**Introduction**

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The Elekta linac includes a single flattening filter in the path of the 6 MV beam, to balance the effect on the beam profile from the strongly forward-peaked photon fluence produced by bremsstrahlung in the target. Previous authors have reported that Elekta flattening filters have been made from iron [1,2] or an alloy of iron [3].

The process of setting up an accurate model of the Elekta 6 MV flattening filter using BEAMnrc is simple and straightforward, but must be informed and careful. The composition of the iron-alloy needs to be known and defined in the model. The shape of the flattening filter deviates subtly from a simple cone and modelling all of the deviations accurately requires a number of ‘layers’ to be defined in the component module [4]. The flattening filter is held in place, through all movements of the linac gantry, by a supporting bracket, the geometry and composition of which must also be included in any fully-detailed model.

It is therefore interesting (if not important) to examine the possibility of using a simpler model of the flattening filter, to see whether the complex material, the various layers and the supporting bracket are all required to produce dosimetrically accurate results.

In this work, the model flattening filter is replaced with iron and with air, to show the respective effects of slightly altering its composition and removing it altogether. For comparison, model flattening filters composed of aluminium, copper and lead are also simulated, to show the effects of simulating this component using very different materials.

The geometry of the virtual flattening filter is simplified, firstly, by removing its peripheral components, which lie outside the final, collimated path of the beam. The radii of the model flattening filters simulated are

Rfilter/Rfield=1.03, 0.84, 0.71, 0.69,

where Rfield is the maximum radius of a 40cm x 40cm field (Rfield=28.28cm) and Rfilter is the model flattening filter radius, projected to the isocentre. The flattening filter is also modeled without its supporting bracket.

Secondly, the geometry of the virtual flattening filter is simplifed by reducing the number of layers with which it is modelled. Representations of the simplified flattening filter geometries modeled here are shown in Figure 1.

Finally, we simplify the process of designing the model flattening filter by not using the maximum precision obtainable from manufacturer’s specifications and, rather, simulating the flattening filter with all of its radii rounded first to whole centimetres and then to whole milimetres.

*Figure 1:**Schematic cross-section of flattening filter, three simplified models. (Not to scale.)*

**Results:**

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*Figure 2: (a) Lateral profiles and (b) energy spectra at exit plane, for flattening filter made, to the same design, from various materials. Lateral profiles are normalised to the detailed-model dose on the CAX and are generated at 8.5 cm depth. The ‘population’ in the each energy spectrum is as defined for Figure 1 here. Solid lines are detailed model linac data; crosses are for linac without flattening filter; diamonds are for linac with Al flattening filter; squares are for linac with Fe flattening filter; triangles are for linac with Cu flattening filter; and circles are for linac with Pb flattening filter. (Some data points omitted for clarity.)*

Figure 2 illustrates the results of constructing the flattening filter from iron, rather than a complex iron-alloy, and shows that this simplification of a vital linac component produces very little alteration of the resulting dose or energy spectrum. Figure 2 also shows the results of modelling the flattening filter as made from various other elements and indicates that radically changing the composition of the flattening filter markedly alters the profile of the resulting flattened beam.

*Figure 3: Lateral profiles for flattening filter with various widths, lateral normalised to the detailed-model dose on the CAX and generated at 8.5 cm depth. If R/Rfield denotes ratio of radius of flattening filter to maximum field radius at base of flattening filter, for a 40cm x 4cm at z=100cm: solid lines are detailed model linac data; diamonds are for linac with detailed flattening filter, without support bracket; triangles are for R/Rfield=1.03; crosses are for R/Rfield=0.84; stars are for R/Rfield=0.71; and plus signs are for R/Rfield=0.69. (Some data points omitted for clarity.)*

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A simplification of the model that has a negligible effect on the results is the removal of the support structure that attaches to the flattening filter at its perimeter. Figure 3 shows how the the absence of those components of the flattening filter located outside the final, collimated field have a negligible effect on the resulting dose, while narrowing the flattening filter so that its radius is less than Rfield detrimentally effects the flatness of the resulting field.

*Figure 4: Lateral profiles for flattening filter modelled (a) with various shapes and (b) to various degrees of precision. Profiles are normalised to the detailed-model dose on the CAX and are generated at 8.5 cm depth. In (a): solid line is detailed model linac data; diamonds are for flattening filter with two layers; squares are for flattening filter with three layers; and triangles are for flattening filter with four layers. In (b): solid line is detailed model linac data; crosses are for flattening filter modeled to nearest milimetre; and squares are for flattening filter modeled to nearest centimetre. (Some data points omitted for clarity.)*

Reducing the number of conical sections (layers) which make up the model flattening filter (as shown in Figure 1) produces the results shown in Figure 4(a). Evidently, simulating the flattening filter in just two layers is insufficient. Even four layers are inadequate to model this component. Figure 4(b) illustrates the difference between simulating the flattening filter to the maximum precision obtainable from manufacturer’s specifications and simulating the flattening filter with all of its radii rounded first to whole centimetres and then to whole milimetres.

**References**

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**1. C. Ongaro, A. Zanini, U. Nastasi, J. Rodenas, G. Ottaviano, C. Manfredotti, “Analysis of photoneutron spectra produced in medical accelerators”, Phys. Med. Biol. 45, L55-L61 (2000)**

**2. C. Ongaro, J. Rodenas, A. Leon, J. Perez, A. Zanini, K. Burn, “Monte Carlo simulation and experimental evaluation of photoneutron spectra produced in medical linear accelerators”, in 1999 Particle Accelerator Conference Proceedings (New York, 1999), pp. 2531-2533**

3. G. Giannini, “Photon neutron radiotherapy”, in Calor 2004, International Conference on Calorimetry in High Energy Physics, Proceedings (Perugia, 2004)

4. D. W. O. Rogers, B. Walters, I. Kawrakow, BEAMnrc Users Manual (Ionising Radiation Standards, National Research Council of Canada, (Ottawa, 2004)

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