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 1242 products
-
46/2020 - 07/21/2020
Bucelli, M.; Salvador, M.; Dede', L.; Quarteroni, A.
Multipatch Isogeometric Analysis for Electrophysiology: Simulation in a Human Heart | Abstract | | In the framework of cardiac electrophysiology for the human heart, we apply multipatch NURBS-based Isogeometric Analysis for the space discretization of the Monodomain model. Isogeometric Analysis (IGA) is a technique for the solution of Partial Differential Equations (PDEs) that facilitates encapsulating the exact representation of the computational geometry by using basis functions with high-order continuity. IGA features very small numerical dissipation and dispersion if compared to other methods for the solution of PDEs. The use of multiple patches allows to overcome the conventional limitations of single patch IGA, thanks to the gained flexibility in the design of the computational domain, especially when its representation is quite involved as in bioengineering applications. We propose two algorithms for the preprocessing of CAD models of complex surface and volumetric NURBS geometries with cavities, such as atria and ventricles: our purpose is to obtain geometrically and parametrically conforming NURBS multipatch models starting from CAD models. We employ those algorithms for the construction of an IGA realistic representation of a human heart. We apply IGA for the discretization of the Monodomain equation that describes the evolution in space and time of the cardiac action potential. This PDE is coupled with suitable microscopic models to define the behavior at cellular scale: Courtemanche-Ramirez-Nattel model for the atrial simulation, and Luo-Rudy model for the ventricular one. Numerical simulations on realistic human atria and ventricles geometries are carried out, obtaining accurate and smooth excitation fronts by combining IGA with the multipatch approach for the geometrical representation of the computational domains, either surfaces for the atria or solids for the ventricles. |
-
45/2020 - 07/21/2020
Gatti, F.; Menafoglio, A.; Togni, N.; Bonaventura, L.; Brambilla, D.; Papini, M; Longoni, L.
A novel dowscaling procedure for compositional data in the Aitchison geometry with application to soil texture data | Abstract | | In this work, we present a novel downscaling procedure for compositional quantities based on the Aitchison geometry. The method is able to naturally consider compositional constraints, i.e. unit-sum and positivity. We show that the method can be used in a block sequential Gaussian simulation framework in order to assess the variability of downscaled quantities. Finally, to validate the method, we test it first in an idealized scenario and then apply it for the downscaling of digital soil maps on a more realistic case study. The digital soil maps for the realistic case study are obtained from SoilGrids, a system for automated soil mapping based on state-of-the-art spatial predictions methods. |
-
44/2020 - 07/21/2020
Masci, C.; Ieva, F.; Paganoni A.M.
EM algorithm for semiparametric multinomial mixed-effects models | Abstract | | This paper proposes an EM algorithm for semiparametric mixed-effects
models dealing with a multinomial response. In multinomial mixed-effects models, in order to obtain the marginal distribution of the response, random effects need to be integrated out. In a full parametric context, where random effects follow a multivariate normal distribution, this is often computationally infeasible. We propose an alternative novel semiparametric approach in which random effects follow a multivariate discrete distribution with an a priori unknown number of support points, that is allowed to differ across categories.
The advantage of this modelling is twofold: the discrete distribution
on random effects allows, first, to express the marginal density as a weighted sum, avoiding numerical problems typical of the integration and, second, to identify a latent structure at the highest level of the hierarchy, where groups are clustered into subpopulations. The paper shows a simulation study to evaluate the method’s performance and applies the proposed algorithm to a real case study for predicting higher education student dropout, comparing the results with the ones of a full parametric method. |
-
42/2020 - 06/25/2020
Miglio, E.; Parolini, N.; Quarteroni, A.; Verani, M.; Zonca, S.
A spatio-temporal model with multi-city mobility for COVID-19 epidemic | Abstract | | The COVID-19 epidemic is the last of a long list of pandemics that have affected human kind in the last century. The virus spread very quickly all over the world due to the structure of modern society where mobility is very high.
In this paper we aim at a critical study of a multi-city model consisting of 8 compartments for describing the spreading of a disease. A convenient parameter calibration is implemented with the aim of reproducing the past history of the epidemic and of exploring its predicting capabilities. |
-
43/2020 - 06/23/2020
Dede’, L.; Regazzoni, F.; Vergara, C.; Zunino, P.; Guglielmo, M.; Scrofani, R.; Fusini, L.;Cogliati, C.; Pontone, G.; Quarteroni, A.
Modeling the effect of COVID-19 on the cardiac function: A computational study
| Abstract | | Emerging studies address how COVID-19 infection can impact the cardiovascular system. This relates particularly to the development of myocardial injury, acute coronary syndrome, myocarditis, arrhythmia, and heart failure. Prospective treatment approach is advised for these patients. To study the interplay between local changes (reduced contractility), global variables (peripheral resistances, heart rate) and the cardiac function, we considered a lumped parameters computational model of the cardiovascular system. Our mathematical model allows to simulate the systemic and pulmonary circulations, the four cardiac valves and the four heart chambers, through equations describing the underlying physical processes. By the assessment of conventionally relevant parameters of cardiac function obtained through our numerical simulations, we propose our computational model as an effective method to evaluate short-term prognosis both in patients with normal and impaired cardiac function at baseline affected by mild or severe COVID-19. |
-
41/2020 - 06/07/2020
Cannistrà,M.; Masci, C.; Ieva, F.; Agasisti, T.; Paganoni, A.M.
Not the magic algorithm: modelling and early-predicting students dropout through machine learning and multilevel approach | Abstract | | According to OECD, almost 30 per cent of students leave tertiary education programs without obtaining
a degree. This number measures a dead loss of human capital and a waste of public and private
resources. This paper contributes to the existing knowledge about students dropout by combining a
theoretical-based model with a data-driven approach to detect students who are more likely to leave
university in the first year. We propose the use of multilevel statistical models and machine learning
methods, applied to administrative data from a leading Italian university. The findings are encouraging,
as the methodology is able to predict at-risk students very precisely. We provide evidence of
the essential role of data relative to early performance (i.e. grades obtained in the first semester).
Moreover, the selection of major strongly influences the probability of dropping out. |
-
40/2020 - 06/07/2020
Fresca, S.; Manzoni, A.; Dedè, L.; Quarteroni, A.
Deep learning-based reduced order models in cardiac electrophysiology | Abstract | | Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the formulation and numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential, that is the polarization/depolarization cycle occurring at every heart beat that models the time evolution of the electrical potential across the cell membrane, as well as a set of ionic variables. Multiple solutions of these systems, corresponding to different model inputs, are required to evaluate outputs of clinical interest, such as activation maps and action potential duration. More importantly, these models feature coherent structures that propagate over time, such as wavefronts. These systems can hardly be reduced to lower dimensional problems by conventional reduced order models (ROMs) such as, e.g., the reduced basis (RB) method. This is primarily due to the low regularity of the solution manifold (with respect to the problem parameters) as well as to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To overcome this difficulty, in this paper we propose a new, nonlinear approach which exploits deep learning (DL) algorithms to obtain accurate and efficient ROMs, whose dimensionality matches the number of system parameters. Our DL approach combines deep feedforward neural networks (NNs) and convolutional autoencoders (AEs). We show that the proposed DL-ROM framework can efficiently provide solutions to parametrized electrophysiology problems, thus enabling multi-scenario analysis in pathological cases. We investigate three challenging test cases in cardiac electrophysiology and prove that DL-ROM outperforms classical projection-based ROMs. |
-
39/2020 - 06/07/2020
Martinolli, M.; Biasetti, J.; Zonca, S.; Polverelli, L.; Vergara, C.
Extended Finite Element Method for Fluid-Structure Interaction in Wave Membrane Blood Pumps | Abstract | | Numerical simulations of cardiac blood pump systems are integral to the optimization of device design, hydraulic performance and hemocompatibility. In wave membrane blood pumps, blood propulsion arises from the wave propagation along an oscillating immersed membrane, which generates small pockets of fluid that are pushed towards the outlet against an adverse pressure gradient.
We studied the Fluid-Structure Interaction between the oscillating membrane and the blood flow via three-dimensional simulations using the Extended Finite Element Method, an unfitted numerical technique that avoids remeshing by using a fluid fixed mesh.
Our three-dimensional numerical simulations in a realistic pump geometry highlighted the role of the membrane deformation in promoting a blood flow towards the outlet despite of a resistive pressure gradient. We also simulated the pump system at different pressure conditions and we validated the numerical results against textit{in-vitro} experimental data. |
|
