A new penumbra generator for electron fields matching - UCSF ...

A new penumbra generator for electron fields matching 

B. Lachance, D. Tremblay, and J. Pouliot 

Centre Hospitalier Universitaire de Québec, Pavillon L’Hôtel-Dieu de Québec, Québec, Canada 

Received 26 February 1996; accepted for publication 23 January 1997 

Abutment of two or more electron fields to irradiate extended areas may lead to significant dose 

inhomogeneities in the junction region. This paper describes the geometric and dosimetric characteristics 

of a device developed to modify the penumbra of an electron beam and thereby improve 

the dose uniformity in the overlap region when fields are abutted. The device is a Lipowitz metal 

block placed on top of the electron applicator’s insertion plate and positioned to stop part of the 

electron beam on the side of field abutment. The air-scattered electrons beyond the block increase 

the penumbra width from about 1.4 to 2.7–3.4 cm with an SSD of 100 cm. The modified penumbra 

is broad and almost linear at all depths for the 9 and 12 MeV electron beams used in this study. 

Film dosimetry was used to obtain beam profiles and isodose distributions of single modified beams 

and matched fields of 9 and 12 MeV as well as matched fields of both energies. Computer simulation 

was used to optimize the skin gap to be used and to quantify the dose uniformity as a function 

of the field separation for both modified and nonmodified beams. Results are presented for various 

field configurations. Without the penumbra generator, lateral setup errors of 2–3 mm may introduce 

dose variations of 20% or more in the junction region. Similar setup errors cause less than 5% dose 

variations when the penumbra generator is used to match the fields. The potential of the technique 

for the irradiation of curved surfaces is presented. A possible method for implementing the modified 

penumbra into a conventional treatment planning system is evaluated. © 1997 American 

Association of Physicists in Medicine. S0094-24059701404-1 

Key words: electron beam, field matching, beam-edge modification, penumbra generator 

I. INTRODUCTION 

Treatment with megavoltage electron beams is ideal for irradiating 

shallow seated tumors because of their limited range 

in tissues. However, the treatment of extended areas with 

electrons often requires the use of two or more adjacent 

fields. In such cases, unacceptably large dose variations may 

arise at the junction of the fields. These dose variations come 

from the presence of large bulges in the low value isodose 

curves created by electron beam divergence and lateral scattering 

in tissues. Overlapping of these bulges creates a highdose 

region at depth, while the constriction of the isodose 

curves near the surface may produce a low-dose region, depending 

critically on the field separation. To overcome this 

problem, several authors have proposed techniques for 

matching electron beam edges in such a way as to make the 

overlap region as uniform as possible. The simplest approach 

to the problem is to optimize the skin gap between the two 

adjacent electron field edges. 1–3 The increased lateral scatter 

of low-energy electrons and the machine specific characteristics 

of an electron beam penumbra make the determination 

of an optimized skin gap somewhat complicated. Optimization 

is achieved by a complete set of trial and error measurements, 

and optimal gaps obtained for one treatment unit cannot 

be used with other treatment units. The main limitation to 

the usefulness of the optimized skin gap technique is the 

strong sensitivity of the dose distribution in the field junction 

region to small deviations in field separation or in the angulation 

of the incident electron beams, making it strongly dependent 

on positioning errors. 

Other field abutment techniques are based on beam-edge 

modifying devices which act to broaden the electron beam 

penumbra, and thus facilitate field matching. 1,4,5 The aim of 

beam-edge modification is to obtain an electron beam with a 

penumbra characterized by widely and evenly spaced parallel 

isodose lines at the edge of the field to be matched. Such 

parallel isodose lines produce a beam edge whose shape is 

independent of depth, with a penumbra width broad enough 

to obtain a smooth dose gradient. With two beam edges 

modified in this way, one being the mirror image of the 

other, an ideal matching can be achieved over the entire 

depth, width, and length of the overlap region. 

An excellent description of the problem of electron beam 

matching and the aims of beam-edge modification is given 

by Kalend et al., 4 who proposed a comb-shaped beam-edge 

modifier made of a low melting-point alloy. The shape, 

width, and length of the comb determined the gradient of the 

penumbra of the electron beam. Dose uniformity was 

achieved by abutting two fields, each modified by a comb. 

To eliminate ripples in profiles in the match plane at shallow 

depths, they had to use two phase-shifted complementary 

combs. Because of the precision needed in the fabrication 

and positioning of the device, this technique is difficult to 

implement clinically. 

Kurup et al. 5 proposed a method using plastic wedge penumbra 

generators. Polystyrene wedges were inserted into the 

electron beam to increase the penumbra under the thick part 

of the wedge. These electron wedges can be designed from a 

few measurements, and they were quite successful in im- 

485 Med. Phys. 24 (4), April 1997 0094-2405/97/24(4)/485/11/$10.00 © 1997 Am. Assoc. Phys. Med. 

485

486 Lachance, Tremblay, and Pouliot: New penumbra generation 486 

proving the dosimetry of the junction region; however, the 

presence of the wedges causes a slight degradation of the 

beam energy and penetration. Furthermore, the penumbra 

broadening occurs at all field edges in the thick part of the 

wedge and is not limited to the region of abutment. 

Another approach is to match electron beams without the 

secondary collimation. 6,7 Such beams have profiles close to 

Gaussian and are therefore easy to match at 50% intensity 

points to produce a homogeneous dose distribution across a 

large field. This method is successfully used by a few centers 

as an electron beam pseudoarc technique 7–11 for the treatment 

of large superficial volumes which follow curved surfaces; 

but the dosimetric gain comes at the expense of the 

setup time in the treatment room because of the necessary 

lead shielding on the patient to provide a sharp dose cutoff at 

the edges of the composite treatment field. 

In this paper, we describe a new and simple method to 

modify an electron beam to produce a wide penumbra and 

yield an excellent dose uniformity at the junction between 

adjacent electron fields. The new penumbra generator consists 

of a metal block made of Lipowitz metal and placed on 

the applicator insertion plate to stop part of the electron 

beam on the side of the field abutment. In this configuration, 

the electrons of the unblocked part of the beam have a large 

distance to be scattered in air under the block before reaching 

the patient, and with little disturbance from the electron applicator. 

The result is a wide and smooth penumbra, ideal for 

field matching. The penumbra broadening occurs only at the 

edge of abutment, while the remaining field boundaries are 

defined near the patient in the usual way with the electron 

cone. 

The objectives of this study are to present a systematic 

evaluation of modified electron field matching on a flat surface 

to better understand the behavior and physical characteristics 

of the penumbra generator, and to investigate the 

feasibility of using this technique for matching electron 

fields on curved surfaces in order to irradiate the thoracic 

region. The first objective involves obtaining a quantitative 

indicator of the dose uniformity in the junction region and 

optimizing the field separation. Because of the large amount 

of data required, we limit our discussion to the dosimetry of 

9 and 12 MeV electron beams used more frequently at our 

institution. These electron beam energies are widely documented 

for the treatment of extensive chest-wall 

recurrence. 5,6,12–14 

II. METHODS AND MATERIALS 

A. Adjacent electron beams on a flat surface 

The penumbra generator and the setup used for measurements 

are depicted in Fig. 1. The device is a Cerrobend block 

placed on top of the applicator’s insertion plate see Fig. 

1a to stop part of the electron beam on the side of the field 

abutment. Cerrobend is a trade name for Lipowitz metal: 

50% bismuth, 27% lead, 13% cadmium, and 10% tin. The 

insertion plate of the applicator and the penumbra generator 

are situated 44 cm above the surface of a phantom placed at 

the nominal source-surface distance SSD of 100 cm. The 

Medical Physics, Vol. 24, No. 4, April 1997 

FIG. 1. Experimental setup showing: a The Siemens electron applicator 

with the penumbra generator placed on the insertion plate. The measurement 

point of the distance X is indicated. SI indicates the base of the applicator 

where tertiary collimation is provided by the insertion of Shields insert 

defining the field boundaries. b The two matched fields light fields are 

pictured with the gap measured at the phantom surface. 

block is aligned parallel to the edge of the beam to be 

matched. Its relative position with respect to the center of the 

field the distance X, is defined as the distance between the 

central axis of the beam and the position of the edge of the 

light field under the block Fig. 1a. This distance is measured 

on top of the custom-made cutouts insert shields insert 

SI in Fig. 1a, which is approximately 6 cm above the 

phantom patient surface at the nominal SSD of 100 cm. 

This measurement point was chosen for convenience, and the 

corresponding distance at the surface of the phantom can be 

found from a simple scaling factor. The gap Fig. 1b between 

adjacent modified electron beams is measured between 

the light fields at the surface of the phantom patient. 

Comparative measurements were carried out to evaluate 

how the modified penumbra is affected by either varying the 

thickness of the block or accounting for beam divergence. 

Tests were performed with a 9-mm-thick block and with 20-


mm-thick blocks having either a divergent edge for various 

distance X or a straight edge. These tests showed that no 

measurable change in the modified penumbra all other parameters 

being the same is visible when using either of the 

blocks. Thus, provided that the thickness of the block is 

larger than the electron range in the material, changing the 

thickness of the block has little effect on this technique. 

Also, accounting for beam divergence would only be an additional 

complication providing no dosimetric gain. All the 

data reported here were collected with a penumbra generator 

having a straight edge and a thickness of 2 cm. According to 

transmission measurements performed by Purdy and Choi, 15 

this thickness of Cerrobend is required to attenuate the 12 

MeV open electron beam dose to the 97% level with a 

2525 cm 2 applicator. The thickness used ensures that for 

all distances X, only a weak bremsstrahlung contamination is 

transmitted through the block so that this is not of a major 

concern and that the penumbra generator provides sufficient 

attenuation to allow a simple extension of the technique to 

higher electron beam energies. 

For clinical applications, a frame made of thin aluminum 

plates is used to support the Cerrobend blocks. The size of 

the frame is sufficient to completely clear the opening in the 

insertion plate of the electron applicator. One such frame is 

used for every modified electron field. Four holes are drilled 

in the insertion plate, and the aluminum frame is screwed to 

the applicator. The penumbra generator is firmly taped in its 

appropriate position on the aluminum frame during the first 

treatment fraction. For subsequent fractions, one simply has 

to screw back in place the whole assembly consisting of the 

block taped on its aluminum support. The screw holes placed 

in the aluminum frame are 2 cm slots which provide the 

needed flexibility to obtain a perfect lateral alignment of the 

penumbra generator from day to day. 

Film dosimetry was used in this study to obtain isodose 

distributions and beam profiles at various depths in phantom. 

Ready-pack Kodak XV-2 films were placed in phantom in a 

plane parallel to the central axis of the beam. The films were 

aligned in the crossplane direction at the center of the field. 

A30cm30 cm30 cm polystyrene phantom consisting of 

2.5 cm slabs stacked together was used. The setup was designed 

to minimize the effects of potential film artifacts. The 

film jacket was punctured at each corner and the entire assembly, 

consisting of the phantom slabs and the aligned film, 

was tightly clamped together with a large carpenter clamp to 

avoid any perturbation to the dose distributions caused by air 

trapped in the film jacket. The films were kept in their jacket 

during irradiation to exclude light and Čerenkov emissions. 

The film edge facing the source was carefully aligned with 

the phantom surface. The excess wrapper extending beyond 

the film edge was folded over to one side and taped to the 

phantom. 

The sensitometric curve was obtained for each batch of 

films used in this study, and our Kodak XV-2 films showed a 

linear response to dose up to about 40 cGy. For this linear 

portion of the curve, the net optical density can be used for 

relative dose measurements without any corrections. Hence, 

unless otherwise specified, 40 monitor units MU 38 cGy 


at the depth of maximum dose in polystyrene were used to 

irradiate films, ensuring that no absolute dose larger than the 

upper limit of the linear portion of the sensitometric curve is 

recorded on film and that isodensity curves can be considered 

as isodose curves. 

All measurements were made using the 9 and 12 MeV 

electron beams from a Siemens Mevatron KD-2 linear accelerator. 

Film dosimetry was performed with a Wellhöfer dosimetry 

system WP600. Experiments were performed for 

the following clinically useful electron cones: 1010, 15 

15, and 2020 cm 2 . All the isodose distributions presented 

in this paper were obtained with the phantom surface placed 

at the nominal SSD of 100 cm. The effect of extended SSDs 

105 and 110 cm on the modified penumbra width and on 

the gaps to be used for field abutment was investigated by 

beam profile measurements performed in water with the 

scanning ionization chamber of the Wellhöfer. 

The initial data were taken by irradiating films with a 

single modified beam for various distances X and for all the 

electron cones used. Beam profiles at seven different depths 

were extracted from these films and saved in an ASCII format 

from the Wellhöfer. The depth of the saved profiles was 

chosen to uniformly cover the dose distribution down to the 

50% isodose line, thus covering the range of depths of clinical 

interest. The depths chosen were 0.8, 1,3, 1.8, 2.0, 2.7, 

3.2, and 3.6 cm for the 9 MeV electron beams and 0.8, 1.5, 

2.0, 2.5, 3.3, 3.8, and 4.5 cm for the 12 MeV beams. These 

profiles were then fed into a custom-made computer program 

which generates a mirror image of the profiles and fictitiously 

combines them with various gaps between the two 

fields. The resulting combined profiles were used to find an 

optimal gap for various distances X, for the 9 and 12 MeV 

beams, and for the three electron cones used. This procedure 

was also performed with regular electron beams for comparison 

with the results obtained for modified beams. On-line 

visualization of the composite profiles and quantification of 

the uniformity of the resulting dose distribution for different 

gaps between the fields was provided by the program. 

Bagne 2 has defined the depth dose ratio DDR to analyze 

the composite dose distribution of adjacent fields. The DDR 

is defined as the ratio of the dose at a depth d on the midseparation 

axis to the dose at the same depth on the central 

axis of a single field, 

PDD d at midseparation axis 

DDR d . 

PDD d at central axis 

The shortcoming of the DDR method of evaluating abutment 

of electron beams is that only doses along the junction line 

are evaluated. This interesting concept fails to account for 

possible hot or cold spots outside of the midseparation plane 

and there is no specification of the volume of the possible 

high or low dose regions. For these reasons, another indicator 

has been defined. In this study, the parameter chosen to 

describe the goodness of the composite dose distribution for 

a particular field separation is the average field flatness 

AFF, defined as the average value of the flatness for the 

five shallowest composite profiles generated by our custom-


made program. Here, the flatness definition used for a given 

composite profile at a depth d is the largest absolute value 

between 

maximum dose dcentral dose d 

central dose 

d 

and 

central dose dminimum dose d 

central dose , 

d 

where the central dose is the dose value at midseparation 

axis, and the maximum and minimum dose values are taken 

from within 80% of the composite field width. This AFF is a 

good indicator of the dose uniformity throughout the volume 

of clinical interest, and it also provides a good basis for 

quantitative comparison with results obtained when matching 

unmodified beams. The optimal gap for a given set of 

parameters beam energy, distance X, and electron cone size 

is the one which minimizes the AFF. 

The precision of the actual off-axis distances fed into our 

custom-made program was limited by the method used to 

identify the beam central axis position on the films irradiated 

with a single modified beam. Any misalignment with respect 

to the beam central axis was reflected in the values of optimal 

gaps obtained with our program. To account for this, 

verification films were doubly exposed with the modified 

beams matched with the field separation prescribed by the 

output of the program. Profiles extracted from these verification 

films were reproduced by our custom-made program 

with the beam profiles extracted from single modified beam 

exposures the initial data. This reconstruction of matched 

beam profiles provided the correction needed on the previously 

obtained optimal gaps. With this iterative procedure, 

we obtained a 0.5 mm precision on the optimal gaps to be 

used with a given set of conditions, namely, beam energy, 

distance X, and electron cone size. 

Isodose measurements were made by irradiating films 

with two modified beams matched with the optimal gaps. 

Results are presented for 9 and 12 MeV beams and for 

matched beams of both energies. The beam’s-eye-view composite 

dose distribution was measured for selected geometries 

to verify that this technique also works well for the 

off-axis planes. 

The output factor of the modified electron beams must be 

considered for clinical applications. Determination of the 

output factor was achieved by comparison of ionization measurements 

performed in water with a Farmer chamber 

Nuclear Enterprises, NE 2581. Readings were taken at a 

depth of d max at the center of both the modified electron 

beams and the same energy beam with the unmodified electron 

applicators. In the case of the modified beams, the center 

of the field was defined as the center of the light field at 

the phantom surface for an SSD of 100 cm. This field center 

does not correspond to the usual central axis of the open 

field. The isodose distributions for electron beams incident 

on flat surfaces presented in this paper were normalized to 


FIG. 2. Experimental setup for irradiation of the Rando phantom with three 

9 MeV modified beams. Two penumbra generators are used for the central 

field. The light fields are pictured. 

100% at the usual depth of d max for an open field and at the 

center of a single modified field defined above. 

To facilitate the clinical application of this technique, it is 

desirable to implement the generated penumbra into computerized 

treatment planning. A possible approach to this problem 

was evaluated with our commercial treatment planning 

system. THERAPLAN Plus, Theratronics International 

Limited, Kanata, Ontario, Canada. The solution proposed 

uses the ability of the system to allow beam modifiers for 

electron beams. Indeed, with Theraplan Plus, the algorithm 

used to compute electron dose distributions is almost the 

same as the one used for photon beams. Although the algorithm 

is somewhat artificial for electron beams, it provides 

good results and has the advantage of allowing beam modifiers. 

The modified penumbra is obtained simply by optimizing 

the modifier shape in order to match the measured data. 

An example of computed modified penumbra is presented 

see Fig. 10. 

B. Application to irradiation of curved surfaces 

In order to apply the technique on curved surfaces, a few 

tests were performed with an anthropomorphic phantom 

Rando phantom. A piece of film was cut in the dark room 

to conform to the shape of a Rando slice and sandwiched, 

light proof, between two slices. A few slices were then added 

on both sides of the ‘‘sandwich’’ and the whole assembly 

was tightly clamped together. A given arc along the film 

edge was chosen as a target area, and this was irradiated with 

three 9 MeV modified beams. The tests were performed with 

the 1515 cm 2 electron applicator. The technique is similar 

to the three-field wraparound technique described by 

Norris, 13 except that the dosimetry of the field junctions is 

improved by the penumbra generators. Here, the central field 

had to be modified at both edges to ensure good matching 

with the two lateral fields see Fig. 2.


FIG. 3. Electron beam profiles modified by the penumbra generator. Data are 

obtained with a 9 MeV beam and the 1515 cm 2 applicator with a distance 

X of 3 cm. 

For a given target area, the gantry angles and the field 

sizes distances X are determined in the following way. 

First, the gantry angles are chosen so that each beam covers 

its intended area without too much obliquity, so that the isodose 

curves are not excessively shifted toward the surface. 

Then, the matchline positions are chosen to minimize the 

incidence angle at the edges of abutment in order for the 

overlapping of the modified field edges evaluated for flat 

surfaces to be approximately valid. The distances X to be 

used for each beam are automatically determined once the 

gantry angles and the matchline positions are chosen, since 

all beams are kept at the nominal SSD. Successive film measurements 

performed in the Rando phantom are then used to 

empirically derive the ideal weight for the central field. 

III. RESULTS AND DISCUSSION 

A. Adjacent electron beams of the same energy: Flat 

surfaces 

Figure 3 shows a typical set of beam profiles modified by 

the penumbra generator. They are for the 9 MeV electron 

beam with the 1515 cm 2 applicator and a distance X of 3 

cm. The profiles show a penumbra which is smooth and linear 

over a broad width at all depths. Such a linear dose 

gradient around the 50% intensity point is ideal for obtaining 

a perfect match. Beam profiles measured at d max and at 

nominal SSD showed that the penumbra width measured 

between the 80% and 20% dose values was increased from 

about 1.4 to 3–3.4 cm depending on the distance X and the 

electron cone size for 9 MeV electrons. The 12 MeV penumbra 

was increased from about 1.3 to 2.7–2.9 cm under the 

same conditions. These penumbra widths are comparable to 

those obtained by Kurup et al. 5 It was found that the penumbra 

width eventually decreases past a certain distance X. This 

corresponds to the point where the edge of the shields insert 

SI on Fig. 1a begins to interfere with the air-scattered 

electrons. For both energies this effect becomes clearly observable 

at about X4, 6, and 8 cm for the 1010, 1515, 

and 2020 cm 2 applicators, respectively. The resulting con- 


FIG. 4. Electron isodose curves for beams with penumbra modified by the 

penumbra generator: a 9 MeV, 1515 cm 2 applicator and distance X3 

cm; b 12 MeV, 1515 cm 2 applicator and distance X3 cm. The arrows 

indicate the position of the light field edge at the surface of the phantom. 

striction of the low value isodose curves near the surface 

results in a degraded uniformity of the dose distribution in 

the junction region, which is reflected as an increased AFF 

for large distances X see Table I. 

Figure 4 shows isodose distributions for modified beams 

at a 9 MeV and b 12 MeV. Both distributions were obtained 

with the 1515 cm 2 applicator and a distance X of 3 

cm. The modified edges correspond in all essential respects 

to the ideal penumbra described earlier. Namely, the iso- 

FIG. 5. Electron isodose curves for adjacent fields matched using the penumbra 

generator: a both fields are 9 MeV beams with the 1010 cm 2 

applicator and distance X of 2 cm; b both fields are 12 MeV beams with 

the 1515 cm 2 applicator and distance X of 4 cm.


FIG. 6. Beam’s-eye-view composite dose distributions for adjacent fields 

matched using the penumbra generator: a both fields are 12 MeV beams 

with the 1515 cm 2 applicator and distance X of4cmdose distribution 

recorded at the depth of maximum dose of 2.5 cm; b matched fields of 9 

and 12 MeV with the 1515 cm 2 applicator and distance X of 3 cm, 40 MU 

37.2 cGy at the depth of d max in polystyrene for the 9 MeV beam and 39 

MU 36.7 cGy at the depth of d max in polystyrene for the 12 MeV beam 

dose distribution recorded at the depth of maximum dose for the 9 MeV 

beam: 2 cm. 

doses are widely and evenly spaced, and they are quite parallel 

to the beam axis. The arrows indicate the position of the 

light field at the surface of the phantom. For a given energy, 

the shape of the isodose distribution in the penumbra region 

was found to be slightly influenced by the distance X. This is 

true up to the point where the effect of the electron cone wall 

becomes important, as discussed previously. 

Examples of isodose distributions for abutted electron 

beams are presented in Fig. 5 for: a 9 MeV beams with the 

1010 cm 2 applicator and distance X of 2 cm, and b 12 

MeV beams with the 1515 cm 2 applicator and distance X 

of 4 cm. The curves indicate small less than 2% variations 

in the match region for both energies. The beam’s-eye-view 

composite dose distribution for the example presented in Fig. 

5b is shown in Fig. 6a. This dose distribution was recorded 

in a polystyrene phantom at the depth of maximum 

dose 2.5 cm. The beam’s-eye-view composite dose distribution 

shows that the technique works well for the off-axis 

planes since a good dose uniformity is achieved over the 


entire match plane. The field sizes presented in Fig. 5 could 

be obtained more simply on a flat surface by using a larger 

electron applicator with secondary shields defining the field 

boundaries near the patient’s skin. The examples of Fig. 5 

are presented to illustrate the dose uniformity achievable. In 

practice, field sizes of up to 3620 cm 2 with the 2020 

cm 2 applicator can be obtained using this technique. AFF 

values ranging from 1.7% to 5.6% for optimal field separations 

were obtained for distances X where the effect of the 

electron cone wall was not a problem. 

The optimal gaps measured see Fig. 7, and the corresponding 

calculated AFF values for various distances X are 

given in Table I. The measured output factors for the modified 

electron beams are also given in Table I. Figure 7 reveals 

that the optimal gaps mm to be used as a function of 

the distance X cm can be well approximated by linear functions. 

Only the slopes of the linear fits are needed to obtain 

the gap to be used for a given distance X. Slopes close to 1 

were obtained for the 1515 and 2020 cm 2 cones, while 

for the 1010 cm 2 cone the slopes were close to 1.5. This 

dependence of the optimal gap on the distance X is probably 

the result of the combined effect of the increased beam divergence 

under the penumbra generator for larger values of 

X and the virtual source distance being shorter than the light 

source distance the nominal source position. Because of 

this increased divergence the 50% isodose is displaced away 

from the light field edge as the distance X is made larger. 

Therefore, it is necessary to increase the field separation in 

order to match the 50% isodoses of both fields as the distance 

X is made larger. 

The above assumption is strongly supported by first-order 

trigonometric calculations. The distance measured at the 

phantom surface between the light field projection under the 

penumbra generator and the ray line emanating from the virtual 

source position was connected analytically to the actual 

distance X. This distance should correspond to half of the 

skin gap necessary to obtain an optimal dosimetric match 

with a given distance X. The virtual source position was 

measured 16 for both 9 and 12 MeV beams with the full width 

at half-maximum method. For both energies, the values obtained 

are 95 cm for large field sizes 1515 and 2020 

cm 2 and 93 cm for the 1010 cm 2 cone. Using these values, 

the ratio of the optimal gap over the distance X predicted by 

trigonometric calculations at nominal SSD are 0.092 for 

large field sizes 1515 and 2020 cm 2 and 0.134 for the 

1010 cm 2 cone. These values are well correlated with the 

ones determined experimentally Fig. 7. This geometric approach 

predicts a small dependence of optimal gap on the 

applied SSD for large virtual source distances. For example, 

with a virtual source distance of 95 cm, the ratio of the 

optimal gap over the distance X should change from 0.092 

for an SSD of 100 cm to 0.113 for an SSD of 110 cm. This 

small dependence on SSD was confirmed by modified beam 

profile measurements performed in water for extended SSDs 

105 and 110 cm. In these experiments, the measured 50% 

intensity position in the modified penumbra was compared to 

the known position of the light field projection at the phantom 

surface for various distance X. Results indicate that, for


TABLE I. Measured optimal gaps, calculated average field flatness and output factors as a function of the 

distance X. 

Distance X 

cm0.1 

Optimal gap 

mm0.5 

extended SSDs, the optimal gaps to be used are very similar 

to those presented in Fig. 7. Thus, for large virtual source 

distances, the only important effect of extended SSD is to 

further spread the modified penumbra. However, the reader 

must be aware that the dependence of optimal gap on the 

applied SSD should be more pronounced with shorter virtual 

source distances, such that the proposed technique should not 

be applied clinically without experimental verifications of 

the optimal gaps to be used. 

Experiments were performed with standard unmodified 

electron beams in order to quantify clearly the gain in dose 

uniformity provided by the use of the penumbra generator to 

match adjacent fields. The dosimetry procedure described in 

Sec. II A was applied to unmodified electron beams in order 

to see how their AFFs would compare to the ones obtained 

when using the penumbra generator. We found that for optimal 

field separations the AFFs of matched regular 9 MeV 

beams were 8.6%, 9.6%, and 12.9% for the 1010, 1515, 

and 2020 cm 2 electron cones, respectively. For the 12 MeV 

beam, these values are 9.2%, 12.3%, and 16.2%. In addition 

to providing a better dose uniformity in the junction region, 

the penumbra generator makes the dose uniformity less sensitive 

to positioning errors. This is shown for 9 MeV electron 

beams in Fig. 8, where AFF is plotted as a function of field 

separation for a typical modified beam square symbols and 

for a regular 1515 cm 2 field diamond symbols. Lateral 

setup errors at the field junction of the order of 2 mm might 

cause only about 3.5% variation in the AFF, compared to 


9 MeV 12 MeV 

AFF 

% 

Output factor 

0.002 

Optimal gap 

mm0.5 

AFF 

% 

Output factor 

0.002 

10 cm10 cm applicator 10 cm10 cm applicator 

0.0 0.5 2.49 0.869 0.5 3.57 0.904 

1.0 ••• ••• 0.923 2.0 3.02 0.945 

2.0 3.0 2.18 0.950 2.5 2.34 0.961 

3.0 4.5 4.14 0.966 4.5 3.74 0.973 

4.0 5.5 13.08 0.978 6.5 10.48 0.980 


0.0 0.0 1.80 0.953 0.5 1.85 0.970 

1.0 ••• ••• 0.971 ••• ••• 0.982 

2.0 ••• ••• 0.981 1.5 2.16 0.985 

3.0 2.0 1.92 0.986 2.5 2.53 0.988 

4.0 5.0 3.25 0.990 4.5 3.61 0.989 

5.0 5.5 4.37 0.992 5.0 4.86 0.990 

6.0 7.5 10.30 0.993 7.0 9.02 0.991 

6.5 7.0 15.79 0.993 7.0 12.80 0.991 


0.0 1.0 2.70 0.986 0.5 1.71 0.996 

1.0 ••• ••• 0.992 ••• ••• 0.998 

2.0 1.0 1.85 0.994 1.0 1.99 0.997 

3.0 2.0 2.28 0.996 2.5 2.48 0.997 

4.0 ••• ••• 0.998 3.5 2.93 0.998 

5.0 5.0 3.91 0.997 ••• ••• 0.998 

6.0 6.0 3.69 0.999 5.0 4.64 0.997 

7.0 7.0 5.19 0.998 6.0 5.59 0.997 

8.0 8.0 9.75 0.999 ••• ••• 0.996 

more than 12% in the absence of the penumbra generator. 

Results with other X values at 9 and 12 MeV are similar. 

The percent depth dose PDD at beam central axis for the 

standard electron beams and at midseparation axis for 

matched modified beams are compared in Fig. 9. Here, the 

midseparation axis is the one passing through the fields 

matchline position, as it is used in the definition of the DDR. 

The PDDs at midseparation axis are for the composite dose 

distributions presented in Fig. 5, while the PDDs at central 

axis are for the corresponding standard electron cones. The 9 

MeV curves are almost identical and the DDR values are 

close to 1 for the entire range of depths. For the 12 MeV 

curves, deviation between the central axis and midseparation 

axis PDDs is only significant very close to the surface, with 

a surface dose about 6% lower at midseparation axis. These 

examples are representative of what is obtained when matching 

modified beams at optimal field separation or with a 

lateral deviation from optimal gap of up to 3 mm. Therefore, 

neither the surface dose nor the bremsstrahlung tail are 

significantly affected by the placement of the penumbra generator 

in the field. The photon contamination is increased by 

about 1% for 9 MeV electrons, while this value is about 2% 

for 12 MeV electron beams. 

The results of using our treatment planning system to 

model the modified 9 MeV beam presented in Fig. 4a are 

shown by the dotted lines in Fig. 10. The modified penumbra 

was obtained by applying a beam modifier whose shape has 

been manually optimized to match the measured data. The


FIG. 7. Optimal gaps as a function of the distance X for the 9 and 12 MeV modified electron beams and the 1010, 1515, and 2020 cm 2 applicators. The 

straight lines are linear fits to the data. 

agreement between the measured and calculated data is 

clearly satisfactory for illustrative purposes. 

B. Adjacent electron beams of different energies: Flat 

surfaces 

Abutted fields of different energies are shown in Fig. 11. 

They are for a the 1010 cm 2 electron cone with a distance 

X of 2 cm, and b the 1515 cm 2 electron cone with a 

distance X of 3 cm. Unequal weights had to be used for the 

9 and 12 MeV modified beams to account for their different 

output factors and the slight energy dependence of the film 

response. The isodose distributions presented were normalized 

to 100% at a depth of d max 2 cmand at the center as 

defined in Sec. II A of the 9 MeV modified beam. The composite 

dose distributions present small variations 3% 

caused by the unequal penumbra width of the 9 and 12 MeV 

beams. Being slightly wider, the 9 MeV penumbra contributes 

more on the 12 MeV side than the 12 MeV penumbra 

does on the 9 MeV side. As a result, beam profiles at a depth 

of about 2 cm exhibit a hump on the 12 MeV side and a 

small hollow on the 9 MeV side. However, these variations 

are acceptably small, and the 90% and 80% isodose surfaces 

are found to be very smooth. This is further illustrated in Fig. 

6b, which shows the beam’s-eye-view composite dose dis- 


tribution for the example presented in Fig. 11b. This dose 

distribution was recorded in a polystyrene phantom at the 

depth of maximum dose for the 9 MeV electron beam 2 

cm. Therefore beams of different energies can be matched 

with good dose uniformity by using the same optical gaps 

presented in Table I. The optimal gaps found for 9 and 12 

MeV beams are equal within the experimental uncertainty 

for a given distance X. Thus, taking the optimal gap value for 

9 or 12 MeV will ensure good dose uniformity when matching 

beams of either energy. 

C. Adjacent electron beams on curved surfaces 

An example of achievable dose distributions with three 9 

MeV electron fields is presented in Fig. 12. This dose distribution 

was obtained in the Rando phantom with the following 

field parameters: Field A refer to Fig. 11 is an AP field 

0° gantry angle with a distance X of 2.8 cm, field B has a 

gantry angle of 39° and distances X of 2.35 cm on field A 

and field C sides, field C has a gantry angle of 78° and a 

distance X of 0.65 cm. All fields were positioned at nominal 

SSD and the monitor units used were: 40, 32, and 40 for 

fields A, B, and C, respectively. These number of monitor 

units correspond to doses at d max and at the center of each 

field as defined in Sec. II A of 39.4, 24.3, and 38.6 cGy,


FIG. 8. Average field flatness AFF as a function of field separation for 

adjacent electron beams: squares are for 9 MeV beams modified by the 

penumbra generator, with the 1515 cm 2 applicator and a distance X of 4 

cm; diamonds are for standard unmodified 9 MeV beams with the 1515 

cm 2 applicator. 

respectively. The dose distribution presented in Fig. 12 was 

normalized to 100% at the depth of maximum dose along the 

beam central axis of the central field. The skin gaps used are 

simple averages of the optimal gaps Table I obtained previously 

on flat surfaces for the different distances X to be 

matched. The curves indicate no important variations near 

the field junctions. The dose in the central field region is 

slightly higher about 2%, but the uniformity of the dose 

distribution in the whole target volume is excellent. The iso- 

FIG. 9. Percent depth doses PDDs at beam central axis for the standard 

electron beams and at midseparation axis for matched modified beams. The 

PDDs at midseparation axis are for 9 MeV beams with the 1010 cm 2 

applicator and distance X of2cmopen circles; and for 12 MeV beams 

with the 1515 cm 2 applicator and distance X of4cmdiamonds. PDDs at 

central axis are for the 9 MeV beam with the standard 1010 cm 2 electron 

applicator dashed curve; and for the 12 MeV beam with the standard 

1515 cm 2 electron applicator solid curve. 


FIG. 10. An enlargement of the modified penumbra of Fig. 4a for the 9 

MeV beam with a distance X of 3 cm. The dashed lines represent computer 

calculations obtained with our treatment planning system. 

doses smoothly follow the phantom surface and the 90% and 

80% isodose curves uniformly cover the selected target area. 

Such uniform distributions should be obtainable for a wide 

range of curvatures and target volumes with appropriate positioning 

of the fields and adequate selection of the beam 

weights. 

In the example presented in Fig. 12 a relatively small 

central field was used. In this case, an important part of the 

dose imparted in the central field region is contributed by the 

modified field edges of the two lateral fields. This contribu- 

FIG. 11. Electron isodose curves for adjacent fields matched using the penumbra 

generator. Both distributions are for matched fields of 9 and 12 MeV 

with: a the 1010 cm 2 electron applicator and distance X of 2 cm, 40 MU 

36 cGy at the depth of d max in polystyrene for the 9 MeV beam and 38 MU 

35.1 cGy at the depth of d max in polystyrene for the 12 MeV beam; b the 

1515 cm 2 applicator and distance X of 3 cm, 40 MU 37.2 cGy at the 

depth of d max in polystyrene for the 9 MeV beam and 39 MU 36.7 cGy at 

the depth of d max in polystyrene for the 12 MeV beam.


FIG. 12. An experimental isodose distribution obtained in the Rando phantom. 

The three fields used are indicated and the arrows indicate the field 

junctions. The tick marks on the beam central axis lines indicate the centimeter 

scale. See the text for experimental details. 

tion from the lateral fields has to be quantified clearly in 

order to correctly choose the weight to be used for the central 

field. Excellent dose distributions can be obtained by trial 

and error, but the problem of the central field weight will 

require further investigations. 

In these experiments, the rationale for using a small central 

field was to minimize the angle of incidence at the abutting 

field edges and to prevent large additional air gaps produced 

by the extended SSD. When the radius of curvature is 

not too small in the central field region, another approach 

would be to use a larger central field, thus minimizing the 

problem associated with the contribution from the lateral 

fields. In this case, the central field weight would no longer 

be a problem since only the output factor of the modified 

beam is needed. This will have to be further investigated to 

come up with a systematic approach for curved surfaces irradiation. 

A detailed study of the changes in the modified 

penumbra under oblique incidence will be required. 

For the tests performed with the Rando phantom we successfully 

used the same optimal gaps Table I obtained previously 

on flat surfaces for the different distances X to be 

matched. The technique is quite insensitive to lateral setup 

precision and using the skin gaps obtained by experiments 

with flat surfaces was found to provide adequate dose uniformity 

in the junction regions when matching fields on 

curved surfaces. This tends to confirm the slight dependence 

of optimal gap on SSD discussed previously. 

The tests described in Sec. II B and the example presented 

above were designed to tackle the somewhat complicated 

clinical situations involving large arc angles and necessitating 

the use of multiple fields. However, even with a two 

field technique, the penumbra generator can find interesting 

applications when the curvature of the region to be treated 

prohibits the use of a single field. In such clinical situations, 

the technique can be implemented in a relatively straightforward 

manner since there is no problem related to the beam 


weights. The first step is to establish the fields needed to 

obtain a good dosimetric coverage of the intended target 

area, based on the principles described in Sec. II B. Once the 

fields are chosen, the output factor of each modified beam is 

measured with both the custom-made cutout and the penumbra 

generator in place. Finally, the skin gaps to be used can 

be verified or established by measurements in phantom. A 

refined implementation of the modified penumbra into the 

treatment planning system will allow one to easily tackle a 

wider range of clinical situations without the need for measurements 

in phantom. 

This technique has the advantage that the percent depth 

dose characteristics of the resulting composite dose distribution 

are essentially the same as that for the standard beam of 

the same energy incident on a flat phantom. This allows for 

an easy manual treatment planning and dose prescription 

procedure. Also, the field boundaries can be defined in the 

simple usual way with secondary shields custom-made cutouts 

inserted into the standard electron cone near the patient’s 

skin at SI on Fig. 1a, while the field matching zone 

is defined by the penumbra generator. No lead shielding on 

the patient is necessary. When using the penumbra generator 

with shields, the intended dosimetric junction line position 

must be chosen such that the shape of the composite treatment 

field in the junction region allows a complementary 

matching of both modified field edges throughout the volume 

of the junction. Also, the cutouts must be opened wide at the 

field junctions beyond the dosimetric junction line to avoid 

interference with the air-scattered electrons under the block. 

The penumbra generator technique is limited to a single 

slice optimization. However, the dose dependence on longitudinal 

variations in SSD is less critical with this approach 

since it basically uses regular stationary fields than with 

electron arc. Thus, the technique proposed could prove to be 

an interesting alternative for a wide range of clinical situations, 

even though it is clear that electron arc is still the 

method of choice to treat large superficial volumes which 

follow curved surfaces. 

IV. SUMMARY 

A new approach for the modification of an electron beam 

penumbra to improve field abutment has been presented. 

Beam-edge modification by means of a low melting point 

alloy block placed on the electron applicator’s insertion plate 

was found to yield a beam penumbra sufficiently wide and 

linear to ensure good dose uniformity at the field junction. 

The dose distribution in the junction region was shown to be 

much less sensitive to positioning errors then when regular 

fields are matched. Since the device acts mainly by complete 

absorption of part of the electron beam, it modifies the beam 

without degrading its energy. Clinical application demonstrated 

that the technique is easy to implement and can be 

introduced into the daily routine of a radiotherapy department. 

Furthermore, the device is simple and inexpensive, and 

no special measurement is needed for its design. The block 

has simply to be of a thickness larger than the maximum


electron range in the material, and its length and width have 

to be correctly chosen to cover the part of the beam to be 

blocked. 

A wide range of field sizes can be obtained with the existing 

square electron applicators by varying the distances X 

used. This provides the needed flexibility to irradiate different 

target areas. Furthermore, the technique was shown to be 

useful for matching electron beams of different energy. 

These two characteristics can prove to be useful when faced 

with a target volume of a complicated shape. 

The potential of the technique for the irradiation of curved 

surfaces was presented. It is universally accepted that the 

modality of choice for treatment of large superficial tumors 

which follow curved surfaces is the electron arc. Unfortunately, 

this technique is complex and time consuming in 

planning, and not all the centers can implement it. The technique 

proposed here could prove to be a simple and acceptable 

alternative to electron arcs for chest-wall and other 

curved surfaces irradiation when the off-central axis contours 

do not differ too much from the central axis contour such 

that the target volumes can be approximated by cylindrical 

geometries. 

ACKNOWLEDGMENT 

We would like to thank Ervin B. Podgorsak of the Department 

of Medical Physics, McGill University, Montreal 

General Hospital, for his constructive input and discussions. 

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