Transport under magnetic fields with the EGSnrc simulation toolkit - - PowerPoint PPT Presentation

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Transport under magnetic fields with the EGSnrc simulation toolkit - - PowerPoint PPT Presentation

Jun 29, 2023 260 likes •840 views

Transport under magnetic fields with the EGSnrc simulation toolkit Ernesto Mainegra-Hing, Frdric Tessier, Blake Walters Measurement Science and Standards, National Research Council Canada Hugo Bouchard Universit de Montral and

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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

  • n 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

  • n magnetic field

New dosimetry? cavity

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Orange Bible

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Equation of motion

𝑤 = 𝑤 0 + 1 𝑛0𝛿 𝐹 𝑒𝑢′ 𝑮𝒇𝒎 𝐹 𝑢′ + 𝑮𝒋𝒐 𝐹 𝑢′ + 𝑮𝒇𝒏 𝑦 𝑢′ , 𝐹 𝑢′ , 𝑣 𝑢′

𝑢

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:

𝑤 = 𝑤 0 + 𝑢 𝑛0𝛿 𝐹0 𝑮𝒇𝒎 𝐹0 + 𝑮𝒋𝒐 𝐹0 + 𝑮𝒇𝒏 𝑦 0, 𝐹0, 𝑣

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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:

𝑤 = 𝑤 0 + ∆𝑤 𝑁𝐷 + 𝑢 𝑛0𝛿 𝐹0 𝑮𝒇𝒏 𝑦 0, 𝐹0, 𝑣

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

∆𝑦 = 𝑣 0∆𝑡 + ∆𝑡 2 ∆𝑣 ∆𝑦 = 𝑣 0∆𝑡 ∆𝑣 = ∆𝑣 𝑁𝐷 + ∆𝑣 𝑓𝑛

the change in the particle’s direction is

MC step

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vacuum

𝑠 = 𝑛𝑑 𝑓𝐶 𝛿2 − 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

𝐸 = 𝑂0/𝑛𝑈 ∙ 𝐹

  • Uniform electron source per unit mass N0/mT
  • Medium of uniform composition but varying

density where 𝐹 is the average energy emitted

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Fano theorem provides a rigorous test

If the source emits electrons of energy E0:

𝐸/𝑂0 = 𝐹0/𝑛𝑈

For a MC simulation fulfilling Fano conditions, the dose per particle in any region i is expected to be:

𝐸𝑗/𝑂0 = 𝐹0/𝑛𝑈

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 Monte Carlo / Theory 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 𝑡2 × 𝑈𝐷𝑄𝑉 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)