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 1275 products
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12/2010 - 04/21/2010
Sacco, Riccardo; Causin, Paola; Zunino, Paolo; Raimondi, Manuela T.
A multiphysics/multiscale numerical simulation of scaffold-based cartilage regeneration under interstitial perfusion in a bioreactor | Abstract | | Articular cartilage is a connective tissue consisting of a relatively few number of cells, the chondrocytes (CCs), that are immersed in an extensive hydrated matrix, composed primarily of proteoglycans and collagens.
In vitro tissue engineering has been investigated as a potential source of functional tissue constructs for cartilage repair, as well as a model system for controlled studies of cartilage development and function. Among the different kinds of devices for the cultivation of 3D cartilage cell colonies, we consider here polymeric scaffold-based perfusion bioreactors. The perfusion fluid supplies nutrients and oxygen to the growing biomass. At the same time, the fluid-induced shear acts as a physiologically relevant stimulus for the metabolic activity of CCs, because it may enhance cell proliferation and
metabolism, provided that the shear stress level is moderate. In this complex environment, mathematical and computational modeling may help in the optimal design of the bioreactor configuration. In this perspective, we propose a computational model for the simulation of the biomass growth, under given inlet and geometrical conditions. Precisely, we consider a two-step approach. First, we perform a simplified short term analysis in which only biomass growth is taken into account, the nutrient concentration and
the fluid-induced shear stress being assumed constant in time and uniform in space. This allows us to calibrate the biomass growth model with respect to the shear stress dependence on experimental data. Then, we carry out a full analysis where the nutrient concentration and perfusion velocity change in time and space and the growing biomass modifies the porosity
of the scaffold matrix, altering the fluid flow. The model parameters are consistently derived from volume averaging techniques that allow us to upscale the microscopic structural properties to the macroscopic level. The predictions we obtain in this way are significant for long times of culture. |
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11/2010 - 04/20/2010
Biscari, Paolo; Minisini, Sara; Pierotti, Dario; Verzini, Gianmaria; Zunino, Paolo
Controlled release with finite dissolution rate | Abstract | | We consider a two-phase generalization of the classical Higuchi’s model for controlled drug release. The drug is assumed to be prepared in a drug eluting stent in its solid phase by immersion in a polymeric matrix which eventually delivers the drug when it reaches the free end. We derive a single effective evolution equation, which we prove to be equivalent to the original system of two coupled PDE’s. We provide analytical estimates for the asymptotic regimes of large and small diffusion. Results from numerical simulations allow then to fill up the gap, and understand the behavior of the system in intermediate regimes. |
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10/2010 - 03/22/2010
Quarteroni, Alfio; Ruiz Baier, Ricardo
Analysis of a fi nite volume element method for the Stokes problem | Abstract | | In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in
di fferent norms are obtained by establishing the adequate connection between the finite volume
and stabilized finite element formulations. A superconvergence result is also derived by using a
postprocessing projection method. The stabilization of the continuous lowest equal order pair fi nite volume element discretization (P1 - P1) is achieved by enriching the velocity space with bubble-like functions. Finally, some numerical experiments that con firm the predicted behavior of the method are provided. |
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09/2010 - 02/26/2010
Sangalli, Laura M.; Secchi, Piercesare; Vantini, Simone; Vitelli, Valeria
Joint Clustering and Alignment of Functional Data: an Application to Vascular Geometries | Abstract | | We show an application of the k-mean alignment method presented in Sangalli et al. (2010b). This is a method for jointly clustering and aligning
functions that puts in a unique framework two widely used methods of functional data analysis: Procrustes continuous alignment and functional
k-mean clustering. These two methods turn out to be two special cases of the new method. In detail we use this algorithm to analyze 65 internal
carotid arteries (ICA) in relation to the presence and rupture of cerebral aneurysms. Some interesting issues, amenable of a biological interpretation and pointed out by the analysis, are briefly discussed. |
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08/2010 - 02/25/2010
Ieva, Francesca; Paganoni, Anna Maria
Multilevel models for clinical registers concerning STEMI patients in a complex urban reality: a statistical analysis of MOMI^2 survey | Abstract | | In this work we describe statistical analyses conducted on MOMI^2 (MOnth MOnitoring Myocardial Infarction in Milan) survey, a collection of data
concerning patients admitted with STEMI (ST-Elevation Myocardial Infarction) diagnosis in one of the hospitals belonging to the Network in
Milan urban area. The main goal of the analyses is statistical exploration, description and model of collected data in order to answer specific clinical questions (i.e. if the result of certain healthcare policy is less or more effective than another one, if the logistic organization or time scheduling of Emergency Room (ER) and rescue units can be improved, etc). Such results can be used as an effective support to decisional process for clinical and organizational governance. The fundamental result of this study is not only the use of advanced and innovative statistical tools, but also the social impact of the achieved results thanks to the synergic interaction between statisticians and physicians. |
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07/2010 - 02/24/2010
Sangalli, Laura M.; Secchi, Piercesare; Vantini, Simone; Vitelli, Valeria
Functional clustering and alignment methods with applications | Abstract | | We consider the issue of classification of functional data and, in particular, we deal with the problem of curve clustering when curves are misaligned. In the proposed setting, we aim at jointly aligning and clustering the curves, via the solution of an optimization problem. We describe an iterative procedure for the solution of the optimization problem, and we detail two alternative specifications of the procedure, a k-mean version and a k-medoid version. We illustrate via applications to real data the robustness of the alignment and clustering procedure under the different specifications. |
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06/2010 - 02/23/2010
Alastruey, Jordi; Passerini, Tiziano; Formaggia, Luca; Peirò, Joaquim
The effect of visco-elasticity and other physical properties on aortic and cerebral pulse waveforms: an analytical and numerical study | Abstract | | The nonlinear one-dimensional equations of blood flow in Voigttype visco-elastic vessels are numerically solved using both a Taylor-Galerkin and a discontinuous Galerkin scheme to study the effects on aortic and cerebral pulse waveforms of wall visco-elasticity, fluid viscosity, wall compliances and resistances, flow inertia, cardiac ejection, and outflow pressure. A linear analysis of these equations shows that wave dispersion and dissipation is caused by wall viscosity at high frequencies and fluid viscosity at low frequencies. During approximately the last three fourths of diastole the inertial effects of the flow can be neglected, and pressures tend to a space-independent shape dictated by global quantities (cardiac ejection, total peripheral resistance and compliance, and outflow pressure) and the viscous modulus of each arterial segment. During this period, the area-pressure curve reduces to a line whose slope provides a better approximation to the local pulse wave speed than do current techniques based on simultaneous pressure and velocity measurements. The viscous modulus can be estimated from the area of the area-pressure loop. Our findings are important for the identification and estimation of haemodynamic quantities related to the prevention, diagnosis and treatment of disease.
Keywords: Pulse wave propagation; pulse wave speed; circulatory system; circle of Willis; one-dimensional modelling; Voigt-type viscoelasticity; Taylor-Galerkin methods; discontinuous Galerkin methods. |
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05/2010 - 02/22/2010
Longoni, Matteo; Malossi, A.C.I.; Quarteroni, Alfio; Villa, Andrea
A complete model for non-Newtonian sedimentary basins in presence of faults and compaction phenomena | Abstract | | In this paper we present a model and a complete numerical tool for simulating the three-dimensional dynamics of realistic stratified
sedimentary basins. We developed dedicated mathematical algorithms to include most of the key physical aspects such as the movement of
the basement, the non-Newtonian behavior of the sediments, the effects of faults and the presence of compaction phenomena. This approach is mandatory to capture all the three-dimensional effects of realistic evolution dynamics, whose duration is about millions of years and to provide reliable results. In this work we apply our methods to a realistic and topologically complex sedimentary system. |
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