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. ^

Thoracic target volume delineation using various maximum-intensity projection computed tomography image sets for stereotactic body radiation therapy

The motion of lung tumors during respiration makes the accurate delivery of radiation therapy to the thorax difficult because it increases the uncertainty of target position. The adoption of four-dimensional computed tomography (4D-CT) has allowed us to determine how a tumor moves with respiration for each individual patient. Using information acquired during a 4D-CT scan, we can define the target, visualize motion, and calculate dose during the planning phase of the radiotherapy process. One image data set that can be created from the 4D-CT acquisition is the maximum-intensity projection (MIP). The MIP can be used as a starting point to define the volume that encompasses the motion envelope of the moving gross target volume (GTV). Because of the close relationship that exists between the MIP and the final target volume, we investigated four MIP data sets created with different methodologies (3 using various 4D-CT sorting implementations, and one using all available cine CT images) to compare target delineation. It has been observed that changing the 4D-CT sorting method will lead to the selection of a different collection of images; however, the clinical implications of changing the constituent images on the resultant MIP data set are not clear. There has not been a comprehensive study that compares target delineation based on different 4D-CT sorting methodologies in a patient population. We selected a collection of patients who had previously undergone thoracic 4D-CT scans at our institution, and who had lung tumors that moved at least 1 cm. We then generated the four MIP data sets and automatically contoured the target volumes. In doing so, we identified cases in which the MIP generated from a 4D-CT sorting process under-represented the motion envelope of the target volume by more than 10% than when measured on the MIP generated from all of the cine CT images. The 4D-CT methods suffered from duplicate image selection and might not choose maximum extent images. Based on our results, we suggest utilization of a MIP generated from the full cine CT data set to ensure a representative inclusive tumor extent, and to avoid geometric miss.

THEORETICAL STUDIES ON THE METHODS OF RECONSTRUCTING PHYLOGENETIC TREES FROM DNA SEQUENCE DATA (MOLECULAR EVOLUTION, HOMINOID EVOLUTION, COMPUTER SIMULATION)

(1) A mathematical theory for computing the probabilities of various nucleotide configurations is developed, and the probability of obtaining the correct phylogenetic tree (model tree) from sequence data is evaluated for six phylogenetic tree-making methods (UPGMA, distance Wagner method, transformed distance method, Fitch-Margoliash's method, maximum parsimony method, and compatibility method). The number of nucleotides (m*) necessary to obtain the correct tree with a probability of 95% is estimated with special reference to the human, chimpanzee, and gorilla divergence. m* is at least 4,200, but the availability of outgroup species greatly reduces m* for all methods except UPGMA. m* increases if transitions occur more frequently than transversions as in the case of mitochondrial DNA. (2) A new tree-making method called the neighbor-joining method is proposed. This method is applicable either for distance data or character state data. Computer simulation has shown that the neighbor-joining method is generally better than UPGMA, Farris' method, Li's method, and modified Farris method on recovering the true topology when distance data are used. A related method, the simultaneous partitioning method, is also discussed. (3) The maximum likelihood (ML) method for phylogeny reconstruction under the assumption of both constant and varying evolutionary rates is studied, and a new algorithm for obtaining the ML tree is presented. This method gives a tree similar to that obtained by UPGMA when constant evolutionary rate is assumed, whereas it gives a tree similar to that obtained by the maximum parsimony tree and the neighbor-joining method when varying evolutionary rate is assumed. ^