Water equivalent thickness values of materials used in beams of protons, helium, carbon and iron ions

Abstract

Heavy charged particle beam radiotherapy for cancer is of increasing interest because it delivers a highly conformal radiation dose to the target volume. Accurate knowledge of the range of a heavy charged particle beam after it penetrates a patient's body or other materials in the beam line is very important and is usually stated in terms of the water equivalent thickness (WET). However, methods of calculating WET for heavy charged particle beams are lacking. Our objective was to test several simple analytical formulas previously developed for proton beams for their ability to calculate WET values for materials exposed to beams of protons, helium, carbon and iron ions. Experimentally measured heavy charged particle beam ranges and WET values from an iterative numerical method were compared with the WET values calculated by the analytical formulas. In most cases, the deviations were within 1 mm. We conclude that the analytical formulas originally developed for proton beams can also be used to calculate WET values for helium, carbon and iron ion beams with good accuracy.

Figure 1

(a) Schematic diagram of the fixed horizontal proton beam line configuration at the MPRI (Courtesy of Indiana University Cyclotron Facility). (b) Experimental apparatus at the end of the proton beam line at the MPRI for measuring the WET of one material (a lung substitute plastic slab).

Figure 2

Maximum deviations, ΔR_max, in WET values calculated by the analytical formulas relative to that given by the NM for (a) lead, (b) aluminum and (c) PMMA. The thicknesses of materials used were 1.5 cm lead, 2 cm aluminum and 10 cm PMMA for helium ions; 1.2 cm lead, 1.5 cm aluminum and 10 cm PMMA for carbon ions; 0.1 cm lead, 0.2 cm aluminum and 0.3 cm PMMA for iron ions.