Rotational positional error-corrected linear set-up margin calculation technique for lung stereotactic body radiotherapy in a dual imaging environment of 4-D cone beam CT and ExacTrac stereoscopic imaging

Abstract

Objective

Accurate calculation of set-up margin is a prerequisite to arrive at the most optimal clinical to planning target volume margin. The aim of this study was to evaluate the compatibility of different on-board and in-room stereoscopic imaging modalities by calculating the set-up margins (SM) in stereotactic body radiotherapy technique accounting and unaccounting for rotational positional errors (PE). Further, we calculated separate SMs one based on residual positional errors and another based on residual + intrafraction positional errors from the imaging data obtained in a dual imaging environment.

Materials and methods

A total of 22 lung cancer patients were included in this study. For primary image guidance, four-dimensional cone beam computed tomography (4-D CBCT) was used and stereoscopic ExacTrac was used as the auxiliary imaging. Following table position correction (TPC) based on the initial 4-D CBCT, another 4-D CBCT (post-TPC) and a pair of stereoscopic ExacTrac images were obtained. Further, during the treatment delivery, a series of ExacTrac images were acquired to identify the intrafraction PE. If a, b and c were the observed translational shifts in lateral (x-axis), longitudinal (y-axis) and vertical direction (z-axis) and α, β and γ were the rotational shifts in radians about the same axes, respectively, then the resultant translational vectors (A, B and C) were calculated on the basis of translational and rotational values. Set-up margins were calculated using residual errors post-TPC only and also using intrafraction positional errors in addition to the residual errors.

Results

Residual and residual + intrafraction SM were calculated from a dataset of 82 CBCTs and 189 ExacTrac imaging sessions. CBCT-based mean ± SD shifts in translational and rotational directions were 0.3 ± 1.8 mm, 0.1 ± 1.8 mm, − 0.4 ± 1.6 mm, 0.1 ± 0.4°, 0.0 ± 1.0° and 0.3 ± 0.7°, respectively, and for ExacTrac − 0.1 ± 1.8 mm, 0.2 ± 2.4 mm, − 0.6 ± 1.8 mm, 0.1 ± 1.2°, − 0.2 ± 1.3° and − 0.1 ± 0.6°, respectively. Residual SM without considering the rotational correction in x, y and z directions were 5.0 mm, 4.5 mm and 4.4 mm; rotation-corrected SM were 4.4 mm, 4.0 mm and 5.5 mm, respectively. Residual plus intrafraction SM were 5.5 mm, 6.6 mm and 6.2 mm without considering the rotational corrections, whereas they were 5.0 mm, 6.3 mm and 6.2 mm with rotational errors accounted for.

Conclusion

Accurate calculation of set-up margin is required to find the clinical to planning target volume margin. Primary and auxiliary imaging margins fall in the range of 4.0 to 5.5 mm and 5.0 to 7.0 mm, respectively, indicating a higher SM for X-ray-based planar imaging techniques over three-dimensional cone beam images. This study established the degree of mutual compatibility between two different kinds of widely used set-up imaging modalities, on-board CBCT and in-room stereoscopic imaging ExacTrac. It also describes the technique to calculate the residual and residual plus intrafraction SM and its variation in a dual imaging environment accounting for rotational PE in stereotactic body radiotherapy of lung.

Appendix: Theory of rotational error correction for inertial frame of references

We begin with explaining the theory of rotational correction in inertial frame of reference, considering two different scenarios. First, the origin of the coordinate system or origin (isocentre) is off from the tumour centre; in the second scenario, isocentre is at the tumour centre. Figure

Fig. 5

Theory of rotational error correction: when tumour centre is away from isocentre. In such scenario, a Galilean/linear transformation is required along with the rotation to obtain the desired angle

5A graphically explains the situation when tumour centre is away from the centre of the coordinate system (origin) or isocentre. In the left panel, in the solid coordinate system the solid arrow crosses the solid star in certain angle. A certain amount of rotational error, analogous to the patient positional set-up error, was introduced to the solid star and identified as dotted. As shown in the left panel of Appendix Figure 5, it is not possible to find the same angle between dotted arrow–star to that of solid arrow–star only by a rotation. In such situation, a linear coordinate transformation or Galilean transformation is required to obtain a new origin and further apply the rotational correction. Right panel of Figure 5A shows that it is possible to find the appropriate dotted arrow–star puncture angle to that of the solid arrow–star before the introduction of rotational error.

In the second scenario as shown in Fig. 5b, isocentre is at the tumour centre offers a much more simpler geometrical condition. No linear coordinate transformation is required to obtain the desired angle. The solid star can be punctured by the solid arrow in the same angle as that of dotted star–arrow combination only by a rotation of the coordinate system (Fig. 6).

Fig. 6

When tumour centre at the origin/isocentre: In this scenario, no translation of the coordinate system (or Galilean transformation) is required to obtain the desired angle between the star and arrow of the black and red coordinate system

Scenario I: When tumour centre away from isocentre.