Transport under magnetic fields with the EGSnrc simulation ... CIRMS- Presen… · Transport in...
Transcript of Transport under magnetic fields with the EGSnrc simulation ... CIRMS- Presen… · Transport in...
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Measurement Science and Standards, National Research Council Canada
Transport under magnetic fields with the EGSnrc simulation toolkit Ernesto Mainegra-Hing, Frédéric Tessier, Blake Walters
Hugo Bouchard
Université de Montréal and
National Physics Laboratory (UK)
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+
MRI
External RT
=
MRI-guided Radiation Therapy
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Magnetic field effect on dose distribution
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electron tracks
air
water
pencil beam of 10 MeV electrons
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electron tracks
air
water
pencil beam of 10 MeV electrons
B = 1 T
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pencil beam of 10 MeV electrons
water
air
air
water electron
return effect
B = 1 T
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B PTW30013
60Co
air
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PTW chamber irradiated by parallel 60Co beam
significant dependence on magnetic field
New dosimetry? cavity
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Orange Bible
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Equation of motion
𝑣 = 𝑣 0 +1
𝑚0𝛾 𝐸 𝑑𝑡′ 𝑭𝒆𝒍 𝐸 𝑡′ + 𝑭𝒊𝒏 𝐸 𝑡′ + 𝑭𝒆𝒎 𝑥 𝑡′ , 𝐸 𝑡′ , 𝑢 𝑡′
𝑡
0
The equation of motion in the force formulation for transport in a medium under the effect of an EM field can be written as
stochastic deterministic
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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
𝑚0𝛾 𝐸0
𝑭𝒆𝒍 𝐸0 + 𝑭𝒊𝒏 𝐸0 + 𝑭𝒆𝒎 𝑥 0, 𝐸0, 𝑢 0
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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
𝑚0𝛾 𝐸0
𝑭𝒆𝒎 𝑥 0, 𝐸0, 𝑢 0
Interactions with medium and external field treated independently!
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Bielajew’s implementation
Neglecting lateral deflection Ds/2 one gets for the position change
Expressing the time t as a function of the total path length Ds to first order gives
∆𝑥 = 𝑢 0∆𝑠 +∆𝑠
2∆𝑢
∆𝑥 = 𝑢 0∆𝑠
∆𝑢 = ∆𝑢 𝑀𝐶 + ∆𝑢 𝑒𝑚
the change in the particle’s direction is MC step
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vacuum
𝑟 = 𝑚𝑐
𝑒𝐵𝛾2 − 1
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vacuum
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vacuum 3 kinds of errors
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vacuum 1. error in position
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vacuum 2. error in radius
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vacuum
3. error in energy deposition (in medium)
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vacuum
1
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vacuum
0.84
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vacuum
0.58
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vacuum
0.01
forever
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Fano theorem provides a rigorous test
𝐷 = 𝑁0/𝑚𝑇 ∙ 𝐸
• Uniform electron source per unit mass N0/mT
• Medium of uniform composition but varying density
where 𝐸 is the average energy emitted
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Fano theorem provides a rigorous test
If the source emits electrons of energy E0:
𝐷/𝑁0 = 𝐸0/𝑚𝑇
For a MC simulation fulfilling Fano conditions, the dose per particle in any region i is expected to be:
𝐷𝑖/𝑁0 = 𝐸0/𝑚𝑇
Use this to verify the accuracy of the electron transport algorithm!
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“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 …”
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1. Isotropic uniform source per unit mass
2. Magnetic field B scales with mass density
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0.001 0.01 0.1 1
identical atomic properties (air)
2 cm
in water phantom
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0.001 0.01 0.1 1
uniform source of electrons, per unit mass
electron tracks
in water phantom
100 keV
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0.001 0.01 0.1 1 1.01
1.00
0.99
Mo
nte
Car
lo /
Th
eory
this is what we mean when we say that EGSnrc is accurate at the 0.1% level
in water phantom
0 T
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water
12 regions
Fano test 1 (PTW30013)
d d
d
d
d > RCSDA(Emax)
Same material, different densities
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?
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water
12 regions
Fano test 1 for a PTW30013
Same material, different densities
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Powerful diagnostic
tool !!!
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PTW30013 cavity dose
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1 MeV
PTW30013 cavity dose
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ξ = 1
𝑠2 × 𝑇𝐶𝑃𝑈
Measuring efficiency
How long needed to achieve desired uncertainty?
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cavity dose
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cavity dose
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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.
Conclusionss
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Measurement Science and Standards, National Research Council Canada
Transport under magnetic fields with the EGSnrc simulation toolkit Ernesto Mainegra-Hing, Frédéric Tessier, Blake Walters
Hugo Bouchard
Université de Montréal and
National Physics Laboratory (UK)