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In order to accurately calculate dose distributions for patients in radiation therapy, it is necessary to define and consider in the calculations any inhanogeneities present in the irradiated volume. This study evaluates the mathematical foundations of a new method to determine the local densities (attenuation coefficients or electron concentrations). This method is based on measurements of the way in which the body section transmits high energy photons for a number of angular projections and a mathematical transform to reconstruct the point-for-point density. Several such reconstruction methods have been presented in the literature. This work deals with the application of these techniques to the radiotherapy problem by investigating which transform is most suitable and what the requirements are on the measurement technique. Four algorithms for reconstructing the attenuation coefficients within the body have been compared: 1. the convolution method; 2. the use of a simple numerical solution of the Radon transform; 3. the use of the fast Fourier algorithm to implement the Fourier transform reconstruction method; 4. the iterative Algebraic Reconstruction Technique (ART). The comparison has been based on the precision of the reconstruction method when applied to computer simulated transmission data. The problem of statistical fluctuations in the transmitted signal has been considered as has the problem of scattered radiation reaching the detector. Patient dose has been evaluated and the number of transmission measurements needed for a particular resolution has been determined. The results show that the first three methods give reconstructions that are quite similar in terms of their faithfulness of reproducing a known distribution of attenuation coefficients. The ART method did not perform as well as the others. Among methods (1), (2) and (3), the fast Fourier transform technique proved to be some 15 times more efficient in terms of computation time. Our findings also indicate that, for the radiotherapy problem, a total of about 25 projections are sufficient for obtaining an acceptable resolution.
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