title: Geometrical splitting technique to improve the computational efficiency in Monte Carlo calculations for proton therapy.
abstract: OBJECTIVE
  To present the implementation and validation of a geometrical based variance reduction technique for the calculation of phase space data for proton therapy dose calculation.
  
  
  METHODS
  The treatment heads at the Francis H Burr Proton Therapy Center were modeled with a new Monte Carlo tool (TOPAS based on Geant4). For variance reduction purposes, two particle-splitting planes were implemented. First, the particles were split upstream of the second scatterer or at the second ionization chamber. Then, particles reaching another plane immediately upstream of the field specific aperture were split again. In each case, particles were split by a factor of 8. At the second ionization chamber and at the latter plane, the cylindrical symmetry of the proton beam was exploited to position the split particles at randomly spaced locations rotated around the beam axis. Phase space data in IAEA format were recorded at the treatment head exit and the computational efficiency was calculated. Depth-dose curves and beam profiles were analyzed. Dose distributions were compared for a voxelized water phantom for different treatment fields for both the reference and optimized simulations. In addition, dose in two patients was simulated with and without particle splitting to compare the efficiency and accuracy of the technique.
  
  
  RESULTS
  A normalized computational efficiency gain of a factor of 10-20.3 was reached for phase space calculations for the different treatment head options simulated. Depth-dose curves and beam profiles were in reasonable agreement with the simulation done without splitting: within 1% for depth-dose with an average difference of (0.2 ± 0.4)%, 1 standard deviation, and a 0.3% statistical uncertainty of the simulations in the high dose region; 1.6% for planar fluence with an average difference of (0.4 ± 0.5)% and a statistical uncertainty of 0.3% in the high fluence region. The percentage differences between dose distributions in water for simulations done with and without particle splitting were within the accepted clinical tolerance of 2%, with a 0.4% statistical uncertainty. For the two patient geometries considered, head and prostate, the efficiency gain was 20.9 and 14.7, respectively, with the percentages of voxels with gamma indices lower than unity 98.9% and 99.7%, respectively, using 2% and 2 mm criteria.
  
  
  CONCLUSIONS
  The authors have implemented an efficient variance reduction technique with significant speed improvements for proton Monte Carlo simulations. The method can be transferred to other codes and other treatment heads.
authors.affiliation: Benemérita Universidad Autónoma de Puebla, 18 Sur and San Claudio Avenue, Puebla, Puebla 72750, Mexico. joserm84@gmail.com
authors.forename: José
authors.initials: J
authors.lastname: Ramos-Méndez
authors.forename: Joseph
authors.initials: J
authors.lastname: Perl
authors.forename: Bruce
authors.initials: B
authors.lastname: Faddegon
authors.forename: Jan
authors.initials: J
authors.lastname: Schümann
authors.forename: Harald
authors.initials: H
authors.lastname: Paganetti
mesh_terms: D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D009010:Monte Carlo Method; D061766:Proton Therapy; D011874:Radiometry / Q000379:methods*; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D011882:Radiotherapy, High-Energy / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012984:Software; D011522:Protons
chemical_list: D011522:Protons
references.citation: Nucl Technol. 2009 Dec 1;168(3):736-740
references.pmid: 20865140
references.citation: Phys Med Biol. 2012 Jun 7;57(11):3281-93
references.pmid: 22572154
references.citation: Med Phys. 2004 Oct;31(10):2883-98
references.pmid: 15543798
references.citation: Med Phys. 2012 Nov;39(11):6818-37
references.pmid: 23127075
references.citation: Med Phys. 1998 May;25(5):656-61
references.pmid: 9608475
references.citation: Phys Med Biol. 2011 Feb 21;56(4):903-18
references.pmid: 21248389
references.citation: Phys Med Biol. 2012 Jun 7;57(11):3295-308
references.pmid: 22572201
references.citation: Phys Med Biol. 2009 Jan 7;54(1):N21-8
references.pmid: 19075361
references.citation: Phys Med Biol. 2005 Mar 7;50(5):1001-10
references.pmid: 15798272
references.citation: Phys Med Biol. 2008 Sep 7;53(17):4825-53
references.pmid: 18701772
references.citation: Phys Med Biol. 2010 Feb 7;55(3):711-21
references.pmid: 20071752
references.citation: Phys Med Biol. 2002 Mar 7;47(5):747-64
references.pmid: 11931469
references.citation: Phys Med Biol. 2007 Jun 21;52(12):3369-87
references.pmid: 17664549
references.citation: Phys Med Biol. 2012 Dec 7;57(23):7783-97
references.pmid: 23128424
references.citation: Med Phys. 2007 Dec;34(12):4818-53
references.pmid: 18196810
references.citation: Med Phys. 2006 Aug;33(8):3046-56
references.pmid: 16964882
references.citation: Med Phys. 2008 Apr;35(4):1521-31
references.pmid: 18491547
references.citation: Phys Med Biol. 1999 May;44(5):1219-30
references.pmid: 10368014
references.citation: Med Phys. 2009 Dec;36(12):5451-66
references.pmid: 20095258
references.citation: Phys Med Biol. 2007 Jul 21;52(14):4345-60
references.pmid: 17664612
references.citation: Phys Med Biol. 2005 Nov 21;50(22):5229-49
references.pmid: 16264250
references.citation: Phys Med Biol. 2007 Jul 7;52(13):3913-30
references.pmid: 17664585
references.citation: Phys Med Biol. 2009 Jul 7;54(13):4131-49
references.pmid: 19521002
references.citation: Phys Med Biol. 2007 Aug 7;52(15):4569-84
references.pmid: 17634651
references.citation: Med Phys. 2010 Sep;37(9):4960-70
references.pmid: 20964215
references.citation: Med Phys. 2004 Aug;31(8):2263-73
references.pmid: 15377093
references.citation: Phys Med Biol. 2002 May 21;47(10):1671-89
references.pmid: 12069086
references.citation: Phys Med Biol. 2012 Jun 7;57(11):R99-117
references.pmid: 22571913
references.citation: Med Phys. 2011 Nov;38(11):5887-95
references.pmid: 22047353
references.citation: Phys Med Biol. 2012 Oct 21;57(20):6381-93
references.pmid: 22996039
references.citation: Med Phys. 2004 Jul;31(7):2107-18
references.pmid: 15305464