work, we investigate the hemodynamics of different HCM patients by means of computational hemodynamics, aiming at quantifying the effects of this pathology on blood flow and pressure gradients and thus providing clinical indications that may help diagnosis and the design of surgical treatment (septal myectomy). To this aim, we employ an enhanced version of an image-based computational pipeline proposed in a previous work, integrating fluid dynamics simulations with geometrical and functional data reconstructed from standard cine-MRI acquisitions. Blood flow is modelled as an incompressible Newtonian fluid, The corresponding Navier-Stokes equations are solved in a moving domain obtained from cine-MRI, whereas the valve leaflets are accounted for by a resistive method. |
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28/2021 - 05/18/2021
Ferro, N.; Perotto, S.; Bianchi, D.; Ferrante, R.; Mannisi, M.
Design of cellular materials for multiscale topology optimization: application to patient-specific orthopedic devices | Abstract | | A flexible multiscale topology optimization methodology is introduced in order to associate different areas of the design domain with diverse microstructures extracted from a dictionary of optimized unit cells. The generation of the dictionary is carried out by exploiting microSIMPATY algorithm, which promotes the design of free-form layouts. The proposed methodology is particularized to the design of orthotic devices for the treatment of foot diseases. Different patient-specific settings drive the prototyping of customized insoles, which are numerically verified and successively validated in terms of mechanical performances and manufacturability. |
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27/2021 - 05/14/2021
Scimone, R.; Menafoglio, A.; Sangalli, L.M.; Secchi, P.
A look at the spatio-temporal mortality patterns in Italy during the COVID-19 pandemic through the lens of mortality densities | Abstract | | With the tools and perspective of Object Oriented Spatial Statistics, we analyze official daily data on mortality from all causes in the provinces and municipalities of Italy for the year 2020, the first of the COVID-19 pandemic. By comparison with mortality data from 2011 to 2019, we assess the local impact of the pandemic as perturbation factor of the natural spatio-temporal death process. For each Italian province, mortality data are represented by the densities of time of death in the year. Densities are regarded as functional data belonging to the Bayes space B^2 where we use functional-on-functional linear models to predict the expected mortality in 2020, based on mortality in previous years, and we compare predictions with actual observations to assess the impact of the pandemic. Through spatial downscaling of the provincial data down to the municipality level, we identify spatial clusters characterized by mortality densities anomalous with respect to those predicted based on mortality data of the nearby areas. This analysis pipeline could be extended to indexes different from death counts, measured at a granular spatio-temporal scale, and used as proxies for quantifying the local disruption generated by the pandemic. |
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26/2021 - 05/14/2021
Vigano, L.; Sollini, M.; Ieva, F.; Fiz, F.; Torzilli, G.
Chemotherapy-Associated Liver Injuries: Unmet Needs and New Insights for Surgical Oncologists | Abstract | | Chemotherapy-associated liver injuries (CALI) were the focus of several research studies some years ago when they were associated with modern treatments for colorectal metastases and operative outcomes of liver resection. An intensive, multidisciplinary commitment was designed to elucidate their pathogenesis, risk factors, clinical impact, diagnosis, and prevention. CALI are still part of our clinical practice and clinicians have further reasons to pursue CALI diagnosis.
This is mandatory to assess the effectiveness of any measure to reduce or prevent liver injuries. Second, diagnosis is needed in case of recurrent disease when patients require new chemotherapy lines and repeated surgery.
CALI are crucial to predict tolerance to treatment and operative risks. Finally, the identification of CALI is needed as long as they have some oncological impact. Even if not associated with prognosis, some studies highlighted an inverse relationship between CALI and response to chemotherapy (tumor regression is less evident in patients with severe injuries). |
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24/2021 - 04/26/2021
Regazzoni, F.; Chapelle, D.; Moireau, P.
Combining Data Assimilation and Machine Learning to build data-driven models for unknown long time dynamics - Applications in cardiovascular modeling | Abstract | | We propose a method to discover differential equations describing the long-term dynamics of phenomena featuring a multiscale behavior in time, starting from measurements taken at the fast-scale. Our methodology is based on a synergetic combination of Data Assimilation (DA), used to estimate the parameters associated with the known fast-scale dynamics, and Machine Learning (ML), used to infer the laws underlying the slow-scale dynamics. Specifically, by exploiting the scale separation between the fast and the slow dynamics, we propose a decoupling of time scales that allows to drastically lower the computational burden. Then, we propose a ML algorithm that learns a parametric mathematical model from a collection of time series coming from the phenomenon to be modeled. Moreover, we study the interpretability of the data-driven models obtained within the black-box learning framework proposed in this paper. In particular, we show that every model can be rewritten in infinitely many different equivalent ways, thus making intrinsically ill-posed the problem of learning a parametric differential equation starting from time series. Hence, we propose a strategy that allows to select a unique representative model in each equivalence class, thus enhancing the interpretability of the results. We demonstrate the effectiveness and noise-robustness of the proposed methods through several test cases, in which we reconstruct several differential models starting from time series generated through the models themselves. Finally, we show the results obtained for a test case in the cardiovascular modeling context, which sheds light on a promising field of application of the proposed methods. |
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