Optimal sampling schedule for dosimetry: A simulation study.

Objectives: For dosimetry in nuclear medicine, the areas under the organ time-activity curves have to be determined. To reduce resources, the biokinetics and areas under the curves (AUCs) are predicted based on a small number of measured time points. However, the sampling scheme may influence the calculated AUCs and therefore the predicted absorbed doses considerably. In contrast to existing methods for determining the optimal sampling schedule, a general and flexible approach - e.g. taking into account clinical time boundary conditions and the error of the data - was developed and investigated in this work.

Methods: Biokinetic data of a male meningioma-patient (age: 31, tumor volume: 87 ml) for one pre-therapeutic cycle with In-111-DOTATATE were generated with a physiologically-based pharmacokinetic model [Kletting et al., J Nucl Med, 57 (2016) 503]. Random noise (multiplicative, Gaussian with mean: 0; SD = 0.05, 0.1, 0.2) was added to activity data at 4 time points (t₁, t₂ ∈ [0.5, 1.0, &#8943;, 8.0] h p.i. with t₁ < t₂; t₃ ∈ [24, 25, &#8943;, 32] h p.i.; t₄ ∈ [48, 50, 52, 54, 56, 72, 76, 80, 96, 100, 104] h p.i.). Subsequently, a bi-exponential function (A₁ ∙ exp(-λ₁ ∙ t) - A₁ ∙ exp(-λ₂ ∙ t)) was fitted to the noisy data. Ten thousand replications were performed and analyzed for each investigated measurement scheme. The optimal sampling schedule was defined as the schedule with the lowest mean relative variability RV_RMSE of the AUC (root-mean-square error divided by the true AUC value). Furthermore, the importance of accuracy of each time point of the optimal schedule was investigated. Therefore, all but one time point were fixed and the number of replications with AUCs deviating more than 5% from the true AUC value were determined.

Results: The determined optimal sampling schedules for Gaussian noise values with SD = 0.05, 0.1, 0.2 were (2, 2.5, 32, 96) h p.i., (2, 8, 31, 96) h p.i. and (6, 8, 28, 104) h p.i., respectively, with RV_RMSE values of 0.028, 0.057 and 0.116. The first quartile, median and third quartile of the determined relative AUCs for a noise with a SD = 0.05, 0.1, 0.2 were (-1.74, 0.16, 2.05) %, (-3.56, 0.32, 4.14) % and (-7.56, 0.11, 7.76) %, respectively. For the optimal schedules with a noise value with SD of 0.05, 0.1 and 0.2, 7.6%, 38% and 66% of the 10000 AUCs deviated more than 5% from the true AUC value. The last time point was the most important for all noise levels. For example, a shift of the last time point t₄ to 48 h p.i. increased the percentages of AUCs deviating more than 5% to 94%, 83% and 86% for noise values with SD = 0.05, 0.1, 0.2, respectively. The second most important time point was determined to be t₁. A shift of t₁ to 0.5 h p.i. increased the percentage of AUCs deviating more than 5% to 23%, 48% and 69% for noise values with SD = 0.05, 0.1, 0.2, respectively. Variations of t₂ and t₃ resulted in an increase below 3.5 percentage points. Conclusion: A method to determine the optimal sampling schedule for dosimetry, which e.g. considers the clinical working hours and the measurement errors, was developed and employed. The simulation study showed that the optimal sampling schedule increases the accuracy and precision of AUCs for dosimetry considerably.