Multivariate analysis for the estimation of target localization errors in fiducial marker-based radiotherapy.

Purpose: To assess the target localization error (TLE) in terms of the distance between the target and the localization point estimated from the surrogates (|TMD|), the average of respiratory motion for the surrogates and the target (|aRM|), and the number of fiducial markers used for estimating the target (n).

Methods: This study enrolled 17 lung cancer patients who subsequently underwent four fractions of real-time tumor tracking irradiation. Four or five fiducial markers were implanted around the lung tumor. The three-dimensional (3D) distance between the tumor and markers was at maximum 58.7 mm. One of the markers was used as the target (Pt), and those markers with a 3D |TMDn| ≤ 58.7 mm at end-exhalation were then selected. The estimated target position (Pe) was calculated from a localization point consisting of one to three markers except Pt. Respiratory motion for Pt and Pe was defined as the root mean square of each displacement, and |aRM| was calculated from the mean value. TLE was defined as the root mean square of each difference between Pt and Pe during the monitoring of each fraction. These procedures were performed repeatedly using the remaining markers. To provide the best guidance on the answer with n and |TMD|, fiducial markers with a 3D |aRM ≥ 10 mm were selected. Finally, a total of 205, 282, and 76 TLEs that fulfilled the 3D |TMD| and 3D |aRM| criteria were obtained for n = 1, 2, and 3, respectively. Multiple regression analysis (MRA) was used to evaluate TLE as a function of |TMD| and |aRM| in each n.

Results: |TMD| for n = 1 was larger than that for n = 3. Moreover, |aRM| was almost constant for all n, indicating a similar scale for the marker's motion near the lung tumor. MRA showed that |aRM| in the left-right direction was the major cause of TLE; however, the contribution made little difference to the 3D TLE because of the small amount of motion in the left-right direction. The TLE calculated from the MRA ((MRA)TLE) increased as |TMD| and |aRM| increased and adversely decreased with each increment of n. The median 3D (MRA)TLE was 2.0 mm (range, 0.6-4.3 mm) for n = 1, 1.8 mm (range, 0.4-4.0 mm) for n = 2, and 1.6 mm (range, 0.3-3.7 mm) for n = 3. Although statistical significance between n = 1 and n = 3 was observed in all directions, the absolute average difference and the standard deviation of the (MRA)TLE between n = 1 and n = 3 were 0.5 and 0.2 mm, respectively.

Conclusions: A large |TMD| and |aRM| increased the differences in TLE between each n; however, the difference in 3D (MRA)TLEs was, at most, 0.6 mm. Thus, the authors conclude that it is acceptable to continue fiducial marker-based radiotherapy as long as |TMD| is maintained at ≤58.7 mm for a 3D |aRM|  ≥  10 mm.