Useful island block geometries of a passive intensity modulator used for intensity‐modulated bolus electron conformal therapy

Abstract Purpose This project determined the range of island block geometric configurations useful for the clinical utilization of intensity‐modulated bolus electron conformal therapy (IM‐BECT). Methods Multiple half‐beam island block geometries were studied for seven electron energies 7‐20 MeV at 100 and 103 cm source‐to‐surface distance (SSD). We studied relative fluence distributions at 0.5 cm and 2.0 cm depths in water, resulting in 28 unique beam conditions. For each beam condition, we studied intensity reduction factor (IRF) values of 0.70, 0.75, 0.80, 0.85, 0.90, and 0.95, and hexagonal packing separations for the island blocks of 0.50, 0.75, 1.00, 1.25, and 1.50 cm, that is, 30 unique IM configurations and 840 unique beam‐IM combinations. A combination was deemed acceptable if the average intensity downstream of the intensity modulator agreed within 2% of that intended and the variation in fluence was less than ±2%. Results For 100 cm SSD, and for 0.5 cm depth, results showed that beam energies above 13 MeV did not exhibit sufficient scatter to produce clinically acceptable fluence (intensity) distributions for all IRF values (0.70–0.95). In particular, 20 MeV fluence distributions were unacceptable for any values, and acceptable 16 MeV fluence distributions were limited to a minimum IRF of 0.85. For the 2.0 cm depth, beam energies up to and including 20 MeV had acceptable fluence distributions. For 103 cm SSD and for 0.5 cm and 2.0 cm depths, results showed that all beam energies (7–20 MeV) had clinically acceptable fluence distributions for all IRF values (0.70–0.95). In general, the more clinically likely 103 cm SSD had acceptable fluence distributions with larger separations (r), which allow larger block diameters. Conclusion The geometric operating range of island block separations and IRF values (block diameters) producing clinically appropriate IM electron beams has been determined.

Conclusion: The geometric operating range of island block separations and IRF values (block diameters) producing clinically appropriate IM electron beams has been determined.

| INTRODUCTION
Electron beam therapy has been a standard modality in radiation treatment for over 60 years. Electron beams with energies between 6 and 20 MeV (R 90 = 1.8-6.0 cm) are characterized by high surface dose, relatively uniform dose plateau, sharp distal dose fall off, and low exit x-ray dose. These characteristics have allowed superficial cancers within 6 cm of surface to be treated while minimizing dose to underlying critical structures. 1 Historically, electrons have been the modality of choice for (1) the treatment of skin, lip, and head and neck tumors, (2) boost doses to superficial lymph nodes, and (3) post-mastectomy chest wall irradiation. [2][3][4][5] Electron therapy planning often utilizes a single beam of energy just sufficient for R 90 of the electron beam to exceed maximum planning target volume (PTV) depth. However, delivery is often complicated by internal heterogeneities, irregular patient surface, and variable depth of the distal PTV surface resulting in needless overdosing of distal structures, in which case some form of electron conformal therapy (ECT) is desirable. 6 The goals of electron conformal therapy are to conform the distal 90% dose surface to the distal surface of the PTV, provide a homogeneous or prescribed heterogeneous dose to the PTV, and maximize dose sparing of critical structures deep to the PTV. 6 One of three methods described by Hogstrom et al. 6 is Bolus ECT, which uses a single energy electron beam to deliver a dose distribution that conforms the 90% dose surface to the distal surface of the PTV. This is accomplished by using variable-thickness bolus, a nearly water-equivalent material which is placed on the patient surface.
Algorithms for bolus design were first created by Low et al. 7  Bolus ECT has been used for multiple sites, which include posterior chest wall 8,13,14 ; post-mastectomy chest wall [14][15][16][17] ; ear, parotid, and buccal mucosa, 14,18 nose, 19 and extremities (hand and foot). 8 The irregular upstream bolus surface can often cause undesirable dose heterogeneities in the PTV. However, it was shown by Kudchadker et al. 14 that the introduction of modest intensity modulation (70%-100%) across the beam can significantly reduce PTV heterogeneity for some patients.
Initially, delivery of intensity modulation was envisioned using eMLCs, such as those reported by Hogstrom et al. 20 and Gauer et al. 21 ; however, access to said devices by the typical clinic has not been forthcoming. As an alternative, Hogstrom et al. 22 reported a passive method for electron intensity modulation, which consists of a matrix of variable small-diameter, high-density island blocks, as shown in Fig Hence, there are an infinite number of potential configurations for a single d/r ratio. Making d too small has the undesired effects of   in a hexagonal array with separation r and block diameter d. A schematic of one such block matrix is shown in Fig. 3. Plots of relative fluence vs x position at y = 0 were generated. Each intensity modulator was assumed to be located in the 20 × 20 cm 2 block aperture, that is, 95 cm SCD.  is, the distance required to modify the intensity. Fig. 4 illustrates these three metrics. These data are also useful for estimating the maximum island block separation for a given patient IM-BECT geometry, which allows the fewest number of island blocks and the largest island block diameters, minimizing cost and effect of electron scatter into T A B L E 2 Metrics summary for 10 MeV at 103 cm source-to-surface distance (SSD) at y = 0 cm 20 × 20 cm 2 half-modulated field for z = 0.5 cm (middle columns) and z = 2.0 cm (right columns). Resulting plots are exemplified in Fig. 11 for the highest three energies (13,16,and 20 MeV

3.D | Evaluation of d T
Though d T had no formal pass/fail limit, for clinical use, the smallest d T is preferred because it is a measure of how rapidly intensity could be modulated. Table 4 summarizes d T values for a representative subset of all studied geometries at 103 cm SSD. From these results, it can be concluded that d T trends smaller for higher energy, smaller SSD, shallower depth, just as penumbra widths at beam edges trend.
Also, d T trends smaller for IRF values closer to 1.0, simply a result of a gradient changing less over a shorter distance.
Distance of transition monotonically decreased with energy, following an approximately 1/E dependence, similar to that of σ θx . This is illustrated by Fig. 12, which plots results at z = 0.5 and 2.0 cm for T A B L E 3 Metrics summary for 16 MeV at 103 cm source-to-surface distance (SSD) at y = 0 cm 20 × 20 cm 2 half-modulated field for z = 0.5 cm (middle columns) and z = 2.0 cm (right columns).   T A B L E 5 Range of intensity reduction factors (IRF ≥ 0.70) of half-beam intensity modulators (cf Fig. 3) that meet acceptability criteria (ΔI R ≤ 4%) at 100 cm source-to-surface distance (SSD) and depths in water of z = 0.5 cm (top) and z = 2.0 cm (bottom).

| SUMMARY AND CONCLUSION
The objective of this study was to determine combinations of block diameter and hexagonal grid separation, which could be used to produce clinically acceptable intensity distributions for IM-BECT, while minimizing ΔI R and d T . A pencil beam algorithm was used to calcu- Results showed that (1) the average intensity agreed with the intended intensity within 0.001 as long as ΔI R was within a clinically acceptable range (≤0.04) and (2) ΔI R was clinically acceptable in limited regions of E, SSD, r, IRF, and z space. For example, the use of 20 MeV beams was precluded at 100 cm SSD and shallow depth (z = 0.5 cm), and the 16 MeV beam was limited to cases with IRF ≥ 0.85. However, using a more clinical 103 cm SSD, ΔI R was acceptable for all energies (7-20 MeV) and depths (z = 0.5 and 2.0 cm).
Also, the data provided plots for specific conditions from which the maximum island block separation (r max ) could be extracted.
Although selecting solutions with the largest block separation (r) and thus the largest diameter blocks may have some fabrication and block scatter advantages, this comes with the disadvantage of slightly increased distance of transition (d T ), which could limit the gradient of sharply varying intensity-modulating patterns. If necessary, these competing effects can be properly balanced in the planning process, which will depend on the wide range of data computed for this study.
We conclude that these data are useful in determining island block hexagonal separation and hence island block diameters required to produce electron beam intensity modulators for individual patients receiving IM-BECT.