Transcript ICCR 2000 - Harvard University

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
Contents
•
•
•
•
Constraints in IMRT optimization
Projection onto convex sets
Clinical case
Conclusions
Volume
Maximum dose constraint
max
D
Dose
Volume
DVH constraint
max
V
max
D
Dose
EUD constraint I
Equivalent uniform dose, EUD:
1/ a
1
a
EUD    Di 
 N i 1

N
Tumor:
Normal tissue:
a negative
a positive
Niemierko, MedPhys 1999
Volume
EUD constraint II
EUD( D)  EUDmax
EUD( D' )  EUDmax
Dose
POCS – Projection onto convex set
D2
D
x
D‘
x
EUD  EUDmax
EUD  EUDmax
Convex set {D | EUD( D)  EUDmax }
D1
POCS – Math I
N
I.
2
(
D

D
'
)
 i i  min
i 1
II . EUD( D' )  EUDmax
Extrema on a bounded surface
 Use Lagrange Multipliers
POCS – Math II
Implicit definition of new dose constraint D‘j in voxel j:
D j  D' j
D'(ja 1)

EUD  EUDmax
( a 1)
EUDmax
Single EUD constraint  individual physical constraints
for every organ voxel
 Easy to implement into existing IMRT planning tools
(keep objective function, gradients, optimization alg.)
POCS – Example Serial Organ
100
Current Dose
Projected to EUD=33 Gy:
a = 7.4
Relative Volume (%)
80
60
40
20
0
0
20
40
Dose (Gy)
60
POCS – Example Serial/Parallel Organ
100
Current Dose
Projected to EUD=33 Gy:
a = 7.4
a = 1.0
Relative Volume (%)
80
60
40
20
0
0
20
40
Dose (Gy)
60
POCS – Example Target
100
Relative Volume (%)
80
60
40
Current Dose
Projection to EUD=66Gy,
a = -10
20
0
0
20
40
Dose (Gy)
60
Clinical case: head and neck tumor
Brainstem
Parotid
Target
Spinal cord
Results
100
Target
Brainstem
Spinal Cord
Parotis
Relative Volume (%)
80
60
Organ
EUDConstraint
(Gy)
40
Brainstem
Max=15
15.13
20
Spinal
Cord
Max=25
25.25
Parotis
Max=25
25.25
Target
Dmin=75Gy
0
0
20
40
60
Dose (Gy)
80
EUD
(Gy)
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