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 1251 products
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28/2023 - 03/24/2023
Zingaro, A.; Vergara, C.; Dede', L.; Regazzoni, F.; Quarteroni, A.
A comprehensive mathematical model for myocardial perfusion | Abstract | | We present a novel mathematical model that simulates myocardial blood perfusion by embedding multiscale and multiphysics features. Our model incorporates cardiac electrophysiology, active and passive mechanics, hemodynamics, reduced valve modeling, and a multicompartment Darcy model of perfusion . We consider a fully coupled electromechanical model of the left heart that provides input for a fully coupled Navier-Stokes - Darcy Model for myocardial perfusion. The fluid dynamics problem is modeled in a left heart geometry that includes large epicardial coronaries, while the multicompartment Darcy model is set in a biventricular domain. Using a realistic and detailed cardiac geometry, our simulations demonstrate the accuracy of our model in describing cardiac perfusion, including myocardial blood flow maps. Additionally, we investigate the impact of a regurgitant aortic valve on myocardial perfusion, and our results indicate a reduction in myocardial perfusion due to blood flow taken away by the left ventricle during diastole. To the best of our knowledge, our work represents the first instance where electromechanics, hemodynamics, and perfusion are integrated into a single computational framework. |
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27/2023 - 03/22/2023
Beirao da Vega, L.; Canuto, C.; Nochetto, R.H.; Vacca, G.; Verani, M.
Adaptive VEM for variable data: convergence and optimality | Abstract | | We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization-free a posteriori error estimators recently derived in [8]. The crucial property, that also plays a central role in this paper, is that the stabilization term can be made arbitrarily small relative to the a posteriori error estimators upon increasing the stabilization parameter. Our AVEM concatenates two modules, GALERKIN and DATA. The former deals with piecewise constant data and is shown in [8] to be a contraction between consecutive iterates. The latter approximates general data by piecewise constants to a desired accuracy. AVEM is shown to be convergent and quasi-optimal, in terms of error decay versus degrees of freedom, for solutions and data belonging to appropriate approximation classes. Numerical experiments illustrate the interplay between these two modules and provide computational evidence of optimality |
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26/2023 - 03/18/2023
Artoni, A.; Antonietti, P.F.; Corradi, R.; Mazzieri, I.; Parolini, N.; Rocchi, D.; Schito P.; Semeraro, F.F.;
AeroSPEED: a high order acoustic solver for aeroacoustic applications | Abstract | | We propose AeroSPEED, a solver based on the Spectral Element Method (SEM) that solves the aeroacoustic Lighthill's wave equation. First, the fluid solution is computed employing a cell centered Finite Volume method. Then, AeroSPEED maps the sound source coming from the flow solution onto the acoustic grid, where finally the Lighthill's wave equation is solved.
An ad-hoc projection strategy is adopted to apply the flow source term in the acoustic solver.
A model problem with a manufactured solution and the Noise Box test case are used as benchmark for the acoustic problem. We studied the noise generated by the complex flow field around tandem cylinders as a relevant aeroacoustic application. AeroSPEED is an effective and accurate solver for both acoustics and aeroacoustic problems. |
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25/2023 - 03/16/2023
Bonetti, S.; Botti, M.; Mazzieri, I.; Antonietti, P.F.
Numerical modelling of wave propagation phenomena in thermo-poroelastic media via discontinuous Galerkin methods | Abstract | | We present and analyze a high-order discontinuous Galerkin method for the space discretization of the wave propagation model in thermo-poroelastic media. The proposed scheme supports general polytopal grids.
Stability analysis and hp-version error estimates in suitable energy norms are derived for the semi-discrete problem. The fully-discrete scheme is then obtained based on employing an implicit Newmark-$beta$ time integration scheme. A wide set of numerical simulations is reported, both for the verification of the theoretical estimates and for examples of physical interest. A comparison with the results of the poroelastic model is provided too, highlighting the differences between the predictive capabilities of the two models. |
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24/2023 - 03/02/2023
Costa, G.; Cavinato, L.; Fiz, F.; Sollini, M.; Chiti, A.; Torzilli, G.; Ieva, F.; Viganò, L.
Mapping Tumor Heterogeneity via Local Entropy Assessment: Making Biomarkers Visible | Abstract | | Advanced imaging and analysis improve prediction of pathology data and outcomes in several tumors, with entropy-based
measures being among the most promising biomarkers. However, entropy is often perceived as statistical data lacking
clinical significance. We aimed to generate a voxel-by-voxel visual map of local tumor entropy, thus allowing to (1) make
entropy explainable and accessible to clinicians; (2) disclose and quantitively characterize any intra-tumoral entropy heterogeneity; (3) evaluate associations between entropy and pathology data. We analyzed the portal phase of preoperative
CT of 20 patients undergoing liver surgery for colorectal metastases. A three-dimensional core kernel (5×5×5 voxels)
was created and used to compute the local entropy value for each voxel of the tumor. The map was encoded with a color
palette. We performed two analyses: (a) qualitative assessment of tumors’ detectability and pattern of entropy distribution;
(b) quantitative analysis of the entropy values distribution. The latter data were compared with standard Hounsfield data
as predictors of post-chemotherapy tumor regression grade (TRG). Entropy maps were successfully built for all tumors.
Metastases were qualitatively hyper-entropic compared to surrounding parenchyma. In four cases hyper-entropic areas
exceeded the tumor margin visible at CT. We identified four “entropic” patterns: homogeneous, inhomogeneous, peripheral rim, and mixed. At quantitative analysis, entropy-derived data (percentiles/mean/median/root mean square) predicted
TRG (p<0.05) better than Hounsfield-derived ones (p=n.s.). We present a standardized imaging technique to visualize
tumor heterogeneity built on a voxel-by-voxel entropy assessment. The association of local entropy with pathology data
supports its role as a biomarker. |
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23/2023 - 02/27/2023
Bertoletti, A.; Cannistrà, M.; Diaz Lema, M.; Masci, C.; Mergoni, A.; Rossi, L.; Soncin, M.
The Determinants of Mathematics Achievement: A Gender Perspective Using Multilevel Random Forest | Abstract | | This paper investigates the determinants of mathematics performance
by gender, exploiting a multilevel random forest approach. OECD PISA
2018 data from 28 European countries are employed to explore the performance
of male and female students as a function of students’ family
characteristics, their attitudes towards education, and class and school
environment. Results show that the gender gap in favour of boys persists
in most European countries. However, teacher and school practices like
fostering student reading and creating a cooperative environment allow
mitigating the influence of family background in countries without gender
gap. Policy implications to foster performance equality are provided. |
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22/2023 - 02/27/2023
Su, Y.; Riccobelli, D.; Chen, Y; Chen, W; Ciarletta, P
Tunable morphing of electroactive dielectric-elastomer balloons | Abstract | | Designing smart devices with tunable shapes has important applications in industrial manufacture. In this paper, we investigate the nonlinear deformation and the morphological transitions between buckling, necking, and snap-through instabilities of layered DE balloons in response to an applied radial voltage and an inner pressure. We propose a general mathematical theory of nonlinear electro-elasticity able to account for finite inhomogeneous strains provoked by the electro-mechanical coupling.
We investigate the onsets of morphological transitions of the spherically symmetric balloons using the surface impedance matrix method. Moreover, we study the nonlinear evolution of the bifurcated branches through finite element numerical simulations. Our analysis demonstrates the possibility to design tunable DE spheres, where the onset of buckling and necking can be controlled by geometrical and mechanical properties of the passive elastic layers. Relevant applications include soft robotics and mechanical actuators. |
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21/2023 - 02/26/2023
Cavinato, L.; Sollini, M.; Ragni, A.; Bartoli, F.; Zanca, R.; Pasqualetti, F.; Marciano, A.; Ieva, F.; and Erba, A.P.
Radiomics-based Inter-lesion Relation Network to Describe [18F]FMCH PET/CT Imaging Phenotypes in Prostate Cancer | Abstract | | Advanced image analysis, including radiomics, has recently acquired recognition as a source of biomarkers, although there are some technical and methodological challenges to face for its application in the clinic. Among others, proper phenotyping of metastatic or systemic disease where multiple lesions coexist is an issue, since each lesion contributes to characterization of the disease. Therefore, the radiomic profile of each lesion should be modeled into a more complex architecture able to reproduce each “unit” (lesion) as a part of the “entire” (patient). This work aimed to characterize intra-tumor heterogeneity underpinning metastatic prostate cancer using an exhaustive innovative approach which consist of a i) feature transformation method to build an agnostic (i.e., irrespective of pre-existence knowledge, experience, and expertise) radiomic pro-file of lesions extracted from [18F]FMCH PET/CT, ii) qualitative assessment of intra-tumor heterogeneity of patients, iii) quantitative representation of the intra-tumor heterogeneity of patients in terms of the relationship between their lesions’ profiles, to be associated with prognostic factors. We confirmed that metastatic prostate cancer patients encompassed lesions with different radio-mic profiles that exhibited intra-tumor radiomic heterogeneity and that the presence of many radiomic profiles within the same patient impacted the outcome. |
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