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 1249 products
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85/2023 - 11/04/2023
Arnone, E.; De Falco, C.; Formaggia, L.; Meretti, G.; Sangalli, L.M.
Computationally efficient techniques for Spatial Regression with Differential Regularization | Abstract | | We investigate some computational aspects of an innovative class of PDE-regularized statistical models: Spatial Regression with Partial Differential Equation regularization (SR-PDE). These physics-informed regression methods can account for the physics of the underlying phenomena and handle data observed over spatial domains with nontrivial shapes, such as domains with concavities and holes or curved domains. The computational bottleneck in SR-PDE estimation is the solution of a computationally demanding linear system involving a low-rank but dense block. We address this aspect by innovatively using Sherman–Morrison–Woodbury identity. We also investigate the efficient selection of the smoothing parameter in SR-PDE estimates. Specifically, we propose ad hoc optimization methods to perform Generalized Cross-Validation, coupling suitable reformulation of key matrices, e.g., those based on Sherman–Morrison–Woodbury formula, with stochastic trace estimation, to approximate the equivalent degrees of freedom of the problem. These solutions permit high computational efficiency also in the context of massive data. |
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83/2023 - 11/02/2023
Cavinato, L.; Massi, M.C.; Sollini, M.; Kirienko , M.; Ieva, F.
Dual adversarial deconfounding autoencoder for joint batch-effects removal from multi-center and multi-scanner radiomics data | Abstract | | Medical imaging represents the primary tool for investigating and monitoring several diseases, including cancer. The advances in quantitative image analysis have developed towards the extraction of biomarkers able to support clinical decisions. To produce robust results, multi-center studies are often set up. However, the imaging information must be denoised from confounding factors—known as batch-effect—like scanner-specific and center-specific influences. Moreover, in non-solid cancers, like lymphomas, effective biomarkers require an imaging-based representation of the disease that accounts for its multi-site spreading over the patient’s body. In this work, we address the dual-factor deconfusion problem and we propose a deconfusion algorithm to harmonize the imaging information of patients affected by Hodgkin Lymphoma in a multi-center setting. We show that the proposed model successfully denoises data from domain-specific variability (p-value < 0.001) while it coherently preserves the spatial relationship between imaging descriptions of peer lesions (p-value = 0), which is a strong prognostic biomarker for tumor heterogeneity assessment. This harmonization step allows to significantly improve the performance in prognostic models with respect to state-of-the-art methods, enabling building exhaustive patient representations and delivering more accurate analyses (p-values < 0.001 in training, p-values < 0.05 in testing). This work lays the groundwork for performing large-scale and reproducible analyses on multi-center data that are urgently needed to convey the translation of imaging-based biomarkers into the clinical practice as effective prognostic tools. The code is available on GitHub at this https://github.com/LaraCavinato/Dual-ADAE. |
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82/2023 - 10/31/2023
Pozzi, G.; Ciarletta, P.
Geometric control by active mechanics of epithelial gap closure | Abstract | | Epithelial wound healing is one of the most important biological processes occurring during the lifetime of an organism. It is a self-repair mechanism closing wounds or gaps within tissues to restore
their functional integrity. In this work we derive a new diffuse interface approach for modelling the gap closure by means of a variational principle in the framework of non-equilibrium thermodynamics.
We investigate the interplay between the crawling with lamellipodia protrusions and the supracellular tension exerted by the actomyosin cable on the closure dynamics. These active features are modeled
as Korteweg forces into a generalised chemical potential. From an asymptotic analysis, we drive a pressure jump across the gap edge in the sharp interface limit. Moreover, the chemical potential diffuses
as a Mullins-Sekerka system, and its interfacial value is given by a Gibbs-Thompson relation for its local potential driven by the curvature-dependent purse-string tension. The Finite Element simulations show an excellent quantitative agreement between the closing dynamics and the morphology of the edge with respect to existing biological experiments. The resulting force patterns are also in good qualitative agreement with existing traction force microscopy measurements. Our results shed light on the geometrical control of the gap closure dynamics resulting from the active forces that are
chemically activated around the gap edge. |
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81/2023 - 10/31/2023
Buchwald, S.; Ciaramella, G; Salomon, J.; Sugny, D.
A SPIRED code for the reconstruction of spin distribution | Abstract | | In Nuclear Magnetic Resonance (NMR), it is of crucial importance to have
an accurate knowledge of the sample probability distribution corresponding to inhomogeneities of the magnetic fields. An accurate identification of the sample distribution requires a set of experimental data that is sufficiently rich to extract all fundamental information. These data depend strongly on the control fields (and their number) used experimentally. In this work, we present and analyze a greedy reconstruction algorithm, and provide the corresponding SPIRED code, for the computation of a set of control functions allowing the generation of data that are appropriate for the accurate reconstruction of a sample distribution. In particular, the focus is on NMR and the Bloch system with inhomogeneities in the magnetic fields in all spatial directions. Numerical examples illustrate this general study. |
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79/2023 - 10/18/2023
Agosti, A.; Bardin, R.; Ciarletta, P.; Grasselli, M.
A diffuse interface model of tumour evolution under a finite elastic confinement | Abstract | | Diffuse interface models have gained a growing interest in cancer research for their ability to investigate the mechano-biological features during tumour progression and to provide simulation tools for personalised anti-cancer strategies at an affordable computational cost. Here we propose a diffuse interface model for tumour evolution which accounts for an interfacial structure mimicking a finite elastic confinement at the tumour boundary, possibly due either to a localised elastic stress induced by host tissue displacements, or collagen remodelling in the peritumoral area. This model consists of a partial differential equation of the Cahn–Hilliard type, with degenerate mobility, single-well potential, and an elastic nonlocal term acting as the effect of a membrane confinement in the chemical potential. Using mixture theory, we derive the corresponding governing equations from thermodynamic principles based on realistic physical and biological assumptions. First, we introduce a suitable regularized problem in order to deal with the degeneracy set of the mobility and the singularity of the potential. For this problem we find a weak solution and provide a regularity result. Then we establish suitable a priori estimates which are uniform with respect to the regularization parameters. Passing to the limit in the regularized problem, we prove existence results for different classes of weak solutions to the original problem. Finally, we propose a continuous Galerkin Finite-Element discretization of the problem, where the positivity of the discrete solution is enforced through a variational inequality. Numerical simulations in a two-dimensional domain are also discussed in three test cases for illustrative purposes. |
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78/2023 - 10/12/2023
Antonietti, P.F.; Bonizzoni, F.; Corti, M.; Dall'Olio, A.
Discontinuous Galerkin for the heterodimer model of prion dynamics in Parkinson's disease | Abstract | | Neurodegenerative diseases have a significant global impact affecting millions of individuals worldwide. Some of them, known as proteinopathies, are characterized by the accumulation and propagation of toxic proteins, known as prions. Alzheimer's and Parkinson's diseases are relevant of protheinopathies. Mathematical models of prion dynamics play a crucial role in understanding disease progression and could be of help to potential interventions. This article focuses on the heterodimer model: a system of two partial differential equations that describe the evolution of healthy and misfolded proteins. In particular, we propose a space discretization based on a Discontinuous Galerkin method on polygonal/polyhedral grids, which provides flexibility in handling meshes of complex brain geometries. Concerning the semi-discrete formulation we prove stability and a-priori error estimates. Next, we adopt a theta-method scheme for time discretization. Some convergence tests are performed to confirm the theoretical bounds and the ability of the method to approximate travelling wave solutions. The proposed scheme is also tested to simulate the spread of alpha-synuclein in a realistic test case of Parkinson's disease in a two-dimensional sagittal brain section geometry reconstructed from medical images. |
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77/2023 - 10/11/2023
Fumagalli, I.; Corti, M.; Parolini, N.; Antonietti, P. F.
Polytopal discontinuous Galerkin discretization of brain multiphysics flow dynamics | Abstract | | A comprehensive mathematical model of the multiphysics flow of blood and Cerebrospinal Fluid (CSF) in the brain can be expressed as the coupling of a poromechanics system and Stokes' equations: the first describes fluids filtration through the cerebral tissue and the tissue's elastic response, while the latter models the flow of the CSF in the brain ventricles. This model describes the functioning of the brain's waste clearance mechanism, which has been recently discovered to play an essential role in the progress of neurodegenerative diseases. To model the interactions between different scales in the porous medium, we propose a physically consistent coupling between Multi-compartment Poroelasticity (MPE) equations and Stokes' equations. In this work, we introduce a numerical scheme for the discretization of such coupled MPE-Stokes system, employing a high-order discontinuous Galerkin method on polytopal grids to efficiently account for the geometric complexity of the domain. We analyze the stability and convergence of the space semidiscretized formulation, we prove a-priori error estimates, and we present a temporal discretization based on a combination of Newmark's beta-method for the elastic wave equation and the theta-method for the other equations of the model. Numerical simulations carried out on test cases with manufactured solutions validate the theoretical error estimates. We also present numerical results on a two-dimensional slice of a patient-specific brain geometry reconstructed from diagnostic images, to test in practice the advantages of the proposed approach. |
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76/2023 - 10/06/2023
Ieva, F.; Galliani, G.; Secchi, P.
The impact of public transport on the diffusion of COVID-19 pandemie in Lombardy during 2020 | Abstract | | In 2020, the COVID-19 pandemic has impacted the world, affecting health, economy, education, and social behavior. Much concern was raised about the role of mobility in the diffusion of the disease, with particular attention to public transport. lndeed, understanding the relationship between mobility and the pandemic is key for developing effective public health interventions and policy decisions.
In this work, we aim to understand how mobility, and more specifically mobility by public transport, has affected the diffusion of the pandemic at the regional scale. We focus our attention on Lombardy, the most populated ltalian region severely hit by the pandemic in 2020. We explore static mobility data provided by Regione Lombardia, the regional service district, and dynamic mobility data provided by Trenord, a railway operator which serves Lombardy and neighboring areas. We develop an inventive pipeline for the dynamic estimation of Origin-Destination matrices obtained from tickets and passenger counts. This allows us to spot potential triggers in pandemic diffusion enhanced by the concept of proximity induced by mobility. We also develop a novel perspective for assessing the relationship between mobility and overal1 mortality based upon a functional approach combined with a spatial correlation analysis aimed at identifying the diversified effects on mortality in smal1 geographical areas as a result. |
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