Optimisation in proton scanning beams

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Optimisation in proton scanning beams

• First results

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Basic steps

• Calculation of the dose-deposition coefficients
  (ddcs)
• Optimisation of the spot weights

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(No Transcript)
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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)

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spot
Sx and Sy depend on z
? depends on the density and on z
beamlet
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Optimisation a closer look

• Desired dose at point i pi
• Dose delivered at point i di ? aij xj

(sum over all sources j)
Objective function Fobj ? (di - pi)2
(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)
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Optimisation methods

• Conjugate Gradient (CG)
• Simulated Annealing (SA)
• Simultaneous optimisation (PSI)
• Generalised Sampled Pattern Matching (GSPM)
• ( under development)

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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

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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

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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
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Number of parameters 4,798
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ProtonHelios
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Dose-Volume Histograms
Prescription dose 50 Gy (? 2)
Organ constraints 25 Gy in 10 of the distal
organ15 Gy in the proximal organ
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Dose distribution (exclusive fit to the target)
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Dose distribution (fit to all structures)
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Comparison of a few numbers
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Weight distribution
PSI method
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Weight distribution
SA method
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A head tumour
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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.

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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?