Particle filter de-noising of voxel-specific time-activity-curves in personalized ¹⁷⁷Lu therapy

Currently, there is a high interest in ¹⁷⁷Lu targeted radionuclide therapies, which could be attributed to favorable results obtained from ¹⁷⁷Lu compounds targeting neuro-endocrine and prostate tumors. SPECT based dosimetry could be used for deriving dose values for individual voxels, as is the standard in external-beam radiation-therapy (EBRT). For this a time-activity-curve (TAC) at voxel resolution and also a voxel-wise modeling of radiation energy deposition are necessary. But a voxel-wise determination of TACs is problematic, since several confounding factors exist, such as e.g. poor count-statistics or registration inaccuracies, which add noise to the observed activity states. A particle filter (PF) is a class of methods which applies regularization based on a model of the temporal evolution of activity states. The aim of this study is to introduce the application of PFs for de-noising of per-voxel time-activity curves.

We applied a PF for de-noising the TACs of 26 patients, who underwent ¹⁷⁷Lu-DOTATOC or -PSMA therapy. The TACs were obtained from fully-quantitative, serial SPECT(/CT) data, acquired at 4h, 24h, 48h, 72h p.i. The model used in the PF was a mono-exponential decay and its free parameters were determined based on objective criteria. The time-integrated activities (TIA) resulting from the PF (PFF) were compared to the results of a mono-exponential fit (SF) of individual voxels in several volumes of interest (kidneys, spleen, tumors). Additionally, an organ-averaged TIA was derived from whole-organ VOIs and subsequent curve-fitting. This whole-organ TIA was also compared to the whole-organ TIAs obtained from summation of the voxel-wise TIAs from PFF and SF.

The number of particles was set to 1000. Optimal values for noise of observations and noise of the model were 0.25 and 0.5, respectively. The deviation of whole-organ TIAs from conventional organ-based dosimetry and the summation of the voxel-wise TIAs was substantial for SF (kidneys -22.3%, spleen -49.6%, tumor -60.0%), as well as for PFF (kidneys -37.1%, spleen -57.9%, tumor -70.9%). The distribution of voxel-wise half-lives resulting from the PFF method was considerably closer to the organ-averaged value, and the number of implausibly long half-lives (>physical HL) was reduced.

The PFF leads to voxel-wise half-lives, which are more plausible than those resulting from SF. However, one has to admit that voxel-wise fitting generally leads to considerable deviations from the organ-averaged TIA as obtained by conventional whole-organ evaluation. Unfortunately, we did not have ground-truth TIA of our patient data and proper ground-truth could even be impossible to obtain. Nevertheless, there are strong indicators that particle filtering can be used for reducing voxel-wise TAC noise.