Methodological improvement of 3D fluoroscopic analysis for the robust quantification of 3D kinematics of human joints

3D video-fluoroscopy is an accurate but cumbersome technique to estimate natural or prosthetic human joint kinematics. This dissertation proposes innovative methodologies to improve the 3D fluoroscopic analysis reliability and usability. Being based on direct radiographic imaging of the joint, and avoiding soft tissue artefact that limits the accuracy of skin marker based techniques, the fluoroscopic analysis has a potential accuracy of the order of mm/deg or better. It can provide fundamental informations for clinical and methodological applications, but, notwithstanding the number of methodological protocols proposed in the literature, time consuming user interaction is exploited to obtain consistent results. The user-dependency prevented a reliable quantification of the actual accuracy and precision of the methods, and, consequently, slowed down the translation to the clinical practice. The objective of the present work was to speed up this process introducing methodological improvements in the analysis. In the thesis, the fluoroscopic analysis was characterized in depth, in order to evaluate its pros and cons, and to provide reliable solutions to overcome its limitations. To this aim, an analytical approach was followed. The major sources of error were isolated with in-silico preliminary studies as: (a) geometric distortion and calibration errors, (b) 2D images and 3D models resolutions, (c) incorrect contour extraction, (d) bone model symmetries, (e) optimization algorithm limitations, (f) user errors. The effect of each criticality was quantified, and verified with an in-vivo preliminary study on the elbow joint. The dominant source of error was identified in the limited extent of the convergence domain for the local optimization algorithms, which forced the user to manually specify the starting pose for the estimating process. To solve this problem, two different approaches were followed: to increase the optimal pose convergence basin, the local approach used sequential alignments of the 6 degrees of freedom in order of sensitivity, or a geometrical feature-based estimation of the initial conditions for the optimization; the global approach used an unsupervised memetic algorithm to optimally explore the search domain. The performances of the technique were evaluated with a series of in-silico studies and validated in-vitro with a phantom based comparison with a radiostereometric gold-standard. The accuracy of the method is joint-dependent, and for the intact knee joint, the new unsupervised algorithm guaranteed a maximum error lower than 0.5 mm for in-plane translations, 10 mm for out-of-plane translation, and of 3 deg for rotations in a mono-planar setup; and lower than 0.5 mm for translations and 1 deg for rotations in a bi-planar setups. The bi-planar setup is best suited when accurate results are needed, such as for methodological research studies. The mono-planar analysis may be enough for clinical application when the analysis time and cost may be an issue. A further reduction of the user interaction was obtained for prosthetic joints kinematics. A mixed region-growing and level-set segmentation method was proposed and halved the analysis time, delegating the computational burden to the machine. In-silico and in-vivo studies demonstrated that the reliability of the new semiautomatic method was comparable to a user defined manual gold-standard. The improved fluoroscopic analysis was finally applied to a first in-vivo methodological study on the foot kinematics. Preliminary evaluations showed that the presented methodology represents a feasible gold-standard for the validation of skin marker based foot kinematics protocols.

Velocity structure and seismic anisotropy in the crust and upper mantle from Receiver Function analysis: three case studies in Italy

The research for this PhD project consisted in the application of the RFs analysis technique to different data-sets of teleseismic events recorded at temporary and permanent stations located in three distinct study regions: Colli Albani area, Northern Apennines and Southern Apennines. We found some velocity models to interpret the structures in these regions, which possess very different geologic and tectonics characteristics and therefore offer interesting case study to face. In the Colli Albani some of the features evidenced in the RFs are shared by all the analyzed stations: the Moho is almost flat and is located at about 23 km depth, and the presence of a relatively shallow limestone layer is a stable feature; contrariwise there are features which vary from station to station, indicating local complexities. Three seismic stations, close to the central part of the former volcanic edifice, display relevant anisotropic signatures­­­ with symmetry axes consistent with the emplacement of the magmatic chamber. Two further anisotropic layers are present at greater depth, in the lower crust and the upper mantle, respectively, with symmetry axes directions related to the evolution of the volcano complex. In Northern Apennines we defined the isotropic structure of the area, finding the depth of the Tyrrhenian (almost 25 km and flat) and Adriatic (40 km and dipping underneath the Apennines crests) Mohos. We determined a zone in which the two Mohos overlap, and identified an anisotropic body in between, involved in the subduction and going down with the Adiratic Moho. We interpreted the downgoing anisotropic layer as generated by post-subduction delamination of the top-slab layer, probably made of metamorphosed crustal rocks caught in the subduction channel and buoyantly rising toward the surface. In the Southern Apennines, we found the Moho depth for 16 seismic stations, and highlighted the presence of an anisotropic layer underneath each station, at about 15-20 km below the whole study area. The moho displays a dome-like geometry, as it is shallow (29 km) in the central part of the study area, whereas it deepens peripherally (down to 45 km); the symmetry axes of anisotropic layer, interpreted as a layer separating the upper and the lower crust, show a moho-related pattern, indicated by the foliation of the layer which is parallel to the Moho trend. Moreover, due to the exceptional seismic event occurred on April 6th next to L’Aquila town, we determined the Vs model for two station located next to the epicenter. An extremely high velocity body is found underneath AQU station at 4-10 km depth, reaching Vs of about 4 km/s, while this body is lacking underneath FAGN station. We compared the presence of this body with other recent works and found an anti-correlation between the high Vs body, the max slip patches and earthquakes distribution. The nature of this body is speculative since such high velocities are consistent with deep crust or upper mantle, but can be interpreted as a as high strength barrier of which the high Vs is a typical connotation.

Learning with Kernels on Graphs: DAG-based kernels, data streams and RNA function prediction.

In many application domains data can be naturally represented as graphs. When the application of analytical solutions for a given problem is unfeasible, machine learning techniques could be a viable way to solve the problem. Classical machine learning techniques are defined for data represented in a vectorial form. Recently some of them have been extended to deal directly with structured data. Among those techniques, kernel methods have shown promising results both from the computational complexity and the predictive performance point of view. Kernel methods allow to avoid an explicit mapping in a vectorial form relying on kernel functions, which informally are functions calculating a similarity measure between two entities. However, the definition of good kernels for graphs is a challenging problem because of the difficulty to find a good tradeoff between computational complexity and expressiveness. Another problem we face is learning on data streams, where a potentially unbounded sequence of data is generated by some sources. There are three main contributions in this thesis. The first contribution is the definition of a new family of kernels for graphs based on Directed Acyclic Graphs (DAGs). We analyzed two kernels from this family, achieving state-of-the-art results from both the computational and the classification point of view on real-world datasets. The second contribution consists in making the application of learning algorithms for streams of graphs feasible. Moreover,we defined a principled way for the memory management. The third contribution is the application of machine learning techniques for structured data to non-coding RNA function prediction. In this setting, the secondary structure is thought to carry relevant information. However, existing methods considering the secondary structure have prohibitively high computational complexity. We propose to apply kernel methods on this domain, obtaining state-of-the-art results.

Secondary Microseisms Characterization and Green’s Function Extraction at the Larderello-Travale Geothermal Field (Italy)

Over the past ten years, the cross-correlation of long-time series of ambient seismic noise (ASN) has been widely adopted to extract the surface-wave part of the Green’s Functions (GF). This stochastic procedure relies on the assumption that ASN wave-field is diffuse and stationary. At frequencies <1Hz, the ASN is mainly composed by surface-waves, whose origin is attributed to the sea-wave climate. Consequently, marked directional properties may be observed, which call for accurate investigation about location and temporal evolution of the ASN-sources before attempting any GF retrieval. Within this general context, this thesis is aimed at a thorough investigation about feasibility and robustness of the noise-based methods toward the imaging of complex geological structures at the local (∼10-50km) scale. The study focused on the analysis of an extended (11 months) seismological data set collected at the Larderello-Travale geothermal field (Italy), an area for which the underground geological structures are well-constrained thanks to decades of geothermal exploration. Focusing on the secondary microseism band (SM;f>0.1Hz), I first investigate the spectral features and the kinematic properties of the noise wavefield using beamforming analysis, highlighting a marked variability with time and frequency. For the 0.1-0.3Hz frequency band and during Spring- Summer-time, the SMs waves propagate with high apparent velocities and from well-defined directions, likely associated with ocean-storms in the south- ern hemisphere. Conversely, at frequencies >0.3Hz the distribution of back- azimuths is more scattered, thus indicating that this frequency-band is the most appropriate for the application of stochastic techniques. For this latter frequency interval, I tested two correlation-based methods, acting in the time (NCF) and frequency (modified-SPAC) domains, respectively yielding esti- mates of the group- and phase-velocity dispersions. Velocity data provided by the two methods are markedly discordant; comparison with independent geological and geophysical constraints suggests that NCF results are more robust and reliable.