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 1239 products
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64/2022 - 10/05/2022
Massi, M.C., Dominoni, L., Ieva, F., Fiorito, G.
A Deep Survival EWAS approach estimating risk profile based on pre-diagnostic DNA methylation: an application to Breast Cancer time to diagnosis | Abstract | | Previous studies for cancer biomarker discovery based on pre-diagnostic blood DNA methylation profiles, either ignore the explicit modeling of the time to diagnosis (TTD) as in a survival analysis setting, or provide inconsistent results. This lack of consistency is likely due to the limitations of standard EWAS approaches, that model the effect of
DNAm at CpG sites on TTD independently. In this work, we argue that a global approach to estimate CpG sites effect profile is needed, and we claim that such approach should capture the complex (potentially non-linear) relationships interplaying between sites. To prove our concept, we develop a new Deep Learning-based approach assessing the relevance of individual CpG Islands (i.e., assigning a weight to each site) in determining TTD while modeling their combined effect in a survival analysis scenario.
The algorithm combines a tailored sampling procedure with DNAm sites agglomeration, deep non-linear survival modeling and SHapley Additive exPlanations (SHAP) values estimation to aid robustness of the derived effects profile. The proposed approach deal with the common complexities arising from epidemiological studies, such as small sample size, noise, and low signal-to-noise ratio of blood-derived DNAm. We apply our approach to a prospective case-control study on breast cancer nested in the EPIC Italy cohort and we perform weighted gene-set enrichment analyses to demonstrate the biological meaningfulness of the obtained results. We compared the results of Deep Survival EWAS with those of a traditional EWAS approach, demonstrating that our method performs better than the standard approach in identifying biologically relevant pathways. |
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63/2022 - 10/05/2022
Corti, M.; Antonietti, P.F.; Dede', L.; Quarteroni, A.
Numerical Modelling of the Brain Poromechanics by High-Order Discontinuous Galerkin Methods | Abstract | | We introduce and analyze a discontinuous Galerkin method for the numerical modelling of the equations of Multiple-Network Poroelastic Theory (MPET) in the dynamic formulation. The MPET model can comprehensively describe functional changes in the brain considering multiple scales of fluids. Concerning the spatial discretization, we employ a high-order discontinuous Galerkin method on polygonal and polyhedral grids and we derive stability and a priori error estimates. The temporal discretization is based on a coupling between a Newmark $beta$-method for the momentum equation and a $theta$-method for the pressure equations. After the presentation of some verification numerical tests, we perform a convergence analysis using an agglomerated mesh of a geometry of a brain slice. Finally we present a simulation in a three dimensional patient-specific brain reconstructed from magnetic resonance images. The model presented in this paper can be regarded as a preliminary attempt to model the perfusion in the brain. |
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66/2022 - 10/05/2022
Antonietti, P.F.; Liverani, L.; Pata, V.
Lack of superstable trajectories in linear viscoelasticity: A numerical approach | Abstract | | Given a positive operator $A$ on some Hilbert space,
and a nonnegative decreasing summable function $mu$,
we consider the abstract equation with memory
$$
ddot u(t)+ A u(t)- int_0^t mu(s)Au(t-s) ds=0
$$
modeling the dynamics of linearly viscoelastic solids.
The purpose of this work is to provide numerical evidence
of the fact that the energy
$$E(t)=Big(1-int_0^tmu(s)dsBig)|u(t)|^2_1+|dot u(t)|^2
+int_0^tmu(s)|u(t)-u(t-s)|^2_1ds,$$
of any nontrivial solution cannot decay faster than exponential,
no matter how fast might be the decay of the memory kernel $mu$.
This will be accomplished by simulating the integro-differential
equation for different choices of the memory kernel $mu$
and of the initial data. |
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62/2022 - 09/05/2022
Ciaramella, G.; Halpern, L.; Mechelli, L.
Convergence analysis and optimization of a Robin Schwarz waveform relaxation method for periodic parabolic optimal control problems | Abstract | | This paper is concerned with a novel convergence analysis of the
optimized Schwarz waveform relaxation method (OSWRM) for the
solution of optimal control problems governed by periodic parabolic
partial differential equations (PDEs). The new analysis is based on
Fourier-type technique applied to a semidiscrete in time form of the
optimality condition. This leads to a precise characterization of the
convergence factor of the method at the semidiscrete level. Using
this characterization, the optimal transmission condition parameter
is obtained at the semidiscrete level and its asymptotic behavior
as the time discretization converges to zero is analyzed in detail. |
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61/2022 - 09/05/2022
Gregorio, C.; Cappelletto, C.; Romani, S.; Stolfo, D.; Merlo, M.; Barbati, G.
Using marginal structural joint models to estimate the effect of a time-varying treatment on recurrent events and survival: An application on arrhythmogenic cardiomyopathy | Abstract | | In many clinical applications to evaluate the effect of a treatment, randomized control trials are difficult to carry out. On the other hand, clinical observational registries are often available and they contain longitudinal data regarding clinical parameters, drug therapies, and outcomes. In the past, much research has addressed causal methods to estimate treatment effects from observational studies. In the context of time-varying treatments, marginal structural models are often used. However, most analyses have focused on binary outcomes or time-to-the-first event analyses. The novelty of our approach is to combine the marginal structural methodology with the case where correlated recurrent events and survival are the outcomes of interest. Our work focuses on solving the nontrivial problem of defining the measures of effect, specifying the model for the time-dependent weights and the model to estimate the outcome, implementing them, and finally estimating the final treatment effects in this life-history setting. Our approach provides a strategy that allows obtaining treatment effect estimates both on the recurrent events and the survival with a clear causal and clinical interpretation. At the same time, the strategy we propose is based on flexible modeling choices such as the use of joint models to capture the correlation within events from the same subject and the specification of time-dependent treatment effects. The clinical problem which motivated our work is the evaluation of the treatment effect of beta-blockers in arrhythmogenic right ventricular cardiomyopathy (ARVC/D), and the dataset comes from the Trieste Heart Muscle Disease Registry. |
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60/2022 - 08/29/2022
Cortellessa, D.; Ferro, N.; Perotto, S.; Micheletti, S.
Enhancing level set-based topology optimization with anisotropic graded meshes | Abstract | | We propose a new algorithm for the design of topologically optimized lightweight structures, under a minimum compliance requirement. The new process enhances a standard level set formulation in terms of computational efficiency, thanks to the employment of a strategic computational mesh. We pursue a twofold goal, i.e., to deliver a final layout characterized by a smooth contour and reliable mechanical properties.
The smoothness of the optimized structure is ensured by the employment of an anisotropic adapted mesh, which sharply captures the material/void interface. A robust mechanical performance is guaranteed by a uniform tessellation of the internal part of the optimized configuration. A thorough numerical investigation corroborates the effectiveness of the proposed algorithm as a reliable and computationally affordable design tool, both in two- and three-dimensional contexts. |
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59/2022 - 08/29/2022
Boon, W. M.; Fumagalli, A.
A multipoint vorticity mixed finite element method for incompressible Stokes flow | Abstract | | We propose a mixed finite element method for Stokes flow with one degree of freedom per element and facet of simplicial grids. The method is derived by considering the vorticity-velocity-pressure formulation and eliminating the vorticity locally through the use of a quadrature rule. The discrete solution is pointwise divergence-free and the method is pressure robust. The theoretically derived convergence rates are confirmed by numerical experiments. |
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58/2022 - 08/20/2022
Zingaro, A.; Bucelli, M.; Fumagalli, I.; Dede', L; Quarteroni, A.
Modeling isovolumetric phases in cardiac flows by an Augmented Resistive Immersed Implicit Surface Method | Abstract | | A major challenge in the computational fluid dynamics modeling of the heart function is the simulation of isovolumetric phases when the hemodynamics problem is driven by a prescribed boundary displacement.
During such phases, both atrioventricular and semilunar valves are closed: consequently, the ventricular pressure may not be uniquely defined, and spurious oscillations may arise in numerical simulations.}
In this paper, we propose a suitable modification of the Resistive Immersed Implicit Surface (RIIS) method (Fedele et al., 2017) by introducing a reaction term to correctly capture the pressure transients during isovolumetric phases. The method, that we call Augmented RIIS (ARIIS) method, extends the previously proposed ARIS method (This et al., 2020) to the case of a mesh which is not body-fitted to the valves. We test the proposed method on two different benchmark problems, including a new simplified problem that retains all the characteristics of a heart cycle. We apply the ARIIS method to a fluid dynamics simulation of a realistic left heart geometry, and we show that ARIIS allows to correctly simulate isovolumetric phases, differently from standard RIIS method. |
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