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 (P_t), and those markers with a 3D |TMD_n| ≤ 58.7 mm at end-exhalation were then selected. The estimated target position (P_e) was calculated from a localization point consisting of one to three markers except P_t. Respiratory motion for P_t and P_e 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 P_t and P_e 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 (^MRATLE) increased as |TMD| and |aRM| increased and adversely decreased with each increment of n. The median 3D ^MRATLE 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 ^MRATLE 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 ^MRATLEs 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.