1. Direct Consideration of EUD Constraints in IMRT Optimization
Ch. Thieke1,2, Th. Bortfeld1, A. Niemierko1, S. Nill2 1
Dept. of Radiation Oncology
Massachusetts General Hospital
Boston, MA 2
Dept. of Medical Physics
Deutsches Krebsforschungszentrum
Heidelberg
Germany

2. Constraints in IMRT optimization Projection onto convex sets
Contents
Constraints in IMRT optimization
Projection onto convex sets
Clinical case
Conclusions
The talk is divided into following sections:
First, I want to show the principles of the dose calculation by a precalculated matrix Dij in a new inverse planning system developed at the German Cancer Research Center.
Then I want to describe the modification of this matrix by sampling and show some results of dose calculations performed by such a modified matrix Dij Tilde.
I will end with the optimization results for a clinical example case and with the conclusions.

3. Maximum dose constraint
Volume
Voxels in the hatched area will be penalized in the objective function D
max
Dose

4. DVH constraint Volume V D Dose max max
Voxels in the hatched area will be penalized in the objective function D
max
Dose

5. Equivalent uniform dose, EUD:
EUD constraint I
Equivalent uniform dose, EUD:
Niemierko, MedPhys 1999
Tumor: a negative
Normal tissue: a positive

6. EUD constraint II Volume Dose DVH of desired new dose distribution D‘.
In this example the high dose area is more affected than the low dose area. That‘s the case for serial organs with high a.
Parallel organ, extreme a=1: EUD equals mean dose, DVH of D‘ would be just a left-shifted version of the actual one.
Left and lower equations determine, based on actual distr. D, the new prescribed dose D‘.
Dose

7. POCS – Projection onto convex setD2 D x D‘ x
Convex set D1

8. POCS – Math I
Extrema on a bounded surface
Use Lagrange Multipliers

9. POCS – Math II
Implicit definition of new dose constraint D‘j in voxel j:
Single EUD constraint  individual physical constraints for every organ voxel
Easy to implement into existing IMRT planning tools (keep objective function, gradients, optimization alg.)

10. POCS – Example Serial Organ

11. POCS – Example Serial/Parallel Organ

12. POCS – Example Target

13. Clinical case: head and neck tumor
Brainstem
Parotid
Target
Clinical example, head and neck tumor.
Target (with Boost inside, not visible), 3 OAR: spinal cord, brainstem, parotid.
Spinal cord

14. Results Organ EUD- Constraint (Gy) EUD (Gy) Brainstem Max=15 15.13
Spinal Cord
Max=25
25.25
Parotis
Target
Dmin=75Gy

15. Conclusions
EUD constraints can be used for easy to handle, yet clinical meaningful IMRT optimization
Projection onto convex set (POCS) converges fast and stable
Mixing of physical constraints and EUD contraints is possible
Presented method is easy to integrate into existing IMRT planning tools based on physical dose constraints