Evaluation of bone strength: microtomographic tecniques

This thesis is a part of a larger study about the characterization of mechanical and histomorphometrical properties of bone. The main objects of this study were the bone tissue properties and its resistance to mechanical loads. Moreover, the knowledge about the equipment selected to carry out the analyses, the micro-computed tomography (micro-CT), was improved. Particular attention was given to the reliability over time of the measuring instrument. In order to understand the main characteristics of bone mechanical properties a study of the skeletal, the bones of which it is composed and biological principles that drive their formation and remodelling, was necessary. This study has led to the definition of two macro-classes describing the main components responsible for the resistance to fracture of bone: quantity and quality of bone. The study of bone quantity is the current clinical standard measure for so-called bone densitometry, and research studies have amply demonstrated that the amount of tissue is correlated with its mechanical properties of elasticity and fracture. However, the models presented in the literature, including information on the mere quantity of tissue, have often been limited in describing the mechanical behaviour. Recent investigations have underlined that also the bone-structure and the tissue-mineralization play an important role in the mechanical characterization of bone tissue. For this reason in this thesis the class defined as bone quality was mainly studied, splitting it into two sub-classes of bone structure and tissue quality. A study on bone structure was designed to identify which structural parameters, among the several presented in the literature, could be integrated with the information about quantity, in order to better describe the mechanical properties of bone. In this way, it was also possible to analyse the iteration between structure and function. It has been known for long that bone tissue is capable of remodeling and changing its internal structure according to loads, but the dynamics of these changes are still being analysed. This part of the study was aimed to identify the parameters that could quantify the structural changes of bone tissue during the development of a given disease: osteoarthritis. A study on tissue quality would have to be divided into different classes, which would require a scale of analysis not suitable for the micro-CT. For this reason the study was focused only on the mineralization of the tissue, highlighting the difference between bone density and tissue density, working in a context where there is still an ongoing scientific debate.

Enhanced Mixed Integer Programming Techniques and Routing Problems

Mixed integer programming is up today one of the most widely used techniques for dealing with hard optimization problems. On the one side, many practical optimization problems arising from real-world applications (such as, e.g., scheduling, project planning, transportation, telecommunications, economics and finance, timetabling, etc) can be easily and effectively formulated as Mixed Integer linear Programs (MIPs). On the other hand, 50 and more years of intensive research has dramatically improved on the capability of the current generation of MIP solvers to tackle hard problems in practice. However, many questions are still open and not fully understood, and the mixed integer programming community is still more than active in trying to answer some of these questions. As a consequence, a huge number of papers are continuously developed and new intriguing questions arise every year. When dealing with MIPs, we have to distinguish between two different scenarios. The first one happens when we are asked to handle a general MIP and we cannot assume any special structure for the given problem. In this case, a Linear Programming (LP) relaxation and some integrality requirements are all we have for tackling the problem, and we are ``forced" to use some general purpose techniques. The second one happens when mixed integer programming is used to address a somehow structured problem. In this context, polyhedral analysis and other theoretical and practical considerations are typically exploited to devise some special purpose techniques. This thesis tries to give some insights in both the above mentioned situations. The first part of the work is focused on general purpose cutting planes, which are probably the key ingredient behind the success of the current generation of MIP solvers. Chapter 1 presents a quick overview of the main ingredients of a branch-and-cut algorithm, while Chapter 2 recalls some results from the literature in the context of disjunctive cuts and their connections with Gomory mixed integer cuts. Chapter 3 presents a theoretical and computational investigation of disjunctive cuts. In particular, we analyze the connections between different normalization conditions (i.e., conditions to truncate the cone associated with disjunctive cutting planes) and other crucial aspects as cut rank, cut density and cut strength. We give a theoretical characterization of weak rays of the disjunctive cone that lead to dominated cuts, and propose a practical method to possibly strengthen those cuts arising from such weak extremal solution. Further, we point out how redundant constraints can affect the quality of the generated disjunctive cuts, and discuss possible ways to cope with them. Finally, Chapter 4 presents some preliminary ideas in the context of multiple-row cuts. Very recently, a series of papers have brought the attention to the possibility of generating cuts using more than one row of the simplex tableau at a time. Several interesting theoretical results have been presented in this direction, often revisiting and recalling other important results discovered more than 40 years ago. However, is not clear at all how these results can be exploited in practice. As stated, the chapter is a still work-in-progress and simply presents a possible way for generating two-row cuts from the simplex tableau arising from lattice-free triangles and some preliminary computational results. The second part of the thesis is instead focused on the heuristic and exact exploitation of integer programming techniques for hard combinatorial optimization problems in the context of routing applications. Chapters 5 and 6 present an integer linear programming local search algorithm for Vehicle Routing Problems (VRPs). The overall procedure follows a general destroy-and-repair paradigm (i.e., the current solution is first randomly destroyed and then repaired in the attempt of finding a new improved solution) where a class of exponential neighborhoods are iteratively explored by heuristically solving an integer programming formulation through a general purpose MIP solver. Chapters 7 and 8 deal with exact branch-and-cut methods. Chapter 7 presents an extended formulation for the Traveling Salesman Problem with Time Windows (TSPTW), a generalization of the well known TSP where each node must be visited within a given time window. The polyhedral approaches proposed for this problem in the literature typically follow the one which has been proven to be extremely effective in the classical TSP context. Here we present an overall (quite) general idea which is based on a relaxed discretization of time windows. Such an idea leads to a stronger formulation and to stronger valid inequalities which are then separated within the classical branch-and-cut framework. Finally, Chapter 8 addresses the branch-and-cut in the context of Generalized Minimum Spanning Tree Problems (GMSTPs) (i.e., a class of NP-hard generalizations of the classical minimum spanning tree problem). In this chapter, we show how some basic ideas (and, in particular, the usage of general purpose cutting planes) can be useful to improve on branch-and-cut methods proposed in the literature.

Characterization and natural history of different phenotypes in hereditary transthyretin amyloidosis: 40-year experience at a single Italian referral center

- Aims: Hereditary Transthyretin Amyloidosis (ATTRv) is one of the leading etiologies of systemic amyloidosis with more than 135 mutations described and a broad spectrum of clinical manifestations. We aimed to provide a systematic description of a population of individuals carrying pathogenic mutations of transthyretin (TTR) gene and to investigate the major clinical events during follow up. - Methods: Observational, retrospective, cohort study including consecutive patients with mutations of TTR gene, admitted to a tertiary referral center in Bologna, Italy, between 1984 and 2022. - Results: Three hundred twenty-five patients were included: 106 asymptomatic carriers, 49 cardiac phenotype, 49 neurological phenotype and 121 mixed phenotype. Twenty-three different mutations were found, with Ile68Leu (41.8%), Val30Met (19%), and Glu89Gln (10%) being the most common. After a median follow-up of 51 months data from 290 subjects were analyzed; among them 111 (38.3%) died and 123 (42.4%) had a major clinical event (death or hospitalization for heart failure). Nine (11.5%) of the 78 asymptomatic carriers showed signs and symptoms of the disease. Carriers had a prognosis comparable to healthy population, while no significant differences were seen among the three phenotypes adjusted by age. Age at diagnosis, NYHA functional class, left ventricular ejection fraction, mPND score and disease-modifying therapy were independently associated with survival. - Conclusions: This study offers a wide and comprehensive overview of ATTRv from the point of view of a tertiary referral center in Italy. Three main phenotypes can be identified (cardiac, neurological and mixed) with specific clinical and instrumental features. Family screening programs are essential to identify paucisymptomatic affected patients or unaffected carriers of the mutation, to be followed through the years. Lastly, disease-modifying therapy represents an evolving cornerstone of the management of ATTRv, with a great impact on mortality.