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 1268 products
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30/2022 - 05/09/2022
Bonetti S.; Botti M.; Antonietti P.F.
Discontinuous Galerkin approximation of the fully-coupled thermo-poroelastic problem | Abstract | | We present and analyze a discontinuous Galerkin method for the numerical modelling of the fully-coupled quasi-static thermo-poroelastic problem. In particular, for the space discretization we introduce a discontinuous Galerkin method over polygonal and polyhedral grids and we present the stability analysis via two different approaches: first exploiting the Poincarè's inequality and second using the generalized inf-sup condition. Error estimates are derived for the resulting semi-discrete formulation in a suitable mesh dependent energy norm. Numerical simulations are presented in order to validate the theoretical analysis and to show the application of the model to a realistic case test. |
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29/2022 - 05/03/2022
Fumagalli, I.; Polidori, R.; Renzi, F.; Fusini, L.; Quarteroni, A.; Pontone, G.; Vergara, C.
Fluid-structure interaction analysis of transcatheter aortic valve implantation | Abstract | | Transcatheter aortic valve implantation (TAVI) is a minimally invasive intervention for the treatment of severe aortic valve stenosis. The main cause of failure is the structural deterioration of the implanted prosthetic leaflets, possibly inducing a valvular re-stenosis 5-10 years after the implantation. Based solely on pre-implantation data, the aim of this work is to identify fluid-dynamics and structural indices that may predict the possible valvular deterioration, in order to assist the clinicians in the decision-making phase and in the intervention design. Patient-specific, preimplantation geometries of the aortic root, the ascending aorta, and the native valvular calcifications were reconstructed from computed tomography images. The
stent of the prosthesis was modeled as a hollow cylinder and virtually implanted in the reconstructed domain. The fluid-structure interaction between the blood flow, the stent, and the residual native tissue surrounding the prosthesis was simulated by a computational solver with suitable boundary conditions. Hemodynamical and structural indicators were analyzed for five different patients that underwent TAVI – three
with prosthetic valve degeneration and two without degeneration – and the comparison of the results showed a correlation between the leaflets' structural degeneration and the wall shear stress distribution on the proximal aortic wall. This investigation represents a first step towards computational predictive analysis of TAVI degeneration, based on pre-implantation data and without requiring additional peri-operative or follow-up information. Indeed, being able to identify patients more likely to experience degeneration after TAVI may help to schedule a patient-specific timing of follow-up. |
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28/2022 - 05/01/2022
Ciarletta, P.; Pozzi, G.; Riccobelli, D.
The Föppl–von Kármán equations of elastic plates with initial stress | Abstract | | Initially stressed plates are widely used in modern fabrication techniques, such as additive manufacturing and UV lithography, for their tunable morphology by application of external stimuli. In this work, we propose a formal asymptotic derivation of the Föppl–von Kármán equations for an elastic plate with initial stresses, using the constitutive theory of nonlinear elastic solids with initial stresses under the assumptions of incompressibility and material isotropy. Compared to existing works, our approach allows to determine the morphological transitions of the elastic plate without prescribing the underlying target metric of the unstressed state of the elastic body.
We explicitly solve the derived FvK equations in some physical problems of engineering interest, discussing how the initial stress distribution drives the emergence of spontaneous curvatures within the deformed plate. The proposed mathematical framework can be used to tailor shape on demand, with applications in several engineering fields ranging from soft robotics to 4D printing. |
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27/2022 - 04/27/2022
Lazzari J., Asnaghi R., Clementi L., Santambrogio M. D.
Math Skills: a New Look from Functional Data Analysis | Abstract | | Mental calculations involve various areas of the brain. The frontal, parietal and temporal lobes of the left hemisphere have a principal role in the completion of this typology of tasks. Their level of activation varies based on the mathematical competence and attentiveness of the subject under examination and the perceived difficulty of the task. Recent literature often investigates patterns of cerebral activity through fMRI, which is an expensive technique. In this scenario, EEGs represent a more straightforward and cheaper way to collect information regarding brain activity. In this work, we propose an EEG based method to detect differences in the cerebral activation level of people characterized by different abilities in carrying out the same arithmetical task. Our approach consists in the extraction of the activation level of a given region starting from the EEG acquired during resting state and during the completion of a subtraction task. We then analyze these data through Functional Data Analysis, a statistical technique that allows operating on biomedical signals as if they were functions. The application of this technique allowed for the detection of distinct cerebral patterns among the two groups and, more specifically, highlighted the presence of higher levels of activation in the parietal lobe in the population characterized by a lower performance. |
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26/2022 - 04/27/2022
Orlando, G.
A filtering monotonization approach for DG discretizations of hyperbolic problems | Abstract | | We introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. Following an approach already proposed for the Hamilton-Jacobi equations by other authors, we aim at reducing the spurious oscillations that arise in presence of discontinuities when high order spatial discretizations are employed. This goal is achieved using a filter function that keeps the high order scheme when the solution is regular and switches to a monotone low order approximation if it is not. The method has been implemented in the framework of the deal.II numerical library, whose mesh adaptation capabilities are also used to reduce the region in which the low order approximation is used. A number of numerical experiments demonstrate the potential of the proposed filtering technique. |
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25/2022 - 04/27/2022
Cavinato, L; Gozzi, N.; Sollini, M; Kirienko, M; Carlo-Stella, C; Rusconi, C; Chiti, A; Ieva, F.
Perspective transfer model building via imaging-based rules extraction from retrospective cancer subtyping in Hodgkin Lymphoma | Abstract | | Image texture analysis has for decades represented a promising opportunity for cancer assessment and disease progression evaluation, evolving over time in a discipline, i.e., radiomics. However, the road for a complete translation into clinical practice is still hampered by intrinsic limitations. As purely supervised classification models fails in devising univocal imaging-based differences in tumors with different prognosis, cancer subtyping approaches would benefit from the employment of distant supervision, for instance exploiting survival/recurrence information. In this work, we transfer our previous model for Hodgkin Lymphoma subtyping to a multi-center study case. We evaluated model performance in two independent datasets coming from two hospitals, comparing and analyzing the results. Our preliminary data confirmed the instability of radiomics due to across-center lack of reproducibility, leading to meaningful results in one center and poorer performance in the other. We then learnt stratification rules from the first dataset via Random Forest and leveraged those rules to transfer the stratification policy onto the second dataset. In this way, on the one hand, we tested the stratification ability of cancer subtyping in a validation setting and, on the other hand, enriched the noisier dataset with valuable information, in a borrowing strength fashion. The transfer of the model resulted successful. Moreover, having extracted decision rules for cancer subtyping, we were able to draw up risk factors to be considered in clinics. The work shows the potentialities of the proposed pipeline to be further evaluated in larger multi-center datasets, with the goal of translating radiomics into clinical practice. |
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24/2022 - 04/27/2022
Cappozzo, A.; McCrory, C.; Robinson, O.; Freni Sterrantino, A.; Sacerdote, C.; Krogh, V.; Panico, S.; Tumino, R.; Iacoviello, L.; Ricceri, F.; Sieri, S.; Chiodini, P.; Kenny, R.A.; O'Halloran, A.; Polidoro, S.; Solinas, G.; Vineis, P.; Ieva, F.; Fiorito, G.;
A blood DNA methylation biomarker for predicting short-term risk of cardiovascular events | Abstract | | Background. Evidence highlights the epidemiological value of DNA methylation (DNAm) for predicting cardiovascular diseases (CVDs). DNAm surrogates of exposures and risk factors predict diseases and longevity better than self-reported or measured exposures in many cases. Composite biomarkers based on DNAm surrogates, ‘next generation’ epigenetic clocks trained on time-to-death, constitute non-specific biomarkers representing the general health status rather than disease-specific signatures. Training a model on cardiovascular-specific risk factors may improve the identification of
high-risk populations for CVD.
Methods. We developed a DNAm-based biomarker predictive of short-term risk for CVD using a twostep approach: 1) development and validation of novel DNAm surrogates for cardiovascular risk
biomarkers; 2) development and validation of a DNAmCVDscore as a combination of DNAm surrogates. In an independent testing set, we compared the prediction performance of DNAmCVDscore with (a) the ‘next-generation’ epigenetic clock DNAmGrimAge, (b) a DNAm score
for CVD derived through a single-step approach, MRS, and (c) the current state-of-the-art prediction model based on traditional CVD risk factors, SCORE2.
Results. We presented novel DNAm surrogates for BMI, blood pressure, fasting glucose and insulin, cholesterol, triglycerides, and coagulation biomarkers, validated in independent datasets. Further, we
derived a DNAmCVDscore outperforming the model based on traditional CVD risk factors and other epigenetic biomarkers for predicting short-term cardiovascular events.
Conclusions. We provided novel DNAm surrogates useful for future epidemiological research, and we described a DNAm based composite biomarker, DNAmCVDscore, predictive of short-term CVD.
Our results highlight the usefulness of DNAm surrogate biomarkers of risk factors and exposures to identify high-risk populations. |
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23/2022 - 04/27/2022
Masci, C.; Ieva, F.; Paganoni, A.M.
A multinomial mixed-effects model with discrete random effects for modelling dependence across response categories | Abstract | | We propose a Semi-Parametric Mixed-Effects Multinomial regression model to deal with estimation and inference issues in the case of categorical and hierarchical data. The proposed modelling assumes the probability of each response category to be identified by a set of fixed and random effects parameters, estimated by means of an Expectation-Maximization algorithm. Random effects are assumed to follow a discrete distribution with an a priori unknown number of support points. For a K-category response, this method identifies a latent structure at the highest level of grouping, where groups are clustered into (K-1)-dimensional subpopulations. This method is an extension of the multinomial semi-parametric EM algorithm proposed in the literature, in which we relax the independence assumption across random-effects relative to different response categories. Since the category-specific random effects arise from the same subjects, their independence assumption is seldom verified in real data. In this sense, the proposed method properly models the natural data structure, as emerges by the results of simulation and case studies, which highlight the importance of taking into account the data dependence structure in real data applications. |
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