Accelerated Prompt Gamma estimation forclinical Proton Therapy simulations
B.F.B. Huisman1,2, J.M. Létang1, É. Testa2, D. Sarrut1
1 CREATIS, Université de Lyon; CNRS UMR5220; INSERM U1044; INSA-Lyon; Université Lyon 1; Centre Léon Bérard, Lyon, France
2 IPNL, Université de Lyon; CNRS/IN2P3 UMR5822; Université Lyon 1 Lyon, France
1. PURPOSE
There is interest in the particle therapycommunity to use prompt gammas (PG),a natural byproduct of particle treatment,for range verification and eventually dosecontrol (Knopf et al. 2015). However, PGproduction is a rare process and thereforeestimating PGs exiting a patient during aproton treatment plan executed by a MonteCarlo simulation (MC) converges slowly.
Primaries
PGs Exiting patient
Solid angle detector
Post-collimator
Detector Efficiency ?
Reconstruction Eff. ?
103
104
105
106
107
108
109
Cou
nts
Protons
Prompt Gammas
We present a generic PG yield estimator,drop-in usable with any geometry and beamconfiguration. We show a gain of three orders ofmagnitude compared to analog MC. We analyzethe depth profile and the PG energy spectrum ofa simple phantom and a clinical head and neckCT image.
2. CONCEPT
1 2 31. Regular Monte Carlo trackingA regular MC simulation propagates particlesthroughout geometry. The propagation is brokenup into steps, at which point the engine compilesa list of all possible futures, weights them, andusing a random number selects the actual future.2. At each step: Prompt Gamma productionprobabilityParallel to executing this conventional tracking,we may request and store the PG productionprobabilities. At each step, as function of PGenergy, a production probability spectrum isstored at the current voxel.3. Limited MC to touch all relevant voxelsBy propagating a number of primary protons inthis way, we obtain probabilities in all the voxelsthat a beam may touch. We need a minimumnumber of primaries, since we can only requestPG probabilities in the voxels the primary passesthrough. However, we require fewer primarypropagations with respect to a fully analog MC.
ACKNOWLEDGMENTS
This work was partly supported by Labex PRIMESANR-11-LABX-0063, t-Gate ANR-14-CE23-0008,France Hadron ANR-11-INBS-0007 and LYricINCa-DGOS-4664.
3. METHOD
Stage 0:Generate PGdb
Stage 1:Compute PGyd
Stage 2:Propagate PG
through geometry
A voxelized Prompt-Gamma Track LengthEstimator (Kanawati et al. 2015) simulation isbroken up into two stages. A PGdb (Stage 0) ispresupposed, computed once and reused. Itcontains an estimate of the effective linear PGproduction coefficient ΓΓΓZ modulo the densityρZ , per element (k). At the start of Stage 1,the coefficients are computed for the materialsfound in the phantom (eq. 1).
ΓΓΓm(E) = ρmv
kmv∑k=1
ωkΓΓΓZk (E)
ρZk
(1)
SSSi (v) =ΓΓΓmv (Eg )Lg (Eg , v) (2)
Per step, per voxel v in the PGyd, alongsideexecuting the analog MC processes, we computeand add the product of the step length Lg
and ΓΓΓmv , with mv the material at voxel v andg the proton energy bin (eq. 2). Put intowords, we compute the PG yield probabilityenergy spectrum at every step, and add it toany pre-existing spectrum in the current voxelv . The PGyd computed in stage 1 is used asa PG production source in Stage 2. If the useris interested in the PG signal of 1011 protons,the PGyd can be requested to give the expectedoutput for that number of protons. Each PG isthen propagated through the geometry and intothe detector with regular analog MC processes.
4. RESULT SIMPLE PHANTOM
0 50 100 150 200
0.0
0.5
1.0
1.5
2.0
2.5
Inte
grat
edY
ield
[PG
/pro
ton
/vox
el] ×10−3
1 2 3 4 5 6 7 8
0.0
0.5
1.0
1.5
2.0
2.5
×10−3
103 primaries
104 primaries
105 primaries
106 primaries
Reference
0 50 100 150 200
−3−2−1
0123
Inte
grat
edR
el.
Diff
.[%
]
1 2 3 4 5 6 7 8
−3−2−1
0123
0 50 100 150 200
Depth [mm]
−6−4−2
0246
Vox
els
bea
mp
ath
Rel
.D
iff.[%
]
1 2 3 4 5 6 7 8
PG energy [MeV]
−6−4−2
0246
102 103 104
Gain factor w.r.t. Reference
0.0
0.2
0.4
0.6
0.8
1.0
Nu
mb
erof
voxel
s(s
cale
d)
vpgTLE gain distributionMedian gain: 1.40× 103
103 primaries
Min: 6.30× 101
Max: 4.64× 104
104 primaries
Min: 6.19× 101
Max: 3.73× 104
105 primaries
Min: 9.03× 101
Max: 5.21× 104
106 primaries
Min: 8.63× 101
Max: 3.21× 104
101 102 103 104 105 106
Runtime t [s]
0
2
4
6
8
10
12
Rel
ativ
eU
nce
rtai
nty
[%]
Median relative uncertaintyGain: 1.55× 103
vpgTLE, Fit:
2.3×10−1√t
Analog, Fit:
8.9×100√t
5. RESULT CLINICAL PHANTOM
0 20 40 60 80 100 120 140 160
0.0
0.5
1.0
1.5
2.0
Inte
grate
dY
ield
[PG
/p
roto
n/b
in]
×10−3
1 2 3 4 5 6 7 8
0.0
0.5
1.0
1.5
2.0×10−3 103 primaries
104 primaries
105 primaries
106 primaries
Reference
0 20 40 60 80 100 120 140 160
Depth [mm]
−3
−2
−1
0
1
2
3
Inte
grat
edR
el.
Diff
.[%
]
1 2 3 4 5 6 7 8
PG energy [MeV]
−3
−2
−1
0
1
2
3
102 103 104
Gain factor w.r.t. Reference
0.0
0.2
0.4
0.6
0.8
1.0
Nu
mb
erof
voxel
s(s
cale
d)
vpgTLE gain distributionMedian gain: 9.98× 102
103 primariesMin: 0
Max: 2.76× 105
104 primaries
Min: 3.85× 101
Max: 3.29× 104
105 primaries
Min: 4.70× 101
Max: 4.88× 104
106 primaries
Min: 2.70× 101
Max: 8.96× 104
102 103 104 105 106 107
Runtime t [s]
0
10
20
30
40
50
60
70
Rel
ati
veU
nce
rtai
nty
[%]
Median relative uncertaintyGain: 1.03× 103
vpgTLE, Fit:
2.5×100√t
Analog, Fit:
7.9×101√t
6. CONCLUSION
vpgTLE is a generic drop-in alternative forcomputing the expected PG output in voxelizedgeometries. The method reaches a globalgain factor of 103103103 for a clinical CT image andtreatment plan with respect to analog MC. Amedian convergence of 2% for the most distalenergy layer is reached in approximately fourhours on a single core, with the output stabilizedto within 10−4 of an analog reference simulation,when the PG yield along proton range and PGspectrum are considered. Those interested indeveloping and simulating PG detection devices,as well as clinicians studying complex clinicalcases, may benefit from the precision andaccuracy of vpgTLE simulations not offered byanalytic algorithms.The vpgTLE method is open source, fullyintegrated and available in the next Gate release.This study has been submitted to Physics inMedicine and Biology.
REFERENCES
Knopf et al. (2015) Phys. Med. Biol.Kanawati et al. (2015) Phys. Med. Biol.Sterpin et al. (2015) Phys. Med. Biol.
