Clinical experience with positron emission tomography (PET) scanning of sarcoma, using fluorodeoxyglucose (FDG), has established spatial heterogeneity in the standardized uptake values within the tumor mass as a key prognostic indicator of patient survival. But it may be that a more detailed quantitation of the tumor FDG uptake pattern could provide additional insights into risk. The present work develops a statistical model for this purpose. The approach is based on a tubular representation of the tumor mass with a simplified radial analysis of uptake, transverse to the tubular axis. The technique provides novel ways of characterizing the overall profile of the tumor, including the introduction of an approach for the measurement of its phase of development. The phase measure can distinguish between early phase tumors, in which the uptake is highest at the core, and later stage masses, in which there can often be central voids in FDG uptake. Biologically, these voids arise from necrosis and fluid, fat or cartilage accumulations. The tumor profiling technique is implemented using open-source software tools and illustrations are provided with clinically representative scans. A series of FDG-PET studies from 185 patients is used to formally evaluate the prognostic benefit. Significant improvements in the prediction of patient survival and progression are obtained from the tumor profiling analysis. After adjustment for other factors including heterogeneity, a typical one standard deviation increase in phase (as determined by the analysis) is associated with close to 20% more risk of progression or death. The work confirms that more detailed quantitative assessments of the spatial pattern of PET imaging data of tumor masses, beyond the maximum FDG uptake (SUV(max)) and previously considered measures of heterogeneity, provide improved prognostic information for potential input to treatment decisions for future patients.