Technical Note: Single time point dose estimate for exponential clearance

Abstract

Objective: Although personalized dosimetry may be desirable for radionuclide therapy treatments, the multiple time samples required to determine the total integrated activity puts a burden on patients and clinic resources. The aim of this paper is to demonstrate that when some prior knowledge is known about the tracer kinetic parameters, the total integrated activity (and thus radiation dose) can be estimated from a single time sample.

Methods: Mathematical derivations have been performed to generate equations for the total integrated activity in terms of a single time sample of activity for monoexponential and biexponential clearance. Simulations were performed using both exponential models where the rate constants and associated parameters were randomly sampled from distributions with a known mean. The actual total integrated activity for each random sample was compared with the estimated total integrated activity using the mean value of the parameters. Retrospective analysis of 90 Y DOTATOC data from a clinical trial provided a comparison of actual kidney dose with the estimated kidney dose using the single time point approach.

Results: The optimal sampling time for the single point approach was found to be equal to the mean time of the rate constant. The simulation results for the monoexponential and biexpoential models were similar. Regressions comparing the actual and estimated total integrated activity had very high correlations (r2 > 0.95) along with acceptable standard errors of estimate, especially at the optimal sampling point. The retrospective analysis of the 90 Y DOTATOC data also yielded similar results with an r2 = 0.95 and a standard error of estimate of 61 cGy.

Conclusions: In situations where there is prior knowledge about the population averages of kinetic parameters, these results suggest that the single time point approach can be used to estimate the total integrated activity and dose with sufficient accuracy to manage radionuclide therapy. This will make personalized dosimetry much easier to perform and more available to the community.

Keywords: exponential clearance; personalized radionuclide therapy; radiation dose estimate; single sample time.

© 2018 American Association of Physicists in Medicine.

Figures

Figure 1

Monoexponential support data. (a) Plot of the sampling time T for accurately determining A~ when k varies from k^. (b) Plot of the optimal sampling time TOPT as a function of the averaging interval. TOPT is determined by integrating Eq. (5) over the interval 1 − α to 1 + α. The plot indicates that over a relatively large range, TOPT ≈ τ^. (c) Plot of the error in the estimated total integrated activity as a function of the error in the estimated rate constant. Large variations in k from k^ have a relatively small effect on the accuracy of A~∗ over a wide range. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 2

Histograms of the biexponential parameters (c,a, and k2) obtained from the 47 dosimetry studies of the kidneys. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 3

Plots showing the performance of the single time point method. (a) Monoexponential simulation results comparing the actual and estimated total integrated activity for T=τ^. (b) Biexponential simulation results comparing the actual and estimated total integrated activity for T=τ^2. (C) Retroscpective clinical results comparing the kidney radiation dose obtained from conventional mulitple time samples with the single time sample approximation at T = 48 h.