The circular harmonic transform (CHT) solution of the exponential Randon transform (ERT) is applied to single-photon emission computed tomography (SPECT) for uniform attenuation within a convex boundary. An important special case also considered is the linear (unattenuated) Radon transform (LRT). The solution is on the form of an orthogonal function expansion matched to projections that are in parallel-ray geometry. This property allows for efficient and accurate processing of the projections with fast Fourier transform (FFT) without interpolation or beam matching. The algorithm is optimized by the use of boundary conditions on the 2-D Fourier transform of the sinogram. These boundary conditions imply that the signal energy of the sinogram is concentrated in well-defined sectors in transform space. The angle defining the sectors depends in a direct way on the radius of the field view. These results are also obtained for fan-beam geometry and the linear Radon transform (the Fourier-Chebyshev transform of the sinogram) to demonstrate that the boundary conditions are a more general property of the Radon transform and a not a property unique to rectangular coordinates.

A new method is introduced in which the total photon interaction cross sections per electron of human tissues are used to define effective atomic numbers for blood, bone, brain, fat, heart, kidney, liver, lung, muscle, ovary, pancreas, spleen, and water. These effective atomic numbers are equal within 4% from 10 to 200 keV in each soft tissue, whereas for bones of different chemical compositions the variation ranges from 2.86% to 5.03%. This effective atomic number definition is less energy dependent than a previous definition based on the total photon interaction cross section per atom averaged over all elements in the tissue, from which the computed effective atomic numbers varied by as much as 50% (in bone) as a function of photon energy over the energy range from 10 to 200 keV.

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Measurement of dose within tissues and tissue interfaces having sharp density discontinuities and heterogeneities (such as in the lung, esophagus, and rectum) is essential for treatment plan verification and accurate prediction of the prescribed dose. This study examines the feasibility and utility of simplifying standard film dosimetry to measure dose distributions deposited by megavoltage beams in tissue substitutes (such as cork for lung) and anthropomorphic phantoms which closely resemble human tissues having large density heterogeneities and having sharp tissue interfaces. In addition, film dosimetry determined the dose distribution involving superposition of multiple radiation fields and helped evaluate the accuracy of a commercial treatment planning program which incorporates tissue heterogeneity effects through the "effective path length" algorithm. This study shows that these treatment planning programs and simple calculations overestimate the dose delivered within the lower density material in heterogeneous regions.

Noniterative SPECT algorithms based on the Energy-Distance Principle (EDP) and the Circular Harmonic Transform are outlined. These algorithms are characterized by a high signal-to-noise ratio, (SNR)! offer about a 3-to-1 improvement in SNR over conventional SPECT reconstruction not based on EDP, and are minimally affected by scatter and collimator blur.