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
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49/2019 - 12/07/2019
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 - 12/03/2019
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 - 12/03/2019
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 - 12/03/2019
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 - 11/20/2019
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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44/2019 - 11/20/2019
Formaggia, L.; Gatti, F.; Zonca, S.
An XFEM/DG approach for fluid-structure interaction problems with contact | Abstract | | In this work, we address the problem of fluid-structure interaction with moving structures that may come into contact. We propose a penalization contact algorithm implemented in an unfitted numerical framework designed to treat large displacements. In the proposed method, the fluid mesh is fixed and the structure meshes are superimposed to it without any constraint on the conformity. Thanks to the Extended Finite Element Method (XFEM), we can treat discontinuities of the fluid solution on the mesh elements intersecting the structure; the coupling conditions at the fluid structure interface are enforced via a discontinuous Galerkin mortaring technique, which is a penalization method that ensures the consistency of the scheme with the underlining problem. Concerning the contact problem, we consider a frictionless contact model in a master/slave approach. Finally, we perform some numerical tests in the case of contact between a flexible body and a rigid wall and between two deformable structures. |
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43/2019 - 11/09/2019
Antonietti, P.F.; Mazzieri, I.; Migliorini, F.
A space-time discontinuous Galerkin method for the elastic wave equation | Abstract | | In this work we present a new high order space-time discretization method based on a discontinuos Galerkin paradigm for the second order visco-elastodynamics equation. After introducing the method, we show that the resulting space-time discontinuous Galerkin formulation is well-posed, stable and retains optimal rate of
convergence with respect to the discretization parameters, namely the mesh size and the polynomial approximation degree. A set of three-dimensional numerical experiments confirms the theoretical bounds. |
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42/2019 - 11/09/2019
Martino, A.; Guatteri, G.; Paganoni, A.M.
hmmhdd Package: Hidden Markov Model for High Dimensional Data | Abstract | | The R package "hmmhdd" provides some tools to study times series and longitudinal datasets. In particular, the package is based on Hidden Markov Models, i.e. it considers an underlying structure defined by a Markov Model with non-observable states generating a certain type of data, in the multivariate or functional framework. In the former setting, a Gaussian copula models the correlation structure between the components of the observations while, in the latter setting, the data are multivariate functional data and the methods are based on distances between curves. The package is able to estimate all the parameters corresponding to the states of the underlying Markov model, while also computing the optimal state sequence and providing some further helpful tools. |
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