Hybrid 3D analytical linear energy transfer calculation algorithm based on precalculated data from Monte Carlo simulations

Wei Deng, Xiaoning Ding, James E. Younkin, Jiajian Shen, Martin Bues, Steven E. Schild, Samir H. Patel, Wei Liu

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Purpose: The dose-averaged linear energy transfer (LETd) for intensity-modulated proton therapy (IMPT) calculated by one-dimensional (1D) analytical models deviates from more accurate but time-consuming Monte Carlo (MC) simulations. We developed a fast hybrid three-dimensional (3D) analytical LETd calculation that is more accurate than 1D analytical model. Methods: We used the Geant4 MC code to generate 3D LETd distributions of monoenergetic proton beams in water for all energies and used a customized error function to fit the LETd lateral profiles at various depths to the MC simulation. The 3D LETd calculation kernel was a lookup table of these fitted coefficients, and LETd was determined directly from spot energies and voxel coordinates during analytical dose calculations. We validated our new method by comparing the calculated LETd distributions to MC results using 3D Gamma index analysis with 3%/2 mm criteria in 12 patient geometries. The significance of the improvement in Gamma index analysis passing rates over the 1D analytical model was determined using the Wilcoxon rank-sum test. Results: The passing rate of 3D Gamma analysis comparing LETd distributions from the hybrid 3D method and the 1D method to MC simulations was significantly improved from 94.0% ± 2.5% to 98.0% ± 1.0% (P = 0.0003). The typical time to calculate dose and LETd simultaneously using an Intel Xeon E5-2680 2.50 GHz workstation was approximately 2.5 min. Conclusions: Our new method significantly improved the LETd calculation accuracy compared to the 1D method while maintaining significantly shorter calculation time even comparing with the GPU-based fast MC code.

Original languageEnglish (US)
Pages (from-to)745-752
Number of pages8
JournalMedical physics
Issue number2
StatePublished - Feb 1 2020


  • analytical calculation
  • linear energy transfer
  • proton therapy

ASJC Scopus subject areas

  • Biophysics
  • Radiology Nuclear Medicine and imaging


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