Table 1: A summary describing information of some previous investigations for the accuracy of D-LBTE solvers in predicting the doses in heterogeneous simple geometric phantoms using single open fields.

Published investigationsGifford et al. 2006 [22]Vassiliev et al. 2010 [25]Bush et al. 2011 [27]Han et al. 2011 [28]Kan et al. 2012 [30] Lloyd and Ansbacher 2013 [31]

Beam energy18 MV6 and 18 MV6 and 18 MV6 and 18 MV6 MV6 and 18 MV

Field sizes  cm2  cm2  
 cm2  
 cm2
 cm2  
 cm2  
 cm2
 cm2  
 cm2  
 cm2
 cm2  
 cm2  
 cm2
 cm2

Phantom(s)
geometry
One multilayer phantom:
water (0–3 cm),
aluminium, Al (3–5 cm),
lung (5–12 cm),
water (12–30 cm)
One multilayer phantom:
water (0–3 cm),
bone (3–5 cm),
lung (5–12 cm),
water (12–30 cm)
Two phantoms:
(i) one with a single insert of normal lung, light lung, or air in water,
(ii) a bone/lung phantom with several disk-shaped bony structures
One multilayer phantom:
water (0–3 cm),
bone (3–5 cm),
lung (5–12 cm),
water (12–30 cm)
 cm3 of water containing  cm3 of air  cm3 of muscle cube containing  cm3 of stainless steel or titanium alloy

Monte carlo simulationEGS4/Presta,
0.3% statistical uncertainty,
resolution:  cm3 voxels
DOSXYZnrc,
<0.1% statistical uncertainty, resolution:  cm3 voxels, 0.1 cm laterally in penumbra region
DOSXYZnrc
~1% statistical uncertainty in media except up to 4.5% in air, resolution:  cm3 voxels
DOSXYZnrc,
<1% statistical uncertainty,
resolution:  cm3 voxels for most volume,  cm3 near water/bone and bone/lung interfaces
EGS4/Presta,
2.0% statistical uncertainty,
resolution:
1/10 of field dimensions with 0.2 mm bin thickness
DOSXYZnrc,
~1% statistical uncertainty,
resolution:  cm3 voxels

D-LBTE solverAttila codeAcuros
(Transpire, Inc.)
AXB of version 10AXB of version 10AXB of version 10AXB of version 11

Dose distribution examinedPDDPDD and lateral profilesPDD and lateral profilesPDD, lateral profiles, and 3D gamma evaluationPDDPDD and lateral profiles

Difference between D-LBTE solver and Monte Carlo simulationAverage discrepancy is 1.4%, with 2.2% maximum discrepancy observed at water/Al interfaceFor 6 MV, max. discrepancy < 1.5%, with DTA < 0.7 mm in the build-up region. For 18 MV, max. discrepancy < 2.3% with DTA < 0.3 mm in the build-up regionDiscrepancies were within 2% in lung, 3% in light lung, up to 4.5% in air, 1.8% in bone, with slightly larger discrepancy (up to 5%) at interfaces For 6 MV, average discrepancy of 1.1% in PDD and 1.6% in dose profiles. For 18 MV, average discrepancy of 1.6% in PDD and 3.0% and dose profilesDiscrepancies are mostly within 2%, with slightly higher discrepancy (up to 6%) at the air/tissue interface in the secondary build-up regionIn general good agreement between AXB and MC, with an average gamma agreement with a 2%/1mm criteria of 91.3% to 96.8%