Evaluation of additional treatment margins for compensating rotational random errors in linac-based single-isocenter stereotactic radiotherapy for multiple brain metastases

INTRODUCTION

Geometric errors in tumor localization consist of systematic errors and random errors. The systematic errors can be minimized by performing the tumor localization immediately before beam delivery, whereas the random errors are independently observed during beam delivery as a fluctuating stochastic process. For linac-based single-fraction stereotactic radiosurgery of brain metastases, direct error analyses were performed by varying geometric errors to obtain an upper bound for each error under aimed dose-volume constraints [1,2]. Meanwhile, for linac-based fractionated stereotactic radiotherapy for brain metastases, tumor localization errors were mainly discussed in terms of intrafractional random errors [3-6] after minimizing the systematic error by performing cranial bone matching between x-ray projection and digitally reconstructed radiography [3] or cone-beam computer tomography (CBCT) and planning CT images [4-6] immediately before beam delivery. Meyer et al. reported the localization reproducibility using a head phantom and an Elekta CBCT system, showing standard deviations of 0.13 mm and 0.08° during repeated localization calculations [7]. For patient treatment, a thermoplastic mask was also employed for cranial fixation, and a six-degrees-of-freedom couch was used to correct the position and orientation of the tumor [4-6].

When single-isocenter fractionated stereotactic radiotherapy is employed for treating multiple brain metastases, rotational errors need to be considered for a tumor distant to the isocenter. It is not always clear for treatment planners to choose a single isocenter or a multiple isocenter plan for a given tumor distribution in a brain, particularly when the tumors are widely distributed in the brain. Nomoto et al. employed a treatment margin of 2 mm for targets located within 5 cm from the isocenter, whilst 3 mm for the other targets located within 10 cm from the isocenter [8]. On the other hand, Chang derived a formula representing the rotation-oriented additional random errors in spherical and Cartesian coordinate systems [9], which is more theoretical and thus more accurate than the previous approach. To the authors’ knowledge, Chang’s formula has not been applied to real clinical cases. The purpose of this report is to show the amount of additional errors using this formula in our clinical setting, thereby deriving practical treatment margins required for a tumor as a function of the distance from the isocenter. In other words, we can determine the maximum length from the most distant tumor to the isocenter for a single isocenter treatment under a given margin. Treatment margins and the confidence level of dose delivery are also discussed when the additional errors are not considered.

MATERIALS AND METHODS

Data were collected during linac-based fractionated treatment of single brain metastasis for consecutive two patients. An in-house fixation mask with an integrated mouthpiece [10], CBCT XVI 5.0 (Elekta, Crawley, UK), and a six-degrees-of-freedom couch, HexaPOD (Elekta, Crawley, UK) were employed for tumor localization in reference to planning CT images. A six-arc non-coplanar volumetric modulated arc therapy (VMAT) plan with a photon energy of 6 MV was created by a treatment planning system, Monaco version 5.11.03 (Elekta, Crawley, UK), and treatment beams were delivered by a linac, Synergy (Elekta, Crawley, UK). Immediately before each fractionated treatment, the systematic errors were measured by the CBCT unit and corrected by the HexaPOD couch. Immediately after each treatment, intrafractional random errors in translation and rotation were measured by the CBCT unit using a bone matching algorithm. Subsequently, rotational angular errors were converted to rotation-oriented additional translational errors according to Chang’s formula [9] for a virtual secondary tumor distant to the isocenter while the primary tumor remaining at the isocenter. After that, the total random error in each translation direction was calculated to obtain each treatment margin. Written informed consent was obtained from the two patients.

RESULTS

The beam delivery time was 22.6 ± 2.2 min (standard deviation, referred to SD hereinafter). The resulting means and SDs of the translational errors over 27 fractions for the two patients were -0.20 ± 0.37 mm, –0.40 ± 0.34 mm, –0.10 ± 0.26 mm in the lateral, craniocaudal, and anteroposterior directions, respectively, whilst those of the rotational angular errors were 0.23 ± 0.31°, –0.11 ± 0.28°, –0.07 ± 0.33° around each of the above axes, respectively. The SD of the rotation-oriented additional random errors in translation, σ_R (mm), is given by the following Chang’s formula [9]:

(1).

where d (mm) is the length between the isocenter and a distant tumor, σ_δ (°) is the SD of the rotational random errors assuming isotropic σ_δ in the three rotational directions. In reality, σ_δ is not fully isotropic, and therefore, a root-mean-squared (rms) σ_δ of 0.307° was calculated from above data, thereby reducing the formula as follows:

(2).

Based on the above measured data, we can place a virtual secondary tumor at distances of 25, 50 and 100 mm with the primary tumor remaining at the isocenter. Then σ_δ goes to 0.109, 0.219, 0.437 mm, respectively.

Subsequently, the SDs of the total translational random errors of σ_LA, σ_CC, σ_AP for the virtual tumor were obtained by calculating root-sum-squared errors of the translational random errors and the above rotation-oriented additional translational errors σ_R in the lateral (LA), craniocaudal (CC), and anteroposterior (AP) directions, respectively. It is noted that the original translational errors and the additional rotation-oriented translational errors are mutually independent. After that, treatment margins were calculated by 2.5 σ_LA, 2.5 σ_CC and 2.5 σ_AP in each of the three translational directions, where a confidence level of 90% was employed which means that planned doses may be assured for 90% of delivered fractions. Here we assume that the errors follow a zero-mean three-dimensional Gaussian process. The resulting margins, m_LA, m_CC and m_AP, are shown in Table 1. For example, at d = 100 mm, the margin m_LA can be calculated by 2.5 1.43 mm.

Table 1.

Calculated treatment margin in each direction for a tumor at different distances from the isocenter, where LA, CC and AP refer to lateral, craniocaudal and anteroposterior directions, respectively

d (mm)	0	25	50	100
mLA (mm)	0.93	0.96	1.07	1.43
mCC (mm)	0.85	0.89	1.01	1.86
mAP (mm)	0.65	0.70	0.85	1.27

DISCUSSION

We have calculated treatment margins required for a tumor as a function of distance from the isocenter using Chang’s formula. To our knowledge, this is the first report that derives the clinically relevant margins from measured intrafractional random errors in translation and rotation using Chang’s formula. In addition, the maximum length from the most distant tumor to the isocenter can also be calculated for a single isocenter treatment under a given margin, which was not easy previously. Each institution can therefore readily evaluate margins for single-isocenter stereotactic treatment for multiple brain metastases by measuring the random errors in the same way.

Now we evaluate a possible decrease in the confidence level of dose delivery to the secondary distant tumor when the additional margins are not considered. For example, if a required margin is 1.1 mm and an actual margin employed is 1.0 mm, the corresponding confidence level reduces from 90% to 84% according to integral of a spherically symmetric Gaussian distribution from r = 0 to (2.5/1.1) σ in the radial direction, where σ is the SD of the Gaussian distribution. For another example, if a required margin is 1.3 mm and an actual margin employed is 1.0 mm, the corresponding confidence level decreases from 90% to 70% in the same way.

Because we routinely employ an anisotropic margin of 1 mm based on contrast-enhanced 3D FLAIR images [10], Table 1 and above calculation suggest that maximum length from the most distant tumor to the isocenter needs to be 50 mm in our clinical setting to maintain the confidence level of 90%.

Table 2 compares translational and rotational errors measured in this study with those reported in previous studies. It is shown that the rms rotational error of σ_δ in this study using our in-house mask and CBCT is within the range of previous studies. It is also speculated that σ_δ in this study is likely to be smaller than those reported in Lightstone [4] and Naoi [5] using commercial Uni-frame masks (CIVCO radiotherapy, Iowa, USA) and CBCT.

Table 2.

Comparison of means and standard deviations of localization errors in translation and rotation obtained in this study with previous studies

	LA (mm)	CC (mm)	AP (mm)	RLA (°)	RCC (°)	RAP (°)	rms σδ (°)
Verbakel et al.3	−0.04 ± 0.23	−0.01 ± 0.27	−0.06 ± 0.19	0.00 ± 0.20	−0.03 ± 0.15	0.07 ± 0.34	0.24
Lightstone et al.4	0.02 ± 0.47	−0.17 ± 0.91	−0.10 ± 0.37	−0.05 ± 0.49	−0.15 ± 0.49	−0.08 ± 0.66	0.55
Naoi et al.5	−0.01 ± 0.46	−0.11 ± 0.63	−0.13 ± 0.42	0.12 ± 0.34	−0.03 ± 0.42	−0.19 ± 0.57	0.45
Mizukami et al.6	−0.01 ± 0.32	−0.12 ± 0.41	−0.05 ± 0.38	0.07 ± 0.28	0.11 ± 0.22	0.05 ± 0.26	0.25
This study	−0.20 ± 0.37	−0.40 ± 0.34	−0.10 ± 0.26	0.23 ± 0.31	−0.11 ± 0.28	−0.07 ± 0.33	0.31

Verbakel et al.³: Brainlab mask + ExacTrac; Lightstone et al.⁴ and Naoi et al.⁵: Uni-frame mask + CBCT; Mizukami et al.⁶ and this study: in-house mask + CBCT

Table 2 also indicates that the resulting random errors in translation and rotation may depend on the intracranial fixation technique employed in each institution, suggesting that the margin needs to be evaluated in each facility. In addition, one may be able to improve intracranial fixation technique by comparison to data measured in other institutions. We have shown that margins required for single-isocenter stereotactic treatment of multiple brain metastases can be obtained by measuring the random errors in translation and rotation during beam delivery. In other words, it has become clear for treatment planners to choose a single isocenter or a multiple isocenter plan for a given tumor distribution and a margin setting. The limitation of this study may be insufficient number of fractions compared to those in the previous studies shown in Table 2.

In conclusion, additional treatment margins required for compensating rotational random errors have been evaluated in linac-based fractionated single-isocenter stereotactic radiotherapy for multiple brain metastases. In our clinical setting, it was suggested that the maximum length from the most distant tumor to the isocenter needs to be 50 mm. It is recommended that each institution should evaluate the margin for the single isocenter treatment of multiple brain metastases by measuring random errors in translation and rotation during treatment.