On the reduction of imaging time-points for dosimetry in radionuclide therapy

The aim was to develop a theoretical framework for how errors in estimated activities propagate to a dispersion in time-integrated activity in radionuclide-therapy dosimetry and how this affects the comparison of radionuclide-therapy dosimetry schemes.

Formulae for the variance of relative errors of estimated time-integrated activities and relative differences in time-integrated activities between measurement schemes when one or more time-points are removed were derived using the law of propagation of uncertainty for a population of time-activity-curve parameters. The formulae were derived under the assumptions of fixed coefficients of variation for estimated activities, and underlying mono-exponential curves. Analytical predictions were compared with results from numerical simulations and data for kidneys, liver, and spleen from a data-set of 18 patients treated with ¹⁷⁷Lu-DOTA-TATE.

The dispersion in time-integrated activity is minimized if the time-points used for curve fitting have a large dispersion and are centered over the mean of $$ over the population, where $$ is the effective decay constant (i.e., the sum of the biological and physical decay constants). For large dispersions of decay constants in the population, the centering of time-points becomes gradually less important. The analytical expressions replicated the main trends from the numerical simulations. Furthermore, the analytical expressions predicted correctly the optimal reduced imaging schedule in 9 of 12 pairwise comparisons between schedules for patients.

The dispersion of errors and deviations in estimated time-activity curves can be predicted using simple formulae. These formulae have the potential to be used for optimization of dosimetry measurement schemes for established and new radiopharmaceuticals as long as the mean and dispersion of biological half-lives are known in the patient population.