Separability of three-dimensional geometric sensitivity correction in triple-headed gamma camera systems

Abstract

Gamma camera PET (Positron Emission Tomography) offers a low-cost alternative for dedicated PET scanners. However, sensitivity and count rate capabilities of dual-headed gamma cameras with PET capabilities are still limited compared to full-ring dedicated PET scanners. To improve the geometric sensitivity of these systems, triple-headed gamma camera PET has been proposed. As is the case for dual-headed PET, the sensitivity of these devices varies with the position within the field of view (FOV) of the camera. This variation should be corrected for when reconstructing the images. In earlier work, we calculated the two-dimensional sensitivity variation for any triple-headed configuration. This can be used to correct the data if the acquisition is done using axial filters, which effectively limit the axial angle of incidence of the photons, comparable to 2D dedicated PET. More recently, these results were extended to a fully 3D calculation of the geometric sensitivity variation. In this work, the results of these calculations are compared to the standard approach to correct for 3D geometric sensitivity variation. Current implementations of triple-headed gamma camera PET use two independent corrections to account for three-dimensional sensitivity variations: one in the transaxial direction and one in the axial direction. This approach implicitly assumes that the actual variation is separable in two independent components. We recently derived a theoretical expression for the 3D sensitivity variation, and in this work we investigate the separability of our result. To investigate the separability of the sensitivity variations, an axial and transaxial profile through the calculated variation was taken, and these two were multiplied, thus creating a separable function. If the variation were perfectly separable, this function would be identical to the calculated variation. As a measure of separability, we calculated the percentual deviation of the separable function to the original variation. We investigated the separability for several camera configurations and rotation radii. We found that, for all configurations, the variation is not separable , and becomes less separable as the rotation radius tends to smaller values. This indicates that in this case, our sensitivity correction will give better results than the separable correction now applied.