Quantification of variable palmar ligaments around the triquetrum-hamate joint determined by lunate type

The ligaments of the wrist are highly variable and poorly described, which is more obvious on the ulnar side of the wrist. Previous studies highlighted the potential differences within the ligaments of the wrist but no consensus has been reached. Poor tissue description and inconsistent use of terminology hindered the reproducibility of the results. Improved understanding of the morphological variations between carpal bones may facilitate improved understanding of the ligamentous structure within the wrist. This study aims to identify the potential variations between carpal bones that could be used to separate palmar ligamentous patterns around the triquetrum-hamate joint into subgroups within the sample population. Investigations were performed following a detailed nomenclature and a clear definition of ligamentous structures to facilitate detailed description and reproducible results. Quantitative analyses were conducted using 3D modelling technique. Histological sections were then analysed to identify the structure of each ligamentous attachment. Variable patterns of ligamentous attachments were identified. Differences were not only obvious between samples but also between the right and left hands of the same person. These identifications suggested that the palmar ligamentous patterns around the triquetrum-hamate joint are best described as a spectrum with a higher affinity of the triquetrum-hamate-capitate ligament and the lunate-triquetrum ligament to be associated with type I lunate wrists on one extreme and type II lunate wrists with the palmar triquetrum-hamate ligament, triquetrum-hamate-capitate ligament and palmar radius-lunate-triquetrum ligament attachments at the other extreme. Histological analyses confirmed pervious established work regarding the mechanical role of ligaments in wrist joint biomechanics. Also, there were no significant differences between the quantitative data obtained from the Genelyn-embalmed and unembalmed specimens (p>0.05). The current study demonstrated variable ligamentous patterns that suggest different bone restraints and two different patterns of motion. These findings support previous suggestions regarding separating the midcarpal joint into two distinct functional types. Type I wrists were identified with ligamentous attachments that are suggestive of rotating/translating hamate whilst type II wrists identified with ligamentous attachments that are suggestive of flexing/extending hamate motion based upon the patterns of the ligamentous attachments in relation to the morphological features of the underlying lunate type of the wrist. This opens the horizon for particular consideration and/or modification of surgical procedures, which may enhance the clinical management of wrist dysfunction.

Trajectory prediction uncertainty modelling for Air Traffic Management

The anticipated growth of air traffic worldwide requires enhanced Air Traffic Management (ATM) technologies and procedures to increase the system capacity, efficiency, and resilience, while reducing environmental impact and maintaining operational safety. To deal with these challenges, new automation and information exchange capabilities are being developed through different modernisation initiatives toward a new global operational concept called Trajectory Based Operations (TBO), in which aircraft trajectory information becomes the cornerstone of advanced ATM applications. This transformation will lead to higher levels of system complexity requiring enhanced Decision Support Tools (DST) to aid humans in the decision making processes. These will rely on accurate predicted aircraft trajectories, provided by advanced Trajectory Predictors (TP). The trajectory prediction process is subject to stochastic effects that introduce uncertainty into the predictions. Regardless of the assumptions that define the aircraft motion model underpinning the TP, deviations between predicted and actual trajectories are unavoidable. This thesis proposes an innovative method to characterise the uncertainty associated with a trajectory prediction based on the mathematical theory of Polynomial Chaos Expansions (PCE). Assuming univariate PCEs of the trajectory prediction inputs, the method describes how to generate multivariate PCEs of the prediction outputs that quantify their associated uncertainty. Arbitrary PCE (aPCE) was chosen because it allows a higher degree of flexibility to model input uncertainty. The obtained polynomial description can be used in subsequent prediction sensitivity analyses thanks to the relationship between polynomial coefficients and Sobol indices. The Sobol indices enable ranking the input parameters according to their influence on trajectory prediction uncertainty. The applicability of the aPCE-based uncertainty quantification detailed herein is analysed through a study case. This study case represents a typical aircraft trajectory prediction problem in ATM, in which uncertain parameters regarding aircraft performance, aircraft intent description, weather forecast, and initial conditions are considered simultaneously. Numerical results are compared to those obtained from a Monte Carlo simulation, demonstrating the advantages of the proposed method. The thesis includes two examples of DSTs (Demand and Capacity Balancing tool, and Arrival Manager) to illustrate the potential benefits of exploiting the proposed uncertainty quantification method.