### Abstract

Purpose It is clinically essential in IMRT to compare two dose distributions for dose quality assurance (DQA). The gamma index (Low et al, 1998), which combines both dose difference and distance to agreement, provides a quantitative measure of acceptability in DQA. However, its calculations can be time‐consuming and limit its applications to 2‐dimensional dose distributions. In this work, we propose an efficient calculation method. Method By embedding the k‐dimensional reference dose distribution in the (k+1)‐dimensional spatial‐dose space, we then use the Euclidean distance transform to find the distance to the reference dose distribution, regarded as a feature set, for every point in a range of the spatial‐dose space. This leads to a table of gamma indices. And the evaluation of the gamma indices for any dose distribution with respect to the reference dose distribution is simply table‐lookup. Our implementation uses a fast Euclidean distance transform, which was developed in Maurer et al, 2003 and proved to have only linear complexity. Results Using simulated 2‐D dose distributions of size 400×400, the pre‐calculation of the Gamma index table takes 26 sec and the table lookup to evaluate the Gamma index for each test dose distribution takes less than 0.1 sec in a 3GHz PC. On the other hand, it takes about 2400 sec using the exhaustive search on the same PC to evaluate the Gamma index for each test distribution. The speedup for 3D Gamma index calculation is expected to be 10^{4}∼10^{5}. Conclusion Numerical simulations demonstrate the efficiency of our proposed method. Thus, the clinical usage of 3D Gamma index becomes feasible. In addition, the Gamma index table can be used to determine the derivative of Gamma index over the dose distribution, which facilitates the inclusion of Gamma index in treatment planning and/or machine parameters optimization.

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

Number of pages | 1 |

Journal | Medical Physics |

Volume | 34 |

Issue number | 6 |

DOIs | |

State | Published - 2007 |

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### ASJC Scopus subject areas

- Biophysics
- Radiology Nuclear Medicine and imaging

### Cite this

*Medical Physics*,

*34*(6). https://doi.org/10.1118/1.2761292

**MO‐E‐AUD‐06 : Ultra‐Fast Gamma Index Calculation for Quality Assurance and Optimization in Radiotherapy.** / Chen, M.; lu, W.; Chen, Q.; Ruchala, K.; Olivera, G.

Research output: Contribution to journal › Article

*Medical Physics*, vol. 34, no. 6. https://doi.org/10.1118/1.2761292

}

TY - JOUR

T1 - MO‐E‐AUD‐06

T2 - Ultra‐Fast Gamma Index Calculation for Quality Assurance and Optimization in Radiotherapy

AU - Chen, M.

AU - lu, W.

AU - Chen, Q.

AU - Ruchala, K.

AU - Olivera, G.

PY - 2007

Y1 - 2007

N2 - Purpose It is clinically essential in IMRT to compare two dose distributions for dose quality assurance (DQA). The gamma index (Low et al, 1998), which combines both dose difference and distance to agreement, provides a quantitative measure of acceptability in DQA. However, its calculations can be time‐consuming and limit its applications to 2‐dimensional dose distributions. In this work, we propose an efficient calculation method. Method By embedding the k‐dimensional reference dose distribution in the (k+1)‐dimensional spatial‐dose space, we then use the Euclidean distance transform to find the distance to the reference dose distribution, regarded as a feature set, for every point in a range of the spatial‐dose space. This leads to a table of gamma indices. And the evaluation of the gamma indices for any dose distribution with respect to the reference dose distribution is simply table‐lookup. Our implementation uses a fast Euclidean distance transform, which was developed in Maurer et al, 2003 and proved to have only linear complexity. Results Using simulated 2‐D dose distributions of size 400×400, the pre‐calculation of the Gamma index table takes 26 sec and the table lookup to evaluate the Gamma index for each test dose distribution takes less than 0.1 sec in a 3GHz PC. On the other hand, it takes about 2400 sec using the exhaustive search on the same PC to evaluate the Gamma index for each test distribution. The speedup for 3D Gamma index calculation is expected to be 104∼105. Conclusion Numerical simulations demonstrate the efficiency of our proposed method. Thus, the clinical usage of 3D Gamma index becomes feasible. In addition, the Gamma index table can be used to determine the derivative of Gamma index over the dose distribution, which facilitates the inclusion of Gamma index in treatment planning and/or machine parameters optimization.

AB - Purpose It is clinically essential in IMRT to compare two dose distributions for dose quality assurance (DQA). The gamma index (Low et al, 1998), which combines both dose difference and distance to agreement, provides a quantitative measure of acceptability in DQA. However, its calculations can be time‐consuming and limit its applications to 2‐dimensional dose distributions. In this work, we propose an efficient calculation method. Method By embedding the k‐dimensional reference dose distribution in the (k+1)‐dimensional spatial‐dose space, we then use the Euclidean distance transform to find the distance to the reference dose distribution, regarded as a feature set, for every point in a range of the spatial‐dose space. This leads to a table of gamma indices. And the evaluation of the gamma indices for any dose distribution with respect to the reference dose distribution is simply table‐lookup. Our implementation uses a fast Euclidean distance transform, which was developed in Maurer et al, 2003 and proved to have only linear complexity. Results Using simulated 2‐D dose distributions of size 400×400, the pre‐calculation of the Gamma index table takes 26 sec and the table lookup to evaluate the Gamma index for each test dose distribution takes less than 0.1 sec in a 3GHz PC. On the other hand, it takes about 2400 sec using the exhaustive search on the same PC to evaluate the Gamma index for each test distribution. The speedup for 3D Gamma index calculation is expected to be 104∼105. Conclusion Numerical simulations demonstrate the efficiency of our proposed method. Thus, the clinical usage of 3D Gamma index becomes feasible. In addition, the Gamma index table can be used to determine the derivative of Gamma index over the dose distribution, which facilitates the inclusion of Gamma index in treatment planning and/or machine parameters optimization.

UR - http://www.scopus.com/inward/record.url?scp=85024807730&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85024807730&partnerID=8YFLogxK

U2 - 10.1118/1.2761292

DO - 10.1118/1.2761292

M3 - Article

AN - SCOPUS:85024807730

VL - 34

JO - Medical Physics

JF - Medical Physics

SN - 0094-2405

IS - 6

ER -