Nanodosimetric analysis of proton tracks in a spread-out Bragg peak

Heidi Nettelbeck (PTB),

Sonwabile Ngcezu (NMISA, WITS),

Hans Rabus (PTB)

F. Tommasino and M. Durante, Proton Radiobiology, Cancers 2015, 7(1), 353-381; doi:10.3390/cancers7010353

Motivation: Biological Effectiveness of Protons

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Methods

Simulations using Geant4-DNA

➢ Full slow down of 100 MeV protons in liquid water

• only proton interactions

• scoring proton energy and position

➢ 650 nm tracks of protons of start energy between 2 and 99 MeV

• proton & electron interactions

• scoring of coordinates of ionizations & energy imparted

➢ Tracks of 1 MeV protons followed until full slow down

• proton & electron interactions

• scoring of coordinates of ionizations & energy imparted

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Nanodosimetry & Track structure

A particle track passes a target volume of size D at an impact parameter d

Ionisation cluster size: Number n

of ionizations in target volume

(stochastic quantity)

Moments: ( )

=

=0

)(

QPQMi

i

Cumulative frequencies:

( )

==

kkQPQF

)(

Nanodosimetric parameters of

track structure:

Frequency distribution: )( QP

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Nanodosimetric Track Analysis

Radial dependence of F2 at 2 energies

Model for 𝑟 > 𝑟𝑡 inspired

by Wang&Vassiliev (2014)

Phys. Med. Biol. 59, 3657-68 𝒓𝒕

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Further steps towards SOBP

• Fit curves are integrated to give effective track cross section

𝑌𝑖,𝑗 = 2𝜋න0

𝑟2

𝑦 𝑟, 𝑥𝑗|0, 𝐸𝑖 𝑟𝑑𝑟

• Data set of mean position 𝑥𝑗 found for proton energy 𝐸𝑖 and area integral 𝑌𝑖,𝑗 for this energy is

a) spline-interpolated,

b) convoluted with the position straggling distribution

to give pristine “Bragg peaks“

• Method of Jette & Chen, PMB 56 (2011) N131 is used to create “spread-out Bragg peaks“

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Radial integrals in spread-out Bragg peak

0.4 mm

offset

Normalized

to unity here

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Conclusions

• Ionization cluster size distributions simulated as a function of

• the radial distance between target and proton trajectory

• position along the proton path

• Radial dependence was fitted and integrated ➔ effective track cross sections as a function of the proton’s residual range

• Convolution with range distributions gives SOBP

➢Preliminary results indicate that nanodosimetric quantities are enhanced at distal edge of SOBP (& ≈ 0.4 mm range offset)

➢Nanodosimetric signature of enhanced RBE?

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Radial integrals along pristine Bragg peak

73 74 75 76 77 780.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed a

rea inte

gra

l

depth in phantom in mm

Eabs

F1

F2

F3

F4

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Track Analysis – Outer Penumbra

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Positions along proton trajectory

1 10 100

0

10

20

30

40

50

60

70

80

Mean p

ositio

n in m

m

Proton energy in MeV

-3 -2 -1 0 1 2 3

0.0

0.1

0.2

0.3

0.4

0.5

0.6 35

25

15

5

3

1

Fit

frequ

en

cy d

en

sity / m

m-1

relative deviation from mean / mm

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Radial integrals in spread-out Bragg peak

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