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 1148 prodotti
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51/2023 - 02/06/2023
Bucelli, M.; Regazzoni, F.; Dede', L.; Quarteroni, A.
Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: application to cardiac electromechanics | Abstract | | The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Function (RBF) interpolation with Singular Value Decomposition (SVD) to preserve the positivity of the determinant of the deformation gradient tensor. The method involves decomposing the evaluations of the tensor at the quadrature nodes of the source mesh into rotation matrices and diagonal matrices of singular values; computing the RBF interpolation of the quaternion representation of rotation matrices and the singular value logarithms; reassembling the deformation gradient tensors at quadrature nodes of the destination mesh, to be used in the assembly of the electrophysiology model equations. The proposed method overcomes limitations of existing interpolation methods, including nested intergrid interpolation and RBF interpolation of the displacement field, that may lead to the loss of physical meaningfulness of the mathematical formulation and then to solver failures at the algebraic level, due to negative determinant values. Furthermore, the proposed method enables the transfer of solution variables between finite element spaces of different degrees and shapes and without stringent conformity requirements between different meshes, thus enhancing the flexibility and accuracy of electromechanical simulations. We show numerical results confirming that the proposed method enables the transfer of the deformation gradient tensor, allowing to successfully run simulations in cases where existing methods fail. This work provides an efficient and robust method for the intergrid transfer of the deformation gradient tensor, thus enabling independent tailoring of mesh discretizations to the particular characteristics of the individual physical components concurring to the of the multiphysics model. |
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49/2023 - 24/05/2023
Ieva, F.; Ronzulli, M.; Romo, J.; Paganoni, A.M.
A Spearman Dependence Matrix for Multivariate Functional Data | Abstract | | We propose a nonparametric inferential framework for quantifying dependence
among two families of multivariate functional data. We generalize the notion of
Spearman correlation coefficient to situations where the observations are curves generated
by a stochastic processes. In particular, several properties of the Spearman
index are illustrated emphasizing the importance of having a consistent estimator of
the index of the original processes. We use the notion of Spearman index to define
the Spearman matrix, a mathematical object expressing the pattern of dependence
among the components of a multivariate functional dataset. Finally, the notion of
Spearman matrix is exploited to analyze two different populations of multivariate
curves (specifically, Electrocardiographic signals of healthy and unhealthy people),
in order to test if the pattern of dependence between the components is statistically
different in the two cases. |
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48/2023 - 23/05/2023
Renzi, F.; Vergara, C.; Fedele, M.; Giambruno, V.; Quarteroni, A.; Puppini, G.; Luciani, G.B.
Accurate and Efficient 3D Reconstruction of Right Heart Shape and Motion from Multi-Series Cine-MRI | Abstract | | The accurate reconstruction of the right heart geometry and motion from time-resolved
medical images enhances diagnostic tools based on image visualization as well as the
analysis of cardiac blood dynamics through computational methods. Due to the peculiarity
of the right heart morphology and motion, commonly used segmentation and/or
reconstruction techniques, which only employ Short-Axis cine-MRI, lack accuracy in
relevant regions of the right heart, like the ventricular base and the outflow tract. Moreover,
the reconstruction procedure is time-consuming and, in the case of the generation
of computational domains, requires a lot of manual intervention.
This paper presents a new method for the accurate and efficient reconstruction of the
right heart geometry and motion from time-resolved MRI. In particular, the proposed
method makes use of surface morphing to merge information coming from multi-series
cine-MRI (such as Short/Long-Axis and 2/3/4 Chambers acquisitions) and to reconstruct
important cardiac features. It also automatically provides the complete cardiac
contraction and relaxation motion by exploiting a suitable image registration technique.
The method is applied both to a healthy and a pathological (tetralogy of Fallot) case,
and yelds more accurate results than standard procedures. The proposed method is also
employed to provide significant input for computational fluid dynamics. The corresponding
numerical results demonstrate the reliability of our approach in the computation
of clinically relevant blood dynamics quantities. |
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45/2023 - 21/05/2023
Gironi, P.; Petraro, L.; Santoni, S.; Dede', L.; Colosimo, B.M.
A Computational Model of Cell Viability and Proliferation of Extrusion-based 3D Bioprinted Constructs During Tissue Maturation Process | Abstract | | 3D bioprinting is a novel promising solution for living tissue fabrication, with several potential advantages in many different applicative sectors. However, the implementation of complex vascular networks remains among the limiting factors for the production of complex tissues and for bioprinting scale-up. In this work, a physics-based computational model is presented to describe nutrients diffusion and consumption phenomena in bioprinted constructs. The model - a system of Partial Differential Equations that is approximated by means of the Finite Element method - allows for the description of cell viability and proliferation, and it can be easily adapted to different cell types, densities, biomaterials and 3D printed geometries, thus allowing a preassessment of cell viability within the bioprinted construct. The experimental validation is performed on bioprinted specimens to assess the ability of the model to predict changes in cell viability. The proposed model constitutes a proof of concept of digital twinning of biofabricated constructs that can be suitably included in the basic toolkit for tissue bioprinting. |
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44/2023 - 21/05/2023
Fontana, N.; Savaré, L.; Rea, F.; Di Angelantonio, E.; Ieva, F.
Long-term adherence to polytherapy in heart failure patients: a novel approach emphasising the importance of secondary prevention | Abstract | | Heart failure (HF) is a severe and costly clinical syndrome associated with increased healthcare costs and a high burden of mortality and morbidity. Although drug therapy is the mainstay of treatment for heart failure, non-adherence to prescribed therapies is common and is associated with worse health outcomes and increased hospitalizations. In this study, we propose a novel approach using Latent Markov models to analyze drug adherence to polytherapy over time using a secondary database. Our methodology enables us to evaluate patients' drug utilization behaviour, identify complex behavioural patterns, and incorporate them into predictive models to improve clinical outcomes.
The significance of adhering to prescribed therapies for patients' prognosis has been highlighted in this study. Our findings show that adherent patients gained an additional ten months of life over a seven-year follow-up period compared to non-adherent patients. This underscores the importance of secondary prevention and continuous monitoring of heart failure patients. These procedures are crucial for identifying areas of improvement and promoting better adherence to prescribed therapies. |
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42/2023 - 11/05/2023
Tonini, A.; Vergara, C.; Regazzoni, F.; Dedè, L.; Scrofani, R.; Cogliati, C.; Quarteroni, A.
A mathematical model to assess the effects of COVID-19 on the cardiocirculatory system | Abstract | | Impaired cardiac function has been described as a frequent complication of COVID-19-related pneumonia. To investigate possible underlying mechanisms, we represented the cardiovascular system by means of a lumped-parameter 0D mathematical model. The model was calibrated using clinical data, recorded in 58 patients hospitalized for COVID-19-related pneumonia, to make it patient-specific and to compute model outputs of clinical interest related to the cardiocirculatory system. We assessed, for each patient with a successful calibration, the statistical reliability of model outputs estimating the uncertainty intervals. Then, we performed a statistical analysis to compare healthy ranges and mean values (over patients) of reliable model outputs to determine which were significantly altered in COVID-19-related pneumonia. Our results showed significant increases in right ventricular systolic pressure, diastolic and mean pulmonary arterial pressure, and capillary wedge pressure. Instead, physical quantities related to the systemic circulation were not significantly altered. Remarkably, statistical analyses made on raw clinical data, without the support of a mathematical model, were unable to detect the effects of COVID-19-related pneumonia, thus suggesting that the use of a calibrated 0D mathematical model to describe the cardiocirculatory system is an effective tool to investigate the impairments of the cardiocirculatory system associated with COVID-19. |
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41/2023 - 10/05/2023
Corti M.; Bonizzoni, F.; Antonietti, P.F.; Quarteroni, A.M.
Uncertainty Quantification for Fisher-Kolmogorov Equation on Graphs with Application to Patient-Specific Alzheimer Disease | Abstract | | The Fisher-Kolmogorov equation is a diffusion-reaction PDE that is used to model the accumulation of prionic proteins, which are responsible for many different neurological disorders. Likely, the most important and studied misfolded protein in literature is the Amyloid-beta, responsible for the onset of Alzheimer disease. Starting from medical images we construct a reduced-order model based on a graph brain connectome. The reaction coefficient of the proteins is modelled as a stochastic random field, taking into account all the many different underlying physical processes, which can hardly be measured. Its probability distribution is inferred by means of the Monte Carlo Markov Chain method applied to clinical data. The resulting model is patient-specific and can be employed for predicting the disease's future development. Forward uncertainty quantification techniques (Monte Carlo and sparse grid stochastic collocation) are applied with the aim of quantifying the impact of the variability of the reaction coefficient on the progression of protein accumulation within the next 20 years. |
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40/2023 - 06/05/2023
Ballini, E.; Chiappa, A.S.; Micheletti, S.
Reducing the Drag of a Bluff Body by Deep Reinforcement Learning | Abstract | | We present a deep reinforcement learning approach to a classical problem in fluid dynamics, i.e., the reduction of the drag of a bluff body. We cast the problem as a discrete-time control with continuous action space: at each time step, an autonomous agent can set the flow rate of two jets of fluid, positioned at the back of the body. The agent, trained with Proximal Policy Optimization, learns an effective strategy to make the jets interact with the vortexes of the wake, thus reducing the drag. To tackle the computational complexity of the fluid dynamics simulations, which would make the training procedure prohibitively expensive, we train the agent on a coarse discretization of the domain. We provide numerical evidence that a policy trained in this approximate environment still retains good performance when carried over to a denser mesh. Our simulations show a considerable drag reduction with a consequent saving of total power, defined as the sum of the power spent by the control system and of the power of the drag force, amounting to 40% when compared to simulations with the reference bluff body without any jet. Finally, we qualitatively investigate the control policy learnt by the neural network. We can observe that it achieves the drag reduction by learning the frequency of formation of the vortexes and activating the jets accordingly, thus blowing them away off the rear body surface. |
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