Speaker
Description
Quantification of activity levels is a minimum requirement for any radionuclide experiment, including the development of targeted alpha therapies (TATs). Ac-225 (225Ac) is one of the most promising alpha-emitters for TATs. However, the activity levels used for 225Ac experiments are extremely low and cannot be accurately measured by conventional dose calibrators. Dose calibrators are generally ionization chambers operating in the current-integration mode, and do not provide sufficient energy discrimination needed to separate signals from different radionuclides, and lack sufficient photon detection efficiency, especially for high-energy photons such as 440 keV gammas from 213Bi in the 225Ac decay chain, resulting in large statistical measurement fluctuations for low activity and high-energy photon-emitting radionuclides. This limitation is also significant for related theranostic studies that use 134Ce as a surrogate for 225Ac when these studies involve samples containing both radionuclides [1].
Solid-state detectors, including scintillators such as NaI(Tl) and semiconductors such as high-purity germanium (HPGe) and cadmium zinc telluride (CZT), are already being evaluated to address these limitations because they provide energy discrimination in spectroscopic mode. Among these, well-type NaI(Tl)-based scintillation detectors, gamma counters, are commonly available in most laboratories handling radioactive materials. However, their full capability in spectroscopic operation, in addition to energy-dependent gamma counting, to determine the activity levels of radionuclides is not fully exploited, particularly for low activities and mixed gamma energies involving high-energy components. Conventional energy-window counting methods can introduce systematic bias in activity estimates for mixed radionuclide samples due to spectral overlap. Reducing this bias is essential for accurate quantification of low-activity samples. Hence, we evaluated a maximum-likelihood estimation (MLE) framework for quantifying 225Ac alone, 134Ce alone, and mixed samples using a NaI(Tl)-based gamma counter (Hidex AMG) with 2048 channels for gamma spectroscopy. All spectra were acquired over 60-second intervals, with detector deadtime maintained below 7%. Standard solutions were prepared using serial dilution to create a range of known activities. The maximum-likelihood model represents the observed spectrum as a linear combination of normalized, activity-independent templates. These templates are scaled by radionuclide-specific response curves derived from nonparalyzable model fits. The optimization of activity estimates was performed by minimizing the Poisson deviance using the L-BFGS-B (limited-memory Broyden-Fletcher-Goldfarb-Shanno with Bounds) algorithm [2] with non-negativity constraints. Statistical uncertainty was determined using a curvature approximation based on the Hessian matrix at the identified optimum. For comparison, an energy window counting method was applied using a subtraction technique to isolate 225Ac signals in mixed samples. Preclinical testing was conducted on organ and tumor samples from mice that had been co-administered both radionuclides.
The maximum-likelihood estimation method yielded activity values that aligned with known standards for both single and mixed samples (e.g., Figure 1). In the analysis of mixed standards, the maximum-likelihood approach achieved a root mean square error of 5.17% for 134Ce and 5.18% for 225Ac. This represented a reduction in error compared to the energy window counting method, which produced errors of 8.85% and 7.68% for the same radionuclides. The maximum-likelihood approach also reduced systematic bias in activity estimates. Across mixed standards, the mean absolute bias for ¹³⁴Ce and ²²⁵Ac decreased from 7.09% and 6.80% with energy-window counting to 4.83% and 4.08% using the MLE method. For pure ¹³⁴Ce standards, the mean absolute bias decreased from 5.24% with energy-window counting to 2.43% with MLE. For the lowest activity single ¹³⁴Ce sample (1.95 nCi), the window-counting method overestimated activity by 15.44%, whereas the MLE estimate reduced this bias to 6.30%. The results indicated that using templates from high-activity standards reduced bias by providing better counting statistics, especially at the lowest sample activities. In preclinical organ samples, the estimated activities were internally consistent across replicate measurements. The observed distribution of the radionuclides in the mice followed expected patterns, with the liver and kidneys showing elevated uptake. Our study demonstrates that statistical inference using maximum-likelihood estimation is a reproducible method for quantifying low-activity radionuclide samples using widely available NaI(Tl) detectors.
[1] KN Bobba et al., J Nucl Med. 64 (2023), 1076-1082
[2] DC Liu and J Nocedal, Math Program B. 45 (1989), 503-528
The authors acknowledge funding from the National Cancer Institute grant R01CA279203.