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