Transport under magnetic fields with the EGSnrc simulation toolkit

Transcription

1 Transport under magnetic fields with the EGSnrc simulation toolkit Ernesto Mainegra-Hing, Frédéric Tessier, Blake Walters Measurement Science and Standards, National Research Council Canada Hugo Bouchard Université de Montréal and National Physics Laboratory (UK)

2

3 MRI MRI-guided Radiation Therapy + = External RT

4 Magnetic field effect on dose distribution

5 air pencil beam of 10 MeV electrons water electron tracks

6 air pencil beam of 10 MeV electrons water electron tracks B = 1 T

7 air pencil beam of 10 MeV electrons water electron return effect air B = 1 T water

8 air 60 Co PTW30013 B

9 PTW chamber irradiated by parallel 60 Co beam significant dependence on magnetic field New dosimetry? cavity

10

11 Orange Bible

12

13 Equation of motion The equation of motion in the force formulation for transport in a medium under the effect of an EM field can be written as v = v m 0 γ E t dt F el E t + F in E t + F em x t, E t, u t 0 stochastic deterministic

14 Bielajew s implementation Under the assumption of very small steps such that: Field does not changes significantly Energy loss negligible Negligible angular deflection the equation of motion becomes to first order: v = v 0 + t m 0 γ E 0 F el E 0 + F in E 0 + F em x 0, E 0, u 0

15 Bielajew s implementation Under the assumption of very small steps such that: Field does not changes significantly Energy loss negligible Negligible angular deflection the equation of motion becomes to first order: v = v 0 + v MC + t m 0 γ E 0 F em x 0, E 0, u 0 Interactions with medium and external field treated independently!

16 Bielajew s implementation Expressing the time t as a function of the total path length Ds to first order gives x = u 0 s + s 2 u Neglecting lateral deflection Ds/2 one gets for the position change x = u 0 s the change in the particle s direction is u = u MC + u em MC step

17 vacuum r = mc eb γ2 1

18 vacuum

19 vacuum 3 kinds of errors

20 vacuum 1. error in position

21 vacuum 2. error in radius

22 vacuum 3. error in energy deposition (in medium)

23 vacuum 1

24 vacuum 0.84

25 vacuum 0.58

26 0.01 forever vacuum

27

28

29

30 Fano theorem provides a rigorous test Uniform electron source per unit mass N 0 /m T Medium of uniform composition but varying density D = N 0 /m T E where E is the average energy emitted

31 Fano theorem provides a rigorous test If the source emits electrons of energy E 0 : D/N 0 = E 0 /m T For a MC simulation fulfilling Fano conditions, the dose per particle in any region i is expected to be: D i /N 0 = E 0 /m T Use this to verify the accuracy of the electron transport algorithm!

32

33 Fano s theorem does not hold in the presence of static and constant external EM fields. This has the unfortunate consequence of invalidating the Fano cavity test

34 1. Isotropic uniform source per unit mass 2. Magnetic field B scales with mass density

35 identical atomic properties (air) 2 cm in water phantom

36 uniform source of electrons, per unit mass 100 kev electron tracks in water phantom

37 Monte Carlo / Theory T this is what we mean when we say that EGSnrc is accurate at the 0.1% level in water phantom

38 Fano test 1 (PTW30013) d water d d > R CSDA (E max ) d d 12 regions Same material, different densities

39

40

41 ?

42 Fano test 1 for a PTW30013 water 12 regions Same material, different densities

43

44

45 Powerful diagnostic tool!!!

46

47

48

49

50 PTW30013 cavity dose

51 1 MeV PTW30013 cavity dose

52

53 Measuring efficiency ξ = 1 s 2 T CPU How long needed to achieve desired uncertainty?

54 cavity dose

55 cavity dose

56 Conclusionss Transport in electromagnetic field is available in EGSnrc as a first-order correction on the velocity. Ionization chamber dose response calculations pass Fano test in a magnetic field only with significant step size restrictions. Larger step sizes are possible as energy increases or field strength decreases (curvature radius increases) Considering the penalty in efficiency, a more accurate algorithm allowing larger step sizes is desirable. Fano test: powerful tool for benchmarking radiation transport algorithms and testing the correctness of MC simulation parameters.

57 Transport under magnetic fields with the EGSnrc simulation toolkit Ernesto Mainegra-Hing, Frédéric Tessier, Blake Walters Measurement Science and Standards, National Research Council Canada Hugo Bouchard Université de Montréal and National Physics Laboratory (UK)