## Abstract

### 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 [^{177}Lu]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 [^{177}Lu]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 \(A_{1} { }\beta { }e^{{ - \left( {\lambda_{1} + \lambda_{{{\text{phys}}}} } \right)t}} + A_{1} { }\left( {1 - \beta } \right){ }e^{{ - \left( {\lambda_{{{\text{phys}}}} } \right)t}}\) with shared parameter \(\beta\) was selected as the function most supported by the data with an Akaike weight of 97%. Parameters \(A_{1}\) and \(\lambda_{1}\) were fitted individually for every patient while parameter \(\beta { }\) 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.