### Abstract

Purpose: For accurate operation, real‐time tumor tracking devices for radiation therapy require the real‐time position of the radiation target. In this study, we assess Ordinary‐Least‐Squares (OLS) and Partial‐Least‐Squares (PLS) modeling methods for inferring intra‐fraction motion from external markers. Method and Materials: We obtained the concurrent 3D positions of three optically tracked external markers affixed to the skin and the 3D centroid position of a set of three internal fiducials implanted in lung tumors localized with fluoroscopy by the Cyberknife system. We analyzed 134 treatment fractions from 63 patients, each including 40–112 (mean=62) samples spaced at approximately 1–2min. For each fraction, we used a randomly selected subset of N (4–35) points to train OLS and PLS models to infer tumor motion from the positions of the optical markers, and we repeated this process 40 times for each fraction and each N. We then tested the models against the remaining datapoints in that fraction to determine the position error. Results: The PLS mean(±standard deviation) errors decreased monotonically as N increased, from 0.3±2.6cm at N=4 to 0.2±1.4cm at N=35. In contrast, the OLS error peaked (mean=5.3cm) at N=10 training samples, a consequence of the Moore‐Penrose pseudo‐inverse regression technique. OLS errors at N=4 and N=35 were 0.4±4.6cm and 0.2±1.7cm, respectively. PLS and OLS mean and maximum errors converged for large N (approximately N⩾20). To achieve mean errors less than 0.25cm or 0.20cm over the entire dataset with PLS, at least 8 or 18 training samples, respectively, must be used. Conclusion: The results of this study indicate that PLS shows potential as an efficient (few image acquisitions) and accurate (2–3mm) intra‐fraction lung tumor motion modeling technique. Future work will focus on investigating methods for and consequences of non‐random training sample selection.

Original language | English (US) |
---|---|

Number of pages | 1 |

Journal | Medical Physics |

Volume | 36 |

Issue number | 6 |

DOIs | |

State | Published - 2009 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Biophysics
- Radiology Nuclear Medicine and imaging

### Cite this

*Medical Physics*,

*36*(6). https://doi.org/10.1118/1.3182261

**MO‐EE‐A3‐03 : Ordinary Least Squares and Partial Least Squares for Intra‐Fraction Lung Tumor Motion Modeling.** / Malinowski, K.; Mcavoy, T.; George, R.; Dieterich, Sonja; D'souza, W.

Research output: Contribution to journal › Article

*Medical Physics*, vol. 36, no. 6. https://doi.org/10.1118/1.3182261

}

TY - JOUR

T1 - MO‐EE‐A3‐03

T2 - Ordinary Least Squares and Partial Least Squares for Intra‐Fraction Lung Tumor Motion Modeling

AU - Malinowski, K.

AU - Mcavoy, T.

AU - George, R.

AU - Dieterich, Sonja

AU - D'souza, W.

PY - 2009

Y1 - 2009

N2 - Purpose: For accurate operation, real‐time tumor tracking devices for radiation therapy require the real‐time position of the radiation target. In this study, we assess Ordinary‐Least‐Squares (OLS) and Partial‐Least‐Squares (PLS) modeling methods for inferring intra‐fraction motion from external markers. Method and Materials: We obtained the concurrent 3D positions of three optically tracked external markers affixed to the skin and the 3D centroid position of a set of three internal fiducials implanted in lung tumors localized with fluoroscopy by the Cyberknife system. We analyzed 134 treatment fractions from 63 patients, each including 40–112 (mean=62) samples spaced at approximately 1–2min. For each fraction, we used a randomly selected subset of N (4–35) points to train OLS and PLS models to infer tumor motion from the positions of the optical markers, and we repeated this process 40 times for each fraction and each N. We then tested the models against the remaining datapoints in that fraction to determine the position error. Results: The PLS mean(±standard deviation) errors decreased monotonically as N increased, from 0.3±2.6cm at N=4 to 0.2±1.4cm at N=35. In contrast, the OLS error peaked (mean=5.3cm) at N=10 training samples, a consequence of the Moore‐Penrose pseudo‐inverse regression technique. OLS errors at N=4 and N=35 were 0.4±4.6cm and 0.2±1.7cm, respectively. PLS and OLS mean and maximum errors converged for large N (approximately N⩾20). To achieve mean errors less than 0.25cm or 0.20cm over the entire dataset with PLS, at least 8 or 18 training samples, respectively, must be used. Conclusion: The results of this study indicate that PLS shows potential as an efficient (few image acquisitions) and accurate (2–3mm) intra‐fraction lung tumor motion modeling technique. Future work will focus on investigating methods for and consequences of non‐random training sample selection.

AB - Purpose: For accurate operation, real‐time tumor tracking devices for radiation therapy require the real‐time position of the radiation target. In this study, we assess Ordinary‐Least‐Squares (OLS) and Partial‐Least‐Squares (PLS) modeling methods for inferring intra‐fraction motion from external markers. Method and Materials: We obtained the concurrent 3D positions of three optically tracked external markers affixed to the skin and the 3D centroid position of a set of three internal fiducials implanted in lung tumors localized with fluoroscopy by the Cyberknife system. We analyzed 134 treatment fractions from 63 patients, each including 40–112 (mean=62) samples spaced at approximately 1–2min. For each fraction, we used a randomly selected subset of N (4–35) points to train OLS and PLS models to infer tumor motion from the positions of the optical markers, and we repeated this process 40 times for each fraction and each N. We then tested the models against the remaining datapoints in that fraction to determine the position error. Results: The PLS mean(±standard deviation) errors decreased monotonically as N increased, from 0.3±2.6cm at N=4 to 0.2±1.4cm at N=35. In contrast, the OLS error peaked (mean=5.3cm) at N=10 training samples, a consequence of the Moore‐Penrose pseudo‐inverse regression technique. OLS errors at N=4 and N=35 were 0.4±4.6cm and 0.2±1.7cm, respectively. PLS and OLS mean and maximum errors converged for large N (approximately N⩾20). To achieve mean errors less than 0.25cm or 0.20cm over the entire dataset with PLS, at least 8 or 18 training samples, respectively, must be used. Conclusion: The results of this study indicate that PLS shows potential as an efficient (few image acquisitions) and accurate (2–3mm) intra‐fraction lung tumor motion modeling technique. Future work will focus on investigating methods for and consequences of non‐random training sample selection.

UR - http://www.scopus.com/inward/record.url?scp=85024779749&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85024779749&partnerID=8YFLogxK

U2 - 10.1118/1.3182261

DO - 10.1118/1.3182261

M3 - Article

AN - SCOPUS:85024779749

VL - 36

JO - Medical Physics

JF - Medical Physics

SN - 0094-2405

IS - 6

ER -