Reconstruction of time-activity curves in molecular radiotherapy using a Bayesian unfolding

Purpose:

Personalizing Molecular Radiotherapy (MRT) is crucial for enhancing treatment efficacy and minimizing toxicity. The WIDMApp (Wearable Individual Dose Monitoring Apparatus) project aims to estimate patient-specific biokinetics -i.e., time-activity curves (TACs), through several radiation detectors and a data processing system. This study presents an advanced Bayesian unfolding algorithm that avoids assumptions about the functional form of the TACs.

Methods:

The proposed unfolding employs a recursive approach over time to infer organs’ activity. To test the algorithm’s performance, we developed four virtual patient types undergoing prostate cancer treatment with ${}^{177}$Lu, each characterized by different radiopharmaceutical biokinetics based on literature data. MC simulations using the ICRP110 male anthropomorphic phantom modeled radiation detection probabilities by six WIDMApp sensors placed near organs of interest. Using this simulation and literature TAC profiles, we generated Time-Count Curves (TCCs) detected by the sensors. Stability studies assessed the algorithm’s robustness in reconstructing TACs under various noise conditions and initial activity uncertainties.

Results:

The proposed unfolding algorithm inferred organ cumulative activities with errors ranging from 5% to 24%, even when the data were smeared with uniform noise up to 70% and sampling the initial priors from uniform distributions around the true values within 50%.

Conclusions:

We developed and tested a Bayesian unfolding algorithm that does not assume the TACs’ functional form of the organs, able to estimate the TACs from the TCCs. The results obtained are crucial for the ongoing development of WIDMApp and its translation into clinical practice.