1996
Mean energy, energyrange relationships and depthscaling factors for clinical electron beams
Publication
Publication
Medical Physics , Volume 23  Issue 3 p. 361 376
Using Monte Carlo simulations we have studied the electron mean energy, Ē(o), and the most probable energy, E(o,p), at the phantom surface and their relationships with halfvalue depth, R50, and the practical range, R(p), for a variety of beams from five commercial medical accelerators with an energy range of 550 MeV. It is difficult to obtain a relation between R50 and Ē(o) for all electrons at the surface because the number of scattered lowerenergy electrons varies with the machine design. However, using only direct electrons to calculate Ē(o), there is a relationship which is in close agreement with that calculated using monoenergetic beams by Rogers and Bielajew [Med. Phys. 13, 687694 (1986)]. We show that the empirical formula E(o,p)=0.22+1.98R(p)+0.0025R(p)/2 describes accurately the relationship between R(p) and E(o,p) for clinical beams of energies from 5 to 50 MeV with an accuracy of 3%. The electron mean energy, Ē(d), is calculated as a function of depth in water as well as plastic phantoms and is compared both with the relation, Ē(d)=Ē(o)(1d/R(p)), employed in AAPM protocols and with values in the IAEA Code of Practice. The conventional relations generally overestimate Ē(d) over the entire therapeutic depth, e.g., the AAPM and IAEA overestimate Ē(d) at d(max) by up to 20% for an 18 MeV beam from a Clinac 2100C. It is also found that at all depths mean energies are 1%3% higher near the field edges than at the central axis. We calculated depthscaling factors for plastic phantoms by scaling the depth in plastics to the waterequivalent depth where the mean energies are equal. The depthscaling factor is constant with depth in a given beam but there is a small variation (<1.5%) depending on the incident beam energies. Depth scaling factors as a function of R50 in plastic or water are presented for clear polystyrene, white polystyrene and PMMA phantom materials. The calculated depthscaling factor is found to be equal to R50/(water)/R50/(plastic). This is just the AAPM definition of effective density but there are up to 2% discrepancies between our calculated values and those recommended by the AAPM and the IAEA protocols. We find that the depthscaling factors obtained by using the ratio of continuousslowingdown ranges are inaccurate and overestimate our calculated values by 1%2% in all cases. We also find that for accurate work, it is incorrect to use a simple 1/r2 correction to convert from parallel beam depthdose curves to point source depthdose curves, especially for highenergy beams.
Additional Metadata  

clinical electron beams, depthscaling factor, energyrange relations, mean electron energy, Monte Carlo  
dx.doi.org/10.1118/1.597788  
Medical Physics  
Organisation  Department of Physics 
Ding, G.X., Rogers, D.W.O, & Mackie, T.R. (1996). Mean energy, energyrange relationships and depthscaling factors for clinical electron beams. Medical Physics, 23(3), 361–376. doi:10.1118/1.597788
