Mathematical model to calculate the total number of decays in Peptide Receptor Radionuclide Therapy using nonlinear mixed effect modelling

The calculation of an individual total number of decays or time-integrated activities (TIAs) of a radiopharmaceutical for kidneys is desirable for dosimetry in molecular radiotherapy. The accuracy of the TIAs calculation relies heavily on the chosen fit model. Therefore, this study aimed to determine the best mathematical model of 177Lu-DOTATATE in peptide receptor radionuclide therapy (PRRT) using the nonlinear mixed effect (NLME) and model selection method. Pharmacokinetics data of 177Lu-DOTATATE in the kidneys of ten PRRT patients were obtained from the literature (PMID: 33443063). Eleven sums of exponential (SOE) functions were fitted to the pharmacokinetics data in the NLME framework. The model selection was performed based on the goodness of fit test and the corrected Akaike Information Criterion (AICc). The goodness of fit was evaluated based on the fitted graphs visualization, coefficient of variations (CV<50%), and the off-diagonal elements of the correlation matrix (-0,8≤CM≤0,8). In general, all SOE functions were successfully fitted to the pharmacokinetic data of 177Lu-DOTATATE in kidneys. The function f4e(t)=A1/{(αλ1+λphys)-(1-αλ2+λphys)-(2α-1λbc+λphys)}.e-(λphys)t.{αe-λ1t-(1-α)e-λ2t-(2α-1)e-λbct} was selected as the best mathematical model with an AICc weight of 77.58 %.