### Abstract

Aims: To study how the volume of a peripheral isodose line would relate to its isodose value for Gamma Knife^{®} (GK) radiosurgery. Method: A theoretical model was developed to derive the relationship between the volume of a near-target peripheral isodose line and its isodose value. The formula was tested based on cases with uniformly matched target volumes as well as random target volumes ranging from 0.1 to 37 cc. Results: To the second order approximation, the volume of a near-target peripheral isodose line (V) relates to its dose value (D) by the following formula: V/V_{0} = (D/D _{0})^{-3/2}, where D_{0} is the prescription dose and V_{0} is the prescription isodose volume. Applied to patient data, we found V/V_{0} = (D/D_{0})^{γ}, where γ = - 1.50 ± 0.16 at the 95% of the confidence level, and showed excellent agreement with the theoretical prediction. Conclusion: For GK radiosurgery, the near-target peripheral isodose volume relates to its isodose value in a similar fashion as to the way in which the volume of a sphere relates to the inverse of its surface area. Such a predictable relationship justifies the use of a single near-target peripheral isodose volume, as a sufficient measure of the dose to the normal brain.

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

Title of host publication | Radiosurgery |

Pages | 75-83 |

Number of pages | 9 |

Volume | 7 |

DOIs | |

State | Published - 2010 |

Externally published | Yes |

### Publication series

Name | Radiosurgery |
---|---|

Volume | 7 |

ISSN (Print) | 10242651 |

ISSN (Electronic) | 16623940 |

### Fingerprint

### ASJC Scopus subject areas

- Radiology Nuclear Medicine and imaging
- Surgery
- Medicine(all)

### Cite this

*Radiosurgery*(Vol. 7, pp. 75-83). (Radiosurgery; Vol. 7). https://doi.org/10.1159/000288720

**Functional relationship between the volume of a near-target peripheral isodose line and its isodose value for gamma knife® radiosurgery.** / Ma, Lijun; Sahgal, Arjun; Chuang, Cynthia; Descovich, Martina; Petti, Paula; Smith, Vernon; Verhey, Lynn; Barbaro, Nicholas; McDermott, Michael; Huang, Kim; Nakamura, Jean; Sneed, Penny; Larson, David.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Radiosurgery.*vol. 7, Radiosurgery, vol. 7, pp. 75-83. https://doi.org/10.1159/000288720

}

TY - CHAP

T1 - Functional relationship between the volume of a near-target peripheral isodose line and its isodose value for gamma knife® radiosurgery

AU - Ma, Lijun

AU - Sahgal, Arjun

AU - Chuang, Cynthia

AU - Descovich, Martina

AU - Petti, Paula

AU - Smith, Vernon

AU - Verhey, Lynn

AU - Barbaro, Nicholas

AU - McDermott, Michael

AU - Huang, Kim

AU - Nakamura, Jean

AU - Sneed, Penny

AU - Larson, David

PY - 2010

Y1 - 2010

N2 - Aims: To study how the volume of a peripheral isodose line would relate to its isodose value for Gamma Knife® (GK) radiosurgery. Method: A theoretical model was developed to derive the relationship between the volume of a near-target peripheral isodose line and its isodose value. The formula was tested based on cases with uniformly matched target volumes as well as random target volumes ranging from 0.1 to 37 cc. Results: To the second order approximation, the volume of a near-target peripheral isodose line (V) relates to its dose value (D) by the following formula: V/V0 = (D/D 0)-3/2, where D0 is the prescription dose and V0 is the prescription isodose volume. Applied to patient data, we found V/V0 = (D/D0)γ, where γ = - 1.50 ± 0.16 at the 95% of the confidence level, and showed excellent agreement with the theoretical prediction. Conclusion: For GK radiosurgery, the near-target peripheral isodose volume relates to its isodose value in a similar fashion as to the way in which the volume of a sphere relates to the inverse of its surface area. Such a predictable relationship justifies the use of a single near-target peripheral isodose volume, as a sufficient measure of the dose to the normal brain.

AB - Aims: To study how the volume of a peripheral isodose line would relate to its isodose value for Gamma Knife® (GK) radiosurgery. Method: A theoretical model was developed to derive the relationship between the volume of a near-target peripheral isodose line and its isodose value. The formula was tested based on cases with uniformly matched target volumes as well as random target volumes ranging from 0.1 to 37 cc. Results: To the second order approximation, the volume of a near-target peripheral isodose line (V) relates to its dose value (D) by the following formula: V/V0 = (D/D 0)-3/2, where D0 is the prescription dose and V0 is the prescription isodose volume. Applied to patient data, we found V/V0 = (D/D0)γ, where γ = - 1.50 ± 0.16 at the 95% of the confidence level, and showed excellent agreement with the theoretical prediction. Conclusion: For GK radiosurgery, the near-target peripheral isodose volume relates to its isodose value in a similar fashion as to the way in which the volume of a sphere relates to the inverse of its surface area. Such a predictable relationship justifies the use of a single near-target peripheral isodose volume, as a sufficient measure of the dose to the normal brain.

UR - http://www.scopus.com/inward/record.url?scp=77949357369&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949357369&partnerID=8YFLogxK

U2 - 10.1159/000288720

DO - 10.1159/000288720

M3 - Chapter

AN - SCOPUS:77949357369

SN - 9783805593649

VL - 7

T3 - Radiosurgery

SP - 75

EP - 83

BT - Radiosurgery

ER -