Advanced Physics for Brachytherapy 2018
The method … is ready
I have GxM equations of the form (1) @ each voxel (GxMxN vox in total) • begin with E1 (highest energy group) • make an initial guess for • calculate cross sections from (3) & (5) • calculate the expansion from (4) • use these in (2) to calculate q scat,1,n • solve (1) for 1 ) ( ,1 = iter rn 0 )( ,1 n = iter r
P
( ngpq ng scat q rng gt − + , , , ,
ˆ
rng
, )( ,
= +
)( ,
)
)1(
pr r
p
=
1 4
l
G
=
m
q
rng scat
)( rg gls −
r gml
)( Y
)ˆ,( , , =
) ,(
)2(
' ,,
' , ,
l
l
1' l m g =
0
−=
gE − = −
gE −
1 1'
)( rg
' )' ( ) dEdE EfE Erls
,(,
→
)3(
gls
' ,,
' gE
gE
E
g
−
1
N =
m
r gm
)( , rng
l YEf
dEnwn
)( =
) (
) ˆ(
)4(
l
,
,
n
1
gE
gE −
1
rgt
) ( ) ,( dEEfErt
)( , =
)5(
gE
• if convergence criterion not met, re-iterate
• if convergence criterion met, proceed with g=2
BUT…: 1. I need to be efficient (t~ GxMxN vox
x#iters.x order of legendre exp.) & work
with finite voxels 2. I need to account for inhomogeneities 3. I need to work with real sources 4. I need to account for finite patient dimensions
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