Physical optimization criteria Target objective function

1
Physical optimization criteriaTarget objective
function
The target sub-function includes the target
prescription dose and dose-uniformity limits

• Nt number of voxels in target
• Di dose to voxel i
• Dpresc prescribed dose to target
• Dmin minimum dose to voxel i
• Dmax maximum dose to voxel i

ct,min penalty associated with underdosage
ct,max penalty associated with
overdosage Heaviside function
2
Physical optimization criteriaOAR 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, i?Ndv
• cO,max penalty weight for overdosage
• cO,dv penalty weight for violation of
  dose-volume constraint
• Ndv number of voxels in OAR whose dose
  must be below the
• DVH constraint

3
RadiobiologyLinear-quadratic (LQ) model

• The cell survival curve describes the
  relationship between the radiation dose and the
  proportion of cells that survives
• 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.

• LQ model used to compare the biological effect
  of different treatment fractionation schedules

Radiation dose (Gy)
4
Radiobiology gEUD

• gEUD is based on the concept of a generalized
  mean dose, and is a means to reduce a complex 3D
  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
gEUD is not a sigmoid function and does not
predict a response, however, it is a convex
function
- a lt 0 minimum dose (tumour) - a 1 mean dose
(parallel tissue) - a ? 8 maximum dose (serial
tissue)
5
Biological Optimization CriteriaObjective
function example (iii)

• The objective function includes combinations of
  the Logistic function and the gEUD function for
  both target and OARs
• Target sub-function includes the gEUD
  prescription dose and a relative importance
  factor
• OAR sub-functions include the gEUD limit dose and
  relative importance factors