Accurate total tumor lesion metabolic activity (TLA) estimation is critical for tumor staging and follow up studies. Positron emission tomography (PET) successfully images the lesion metabolic activity. Recently, PET images were modeled as a fuzzy Gaussian mixture to delineate tumor lesions accurately [1]. In this work, we propose a statistical lesion activity computation (SLAC) approach to robustly estimate TLA directly from the modeled Gaussian partial volume mixtures. TLA was estimated from 3 state-ofthe-art PET delineation schemes, namely a stochastic (FLAB [1]), a gradient based (GDM [2]) and an adaptive threshold based (ATM [3]) method, for comparison. A threshold based region growing method (T40 -40% threshold) was also evaluated. Synthetic lesions were simulated and reconstructed using maximum likelihood expectation maximization (MLEM) algorithm with 4 iterations over 16 subsets as in clinical routine (post-smoothed with 5mm Gaussian full width half maximum (FWHM)).
Methods: Statistical TLALet the observed PET image and the hidden segmentation map be realizations y = {y s } s∈S and x = {x s } s∈S of the random fields Y = {Y s } s∈S and X = {X s } s∈S respectively, where S = {1, . . . , N } is the set of voxels. Integrating the activity y s over the whole S, the total PET activity (TPA), constituting contributions from the lesion (TLA) and the background activities, can be mathematically defined asThe observed histogram h(ζ) containing the frequency of occurrence for each ζ can be related to the density f (ξ) defining the distribution of Y s = ξ. E(Y s ) is the associated expectation. Let c = {c k } k∈K , where K = {1, . . . , Q}, be the Q class labels associated with the segmentation map. Then Y s can be modeled as a finite mixture of conditional densities such that f (ξ) = k γ k f (ξ | c k ), where γ k stands for the mixing probabilities P (X s = c k ) and f (ξ | c k ) denotes the density defining the distribution ofTo model Y s with the PVE, let the noise associated with the tumor and the background be modeled by 2 Gaussian random variables Y 1 and Y 0 with the density N (µ 1 , σ 2 1 ) (f (ξ | X s = 1)) and N (µ 0 , σ 2 0 ) (f (ξ | X s = 0)) defining the distributions of Y s conditional to X s = 1 and X s = 0 respectively. Then the partial volume activities can be modeled by linear combinations of these independent random variables as. . , M . Therefore, for the tumor and the background, µ M +1 = µ 1 and µ 0 = µ 0 respectively, with 0 = 0 and M +1 = 1. Here c = {0, 1, k }, Q = M +2. In eq. 1, out of the total activity in a fuzzy mixture classoriginates from the tumor lesion. Adding up the contributions from 1 hard class and M fuzzy classes representing tumor and partial volume voxels respectively, we propose that, the statistical TLA can be estimated from TPA as A line profile through the PET image (37, 28, 22, 17, 13 and 10mm lesions) and the ground truth is shown in red and black lines respectively. Area in light gray shade denotes the TLA computed from the delineation profile, where as the area in d...