Deflation of the Finite Pointset Method

In this thesis a deflation method for the Finite Pointset Method (FPM) is presented. FPM is a particle method based on Lagrangian coordinates to solve problems in fluid dynamics. A strong formulation of the occuring differential equations is produced by FPM, and the linear system of equations obtained by an implicit approach is solved by an iterative method such as BiCGSTAB. To improve the convergence rate of BiCGSTAB, the computational domain is divided into a number of deflation cells and a projection between the deflated domain and the original domain is constructed with the help of different ansatz functions, either constant, linear or quadratic. Also, the Moore Penrose pseudoinverse of the projection is computed. Applying the projection and restriction to the linear FPM system, a deflated system is obtained which can easily be solved with a direct method. The deflated solution is then projected onto the full domain. The deflation is tested for a number of test cases in one and two dimensions. Constant ansatz functions provide acceptable results for Dirichlet problems, but give big errors when deflating problems with mixed boundary conditions. Linear ansatz functions provide good approximations which converge to the exact solution as the number of deflation cells increases. Quadratic ansatz functions provide deflated solutions as good as the exact solutions for all test cases but are computationally expensive. The BiCGSTAB convergence rate is improved when using a deflated solution as initial guess, compared to using the zero-vector. The size of the improvement varies between which ansatz functions are used. Overall, the proposed method provides an increased convergence rate in the BiCGSTAB algorithm for FPM. However, the computational effort in the deflation process should also be taken into account

Interstitial photodynamic therapy - diagnostic measurements and treatment in rat malignant experimental tumours

A recently developed multiple fibre system for treating malignant tumours with interstitial photodynamic therapy was used in studies on rats with colon adenocarcinoma inoculated into the muscles of the hind legs. The animals were intraperitonially administrated delta -aminolevulinic acid (ALA), which is metabolised to protoporphyrin IX (PpIX) in the tissue. The treatment system consists of a laser light source, a beam-splitting system dividing the light into three or six output fibres and a dosimetry programme calculating the optimal fibre position within the tumour as well as the treatment time needed to obtain a given threshold value of the light dose. One aim of the study was to compare the treatment outcome with the modelled dosimetry predictions. Tumour reduction was examined three days post treatment. A volume decrease was found in 85\% of the treated tumours. The mean volume reduction was 44\%, with one tumour completely disappearing. Histopathological examination three days post treatment showed substantial necrotic parts which, however, to a smaller extent were present also for non-treated tumours. These results indicated that the tumours have been under treated and the light dose has to be increased. Measurements of the build-up and photo-induced bleaching of PpIX using laser-induced fluorescence were also performed during the experiments

Compact fiber-optic fluorosensor using a continuous-wave violet diode laser and an integrated spectrometer

A compact fluorosensor with a fiber-optic measurement probe was developed, employing a continuous-wave violet diode laser as an exciting source and an integrated digital spectrometer for the monitoring of fluorescence signatures. The system has the dimensions 22x13x8 cm(3), and features 5 nm spectral resolution and an excellent detectivity. Results from measurements on vegetation and human premalignant skin lesions are reported, illustrating the potential of the instrument. (C) 2000 American Institute of Physics. [S0034-6748(00)04508-1]

Analysis of spatial variability in hyperspectral imagery of the uterine cervix in vivo

The use of fluorescence and reflectance spectroscopy in the analysis of cervical histopathology is a growing field of research. The majority of this research is performed with point-like probes. Typically, clinicians select probe sites visually, collecting a handful of spectral samples. An exception to this methodology is the Hyperspectral Diagnostic Imaging (HSDI®) instrument developed by Science and Technology International. This non-invasive device collects contiguous hyperspectral images across the entire cervical portio. The high spatial and spectral resolution of the HSDI instruments make them uniquely well suited for addressing the issues of coupled spatial and spectral variability of tissues in vivo. Analysis of HSDI data indicates that tissue spectra vary from point to point, even within histopathologically homogeneous regions. This spectral variability exhibits both random and patterned components, implying that point monitoring may be susceptible to significant sources of noise and clutter inherent in the tissue. We have analyzed HSDI images from clinical CIN (cervical intraepithelial neoplasia) patients to quantify the spatial variability of fluorescence and reflectance spectra. This analysis shows the spatial structure of images to be fractal in nature, in both intensity and spectrum. These fractal tissue textures will limit the performance of any point-monitoring technology