Advanced Physics for Brachytherapy 2018

1. I need to be efficient

• It is inherently beneficial to work in spherical coordinates to lift the kernel singularity since: dV=dS dr=r 2 dΩ dr = r 2 sinθ dθ dφ dr

j

iρ

D

S jρ

dVjh

=

 =→

1sc

i 1sc,

j i

iρ V

i 1sc, B

) rb

exp(

−





dr dd

S

sin2r







  

2r

r jρ



i

• Instead of evaluating ALL directions around a scerma generating point, I can DISCRETIZE space using a number M of solid angle elements, ΔΩ M , defined by (θ 0 ,φ 0 ) M , and assume scerma does not vary with θ within ΔΩ (i.e. on dS for a given r)

iρ

B

rb )

dr d

=→

1sc,i S

exp(

−

=

 



1scD





j i

jρ

r

iρ

B

r b dr )



1sc,i S

 exp( 0

−





0

jρ

r