EANM practical guidance on uncertainty analysis for molecular radiotherapy absorbed dose calculations

Abstract

A framework is proposed for modelling the uncertainty in the measurement processes constituting the dosimetry chain that are involved in internal absorbed dose calculations. The starting point is the basic model for absorbed dose in a site of interest as the product of the cumulated activity and a dose factor. In turn, the cumulated activity is given by the area under a time-activity curve derived from a time sequence of activity values. Each activity value is obtained in terms of a count rate, a calibration factor and a recovery coefficient (a correction for partial volume effects). The method to determine the recovery coefficient and the dose factor, both of which are dependent on the size of the volume of interest (VOI), are described. Consideration is given to propagating estimates of the quantities concerned and their associated uncertainties through the dosimetry chain to obtain an estimate of mean absorbed dose in the VOI and its associated uncertainty. This approach is demonstrated in a clinical example.

Keywords: Dosimetry; Uncertainty analysis.

Fig. 1

Flow diagram showing chronological sequence of the dosimetry schema demonstrating how uncertainty can propagate between each step

Fig. 2

Uncertainty in outline definition for different voxel sizes

Fig. 3

Signal intensity profiles demonstrating that the gradient of a Gaussian blurred function can be described by the Gaussian function

Fig. 4

a Count density as function of radius for a spherical object with true radius r for a system with ideal resolution (red step function) and realistic system (green curve). b Two-dimensional image planes through the three-dimensional functions H(ρ) and F(ρ) (see text)

Fig. 5

a Count density as function of radius showing observed counts within a VOI of radius ρ (green shaded area). b Two-dimensional image plane with the VOI outlined with radius ρ (red line). c Count rate as a function of VOI volume v corresponding to a particular choice of radius ρ. d Gradient of the count rate with respect to the VOI volume v

Fig. 6

Example plot of S-factor versus mass for the radionuclides indicated for unit density spheres

Fig. 7

¹¹¹In-DOTATATE SPECT and ⁶⁸Ga-DOTATATE PET/CT images of neuroendocrine tumours in a patient treated with ⁹⁰Y-DOTATATE radiopeptide therapy. Arrows indicate the lesions for which doses are to be calculated

Fig. 8

A recovery curve used to correct for partial volume losses for objects of different sizes. The solid line indicates the fitted function and the dotted lines indicate the lower and upper limits of the 95% confidence interval of the fitted function

Fig. 9

Activity versus count rate of reconstructed point sources in air

Fig. 10

TAC for liver (a) and pancreatic (b) lesions. Error bars for each point are the standard uncertainty of the measured activity. Dotted lines indicate the 95% confidence intervals due to systematic uncertainty in activity combined with the parameter uncertainties in the fitting algorithm

Fig. 11

Fractional uncertainty of calculated dosimetric parameters for lesions and normal organs

Fig. 12

Absorbed doses to lesions and normal organs over four treatment cycles. Error bars represent standard uncertainties in the dose values