Double scattering for proton beam spreading

The PSI version of Graphic Turtle is well suited for investigating the double scattering method for proton beam spreading with Monte-Carlo computations. In order to demonstrate this ability, an example from the medical field of 'treatment of ocular tumors with protons' is taken. (It should be mentioned here, that this double scattering method may also be used for more efficiently irradiating electronic spacecraft components in a homogenous field of protons coming from an accelerator.) This double scattering method has first been proposed by Koehler et al [1]. The layout and dimensioning of a possible 'double scattering proton beam line' for ocular treatments is given below [2]:


The computed transmission for this proton beam line is 18.1 % (see loss-table below) and the flatness of the proton field at the target (achieved with double scattering) is within ±2.5 % with a penumbra of around 0.4 mm (see histograms below).

Turtle Input file for the above described proton beam line (The multiple scattering parameters [type code 1 after type code 6] for the line defining the effects of water [H2O] or Tungsten [W] on the proton beam were computed with the auxiliary program MUSCAT [included in the TURTLE package]. Both materials have to be divided into fractions of their total thicknesses [50 * 0.1 mm for water {H2O} and 10 * 3.75 micro-meters for Tungsten {W}].):

 /Double Scattering Example/
 10000000

 15. 1.0  /mm/ 0.1 ;
 15. 11.0 /MeVc/ 0.001 ;
 15. 12.0 /MeV/ 0.001 ;

 1.0  1.0 5.0  1.0 5.0  0.0 0.1 369.1 /BEAM/ ; (Ekin = 70 MeV beam)
 -7.0 .5 .0 .0 .0 .0 .0 /shft/ ;

 16. 3.0 1836.7 /m0/ ; (proton mass)
 16. 165. /MULT/ ; (enable multiple scattering)
 16. 190. 0. 100. /Meta/ ; (output to FOR100.DAT)

 16. 160. /INVS/ ; (enable inverse slits)
 16. 198. 50. ; (concatenate loss-entries in loss-table)
 9. 50. ; (5 mm H2O degrader, Ekin = 62.6 MeV)
  6. 1. 10. 3. 10. /Degr/ ;
  1. 1.719 9.12   523.4 .657 281.7   0.0276 0.098 0.0 /H2O/ ;
  3. 0.0001 ;
 9. 0. ;

 50.0 11.0 347. 357. 0.25 ; (momentum)
 50.0 12.0 61. 66. 0.25 ; (Ekin)
 50.0 2.0 -50. 50. 5. ; (x'[rms] = 12 mr)

 16. 198. 10. ; (concatenate loss-entries in loss-table)
 9. 10. ; (1st scatterer, Tungsten foil 37.5 micron)
  6. 1. 100. 3. 100. /Sca1/ ;
  1. 3.352 6.33   50.48 .506 119.6   0.0155 0.0377 0.0 /W/ ;
  3. 0.00000375 ;
 9. 0. ;

 50.0 11.0 347. 357. 0.25 ; (momentum)
 50.0 12.0 61. 66. 0.25 ; (Ekin)
 50.0 2.0 -50. 50. 5. ; (x'[rms] = 16 mr)

 3. 0.45 ;

 16. 198. 1. ; (reset for loss-table)
 6. 1. 2.5 3. 2.5 /Oclu/ ; (occluding disc, 5mm diameter)

 16. 198. 10. ; (concatenate loss-entries in loss-table)
 9. 10. ; (2nd scatterer, Tungsten foil 37.5 micron)
  6. 1. 100. 3. 100. /Sca2/ ;
  1. 3.352 6.33   50.48 .506 119.6   0.0155 0.0377 0.0 /W/ ;
  3. 0.00000375 ;
 9. 0. ;

 3. 0.98 ;

 16. 161. /Norm/ ; (enable normal slit)
 16. 198. 1. ; (reset for loss-table)
 6. 1. 17.5 3. 17.5 /Aper/ ; (aperture)
 
 3. 0.07 /Targ/ ;

 51. 1. -20. 20. 2. ;
 52. 3. -20. 20. 2. ;
 50. 21. 17.5 19.0 0.1 ; (penumbra, radial edge fall-off, 0.4 mm)

 SENTINEL
 SENTINEL

Summary of particles stopped by apertures.
------------------------------------------

position        type    label        rays

0.0049 m        Slit     Degr     62364.4
0.0050 m        Slit     Sca1      3685.7
0.4550 m        Slit     Oclu    645627.8
0.4551 m        Slit     Sca2      3425.7
1.4351 m        Slit     Aper   7477660.0

total                           8192764.0

The following picture shows the 8 requested histograms. Histogram 8 shows the penumbra, which is about 0.4 mm. Even with 10'000'000 protons running through the proton beam line, the statistical fluctuations are still visible in histograms 7 and 8.

The next picture shows a contour-diagram of histogram 7. This plot consists of 40 equidistant contour lines (2.5 % intensity difference from line to line). Over the whole field inside the penumbra the proton beam distribution is constant within ±2.5 %.

The picture below shows a side-view of histogram 7. Also here the flatness (within ±2.5 %) inside the penumbra of the proton distribution at the target is well visible.

It is very easy with TURTLE to study the different non-nominal beam conditions (misalignments) by applying beam shift parameters (type code 7) different from zero in the Turtle input file. As an example the results on the proton beam at the target location by the displacement of the initial proton beam by +0.5 mm in x from the axis (but still double scattering enabled) is plotted in the next picture:

From the picture above it can be seen, that the double scattering method is very sensitive to lateral proton beam displacements (confirmed by [2]). Therefore, the position of the proton beam spot at the beginning of the proton beam line has to be stabilized to ±0.1 mm during the irradiation of the tumor in order to get a sufficiently even dose distribution at all locations. With other beam-shifts it is relatively easy to test the sensitivity of double scattering to various kinds of displacements. Also the influence of the initial proton beam spot parameters and the momentum spread may be studied. The super-position of different non-nominal conditions may also be simulated e.g. by adding-up the results of different Turtle runs. Because of the statistical requirements of double scattering computations, this may be very time-consuming.

[1] A.M. Koehler, R.J. Schneider and J.M. Sisterson: Flattening of proton dose distributions for large-field radiotherapy. Med Phys 4: p.297-301 (1977).
[2] M. Goitein: Private communication.

Other Proton Beam Therapy Application Examples:
Degrader Design for a 250 MeV Medical Cyclotron
Isotope Production Yield Optimization at PSI
Medical Gantry Optical Design

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Last updated by Urs Rohrer on 4-Jul-2006

visits since 14-06-2006