Imrt

Optimisation of Irradiation Directions in IMRT Planning Rick Johnston Matthias Ehrgott Department of Engineering Science University of Auckland M. Ehrgott, R. Johnston Optimisation of Irradiation Directions in IMRT Planning, OR Spectrum 25(2):251-264, 2003

What is Radiotherapy?

Intensity modulation - improves treatment quality
Inverse planning problem - conflicting objectives to irradiate tumour without damage to healthy organs
IMRT

Model Formulation
Discretisation of Body and Beam
Voxels Bixels gantry

Angle Discretisation
Linearises the problem
A number of LPs to be solved
Replicates physical setup

MOMIP Model
Data
L 1 = lower bound in tumour
U k = upper bound in organ k
R = number of directions to be used
Variables and functions
Intensity vector x = (x 11 ,...,x HN )
Direction choice vector y = (y 1 ,...,y H )
Deviation vector T = (T 1 ,...,T K )
Dose distribution vectors D k = (D k1 ,...,D kMk )

min (T 1 ,...,T K )
D 1 = P 1 x  (L 1 - T 1 ) 1
D k = P k x  (U k + T k ) 1 , k=2,...,K
x hi  My h , h=1,…,H, i=1,…,N
y 1 + ...+y H  R
y h  {0,1} h=1,...,H
T, x  0
To study effect of direction optimisation consider weighted sum min  1 T 1 +  2 T 2 + ... +  K T K Extension of multicriteria model by Hamacher/Küfer

Solution Methods
Two-phase Methods
3. Set Covering
4. LP Relaxation
Integrated Methods
1. Mixed Integer Formulation
2. Local Search Heuristics

Integrated Methods
CPLEX 7.0
If R increases problem becomes easier, objective value improves
For small R and small angle discretisation often no feasible solution found
MIP SOLVER 1

Optimal solution of MIP problem
Isodose curve pictures obtained with prototype software developed at ITWM, Kaiserslautern

Integrated Methods
Alter each gantry position in turn to find better angles
Steepest descent with randomised starting angles
Solve LP for each selection of angles
LOCAL SEARCH 2

Local Search Movie

Two-phase Methods
Intuitive
Considers all angles
Relatively quick
Fully irradiate every voxel in the tumour Avoid damage to healthy organs Benefits: SET COVERING 3

min C 1 y 1 +...+ C S y S
Ay  1
y  {0,1}
a ij =1 if and only if beam j hits voxel i
Weighted angle method
C j is sum of  k /U k over all organs at risk and voxels in beam j
Dose deposition method
C j is sum of  k P k (i,j)/U k over all voxels and all organs at risk

Cost coefficients

Set Covering Solution
MIP Solution

Two-Phase Methods
LP RELAXATION
4 Optimal solution of LP relaxation 10-40 beams used

Results
All methods were successful in generating good treatment plans in a reasonable timeframe (10 min)
Optimal beams were often counterintuitive
Angle optimisation is important if few beams to be used

Solution with equidistant beams
Solution with optimised beams

Comparison Objective 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Problem 1 3 heads Problem 1 4 heads Problem 2 3 heads Problem 2 4 heads Problem 3 3 heads Set Covering LP relaxation Local Search Mixed Integer

Objective vs. Time Objective 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0 2000 4000 6000 8000 10000 12000 Time (s) Local search improvement Set Covering Local Search LP relaxation Mixed Integer

Imrt

by fondas vak on Mar 10, 2010

Accessibility

Categories

Tags

Upload Details

Usage Rights

1 Embed 7

Statistics

Imrt — Presentation Transcript