Voxel-based partial volume correction for accurate quantitative voxel values

Objectives The accuracy of voxelized information (kBq/mL or counts/mL) in emission imaging is limited by spatial resolution (FWHM=2.35σ) producing biases for objects smaller than 2 to 3 FWHM. If the signal distribution is non-uniform within 3σ of the voxel of interest then equilibrium does not exist and spill-in/spill-out may compromise voxel accuracy. We propose and validate a mathematical model to improve the accuracy of quantitative images of arbitrary distribution by bounding the true voxel signal and estimating the spill-in/spill-out for each voxel.

Methods A monotonically increasing parametric dataset is created for each voxel of an emission image by radial integration from the voxel center (r=0) to r=6σ. Each cumulative integration plot from r=3σ to 6σ is fit to a function A*4π /3*r3 + B*ΔV derived assuming a local uniform signal distribution (A) where ΔV is the voxel volume. The constant BΔV represents the converged within 3σ integral of spill-in or spill-out. B>0 implies voxel suffers spill-out, B<0 spill-in, and B=0 implies equilibrium (no partial volume). We tested the proposed model on simulations of 1D&2D datasets containing known signal distributions and 18F-PET/CT images of a small lung lesion (<6 mL) and bladder.

Results Signal accuracy was >99% in simulated 1D&2D datasets. For the tumor, the original maximum value was 10kBq/ml. We obtained A=3.5kBq/ml and B=14kBq/ml for a total of 17.7kBq/ml. This yields (A+B)/original=1.8 indicating substantial spill-out of ~80% and a large error for the original voxel value. For a voxel in the center of the bladder, the original value was 46kBq/ml with A=44kBq/ml, B=7kBq/ml. (A+B)/original=1.11 indicating near-equilibrium at center of bladder and very low spill-out of ~11% as expected. Local signal images (A) closely resemble low-pass filtered original image and spill-in/spill-out images (B) are dynamic that indicate magnitude of errors.

Conclusions A new mathematical model to estimate the accuracy of voxels in quantitative images of arbitrary distribution has been developed. Analysis of additional patients is underway.