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 1314 prodotti
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48/2017 - 30/08/2017
Regazzoni, F.; Dedè, L.; Quarteroni, A.
Active contraction of cardiac cells: a reduced model for sarcomere dynamics with cooperative interactions | Abstract | | We propose a reduced ODE model for the mechanical activation of cardiac myofilaments, which is based on explicit spatial representation of nearest-neighbour interactions. Our model is derived from the cooperative Markov Chain model of Washio et al. 2012, under the assumption of conditional independence of specific sets of events. This physically motivated assumption allows to drastically reduce the number of degrees of freedom, thus resulting in a significantly large computational saving. Indeed, the original Markov Chain model involves a huge number of degrees of freedom (order of 10^21) and is solved by means of the Monte Carlo method, which notoriously reaches statistical convergence in a slow fashion. With our reduced model, instead, numerical simulations can be carried out by solving a system of ODEs, reducing the computational time by more than 10000 times. Moreover, the reduced model is accurate with respect to the original Markov Chain model. We show that the reduced model is capable of reproducing physiological steady-state force-calcium and force-length relationships with the observed asymmetry in apparent cooperativity near the calcium level producing half activation. Finally, we also report good qualitative and quantitative agreement with experimental measurements under dynamic conditions. |
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47/2017 - 29/08/2017
Menghini, F.; Dede, L.; Forti, D.; Quarteroni, A.
Hemodynamics in a left atrium based on a Variational Multiscale-LES numerical model | Abstract | | Standard studies of the cardiovascular system are based on advanced experimental and imaging techniques, however, in the past few years, they are being complemented by computational fluid dynamics simulations of blood
flows with increasing level of details. The vast majority of works dealing with the heart hemodynamics focus on the left ventricle, both in patient-specific and idealized geometries, while the fluid dynamics of the left atrium is much less investigated. In this work we propose a computational model of a left atrium suitable to provide physically meaningful fluid dynamics indications and other outputs as the velocity profile at the mitral valve. A Variational Multiscale model is used to obtain a stable formulation of the Navier-Stokes equations discretized by means of the Finite Element method and to account for turbulence modeling within the framework of Large Eddy Simulation (LES). We present and discuss numerical results regarding the fluid dynamics of the left atrium with the focus on possible transitions to turbulence. We also provide a comparison with the results obtained using a SUPG formulation. |
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46/2017 - 08/08/2017
Agosti, A.; Gower, A.L.; Ciarletta, P.
The constitutive relations of initially stressed incompressible Mooney-Rivlin materials | Abstract | | Initial stresses originate in soft materials by the occurrence of misfits in the undeformed microstruc-
ture. Since the reference configuration is not stress-free, the effects of initial stresses on the hyperelastic
behavior must be constitutively addressed. Notably, the free energy of an initially stressed material
may not possess the same symmetry group as the one of the same material deforming from a naturally
unstressed configuration. This work assumes an explicit dependence of the hyperelastic strain energy
density on both the deformation gradient and the initial stress tensor, taking into account for their inde-
pendent invariants. Using this theoretical framework, a constitutive equation is derived for an initially
stressed body that naturally behaves as an incompressible Mooney-Rivlin material. The strain energy
densities for initially stressed neo-Hookean and Mooney materials are derived as special sub–cases. By
assuming the existence of a virtual state that is naturally stress-free, the resulting strain energy functions
are proved to fulfill the required frame–independence constraints. In the case of plane strain condition,
great simplifications arise in the expression of the constitutive relations. Finally, the resulting constitu-
tive relations prove useful guidelines for designing non-destructive methods for the quantification of the
underlying initial stresses in naturally isotropic materials.
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45/2017 - 06/08/2017
Gasperoni, F.; Ieva, F.; Paganoni, A.M.; Jackson C.H.; Sharples L.D.
Nonparametric frailty Cox models for hierarchical time-to-event data | Abstract | | In this work we propose a novel model for dealing with hierarchical time-to-event data, which is a common structure in healthcare research field (i.e., healthcare providers, seen as groups of patients). The most common statistical model for dealing with this kind of data is the Cox proportional hazard model with shared frailty term, whose distribution has to be specified a priori.
The main objective of this work consists in overcoming this limit by avoiding any a priori hypothesis on the frailty distribution. In order to do it, we introduce a nonparametric discrete frailty, through which we are not just guaranteeing a very good level of flexibility, but we are also building a probabilistic clustering technique, which allows to detect a clustering structure of groups, where each cluster is named latent population.
A tailored Expectation-Maximization algorithm, combined with model selection tech- niques, is proposed for estimating model’s parameters.
Beyond the new methodological contribution, we propose a useful tool for exploring big hierarchical time-to-event data, where it is very difficult to explain all the phenomenon variability through explanatory covariates. We show the power of this model by applying it to a clinical administrative database, where several information of patients suffering from Heart Failure is collected, like age, comorbidities, procedures etc. In this way, we are able to detect a latent clustering structure among healthcare providers. |
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44/2017 - 01/08/2017
Martino, A.; Ghiglietti, A.; Ieva, F.; Paganoni, A.M.
A k-means procedure based on a Mahalanobis type distance for clustering multivariate functional data | Abstract | | This paper proposes a clustering procedure for samples of multivariate functions in (L^2(I))^J, with J>=1. This method is based on a k-means algorithm in which the distance between the curves is measured with a metrics that generalizes the Mahalanobis distance in Hilbert spaces,
considering the correlation and the variability along all the components of the functional data. The proposed procedure has been studied in simulation and compared with the k-means based on other distances typically adopted for clustering multivariate functional data. In these simulations, it is shown that the k-means algorithm with the generalized Mahalanobis distance provides the best clustering performances, both in terms of mean and standard deviation of the number of misclassified curves. Finally, the proposed method has been applied to two real cases studies, concerning ECG signals and growth curves, where the results obtained in simulation are confirmed and strengthened. |
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43/2017 - 01/08/2017
Bottle, A.; Ventura, C.M.; Dharmarajan, K.; Aylin, P.; Ieva, F.; Paganoni, A.M.
Regional variation in hospitalisation and mortality in heart failure: comparison of England and Lombardy using multistate modelling | Abstract | | Heart failure (HF) is a common, serious chronic condition with high morbidity, hospitalisation and mortality. The healthcare systems of England and the northern Italian region of Lombardy share important similarities and have comprehensive hospital administrative databases linked to
the death register. We used them to compare admission for HF and mortality for patients between 2006 and 2012 (n = 37,185 for Lombardy, 234,719 for England) with multistate models. Despite close similarities in age, sex and common comorbidities of the two sets of patients, in Lombardy, HF admissions were longer and more frequent per patient than in England, but short- and medium-term mortality was much lower. English patients had more very short stays, but their very elderly also had longer stays than their Lombardy counterparts. Using a three-state model, the predicted total time spent in hospital showed large differences between the countries: women in England spent an average of 24 days if aged 65 at first admission and 19 days if aged 85; in Lombardy these figures were 68 and 27 days respectively. Eight-state models suggested disease progression that appeared similar in each country. Differences by region within England were
modest, with London patients spending more time in hospital and having lower mortality than the rest of England. Whilst clinical practice differences plausibly explain these patterns, we cannot confidently disentangle the impact of alternatives such as coding, casemix, and the availability and use of nonhospital settings. We need to better understand the links between rehospitalisation frequency and mortality. |
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42/2017 - 27/07/2017
Gower, AL, Shearer, T, Ciarletta P
A new restriction for initially stressed elastic solids | Abstract | | We introduce a fundamental restriction on the strain energy function
and stress tensor for initially stressed elastic solids. The restriction
applies to strain energy functions W that are explicit functions of the
elastic deformation gradient F and initial stress tau , i.e. W := W(F; tau ).
The restriction is a consequence of energy conservation and ensures
that the predicted stress and strain energy do not depend upon an
arbitrary choice of reference configuration. We call this restriction
initial stress reference independence (ISRI). It transpires that most
strain energy functions found in the literature do not satisfy ISRI,
and may therefore lead to unphysical behaviour, which we illustrate
via a simple example. To remedy this shortcoming we derive three
strain energy functions that do satisfy the restriction. We also show
that using initial strain (often from a virtual configuration) to model
initial stress leads to strain energy functions that automatically satisfy
ISRI. Finally, we reach the following important result: ISRI reduces
the number of unknowns in the linear stress tensor for initially stressed
solids. This new way of reducing the linear stress may open new
pathways for the non-destructive determination of initial stresses via
ultrasonic experiments, among others. |
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41/2017 - 26/07/2017
Beretta, E.; Micheletti, S.; Perotto, S.; Santacesaria, M.
Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT | Abstract | | In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to use a distributed shape derivative of a suitable cost functional with respect to movements of the partition. Numerical simulations showing the robustness and accuracy of the method are presented for simulated test cases in two dimensions. |
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