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pencil kernel parameterization:

a r

b r

−

−

A

B

e

+

e

p

z

z

( ) r

z

z

=

A further parameterization of , using the beam quality index

r



TPR2010 as single input parameter:

5

A

)

(

  

  

(

)

i

2

2

2



z

A = −

A z A +

A z

A z

A C =

1 exp

exp

+



TPR

m

, i A

1

2

5

3

4

20/10

a B

m

i

=

1

z

5

)

(

  

  

(

)

i

2

2

2



z

B

B z B +

B z B z +

B C =

=

1 exp −

exp



TPR

m

, i B

1

2

5

3

4

20/10

b

m

i

=

1

z

5

i



a a a z = +

a

C

=



TPR

z

m

, i a

1

2

20/10

m

i

=

1

5

)

(

  

  

(

)

i

2

2

2



b b

b

z b +

b z b z +

b

C

= −

1 exp

exp

=



TPR

z

m

, i b

1

2

5

3

4

20/10

m

i

=

1

10 cm

10 cm

Isocenter distance

10 cm

z z  =  =

D(10 10,

20cm)

TPR

=

20/10

D(10 10,

10cm)

T Nyholm, et al (2006) Radiother Oncol 78 , 347-51.

This is the PK kernel parameterization used in e.g. Scandidos Delta4 software