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 1238 prodotti
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52/2015 - 30/09/2015
Giverso, C.; Scianna, M.; Grillo, A.
Growing Avascular Tumours as Elasto-Plastic Bodies by the Theory of Evolving Natural Configurations | Abstract | | The aim of this article is to propose a simple way of describing a tumour as a linear elastic material from a reference configuration that is continuously evolving in time due to growth and remodelling. The main assumption allowing this simplification is that the tumour mass is a very ductile material, so that it can only sustain moderate stresses while the deformation induced by growth, that can actually be quite big, mainly induces a plastic reorganisation of malignant cells. In mathematical terms this means that the deformation gradient can be split into a volumetric growth term, a term describing the reorganisation of cells, and a term that can be approximated by means of the linear strain tensor. A dimensionless analysis of the importance of the different terms also allows to introduce a second simplification consisting in the decoupling of the equations describing the growth of the tumour mass from those describing the flow of the interstitial fluid. |
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51/2015 - 30/09/2015
Ballarin, F.; Faggiano, E.; Ippolito, S.; Manzoni, A.; Quarteroni, A.; Rozza, G.; Scrofani, R.
Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD–Galerkin method and a vascular shape parametrization | Abstract | | In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data. A centerlines-based parametrization is proposed to efficiently handle geometrical variations. POD–Galerkin reduced-order models are employed to cut down large computational costs. This computational framework allows to characterize blood flows for different physical and geometrical variations relevant in the clinical practice, such as stenosis factors and anastomosis variations, in a rapid and reliable way. Several numerical results are discussed, highlighting the computational performance of the proposed framework, as well as its capability to perform sensitivity analysis studies, so far out of reach. |
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50/2015 - 30/09/2015
Grillo, A.; Guaily, A.; Giverso, C.; Federico, S.
Non-Linear Model for Compression Tests on Articular Cartilage | Abstract | | Hydrated soft tissues, such as articular cartilage, are often modelled as biphasic systems with individually incompressible solid and fluid phases, and biphasic models are employed to fit experimental data in order to determine the mechanical and hydraulic properties of the tissues. Two of the most common experimental setups are confined and unconfined compression. Analytical solutions exist for the unconfined case with the linear, isotropic, homogeneous model of articular cartilage, and for the confined case with the non-linear, isotropic, homogeneous model. The aim of this contribution is to provide an easily implementable numerical tool to determine a solution to the governing differential equations of (homogeneous and isotropic) unconfined and (inhomogeneous and isotropic) confined compression under large deformations. The large-deformation governing equations are reduced to equivalent diffusive equations, which are then solved by means of Finite Difference methods. The solution strategy proposed here could be used to generate benchmark tests for validating complex user-defined material models within Finite Element implementations, and for determining the tissue's mechanical and hydraulic properties from experimental data. |
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49/2015 - 30/09/2015
Ghiglietti, A.; Ieva, F.; Paganoni, A.M.
Statistical inference for stochastic processes: two sample hypothesis tests | Abstract | | In this paper, we present inferential procedures to compare the means of two samples of functional data. The proposed tests are based on a suitable generalization of Mahalanobis distance to the Hibert space of square integrable function defined on a compact interval. We do not require any specific distributional assumption on the processes generating the data. Test procedures are proposed for both the cases of known and unknown variance-covariance structures, and asymptotic properties of test statistics are deeply studied. A simulation study together with a real case data analysis are also presented. |
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48/2015 - 25/09/2015
Ambrosi, D.; Pettinati, V.; Ciarletta, P.
Active stress as a local regulator of global size in morphogenesis | Abstract | | While a general consensus exists that the morphogenesis of living organisms has its roots in genetically encoded information, there is a big debate about the physical mechanisms that actually mediate its control. In embryo development, cells stop proliferating at homeostasis, a target state in terms of physical conditions that can represent, for instance, the shape and size of an organ. However, while control of mitosis is local, the spatial dimension of a tissue is a global information.
How do single cells get aware of that at the same time? Which is their communication mechanism? While morphogen factors are demonstrated to play a key role in morphogenesis, and in particular for shape emergence, they
seem unable to produce a global control on size by themselves and, conversely, many recent experiments suggest that active mechanics plays a role. Here we focus on a paradigmatic larval structure: the imaginal disc that will become the wing of the fruit fly. By a formalization of theoretical conjectures in terms of simple mathematical models, we show that inhomogeneous stress, likely dictated by morphogenetic patterns, is an admissible mechanism to convey locally the global information of organ size. |
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47/2015 - 25/09/2015
Colombo, M. C.; Giverso, C.; Faggiano, E.; Boffano,C.; Acerbi, F.; Ciarletta, P.
Towards the personalized treatment of glioblastoma: integrating patient-specific clinical data in a continuous mechanical model | Abstract | | Glioblastoma multiforme (GBM) is the most aggressive and malignant among brain tumors. In addition to uncontrolled proliferation and genetic instability, GBM is characterized by a diffuse infiltration, developing long protrusions that penetrate deeply along the fibers of the white matter. These features, combined with the underestimation of the invading GBM area by available imaging techniques, make a definitive treatment of GBM particularly difficult.
A multidisciplinary approach combining mathematical, clinical and radiological data has the potential to foster our understanding of GBM evolution in every single patient throughout his/her oncological history, in order to target therapeutic weapons in a patient-specific manner.
In this work, we propose a continuous mechanical model and we perform numerical simulations of GBM invasion combining the main mechano-biological characteristics of GBM with the micro-structural information extracted from radiological images, i.e. by elaborating patient-specific Diffusion Tensor Imaging (DTI) data.
The numerical simulations highlight the influence of the different biological parameters on tumor progression and they demonstrate the fundamental importance of including anisotropic and heterogeneous patient-specific DTI data in order to obtain a more accurate prediction of GBM evolution. The results of the proposed mathematical model have the potential to provide a relevant benefit for clinicians involved in the treatment of this particularly aggressive disease and, more importantly, they might drive progress towards improving tumor control and patient's prognosis. |
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46/2015 - 24/09/2015
Giverso, C.; Verani, M.; Ciarletta P.
Emerging morphologies in round bacterial colonies: comparing volumetric versus chemotactic expansion | Abstract | | Biological experiments performed on living bacterial colonies have demonstrated
the microbial capability to develop finger-like shapes and highly irregular contours,
even starting from an homogeneous inoculum. In this work, we study from
the continuum mechanics viewpoint the emergence of such branched morphologies
in an initially circular colony expanding on the top of a Petri dish coated with
agar. The bacterial colony expansion, based on either a source term, representing
volumetric mitotic processes, or a non-convective mass flux, describing chemotactic
expansion, is modelled at the continuum scale. We demonstrate that the
front of the colony is always linearly unstable, having similar dispersion curves
to the ones characterizing branching instabilities. We also perform finite element
simulations, which not only prove the emergence of branching, but also highlight
dramatic differences between the two mechanisms of colony expansion in the nonlinear
regime. Furthermore, the proposed combination of analytical and numerical
analysis allowed studying the influence of different model parameters on the
selection of specific patterns. A very good agreement has been found between
the resulting simulations and the typical structures observed in biological assays.
Finally, this work provides a new interpretation of the emergence of branched patterns
in living aggregates, depicted as the results of a complex interplay among
chemical, mechanical and size effects. |
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45/2015 - 24/09/2015
Lange, M.; Palamara, S.; Lassila, T.; Vergara, C.; Quarteroni, A.; Frangi, A.F.
Improved hybrid/GPU algorithm for solving cardiac electrophysiology problems on Purkinje networks | Abstract | | The cardiac Purkinje fibres provide an important stimulus to the coordinated
contraction of the heart. We present a numerical algorithm for the
solution of electrophysiology problems on the Purkinje network that is efficient enough to be used on realistic networks with physiologically detailed
membrane models. The algorithm is based on operator splitting and is provided
with three different implementations: pure CPU, hybrid CPU/GPU,
and pure GPU. Compared to our previous work based on the model of
Vigmond et al., we modify the explicit gap junction term at network bifurcations
in order to improve its mathematical consistency. Due to this
improved consistency of the model, we are able to perform a convergence
study against analytical solutions and verify that all three implementations
produce equivalent convergence rates. Finally, we compare the efficiency of
all three implementations on Purkinje networks of increasing spatial resolution
using membrane models of increasing complexity. Both hybrid and
pure-GPU implementations outperform the pure-CPU implementation, but
their relative performance difference depends on the size of the Purkinje
network and the complexity of the membrane model used. |
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