Accuracy and Optimal Timing of Activity Measurements in Estimating Absorbed Dose of Radioiodine in the Treatment of Graves’ Disease

Calculation of the therapeutic activity of radioiodine ¹³¹I for individualized dosimetry in the treatment of Graves’ disease requires an accurate estimate of the thyroid absorbed radiation dose based on a tracer activity administration of ¹³¹I. Common approaches (Marinelli-Quimby formula, MIRD algorithm) use, respectively, the effective half-life of radioiodine in the thyroid and the cumulative activity. Many physicians perform one, two, or at most three tracer dose activity measurements at various times and calculate the required therapeutic activity by ad hoc methods. In this paper, we study the accuracy of estimates of four “target variables”: cumulated activity, effective half-life, maximum activity, and time of maximum activity in the gland. Clinical data from 41 patients who underwent ¹³¹I therapy for Graves’ disease at the University Hospital in Pisa, Italy, are used for analysis. The radioiodine kinetics are described using a nonlinear mixed-effects model that includes a measurement error term, and the distributions of the target variables in the patient population are characterized. Using minimum root mean squared error (RMSE) as the criterion, optimal 1-, 2-, and 3-point sampling schedules are determined for estimation of the target variables, and probabilistic bounds are given for the errors under the optimal designs. An optimization algorithm is developed for computing target variables for arbitrary 1-, 2-, and 3-point activity measurements. Taking into consideration ¹³¹I effective half-life in the thyroid and measurement noise, the optimal 1-point design for cumulated activity is a measurement one week following the tracer dose. Additional measurements give only a slight improvement in accuracy.