Introduction to passive electron intensity modulation

Abstract This work introduces a new technology for electron intensity modulation, which uses small area island blocks within the collimating aperture and small area island apertures in the collimating insert. Due to multiple Coulomb scattering, electrons contribute dose under island blocks and lateral to island apertures. By selecting appropriate lateral positions and diameters of a set of island blocks and island apertures, for example, a hexagonal grid with variable diameter circular island blocks, intensity modulated beams can be produced for appropriate air gaps between the intensity modulator (position of collimating insert) and the patient. Such a passive radiotherapy intensity modulator for electrons (PRIME) is analogous to using physical attenuators (metal compensators) for intensity modulated x‐ray therapy (IMXT). For hexagonal spacing, the relationship between block (aperture) separation (r) and diameter (d) and the local intensity reduction factor (IRF) is discussed. The PRIME principle is illustrated using pencil beam calculations for select beam geometries in water with half beams modulated by 70%–95% and for one head and neck field of a patient treated with bolus electron conformal therapy. Proof of principle is further illustrated by showing agreement between measurement and calculation for a prototype PRIME. Potential utilization of PRIME for bolus electron conformal therapy, segmented‐field electron conformal therapy, modulated electron radiation therapy, and variable surface geometries is discussed. Further research and development of technology for the various applications is discussed. In summary, this paper introduces a practical, new technology for electron intensity modulation in the clinic, demonstrates proof of principle, discusses potential clinical applications, and suggests areas of further research and development.

intensity modulation for electron therapy is not widely available. This paper will describe a passive radiotherapy intensity modulator for electrons (PRIME) capable of creating IM electron fields.
Three types of electron conformal therapy (ECT) either require or could benefit from intensity modulated fields: segmented-field ECT, bolus ECT, and modulated electron radiation therapy (MERT). 7 Heretofore, investigators in these areas envisioned that electron intensity modulation would become available using multileaf collimators (MLCs), similar to x-ray MLCs used to deliver intensity modulated x-ray therapy (IMXT). However, the air gap of x-ray MLCs is too great for their utilization, preventing adequate conformity. 8 Some envisioned intensity modulation using scanned electron beams, 9 which requires helium in the treatment head to reduce multiple Coulomb scattering (MCS), as air produces spot beams that are too broad. 10 This led to work on electron MLC (eMLC) designs by Hogstrom et al., 11 Gauer et al., 12,13 and others, which resulted in a commercially available eMLC provided by a third party (Euromechanics, Schwarzenbruck, Germany; see http://english.euromechanic s.de/electron-multileaf-collimator-emlc/). However, this technology has not resulted in widely available electron IM, possibly due to the high cost of an add-on eMLC, low fraction of electron patients, lack of its ability to deploy/retract, need for its integration into commercially available treatment planning systems (TPS), and other reasons.
The purpose of the present paper is to introduce the potential for utilization of an alternative method, passive electron intensity modulation, which we believe can be practical for many clinical applications. It is a potentially low-cost, readily available technology that parallels the use of physical attenuators (metal compensators) for early IMXT,14 prior to availability of x-ray MLCs. 15 The present paper will discuss the concept of passive intensity modulators, areas of potential clinical applications, various research and development topics to be pursued, and initial work for making the technology clinically available.

2.A | Concept of passive intensity modulators
The passive radiotherapy intensity modulator for electrons (PRIME) is a device, which when inserted into a therapeutic electron beam, delivers an electron fluence (intensity) distribution that varies (modulates) with position in the plane perpendicular to central beam axis. PRIME consists of a collection of (a) small area island blocks in a plane located inside or just upstream of the aperture of a collimating insert, (b) small area island apertures in a collimating insert, or (c) a combination of both. The locations in the plane and the areas of the island blocks and island apertures are selected to deliver a desired intensity-modulated electron fluence distribution.
As an example, Fig. 1(a) illustrates a collection of circular island blocks of varying diameter located on a hexagonal grid inside the aperture of a custom electron collimating insert. Figure 1 F I G . 1. Illustration of types of PRIME devices located inside or just upstream of electron collimating insert. (a) island blocks (dark gray circles) inside collimating aperture (black dashed curve) for 50% ≤ I (x,y) ≤ 100%; (b) island apertures (light gray circles) inside virtual collimating aperture (black dashed curve) for 0% ≤ I(x,y) ≤ 50%; (c) Island blocks (dark gray circles) and island apertures (light gray circles) inside electron collimating aperture. Treatment field (black dashed curve) is composed of both actual aperture with island blocks and virtual aperture in collimating insert with island apertures. I(x,y) is the modulated relative electron intensity at off-axis position (x,y). collimating insert. Figure 1(c) illustrates a combination of the two.
The island blocks and island apertures, shown located on a hexagonal grid in Fig. 1, can be located in any spatial pattern that achieves the desired intensity pattern. Their cross-sectional area can be circular, square, hexagonal, or other shape, although circular shape has the smallest ratio of side surface area to incident area, which should minimize the undesirable effect of MCS electrons escaping the collimating material of the island blocks or island apertures. The thickness of the high-density island block and the thickness of the collimating insert containing the island apertures should be sufficient to stop primary electrons.
Never before has multiple island blocks or island apertures been used to provide electron intensity modulation. Previously, single circular island blocks have been used to protect the lens of the eye, located approximately 0.7 cm under the eye surface, while treating the underlying retina to approximately 70% of "given" dose. 16,17 Also, saw-toothed collimator edges have been used to broaden the penumbra (80%-20%) to match the penumbra of abutting electron fields of differing energies. 18 Although both applications are similarly based on principles of MCS, neither used multiple island blocks to generate an electron beam with full field intensity modulation.

2.A.1 | Intensity modulation 50%-100%
The island block removes most, ideally all, electrons incident on its entry surface from the beam. Figure 2 illustrates for a parallel beam where I o is the intensity with no island blocks. This formula allows an estimate of the block diameter at each point on a hexagonal grid to be calculated based on the desired underlying intensity, where IRF = I desired /I 0 is the desired underlying intensity reduction factor. Because each island block impacts multiple locally desired intensities due to MCS of the electrons, an optimizer based on an inverse planning algorithm is required to determine an optimal intensity modulator design. This should be a function for the treatment planning system.

2.A.2. | Intensity modulation 0%-50%
In this case, more than half of a local area of the field is blocked, for which the same principles as above apply, but for small island apertures in the collimating insert, as opposed to small island blocks within the aperture of the collimating insert.
In the central region of the beam, the relative electron fluence (intensity) in water (1-cm depth) located 1 cm and 8 cm behind a single, small island aperture equals the subtraction kernels shown in Fig. 2; without the island block aperture no electron intensity is transmitted. Again, as the distance between the island apertures and the plane of calculation increases, the resulting electron fluence distribution broadens due to MCS of electrons, as discussed earlier.
In Fig. 4, a half beam of island apertures (0.5 cm diameter) located on a hexagonal grid and separated by 1.5 cm is shown.
The resulting profiles shows an increasing intensity at the edge (x = 0), and away from the edge, the intensity equals the fraction of the beam unblocked by the island apertures (10, 20, and 30%).
By properly selecting the size and the separation of the island apertures within the local area, the desired intensity can be achieved locally. For example, for hexagonally packed circular island apertures of diameter d and separation r, the local intensity is given by The formula allows an estimate of the aperture diameter at each point on a hexagonal grid to be calculated based on the desired underlying intensity, Because each island aperture impacts multiple locally desired intensities due to MCS of the electrons, an optimizer based on an inverse planning algorithm is required to determine an optimal intensity modulator design, and again this should be a function for the treatment planning system. Furthermore, since the primary application of island apertures for producing intensities in the range 0%-50% might be for MERT, for which intensities vary 0%-100%, island blocks would likely be used in conjunction with island apertures.

2.B | Range of island block parameters (d,r) for range of intensity reduction factors
Knowledge of the useful range of sizes (cross-sectional area) for island blocks and island apertures is desirable. Island blocks of circular cross-section packed in a hexagonal grid should be useful for intensity modulated bolus ECT, where IRFs in the range of 0.70 to 1.00 are expected. 19 As IRF depends on (d/r) in Eqs. (1) and (2)

2.C | Construction of intensity modulators
Methods for the construction of intensity modulators are presently under development. This section discusses construction specifications and a prototype, fabricated to illustrate proof of principle.

2.C.1 | Construction constraints
Optimally, the intensity modulator will be small cross-section island The island apertures will be the same thickness (g cm À2 ) as the custom electron insert, usually sufficient to stop electrons from the highest beam energy (20 MeV). It is recommended that the island blocks be the same thickness so as to be able to be used at all electron energies. The collimating material should be a high density metal, possibly the same or similar material as the custom electron inserts. Presently, most inserts are fabricated using low melting point lead alloy (Cerrrobend) 22 or copper. 23 Tungsten alloy is another potential material for the island blocks, its being denser, harder, and less toxic than lead, all advantages for a block material.

2.C.3 | Patient example
Kudchadker et al. 19 showed how IM improved planning target volume (PTV) dose homogeneity for bolus ECT of a head and neck patient (right buccal mucosa). We used the reported intensity distribution for that patient to design an intensity modulator, which closely provided the desired IM dose distribution at a depth of 2 cm in water. Details of the design process for the intensity modulator 20 remain under investigation and will be reported later, but preliminary results for this patient are shown.      postmastectomy chest wall, [26][27][28] head and neck, 29,30 and extremities, 31 and on the.decimal web site.

3.C | Example design of intensity modulator for buccal mucosa patient
One area of improvement for bolus ECT is that the bolus, which rests on the patient surface, has an irregular upstream surface designed to conform the therapeutic dose surface (e.g., 90%) to the distal PTV surface. This irregular surface produces hot/cold spots, increasing dose spread in the PTV from 10% (90%-100%) to as much as 30%. Kudchadker et al. 19 showed that IM bolus ECT can restore the dose spread to 10%-12%. Preliminary investigation by Chambers 20 showed how IM composed of variable-diameter island blocks spaced on a hexagonal grid can provide the needed electron beam intensity modulation.

4.A.4 | Variable surface
It is well known that irregular variations in the patient surface can create hot/cold spots due to MCS and that angled incidence can

4.B | Potential future research and development
Planning and delivery tools necessary for clinical uses of PRIME provide multiple opportunities for research and development. These include, but are not limited to:

| SUMMARY
This paper introduces for the first time a new, potentially practical method for using inexpensive, passive intensity modulators for intensity modulated electron therapy. The passive radiotherapy intensity modulator for electrons (PRIME) consists of a set of island blocks and island apertures appropriately sized and spaced to create the desired intensity pattern. PRIME functions on the premise that diameter and spacing of island blocks and island apertures can be selected so that MCS fills in dose behind island blocks and between island apertures such that locally there is an intensity reduction related to the fraction of beam blocked.
Applications of intensity modulators for multiple forms of modulated electron therapy 7 were discussed. The present authors are focusing on its application to bolus ECT, an existing clinically available technology. The relationship between block diameter and separation of cylindrical blocks on a hexagonal grid was illustrated for bolus ECT, and subsequent publications will report more details of these results. Proof of principle was illustrated by comparing PBA calculated with measured dose for a prototype IM and by designing an IM for a head and neck patient previously treated with bolus ECT.