Download - Pencil Beam Kernel Calculation (1)
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CALCULATION OF A SINGLE PENCIL BEAM KERNEL FROM MEASURED
PHOTON BEAM DATA
Pascal Storchi
Daniel den Hoed Cancer Center
University Hospital Rotterdam
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Calculation of irregular photon fields by pencil beam convolution
D x y z F F x y z K x x y y z dx dy( , , ; ) ( ', ', ) ( ', ', ) ' '
F(x,y,z): fluence of primary photons
K(r,z): pencil beam kernel(r=(x2 + y2)1/2)
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x
y
z
D x y z X F x y z K x x y y z dx dy( , , ; ) ( ', ', ) ( ', ', ) ' '2
Pencil beam model
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Calculation of the pencil beam kernel "theoretical" approach
Pencil beam kernel computed by Monte Carlo techniques:
• Energy spectrum must be known:
– for the pencil beam kernel
– for the primary photon fluence
• Results must be fitted to specific linac.
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Is it possible to extract the pencil beam kernel from measured data ?
Calculation of the pencil beam kernel "empirical" approach
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Is it possible to extract the pencil beam kernel from measured data ?
Answer: Yes
by differentiation of scatter-to-primary ratio, includingan electron disequilibrium factor
Ceberg, Bjängard and Zhu
“Experimental determination of the dose kernelin high-energy x-ray beams”
Med. Phys. 1996
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Is it possible to extract the pencil beam kernel from measured data ?
Other method, pencil beam kernel computed from:
Phantom Scatter Factor (Sp) of square fields 4x4 upto 40x40 cm2
off-axis ratio (penumbra region) of square fields(>5x5 cm2)
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depth boundary envelopedose function profile
D(x,y,z;X2) = Da(z;X2) Pb(x,y,z;X2) Pc(r,z)
Present model
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x
y
z
D x y z X F x y z K x x y y z dx dy( , , ; ) ( ', ', ) ( ', ', ) ' '2
Pencil beam model
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Phantom Scatter Factor
Phantom Scatter Factor Sp(z,X) iscomputed from:
tabulated Sp(z=10 cm,X)
normalized depth dose curveDa(z,X2)
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Calculation of the scatter kernel Ks(R,z)
S R z K z drp s
R
( , ) (r, )0
K R zdS R z
dRsp( , )( , )
Sp(z,X) given for square fields X4 cm (equivalent circular fieldradius R2.3 cm). Linear extrapolation is used in the regionX<4 cm (R<2.3 cm).
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envelope profile only "scatter" measured profile
Fluence of primary photonsfirst guess: intensity profile Pi = envelope profile Pc
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Fluence of primary photons deconvolution of scatter kernel Ks from envelope profile Pc =>
intensity profile Pi
intensity profile
only scatter
measured profile
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Boundary kernel Kb
dP x
dxKb
b
( )(r)
Computed from the boundary profile Pb that has been corrected forthe photon scatter:
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Combination of scatter and boundary kernelsin one single pencil beam kernel
K(0,z) = CKb(0,z)
K(ri,z) = Ks(ri,z) + CKb(ri,z) ,i=1,...,n
ri = (i + ½ )
C = ¼ 2Ks(0,z)
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Steps for the calculation of the pencil beamkernel for a given depth
1. Ks: compute the scatter kernel from the phantom scatter factorsof square fields
2. Pi: compute the intensity profile such that Pc = PiKs
3. Ks: correct the scatter kernel Ks for the influence of Pi
4. Kb: compute the boundary kernel from the profiles of the 102,152, 202, and 252 cm2 fields corrected for the photon scatter
5. K: combine Ks and Kb into one single pencil beam
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Results: square field (20x20 cm2)measurement
calculation
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Results: asymmetric square field (20x20 cm2)measurement
calculation
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Results: rectangular field (30x5 cm2)measurement
calculation
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measurementdiode
calculationpencil beam kernel derivedfrom data measured withionization chamber
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Conclusions
• It is possible to use the PSF and the penumbra region of measured square fields for the derivation of the pencil beam kernel.
• Measurement of the penumbra region must be done with a small detector (diode).