### Abstract

Purpose: To evaluate Hotelling's T^{2} statistic and the input variable squared prediction error (Q^{(X)}) for detecting large respiratory surrogate-based tumor displacement prediction errors without directly measuring the tumor's position. Methods: Tumor and external marker positions from a database of 188 Cyberknife Synchrony™ lung, liver, and pancreas treatment fractions were analyzed. The first ten measurements of tumor position in each fraction were used to create fraction-specific models of tumor displacement using external surrogates as input; the models were used to predict tumor position from subsequent external marker measurements. A partial least squares (PLS) model with four scores was developed for each fraction to determine T^{2} and Q^{(X)} confidence limits based on the first ten measurements in a fraction. The T^{2} and Q^{(X)} statistics were then calculated for every set of external marker measurements. Correlations between model error and both T^{2} and Q^{(X)} were determined. Receiver operating characteristic analysis was applied to evaluate sensitivities and specificities of T^{2}, Q^{(X)}, and T ^{2}∪Q^{(X)} for predicting real-time tumor localization errors >3 mm over a range of T^{2} and Q^{(X)} confidence limits. Results: Sensitivity and specificity of detecting errors >3 mm varied with confidence limit selection. At 95% sensitivity, T^{2}∪Q ^{(X)} specificity was 15, 2 higher than either T^{2} or Q ^{(X)} alone. The mean time to alarm for T^{2}∪Q ^{(X)} at 95 sensitivity was 5.3 min but varied with a standard deviation of 8.2 min. Results did not differ significantly by tumor site. Conclusions: The results of this study establish the feasibility of respiratory surrogate-based online monitoring of real-time respiration-induced tumor motion model accuracy for lung, liver, and pancreas tumors. The T^{2} and Q^{(X)} statistics were able to indicate whether inferential model errors exceeded 3 mm with high sensitivity. Modest improvements in specificity were achieved by combining T^{2} and Q^{(X)} results.

Original language | English (US) |
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Pages (from-to) | 2042-2048 |

Number of pages | 7 |

Journal | Medical Physics |

Volume | 39 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2012 |

Externally published | Yes |

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### Keywords

- radiation targeting
- respiratory motion
- respiratory surrogates
- statistical process control

### ASJC Scopus subject areas

- Biophysics
- Radiology Nuclear Medicine and imaging

### Cite this

*Medical Physics*,

*39*(4), 2042-2048. https://doi.org/10.1118/1.3676690