gms | German Medical Science

48th Meeting of the Particle Therapy Co-Operative Group

Particle Therapy Co-Operative Group (PTCOG)

28.09. - 03.10.2009, Heidelberg

Density scaling of the proton beam spectrum for analytic reconstruction of the SOBP

Meeting Abstract

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  • A. Guemnie Tafo - Fox Chase Cancer Center, Radiation Oncology, Philadelphia, USA

PTCOG 48. Meeting of the Particle Therapy Co-Operative Group. Heidelberg, 28.09.-03.10.2009. Düsseldorf: German Medical Science GMS Publishing House; 2009. Doc09ptcog077

DOI: 10.3205/09ptcog077, URN: urn:nbn:de:0183-09ptcog0772

Published: September 24, 2009

© 2009 Guemnie Tafo.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( You are free: to Share – to copy, distribute and transmit the work, provided the original author and source are credited.



Background: Proton therapy treatments allow for a better sparing of normal tissues and tumor coverage, mainly due to the Bragg peak dose deposition effect. The selection of the Spread Out Bragg Peak (SOBP) necessary for the treatment is performed using the distal and proximal edges of the tumor and rescaling this distance to an effective distance in water. MC simulation studies done in this work showed that in a divergent beam and low-density material, the proton spectrum yielding an SOBP distribution may significantly differ from that obtained using the stretching technique. Stretching of the SOBP calculated in water according to the water equivalent distance may lead to an underestimate of the dose for distal edge of the tumor in the case of a low density material and divergent beam. For this purpose, we derived an analytical formula that takes into account these parameters in the SOBP calculation.

Method and materials: In a previous work, an SOBP spectrum for a parallel proton beam in water was derived. We revised this formula to make it applicable for different medium densities and beam divergences. The model provides very efficient generation of an SOBP spectrum, which accounts for tissue heterogeneities. It is shown that water-equivalent depth-dose scaling used in many treatment planning systems to account for tissue heterogeneity is inadequate. One has to recalculate the spectrum according to the medium density and beam divergence. We showed that the spectrum for the SOBP can be given by: F0(E0)=H(E0-Emin)H(Emax-E0)E0 μ/(Emax 2-E0 2)0.6 where μ is the density and SSD dependent factor. Numerical calculation and comparison with Monte Carlo code are in a good agreement.

Results: Simulations were performed using Fluka Monte Carlo code. We simulated mono energetic Bragg peaks between 90 and 105 MeV in lung ICRP uniform phantom with a density 1 and a density 0.2, using 10x10 cm2 field size and 100 SSD. Then we optimized the proton spectrum in the highest density material in order to obtain a clinical SOBP. We finally used the same spectrum with Bragg peaks calculated in a low-density material. Results of Figure 1 [Fig. 1] showed that the use of the same spectrum for two different density materials might lead to a decrease of the dose toward the distal edge of the tumor. Moreover, higher beam divergence of the proton beam results in more pronounced effect.

These results showed us the importance of recalculating the spectrum when using a low density material. To simplify this procedure, we developed an analytical formula, which takes into account the divergence of the beam (with the inverse square law) and the medium density.

Conclusion: An expression for the proton SOBP spectrum for passive scattering delivery method in hadron therapy for different density materials and beam divergences has been obtained. This could allow a very fast way of generation SOBP spectra for treatment purposes instead of using a water equivalent depth dose curve database.