Advanced Physics for Brachytherapy 2018

Equations for the transport of scerma generated at each point along a transport line

1. I need to be efficient

Δr

1

Δr

2

Under the collapsed cone approximation: • Scerma does not vary with θ within ΔΩ (Bθ, bθ constant along transport line) and scerma generated, emitted and absorbed along transport line

θ

1

r

2

and assuming:

• Scerma generated per unit r is constant within the same voxel (scerma does not vary considerably within voxels)

Averaging dose over all points along Δr2 in voxel 2 :

Δr

Δr

2

2



S ρ 1sc,1 1

B



dr

b r − − 

)] b r dr

D

[1 exp(

)]

exp(

−





1sc1 2 →



1



b

ρ 2



0

0

D1sc1 2 →

=

=

=

Δr

Δr

2

2



S ρ

B

[1 exp( − −  − −   )][1 exp( 1 b r b r b r  

2)]

1sc,1 1



b

ρ 2





2