Inverse treatment planning method

1. An inverse treatment planning method for intensity modulated particle therapy for the treatment of a target within a biological system using at least two fields, each field comprising a plurality of Bragg peaks, the at least two fields being planned to place a defined number of beam spots j from different directions with certain weights w j within the target, wherein the inverse treatment planning method optimizes the weights w j of the beam spots for the at least two fields simultaneously in order to produce a prescribed biological effect within the target by minimizing an objective function based on biological effects ε, the biological effects ε being treated in a linear-quadratic model which describes the biological effects in the target by two parameters α and β, where ε=αD+βD 2 , D denoting a dose, and wherein the two parameters α and β for each voxel i of the target α i and β i are calculated as dose-averaged mean values of α i,j - and √{square root over (β i,j )}-components, which relate to all beam spots j contributing to a total dose D i in the voxel i,

wherein the two parameters α and β for each voxel i of the target (α i and β i ) are calculated as dose-averaged mean values of the form

α

i

=

1

D

i

⁢

∑

j

=

1

N

⁢

w

j

⁢

D

i

,

j

⁢

α

i

,

j

⁢

⁢

and

β

i

=

1

D

i

⁢

∑

j

=

1

N

⁢

w

j

⁢

D

i

,

j

⁢

β

i

,

j

for D i >0,

D

i

=

∑

j

=

1

N

⁢

w

j

⁢

D

i

,

j

with N beam spots contributing to the total dose D j in voxel i.

2. The inverse treatment planning method according to claim 1 , wherein an objective function is minimized, which is based on the formula

F

ɛ

⁡

(

w

→

)

=

∑

i

∈

T

⁢

(

ɛ

i

⁡

(

w

→

)

-

ɛ

T

)

2

with ε i denoting the biological effect in the voxel i of the target, {right arrow over (w)} the weights of the beam spots and ε T the prescribed biological effect of a reference radiation.

3. The inverse treatment planning method according to claim 1 , wherein an objective function is minimized, which is based on the formula

F

ɛ

⁡

(

w

→

)

=

∑

i

∈

T

⁢

(

α

i

⁡

(

w

→

)

⁢

D

i

⁡

(

w

→

)

+

β

i

⁡

(

w

→

)

⁢

D

i

2

⁡

(

w

→

)

-

ɛ

T

)

2

with D i denoting the total dose of the at least two fields in voxel i and α i and β i the α- and β-values at voxel i, wherein

D

i

=

∑

j

=

1

N

⁢

w

j

⁢

D

i

,

j

with D i,j denoting a dose contribution of beam spot j at voxel i for unit fluence, N beam spots contributing to the dose D i at voxel i, and w j denoting a weighting factor of beam spot j and wherein the prescribed biological effect ε T is given by

ε T =α T x D T +β T x D T 2

with α T X and β T X being X-ray response parameters of the target and D T denoting a prescribed photon dose.

4. The inverse treatment planning method according to claim 1 , wherein an objective function is minimized, which includes constraints relating to minimum and maximum biological effect levels for the target and maximum effect levels for organs at risk or normal tissue within the biological system.

5. The inverse treatment planning method according to claim 1 , wherein the α i,j - and √{square root over (β i,j )}-components are derived from a radiobiological model or from measured data for α and β as a function of depth in a single Bragg peak.

6. The inverse treatment planning method according to claim 1 , wherein a constant value β i,j =β i is set, which depends only on a tissue type at voxel i.

7. The inverse treatment planning method according to claim 1 , wherein the α i,j -components are assumed to be laterally constant and are extracted from a single curve as a function of residual range, independent of an initial beam energy.

8. Use of an inverse treatment planning method for intensity modulated particle therapy for the treatment of a target within a biological system using at least two fields, each field comprising a plurality of Bragg peaks, the at least two fields being planned to place a defined number of beam spots j from different directions with certain weights w j within the target, wherein the inverse treatment planning method optimizes the weights w j of the beam spots for the at least two fields simultaneously in order to produce a prescribed biological effect within the target by minimizing an objective function based on biological effects ε, the biological effects ε being treated in a linear-quadratic model which describes the biological effects in the target by two parameters α and β, where ε=αD+βD 2 , D denoting a dose, and wherein the two parameters α and β for each voxel i of the target α i and β i are calculated as dose-averaged mean values of α i,j - and √{square root over (β i,j )}-components, which relate to all beam spots j contributing to a total dose D i in the voxel i for planning the treatment of a tumor with an ion beam containing ions with an atomic number ≧2.

9. A radiation treatment apparatus for delivering a radiation treatment to a target within a biological system comprising

a field unit for generating at least two fields, each field comprising a plurality of Bragg peaks, the at least two fields being provided to place a defined number of beam spots j from different directions with certain weights w j within the target and

a unit for inverse treatment planning being provided for optimizing the weights w j of the beam spots for the at least two fields simultaneously before the radiation treatment in order to produce a prescribed biological effect within the target by minimizing an objective function based on biological effects ε, the biological effects ε being treated in a linear-quadratic model, which describes the biological effects in the target by two parameters α and β, where ε=αD+βD 2 , D denoting a dose, and wherein the two parameters α and β for each voxel i of the target (α i , β i ) are calculated as dose-averaged mean values of α i,j - and √{square root over (β i,j )}-components, which relate to all beam spots j contributing to a total dose D i in the voxel i.