A statistical investigation of the scaling factor method of beta-ray dose distribution derivation: The scaling factor for water to bone
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Reliable methods of estimating doses are essential for the use of beta emitting radionuclides for radiotherapy. The passage of electrons through matter is a very complex phenomenon due to the large number of elastic and inelastic interactions resulting in scattering and energy losses. The analytical solution for the electron transport being intractable, the problem has been addressed by the Monte Carlo technique. Empirical or semiempirical less time consuming methods, such as the scaling factor method, may appear more preferable in practice when dealing with complicated source distributions. The method, proposed by Cross and co-workers [AECL Report Nos. AECL-1617 (1982), AECL 10521 (1992)] consists in the derivation of beta-ray dose distribution in other media from those in water by using a "scaling factor" or "relative attenuation factor" on distance and a closely related renormalization factor imposed by the energy conservation. This work investigates the accuracy of the scaling factor method using a statistical approach, a generalized chi 2 test, focusing on the particular case of potential interest, the scaling factor for water to bone. The direct comparison of the shapes of the depth dose deposition curves in the two media indicates discrepancies of less than 5% up to at least 60% of the range in bone, a depth within which 95% of the initial energy is deposited. The scaling factor derived by this method, 0.9720 +/- 0.0012, confirms the existing experimentally determined value of 0.973 +/- 1% [AECL Report No. AECL-10521 (1992)]. The accuracy of the determination is increased by almost a factor of 10. A way of improving the scaling method, especially for depth over the 60% continuous slowing down approximation range, by using a modulation function is also proposed.
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