### Abstract

Purpose: In IMRT optimization, dose‐deposition coefficient (DDC) matrix is needed to parameterize the contribution of each beamlet to each dose voxel. However, due to the limitation of computer memory and the requirement on computational efficiency, small matrix elements are usually truncated, compromising the resulting plan's quality. Besides, the practice of ignoring multileaf collimator (MLC) transmission in IMRT planning also introduces inaccuracy into the resulting plan. Therefore an IMRT optimization algorithm with fixed point iteration is developed. Methods: For truncation problem, IMRT optimization is implemented as the inner‐loop with truncated DDC matrix. Fixed point iteration, as the outer‐loop, is to recalculate the actual dose with complete DDC matrix and use the difference between the optimized dose and the actual dose as the input for the optimization at the next iteration. MLC transmission can also be incorporated into IMRT planning, by adding this fixed point iteration to optimize the intensity of the already optimized apertures. The convergence and feasibility of this algorithm are mathematically studied using a simplified model. Results: Two head‐and‐neck IMRT cases are used to test our algorithm. It is mathematically proven and experimentally validated on the simplified model that with proper DDC matrix splitting, the fixed point iteration converges, although not to the solution obtained using the complete DDC matrix, but to a solution much closer to it than that from the truncated DDC matrix, in terms of the resulting dose distribution. The experimental results on the patient cases also demonstrate that our algorithm could handle both DDC matrix truncation and MLC transmission problems and give us good plans with comparable dose‐volume histograms and dose distributions. Conclusions: This fixed point iteration scheme can effectively take the DDC matrix truncation and MLC transmission into account during IMRT optimization, and thus solve the efficiency and memory issue while maintaining a reasonable accuracy. This work is supported by Varian Medical Systems through a Master Research Agreement.

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

Pages (from-to) | 3921 |

Number of pages | 1 |

Journal | Medical Physics |

Volume | 39 |

Issue number | 6 |

DOIs | |

State | Published - 2012 |

### Fingerprint

### ASJC Scopus subject areas

- Biophysics
- Radiology Nuclear Medicine and imaging

### Cite this

*Medical Physics*,

*39*(6), 3921. https://doi.org/10.1118/1.4736003

**TU‐G‐BRB‐08 : IMRT Optimization with Fixed Point Iteration.** / Tian, Z.; Jia, X.; Uribe‐sanchez, A.; Gautier, Q.; Graves, Y.; li, N.; Jiang, S.

Research output: Contribution to journal › Article

*Medical Physics*, vol. 39, no. 6, pp. 3921. https://doi.org/10.1118/1.4736003

}

TY - JOUR

T1 - TU‐G‐BRB‐08

T2 - IMRT Optimization with Fixed Point Iteration

AU - Tian, Z.

AU - Jia, X.

AU - Uribe‐sanchez, A.

AU - Gautier, Q.

AU - Graves, Y.

AU - li, N.

AU - Jiang, S.

PY - 2012

Y1 - 2012

N2 - Purpose: In IMRT optimization, dose‐deposition coefficient (DDC) matrix is needed to parameterize the contribution of each beamlet to each dose voxel. However, due to the limitation of computer memory and the requirement on computational efficiency, small matrix elements are usually truncated, compromising the resulting plan's quality. Besides, the practice of ignoring multileaf collimator (MLC) transmission in IMRT planning also introduces inaccuracy into the resulting plan. Therefore an IMRT optimization algorithm with fixed point iteration is developed. Methods: For truncation problem, IMRT optimization is implemented as the inner‐loop with truncated DDC matrix. Fixed point iteration, as the outer‐loop, is to recalculate the actual dose with complete DDC matrix and use the difference between the optimized dose and the actual dose as the input for the optimization at the next iteration. MLC transmission can also be incorporated into IMRT planning, by adding this fixed point iteration to optimize the intensity of the already optimized apertures. The convergence and feasibility of this algorithm are mathematically studied using a simplified model. Results: Two head‐and‐neck IMRT cases are used to test our algorithm. It is mathematically proven and experimentally validated on the simplified model that with proper DDC matrix splitting, the fixed point iteration converges, although not to the solution obtained using the complete DDC matrix, but to a solution much closer to it than that from the truncated DDC matrix, in terms of the resulting dose distribution. The experimental results on the patient cases also demonstrate that our algorithm could handle both DDC matrix truncation and MLC transmission problems and give us good plans with comparable dose‐volume histograms and dose distributions. Conclusions: This fixed point iteration scheme can effectively take the DDC matrix truncation and MLC transmission into account during IMRT optimization, and thus solve the efficiency and memory issue while maintaining a reasonable accuracy. This work is supported by Varian Medical Systems through a Master Research Agreement.

AB - Purpose: In IMRT optimization, dose‐deposition coefficient (DDC) matrix is needed to parameterize the contribution of each beamlet to each dose voxel. However, due to the limitation of computer memory and the requirement on computational efficiency, small matrix elements are usually truncated, compromising the resulting plan's quality. Besides, the practice of ignoring multileaf collimator (MLC) transmission in IMRT planning also introduces inaccuracy into the resulting plan. Therefore an IMRT optimization algorithm with fixed point iteration is developed. Methods: For truncation problem, IMRT optimization is implemented as the inner‐loop with truncated DDC matrix. Fixed point iteration, as the outer‐loop, is to recalculate the actual dose with complete DDC matrix and use the difference between the optimized dose and the actual dose as the input for the optimization at the next iteration. MLC transmission can also be incorporated into IMRT planning, by adding this fixed point iteration to optimize the intensity of the already optimized apertures. The convergence and feasibility of this algorithm are mathematically studied using a simplified model. Results: Two head‐and‐neck IMRT cases are used to test our algorithm. It is mathematically proven and experimentally validated on the simplified model that with proper DDC matrix splitting, the fixed point iteration converges, although not to the solution obtained using the complete DDC matrix, but to a solution much closer to it than that from the truncated DDC matrix, in terms of the resulting dose distribution. The experimental results on the patient cases also demonstrate that our algorithm could handle both DDC matrix truncation and MLC transmission problems and give us good plans with comparable dose‐volume histograms and dose distributions. Conclusions: This fixed point iteration scheme can effectively take the DDC matrix truncation and MLC transmission into account during IMRT optimization, and thus solve the efficiency and memory issue while maintaining a reasonable accuracy. This work is supported by Varian Medical Systems through a Master Research Agreement.

UR - http://www.scopus.com/inward/record.url?scp=85024799740&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85024799740&partnerID=8YFLogxK

U2 - 10.1118/1.4736003

DO - 10.1118/1.4736003

M3 - Article

AN - SCOPUS:85024799740

VL - 39

SP - 3921

JO - Medical Physics

JF - Medical Physics

SN - 0094-2405

IS - 6

ER -