Optimal control of affine connection control systems from the point of view of Lie algebroids

The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems (ACCSs) on Lie groups. In this context, the equations for critical trajectories of the problem are geometrically characterized as a Hamiltonian vector field.

Development of high-resolution gamma cameras based on silicon photosensors

The development of a compact gamma camera with high spatial resolution is of great interest in Nuclear Medicine as a means to increase the sensitivity of scintigraphy exams and thus allow the early detection of small tumours. Following the introduction of the wavelength-shifting fibre (WSF) gamma camera by Soares et al. and evolution of photodiodes into highly sensitive silicon photomultipliers (SiPMs), this thesis explores the development of a WSF gamma camera using SiPMs to obtain the position information of scintillation events in a continuous CsI(Na) crystal. The design is highly flexible, allowing the coverage of different areas and the development of compact cameras, with very small dead areas at the edges. After initial studies which confirmed the feasibility of applying SiPMs, a prototype with 5 5 cm2 was assembled and tested at room temperature, in an active field-of-view of 10 10 mm2. Calibration and characterisation of intrinsic properties of this prototype were done using 57Co, while extrinsic measurements were performed using a high-resolution parallel-hole collimator and 99mTc. In addition, a small mouse injected with a radiopharmaceutical was imaged with the developed prototype. Results confirm the great potential of SiPMs when applied in a WSF gamma camera, achieving spatial resolution performance superior to the traditional Anger camera. Furthermore, performance can be improved by an optimisation of experimental conditions, in order to minimise and control the undesirable effects of thermal noise and non-uniformity of response of multiple SiPMs. The development and partial characterisation of a larger SiPM WSF gamma camera with 10 10 cm2 for clinical application are also presented.