An algorithm for PET tumor volume and activity quantification: without specifying camera's point spread function (PSF)

The authors have developed an algorithm for segmentation and removal of the partial volume effect (PVE) of tumors in positron emission tomography (PET) images. The algorithm accurately measures functional volume (FV) and activity concentration (AC) of tumors independent of the camera's full width half maximum (FWHM).

A novel iterative histogram thresholding (HT) algorithm is developed to segment the tumors in PET images, which have low resolution and suffer from inherent noise in the image. The algorithm is initiated by manually drawing a region of interest (ROI). The segmented tumors are subjected to the iterative deconvolution thresholding segmentation (IDTS) algorithm, where the Van-Cittert's method of deconvolution is used for correcting PVE. The IDTS algorithm is fully automated and accurately measures the FV and AC, and stops once it reaches convergence. The convergence criteria or stopping conditions are developed in such a way that the algorithm does not rely on estimating the FWHM of the point spread function (PSF) to perform the deconvolution process. The algorithm described here was tested in phantom studies, where hollow spheres (0.5-16 ml) were used to represent tumors with a homogeneous activity distribution, and an irregular shaped volume was used to represent a tumor with a heterogeneous activity distribution. The phantom studies were performed with different signal to background ratios (SBR) and with different acquisition times (1 min, 3 min, and 5 min). The parameters in the algorithm were also changed (FWHM and matrix size of the Gaussian function) to check the accuracy of the algorithm. Simulated data were also used to test the algorithm with tumors having heterogeneous activity distribution.

The results show that changing the size and shape of the ROI during initiation of the algorithm had no significant impact on the FV. An average FV overestimation of 30% and an average AC underestimation of 35% were observed for the smallest tumor (0.5 ml) over the entire range of noise and SBR level. The difference in average FV and AC estimations from the actual volumes were less than 5% as the tumor size increased to 16 ml. For tumors with heterogeneous activity profile, the overall volume error was less than 10%. The average overestimation of FV was less than 10% and classification error was around 11%.

The algorithm developed herein was extensively tested and is not dependent on accurately quantifying the camera's PSF. This feature demonstrates the robustness of the algorithm and enables it to be applied on a wide range of noise and SBR within an image. The ultimate goal of the algorithm is to be able to be operated independent of the camera type used and the reconstruction algorithm deployed.