Uncertainty of stochastic parametric approach to bone marrow dosimetry of 89,90Sr

Abstract

The objective of this study is to evaluate the uncertainties of the dosimetric modeling of active marrow (AM) exposure from bone-seeking ^89,90Sr. The stochastic parametric skeletal dosimetry (SPSD) model was specifically developed to study the long-term effects resulting from chronic ^89,90Sr exposure in populations of the radioactively contaminated territories of the Southern Urals region of the Russian Federation. The method permits the evaluation of the dose factors (DF(AM ← TBV) and DF(AM ← CBV)), which convert the radionuclide activity concentration in trabecular (TBV) and cortical (CBV) bone volumes into dose rate in the AM, and their uncertainties. The sources of uncertainty can be subdivided into inherent uncertainties related to the individual variability of the simulated objects and introduced uncertainties related to model simplifications. Inherent uncertainty components are the individual variability of bone chemical composition, bone density, bone micro- and macro-architecture as well as AM distribution within the skeleton. The introduced uncertainties may result from the stylization of bone segment geometry, assumption of uniform cortical thickness, restriction of bone geometry and the selection of the applied voxel resolution. The inherent uncertainty depends on a number of factors of influence. Foremost, it is the result of variability of AM distribution within the skeleton. Another important factor is the variability of bone micro- and macro-architecture. The inherent uncertainty of skeletal-average dose factors was found to be about 40-50%. The introduced uncertainty associated with the SPSD model approach does not exceed 16% and mainly depends on the error of bone-shape stylization. The overall inherent and introduced uncertainties of DF(AM ← TBV) and DF(AM ← CBV) are below 55% and 63%, respectively. The results obtained will be incorporated into the stochastic version of the Techa River Dosimetry System (TRDS-2016MC) that provides multiple realizations of the annual doses for each cohort member to obtain both a central estimate of the individual dose and information on the dose uncertainty.

Fig. 1

Example of segmentation and stylization of scapula. Bone segments with active hematopoiesis in the adult scapula are colored; a – view of the scapula from the front, b – view of the scapula from behind, c, d, e − phantoms of segments acromion, glenoid and lateral margin, respectively. The color of the phantoms (c, d, e) corresponds to the color of the bone segments (a, b). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 2

Results of multiple realizations of DF_i,j(AM ← TBV) for ⁹⁰Sr: a) the normalized RMSD, δ, as a function of sample size, n; the solid line is an exponential smoothing, the dashed lines border the 90% confidence interval; b) the relative variance of variance (VOV); the solid line is an exponential smoothing; the dots are results of numerical experiment.

Fig. 3

Distribution of linearly transformed dose factors $\widetilde{DF}\left(AM\leftarrow CBV\right)$. Solid line is a 3-parameter lognormal fit.

Fig. 4

DF_i,j(AM ← TBV) as a function of voxel resolution. Points are the results of Monte Carlo simulation, solid line is a spline; dashed lines around the spline bound the 90% confidence interval. The vertical line borders the voxel resolution above which the values of DF_i,j(AM ← TBV) differ from the best estimate (with the minimum resolution).

Fig. 5

Scaling of the ⁹⁰Sr DF(AM←TBV) of group TBV2: a) and b) illustrate the dependence of raw and scaled data, respectively, on SS × BV/TV; c) reference function for data obtained using the models with BV/TV = 0.13; d) scaling factor function for recalculation of data with different BV/TV to fixed one (BV/TV = 0.13). Solid lines are the data smoothing; dashed lines bound the 90% prediction intervals; dotted lines are 90% confidence boundaries.

Fig. 6

Dependence of DF_j(AM ← TBV) calculated for ⁹⁰Sr on BV/TV for bone segment phantoms with spongiosa linear dimensions >0.46 cm. Solid line is a fitted function of exponential rise to maximum. Points are the results of calculations. Dashed lines bound the 90% prediction interval.

Fig. 7

Segment-specific ⁹⁰Sr $E\left(BM\leftarrow CBV\right)$ to $E\left(BM\leftarrow TBV\right)$ ratio as a function of Ct.Th for phantoms with linear dimensions >0.46 cm. Solid line is a fitted exponential function. Points are the results of calculations. Dashed lines bound the 90% prediction interval.