- Email: [email protected]
10 MV X-ray beam characteristics from a new 18 MeV linear accelerator
inr. I. Radiation
Oncology
Bid.
Phyr.,
1976. Vol.
1. pp. 705-712.
Permmon
Press.
Printed
in the U.S.A.
10 MV X-RAY BEAM CHARACTERISTICS FROM A NEW 18 MeV LINEAR ACCELERATOR WILLIAM
G. CONNOR, Ph.D., JOHN A. HICKS, Ph.D.,
MAX L. M. BOONE, M.D.,
Ph.D.,
ERIC G. MAYER, M.D.
and ROBERT C. MILLER, M.D. Division of Radiation Oncology, University of Arizona, Medical Center, Tucson, AZ 85724, U.S.A.
Thedoaimelic properth of interest in a megavoltage th~rrpy X-my beam are per cent deptb dose, skin sparhg, penumbra, radiation field flatness and symmetry. The10 MV X-ray beam fromtheVPrian~stesCllnnc18LinearAealcrrrtorisetlldkdwfth~tothesepdnts. Theprimarypofntsofiu&restareaSO%depthdosefora10x10at?fieldat18.0cminwater sod a depth of maximum dose of 2.4 20.1 cm in water. TransmkrslonmeasuremeDtsin alumiaum and lead yielded 50% transmission thkkaesses of 73.2 and 13.4 mm respectively. The flatness of the fields are parametrized as function of 6ehl size and depth. Decrement line plots are graphed and isodose curves for selected field sizes are presented. 1OMV X-ray beam, Do&metric properties, Measuremeat teclmiqwS.
INTRODUCTION The first Varian Associates 18 MeV linear
densitometer. Figure 1 shows the Central Axis (CAX) depth dose measurements obtained with accelerator (CL-l@ was installed in the the three measurement techniques. One can see University of Arizona Medical Center during that the ion chamber and diode measurements March-May 1974. The CL-18 is a klystron are identical within experimental error. The powered standing wave linear accelerator iso- data obtained from film density measurements centrically mounted with a target to isocenter are in agreement to a depth of 20 cm and then the distance of 100 cm. Operational characteristics CAXcurvesstarttochange.TheRP/Vfilmhasa will be described in a subsequent publication. A non-linear characteristic curve over the density 10 MeV electron beam bends through a 270” region of interest.* This film system was thus bendingmagnet before impinging on the target eliminated for use with the 10 MV X-ray beam. to produce X-rays. The purpose of this report is To further check the diode measurements to describe the characteristics of the 10MV against ionization chamber data, beam profles X-ray beam produced by the CL-18. were obtained with the ionization chamber and the diode for both a 10 x 1Ocm’ and a MEASUREMENT TJKHNIQUES 30 x 30 cm2 field size in a water phontom. This Three measurement techniques were used to data is illustrated in Fig. 2. One can again see the measure the central axis (CAX) depth dose very close agreement between the two measurecharacteristics for a 10 x 10 cm’ field size at a ment techniques. There are slight differences in target-to-surface distance (TSD) of IOOcm. the penumbra shoulders at the edges of the First, ionization chamber measurements made fields. These ditferences are probably due with a 0.27 cm3PTW ion chamber from Nuclear primarily to the superior spatial resoluti0n Associates and a Keithley Model 615 digital characteristics of the diode. There could be an electrometer. Second, solid state semi- energy dependenceeff ect involved although the conductor diode measurements were made with diode and ion-chambers do not differ with beam a SHM Automatic Isodose Plotter system and quality as a function of depth in water along the fmally, fdm density measurements were made central axis. This question requires further with a Kodak RP/V 6lm and the SHM investigation but in any event, these considetia705
706
Radiation Oncology 0 Biology ??Physics
/
o-‘.,
, , / , , ,
I
,
,
,
1
I,
1976, Vol. 1, Number 7 and Number 8
I,,
,
I,,
I,,
i
,
,
I
I
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Fig. 1. Central axis depth dose measurements using a 10 x 10 cm’ field and a target to skin distance of 100cm. ?? , Ionization chamber in water; 0, film density; ?? , solid state diode in water. e---
-
Dlodo Ion Chmmbu
I
II I I
a
I I
II 18
16
14
12
10
a
6
4
2 0 2 4 Dletmm OH C&al Axis (cm)
8
8
10
12
14
14
12
in water for 10 x 10 cm’ and a 30 X 30 cm’ fields with a target to skin distance of 100 cm. -, Ionization chamber: ---, solid state diode.
Fig. 2. Beam profiles measured at d,
tions indicate that either measurement technique may be used. The data presented below are thus ah ionization chamber measurements except for the illustrative isodose curves which were generated by a RAD-8 treatment planning system from data measured with the semiconductor diode.
BEAM
QUALITY
Transmission measurements were made in “good”4 geometry with 2.54cm squares of aluminum and lead. The plates were stacked on the accessory tray holder of the accelerator at 42 cm from isocenter. Measurements were normalized to the measured transmission
10 MVX-raybeamcharacteristicsfromanew
18 MeVlinearaccelerator 0 W. G.
through the wire screen accessory holder. The detector used was a 0.2 cm3 Farmer chamber with a Keithley Model 615 digital electrometer and a polarizing voltage of 425 V. The Farmer detector was inserted into a fitted cavity in a polystyrene block with the center of the chamber at 2.5 cm from the surface of the block. The effect of backscatter from the polystyrene phantom below the detector and the 1 cm of masonite supporting the phantom upon the measurement was assumed to be insignificant. The radiation field was 2.5 X 2.5 cm at isocenter and was defined by the collimator on the accelerator. The thickness and density of each of the aluminum and lead plates were individually determined and transmission was plotted against the cumulative thickness determined from the individual measurements as shown in Fig. 3. The lead plates were cut from rolled sheets and thickness varied from 1.70 to 1.65 mm. A density of 11.3 g/cm3 agreed within 2% of measured densities. We believe the variation in measures densities were due to the variation in thickness and uneven cutting of the squares. The thicknesses were averages of three measurements in the central 1.5 cm square region of the sheets. The measurements show a 50% transmission for 13.4 + 0.2 mm of lead. The calculated mass attenuation coefficient has a gradual downward slope from 2 to 13 mm of lead. The relative transmission and mass attenuation
.3J
: 10
. : 30 20 TN+krrm (mm)
‘03
Fig. 3. Relative transmission (-) and Mass Attenuation coellicients (-----) measured in: 0, aluminum; 0, lead. The measurements were made with “good” geometry.
CONNOR et al.
101
coefficients are shown in Fig. 3. The extrapolated zero thickness mass attenuation coefficient for lead as determined from a least squares fit to a straight line of the measured attenuation coefficient for each added sheet of lead was 0.0472 -e 0.0009 cm2/g. Densities for the aluminum plates were within one per cent of 2.70 g/cm3. Thickness of the plates were all 0.320 cm & 0.001 cm. The 80% attenuation thickness was 23.3 mm of aluminum. The 50% attenuation was 73.2 mm extrapolated from data taken from 3 to 35 mm. The mass attenuation coefficient showed a downward slope as a function of total thickness and extrapolated to 0.0366 f. 0.0005 cm’lg for zero thickness of aluminum. The energy value for a monochromatic photon with an absorption coefficient of 0.0472 cm2/g in lead is double valued and is 1.8 MeV on 8.4 MeV.3’ The energy corresponding to an absorption coefficient of 0.0366 cm2/g in aluminum is single valued at 2.80 -t 0.08 MeV?’ Thus, the effective energy of this X-ray beam is 1.8 MeV in lead and 2.8 MeV in aluminum. The difference in effective energy between these materials is due to their atomic structure and the particular X-my spectrum being investigated. Using the value of 18.0 cm for a 50% transmission through water, one can calculate an effective mass absorption coefficient of 0.0385 cm2/g which indicates that the effective energy of the X-ray beam in aluminum is probably close to the effective energy for tissue. BUILD-UP REGION Details of the build-up region are illustrated in Fig. 4. Build up of ionization was measured using a pancake chamber with a separation of 1 mm between the front face and the collecting electrode and a 1 cm circular collecting area. Sheets of polystyrene of density 1.06 g/cm3 and an average thickness of 0.165 g/cm2 were used for build up material. The surface of the topmost sheet was maintained at isocenter. A polarizing voltage of 130 V was used. The average of charges collected for both polarities was plotted as a function of the amount of added polystyrene. The data show an ionization of lO-15% of the
Radiation Chcoloey ??Biology 0 Physics
708
1976, Vol. 1, Number 7 and Number 8
for water was 2.4g/cm2. The per cent depth dose curve goes through a broad maximum and is essentially at 100% at 2.0 cm and remains at 100% until at least 2.6 cm and these d, values are in the central portion of this range. DEPTH DOSE CEAR4CTElUSTICS Fii 5 illustrates the change in the depth .2 .4 .S d 1012i4tS1l)20222426 dose characteristics of the X-ray beam for orpm(gn/d -)4 X 4 cm2, 10 X 10cm2 and 30 x 30cm2 field Fig. 4. Per cent depth dose as a function of depth in sizes. These measurements were made with a the build-up region for a: ?? . 6 x 6cm*; 0, 10 x TSD of 100 cm. From this figure, one can see lOcm’, old ion, A,, new ion chamber); 0, 30 x that the per cent depth dose increases with 30 cm’. field size after depths of 3.5 cm. This is also maximum for field sizes of 6 x 6cm’ and apparent for depths of less than 3.5 cm in Fig. 10 x 10cm2andof 3O%ofthemaximumfora 4. Maximum ionization was obtained at a field size of 30 X 30 cm2 with no build up depth of 2.0 f 0.1 cm and our per cent depth material on the chamber. The 50% points are dose values are normalized to this depth for at 0.28 g/cm’, 0.24 g/cm2 and 0.11 g/cm2 for routine calculational purposes. The 50% ionfield sizes of 6 x 6 cm2, 10 x 10 cm2 and 30 x ization depth in the 10 x 10 cm2 field was 18.0 & 0.1 cm. Table 1 lists the per cent depth 30 cm2 respectively. dose as a function of depth for field sizes from The 90% points are at 1.08g/cm2, 1.00g/cm’ and 0.74g/cm2. Build up curves made for a 4 x 4 to 30 x 30 cm2. Figure 6 illustrates the 10 x 10 field with water as the build up mater- increase of dose per monitor unit at 2.5 cm ial with the exception of a 0.161 g/cm2 thick- depth as a function of fieid size. The field size ness of polystyrene as the iirst added layer of dependence is normalized to 1.0 for a 10 x build up shows a 50% depth of 0.25 g/cm2 and a 10 cm2 field at a TSD of 100cm. The relative dose builds rapidly from 0.85 for 2 x 2 cm2 to 90% depth of 0.95 g/cm’. 1.0 for the 10 x 10 cm2 and then gradually to Dose at the depth of dose maximum (d_) for polystryene was 2.1 g/cm2 -C0.1 g/cm2 and 1.08 for the 32 x 32 cm* field.
Ilt
Table 1. Per cent depth dose as a function of depth for field sizes from 4 x 4 cm2 to 32 X 32 cm2 Field size Depth (cm) 2 4 6 8 10 12 14 16 ;: 22 24 26 28 30
8x8
10X10
14x14
18x18
22x22
26X26 30x30
100 100 94.3 94.4 85.0 86.0 78.7 79.0 69.0 71.5 62.4 64.9 57.1 58.6 52.0 53.1 48.0 42.0 46.3 43.7
100 94.4 87.1 79.2 72.3 66.1 60.2 54.7 45.0 50.1
100 94.9 87.8 80.4 73.5 67.6 61.9 56.7 47.0 51.6
100 95.3 88.0 81.4 74.5 68.2 63.4 57.8 48.3 52.3
loo 95.5 88.5 82.4 75.8 69.0 64.1 58.8 49.6 54.2
100 95.5 88.5 82.5 75.9 69.8 64.7 59.2 50.5 54.3
100 95.5 88.8 82.6 76.4 70.9 65.1 59.6 51.0 55.7
39.7 36.0 32.8 29.6 27.2
40.9 37.1 34.2 30.9 28.3
42.5 39.3 35.4 32.2 29.3
44.1 40.5 36.9 33.8 30.9
45.2 41.2 37.7 34.6 32.1
45.7 42.0 38.6 35.3 32.7
46.9 44.8 41.0 37.6 34.6
4X4
37.6 34.0 30.5 28.7 25.6
10 MVX-raybeamcharacteristicsfromanew
Fig. 5. Central
18 MeVlinearaccelerator
0 W. G.
axis depth dose-measurements for a: ?? , 4 x 4 cm*; 30 x 30 cm*:fieldwithaTSD = 100 cm.
as a Fig. 6. Relative dose per monitor unit at d, function of field size normalizd to a 10 x 1Ocm’ field. TSD = 100 cm.
FIELD FLATNESS AND SYMMETRY Symmetry and flatness measurements were made from beam profiles obtained at 2.5 cm and 10 cm depths. Profiles for 5 x 5, 10 x 10, 15 X 15, 20 x 20 and 35 x 35 cm2 fields obtained with a TSD of 100 cm are shown in Fig. 7. One can see that the symmetry of the X-ray beam is adequate. When utilizing a bent electron beam to produce the X-rays, a major concern is the symmetry and stability of the symmetry of the treatment beam. A drift of up to 5% over a period of time can be seen in asymmetry although it can be adjusted to less than 1% asymmetry at any given time. The profiles vary 6% or less over 90% of beam
CONNOR et al.
?? , 10 x
709
10 cm2; A,
width (within 6% over 80% of the field area) for the various field sizes at a depth of 10 cm. The increase in relative dose at the edge of large fields (35 x 35 cm2) is 6% measured at the depth of dose maximum. From the data in Fig. 6, one can also appreciate the sharpness of the beam definition. Table 2 describes field flatness as a function of depth for various field sizes. The parameters user are the per cent deviations of the maximum or minimums on a profile from the central axis value within 90% of the geometric beam width, according to Chan et al.’ The beam penumbra is small, dropping from an intensity of 90% to 20% in 4mmatd, for the 35 x 35 cm2 field. At a depth of 14.5 cm the distance over which the intensity falls from 90 to 20% increases to 8mm. Decrement line data for various field sizes are’shown in Fig. 8. The graph illustrates how the radiation field conforms to a geometrically perfect field. The radiation field is collimated such that the 50% point on the intensity proflle at a given depth is on the geometrical edge of the field. This implies that the intensity profile is normalized to 100% at the CAX for each depth. One can see from Fig. 8 that the radiation field comes very close to meeting this condition. The projected 50% decremant line for a 35 x 35 cm’ field to a depth of 16.0 mm misses the geometrical edge by ap-
Radiation Oncology ??Biology 0 Physics
710
1976, Vol. I, Number 7 and Number 8
Fig. 7. Beam profiles measured at d, 10 x lo,15
and at a depth of 10cm for field sizes of 5 x 5, x 15.20 x 20 and 35 x 35 cm’, with a TSD = 100 cm.
iIlamc+CAxtoKpointsatd0pm)
-
Fig. 8. Decrement lines as a function of depth for 5 X 5, 10 x 10. 15 X 15, 25 X 25 and 35 x 35 cm2 fields: a, 20% decrement lines; 0, 50% decrement line; A, 90% decrement lines. 0, represent the geometrical points for zero and 16 cm depth.
3 mm, representing the largest error. The closeness of the decrement lines for the various percentages is another measure of the penumbra and can be seen to be excellent. proximately
ISODOSE CURVES
Representative isodose curves for the X-ray beam shown in Figs. 9 and 10, for field sizes of
30 x 30 cm* 5 X 5 cm2, 10 x 10 cm’ and respectively. These isodose curves were generated by our Rad-8 treatment planning systern after data acquisition with a solid state diode. The beam characteristics described above can be appreciated from evaluation of these curves. The penetrability (CAX) of the beam, the sharpness of the penumbra and the flatness of the beam at depth are illustrated.
10 MV X-ray beam characteristics from a new 18 MeV linear accelerator 0 W. G. CONNOR et al.
% 28bth
(cm)
Fig. 9. Isodose curves for a 5 x 5 cm2 and 10 X 10 cm’ fields obtained in water with a diode and a TSD = 100 cm.
Fig. 10. Isodose
curve
for a 30 x 30cm2 field obtained TSD = 100 cm.
in water with a diode and a
711
712
&d&ion
Oncology 0
Biology 0 Physics
1976, Vol. 1, Number 7 and Number 8
Table 2. Field flatness parameters Fieid size depth
5X5
10 X 10
15 x 1.5
20 x 20
(cm)
*FF1
*FF2
FFl
FF2
FFl
FF2
FFl
2.5 6.5 10.5
0 0 0
-5 -5 -6
0 0 0
-2.5 -5 -6
0.5 0.5 0
-2.5 -4 -6
2.5 1 1
14.5
0
-8
0
-6
0
-9
18.5
0
-10
0
-8.5
0
-9
FF2
30 x 30
35 x 35
FFI
FF2
FFl
FF2
-1 -2 -6
3.5 2 1.5
-0.5
4.5 3 1.5
0 0 0
0
-7
1
-6
0
-8.5
0
-10
-41
not determined not determined
*FFl: Per cent difference of the maximum dose on a protile witbin 90% of the botmdaries of the geometric beam from the central axis dose. *Fl?k Percent differences of the minimum dose on a profiie witbin 90% of the boundaries of the geometric beam from the central axis dose.
CONCLIBION The 10 MeV X-ray beam from the Clinac-18 has been evaluated. The symmetry, flatness
and CAX depth doses are adequate and the collimation as evaluated with decrement line data is excellent.
REFERENCES Ghan, F.K., Haymond, H-R., Kagan, A.R., Selby. S.M.: Handbook of Physics and Carbone, G.E., George, F.W.: Comparative Chemistry, 50th Edn. Cleveland, Ohio, Chemical beam data for the 25 MV betatron, 8.6 and 4 MV linear accelerators and 60 units. Radiology 109: 691-701, 1973. Feldman A., DeAlmedia, C.E., Almond, P.: Measurement of electron beam energy with rapid processed 8lm. Med. Phys. l(2): 74-76, 1974. Hodgman. C.D.. Weast, R.C., Slat&land, R.S.,
Rubber, 1%3, pp. 2272-2273. 4. Johns, H.E., Cunningham J.R.: The Physics of Radiology, 3rd Edn. Sp&gBeld, Illinois, C.C. Tllomas, 1971, p. 255. 5. Johns, H-E., Cunningkn, J.R.: The Physics of Radiology, 3rd Edn. Springlield, Illinois, C.C. Thomas, 1971, pp. 744-746.
Oncology
Bid.
Phyr.,
1976. Vol.
1. pp. 705-712.
Permmon
Press.
Printed
in the U.S.A.
10 MV X-RAY BEAM CHARACTERISTICS FROM A NEW 18 MeV LINEAR ACCELERATOR WILLIAM
G. CONNOR, Ph.D., JOHN A. HICKS, Ph.D.,
MAX L. M. BOONE, M.D.,
Ph.D.,
ERIC G. MAYER, M.D.
and ROBERT C. MILLER, M.D. Division of Radiation Oncology, University of Arizona, Medical Center, Tucson, AZ 85724, U.S.A.
Thedoaimelic properth of interest in a megavoltage th~rrpy X-my beam are per cent deptb dose, skin sparhg, penumbra, radiation field flatness and symmetry. The10 MV X-ray beam fromtheVPrian~stesCllnnc18LinearAealcrrrtorisetlldkdwfth~tothesepdnts. Theprimarypofntsofiu&restareaSO%depthdosefora10x10at?fieldat18.0cminwater sod a depth of maximum dose of 2.4 20.1 cm in water. TransmkrslonmeasuremeDtsin alumiaum and lead yielded 50% transmission thkkaesses of 73.2 and 13.4 mm respectively. The flatness of the fields are parametrized as function of 6ehl size and depth. Decrement line plots are graphed and isodose curves for selected field sizes are presented. 1OMV X-ray beam, Do&metric properties, Measuremeat teclmiqwS.
INTRODUCTION The first Varian Associates 18 MeV linear
densitometer. Figure 1 shows the Central Axis (CAX) depth dose measurements obtained with accelerator (CL-l@ was installed in the the three measurement techniques. One can see University of Arizona Medical Center during that the ion chamber and diode measurements March-May 1974. The CL-18 is a klystron are identical within experimental error. The powered standing wave linear accelerator iso- data obtained from film density measurements centrically mounted with a target to isocenter are in agreement to a depth of 20 cm and then the distance of 100 cm. Operational characteristics CAXcurvesstarttochange.TheRP/Vfilmhasa will be described in a subsequent publication. A non-linear characteristic curve over the density 10 MeV electron beam bends through a 270” region of interest.* This film system was thus bendingmagnet before impinging on the target eliminated for use with the 10 MV X-ray beam. to produce X-rays. The purpose of this report is To further check the diode measurements to describe the characteristics of the 10MV against ionization chamber data, beam profles X-ray beam produced by the CL-18. were obtained with the ionization chamber and the diode for both a 10 x 1Ocm’ and a MEASUREMENT TJKHNIQUES 30 x 30 cm2 field size in a water phontom. This Three measurement techniques were used to data is illustrated in Fig. 2. One can again see the measure the central axis (CAX) depth dose very close agreement between the two measurecharacteristics for a 10 x 10 cm’ field size at a ment techniques. There are slight differences in target-to-surface distance (TSD) of IOOcm. the penumbra shoulders at the edges of the First, ionization chamber measurements made fields. These ditferences are probably due with a 0.27 cm3PTW ion chamber from Nuclear primarily to the superior spatial resoluti0n Associates and a Keithley Model 615 digital characteristics of the diode. There could be an electrometer. Second, solid state semi- energy dependenceeff ect involved although the conductor diode measurements were made with diode and ion-chambers do not differ with beam a SHM Automatic Isodose Plotter system and quality as a function of depth in water along the fmally, fdm density measurements were made central axis. This question requires further with a Kodak RP/V 6lm and the SHM investigation but in any event, these considetia705
706
Radiation Oncology 0 Biology ??Physics
/
o-‘.,
, , / , , ,
I
,
,
,
1
I,
1976, Vol. 1, Number 7 and Number 8
I,,
,
I,,
I,,
i
,
,
I
I
/
Fig. 1. Central axis depth dose measurements using a 10 x 10 cm’ field and a target to skin distance of 100cm. ?? , Ionization chamber in water; 0, film density; ?? , solid state diode in water. e---
-
Dlodo Ion Chmmbu
I
II I I
a
I I
II 18
16
14
12
10
a
6
4
2 0 2 4 Dletmm OH C&al Axis (cm)
8
8
10
12
14
14
12
in water for 10 x 10 cm’ and a 30 X 30 cm’ fields with a target to skin distance of 100 cm. -, Ionization chamber: ---, solid state diode.
Fig. 2. Beam profiles measured at d,
tions indicate that either measurement technique may be used. The data presented below are thus ah ionization chamber measurements except for the illustrative isodose curves which were generated by a RAD-8 treatment planning system from data measured with the semiconductor diode.
BEAM
QUALITY
Transmission measurements were made in “good”4 geometry with 2.54cm squares of aluminum and lead. The plates were stacked on the accessory tray holder of the accelerator at 42 cm from isocenter. Measurements were normalized to the measured transmission
10 MVX-raybeamcharacteristicsfromanew
18 MeVlinearaccelerator 0 W. G.
through the wire screen accessory holder. The detector used was a 0.2 cm3 Farmer chamber with a Keithley Model 615 digital electrometer and a polarizing voltage of 425 V. The Farmer detector was inserted into a fitted cavity in a polystyrene block with the center of the chamber at 2.5 cm from the surface of the block. The effect of backscatter from the polystyrene phantom below the detector and the 1 cm of masonite supporting the phantom upon the measurement was assumed to be insignificant. The radiation field was 2.5 X 2.5 cm at isocenter and was defined by the collimator on the accelerator. The thickness and density of each of the aluminum and lead plates were individually determined and transmission was plotted against the cumulative thickness determined from the individual measurements as shown in Fig. 3. The lead plates were cut from rolled sheets and thickness varied from 1.70 to 1.65 mm. A density of 11.3 g/cm3 agreed within 2% of measured densities. We believe the variation in measures densities were due to the variation in thickness and uneven cutting of the squares. The thicknesses were averages of three measurements in the central 1.5 cm square region of the sheets. The measurements show a 50% transmission for 13.4 + 0.2 mm of lead. The calculated mass attenuation coefficient has a gradual downward slope from 2 to 13 mm of lead. The relative transmission and mass attenuation
.3J
: 10
. : 30 20 TN+krrm (mm)
‘03
Fig. 3. Relative transmission (-) and Mass Attenuation coellicients (-----) measured in: 0, aluminum; 0, lead. The measurements were made with “good” geometry.
CONNOR et al.
101
coefficients are shown in Fig. 3. The extrapolated zero thickness mass attenuation coefficient for lead as determined from a least squares fit to a straight line of the measured attenuation coefficient for each added sheet of lead was 0.0472 -e 0.0009 cm2/g. Densities for the aluminum plates were within one per cent of 2.70 g/cm3. Thickness of the plates were all 0.320 cm & 0.001 cm. The 80% attenuation thickness was 23.3 mm of aluminum. The 50% attenuation was 73.2 mm extrapolated from data taken from 3 to 35 mm. The mass attenuation coefficient showed a downward slope as a function of total thickness and extrapolated to 0.0366 f. 0.0005 cm’lg for zero thickness of aluminum. The energy value for a monochromatic photon with an absorption coefficient of 0.0472 cm2/g in lead is double valued and is 1.8 MeV on 8.4 MeV.3’ The energy corresponding to an absorption coefficient of 0.0366 cm2/g in aluminum is single valued at 2.80 -t 0.08 MeV?’ Thus, the effective energy of this X-ray beam is 1.8 MeV in lead and 2.8 MeV in aluminum. The difference in effective energy between these materials is due to their atomic structure and the particular X-my spectrum being investigated. Using the value of 18.0 cm for a 50% transmission through water, one can calculate an effective mass absorption coefficient of 0.0385 cm2/g which indicates that the effective energy of the X-ray beam in aluminum is probably close to the effective energy for tissue. BUILD-UP REGION Details of the build-up region are illustrated in Fig. 4. Build up of ionization was measured using a pancake chamber with a separation of 1 mm between the front face and the collecting electrode and a 1 cm circular collecting area. Sheets of polystyrene of density 1.06 g/cm3 and an average thickness of 0.165 g/cm2 were used for build up material. The surface of the topmost sheet was maintained at isocenter. A polarizing voltage of 130 V was used. The average of charges collected for both polarities was plotted as a function of the amount of added polystyrene. The data show an ionization of lO-15% of the
Radiation Chcoloey ??Biology 0 Physics
708
1976, Vol. 1, Number 7 and Number 8
for water was 2.4g/cm2. The per cent depth dose curve goes through a broad maximum and is essentially at 100% at 2.0 cm and remains at 100% until at least 2.6 cm and these d, values are in the central portion of this range. DEPTH DOSE CEAR4CTElUSTICS Fii 5 illustrates the change in the depth .2 .4 .S d 1012i4tS1l)20222426 dose characteristics of the X-ray beam for orpm(gn/d -)4 X 4 cm2, 10 X 10cm2 and 30 x 30cm2 field Fig. 4. Per cent depth dose as a function of depth in sizes. These measurements were made with a the build-up region for a: ?? . 6 x 6cm*; 0, 10 x TSD of 100 cm. From this figure, one can see lOcm’, old ion, A,, new ion chamber); 0, 30 x that the per cent depth dose increases with 30 cm’. field size after depths of 3.5 cm. This is also maximum for field sizes of 6 x 6cm’ and apparent for depths of less than 3.5 cm in Fig. 10 x 10cm2andof 3O%ofthemaximumfora 4. Maximum ionization was obtained at a field size of 30 X 30 cm2 with no build up depth of 2.0 f 0.1 cm and our per cent depth material on the chamber. The 50% points are dose values are normalized to this depth for at 0.28 g/cm’, 0.24 g/cm2 and 0.11 g/cm2 for routine calculational purposes. The 50% ionfield sizes of 6 x 6 cm2, 10 x 10 cm2 and 30 x ization depth in the 10 x 10 cm2 field was 18.0 & 0.1 cm. Table 1 lists the per cent depth 30 cm2 respectively. dose as a function of depth for field sizes from The 90% points are at 1.08g/cm2, 1.00g/cm’ and 0.74g/cm2. Build up curves made for a 4 x 4 to 30 x 30 cm2. Figure 6 illustrates the 10 x 10 field with water as the build up mater- increase of dose per monitor unit at 2.5 cm ial with the exception of a 0.161 g/cm2 thick- depth as a function of fieid size. The field size ness of polystyrene as the iirst added layer of dependence is normalized to 1.0 for a 10 x build up shows a 50% depth of 0.25 g/cm2 and a 10 cm2 field at a TSD of 100cm. The relative dose builds rapidly from 0.85 for 2 x 2 cm2 to 90% depth of 0.95 g/cm’. 1.0 for the 10 x 10 cm2 and then gradually to Dose at the depth of dose maximum (d_) for polystryene was 2.1 g/cm2 -C0.1 g/cm2 and 1.08 for the 32 x 32 cm* field.
Ilt
Table 1. Per cent depth dose as a function of depth for field sizes from 4 x 4 cm2 to 32 X 32 cm2 Field size Depth (cm) 2 4 6 8 10 12 14 16 ;: 22 24 26 28 30
8x8
10X10
14x14
18x18
22x22
26X26 30x30
100 100 94.3 94.4 85.0 86.0 78.7 79.0 69.0 71.5 62.4 64.9 57.1 58.6 52.0 53.1 48.0 42.0 46.3 43.7
100 94.4 87.1 79.2 72.3 66.1 60.2 54.7 45.0 50.1
100 94.9 87.8 80.4 73.5 67.6 61.9 56.7 47.0 51.6
100 95.3 88.0 81.4 74.5 68.2 63.4 57.8 48.3 52.3
loo 95.5 88.5 82.4 75.8 69.0 64.1 58.8 49.6 54.2
100 95.5 88.5 82.5 75.9 69.8 64.7 59.2 50.5 54.3
100 95.5 88.8 82.6 76.4 70.9 65.1 59.6 51.0 55.7
39.7 36.0 32.8 29.6 27.2
40.9 37.1 34.2 30.9 28.3
42.5 39.3 35.4 32.2 29.3
44.1 40.5 36.9 33.8 30.9
45.2 41.2 37.7 34.6 32.1
45.7 42.0 38.6 35.3 32.7
46.9 44.8 41.0 37.6 34.6
4X4
37.6 34.0 30.5 28.7 25.6
10 MVX-raybeamcharacteristicsfromanew
Fig. 5. Central
18 MeVlinearaccelerator
0 W. G.
axis depth dose-measurements for a: ?? , 4 x 4 cm*; 30 x 30 cm*:fieldwithaTSD = 100 cm.
as a Fig. 6. Relative dose per monitor unit at d, function of field size normalizd to a 10 x 1Ocm’ field. TSD = 100 cm.
FIELD FLATNESS AND SYMMETRY Symmetry and flatness measurements were made from beam profiles obtained at 2.5 cm and 10 cm depths. Profiles for 5 x 5, 10 x 10, 15 X 15, 20 x 20 and 35 x 35 cm2 fields obtained with a TSD of 100 cm are shown in Fig. 7. One can see that the symmetry of the X-ray beam is adequate. When utilizing a bent electron beam to produce the X-rays, a major concern is the symmetry and stability of the symmetry of the treatment beam. A drift of up to 5% over a period of time can be seen in asymmetry although it can be adjusted to less than 1% asymmetry at any given time. The profiles vary 6% or less over 90% of beam
CONNOR et al.
?? , 10 x
709
10 cm2; A,
width (within 6% over 80% of the field area) for the various field sizes at a depth of 10 cm. The increase in relative dose at the edge of large fields (35 x 35 cm2) is 6% measured at the depth of dose maximum. From the data in Fig. 6, one can also appreciate the sharpness of the beam definition. Table 2 describes field flatness as a function of depth for various field sizes. The parameters user are the per cent deviations of the maximum or minimums on a profile from the central axis value within 90% of the geometric beam width, according to Chan et al.’ The beam penumbra is small, dropping from an intensity of 90% to 20% in 4mmatd, for the 35 x 35 cm2 field. At a depth of 14.5 cm the distance over which the intensity falls from 90 to 20% increases to 8mm. Decrement line data for various field sizes are’shown in Fig. 8. The graph illustrates how the radiation field conforms to a geometrically perfect field. The radiation field is collimated such that the 50% point on the intensity proflle at a given depth is on the geometrical edge of the field. This implies that the intensity profile is normalized to 100% at the CAX for each depth. One can see from Fig. 8 that the radiation field comes very close to meeting this condition. The projected 50% decremant line for a 35 x 35 cm’ field to a depth of 16.0 mm misses the geometrical edge by ap-
Radiation Oncology ??Biology 0 Physics
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1976, Vol. I, Number 7 and Number 8
Fig. 7. Beam profiles measured at d, 10 x lo,15
and at a depth of 10cm for field sizes of 5 x 5, x 15.20 x 20 and 35 x 35 cm’, with a TSD = 100 cm.
iIlamc+CAxtoKpointsatd0pm)
-
Fig. 8. Decrement lines as a function of depth for 5 X 5, 10 x 10. 15 X 15, 25 X 25 and 35 x 35 cm2 fields: a, 20% decrement lines; 0, 50% decrement line; A, 90% decrement lines. 0, represent the geometrical points for zero and 16 cm depth.
3 mm, representing the largest error. The closeness of the decrement lines for the various percentages is another measure of the penumbra and can be seen to be excellent. proximately
ISODOSE CURVES
Representative isodose curves for the X-ray beam shown in Figs. 9 and 10, for field sizes of
30 x 30 cm* 5 X 5 cm2, 10 x 10 cm’ and respectively. These isodose curves were generated by our Rad-8 treatment planning systern after data acquisition with a solid state diode. The beam characteristics described above can be appreciated from evaluation of these curves. The penetrability (CAX) of the beam, the sharpness of the penumbra and the flatness of the beam at depth are illustrated.
10 MV X-ray beam characteristics from a new 18 MeV linear accelerator 0 W. G. CONNOR et al.
% 28bth
(cm)
Fig. 9. Isodose curves for a 5 x 5 cm2 and 10 X 10 cm’ fields obtained in water with a diode and a TSD = 100 cm.
Fig. 10. Isodose
curve
for a 30 x 30cm2 field obtained TSD = 100 cm.
in water with a diode and a
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1976, Vol. 1, Number 7 and Number 8
Table 2. Field flatness parameters Fieid size depth
5X5
10 X 10
15 x 1.5
20 x 20
(cm)
*FF1
*FF2
FFl
FF2
FFl
FF2
FFl
2.5 6.5 10.5
0 0 0
-5 -5 -6
0 0 0
-2.5 -5 -6
0.5 0.5 0
-2.5 -4 -6
2.5 1 1
14.5
0
-8
0
-6
0
-9
18.5
0
-10
0
-8.5
0
-9
FF2
30 x 30
35 x 35
FFI
FF2
FFl
FF2
-1 -2 -6
3.5 2 1.5
-0.5
4.5 3 1.5
0 0 0
0
-7
1
-6
0
-8.5
0
-10
-41
not determined not determined
*FFl: Per cent difference of the maximum dose on a protile witbin 90% of the botmdaries of the geometric beam from the central axis dose. *Fl?k Percent differences of the minimum dose on a profiie witbin 90% of the boundaries of the geometric beam from the central axis dose.
CONCLIBION The 10 MeV X-ray beam from the Clinac-18 has been evaluated. The symmetry, flatness
and CAX depth doses are adequate and the collimation as evaluated with decrement line data is excellent.
REFERENCES Ghan, F.K., Haymond, H-R., Kagan, A.R., Selby. S.M.: Handbook of Physics and Carbone, G.E., George, F.W.: Comparative Chemistry, 50th Edn. Cleveland, Ohio, Chemical beam data for the 25 MV betatron, 8.6 and 4 MV linear accelerators and 60 units. Radiology 109: 691-701, 1973. Feldman A., DeAlmedia, C.E., Almond, P.: Measurement of electron beam energy with rapid processed 8lm. Med. Phys. l(2): 74-76, 1974. Hodgman. C.D.. Weast, R.C., Slat&land, R.S.,
Rubber, 1%3, pp. 2272-2273. 4. Johns, H.E., Cunningham J.R.: The Physics of Radiology, 3rd Edn. Sp&gBeld, Illinois, C.C. Tllomas, 1971, p. 255. 5. Johns, H-E., Cunningkn, J.R.: The Physics of Radiology, 3rd Edn. Springlield, Illinois, C.C. Thomas, 1971, pp. 744-746.