7.65 ±0.05 mm of lead. The maximum energy of the bremsstrahlung photons was calibrated using the threshold for the D(-y,n)H reaction at

Transcription

1 Am 7Roentgenolia6:ia6oia65, 1976 CENTRAL AXIS DEPTH DOSE FOR A 2.5 MV VAN DE GRAAFF GENERATOR DAVID W. ANDERSON, DAVID E. RAESIDE, REBA I. ADAMS, AND MYRON R. GOEDE 2 ABSTRACT: Central axis percentage depth dose values and isodose curves for the bremsstrahlung beam from a 2.5 MV Van de Graaff generator were measured with a water phantom at 100 cm targettosurface distance. Tissueair ratios were calculated from the central axis depth dose data. Use of the 2.5 MV percentage depth dose values are necessary for treatment planning since they are substantially larger than the values given in compilations for 2.0 MV beams. INTRODUCTION Increased output and increased percentage depth dose are two advantages to operation of a Van de Graaff bremsstrahlung generator at 2.5 MV rather than 2.0 MV. The generator used for radiation therapy at the University of Oklahoma Health Sciences Center was recently modified for 2.5 MV operation with the result that the dose rate was increased by a factor of I.8. Subsequent to the modification, measurements required for obtaining central axis percentage depth dose tables and isodose curves for a variety of fields were made. The complete tables and several of the isodose curves are presented here since they may prove useful in other institutions anticipating similar modifications. EXPERIMENTAL APPARATUS AND TECHNIQUE The generator used as the radiation source was an electrostatic electron accelerator (Van de Graaff) manufactured by High Voltage Engineering Corporation ( Burlington, Massachusetts) and operated at 2.5 MV. A tungsten transmission target 2.3 mm thick and mounted on a 1.8 mm copper backing in the end ofthe accelerator tube was used to produce the radiation beam. No field flattener was used, but additional filtration due to cooling water jacket, an exposure rate monitor, and a light field mirror was sufficient to produce a beam with a halfvalue thickness of 7.65 ±0.05 mm of lead. The maximum energy of the bremsstrahlung photons was calibrated using the threshold for the D(y,n)H reaction at MeV [I]. A sample of 25 g of heavy water was irradiated at various indicated terminal voltages with a silver sheet wrapped around the teflon sample holder. The f3 activity induced in the silver was counted after the irradiation as the mdicator of reaction yield. A linear plot of yield versus indicated voltage was easily extended to zero yield to verify threshold terminal voltage to within ± io kv. The focal spot size for the accelerator beam was measured using a device made of laminated strips of lead alternating with paper spacers in a holder i cm long with a film packet placed at the end. The first exposure was followed by a second with the lamination direction rotated through 90#{176}. The effective focal spot size was 2.5X3.0 mm on the film. Dose profile measurements for the bremsstrahlung beam were made at ioo cm targettosurface distance for a I0XI0 cm field and a 25 X 25 cm field. In separate measurements, lithium borate thermoluminescent dosimeters and later a low sensitivity nonscreen radiographic film were sandwiched between pieces of plexiglass 0.5 cm thick. Film density measurements were corrected using the characteristic curve for the film for 60Co radiation. The 1 Department of Radiological Sciences, University of Oklahoma Health Sciences Center, Oklahoma City, Oklahoma Present address: St. Francis Hospital, Tulsa, Oklahoma

2 CENTRAL AXIS DEPTH DOSE 1261 measurements both showed a narrow penumbra region at the field edges with the dose falling from 90% to 10% of the central axis value within I cm of lateral distance. A tail on the dose profile extended laterally from the field edge with relative dose less than 2% of the central axis value at 4 cm lateral distance. Since the transmission of the 7.6 cm lead collimator blocks was less than 1%, the tail must be partially attributed to scatter from the collimator block faces. Since no flattening filter was used, the dose profile was noticeably forward peaked. At central axis and laterally to within I cm of the field edge, the dose was well described by the form D(x) = D(o) exp (ax2). The variable x is defined here as the radial distance in centimeters from the central axis at the usual treatment distance. The coefficient a is the peaking parameter. A least square fit of the 2.5 MV data to this function gave the value avdg (6. ± o.8)io. This is substantially larger than the peaking parameter for our 60Co teletherapy machine obtained in a similar manner at 8o cm without trimmers. For that machine, ac0 = (.o ± o.6)io. The effects of the forward peaking on the isodose curves are discussed later. Determination of the depth necessary for electron buildup was accomplished using thermoluminescent dosimeters made of lithium borate imbedded in teflon. The dosimeters were io.o mm in diameter and only 0.1 mm thick. They were placed in a phantom consisting of plexiglass sheets of I.0 mm thickness. The arrangement for irradiation was such that no two dosimeters overlapped. Irradiation at 2.5 MV and 100 cm distance with a lox 10 cm field was chosen. The dosimeter response showed a maximum at a depth of 3.8 ±0.1 mm. Under the assumption that the depth of the dose maximum is proportional to electron range in the medium, a value of ±0. mm was calculated for the buildup depth in water [2]. Dose versus depth data were taken with a computer controlled system (Artonix, Inc., St. Louis, Missouri). A pair of ionization chambers 0.5 cm in diameter and i. cm in length with tissueequivalent walls were used. The chambers used meet the recommended standards of the ICRU [s]. Mounting rods were made of teflon. One chamber served as the beam intensity monitor and was located at the periphery of the field. The other chamber served as the underwater probe and was moved about in a plexiglass water tank with a surface area of 52 X 53 cm and a depth of 50 cm. This volume was sufficient to allow ample peripheral water even for our largest field (20 X 20 cm) and deepest measurement ( 28 cm). The water temperature was 21#{176} C (densi ty = g/cm3). Two shielded preamplifiers were used to drive the chamber signals to the electrometer located outside of the radiation room. Data points were taken as the ratio of the response of the underwater probe to that of the monitor probe to minimize the effects of fluctuating exposure rates. With the automated scan several minutes were required to acquire a full set ofdata for a given field. The true probe depths (controlled remotely) were found to be within. mm of the desired depths in all situations. The targettosurface distance for the irradiations was determined to be 100.0±0.5 cm. The effects of scattered radiation on the preamplifiers and cables were tested by placing the movable probe near the bottom of the tank and outside the field limits for a I 5 X I 5 cm field. The response was small but measurable with the beam on. A similar reading taken with a thick cylindrical lead cap over the chamber was reduced substantially. This indicated that the preamplifier and cable response due to scattered radiation was very small. The magnitude of the preamplifier and cable response during operation is estimated to be less than i% of central axis values at com

3 1262 ANDERSON ET AL. I I I I F I I I I 1041 U) 0 0 I 0 z U ,( The ion chamber response ratios ob 3( 2( I.l l t_ I IZ DEPTH FIG. I.Central axis percentage depth doses calculated from functional fit. Radius of data points indicates standard deviation. parable depths for moderate field size and depth. As an overall check on the experimental technique, several runs were made at 2.0 MV. The central axis percentage depth dose data obtained were similar to values in standard compilations [4]. The magnitude of the deviations between our raw values and the accepted values was i..% of the local dose for depths between i and 20 cm for a ioxio cm field. The data runs at 2.5 MV were then made. A total of 40 separate and complete isodose curves were obtained with i,440 individual measurements for central axis response ratios. The standard deviations for the central axis values for a single field and depth were less than i% on the average. (cm) tamed at the central axis were averaged at each depth for each field size investigated and normalized to ioo.o% at the depth of 0.45 cm to produce the percentage depth dose values P(d). To minimize subjective errors, a regression analysis technique was used to generate smooth curves from the data. When such an analysis is performed with a computer, a quantitative measure of the precision of the fit can easily be calculated as part of the program. A similar measure of the precision of the fit has rarely been given when curves are drawn by hand through raw data points. In this case, the values were fit by cornputer to a smooth curve with the form /d+ P(d) = ioo() exp [y(d a\ RESULTS where d is the depth in water, m is the depth of the maximum dose, and a, f3, and

4 CENTRAL AXIS DEPTH DOSE I 263 Fic. 2.Isodose curves for I 2 X I 2 cm and 6 X 6 cm fields. Solid lines indicate shapes measured for 2. 5 MV beam. Dashed curves indicate shapes for beam from 60Co machine at 8o cm without trimmers. Details in edgeoffield effects masked on these curves because ionization chamber used in measurement had 0.5 cm diameter. 7 are constants determined by the cornputer analysis for each field. Scattered radiation in the field at central axis is known to be a function of the areaperimeter ratio [57] defined as (zl/p)d= field area at deph d/field perimeter at depth d. Because of this, the values of a, fi, and y were fit by computer to a power series in.1/p so that all field sizes could be represented. Using the results of this procedure, the final percentage depth dose values, defined as F[d, (il/p)m], are calculable for all depths and fields. Values of this percentage depth dose are tabulated in table for common square fields. It should be noted that the depth dose values for the oxo cm field in table are the result of extrapolation to A/P=o of measurements for 5everal small fields. To check the analysis technique, the calculated values taken from the table were compared with the data for each field. The precision of the fit was indicated by the average magnitude of the difference between these quantities. For our data the average deviation was only o.8% of the local values, and the largest deviation was I.% of the local value. Thus the fitting procedure was adequate for the data obtained. Figure I shows two of the continuous central axis percentage depth dose curves plotted from the calculated ppints in table I and from the function. The experimental data points are also given on the figure for comparison. The functional form and fitting technique is shown to be adequate. Table 2 contains the values of the central axis tissueair ratios for the 2.5 MV beam. These numbers were calculated from the smooth curves for percentage depth dose. For this calculation, the following expres

5 1264 ANDERSON ET AL. TABLE I PERCENTAGE DEPTH DOSES AT 2.5 MV FIELD (CM) AND BACKSC AFTER FACTOR oxo 4X4 Xg 6X6 8X8 ioxio 12X12 Xi aoxao DEPTH (CM) I.025 i.o i o ! o o o o I #{231}o o o I o i8.o i i io NOTE.IOO cm. targettosurface distance. sion was used [8]: T[d, (A/P)d] = (TSD + d B[(A/P)] P[d, (A/P)m] \TSD+m/ ( 100 In this equation the tissueair ratio (T) is a function of depth d and the area perimeter ratio at that depth, (il/p)d. The symbol TSD denotes the targettosurface distance (Ioo cm), and m is the depth of the maximum dose. Note that the relationship between the areaperimeter ratios is /100 + d (A/P)d (A/P)m ( \I00 + m The backscatter factors B[(il/P)m] were measured with the chamber described previously. The results in tables I and 2 can be cornpared with the published results for 2.0 MV beams [4] and 60Co beams at 100 cm. Central axis percentage depth dose values at 2.5 MV are generally from 1% to #{231}% larger than those for 2.0 MV beams for most fields at substantial depths. However, the 2.5 MV percentage depth dose values generally are not as large as values for 60Co beams at 100 cm distances. Figure 2 shows isodose curves obtained for a 6 x 6 cm field and a I 2 X I 2 cm field. As expected, the 60Co curves show considerably more penumbra than the 2.5 MV curves. However, the 2.5 MV isodose lines show more forward peaking than the 60Co lines. As depth increases, the effects of penumbra and forward peaking become more difficult to distinguish, and compa

6 CENTRAL AXIS DEPTH DOSE I 265 TABLE 2 TIssuEAIR RATIOS AT 2.5 MV FIELD (CM) DEPTH(CM) oxo 4X4 6X6 8X8 I0XI0 I2XII I5X15 20X #{149} o o i6.o 27.0 x8.o o.866 o.8o o o.858 o.8o o.6o ! rable isodose lines from the two sources have similar curvature. ACKNOWLEDGMENT Our thanks to Dr. Joseph C. Giarratano for suggesting the use of heavy water in the machine energy calibration. REFERENCES I. Mattauch L, Thiele J, Wapstra A. Mass excess values. Nuci Phys 67 : 140, Pages L, Bertel E, Joifre H, Sklavenitis L: Energy loss, range, and bremsstrahlung yield for io kev to 100 MeV electrons. Atomic Data :69125, ! 0.46! o.85i o.8io ! o.6o ! o x.o6 i.oo o.88o ! International Commission on Radiation Units and Measurements: Report 23, Measurement of absorbed dose in a phantom irradiated by a single beam of x or gamma rays, 1973, p 3 4. Cohen M, Jones DEA, Green D: Central axis depth dose data for use in radiotherapy. Br 7 Radiol I I, suppl : 475 I, I Sterling TD, Perry H, Katz L: Automation of radiation treatment planning. Br 7 Radiol 37: , Wrede DE : Practical aspects of area/perimeter. Bul/Am Assoc Phys Med 6 737k, I Wrede DE: Central axis tissueair ratios as a function of area/perimeter at depth. Phys Med Biol 17:548554, Johns HE, Cunningham JR: The Physics of Radiology. Springfield, Thomas, 1969

7 This article has been cited by: 1. A. Bridier, H. Beauvais, A. Dutreix On the use of a quality index to specify high energy photon beams. Radiotherapy and Oncology 5:1, [CrossRef]