Abstract
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Introduction: Treatment planning of Lu-177-labelled PSMA (Lu-177-PSMA) therapy using a physiologically-based pharmacokinetic (PBPK) model requires knowledge of its parameters [1]. In this work, we identify the most important parameters that significantly affect the estimation and uncertainty of kidneys and tumor biologically effective doses (BEDs) in Lu-177-PSMA therapy using global sensitivity analysis (GSA), i.e. the Morris Screening (MS) and the extended Fourier Amplitude Sensitivity Test (eFAST) [2-4].
Methods: GSA was performed for a whole-body PBPK model that has been developed for Lu-177-PSMA therapy [5]. The total injection was 100 nmol. The PBPK model includes two tumors (TU1 and TU2) and tumor remainder (TUR). Parameters of interest for the GSA analysis were the assumed or estimated parameters [5], e.g. the receptor density and degradation rate. First, 51 parameters were screened using the MS with BEDs of kidneys and tumor as the output of interest. The Morris function from the well-established GSA SAFE toolbox (https://www.safetoolbox.info/) was used for the analyses. The following setting was used for the MS: parameters with log-normal distribution, Latin-hypercube sampling strategy, and one-at-the time sampling method with 10,400 model evaluations. The ten input parameters with the highest mean of the elementary effect were collected for tumors and kidneys. These ten most important parameters obtained from MS were quantitatively analyzed and ranked using an in-house eFAST algorithm (written in MATLAB R2019a) based on their main (Si) and total (Sti) effects. The chosen eFAST settings were interference factor 4, parameters with log-normal distribution, Latin-hypercube sampling strategy, and frequency-based sampling method with convergence test up to 4097 model evaluations.
Results: The five most important parameters that affect the estimation of the kidneys BED based on eFAST were receptor density RK (Si=0.21, Sti=0.30), degradation rate λK (Si=0.17, Sti=0.27), internalization rate intK (Si=0.13, Sti=0.18), age-dependent flow fkc (Si=0.10, Sti=0.15) and sieving coefficient SCOP (Si=0.07, Sti=0.09). Receptor density and flow were identified as the most important parameters that strongly affect the estimation of BED in tumors, e.g. in TU1: receptor density RTU1 (Si=0.43, Sti=0.77), tumor flow ftu2 (Si=0.05, Sti=0.26), degradation rate λTU2 (Si=0.04, Sti=0.16), age-dependent flow fkc (Si=0.03, Sti=0.11) and filtration fraction filfrac (Si=0.02, Sti=0.05). For TU1, all other parameters have Si and Sti less than 0.02 and 0.05, respectively.
Conclusions: We have shown the first implementation of a GSA for a whole-body PBPK model that has been developed for Lu-177-PSMA therapy. By using GSA analysis, we can identify the most important PBPK parameters that affect the accuracy of the BED prediction for treatment planning in molecular radiotherapy. Based on the results, we propose a measurement of some parameters before Lu-177-PSMA therapy, e.g. RK, RTU and ftu, to decrease the uncertainty of the predicted BED. References [1]. Hardiansyah et al. Cancer Biother Radiopharm. 2016 [2]. Campolongo and Saltelli. Reliab. Eng. Syst. 1997 [3]. Saltelli. Technometrics. 1999 [4]. Marino S. et al. J. Theor. Biol. 2008 [5]. Begum et al. J Nucl Med. 2018