Background The calculation of time-integrated activities (TIAs) for tumours and organs is required for dosimetry in molecular radiotherapy. The accuracy of the calculated TIAs is highly dependent on the chosen fit function. Selection of an adequate function is therefore of high importance. However, model (i.e. function) selection works more accurately when more biokinetic data are available than are usually obtained in a single patient. In this retrospective analysis, we therefore developed a method for population-based model selection that can be used for the determination of individual time-integrated activities (TIAs). The method is demonstrated at an example of [177Lu]Lu-PSMA-I&T kidneys biokinetics. It is based on population fitting and is specifically advantageous for cases with a low number of available biokinetic data per patient. Methods Renal biokinetics of [177Lu]Lu-PSMA-I&T from thirteen patients with metastatic castration-resistant prostate cancer acquired by planar imaging were used. Twenty exponential functions were derived from various parameterizations of mono- and bi-exponential functions. The parameters of the functions were fitted (with different combinations of shared and individual parameters) to the biokinetic data of all patients. The goodness of fits were assumed as acceptable based on visual inspection of the fitted curves and coefficients of variation CVs < 50%. The Akaike weight (based on the corrected Akaike Information Criterion) was used to select the fit function most supported by the data from the set of functions with acceptable goodness of fit. Results The function $$A_{1} { }\beta { }e^{{ - \left( {\lambda_{1} + \lambda_{{{\text{phys}}}} } \right)t}} + A_{1} { }\left( {1 - \beta } \right){ }e^{{ - \left( {\lambda_{{{\text{phys}}}} } \right)t}}$$ A 1 β e - λ 1 + λ phys t + A 1 1 - β e - λ phys t with shared parameter $$\beta$$ β was selected as the function most supported by the data with an Akaike weight of 97%. Parameters $$A_{1}$$ A 1 and $$\lambda_{1}$$ λ 1 were fitted individually for every patient while parameter $$\beta { }$$ β was fitted as a shared parameter in the population yielding a value of 0.9632 ± 0.0037. Conclusions The presented population-based model selection allows for a higher number of parameters of investigated fit functions which leads to better fits. It also reduces the uncertainty of the obtained Akaike weights and the selected best fit function based on them. The use of the population-determined shared parameter for future patients allows the fitting of more appropriate functions also for patients for whom only a low number of individual data are available.
In vivo alpha particle generators have great potential for the treatment of neuroendocrine tumors in alpha-emitter-based peptide receptor radionuclide therapy (α-PRRT). Quantitative pharmacokinetic analyses of the in vivo alpha particle generator and its radioactive decay products are required to address concerns about the efficacy and safety of α-PRRT. A murine whole-body physiologically based pharmacokinetic (PBPK) model was developed for 212Pb-labeled somatostatin analogs (212Pb-SSTA). The model describes pharmacokinetics of 212Pb-SSTA and its decay products, including specific and non-specific glomerular and tubular uptake. Absorbed dose coefficients (ADC) were calculated for bound and unbound radiolabeled SSTA and its decay products. Kidneys received the highest ADC (134 Gy/MBq) among non-target tissues. The alpha-emitting 212Po contributes more than 50% to absorbed doses in most tissues. Using this model, it is demonstrated that α-PRRT based on 212Pb-SSTA results in lower absorbed doses in non-target tissue than α-PRRT based on 212Bi-SSTA for a given kidneys absorbed dose. In both approaches, the energies released in the glomeruli and proximal tubules account for 54% and 46%, respectively, of the total energy absorbed in kidneys. The 212Pb-SSTA-PBPK model accelerates the translation from bench to bedside by enabling better experimental design and by improving the understanding of the underlying mechanisms.
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