A LAPLACE TRANSFORM PAIR MODEL TO DETERMINE BREMSSTRAHLUNG SPECTRA FROM ATTENUATION DATA (RADIATION, X-RAY, SPECTRAL MODELING)

Every x-ray attenuation curve inherently contains all the information necessary to extract the complete energy spectrum of a beam. To date, attempts to obtain accurate spectral information from attenuation data have been inadequate.^ This investigation presents a mathematical pair model, grounded in physical reality by the Laplace Transformation, to describe the attenuation of a photon beam and the corresponding bremsstrahlung spectral distribution. In addition the Laplace model has been mathematically extended to include characteristic radiation in a physically meaningful way. A method to determine the fraction of characteristic radiation in any diagnostic x-ray beam was introduced for use with the extended model.^ This work has examined the reconstructive capability of the Laplace pair model for a photon beam range of from 50 kVp to 25 MV, using both theoretical and experimental methods.^ In the diagnostic region, excellent agreement between a wide variety of experimental spectra and those reconstructed with the Laplace model was obtained when the atomic composition of the attenuators was accurately known. The model successfully reproduced a 2 MV spectrum but demonstrated difficulty in accurately reconstructing orthovoltage and 6 MV spectra. The 25 MV spectrum was successfully reconstructed although poor agreement with the spectrum obtained by Levy was found.^ The analysis of errors, performed with diagnostic energy data, demonstrated the relative insensitivity of the model to typical experimental errors and confirmed that the model can be successfully used to theoretically derive accurate spectral information from experimental attenuation data. ^

Theoretical and experimental studies of linkage disequilibrium in human populations

Linkage disequilibrium (LD) is defined as the nonrandom association of alleles at two or more loci in a population and may be a useful tool in a diverse array of applications including disease gene mapping, elucidating the demographic history of populations, and testing hypotheses of human evolution. However, the successful application of LD-based approaches to pertinent genetic questions is hampered by a lack of understanding about the forces that mediate the genome-wide distribution of LD within and between human populations. Delineating the genomic patterns of LD is a complex task that will require interdisciplinary research that transcends traditional scientific boundaries. The research presented in this dissertation is predicated upon the need for interdisciplinary studies and both theoretical and experimental projects were pursued. In the theoretical studies, I have investigated the effect of genotyping errors and SNP identification strategies on estimates of LD. The primary importance of these two chapters is that they provide important insights and guidance for the design of future empirical LD studies. Furthermore, I analyzed the allele frequency distribution of 26,530 single nucleotide polymorphisms (SNPs) in three populations and generated the first-generation natural selection map of the human genome, which will be an important resource for explaining and understanding genomic patterns of LD. Finally, in the experimental study, I describe a novel and simple, low-cost, and high-throughput SNP genotyping method. The theoretical analyses and experimental tools developed in this dissertation will facilitate a more complete understanding of patterns of LD in human populations. ^