Statistical modeling of the PET maximum voxel

Objectives Maximum voxel image intensity (MVx) or SUV is often used to measure tumor uptake in PET. To better understand MVx reproducibility and dependence on noise and region-of-interest (ROI) size, we modeled MVx measurement assuming log-normal (LN) distributed single-voxel image intensities (Vx) and tested the model with a uniform phantom.

Methods PET-CT scans of a cylindrical Cu-64, water phantom were acquired in list mode, divided into multiple frames and reconstructed by OSEM with post smoothing (resolution 7 mm). Frame duration and activity concentration were varied to obtain a wide noise range. MVx, average Vx (AVx) and Vx standard deviation [SD(Vx)] were determined for multiple, circular ROIs centered a fixed distance from the coregistered phantom-scanner axis. Data for each ROI were averaged over 8-10 frames, and multiple equivalent ROIs were used to estimate expectation values (E) for MVx/AVx, MVx coefficient of variation [CV(MVx)], SD(Vx) and SD(AVx). E[SD(Vx)] and E[SD(AVx)] were in turn used to calculate the square root of the diagonal elements (sigma) of the ROI image covariance matrix and NI, the number of effectively independent observations per ROI. Monte Carlo simulations of E[MVx/AVx] and E[CV(MVx)] were performed for measured E[sigma/AVx],E[NI] combinations by recording maximum Vx for NI random samples from a LN distribution of unity median and logarithmic variance corresponding to E[sigma/AVx] (10,000 repeats). The model was tested for 5 combinations of noise [E(sigma/AVx) range 0.20 to 0.53] and ROI diameter (range 10-40mm).

Results As noise increased, the model increasingly underestimated E[MVx/AVx] [mean relative error (MRE) -10%, range -3 to -22%] and overestimated E[CV(MVx)] [MRE 20%, range 9 to 36%]. Notably, measured Vx distributions departed increasingly from LN shape with increasing noise.

Conclusions The LN model qualitatively reproduced MVx noise and ROI size dependencies, but underestimated average MVx and overestimated MVx random variability. We are seeking alternative models