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Open Access Publications from the University of California


  • Author(s): Gu, Wenbo
  • Advisor(s): Sheng, Ke
  • et al.


The unified framework is formulated to include a dose fidelity term, a heterogeneity-weighted group sparsity term, and a sensitivity regularization term. The dose fidelity term encourages less physical dose deviation from ideal distribution. The L2,1/2-norm group sparsity is used to reduce the number of active beams from the initial 1162 evenly distributed non-coplanar candidate beams, to between 2 and 4. A heterogeneity index, which evaluates the lateral tissue heterogeneity of a beam, is used to weigh the group sparsity term. With this index, beams more resilient to setup uncertainties are encouraged. There is a symbiotic relationship between the heterogeneity index and the sensitivity regularization; the integrated optimization framework further improves beam robustness against both range and setup uncertainties. This Sensitivity regularization and Heterogeneity weighting based BOO and FMO framework (SHBOO-FMO) was tested on two skull-base tumor (SBT) patients and two bilateral head-and-neck (H&N) patients. The conventional CTV-based optimized plans (Conv) with SHBOO-FMO beams (SHBOO-Conv) and manual beams (MAN-Conv) were compared to investigate the beam robustness of the proposed method. The dosimetry and robustness of SHBOO-FMO plan were compared against the manual beam plan with CTV-based voxel-wise worst-case scenario approach (MAN-WC).


With SHBOO-FMO method, the beams with superior range robustness over manual beams were selected while the setup robustness was maintained or improved. On average, the lowest [D95%, V95%, V100%] of CTV were increased from [93.8%, 91.0%, 70.6%] in MAN-Conv plans, to [98.6%, 98.6%, 96.1%] in SHBOO-Conv plans with range uncertainties. With setup uncertainties, the average lowest [D98%, D95%, V95%, V100%] of CTV were increased from [92.0%, 94.8%, 94.3%, 78.9%] in MAN-Conv plans, to [93.5%, 96.6%, 97.0%, 91.9%] in SHBOO-Conv plans. Compared with the MAN-WC plans, the final SHBOO-FMO plans achieved comparable plan robustness and better OAR sparing, with an average reduction of [Dmean, Dmax] of [6.3, 6.6] GyRBE for the SBT cases and [1.9, 5.1] GyRBE for the H&N cases from the MAN-WC plans.


A novel robust optimization method was developed for IMPT. It integrates robust BOO and robust FMO into a unified framework, and the resulting optimization problem can be solved efficiently. Compared with the current clinical practice, where beam angles are manually selected and fluence map is optimized by worst-case method, the planning efficiency is improved, and it generates plans with superior dosimetry and good robustness.

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