Approximation of time-uptake curve to a modified Bateman equation based on three uptake tests — potential value for dosimetry of corpuscular radiation

Abstract

BACKGROUND: Many models of assessing radiopharmaceutical kinetics for dosimetry have been developed, starting from the formula of Marinelli. They are either inaccurate or require taking multiple patient uptake measurements.

MATERIAL AND METHODS: Radiotracer behavior is approached to a modified Bateman equation (“biphasic model”). The calculated effective half time, maximum uptake and the cumulated uptake according to the biphasic model is compared to the values obtained with the most popular Marinelli’s method (“simplified model”). The calculations can be performed by free online-accessible software on the site: www.nuk.bieganski.org (“Calculator”).

RESULTS: Using of the software allows a direct comparison of the obtained effective half times according to both, the simplified and the biphasic, models. Further errors can come from imprecise measure of the maximum uptake value (especially, when the time of the measurement differs from the true point of the maximum uptake) and from neglecting of the ascending branch of the time-uptake curve. It is possible to compare the cumulated uptake values according to both models (“correction factor”). The results can be combined with the widely known formula of Marinelli. The operations require only one additional uptake measurement, which could be performed shortly after the i.v. administration of the radiotracer, i.e., during the same visit of the patient.

CONCLUSION: The proposed theoretic model could be verified practically for some i.v.-administered radiopharmaceuticals.