CALCULATION OF A SINGLE PENCIL BEAM KERNEL FROM MEASURED

PHOTON BEAM DATA

Pascal Storchi

Daniel den Hoed Cancer Center

University Hospital Rotterdam

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)

x

y

z

D x y z X F x y z K x x y y z dx dy( , , ; ) ( ', ', ) ( ', ', ) ' '2

Pencil beam model

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.

Is it possible to extract the pencil beam kernel from measured data ?

Calculation of the pencil beam kernel "empirical" approach

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

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)

depth boundary envelopedose function profile

D(x,y,z;X2) = Da(z;X2) Pb(x,y,z;X2) Pc(r,z)

Present model

x

y

z

D x y z X F x y z K x x y y z dx dy( , , ; ) ( ', ', ) ( ', ', ) ' '2

Pencil beam model

Phantom Scatter Factor

Phantom Scatter Factor Sp(z,X) iscomputed from:

tabulated Sp(z=10 cm,X)

normalized depth dose curveDa(z,X2)

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).

envelope profile only "scatter" measured profile

Fluence of primary photonsfirst guess: intensity profile Pi = envelope profile Pc

Fluence of primary photons deconvolution of scatter kernel Ks from envelope profile Pc =>

intensity profile Pi

intensity profile

only scatter

measured profile

Boundary kernel Kb

dP x

dxKb

b

( )(r)

Computed from the boundary profile Pb that has been corrected forthe photon scatter:

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)

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

Results: square field (20x20 cm2)measurement

calculation

Results: asymmetric square field (20x20 cm2)measurement

calculation

Results: rectangular field (30x5 cm2)measurement

calculation

measurementdiode

calculationpencil beam kernel derivedfrom data measured withionization chamber

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).