Evangelos Matsinos, Barbara Schaffner, Wolfgang Kaissl

Varian Medical SystemsBaden, Switzerland

Technology for peopleBetter technology. Better outcomes.

Optimisation in proton scanning beams

First results…

Better technology. Better outcomes. EM, May 2002 Page 2

Basic steps

Calculation of the dose-deposition coefficients (ddc’s)

Optimisation of the spot weights

Better technology. Better outcomes. EM, May 2002 Page 3

Better technology. Better outcomes. EM, May 2002 Page 4

Spots and beamlets

Beam beamlets or pencil beams (defined by the resolution of the calculation grid)

The dose from each beamlet is evaluated (at the vertices of the calculation grid)

The spot dose is calculated (as the sum of the dose contributions of the corresponding beamlets, weighted for the position of each beamlet within the spot)

Better technology. Better outcomes. EM, May 2002 Page 5

beamlet

spot

depends on the density and on z

Sx and Sy depend on z

Better technology. Better outcomes. EM, May 2002 Page 6

Optimisation: a closer look

Desired dose at point i: pi

Dose delivered at point i: di = aij xj

(sum over target points)

+ contribution due to the violation of dose-limit constraints (for targets and

organs)+ contribution due to the violation of dose-volume constraints (for organs)

Objective function: Fobj = (di - pi)2

(sum over all sources j)

Better technology. Better outcomes. EM, May 2002 Page 7

Optimisation methods

Conjugate Gradient (CG)

Simulated Annealing (SA)*

‘Simultaneous’ optimisation (PSI)

Generalised Sampled Pattern Matching (GSPM)*

(* = under development)

Better technology. Better outcomes. EM, May 2002 Page 8

Strategy in the optimisation Pre-optimisation Reasonable initial ‘guess’ for the weights Convergence two consecutive iterations yield improvement below 5% Main optimisation Full implementation of a method Convergence two consecutive iterations yield improvement below 0.1%

Better technology. Better outcomes. EM, May 2002 Page 9

Toy example

A phantom has been created with three important structures: one target and two organs; some inhomogeneity has been introduced (an additional structure simulating the presence of a bone)

Pixel size: 2.5mm Spot advance in y (scanning direction): 2.5mm Spot advance in x: 5mm Cut-off for dose contributions: 3 standard

deviations

Better technology. Better outcomes. EM, May 2002 Page 10

Target: 2,412 points, 57.27 cm3

Distal Organ: 2,166 points, 48.34 cm3

Proximal Organ: 683 points, 15.49 cm3

Number of points: 5,261

Better technology. Better outcomes. EM, May 2002 Page 11

Number of parameters: 4,798

Better technology. Better outcomes. EM, May 2002 Page 12

ProtonHelios

Better technology. Better outcomes. EM, May 2002 Page 13

Dose-Volume Histograms

Prescription dose: 50 Gy ( 2%)Organ constraints: 25 Gy in 10% of the distal organ;15 Gy in the

proximal organ

Better technology. Better outcomes. EM, May 2002 Page 14

Dose distribution (exclusive fit to the target)

Better technology. Better outcomes. EM, May 2002 Page 15

Dose distribution (fit to all structures)

Better technology. Better outcomes. EM, May 2002 Page 16

Comparison of a few numbers

Method

Minimal Fobj

Relative time

Target dose (Gy)

Maximal

weight

CG 36,902 3.8749.6

2.316.03

SA 35,621 4.9249.6

2.317.15

PSI 37,440 1.0049.7

2.351.97

GSPM --- 1.3349.9

1.96.74

Better technology. Better outcomes. EM, May 2002 Page 17

Weight distribution

PSI method

Better technology. Better outcomes. EM, May 2002 Page 18

Weight distribution

SA method

Better technology. Better outcomes. EM, May 2002 Page 19

A head tumour

Better technology. Better outcomes. EM, May 2002 Page 20

Conclusions

As far as the dose distribution is concerned, three optimisation methods (CG, SA, and PSI) yield results which seem to be in good agreement. Very similar dose distributions may be obtained on the basis of very different weight distributions.

The use of raw (unfiltered) weights does not seem to create cold/hot spots within the irradiated volume. It remains to be seen whether, in some occasions, filtering will be called for.

Better technology. Better outcomes. EM, May 2002 Page 21

Under consideration…

Other forms of the objective function to be tried?

Strategy in the optimisation: an improvement of about 25% was found in the execution time in case that the target dose is firstly optimised (with vanishing dose everywhere else)

Other optimisation methods to be tried?