A Bayesian numerical homogenization method for elliptic multiscale inverse problems

A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly oscillatory tensor from measurements of the fine scale solution at the boundary, using a coarse model based on numerical homogenization and model order reduction. We provide a rigorous Bayesian formulation of the problem, taking into account different possibilities for the choice of the prior measure. We prove well-posedness of the effective posterior measure and, by means of G-convergence, we establish a link between the effective posterior and the fine scale model. Several numerical experiments illustrate the efficiency of the proposed scheme and confirm the theoretical findings

Coupled Mathematical Models for Heart Integration: A Stability Study

In this thesis we consider a fully coupled model which aims at reproducing some qualitative features of the electro-mechanical activity of the heart. The models used to describe both the electrical and mechanical activities are relatively simple. However, coupling them together can give rise to numerical instabilities or incorrect predictions. After having introduced each of the sub-models of the fully coupled system we perform some numerical experiments to draw some insights on the numerical approximation of this problem. Firstly we focus on the numerical approximation of the Aliev-Panfilov model, which controls the electrical activation of the muscle. We verify that different approaches can be followed to solve such a problem by the finite element method reducing the computational effort. However each approach can lead to inaccurate predictions of the front velocity. Then we suggest also two numerical schemes for time integration particularly suited for PDEs such as the Aliev-Panfilov model: the operator splitting method and the Runge-Kutta-Chebyshev method. When considering the fully coupled problem, we examine two ways of reducing the computational cost: treating some of the coupling terms explicitly or solving the linearised system iteratively. We verify that with the first choice we can experience numerical instabilities depending on the numerical scheme used for time integration. On the other hand, when solving the linearised system iteratively, key points to solve the problem efficiently are the choice of an adaptive stopping criterion and a good preconditioner. From the numerical experiments performed we conclude that the coupling between the active stress and the mechanics is very influential on the stability of the system and on the convergence of the residuals

Penalization and Bayesian numerical methods for multiscale inverse problems

In this thesis we consider inverse problems involving multiscale elliptic partial differential equations. The name multiscale indicates that these models are characterized by the presence of parameters which vary on different spatial scales (macroscopic, microscopic, mesoscopic, etc.). The variations at the smallest scales make these equations very difficult to approximate also when considering forward problems, since classical numerical methods require a mesh resolution at the finest scales, hence a computational cost that is often prohibitive. For this reason one prefers to apply homogenization or effective methods which, neglecting what happens at the smallest scales, are able to provide accurate macroscopic solutions to the problem. For what concerns the solution of inverse problems, we propose then a new numerical algorithm based on homogenization techniques, model order reduction and regularization methods. First, we consider elliptic operators whose tensor varies on a microscopic scale. Under the assumption that the nature of its micro structure is known, we aim at recovering a macroscopic parameterization of the tensor from measurements originating from the full multiscale model, using homogenization. Practical examples include multi-phase media whose constituents are known, but their respective volume fraction is unknown. We consider the Calderón's formulation of the inverse problem. We prove that, under some regularity assumptions on the fine scale tensor, the effective inverse problem, with observed data consisting of the homogenized Dirichlet to Neumann (DtN) map, is also well-posed. We then solve the problem by considering finite measurements of the multiscale DtN map and using Tikhonov regularization, and we establish a convergence result of the solution by means of G-convergence. In a second stage, we consider a Bayesian approach which allows for uncertainty quantification of the results. We prove existence and well-posedness of the effective posterior probability measure, obtained by homogenization of the observation operator. By means of G-convergence we characterize the discrepancy between the fine scale and the homogenized model, and we prove convergence of the effective posterior towards the fine scale posterior in terms of the Hellinger distance. We also propose a numerical procedure to estimate the homogenization error statistics, which, if included in the inversion process, allow to account for approximation errors. Finally, we deal with multiscale inverse problems for the linear elasticity equation. In this context we assume that the heterogeneity of the material is determined by its geometry rather than by the coefficients of the equation. In particular, we consider porous media with random perforations and, following the Bayesian approach, we solve the inverse problem of determining the elastic properties of an hypothetical isotropic material. We prove the existence and well-posedness of the effective posterior measure, as well as its convergence in the fine scale limit by means of G-convergence. We conclude by describing a new probabilistic numerical method which computes a new posterior measure that accounts for approximation errors and reveals the uncertainty intrinsic in the numerical method

A Bayesian numerical homogenization method for elliptic multiscale inverse problems

A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly oscillatory tensor from measurements of the fine scale solution at the boundary, using a coarse model based on numerical homogenization and model order reduction. We provide a rigorous Bayesian formulation of the problem, taking into account different possibilities for the choice of the prior measure. We prove well-posedness of the effective posterior measure and, by means of G-convergence, we establish a link between the effective posterior and the fine scale model. Several numerical experiments illustrate the efficiency of the proposed scheme and confirm the theoretical findings

Midterm results of edge-to-edge mitral valve repair without annuloplasty

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Nordic Walking can be incorporated in the exercise prescription to increase aerobic capacity, strength and quality of life for elderly: a systematic review and meta-analysis.

Abstract The aim of this systematic review and meta-analysis was to summarize and analyze the effects of Nordic Walking on physical fitness, body composition and quality of life in the elderly. METHODS: keyword "Nordic Walking" associated with "elderly" AND/OR "aging" AND/OR "old subjects" AND/OR "aged" AND/OR "older adults" were used in the onlines database Medline, Embase, PubMed, Scopus, PsycINFO and SPORTDiscus. Only studies written in English language and published in peer-reviewed journals were considered. A meta-analysis was performed and effect sizes calculated. RESULTS: 15 studies were identified; age of participants ranged from 60 to 92 years old. Comparing with a sedentary group, effect sizes showed that Nordic Walking was able to improve dynamic balance (0.30), functional balance (0.62), muscle strength of upper (0.66) and lower limbs (0.43), aerobic capacity (0.92), cardiovascular outcomes (0.23), body composition (0.30) and lipid profile (0.67). It seemed that Nordic Walking had a negative effect on static balance (-0.72). Comparing with a walking (alone) training, effect sizes showed that Nordic Walking improved the dynamic balance (0.30), flexibility of the lower body (0.47) and quality of life (0.53). Walking training was more effective in improving aerobic capacity (-0.21). Comparing Nordic Walking with resistance training, effect sizes showed that Nordic Walking improved dynamic balance (0.33), muscle strength of the lower body (0.39), aerobic capacity (0.75), flexibility of the upper body (0.41), and the quality of life (0.93). CONCLUSIONS: Nordic Walking can be considered as a safe and accessible form of aerobic exercise for the elderly population, able to improve cardiovascular outcomes, muscle strength, balance ability and quality of life

Selective reduction of the septolateral dimensions in functional mitral regurgitation by modified-shape ring annuloplasty

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Flexibility and Strength Effects of Adapted Nordic Walking and Myofascial Exercises Practice in Breast Cancer Survivors and Analysis of Differences

Breast cancer treatments can elicit negative kinesiological side effects concerning both the posture and functional status of breast cancer survivors. As our body is functionally organized in myofascial meridians, physical exercise practice should favor a whole-body approach rather than a local one. The aim of the study was to investigate and compare the effects of two whole-body disciplines, i.e., adapted Nordic Walking and myofascial exercise, on the flexibility and strength performances in BCS. One hundred and sixty breast cancer survivors were trained three times per week for 12 weeks through adapted Nordic Walking or myofascial exercise. Handgrip, sit and reach, back scratch, and single leg back bridge tests and body composition were assessed at the beginning and completion of the training period. Linear mixed models showed no significant changes in body composition, whereas flexibility (p < 0.001), strength (p < 0.001), and muscle quality index (p = 0.003) changed independently from the treatment. When data modification has been analyzed according to sub-sample membership, no significant differences have been observed. Age, radiation therapy, and chemotherapy seem to have independent effects on several investigated variables. Twelve weeks of adapted myofascial exercise and Nordic Walking led to significant changes in flexibility, strength, and muscle quality in breast cancer survivors, with no apparent superiority of one approach over the other

Kinesiology Students' Perception Regarding Exercise Oncology: A Cross-Sectional Study

none13noDelivering physical activity in cancer care requires knowledge, competence, and specific skills to adapt the exercise program to the patients' specific needs. Kinesiology students could be one of the main stakeholders involved in the promotion of physical activity. This study aims to investigate the knowledge, perception, and competence about exercise in patients with oncological disease in a sample of students attending the Sports Science University. A total of 854 students (13% response rate) from four Italian universities completed the online survey between May and June 2021. About half of the study participants identified the correct amount of aerobic (44%) and strength (54%) activities proposed by the American College of Sports Medicine for patients with cancer. Almost all the students recognized the importance of physical activity in cancer prevention (96%), in the management of cancer before surgery (96%), during anticancer treatments (84%), and after therapies completion (98%). On the contrary, they reported a lack of university courses dedicated to cancer diseases, psychological implications, and prescription of physical activity in all types of cancer prevention. Overall, few students felt qualified in delivered counseling about physical activity and individual or group-based exercise programs in patients with cancer. Logistic regression revealed that the students attending the Master's Degree in Preventive and Adapted Physical Activity were more likely to have knowledge and competence than other students. The present study suggests that kinesiology universities should increase the classes and internships about exercise oncology to train experts with specific skills who are able to adequately support patients in their lifestyle modification.Avancini, Alice; Ferri Marini, Carlo; Sperduti, Isabella; Natalucci, Valentina; Borsati, Anita; Pilotto, Sara; Cerulli, Claudia; Barbieri, Elena; Lucertini, Francesco; Lanza, Massimo; Parisi, Attilio; Grazioli, Elisa; Di Blasio, AndreaAvancini, Alice; Ferri Marini, Carlo; Sperduti, Isabella; Natalucci, Valentina; Borsati, Anita; Pilotto, Sara; Cerulli, Claudia; Barbieri, Elena; Lucertini, Francesco; Lanza, Massimo; Parisi, Attilio; Grazioli, Elisa; Di Blasio, Andre