In vivo measurement of local tissue characteristics by modern bioimaging techniques such as positron emission tomography (PET) provides the opportunity to analyze quantitatively the role that tissue heterogeneity may play in understanding biological function. This paper develops a statistical measure of the heterogeneity of a tissue characteristic that is based on the deviation of the distribution of the tissue characteristic from a unimodal elliptically contoured spatial pattern. An efficient algorithm is developed for computation of the measure based on volumetric region of interest data. The technique is illustrated by application to data from PET imaging studies of fluorodeoxyglucose utilization in human sarcomas. A set of 74 sarcoma patients (with five-year follow-up survival information) were evaluated for heterogeneity as well as a number of other potential prognostic indicators of survival. A Cox proportional hazards analysis of these data shows that the degree of heterogeneity of the sarcoma is the major risk factor associated with patient death. Some theory is developed to analyze the asymptotic statistical behavior of the heterogeneity estimator. In the context of data arising from Poisson deconvolution (PET being the prime example), the heterogeneity estimator, which is a non-linear functional of the PET image data, is consistent and converges at a rate that is parametric in the injected dose.
We have been exploring techniques for evaluation of fluoro-deoxyglucose (FDG) utilization characteristics in human sarcomas measured with positron emission tomography. In previous work, a measure of spatial heterogeneity based on evaluating the deviation of the FDG utilization distribution within the tumor region from a unimodal elliptically contoured spatial pattern was developed. This measure was shown to be a strong prognostic indicator of time to death. The present work explores a more general measure of heterogeneity which incorporates tumor boundary information. The approach relies on the use of a non-parametric representation for the tumor boundary surface. A set of 179 sarcoma patients with follow-up are evaluated with this technique. The results are analyzed to obtain empirical insight into the factors explaining elliptical heterogeneity. In terms of patient survival, the incorporation of the more sophisticated measure of spatial heterogeneity shows some potential improvement in the prediction risk. Further data will enable us to obtain a clearer empirical understanding of the role of the surface information in the measurement of tumor heterogeneity.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.