Theoretical aspects on the use of single-time-point dosimetry for radionuclide therapy

Objective: This study considers the error distributions for time-integrated activity (TIA) of single-time-point (STP) methods for patient-specific dosimetry in radionuclide therapy. Approach: The general case with the same pharmaceutical labelled with different radionuclides for imaging and therapy are considered for a mono-exponential time-activity curve. Two methods for STP dosimetry, both based on the combination of one activity estimate with the population-mean effective decay constant, are investigated. The cumulative distribution functions (CDFs) and the probability density functions for the two methods are analytically derived for arbitrary distributions of the biological decay constant. The CDFs are used for determining 95 % coverage intervals of the relative errors for different combinations of imaging time points, physical decay constants, and relative standard deviations of the biological decay constant. Two examples, in the form of kidney dosimetry in [177Lu]Lu-DOTA-TATE therapy and tumour dosimetry for Na[131I]I therapy for thyroid cancer with dosimetry based on imaging of Na[124I]I, are also studied in more detail with analysis of the sensitivity with respect to errors in the mean biological decay constant and to higher moments of the distribution. Main results: The distributions of the relative errors are negatively skewed, potentially leading to the situation that some TIA estimates are highly underestimated even if the majority of estimates are close to the true value. Significance: The main limitation of the studied STP dosimetry methods is thereby the risk of large underestimations of the TIA.