Development of musculoskeletal models for the design and the pre-clinical validation of hip resurfacing prosthesis

Background. The surgical treatment of dysfunctional hips is a severe condition for the patient and a costly therapy for the public health. Hip resurfacing techniques seem to hold the promise of various advantages over traditional THR, with particular attention to young and active patients. Although the lesson provided in the past by many branches of engineering is that success in designing competitive products can be achieved only by predicting the possible scenario of failure, to date the understanding of the implant quality is poorly pre-clinically addressed. Thus revision is the only delayed and reliable end point for assessment. The aim of the present work was to model the musculoskeletal system so as to develop a protocol for predicting failure of hip resurfacing prosthesis. Methods. Preliminary studies validated the technique for the generation of subject specific finite element (FE) models of long bones from Computed Thomography data. The proposed protocol consisted in the numerical analysis of the prosthesis biomechanics by deterministic and statistic studies so as to assess the risk of biomechanical failure on the different operative conditions the implant might face in a population of interest during various activities of daily living. Physiological conditions were defined including the variability of the anatomy, bone densitometry, surgery uncertainties and published boundary conditions at the hip. The protocol was tested by analysing a successful design on the market and a new prototype of a resurfacing prosthesis. Results. The intrinsic accuracy of models on bone stress predictions (RMSE < 10%) was aligned to the current state of the art in this field. The accuracy of prediction on the bone-prosthesis contact mechanics was also excellent (< 0.001 mm). The sensitivity of models prediction to uncertainties on modelling parameter was found below 8.4%. The analysis of the successful design resulted in a very good agreement with published retrospective studies. The geometry optimisation of the new prototype lead to a final design with a low risk of failure. The statistical analysis confirmed the minimal risk of the optimised design over the entire population of interest. The performances of the optimised design showed a significant improvement with respect to the first prototype (+35%). Limitations. On the authors opinion the major limitation of this study is on boundary conditions. The muscular forces and the hip joint reaction were derived from the few data available in the literature, which can be considered significant but hardly representative of the entire variability of boundary conditions the implant might face over the patients population. This moved the focus of the research on modelling the musculoskeletal system; the ongoing activity is to develop subject-specific musculoskeletal models of the lower limb from medical images. Conclusions. The developed protocol was able to accurately predict known clinical outcomes when applied to a well-established device and, to support the design optimisation phase providing important information on critical characteristics of the patients when applied to a new prosthesis. The presented approach does have a relevant generality that would allow the extension of the protocol to a large set of orthopaedic scenarios with minor changes. Hence, a failure mode analysis criterion can be considered a suitable tool in developing new orthopaedic devices.

Generation and characterization of mouse models of Small cell lung cancer and Basal cell carcinoma for the preclinical evaluation of new therapies

Background. Human small cell lung cancer (SCLC) accounting for approximately 15-20% of all lung cancers, is an aggressive tumor with high propensity for early regional and distant metastases. Although the initial tumor rate response to chemotherapy is very high, SCLC relapses after approximately 4 months in ED and 12 months in LD. Basal cell carcinoma (BCC) is the most prevalent cancer in the western world, and its incidence is increasing worldwide. This type of cancer rarely metastasizes and the death rate is extraordinary low. Surgery is curative for most of the patients, but for those that develop locally advanced or metastatic BCC there is currently no effective treatment. Both types of cancer have been deeply investigated and genetic alterations, MYCN amplification (MA) among the most interesting, have been found. These could become targets of new pharmacological therapies. Procedures. We created and characterized novel BLI xenograft orthotopic mouse models of SCLC to evaluate the tumor onset and progression and the efficacy of new pharmacological strategies. We compared an in vitro model with a transgenic mouse model of BCC, to investigate and delineate the canonical HH signalling pathway and its connections with other molecular pathways. Results and conclusions. The orthotopic models showed latency and progression patterns similar to human disease. Chemotherapy treatments improved survival rates and validated the in vivo model. The presence of MA and overexpression were confirmed in each model and we tested the efficacy of a new MYCN inhibitor in vitro. Preliminar data of BCC models highlighted Hedgehog pathway role and underlined the importance of both in vitro and in vivo strategies to achieve a better understanding of the pathology and to evaluate the applicability of new therapeutic compounds

Modeling the spatial dynamics of economic models

The advances that have been characterizing spatial econometrics in recent years are mostly theoretical and have not found an extensive empirical application yet. In this work we aim at supplying a review of the main tools of spatial econometrics and to show an empirical application for one of the most recently introduced estimators. Despite the numerous alternatives that the econometric theory provides for the treatment of spatial (and spatiotemporal) data, empirical analyses are still limited by the lack of availability of the correspondent routines in statistical and econometric software. Spatiotemporal modeling represents one of the most recent developments in spatial econometric theory and the finite sample properties of the estimators that have been proposed are currently being tested in the literature. We provide a comparison between some estimators (a quasi-maximum likelihood, QML, estimator and some GMM-type estimators) for a fixed effects dynamic panel data model under certain conditions, by means of a Monte Carlo simulation analysis. We focus on different settings, which are characterized either by fully stable or quasi-unit root series. We also investigate the extent of the bias that is caused by a non-spatial estimation of a model when the data are characterized by different degrees of spatial dependence. Finally, we provide an empirical application of a QML estimator for a time-space dynamic model which includes a temporal, a spatial and a spatiotemporal lag of the dependent variable. This is done by choosing a relevant and prolific field of analysis, in which spatial econometrics has only found limited space so far, in order to explore the value-added of considering the spatial dimension of the data. In particular, we study the determinants of cropland value in Midwestern U.S.A. in the years 1971-2009, by taking the present value model (PVM) as the theoretical framework of analysis.

Exploiting spectrally resolved satellite observations to assess the performance of climate models

The accurate representation of the Earth Radiation Budget by General Circulation Models (GCMs) is a fundamental requirement to provide reliable historical and future climate simulations. In this study, we found reasonable agreement between the integrated energy fluxes at the top of the atmosphere simulated by 34 state-of-the-art climate models and the observations provided by the Cloud and Earth Radiant Energy System (CERES) mission on a global scale, but large regional biases have been detected throughout the globe. Furthermore, we highlighted that a good agreement between simulated and observed integrated Outgoing Longwave Radiation (OLR) fluxes may be obtained from the cancellation of opposite-in-sign systematic errors, localized in different spectral ranges. To avoid this and to understand the causes of these biases, we compared the observed Earth emission spectra, measured by the Infrared Atmospheric Sounding Interferometer (IASI) in the period 2008-2016, with the synthetic radiances computed on the basis of the atmospheric fields provided by the EC-Earth GCM. To this purpose, the fast σ-IASI radiative transfer model was used, after its validation and implementation in EC-Earth. From the comparison between observed and simulated spectral radiances, a positive temperature bias in the stratosphere and a negative temperature bias in the middle troposphere, as well as a dry bias of the water vapor concentration in the upper troposphere, have been identified in the EC-Earth climate model. The analysis has been performed in clear-sky conditions, but the feasibility of its extension in the presence of clouds, whose impact on the radiation represents the greatest source of uncertainty in climate models, has also been proven. Finally, the analysis of simulated and observed OLR trends indicated good agreement and provided detailed information on the spectral fingerprints of the evolution of the main climate variables.

Incompressible limit and well-posedness of PDE models of tissue growth

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. A coupled system of equations describes the cell density and the nutrient concentration and the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state.

Development of multicomponent models for the prediction of lubricant oil-fuel dilution in internal combustion engines

The current environmental crisis is forcing the automotive industry to face tough challenges for the Internal Combustion Engines development in order to reduce the emissions of pollutants and Greenhouse gases. In this context, in the last decades, the main technological solutions adopted by the manufacturers have been the direct injection and the engine downsizing, which led to the rising of new concerns related to the fuel-cylinder walls physical interaction. The fuel spray possibly impacts the cylinder liner wall, which is wetted by the lubricant oil thus causing the derating of the lubricant properties, increasing the oil consumption, and contaminating the lubricant oil in the crankcase. Also, concerning hydrogen fuelled internal combustion engines, it is likely that the high near-wall temperature, which is typical of the hydrogen flame, results in the evaporation of a portion of the lubricant oil, increasing its consumption. With regards on the innovative combustion systems and their control strategies, optical accessible engines are fundamental tools for experimental investigations on such combustion systems. Though, due to the optical measurement line, optical engines suffer from a high level of blow-by, which must be accounted for. In light of the above, this thesis work aims to develop numerical methodologies with the aim to build useful tools for supporting the design of modern engines. In particular, a one-dimensional modelling of the lubricant oil-fuel dilution and oil evaporation has been performed and coupled with an optimization algorithm to achieve a lubricant oil surrogate. Then, a quasi-dimensional blow-by model has been developed and validated against experimental data. Such model, has been coupled with CFD 3D simulations and directly implemented in CFD 3D. Finally, CFD 3D simulations coupled with the VOF method have been performed in order to validate a methodology for studying the impact of a liquid droplet on a solid surface.

Aspects of Integrability in Gauge/String Correspondence

In this thesis, we present our work about some generalisations of ideas, techniques and physical interpretations typical for integrable models to one of the most outstanding advances in theoretical physics of nowadays: the AdS/CFT correspondences. We have undertaken the problem of testing this conjectured duality under various points of view, but with a clear starting point - the integrability - and with a clear ambitious task in mind: to study the finite-size effects in the energy spectrum of certain string solutions on a side and in the anomalous dimensions of the gauge theory on the other. Of course, the final desire woul be the exact comparison between these two faces of the gauge/string duality. In few words, the original part of this work consists in application of well known integrability technologies, in large parte borrowed by the study of relativistic (1+1)-dimensional integrable quantum field theories, to the highly non-relativisic and much complicated case of the thoeries involved in the recent conjectures of AdS5/CFT4 and AdS4/CFT3 corrspondences. In details, exploiting the spin chain nature of the dilatation operator of N = 4 Super-Yang-Mills theory, we concentrated our attention on one of the most important sector, namely the SL(2) sector - which is also very intersting for the QCD understanding - by formulating a new type of nonlinear integral equation (NLIE) based on a previously guessed asymptotic Bethe Ansatz. The solutions of this Bethe Ansatz are characterised by the length L of the correspondent spin chain and by the number s of its excitations. A NLIE allows one, at least in principle, to make analytical and numerical calculations for arbitrary values of these parameters. The results have been rather exciting. In the important regime of high Lorentz spin, the NLIE clarifies how it reduces to a linear integral equations which governs the subleading order in s, o(s0). This also holds in the regime with L ! 1, L/ ln s finite (long operators case). This region of parameters has been particularly investigated in literature especially because of an intriguing limit into the O(6) sigma model defined on the string side. One of the most powerful methods to keep under control the finite-size spectrum of an integrable relativistic theory is the so called thermodynamic Bethe Ansatz (TBA). We proposed a highly non-trivial generalisation of this technique to the non-relativistic case of AdS5/CFT4 and made the first steps in order to determine its full spectrum - of energies for the AdS side, of anomalous dimensions for the CFT one - at any values of the coupling constant and of the size. At the leading order in the size parameter, the calculation of the finite-size corrections is much simpler and does not necessitate the TBA. It consists in deriving for a nonrelativistc case a method, invented for the first time by L¨uscher to compute the finite-size effects on the mass spectrum of relativisic theories. So, we have formulated a new version of this approach to adapt it to the case of recently found classical string solutions on AdS4 × CP3, inside the new conjecture of an AdS4/CFT3 correspondence. Our results in part confirm the string and algebraic curve calculations, in part are completely new and then could be better understood by the rapidly evolving developments of this extremely exciting research field.

Non perturbative aspects of non equilibrium physics in two dimensional models

The present manuscript focuses on out of equilibrium physics in two dimensional models. It has the purpose of presenting some results obtained as part of out of equilibrium dynamics in its non perturbative aspects. This can be understood in two different ways: the former is related to integrability, which is non perturbative by nature; the latter is related to emergence of phenomena in the out of equilibirum dynamics of non integrable models that are not accessible by standard perturbative techniques. In the study of out of equilibirum dynamics, two different protocols are used througout this work: the bipartitioning protocol, within the Generalised Hydrodynamics (GHD) framework, and the quantum quench protocol. With GHD machinery we study the Staircase Model, highlighting how the hydrodynamic picture sheds new light into the physics of Integrable Quantum Field Theories; with quench protocols we analyse different setups where a non-perturbative description is needed and various dynamical phenomena emerge, such as the manifistation of a dynamical Gibbs effect, confinement and the emergence of Bloch oscillations preventing thermalisation.

Quantitative susceptibility mapping as biomarker of neurodegeneration: methodological models and clinical applications

Quantitative Susceptibility Mapping (QSM) is an advanced magnetic resonance technique that can quantify in vivo biomarkers of pathology, such as alteration in iron and myelin concentration. It allows for the comparison of magnetic susceptibility properties within and between different subject groups. In this thesis, QSM acquisition and processing pipeline are discussed, together with clinical and methodological applications of QSM to neurodegeneration. In designing the studies, significant emphasis was placed on results reproducibility and interpretability. The first project focuses on the investigation of cortical regions in amyotrophic lateral sclerosis. By examining various histogram susceptibility properties, a pattern of increased iron content was revealed in patients with amyotrophic lateral sclerosis compared to controls and other neurodegenerative disorders. Moreover, there was a correlation between susceptibility and upper motor neuron impairment, particularly in patients experiencing rapid disease progression. Similarly, in the second application, QSM was used to examine cortical and sub-cortical areas in individuals with myotonic dystrophy type 1. The thalamus and brainstem were identified as structures of interest, with relevant correlations with clinical and laboratory data such as neurological evaluation and sleep records. In the third project, a robust pipeline for assessing radiomic susceptibility-based features reliability was implemented within a cohort of patients with multiple sclerosis and healthy controls. Lastly, a deep learning super-resolution model was applied to QSM images of healthy controls. The employed model demonstrated excellent generalization abilities and outperformed traditional up-sampling methods, without requiring a customized re-training. Across the three disorders investigated, it was evident that QSM is capable of distinguishing between patient groups and healthy controls while establishing correlations between imaging measurements and clinical data. These studies lay the foundation for future research, with the ultimate goal of achieving earlier and less invasive diagnoses of neurodegenerative disorders within the context of personalized medicine.