Medwal Dosimctrl'. Vol. 17, pp. 207-21 I

0739-021 I/92 $6.00 + .00 ('opyrighl ~ 1903 American Association of Medical Dosimetrists

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DOSIMETRY

USING

OF

SHAPED

A RADIAL

ELECTRON

INTEGRATION

FIELDS

METHOD

R. M U L L E R - R U N K E L , P H . D . Saint Margaret Mercy Health Care Centers, North Campus, Oncology Center, 5454 Hohman Avenue, Hammond, IN 46320, U.S.A. Abstract--The feasibility of an analytical approach to calculate monitor units for shaped electron fields is investigated. A radial integration method is used to calculate the dose at prescription depth from an average output factor and an average depth dose. This concept, as implemented in a commercial planning system, has been tested on various arbitrary fields, and 66 shaped electron fields clinically used for head and neck, chestwall, internal mammary, breast boost, and skin lesions. The measured and prescribed doses agreed within 3.5% or better for 71% of all clinical fields tested; for 91% the agreement was 5.5% or better. The greatest discrepancy (-7.2%) was found for a narrow, long internal mammary field. All treatments were administered on a linear accelerator with electron energies between 6 and 20 MEV. Key Words: Electron dosimetry, Shaped electron fields, Dose verification.

INTRODUCTION

M A T E R I A L S AND M E T H O D S

Individually shaped electron fields are obtained by fabricating 1 cm thick cerrobend inserts, which are placed either inside the electron cone or mounted on a tray that rests on trimmer bars. I A shaped insert may alter the output as well as the penetration of an electron beam. Traditionally, the altered output at the depth of dose maximum (dmax) is measured, and the monitor units (MU) are adjusted accordingly. The treatment dose is often prescribed to the 90% or 85% isodose line, measured for the open cone. The electron energy is chosen such that the t u m o r (or target) depth falls within the prescribed isodose. Only when the target depth determines the energy as well as the prescription isodose can a precise minimum target dose be achieved. Not always are altered percent depth doses (%DD) measured for each individual insert. For small shaped electron fields this can lead to a significant underdose of the target volume, easily exceeding 10%. 2 These uncertainties in target dose have often been tacitly accepted. It is time consuming to measure all required parameters for each individual cutout, and an analytical approach is desirable. Some analytic methods for the dosimetry of shaped electron fields have been developed in the past, 3'4'5 the most common being the pencil beam algorithm. The integration method evaluated here was developed by Jones et al. 6 for accelerators that employ cones. It corrects for altered output as well as changed depth dose for the individually shaped insert.

The dose per MU to a point in tissue (Dp) is calculated according to eqn ( 1) as the product of the dose per MU for the open cone (Do) at reference depth, an inverse square factor (VSD = virtual source distance, s = distance to calibration plane, d = depth in tissue), an average tissue depth ratio (TXR) and an average output or cutout factor (CF). Dp = D o ×

VSD ]2 VSD + s + d ×~

[CF]r,

~ [TXg]r, × i=1

(1)

i=1

The TXRs are calculated, as described below, from measured %DD data in an analogous way as TPRs for photons. They are a function of energy, field size, and depth in tissue. The CF is defined as the ratio of ionization measured with and without the field shaping insert in place. 6 It is a function of energy, cone size, shape of insert, and source to surface distance (SSD). The average T X R and CF are calculated in 10degree steps: the T X R as a function of radii (q), around the field perimeter, the CF as a function of radii and c o n e size. 6 These values are interpolated from a library of measured input data, which is described in more detail below. This algorithm is implemented in the ADAC RTP planning system (software version 3A l) in its program CUTOUT.* * ADAC Laboratories,Milpitas, CA.

207

208

Medical Dosimetry

Volume17, Number 4, 1992

Table I. Measured and prescribed doses for non-standard SSDs

Energy depth

SSD

98

1.012

1.000

0.998

-0..2%

6 MEV 1.2 crn

100 102 105 I I0

1.006 1.003 0.998 0.988

0.981 0.983 0.965 0.950

1.026 0.986 1.030 1.038

+2.6% - 1.4% +3.0% +3.8%

98 100 102 105 I 10

1.006 1.014 1.002 1.005

1.000 0.990 0.987 0.983 0.976

0.986 1.010 1.001 1.016 1.011

1.000

1.017 1.013 1.010 1.000

9 MEV 2.0 cm

12 MEV 2.5cm

16 MEV 2.5 cm

20 MEV 2.0 cm

98 100 102

Measured Calculat,ed Dose Measured/ CF CF Dose Calculat.ed

0.984

105

1.017 1.013 1.009 1.000

110

0.992

98 100 102 105

1.021 1.009 1.008 0.991

110

0.993

1.000 1,000

98 100 102 105 110

1.026 1.013 1.012 0.997 0,991

1.000 1.000 1.000 1.000 1.000

Patient treatments were administered on a linear accelerator (Varian CL-1800),* which provides electron beams of nominal energies from 6 to 20 MeV. Five cones are available for square fields between 6 and 25 cm side length. All measurements were performed with a Markus parallel plate ionchamber in an electron solid water phantom (RMI 457). The AAPM TG 21 protocol was used to calculate doses from measured ionizationfl For this purpose, solid water was considered equivalent to real water) ,9 As input data, percent depth doses, virtual source distances, and cutout factors are required. Percent depth doses were measured for each electron cone and energy. For the smallest, the 6 × 6 cm cone, %DD were also measured with the 4 x 4 c m insert and an insert that had a central circular cutout of 2.5 cm diameter. Virtual source distances for each

t Varian Associates, Inc., Palo Alto, CA.

1.000 1.000 1.000 I.O00 1,000 1.000 1.000

A%

- 1.4%

+ 1.0% +0.1% + 1.6% + I.I% + 1.7% + 1.3%

+ 1.0% ±0% -0.8%

0.992 1.007 0.999 0.997 0.990 0.985

+0,7% -0.1% -0.3%

1.006 1.003 1.000 0.984

+0.6% +0.3% ±0% -1.6%

0.985

-I .5%

- 1.0% -I.5%

field were calculated from ionization measurements at 100 and 110 cm nominal SSD. T X R s were then calculated from the measured %DDs according to eqn (2). I,'SD + d ]2

TXR = - ~

~_ dooJ ×

%DD 10---0

(2)

For each energy, dmax for the larger cones (15 × 15 cm and beyond) was chosen as reference depth (do, listed in the first column of Table 1). The assumption is made that T X R s for square fields are the same as for circular fields inscribed in the square. 6 Cutout factors were measured with two inserts (6 and 2.5 cm diameter) for each cone at four different distances from the isocenter (IC): 3 cm above IC, at IC, and at 5 and 10 cm below 1C. For this purpose, the surface of the Markus chamber was placed at the respective distance under a slab of 5 m m solid water, as recommended. 6

Dosimetry of shaped electron fields• R. MULLER-RUNKEL RESULTS

209

cones. %DDs were therefore compared for a circular cutout of 6 cm diameter in a 6 × 6 and a 25 x 25 cm cone. For 6 MEV, the depth doses agree well over the entire range. For 20 MEV, they agree within 3% or better up to the depth of the 80% depth dose, i.e., over the range of therapeutic interest. It should be noted that a 6 cm circular cutout in a 25 × 25 cm cone is unlikely to be encountered clinically. It was used here as an extreme test case.

To study the applicability of eqn (I), systematic checks were performed first to test each of its components. Subsequently, 66 shaped electron fields, used clinically on consecutive patients, were evaluated. The systematic checks included the following:

Nonstandard SSDs. With a circular cutout of 10 cm diameter in the 15 x 15 cm cone (65% blocking), doses were measured for each energy at the respective reference depth, for nominal SSDs of 98, 100, 102, 105, and 110 cm, (Table 1). Except for 6 MEV, measured and calculated doses agree within better than 2% for all SSDs. For 6 MEV, a discrepancy of 3.8% was measured at 110 cm SSD. The inverse square factor corrects for output variation but not for variation in depth dose with increased SSD. As expected, this is most notable at low energies and large SSDs.

Cutout factors .fop" elongated fields. Inserts were produced for the 20 x 20 cm cone with cutouts measuring 2 x 16, 5 X 16, 10 x 16and 15 x 16cm. Dose measurements were performed, for each energy at reference depth, with the p h a n t o m at 100 cm SSD. Except for the smallest cutout (2 x 16 cm) and medium energies (9 and 12 MEV), agreement between measured and calculated dose is better than 3.5% (Table 2). For the smallest cutout, the percentage underdose is also listed, i f M U s calculated for the open cone were

%DDfor arbitrao, cutouts. Equation (1) will assign the same T X R to identical cutouts in different

Table 2. Measured and prescribed doses for elongated fields. ~%

A% w/MU I open cone

0,987 1.034 1.009 1.000 0.997

- 13% +3.4% +0.9% +0% -0.3%

- 13.4%

0.903 1.009 1.003 0.996 1.003

-9.7% +0.9% +0.3% -0.4% +0.3%

-I 7.3%

0.913 I.Ol I 1.024 1.018

-8.7% +I.1% I +2.3%

-14.3%

Energy I Cutout IMeasured Calculaled Dose Measured/I

depth 6 MEV 1.2 cm

9 MEV 2.0 cm

12 MEV 2.5crn

CF

CF

Dose Calculated

2 x 16 5 x 16 I0 x 16 15 x 16 20 x 20

0.853 1.009 1.0I0 1.006 1.000

0.862 0.963 0.989 0,996 1.000

2 x 16 5 x 16 I0 x 16 I5 x 16 20 x 20

0.822 1.003 1.001 1.010 I.O00

0.904 0,978 0.994 0.998 1.000

I

2x16 0.853 1 0.939 J 5 x 16 1.002 I 0.998 IOxI6 I 1.015 j I.O00

15x 16 1 1.009 I I.OOO ] 20 x 20 J 1.000 1 1.000 I 16 MEV 2.5 cm

20 MEV 2.0cm

1.003

+1.7% +0.3~

I I 1.000 I 1.000 I I.O00 I

0.967 1.010 1.020 1.015 1.002

-3.3% + 1.0% +2.0%

t 0.995 1.000 I

0.998 1.021

-0.2% +2.0%

I

1.000

1.023

+2.3%

1.013 1 1.000

1.014

+1.4%

1.001

+0.I%

2 x 16 5 x 16 lOx 16 ISx 16 20 x 20

0933 1.008 1.018 1.012 1,000

2x16 5 x I6 I0 x 16

0.992

15x16 20 x 20

1.000

1.019 1.022

0.968 1.000

1.000

I 1

-6.5%

+ 1.4% +0.2%

-0.7%

210

Medical Dosimetry

used. There is a clear improvement with eqn (1) over the open cone calculation.

Clinical fields. 66 shaped electron fields were used clinically for treatment of chestwall and ribs ( 12 cases), internal m a m m a r y (4), breast boost (18), head and neck (13) and skin lesions (19). Field sizes and shapes varied widely; fields used for skin lesions were as small as 1.8 cm in diameter. Doses were prescribed to a target depth as determined by tomography or ultrasound. All measurements were made at the depth of dose prescription and at the clinically used SSD. Figures 1 and 2 demonstrate the overall improvement in agreement between measured and prescribed doses for the 66 patients studied: when MUs are calculated with eqn (1) (Fig. 1), the measured and prescribed doses agreed within 3.5% or better for 71% of all clinical fields. For 91% the agreement was 5.5% or

Volume 17, Number 4, 1992

better. The greatest discrepancy (-7.2%) was found for a narrow, long internal m a m m a r y field. Had monitor units been calculated for the open cone (Fig. 2), 20% of all patients would have received underdoses in excess of 10% of the prescribed dose. CONCLUSION The integration method evaluated here proved particularly useful for very small fields, but should be used with some judgment for narrow, elongated fields in large cones. Other analytic approaches 3"4'5 claim comparable accuracy. However, reports of verification with clinically used fields are scarce. The a m o u n t of initial input data required is considerable (6 energies, 7 field sizes, 4 distances). However, like any initial calibration, this is a one-time effort that is rewarded in the daily routine when the

CUTOUT C a l c u l a t i o n 15--

I0

m m o L

m

E Z

(measured dose / p r e s c r i b e d

dose

-

1) x 100

Fig. I. Agreement between prescribed and measured doses for 66 patients. MUs calculated with eqn (1).

Dosimetry of shaped electron fields • R. MULLER-RUNKEL

211

Open Cone C a l c u l a t i o n 10

ul (n

5

~J lira Q t_ (g ,Q

E

4

Z

(measured

dose / prescribed

dose

-

1) x i0 0

Fig. 2. A g r e e m e n t between prescribed a n d m e a s u r e d doses ~ r 66 patients. M U s calculated ~ r open cone.

shape of the cutout is digitized and MUs are calculated by the computer without further requirement of accelerator time. REFERENCES I. Muller-Runkel, R.; Ovadia, J.; Borger, F.; Culbert, H.; Rohowsky, B.; A shaping device for irregular electron fields for the Therac 20 accelerator. Med. Phys. 12:90-92; 1985. 2. Niroomand-Rad, A.; Film dosimetry of small elongated electron beams for treatment planning. Med. Phys. 16:655-662: 1989. 3. Choi, M.C., Prasad, S.C.: Purdy, J.A.: Electron-beam irregular field dose computations using concepts of scatter-phantom-ratio. Med. Ph)'s. 6:334, Abstract C6; 1979. 4. Mills, M.D., Hogstrom, K.R.: Fields, R.S.; Determination of

electron beam output factors for a 20 MeV linear accelerator. Med Phys. 12:473-476; 1985. 5. Van de Geijn, J.: Chin, B.: Pochobradsky. J., Miller, R.W.; A new model for computerized clinical electron dosimetry. Med. Ph)'s. 14:577-584; 1987. 6. Jones, D.; Andre, P.; Washington, J.T.: Hafermann, M.D.; A method for the assessment of the output of irregularly shaped electron fields. B.J.R. 63:59-64; 1990. 7. AAPM Radiation Therapy Committee Task Group 21. Protocol for the determination of absorbed dose from high energy proton and electron beams. Med. Phys. 10:741-771 ; 1983. 8. Constantinou, C. Comparison of solid water, polystyrene and acrylic plastic for photon and electron beam calculations. Med. Ph)'s. 13:580, Abstract FI9: 1986. 9. Khan, F. et al. Clinical electron-beam dosimetry: Report of AAPM Radiation Therapy Committee Task Group No. 25. Med. Phys. 18:73-109: 1991.