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 1238 products
-
05/2016 - 02/16/2016
Alfio Quarteroni, A.; Lassila, T.; Rossi, S.; Ruiz-Baier, R.
Integrated Heart - Coupling multiscale and multiphysics models for the simulation of the cardiac function | Abstract | | Mathematical modelling of the human heart and its function can expand our understanding of various cardiac diseases, which remain the most common cause of death in the developed world. Like other physiological systems, the heart can be understood as a complex multiscale system involving interacting phenomena at the molecular, cellular, tissue, and organ levels. This article addresses the numerical modelling of many aspects of heart function, including the interaction of the cardiac electrophysiology system with contractile muscle tissue, the sub-cellular activation-contraction mechanisms, as well as the haemodynamics inside the heart chambers. Resolution of each of these sub-systems requires separate mathematical analysis and specially developed numerical algorithms, which we review in detail. By using specific sub-systems as examples, we also look at systemic stability, and explain for example how physiological concepts such as microscopic force generation in cardiac muscle cells, translate to coupled systems of differential equations, and how their stability properties influence the choice of numerical coupling algorithms. Several numerical examples illustrate three fundamental challenges of developing multiphysics and multiscale numerical models for simulating heart function, namely: (i) the correct upscaling from single-cell models to the entire cardiac muscle, (ii) the proper coupling of electrophysiology and tissue mechanics to simulate electromechanical feedback, and (iii) the stable simulation of ventricular haemodynamics during rapid valve opening and closure.
Key words: Integration of cardiac function, Coupling of multiphysics and multiscale models, Electrophysiology, Nonlinear elasticity, Navier-Stokes equations, Reaction-diffusion systems, Finite element methods, Stability analysis, Numerical simulation |
-
04/2016 - 01/01/2016
Pettinati, V.; Ambrosi, D; Ciarletta P.; Pezzuto S.
Finite element simulations of the active stress in the imaginal disc of the Drosophila Melanogaster | Abstract | | During the larval stages of development, the imaginal disc of Drosphila Melanogaster is composed by a monolayer of epithelial cells, which undergo a strain actively produced by the cells themselves. The well organized collective contraction produces a stress field that seemingly has a double morphogenetic role: it orchestrates the cellular organization towards
the macroscopic shape emergence while simultaneously providing a local information on the organ size. Here we perform numerical simulations of such a mechanical control on morphogenesis at a continuum level, using a three-dimensional finite model that accounts for the active cell contraction. The numerical model is able to reproduce the (few) known
qualitative characteristics of the tensional patterns within the imaginal disc of the fruit fly. The computed stress components slightly deviate from planarity, thus confirming the previous theoretical assumptions of a nonlinear elastic analytical model, and enforcing the hypothesis that the mechanical stress may act as a size regulating signal that locally scales
with the global dimension of the domain. |
-
03/2016 - 01/01/2016
Tarabelloni, N.; Ieva, F.
On Data Robustification in Functional Data Analysis | Abstract | | The problem of outlier detection in high dimensional settings is nowadays a crucial point for a number of statistical analysis. Outliers are often considered as an error or noise, instead, they may carry important information on the phenomenon under study. If not properly identified, they may lead to model misspecification, biased parameter estimation and incorrect results, especially in those contexts where the number of available statistical units is lower than the number of parameters (for example, Functional Data Analysis).
In this paper we introduce a robustly adjusted version of the functional boxplot, which is the most common tool adopted to perform outlier detection in Functional Data Analysis. A crucial element of the functional boxplot is the inflation factor of the fences, controlling the proportion of observations flagged as outlier. After an overview of the methods and tools currently available in the literature, we will describe a robust method to compute a data-driven value for such inflation factor. In doing so, we will make use of robust estimators of variance-covariance operators and the corresponding eigenvalues and eigenfunctions.
Two simulation studies are proposed to give direct insights into the use of the proposed functional boxplot, and test both the robustness and accuracy of robust variance-covariance estimators, together with the performances of the functional boxplot in recognising truly outlying observations. |
-
02/2016 - 01/01/2016
Crivellaro, A.; Perotto, S.; Zonca, S.
Reconstruction of 3D scattered data via radial basis functions by efficient and robust techniques | Abstract | | We propose two algorithms to overcome separately two of the most constraining limitations of surface reconstruction methods in use. In particular, we focus on the large amount of data characterizing standard acquisitions by scanner and the noise intrinsically introduced by measurements. The first algorithm represents an adaptive variant of the multi-level interpolating approach proposed in [Ohtake et al., ACM Transactions on Graphics, 2003], based on an implicit surface representation via radial basis functions. The second procedure is based on a least-squares approximation to filter noisy data. An extensive numerical validation is performed to check the performances of the proposed techniques. |
-
01/2016 - 01/01/2016
Domanin, M.; Buora, A.; Scardulla, F.; Guerciotti, B.; Forzenigo, L.; Biondetti, P.; Vergara, C.
Computational fluid-dynamic analysis of carotid bifurcations after endarterectomy: closure with patch graft versus direct suture | Abstract | | Objectives. This study aims at comparing by means of computational fluid-dynamics (CFD) the hemodynamics before and after carotid endarterectomy (CEA), and, after CEA, between patch graft (PG) and direct suture (DS) closures.
Design. We analyzed wall shear stress (WSS), velocities, and vorticity before and after CEA, to highlight the effect of surgery on hemodynamics, and time averaged WSS (TAWSS), oscillatory shear index (OSI) and relative residence time (RTT) after CEA to highlight the differences in terms
of risk of restenosis between PG and DS.
Methods. Thirteen cases underwent CEA for stenosis > 70% and were closed with 9 PG and 4 DS. For each of them we measured the flow with Doppler Ultrasound (DUS) and reconstructed geometries from Magnetic Resonance Angiography (MRA).
Results. The mean value of the spatial averaged TAWSS was 1.0 Pa for PG and 1.5 Pa for DS, whereas it was 0.03 for PG and 0.07 for DS in the case of OSI. The percentage areas with low TAWSS and high OSI resulted wider for PG in comparison to DS (TAWSS: 66.2% for PG and 37.2% for DS; OSI: 10.1% for PG and 3.7% for OSI). RRT values resulted higher in the PG group.
In particular, the mean of the averaged-in-space values was 4.4 1/Pa for PG and 1.6 1/Pa for DS, whereas the PA with high RRT were 22.5% and 6.5%, respectively.
Conclusions. The carotid regions with percentage area of low TAWSS, high OSI and high RRT were wider in the PG group when compared with DS. Thus, hemodynamic conditions more prone to restenosis were observed for PG. The increase of the cross-section area created by PG could induce flow disturbances with potential consequences on long term outcomes. Selective use of PG should consider specific conditions of the patients. |
-
63/2015 - 12/10/2015
Lancellotti, R.M.; Vergara, C.; Valdettaro, L.; Bose, S.; Quarteroni, A.
Large Eddy Simulations for blood fluid-dynamics in real stenotic carotids | Abstract | | In this paper, we consider Large Eddy Simulations (LES) for human stenotic
carotids in presence of atheromasic plaque. It is well known that in such
a pathological condition, transitional effects to turbulence may occur, with
relevant clinical implications such as plaque rupture. The first aim of this
work is to provide a way to define a Direct Numerical Simulation (DNS).
In our context turbulence is not statistically homogeneous isotropic and
stationary. We define mesh size and time step by considering the reduced
model of a 2D shear layer. Then, we compare the performance of LES
model (both static and dynamic) and of mixed LES models (where also a
similarity model is considered) with that of DNS in a realistic scenario of
a carotid. The results highlight the effectiveness of the LES models in
terms of accuracy, especially for the static model. |
-
62/2015 - 12/10/2015
Signorini, M.; Zlotnik, S.; Díez, P.
Proper Generalized Decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems. | Abstract | | The identification of the geological structure from seismic data is formulated as an inverse problem. The properties and the shape of the rock formations in the subsoil are described by material and geometric parameters, which are taken as input data for a predictive model. Here, the model is based on the Helmholtz equation, describing the acoustic response of the system for a given wave length. Thus, the inverse problem consists in identifying the values of these parameters such that the output of the model agrees the best with observations. This optimization algorithm requires multiple queries to the model with different values of the parameters. Reduced Order Models are especially well suited to significantly reduce the computational overhead of the multiple evaluations of the model.
In particular, the Proper Generalized Decomposition (PGD) produces a solution explicitly stating the parametric dependence, where the parameters play the same role as the physical coordinates. A PGD solver is devised to inexpensively explore the parametric space along the iterative process. This exploration of the parametric space is in fact seen as a post-process of the generalized solution. The approach adopted demonstrates its viability when tested in two illustrative examples.
|
-
61/2015 - 11/21/2015
Tagliabue, A.; Dedè, L.; Quarteroni, A.
Fluid dynamics of an idealized left ventricle: the extended Nitsche’s method for the treatment of heart valves as mixed time varying boundary conditions | Abstract | | In this work, we study the blood flow dynamics in idealized left ventricles (LV) of the human heart modelled by the Navier-Stokes equations with mixed time varying boundary conditions (BCs). The latter are introduced for simulating the functioning of the aortic and mitral valves. Based on the extended Nitsche’s method firstly presented in [Juntunen and Stenberg, Mathematics of Computation, 2009], we propose a formulation allowing an efficient and straightforward numerical treatment of the opening and closing phases of the heart valves which are associated to different kind of BCs, namely natural and essential. Moreover, our formulation includes terms preventing the numerical instabilities associated to backflow divergence, i.e. nonphysical reinflow at the valves. We present and discuss numerical results for the LV obtained by means of Isogeometric Analysis for the spatial approximation with the aim of both analysing the formulation and showing the effectiveness of the approach. In particular, we show that the formulation allows to reproduce meaningful results even in idealized LV. |
|
