Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1349 prodotti
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52/2019 - 12/12/2019
Cerroni, D.; Radu, A. R. ; Zunino, P.
Numerical solvers for a poromechanic problem with a moving boundary | Abstract | | We study a poromechanic problem in presence of a moving boundary.
The poroelastic material is described by means of the Biot model while the moving boundary accounts for the effect of surface erosion of the material. We focus on the numerical approximation of the problem, in the framework of the finite element method. To avoid re-meshing along with the evolution of the boundary, we adopt the cut finite element approach. The main issue of this strategy consists of the ill-conditioning of the finite element matrices in presence of cut elements of small size. We show, by means of numerical experiments and theory, that this issue significantly decreases the performance of the numerical solver. For this reason, we propose a strategy that allows to overcome the ill-conditioned behavior of the discrete problem. The resulting solver is based on the fixed stress approach, used to iteratively decompose the Biot equations, combined with the ghost penalty stabilization and preconditioning applied to the pressure and displacement sub-problems respectively. |
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51/2019 - 10/12/2019
Parolini, N.; Riccobene, C.; Schenone, E.
Reduced models for liquid food packaging systems | Abstract | | Simulation tools are nowadays key elements for effective production, design and maintenance processes in various industrial applications. Thanks to the advances that have been achieved in the past three decades, accurate and efficient solvers for computational fluid dynamics and computational mechanics are routinely adopted for the design of many products and systems. However, the most accurate models accounting for the complete three-dimensional complex physics (of even multi-physics) are not always the best option to pursue, in particular in the preliminary design phase or whenever very fast evaluations are required. In this paper, we present a set of reduced numerical models that have been developed in the past few years to support the design of paperboard packaging systems. |
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50/2019 - 07/12/2019
Lusi, V.; Moore, T. L.; Laurino, F.; Coclite, A.; Perreira, R.; Rizzuti, I.; Palomba, R.; Zunino, P.; Duocastella, M.; Mizrahy, S.; Peer, D.; Decuzzi, P.
A tissue chamber chip for assessing nanoparticle mobility in the extravascular space | Abstract | | Although a plethora of nanoparticle configurations have been proposed over the past 10 years, the uniform and deep
penetration of systemically injected nanomedicines into the diseased tissue stays as a major biological barrier. Here, a
‘tissue chamber’ chip is designed and fabricated to study the extravascular transport of small molecules and
nanoparticles. The chamber comprises a collagen slab, deposited within a PDMS mold, and an 800 mm channel for the
injection of the working solution. Through fluorescent microscopy, the dynamics of molecules and nanoparticles was
estimated within the gel, under different operating conditions. Diffusion coefficients were derived from the analysis of
the particle mean square displacements (MSD). For validating the experimental apparatus and the protocol for data
analysis, the diffusion D of FITC-Dextran molecules of 4, 40 and 250 kDa was first quantified. As expected, D reduces
with the molecular weight of the Dextran molecules. The MSD-derived diffusion coefficients were in good agreement
with values derived via fluorescence recovery after photobleaching (FRAP), an alternative technique that solely applies
to small molecules. Then, the transport of six nanoparticles with similar hydrodynamic diameters (~ 200 nm) and
different surface chemistries was quantified. Surface PEGylation was confirmed to favor the diffusion of nanoparticles
within the collagen slab, whereas the surface decoration with hyaluronic acid (HA) chains reduced nanoparticle
mobility in a way proportionally to the HA molecular weight. To assess further the generality of the proposed approach,
the diffusion of the six nanoparticles was also tested in freshly excited brain tissue slices. In these ex-vivo experiments,
the diffusion coefficients were 5-orders of magnitude smaller than for the ‘tissue chamber’ chip. This was mostly
ascribed to the lack of a cellular component in the chip. However, the trends documented for PEGylated and HA-coated
nanoparticles in vitro were also confirmed ex-vivo. This work demonstrates that the ‘tissue chamber’ chip can be
employed to effectively and efficiently test the extravascular transport of nanomedicines while minimizing the use of
animals. |
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49/2019 - 07/12/2019
Cicchetti, A.; Laurino, F.; Possenti, L.; Rancati, T.; Zunino, P.
In silico model of the early effects of radiation therapy on the microcirculation and the surrounding tissues | Abstract | | Background: Radiation-induced organ dysfunction are frequently described by
Normal Tissue Complication Probability models. The approximations of this
radiobiological approach do not allow to consider the important role played by
the microvasculature not only in the dose-response of the blood vessels, but also
of the organs where it is located. To this purpose we presented a computational
model of the damage induced by RT on the microcirculation and of its effects on
the normal tissues surrounding the tumour. Material and Methods: The effects
of the ionizing radiation on the capillary bed are mediated by the inflamma-
tory response. We derived from a literature search the possible morphological
and functional variations of the network due to the process of the acute in-
flammation. Specifically, we considered a vasodilation, an increased membrane
permeability with a consequent fluid extravasation and an increasing in the wall
elasticity. These perturbations to the system were included in a computational
model, already able to describe the physics of the microcirculation and of its ex-
changes with the surrounding tissues. Results:Two computational descriptions
were considered. In the first one, we changed a set of 4 parameters associated
to the increased fluid exchange from the health scenario at the baseline to a
seriously compromised scenario with the oedema formation. The second study
investigated the effect of a perturbation to the vessel wall elasticity. Conclu-
sions: These simulations represent a first step towards the challenging objective
of understanding, and describing in a mechanistic way the effects of radiation
on the vascular microenvironment. |
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48/2019 - 03/12/2019
Di Gregorio, S.; Fedele, M.; Pontone, G.; Corno, A.F.; Zunino, P.; Vergara, C.; Quarteroni, A.
A multiscale computational model of myocardial perfusion in the human heart | Abstract | | In this paper we present a multiscale model for human cardiac perfusion which accounts for the different length scales of the vessels in the coronary tree. Epicardial vessels are represented with fully
three-dimensional (3D) fluid-dynamics, whereas intramural vessels are modeled as a multi-compartment porous medium. The coupling of these models takes place through interface conditions based on the continuity of mass and momentum. To estimate the physical parameters of the multi-compartment model, a virtual intramural vascular network is generated using a novel algorithm which works in non-convex domains. Modeling epicardial vessels with a 3D model and intramural ones with a porous medium approach makes it possible to apply the proposed strategy to patient-specific heart geometries reconstructed from clinical imaging data. We also address the derivation of numerical solvers for the coupled problem. In particular, we propose a splitting algorithm for the monolithic problem, with the corresponding convergence analysis, and a suitable preconditioner for the multi-compartment porous sub-model. Finally, we test the computational framework in a realistic human heart, and we obtain results that fall in the physiological range for both pressures and local myocardial flows. |
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47/2019 - 03/12/2019
Spreafico, M.; Ieva, F.
Dynamic monitoring of the effects of adherence to medication on survival in Heart Failure patients: a joint modelling approach exploiting time-varying covariates | Abstract | | Adherence to medication is the process by which patients take their drugs as prescribed, and represents an issue in pharmacoepidemiological studies. Poor adherence is often associated with adverse health conditions and outcomes, especially in case of chronic diseases such as Heart Failure (HF). This turns out in an increased request for healthcare services, and in a greater burden for the healthcare system. In recent years there has been a substantial growth in pharmacotherapy research, aimed at studying effects and consequences of proper/improper adherence to medication both for the increasing awareness of the problem and for the pervasiveness of poor adherence among patients. However, the way adherence is computed and accounted for into predictive models is far from being informative as it may be. In fact, it is usually analysed as a fixed baseline covariate, without considering its time-varying behaviour. The purpose and novelty of this study is to define a new personalized monitoring tool exploiting time-varying definition of adherence to medication, within a joint modelling approach. In doing so, we are able to capture and quantify the association between the longitudinal process of dynamic adherence to medication with the long-term survival outcome. Another novelty of this approach consists of exploiting the potential of healthcare administrative databases in order to reconstruct the dynamics of drugs consumption through pharmaceutical administrative registries. In particular, we analysed administrative data provided by Regione Lombardia - Healthcare Division related to patients hospitalized for Heart Failure between 2000-2012. |
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46/2019 - 03/12/2019
Di Iorio, J.; Vantini, S.
funBI: a Biclustering Algorithm for Functional Data | Abstract | | In order to group objects, a wide literature of methods, the majority of them known as clustering and biclustering methods, was created. In the meanwhile, the scientific community tried to defy the curse of dimen- sionality, dealing with problems characterized by data with one infinite continuous dimension: functional data. Even if many old and new clus- tering algorithms were generalized to these new types of data, biclustering methods did not share the same destiny. This paper fills the literature gap by defining the concept of bicluster for data described as a set of functions, and by introducing funBI, the first biclustering algorithm that permits to find functional biclusters, i.e. subsets of functions that exhibit similar behaviour across the same continuous subsets of the domain. funBI is a three-step algorithm based on DIANA, the most famous divisive hierar- chical clustering method. The use of DIANA allows to visualize and to guide the searching procedure using dendrograms and cutting thresholds. Biclustering Clustering Functional data |
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45/2019 - 20/11/2019
Regazzoni, F.; Dedè, L.; Quarteroni, A.
Active force generation in cardiac muscle cells: mathematical modeling and numerical simulation of the actin-myosin interaction | Abstract | | Cardiac in silico numerical simulations are based on mathematical models describing the physical processes involved in the heart function. In this review paper, we critically survey biophysical detailed mathematical models describing the subcellular mechanisms behind mechanical activation, that is the process by which the chemical energy of ATP (adenosine triphosphate) is transformed into mechanical work, thus making the muscle tissue contract. While presenting these models, that feature different levels of biophysical detail, we analyze the trade-off between the accuracy in the description of the subcellular mechanisms and the number of parameters that need to be estimated from experiments. Then, we focus on a generalized version of the classic Huxley model, that is able of reproducing the main experimental characterizations associated to the time scales typical of an heartbeat - such as the force-velocity relationship and the tissue stiffness in response to small steps - featuring only four independent parameters. Finally, we show how those parameters can be calibrated starting from macroscopic measurements available from experiments. |
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