01.12.2017 | Research | Ausgabe 1/2017 Open Access

# Radiotoxicity in robotic radiosurgery: proposing a new quality index for optimizing the treatment planning of brain metastases

- Zeitschrift:
- Radiation Oncology > Ausgabe 1/2017

## Electronic supplementary material

## Background

## Methods

### Derivation of a model for estimating a minimal-V12

_{12}is the radial distance between the tumor surface and the 12 Gy isodose-line. It depends on the prescribed dose and steepness of the dose gradient \( \overrightarrow{\nabla}D \) and can be derived using an approximation of the mean dose gradient \( \left\langle \left|\overrightarrow{\nabla}D\right|\right\rangle \) between the tumor surface and the 12 Gy isodose-line:

### Model validation and application

## Results

### Model derivation and validation

65% at 16 Gy | 65% at 18 Gy | 65% at 20 Gy | 65% at 22 Gy | |
---|---|---|---|---|

A | 20.913 | 21.732 | 21.692 | 21.666 |

b | −0.105 | −0.109 | −0.109 | −0.113 |

y _{0}
| 5.397 | 4.680 | 4.067 | 3.715 |

R ^{2}
| 0.991 | 0.993 | 0.995 | 0.997 |

### Model application on patient data

_{1}= 0.18 ml, V

_{2}= 0.14 ml, V

_{3}= 1.11 ml) resulted in a deviation of 38%, whereas another case with 3 metastases (one large tumor volume V

_{1}= 4.41 ml, two smaller lesions: V

_{2}= 0.21 ml, V

_{3}= 0.12 ml) resulted in a deviation of only 8%. Index f12 showed no dependence on the number of metastases while using Eq. 5 for the determination of V12 (Fig. 3c) whereas a trend to larger f12 values with the increasing number of metastases was observable when using Eq. 6 (Fig. 3d).

Index f12 | Range | Mean | SD | Number of treatments (singular/multiple) |
---|---|---|---|---|

f12 _{all data}
| 1.12–4.22 | 1.91 | 0.47 | 80 (40/40) |

f12 _{multiple, Eq.}
5
| 1.13–4.22 | 2.02 | 0.52 | 40 (0/40) |

f12 _{singular}
| 1.12–2.70 | 1.80 | 0.39 | 40 (40/0) |

f12 _{mixed location}
| 1.13–4.22 | 2.02 | 0.63 | 23 (0/23) |

f12 _{in the parenchyma}
| 1.12–2.70 | 1.92 | 0.34 | 46 (31/15) |

f12 _{peripheral location}
| 1.15–2.70 | 1.63 | 0.51 | 11 (9/2) |

^{2}= 0.52, Fig. 5b). For the used patient collective, nCI ranged from 1.05 up to 1.78 (mean = 1.21 ± 0.11). Index f12 was independent of treatment time (Fig. 5c) and of the total number of MUs (Fig. 5d).

## Discussion

_{singular}= 1.80 ± 0.39) and multiple metastases (f12

_{multiple}= 2.02 ± 0.52) were comparable within the standard deviation. Depending on the distance between multiple metastases, dose bridges may occur, which can result in higher V12 s compared to singular metastases. Our model takes the number of metastases into account (Eq. 5), but not the effect of dose bridges. Narayanasamy et al. showed that the total treatment volume is a better predictor of whole brain dose from gamma knife based SRS than the number, shape, or location of the lesions [28] while Sahgal et al. found a significant increase in V12 with increasing number of targets for multitarget SRS [29]. In our study, we found that tumor location shows little influence on the resulting V12 s of the CK plans, while V12 is dependent on the number of metastases and a more precise determination of V12 for multiple metastases is achieved when applying the model to each individual metastasis (cf. Fig. 3).