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

brent.huisman@creatis.insa-lyon.fr

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.