UBC Theses and Dissertations
Dose calculations relating to the use of negative pi-mesons for radiotherapy Henry, Marguerite Irene
Physical (or absorbed) dose distributions and biologically effective distributions are calculated in this thesis for (a) monoenergetic beams (b) "shaped" continuous energy spectra of negative pi-mesons. The results of these calculations confirm qualitatively the claims made for the advantages of negative pi-mesons for radiotherapy and give some quantitative measures of these advantages. The first and most detailed calculations include only dose contributions from primary pions and from the charged particles released in the nuclear disintegrations which occur at the end of the negative pion tracks. The physical dose calculations are based on published data on the number and energy of the charged particles from these disintegrations and on published range-energy-stopping power data for the primary pions and for the charged disintegration products. Two physical dose calculations are made, assuming (a) 29.0 MeV and (b) 35.6 MeV total kinetic energy per pion capture of the charged particles from the "stars". These calculations show that, for a monoenergetic beam having a 20 cm range, the dose at the Bragg peak is 10 to 12 times the entrance dose. Biologically effective dose distributions are calculated, both for aerobic and for anoxic conditions, using available (but uncertain) data for the dependence of (a) "relative biological effectiveness" (RBE) and (b) "oxygen enhancement ratio" (OER) on the stopping power of the medium. All calculations are repeated for two different assumptions with respect to dependence of "RBE" on stopping power. On the assumptions made, for a monoenergetic beam in the Bragg peak the effective RBE and the effective OER are approximately 1.9 and 1.65, respectively, for the lower RBE values used and about 2.5 and 1.55, respectively, for the higher RBE values. The calculations for continuous energy spectra of negative pions demonstrate the possibility of selecting a "shaped" spectrum which gives an essentially constant dose through a specified depth with a surface dose which is only 25 to 30% of this constant dose. For a spectrum chosen to give constant biologically effective dose from 12 to 20 cm depth, assuming the lower RBE values (referred to above), the effective RBE increases from about 1.35 at 12 cm to I.65 at 20 cm and the effective OER decreases from about 2.00 to 1.75 over the same depth interval. Assuming the higher RBE values, the corresponding range of effective RBE values is from 1.6 to 2.1 and the range of effective OER values I.85 to 1.65. An attempt is made to estimate corrections for the effects which were neglected in the detailed calculations, namely, (a) muon and electron contamination of the incident pion beam, (b) loss of pions from the beam by interactions with nuclei of the medium before coming to rest and (c) dose contributions from neutrons released in the "stars" at the end of the pion tracks. When these corrections are made, it is shown for a monoenergetic beam of 20 cm range that the ratio of the maximum dose in the Bragg peak to the surface dose is about 6.5 in good agreement with published experimental results. Also, it is shown that, when all corrections are taken into account, for a "shaped" spectrum which delivers a constant physical dose from 12 to 20 cm depth, about 30% of the total energy absorbed in the patient is absorbed within the constant dose region. Calculated values of RBE and OER are compared with published experimental values but the validity of the comparison is very questionable.
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