Three-dimensional photon detection kernels and their application to SPECT reconstruction.

In single photon emission computed tomography (SPECT), three-dimensional photon detection kernels characterize the probabilities that photons emitted by radio-isotopes in different parts of the source region will be detected at particular projection pixels of the projection images. Monte Carlo modelling is used to study these kernels for the case of parallel hole collimators. The use of vectorized Monte Carlo computer code speeds the modelling computations. The contributions of direct and scattered photons to projection data in a transverse plane from neighbouring planes are significant for the case of uniform activity within a water-filled cylinder. A reconstruction method using the 3D kernels is proposed in which projection measurements in three adjacent planes are used simultaneously to estimate the source activity of the center plane. This multiple slice method accounts for the fact that photons detected in a given transverse plane may have originated in other transverse planes with different activity distributions. The matrix equations for image reconstruction are solved using generalized matrix inverses. The new method shows compensation for 3D photon detection effects when applied to projection data from a numerical simulation and a cardiac phantom experiment. Quantitation for the numerical study is improved compared with results from a single slice reconstruction method.