Physical optimization criteria Target objective function The target
Physical optimization criteria Target objective function The target sub-function includes the target prescription dose and doseuniformity limits Nt = number of voxels in target ct, min = penalty associated with underdosage ct, max = penalty associated with overdosage Di = dose to voxel i Dpresc = prescribed dose to target Heaviside function* Dmin = minimum dose to voxel i Dmax = maximum dose to voxel i
Physical optimization criteria OAR objective function The OAR sub-functions include maximum dose and DVH-limits NO = number of voxels in OAR Dmax = maximum dose to voxel i Ddv = maximum dose to voxel i, iєNdv c. O, max = penalty weight for overdosage c. O, dv = penalty weight for violation of dose-volume constraint Ndv = number of voxels in OAR whose dose must be below the DVH constraint
Radiobiology Linear-quadratic (LQ) model • The cell survival curve describes the relationship between the radiation dose and the proportion of cells that survives Surviving fracions of cells 1 ad bd 2 0. 1 • The surviving fraction of target cells SF(d), after a single radiation dose d can be fitted to experimental data using an exponential function with the parameters a and b. 0. 01 0. 001 4 a/b 12 16 Radiation dose (Gy) LQ model used to compare the biological effect of different treatment fractionation schedules
Radiobiology g. EUD • g. EUD is based on the concept of a generalized mean dose, and is a means to reduce a complex 3 D dose distribution to a single, biologically representative dose value • The a parameter is tissue specific and describes the volume effect of the tissue under consideration D = total dose a = tissue specific volume parameter N = number of voxels in tissue Di = dose in voxel i g. EUD is not a sigmoid function and does not predict a response, however, it is a convex function… - a < 0: minimum dose (tumour) - a ≈ 1: mean dose (parallel tissue) - a → ∞: maximum dose (serial tissue)
Biological Optimization Criteria Objective function example (iii) • The objective function includes combinations of the Logistic function and the g. EUD function for both target and OARs • Target sub-function includes the g. EUD prescription dose and a relative importance factor • OAR sub-functions include the g. EUD limit dose and relative importance factors
- Slides: 5