Collimatorless Scintigraphy for Imaging Extremely Low Activity Targeted Alpha Therapy (TAT) with Weighted Robust Least Squares (WRLS)

Abstract

A technology for imaging extremely low photon flux is an unmet need, especially in targeted alpha therapy (TAT) imaging, which requires significantly improved sensitivity to detect as many photons as possible while retaining a reasonable spatial resolution. In scintigraphy using gamma cameras, the radionuclide collimator rejects a large number of photons that are both primary photons and scattered photons, unsuitable for photon-starved imaging scenarios like imaging TAT. In this paper we develop a min-min weighted robust least squares (WRLS) algorithm to solve a general reconstruction problem with uncertainties and validate it with the extreme scenario: collimatorless scintigraphy. Ra-223, a therapeutic alpha emitting radionuclide whose decay chain includes x-ray and gamma-ray photons, is selected for an exploratory study. Full Monte Carlo simulations are performed using Geant4 to obtain realistic projection data with collimatorless scintigraphy geometry. The results show that our proposed min-min WRLS algorithm could successfully reconstruct point sources and extended sources in the collimatorless scintigraphy with a resolution close to its system resolution and figures of merit (FOM) better than the collimator-based scintigraphy for extremely low activity TAT. This approach could be expanded as a 3D algorithm, which could lead to 3D collimatorless SPECT.

Keywords: Collimatorless scintigraphy; Image reconstruction; TAT; WRLS.

Fig. 1:

Monte Carlo simulation setup with Geant4 in (a) collimatorless scintigraphy and (b) collimator-based scintigraphy. The CZT detector is shown in green and the collimator is shown in blue. Ra-223 particles are shown as the yellow dots in the center of the water phantom whose boundaries are in orange color.

Fig. 2:

(a) The solid angle estimation of the system matrix $\tilde{A}$ and (b) the uncertainty set of the collimatorless geometry. A fixed value of $\nu =\frac{1}{\max (\tilde{A}-\widehat{A})}-1$ is chosen so that $\tilde{A}+\nu (\tilde{A}-\widehat{A})$ is on the boundary of the feasible set $\mathcal{F}.\eta \in \left[\frac{\min \tilde{A}}{\min \tilde{A}-1},1\right]$ is tunable and close to zero, determining which uncertainty set is closest to A_real.

Fig. 3:

(a) NMSE, (b) PSNR and (c) SSIM as a function of ζ to evaluate the overall performance of the min-min WRLS algorithm when setting $\nu =\frac{1}{\max (\tilde{A}-\widehat{A})}-1=0.00374$ and η = −0.005. 1e7 decayed Ra-223 particles are initialized as point sources at (0, 0, 0) cm, (0, 1, 0) cm and (0, 2, 0) cm, and disk sources with D = 1 cm and D = 2 cm at (0, 0, 0) cm.

Fig. 4:

Ground truth, projections without a collimator, and reconstruction of a single point source at (a) (0, 0, 0) cm, (b) (0, 1, 0) cm, and (c) (0, 2, 0) cm, and two point sources with a distance of (d) 1 cm and (e) 2 cm when 1e7 decayed Ra-223 particles are simulated.

Fig. 5:

Ground truth, projections with and without a collimator, and reconstruction of disk sources at (0, 0, 0) cm with (a) D = 1 cm and 30 nCi/ml (1e7 decayed Ra-223), (b) D = 1 cm and 3 nCi/ml (1e6 decayed Ra-223), (c) D = 2 cm and 7.5 nCi/ml (1e7 decayed Ra-223), (d) and (e) D = 2 cm and 0.75 nCi/ml (1e6 and 2e6 decayed Ra-223) with a corresponding measuring time of 30 min.