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 r

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

r'

1

2

and assuming:

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

Dose from points along Δr1 in voxel 1, to a point in voxel 2 :

ρ1



  =

B

) b r d dr

D

=

S

exp(

−

Mass energy absorption term [cm 2 /g]

 

1sc1 2 →

1sc,1





ρ2

r  

term [J/cm 2 ]

Ψ

r r +

1sc

1

ρ1



B

b r 



S

exp(

−

') dr

=



1sc,1



Attenuation term

ρ2

r



S ρ 1sc,1 1 exp(

B

B

ρ1





b r 

b r

=

−

)[1 exp( −

− 

)]

b r 

b r − − 



S

exp(

−

)[1 exp(

)]



1sc,1



1

1

b

ρ 2

b

ρ2



