hr.
J
Radiorion
Bwl. Phyl. Vol All nghts reserved.
Oncoiog~
Prmted in the U.S.A
21. PP 695-702 Copyright
0360.3016191 $3.W + .Ml 0 I991 Pergamon Press plc
??Original Contribution
DOSE IN BONE AND TISSUE NEAR BONE-TISSUE INTERFACE FROM ELECTRON BEAM ALMON
S.
SHIU, PH.D.
AND KENNETH R. HOGSTROM, PH.D.
Department of Radiation Physics, The University of Texas M. D. Anderson Cancer Center, I5 15 Holcombe Blvd., Houston, TX 77030 This work has quantitatively studied the variation of dose both within bone and in unit density tissue near bone-tissue interfaces. Dose upstream of a bone-tissue interface is increased because of an increase in the backscattered electrons from the bone. The magnitude of this effect was measured using a thin parallel-plate ionization chamber upstream of a polymethyl methacrylate (PMMA)-hard bone interface. The electron backscatter factor (EBF) increased rapidly with bone thickness until a full EBF was achieved. This occurred at approximately 3.5 mm at 2 MeV and 6 mm at 13.1 MeV. The full EBF at the interface ranged from approximately 1.018 at 13.1 MeV to 1.05 at 2 MeV. It was also observed that the EBF had a dependence on the energy spectrum at the interface. The penetration of the backscattered electrons in the upstream direction of PMMA was also measured. The dose penetration fell off rapidly in the upstream direction of the interface. Dose emhancement to unit density tissue in bone was measured for an electron beam by placing thermoluminescent dosimeters (TLDs) in a PMMA-bone-PMMA phantom. The maximum dose enhancement in bone was approximately 7% of the maximum dose in water. However, the pencil-beam algorithm of Hogstrom et al. predicted an increase of only 1% , primarily owing to the inverse-square correction. Film was also used to measure the dose enhancement in bone. The film plane was aligned either perpendicular or parallel to the central axis of the beam. The film data indicated that the maximum dose enhancement in bone was approximately 8% for the former film alignment (which was similarly predicted by the TLD measurements) and 13% for the IaUer film alignment. These results confirm that the X ray film is not suitable to be irratiated “edge on” in an inhomogeneous phantom without making perturbation corrections resulting from the film acting as a long narrow inhomogeneous cavity within the bone. In addition, the results give the radiotherapist a basis for clinical judgment when electron beams are used to treat lesions behind bone or near bony structures. We feel these data enhance the ability to recognize the shortcomings of the current dose calculation algorithm used clinically. Electron backscatter factor, Electron beam, Bone-tissue interface, Inhomogeneous phantom. INTRODUCTION
portals, which increases the total tumor dose to the initial gross disease. However, these lesions are often shadowed by bone, particularly the mandible or teeth during treatment. Therefore, the electrons are perturbed by the pressence of bone. Several published studies (3,7,10,12-13) have indicated the dose penetration is reduced behind the bone, but is enhanced in unit-density tissue upstream from the edge of the bone-tissue interface. However, a quantitative study has not been explicitly presented for either dose enhancement due to backscattered electrons at bone-tissue interface, or dose enhancement within the bone due to the increased angulation and increased number of delta rays. Laughlin et al. (10) used aluminum or magnesium to simulate bone in a Presdwood phantom. Using a 20-MeV electron beam, they studied film dosimetry by inserting a sheet of film between two magnesium sheets to measure dose in the magnesium. The central axis of the electron beam was orientated perpendicular to the sheet of the film. The film
Dose at any point in an electron beam is primarily due to electrons traveling in a direction making an acute angle with the incident beam; however, a small contribution to dose arises from electrons traveling in a direction with a vector component opposite the incident beam. Such electrons are referred to as backscattered electrons and are generated primarily from delta rays undergoing subsequent multiple Coulomb scattering. The backscattered electrons will affect the charged particle equilibrium, and hence, the dose distribution in the interface region between two media. The dose at such an interface increases with increasing atomic number of backscattering material and with decreasing energy of the incident electrons (4,5,8,13,16). Lesions of the head and neck, the floor of the mouth, tonsillar fossa, and posterolateral pharyngeal wall are typically treated with a boost electron beam through reduced
Reprint requests to: Almon S. Shiu, Ph.D. Acknowledgements-This
investigation
NC1 grant CA-06294. Accepted for publication
was supported in part by
695
22 February
1991.
696
Biology 0 Physics I. J. Radiation Oncology ??
PTW 0.04 cc Pualld
August 1991, Volume 21, Number 3
Plats ionization Chamber k)
b)
hl
Active
Volume
! 2mrn y+-)
Fig. 1. Experimental
arrangement
for measurement
results indicated that, within a 14-mm thickness of magnesium, dose was enhanced by a maximum of approximately 8%. Prasad et al. (13) also studied the dose enhancement in bone relative to the dose in polystyrene using film and TLD for the measurements; they reported an increase in dose of approximately 18%, 12%, and 11% for 15-, 12-, and 9-MeV electron beams, respectively. We will demonstrate that Prasad’s film measurements have overestimated the dose enhancement in bone. The purpose of this work was: (a) to study the variation of dose at or near bone-tissue interface and within the bone quantitatively, and hence, better understand how the physical parameters govern backscattered electrons; (b) to evaluate the accuracy of M.D. Anderson Cancer Center (MDACC) pencil-beam algorithm (7), which models neither the change of fluence near the interface of an inhomogeneity (due to backscatter), nor the increase of fluence inside the inhomogeneity (due to an increase in secondary electron production); and (c) to provide a basis for clinical judgment and to recognize the shortcomings of the current dose calculation algorithm. METHODS
AND MATERIALS
The first set of measurements was designed to measure the dependence of the electron backscatter factor on the thickness of bone and the energy spectrum of electrons at the PMMA-bone interface. PMMA material was chosen to substitute the unit density tissue because a thin-window parallel plate ionization chamber with a cylindrical PMMA body was used for these measurements. The second set of measurements was designed to measure the upstream penetration in PMMA of the backscattered electrons. The third set of measurements was to determine the central-axis depth dose of the beam in a PMMA-bone-PMMA phan*Mevatron CA.
77, Siemens Medical Laboratories,
Inc., Concord,
of backscattered
electrons.
tom. These latter measurements allowed a quantitative comparison of dose with that calculated by the MDACC pencil-beam algorithm. All measurements were made using the 7-, lo-, 12-, 15-, and 18-MeV electron beams, produced by a linear accelerator (11). * A. Measurement setup 1: variable bone thickness and energy spectrum The thin-window surface of a 0.04-cm3 parallel-plate ionization chambert was placed at a depth of 2.1 cm in PMMA such that the thin window was proximal to the bone slab and distal to the phantom surface, as illustrated in Figure 1. The face of the thin window was placed at the exit surface of the PMMA slab housing the chamber. The chamber consists of a cylindrical acrylic body containing an active volume 5 mm dia. X 2 mm thick. For a selected electron energy setting on the accelerator, the ionization current was first measured in the homogeneous PMMA phantom for a 10 X lo-cm field at 100 cm SSD; see Figure l(a). Next, a variable-thickness slab of SR4 bone substitute (2) with a physical density of 1.725 gm cm-3 was inserted between the thin window of the ionization chamber and deeper slabs of PMMA. Again the ionization current was measured; see the setup shown in Figure l(b). Electron backscatter factor (8) (EBF) is defined as the quotient of the ionization current value with a slab of bone present to that with a homogeneous phantom (i.e., PMMA) in the beam. Successive layers of bone were inserted between bone and PMMA until the ionization current reached a plateau. The most probable energy E,(z) at depth of measurement in the phantom was calculated from the following formula (6):
E,(z) =
qou - ;) . P
tMarkus, Germany.
Physikalisch-Technische
Werkstltten,
(1) Freigburg,
Dose in bone and tissue 0 A. S.
SHIU AND K.
691
R. HOCSTROM
Table l(a). The electron-beam nominal energies, the most probable initial energies, and the most probable energies at depth of 2.1 cm (PMMA-bone interface) for the measurement of EBF as a function of bone thickness and the most probable
energy at the interface.
Nominal energy WV)
The most probable initial energy (MeV)
The most probable energy at interface (MeV)
7.1 10.0 11.8 14.8 17.8
2.0 5.1 6.9 10.0 13.1
7 10 12 15 18
This formula shows that the most probable electron energy, EP, decreases linearly with the absorber thickness z. Ionization measurements in water were used to determine the practical range, RP, for the calculation of the most probable initial electron energy, EP,O, in the formula. The nominal energies, the most probable initial energies, and the most probable energies at depth of 2.1 cm of the interface for these measurements are listed in Table l(a). This geometry was used for irradiation with the most probable energy at interfaces of 6.9 and 5.1 MeV, respectively. To measure the EBF dependent on the energy spectrum, the 15 and 12-MeV electron beams were used with the chamber-bone interface at depths of 3.44 and 2.10 cm, which corresponded to the same most probable energy of 6.9 MeV at the interface. Similarly, the 15 and lo-MeV electron beams were also used with the chamber-bone interface at depths of 4.23 and 2.1 cm, which corresponded to the same most probable energy of 5.1 MeV at the interface. The nominal energies, the most probable initial energies, the depths of chamber-bone interface, and the most probable energies at the interface are listed in Table l(b). B. Measurement backscattered
setup 2: upstream penetration
of
electrons
The following experiment was designed upstream penetration of the backscattered
to measure the electrons that
Table l(b). The electron-beam nominal energies, the most probable initial energies, depths of PMMA-bone interface, and the most probable energies at interface for the measurement of the EBF as a function of the energy spectrum
Nominal energy (MeV) 15 12 15 10
The most probable initial energy (MeV)
Depths of PMMA-bone interface (cm)
The most probable energy at interface (MeV) _
14.8 11.8 14.8 10.0
3.44 2.10 4.23 2.10
6.9 6.9 5.1 5.1
I\
PMMA
lo”iz.tio”
Ch.nlbe,
Fig. 2. The experimental setup for the measurement of the penetration of the backscattered electrons in the “upstream” direction.
travel from the thick (maximum EBF) bone slabs in the direction opposite to the beam. In the setup, the phantom consisted of (a) several sheets of PMMA totalling 2.25-cm in thickness, which included the slab housing for the chamber, (b) several bone slabs totalling 1.898-cm in thickness, and (c) several PMMA slabs totalling 8-cm in thickness. A parallel-plate ionization chamber, with the thin window facing the opposite direction of the incident beam, was used to measure ionization, and is shown in Figure 2. First, ionization was measured with the window of the chamber flush against the first slab of bone for the 7-MeV electron beam of a 10 X IO-cm field at 100 cm SSD. Subsequently, successive sheets of PMMA were removed from the upstream PMMA and placed between the bone and the ionization chamber so as to maintain a constant SSD. In this manner, the depth from the phantom surface to the PMMA-bone interface was also kept constant. In addition, measurements were also made without bone, such that the bone slabs were replaced by a PMMA slab of equal thickness (1.898 cm) to permit the determination of EBF. Thus, we measured the upstream penetra tion of backscattered electrons for each intervening thickness. Then, we repeated the measurements for lo-, 15-, and 18-MeV electron beams. The nominal energies, the initial energies, and the most probable energies at a depth of 2.25 cm of the interface for this measurements are listed in Table 2.
Table 2. The electron-beam nominal energies, the most probable initial energies, and the most probable energies at depth of 2.25 cm of the interface for the measurement of upstream penetration of backscattered electrons
Nominal energy (MeV) 7 10 15 18
The most probable initial energy (MeV) 7.1 10.0 14.8 17.8
The most probable energy at interface WV) 1.6 4.7 9.7 12.7
698
I. J. Radiation Oncology ?? Biology 0 Physics 15 ~WELKTRCN
August 1991, Volume 21, Number 3
F&m
M / 1.19 CMBONE
8.00 UI PYMA
CAVITY HOST
TO
LIF POWDER
I SIDE VIEW (b)
I l2cn
(4 Fig. 3. (a) Experimental setup for the centeral-axis %DD measurement in a PMMA-bone-PMMA phantom using TLD. 15MeV electrons; 8 x 8-cm field; lOO-cm SSD. (b) A schematic drawing of a bone or PMMA slab with a 6-mm diameter, 0.3-mm deep cavity located in the center of the slab for containing the LiF powder.
C. Measurement setup 3: dose enhancement within an inhomogeneous slab (bone) phantom The dose in bone and near the bone-tissue interface is an important clinical issue. Because of the high atomic number of calcium in bone, a dose increase is expected because an increased fluence results from bone having an increased multiple scattering per unit energy loss relative to that for unit density tissue. This increased dose is particularly significant in treatment of anatomical areas with hard bone, such as the mandible. To simulate that geometry a PMMA-bone-PMMA slab phantom, shown in Figure 3(a), was used. The effects of bone on the central-axis absorbed dose curve were studied using 15MeV electron beam in the PMMA-bone-PMMA phantom for a 8 X g-cm field at lOO-cm SSD. The relative electron density with respect to water for PMMA and bone are 1.136 and 1.607, respectively, and the linear scattering power ratios with respect to water for PMMA and bone are 1.023 and 2.351, respectively. These parameters were used in the dose calculations. Lithium fluoride (LiF) powder (TLD-100) was used as the absorbed dose detector and was contained in a cylindrical cavity of 6-mm diameter and 0.3~mm deep in the direcfMark IV, model 1100, Radiation Detection Company, tain View, CA.
Moun-
tion of the primary beam. The TLDs were located on the surface and were centered in a slab (0.325-cm thick bone or PMMA), as depicted in Figure 3(b). The LiF powder was distributed evenly in the cavity. Approximately 27 mg of the LiF was used so that the powder formed a flat surface with the surface of the slab. The locations of the slab, and thus the depths of the TLD powders, were varied to develop a central-axis thermoluminescence (TL) versus depth curve. TL per unit mass of the irradiated LiF powder was measured using a balance and a TLD reader.+ To calibrate the TL sensitivity, a set of reference TLDs, placed at a depth of maximum dose in water, was irradiated to a dose of 200 cGy during the measurement session for a 10 x lo-cm field at lOO-cm SSD. The derived calibration factor was used to convert the TL to dose for all TLD’s. A supralinearity correction to the sensitivity, normalized to 200 cGy, was then used to correct for non-linear dose response. Linearity of TL response was measured by exposing the TLD that was placed at a depth of maximum dose using a @?o beam with a variety of doses (e.g., O-400 cGy). XTL-2 film$ was also used as a detector for the PMMA-bone-PMMA phantom. The film was sandwiched §Eastman Kodak Company,
Rochester,
NY.
Dose in bone and tissue 0 A. S. 15
MeV
Electron
SHIU AND
K. R.
699
HOGSTROM
Beam
1
I 1
0.8lcm
-
1.20om
I
PMMA
Film
I
Film
(b)
-7
1132"PMMA
(4
Fig. 4. Experimental setup for the central-axis %DD measurement in a PMMA-bone-PMMA phantom using film. 15 MeV electrons; 8 x 8-cm field; lOO-cm SSD. The film plane was aligned (a) parallel or (b) perpendicular to the central-axis of the beam and (c) the film plane was aligned similar to (a) except the film was sandwiched between two 0.8-mm thick PMMA sheets, then sandwiched by two half PMMA-bone-PMMA phantoms to simulate the makeup of the Rando phantom.
between two slabs of bone such that the film plane was aligned with either the perpendicular or the parallel direction relative to the central axis of the beam. The setup for the two orientations for the film irradiation is depicted in Figure 4(a) and 4(b), respectively. The reason for irradiating the film edge-on in a PMMA-bone-PMMA phantom is to simulate a similar study by Prasad et al. (13). They sandwiched the film between two sections of anthropromorphic Rando phantom** and evaluated the influence of mandibular bone and teeth on the dose distribution. In setup process, we noticed that each side of the Rando phantom section has a very thin layer (- 0.5 mm) of protective coating which is tissue-like material. Therefore, the protective coating layers and film, together, become a long narrow cavity with respect to bone. To simulate the protective coating in the PMMA-bone-PMMA pantom study, the film was sandwiched between two 0.8-mm thick PMMA sheets that in turn were sandwiched by two phantoms of PMMA-bone-PMMA material. The film was irradiated “edge on” with the setup illustrated in Figure 4(c).
RESULTS
AND DISCUSSION
A. Dependence on bone thickness and energy Plots of the EBF versus bone thickness for 2.0-, 5.1-, 6.9-, lO.O-, and 13.1-MeV the most probable energies, respectively, at interface (2.1 cm deep from the surface of phantom) are shown in Figure 5. It is observed that the EBF increases with thickness of bone until a full electron backscatter factor is achieved. This occurs at approximately 3.5 mm at 2 MeV and 6 mm at 13.1 MeV. The full **Alderson Research Laboratory, Stamford, CT.
EBF at the interface ranges from approximately 1 .O 18 at 13.1 MeV to 1.05 at 2 MeV. The results, as illustrated in Figure 6, demonstrate that for the given most probable energy (e.g., 5.1 MeV) at the bone interface, the full EBF increases from 1.036 to 1.046 with a respective increase in the most probable initial electron energy from 10.0 to 14.8 MeV. Similar results are seen for the most probable energy of 6.9 MeV at the bone interface. This effect is attributed to the electrons with a higher most probable initial energy experiencing more secondary electron production and more energy straggling having passed through a greater pathlength in the material; these combined effects thus result in a broader energy spectrum and more low energy electrons at the bone-PMMA interface. The results also indicate that for the given most probable energy at interface, the thickness of bone at which the full EBF occurs is not particularly dependent on the energy spectrum of the electrons. B. Penetration of backscattered electrons The EBF, as a function of distance upstream from the PMMA-bone interface, is shown in Figure 7(a) for the most probable energies at 2.25-cm depth of 1.6, 4.7, 9.7, and 12.7 MeV. The penetration, expressed in terms of the relative backscatter intensity, is illustrated in Figure 7(b). The relative backscatter intensity is defined as the ratio of the amount of backscatter in PMMA determined at distance upstream from the PMMA-bone interface to the amount of backscatter determined at the bone surface. The relative backscatter intensity at the two lower energies approximately exhibits an exponential dependence on the upstream thickness of PMMA. This normally implies that the
I. J. Radiation Oncology ??Biology ??Physics
700
1.00
’
0
’c
’
1
’
’
I
j
10
5
Bone
Thickness
’
15
August 1991, Volume 21, Number 3
2
20
ia)
(mm)
Depth Upttrclm
in PUMA (mm)
Fig. 5. Dependence of electron backscatter on bone thickness and the most probable energy of electrons (E,(z)), as determined at
bone surface. The maximum uncertainty of the data was approximately 1%. The curves represent the fit of the experimental data.
backscattered fluence consists of electrons of a wide range of energies analogous to an energy spectrum for beta decay. At the higher energies there appears to be two exponential species. The relative backscatter intensity reduces to one-half of the maximum backscatter intensity within 2-mm thickness of PMMA in the upstream direction for all energies investigated (5 12.7 MeV). In fact, the one halfvalue-backscatter thickness of PMMA in the upstream direction changes very little (1.4 to 1.6 mm) from 5 to 13 MeV. This implies that the majority of the backscattered electrons are of low energy. However, the two half-valuebackscatter thickness of PMMA in the upstream direction vary from 2.7 to 4.2 mm for 5 to 13 MeV. This implies existence of a high-energy component in the backscattered electrons. C. Dose enhancement within an inhomogeneous slab (bone) phantom All measurements and calculations are normalized such that 100% equals the maximum dose on central axis for the
1.00
0
c
b
“95
‘1
‘1, ““I 10 Bone
Thickness
15
(‘@“20I’
(mm)
Fig. 6. Dependence of electron backscatter on energy spectrum (the most probable energy of electrons at bone surface, E,(z), are the same). The maximum uncertainty of the data was approximately 1%. The curves represent the fit of the experimental data.
1”
“10 lb)
LLLU I,/, 6
Depth
/, ,,, 6
Upstream
Ii,
(1 2
4
in PYYA
h\\\\\ 0
\ 18.OBrnrn
Imm)
Fig. 7. (a) Electron backscatter factor vs depth in PMMA in the “upstream” direction of the primary beam (for different the most probable energy at interface, E,(z)). The maximum uncertainty of data was within 4%. The curves represent the fit of the experimental data. (b) Penetration of backscattered electrons in PMMA in the “upstream” direction of the primary beam (for different the most probable energy at interface, E,(z)). The curves represent the fit of the experimental data.
field size of interest in a water phantom at a lOO-cm SSD. All differences and errors are reported as a percentage of the 100% dose; for example, if a calculated value of 30% is compared to a measured value of 25%, the difference is 5%. Figure 8 illustrates the central-axis depth-dose curve for the 15 MeV, 8 X 8-cm field that was measured at a lOO-cm SSD in a PMMA-bone-PMMA slab phantom. The maximum dose enhancement in bone (actual dose to a water miniphantom at that point in the bone or PMMA medium) is approximately 7% of the maximum dose in water. The central-axis depth dose was calculated using the pencil-beam algorithm of Hogstrom (7) and compared with the measured results. The calculation indicates a maximum dose of 101% (reflecting an increase of only l%), primarily due to the inverse square correction arising from bone placing the effective depth of calculation closer to the virtual source than that in water. The remaining increase is not predicted because the pencil-beam algorithm of Hogstrom et al. does not account for the increased electron fluence due to the increased angulation of the electrons in
Dose
in
bone and tissue
??A. S.
SHIU AND
K.
120
R.
701
HW.XTROM
1/
“““““i”“/““I”“.
o LiF Powder + XTL-Z(perpendicular)
-
XTL-‘2(perallel)
“, :: 1
60 I’dMA
Hone
60
PMMA
P ,fLIA Bone
40
PUMA
40
Depth
0
,n PMMA (cm)
2
4
6 Depth
11) Fig. 8. Measured vs calculated central-axis depth-dose curves in PMMA-bone-PMMA phantom. 15MeV electrons; 8 x 8-cm field; IOO-cm SD. The uncertainty of TLD data was approximately 2%.
10 in PYUA
12
(cm)
o LiF Powder + XTL-B(perpendicular) -
XTL-B(parallel)
B B
bone and the increased number of backscattered electrons and delta rays. The increase in dose at the upstream interface is due to backscattered electrons, whereas the increase at the downstream interface is due to the increase in beam angulation of the primary electrons and in secondary electrons traveling in the forward direction. Figure 9(a) illustrates the central-axis depth-dose curve measured with film for the 15MeV electrons incident on the PMMA-bone-PMMA slab phantom. When the film plane was aligned perpendicular to the central axis of the beam, the maximum dose enhancement in bone was approximately 8%, which agrees with the TLD data. However, when the film plane was aligned parallel to the central axis of the beam, the dose in bone was greater than that predicted by the other two methods, having a maximum dose enhancement in bone of approximately 13%. These results confirm that x-ray film is not suitable to be irradiated “edge on” in an inhomogeneous phantom without making perturbation corrections resulting from the film acting as a long narrow inhomogeneous cavity within the bone. These results have significant implications for the results reported by Prasad et al. In their measurement, the film was sandwiched between the bone and polystyrene slabs and irradiated edge on. For 15MeV electrons, their film data indicated a maximum dose enhancement of 20% in hard bone with relative electron density of 1.73 to water. They also used TLD chips to verify the maximum dose enhancement in bone (only one point). However, for that setup the authors did not state how the TLD chips were orientated with respect to the direction of the beam. They stated that the TLD data indicated a similar magnitude of dose enhancement in bone (16%). However, our results indicated that the film irradiated edge on did not agree with the TLD and film data (film plane perpendicular to the direction of central axis of the beam). We suspect that the Prasad et al. TLD data may have overestimated the increased dose in bone due to the TLD chip size and the orientation of the chips with respect to the beam.
; s
60
9
Depth
m PMMA (cm)
lb)
Fig. 9. (a) Plot of central-axis depth-dose curve in a PMMAbone-PMMA phantom obtained from film aligned parallel to the central axis of the beam (solid curve). The TLD data ( 0 ) also shown for comparison. Measurements of dose within the bone obtained from film aligned perpendicular to the central axis of the beam is indicated by a ( + ) sign. (b) Plot of central-axis depthdose curve in a PMMA-bone-PMMA phantom obtained from film aligned parallel to the central axis of the beam (solid curve). The only difference of the irradiation geometry was the film sandwiched between two 0.8-mm thick PMMA sheets to simulate the coating on each section of Rando phantom.
Prasad et al. also placed film between two sections of the Rando phantom and irradiated edge on. For 15MeV electrons, they reported a maximum dose enhancement of 10% in bone with the relative electron density of 1.60 to water. However, we used computed tomography (CT) to scan sections 5 and 6 of the Rando phantom. The average electron density for the mandible and teeth is 1.37 with respect to water, instead of 1.60 reported by Prasad et al. From the CT scan, only a thin layer of outer surface of mandibular bone and teeth has the relative electron density of 1.6 - 1.7 with respect to water. We tried to simulate the Rando phantom study of Prasad et al. as we addressed previously in the measurement setup 3. Each side of a Rando phantom section has a thin layer of protective coating. A thin PMMA sheet was used to simulate the protective coating in the PMMA-bone-PMMA phantom. The maximum dose enhancement in bone was even greater (17% of the maximum dose in water), as depicted in Fig-
702
I.
J. Radiation Oncology 0 Biology 0 Physics
ure 9(b) because the width of the long, narrow cavity with respect to bone was increased from 0.2 mm to 1.8 mm.
CONCLUSION At the PMMA-bone interface, the amount of backscatter is not only dependent on the most probable energy of the electrons, but is also dependent on the energy spectrum. This is observed by both the magnitude of the EBF and the penetration of the electrons upstream. Since the lower energy electrons are easier to be scattered backward than the higher energy electrons, the electron fluence at an interface has a greater increase for the lower energy electrons. However, these backscattered electrons did not penetrate as deeply in PMMA upstream from the PMMA-bone interface. The full EBF at the interface ranges from approximately 1.018 at 13.1 MeV to 1.05 at 2 MeV. The bone thickness at which the full EBF occurs is approximately 3.5 mm at 2 MeV and 6 mm at 13.1 MeV. Clinically, when electrons are used to treat lesions near bony structure, the dose at interface is increased because of backscattered electrons. Typically this dose increase is 2 to 5% of the dose in tissue at the same point. This magnitude of dose increase should be clinically acceptable. The dose enhancement in bone was investigated using a 15-MeV irradiation of a PMMA-bone-PMMA phantom to simulate irradiation of the mandible. An increase in dose may be attributed to the increased electron fluence from: (a) an increased angulation of the electrons in bone and (b) the increasing number of backscattered electrons and delta rays. The maximum dose enhancement in a hard bone was approximately 7% of the maximum dose in water, which
August 1991,
Volume 21. Number 3
is similar to that previously reported by Laughlin er al. for magnesium. However, the bone in patients is rarely this dense and thick. Therefore, one can expect the increased dose in bone to be probably much less than 7%. Future measurements of dose in a PMMA-bone-PMMA phantom at energies other than 15-MeV electrons would allow us to have a better understanding of the relationship between the magnitude of the dose in bone and the electron beam energy. Nontheless, the results of this paper give the radiotherapist a basis to judge clinically the maximum increase in dose for bone (when electron beams are used either to treat lesions behind bone or near bony structure). In this paper, we also demonstrated an overestimation of the increased dose in bone that arises if a film is irradiated edge on in an inhomogeneous (bone) phantom. We propose that there is a need for a perturbation correction factor if film is irradiated edge on in an inhomogeneous phantom. The placement of film in this orientation appears to explain the overestimation of dose in bone reported by Prasad et al. The MDACC pencil-beam algorithm (7), which underestimates by as much as 6% the increased dose in bone, has been modified (14) to account for the increased fluence due to an increased angulation of electrons in bone. The calculation obtained from the modified algorithm indicates that an increase of 2-3% in bone is due to the increased angulation; the additional 34% increase is probably due to the increasing number of secondary electrons, which is not accounted for by this algorithm. However, the redefinition pencil-beam algorithm (15) can be made to calculate dose around bone with an accuracy of 3% or better by incorporating secondary electron transport effects.
REFERENCES 1. AAPM, Task Group 21, Radiation Therapy Committee. A protocol for the determination of absorbed dose from highenergy photon and electron beams. Med. Phys. 10: 741-771; 1983. 2. Constantiou, C.; Attix, F. H.; Paliwal, B. R. Epoxy resin based tissue substitute. Br. J. Radiol. 5: 814-821; 1977. 3. Dahler, A.; Baker, A. S.; Laughlin, J. S. Compreshensive electron beam treatment planning. Ann. NY Acad. Sci. 161: 198-213; 1969. 4. Dressel, R. W. Retrofugal electron flux from massive targets irradiated by a monoenergetic primary beam. Phys. Rev. 144: 332; 1966a. 5. Dressel, R. W. Energy spectra of the retrofugal electron flux from massive targets. Phys. Rev. 144: 344; 1966b. 6. Harder, D. Energiespektren schneller elektronen in verschiedenen tiefen. In: Zuppinger, A., Poretti, G., eds. Symposium on high-energy electrons. Berlin: Springer-Verlag; 1965: 260. Hogstrom, K. R.; Mills, M. D.; Almond, P. R. Electron beam dose calculations. Phys. Med. Biol. 26: 445-459; 1981. Klevenhagen, S. C.; Lambert, G. D.; Arbabi, A. Backscattering in electron beam therapy for energies between 3 and 35 MeV. Phys. Med. Biol. 27: 363-373; 1982. Lambert, G. D.; Klevenhagen, S. C. Penetration of back-
scattered electrons in polystyrene for energies between 25 MeV. Phys. Med. Biol. 27: 721-725; 1982.
1 and
10. Laughin, J. S.; Lundy, A.; Phillips, R.; Chu, F.; Sattar, A. Electron beam treatment planning in inhomogeneous tissue. Radiology 85: 524-531; 1965. 11. Meyer, J. A.; Palta, J. R.; Hogstrom, K. R. Demonstration of relatively new electron dosimetry measurement techniques on the mevatron 80. Med. Phys. 11: 670-677; 1984. 12. Pohlit, W. Calculated and measured dose distribution in inhomogeneous materials and patients. Ann. NY Acad. Sci. 161: 189-197; 1969. 13. Prasad, S. C.; Ames, T. E.; Howard, T. B.; Bassano, D. A.; Chung, C. T.; King, G. A.; Segerman, R. H. Dose enhancement in bone in electron beam therapy. Radiology 151: 513516; 1984. electron beam dose calcula14. Shiu, A. S. Three-dimensional tions. Ph.D. dissertation, Univ. of Texas Graduate School of Biomedical Sciences, Houston, Texas; 1988. 15. Shiu, A. S.; Hogstrom, K. R. Pencil-beam redefinition algorithm for electron dose distributions. Med. Phys. 18:7-18; 1991. 16. Tabata, T. Backscattering of electrons from 3.2 to 14 MeV. Phys. Rev. 162: 336; 1967.
J
Radiorion
Bwl. Phyl. Vol All nghts reserved.
Oncoiog~
Prmted in the U.S.A
21. PP 695-702 Copyright
0360.3016191 $3.W + .Ml 0 I991 Pergamon Press plc
??Original Contribution
DOSE IN BONE AND TISSUE NEAR BONE-TISSUE INTERFACE FROM ELECTRON BEAM ALMON
S.
SHIU, PH.D.
AND KENNETH R. HOGSTROM, PH.D.
Department of Radiation Physics, The University of Texas M. D. Anderson Cancer Center, I5 15 Holcombe Blvd., Houston, TX 77030 This work has quantitatively studied the variation of dose both within bone and in unit density tissue near bone-tissue interfaces. Dose upstream of a bone-tissue interface is increased because of an increase in the backscattered electrons from the bone. The magnitude of this effect was measured using a thin parallel-plate ionization chamber upstream of a polymethyl methacrylate (PMMA)-hard bone interface. The electron backscatter factor (EBF) increased rapidly with bone thickness until a full EBF was achieved. This occurred at approximately 3.5 mm at 2 MeV and 6 mm at 13.1 MeV. The full EBF at the interface ranged from approximately 1.018 at 13.1 MeV to 1.05 at 2 MeV. It was also observed that the EBF had a dependence on the energy spectrum at the interface. The penetration of the backscattered electrons in the upstream direction of PMMA was also measured. The dose penetration fell off rapidly in the upstream direction of the interface. Dose emhancement to unit density tissue in bone was measured for an electron beam by placing thermoluminescent dosimeters (TLDs) in a PMMA-bone-PMMA phantom. The maximum dose enhancement in bone was approximately 7% of the maximum dose in water. However, the pencil-beam algorithm of Hogstrom et al. predicted an increase of only 1% , primarily owing to the inverse-square correction. Film was also used to measure the dose enhancement in bone. The film plane was aligned either perpendicular or parallel to the central axis of the beam. The film data indicated that the maximum dose enhancement in bone was approximately 8% for the former film alignment (which was similarly predicted by the TLD measurements) and 13% for the IaUer film alignment. These results confirm that the X ray film is not suitable to be irratiated “edge on” in an inhomogeneous phantom without making perturbation corrections resulting from the film acting as a long narrow inhomogeneous cavity within the bone. In addition, the results give the radiotherapist a basis for clinical judgment when electron beams are used to treat lesions behind bone or near bony structures. We feel these data enhance the ability to recognize the shortcomings of the current dose calculation algorithm used clinically. Electron backscatter factor, Electron beam, Bone-tissue interface, Inhomogeneous phantom. INTRODUCTION
portals, which increases the total tumor dose to the initial gross disease. However, these lesions are often shadowed by bone, particularly the mandible or teeth during treatment. Therefore, the electrons are perturbed by the pressence of bone. Several published studies (3,7,10,12-13) have indicated the dose penetration is reduced behind the bone, but is enhanced in unit-density tissue upstream from the edge of the bone-tissue interface. However, a quantitative study has not been explicitly presented for either dose enhancement due to backscattered electrons at bone-tissue interface, or dose enhancement within the bone due to the increased angulation and increased number of delta rays. Laughlin et al. (10) used aluminum or magnesium to simulate bone in a Presdwood phantom. Using a 20-MeV electron beam, they studied film dosimetry by inserting a sheet of film between two magnesium sheets to measure dose in the magnesium. The central axis of the electron beam was orientated perpendicular to the sheet of the film. The film
Dose at any point in an electron beam is primarily due to electrons traveling in a direction making an acute angle with the incident beam; however, a small contribution to dose arises from electrons traveling in a direction with a vector component opposite the incident beam. Such electrons are referred to as backscattered electrons and are generated primarily from delta rays undergoing subsequent multiple Coulomb scattering. The backscattered electrons will affect the charged particle equilibrium, and hence, the dose distribution in the interface region between two media. The dose at such an interface increases with increasing atomic number of backscattering material and with decreasing energy of the incident electrons (4,5,8,13,16). Lesions of the head and neck, the floor of the mouth, tonsillar fossa, and posterolateral pharyngeal wall are typically treated with a boost electron beam through reduced
Reprint requests to: Almon S. Shiu, Ph.D. Acknowledgements-This
investigation
NC1 grant CA-06294. Accepted for publication
was supported in part by
695
22 February
1991.
696
Biology 0 Physics I. J. Radiation Oncology ??
PTW 0.04 cc Pualld
August 1991, Volume 21, Number 3
Plats ionization Chamber k)
b)
hl
Active
Volume
! 2mrn y+-)
Fig. 1. Experimental
arrangement
for measurement
results indicated that, within a 14-mm thickness of magnesium, dose was enhanced by a maximum of approximately 8%. Prasad et al. (13) also studied the dose enhancement in bone relative to the dose in polystyrene using film and TLD for the measurements; they reported an increase in dose of approximately 18%, 12%, and 11% for 15-, 12-, and 9-MeV electron beams, respectively. We will demonstrate that Prasad’s film measurements have overestimated the dose enhancement in bone. The purpose of this work was: (a) to study the variation of dose at or near bone-tissue interface and within the bone quantitatively, and hence, better understand how the physical parameters govern backscattered electrons; (b) to evaluate the accuracy of M.D. Anderson Cancer Center (MDACC) pencil-beam algorithm (7), which models neither the change of fluence near the interface of an inhomogeneity (due to backscatter), nor the increase of fluence inside the inhomogeneity (due to an increase in secondary electron production); and (c) to provide a basis for clinical judgment and to recognize the shortcomings of the current dose calculation algorithm. METHODS
AND MATERIALS
The first set of measurements was designed to measure the dependence of the electron backscatter factor on the thickness of bone and the energy spectrum of electrons at the PMMA-bone interface. PMMA material was chosen to substitute the unit density tissue because a thin-window parallel plate ionization chamber with a cylindrical PMMA body was used for these measurements. The second set of measurements was designed to measure the upstream penetration in PMMA of the backscattered electrons. The third set of measurements was to determine the central-axis depth dose of the beam in a PMMA-bone-PMMA phan*Mevatron CA.
77, Siemens Medical Laboratories,
Inc., Concord,
of backscattered
electrons.
tom. These latter measurements allowed a quantitative comparison of dose with that calculated by the MDACC pencil-beam algorithm. All measurements were made using the 7-, lo-, 12-, 15-, and 18-MeV electron beams, produced by a linear accelerator (11). * A. Measurement setup 1: variable bone thickness and energy spectrum The thin-window surface of a 0.04-cm3 parallel-plate ionization chambert was placed at a depth of 2.1 cm in PMMA such that the thin window was proximal to the bone slab and distal to the phantom surface, as illustrated in Figure 1. The face of the thin window was placed at the exit surface of the PMMA slab housing the chamber. The chamber consists of a cylindrical acrylic body containing an active volume 5 mm dia. X 2 mm thick. For a selected electron energy setting on the accelerator, the ionization current was first measured in the homogeneous PMMA phantom for a 10 X lo-cm field at 100 cm SSD; see Figure l(a). Next, a variable-thickness slab of SR4 bone substitute (2) with a physical density of 1.725 gm cm-3 was inserted between the thin window of the ionization chamber and deeper slabs of PMMA. Again the ionization current was measured; see the setup shown in Figure l(b). Electron backscatter factor (8) (EBF) is defined as the quotient of the ionization current value with a slab of bone present to that with a homogeneous phantom (i.e., PMMA) in the beam. Successive layers of bone were inserted between bone and PMMA until the ionization current reached a plateau. The most probable energy E,(z) at depth of measurement in the phantom was calculated from the following formula (6):
E,(z) =
qou - ;) . P
tMarkus, Germany.
Physikalisch-Technische
Werkstltten,
(1) Freigburg,
Dose in bone and tissue 0 A. S.
SHIU AND K.
691
R. HOCSTROM
Table l(a). The electron-beam nominal energies, the most probable initial energies, and the most probable energies at depth of 2.1 cm (PMMA-bone interface) for the measurement of EBF as a function of bone thickness and the most probable
energy at the interface.
Nominal energy WV)
The most probable initial energy (MeV)
The most probable energy at interface (MeV)
7.1 10.0 11.8 14.8 17.8
2.0 5.1 6.9 10.0 13.1
7 10 12 15 18
This formula shows that the most probable electron energy, EP, decreases linearly with the absorber thickness z. Ionization measurements in water were used to determine the practical range, RP, for the calculation of the most probable initial electron energy, EP,O, in the formula. The nominal energies, the most probable initial energies, and the most probable energies at depth of 2.1 cm of the interface for these measurements are listed in Table l(a). This geometry was used for irradiation with the most probable energy at interfaces of 6.9 and 5.1 MeV, respectively. To measure the EBF dependent on the energy spectrum, the 15 and 12-MeV electron beams were used with the chamber-bone interface at depths of 3.44 and 2.10 cm, which corresponded to the same most probable energy of 6.9 MeV at the interface. Similarly, the 15 and lo-MeV electron beams were also used with the chamber-bone interface at depths of 4.23 and 2.1 cm, which corresponded to the same most probable energy of 5.1 MeV at the interface. The nominal energies, the most probable initial energies, the depths of chamber-bone interface, and the most probable energies at the interface are listed in Table l(b). B. Measurement backscattered
setup 2: upstream penetration
of
electrons
The following experiment was designed upstream penetration of the backscattered
to measure the electrons that
Table l(b). The electron-beam nominal energies, the most probable initial energies, depths of PMMA-bone interface, and the most probable energies at interface for the measurement of the EBF as a function of the energy spectrum
Nominal energy (MeV) 15 12 15 10
The most probable initial energy (MeV)
Depths of PMMA-bone interface (cm)
The most probable energy at interface (MeV) _
14.8 11.8 14.8 10.0
3.44 2.10 4.23 2.10
6.9 6.9 5.1 5.1
I\
PMMA
lo”iz.tio”
Ch.nlbe,
Fig. 2. The experimental setup for the measurement of the penetration of the backscattered electrons in the “upstream” direction.
travel from the thick (maximum EBF) bone slabs in the direction opposite to the beam. In the setup, the phantom consisted of (a) several sheets of PMMA totalling 2.25-cm in thickness, which included the slab housing for the chamber, (b) several bone slabs totalling 1.898-cm in thickness, and (c) several PMMA slabs totalling 8-cm in thickness. A parallel-plate ionization chamber, with the thin window facing the opposite direction of the incident beam, was used to measure ionization, and is shown in Figure 2. First, ionization was measured with the window of the chamber flush against the first slab of bone for the 7-MeV electron beam of a 10 X IO-cm field at 100 cm SSD. Subsequently, successive sheets of PMMA were removed from the upstream PMMA and placed between the bone and the ionization chamber so as to maintain a constant SSD. In this manner, the depth from the phantom surface to the PMMA-bone interface was also kept constant. In addition, measurements were also made without bone, such that the bone slabs were replaced by a PMMA slab of equal thickness (1.898 cm) to permit the determination of EBF. Thus, we measured the upstream penetra tion of backscattered electrons for each intervening thickness. Then, we repeated the measurements for lo-, 15-, and 18-MeV electron beams. The nominal energies, the initial energies, and the most probable energies at a depth of 2.25 cm of the interface for this measurements are listed in Table 2.
Table 2. The electron-beam nominal energies, the most probable initial energies, and the most probable energies at depth of 2.25 cm of the interface for the measurement of upstream penetration of backscattered electrons
Nominal energy (MeV) 7 10 15 18
The most probable initial energy (MeV) 7.1 10.0 14.8 17.8
The most probable energy at interface WV) 1.6 4.7 9.7 12.7
698
I. J. Radiation Oncology ?? Biology 0 Physics 15 ~WELKTRCN
August 1991, Volume 21, Number 3
F&m
M / 1.19 CMBONE
8.00 UI PYMA
CAVITY HOST
TO
LIF POWDER
I SIDE VIEW (b)
I l2cn
(4 Fig. 3. (a) Experimental setup for the centeral-axis %DD measurement in a PMMA-bone-PMMA phantom using TLD. 15MeV electrons; 8 x 8-cm field; lOO-cm SSD. (b) A schematic drawing of a bone or PMMA slab with a 6-mm diameter, 0.3-mm deep cavity located in the center of the slab for containing the LiF powder.
C. Measurement setup 3: dose enhancement within an inhomogeneous slab (bone) phantom The dose in bone and near the bone-tissue interface is an important clinical issue. Because of the high atomic number of calcium in bone, a dose increase is expected because an increased fluence results from bone having an increased multiple scattering per unit energy loss relative to that for unit density tissue. This increased dose is particularly significant in treatment of anatomical areas with hard bone, such as the mandible. To simulate that geometry a PMMA-bone-PMMA slab phantom, shown in Figure 3(a), was used. The effects of bone on the central-axis absorbed dose curve were studied using 15MeV electron beam in the PMMA-bone-PMMA phantom for a 8 X g-cm field at lOO-cm SSD. The relative electron density with respect to water for PMMA and bone are 1.136 and 1.607, respectively, and the linear scattering power ratios with respect to water for PMMA and bone are 1.023 and 2.351, respectively. These parameters were used in the dose calculations. Lithium fluoride (LiF) powder (TLD-100) was used as the absorbed dose detector and was contained in a cylindrical cavity of 6-mm diameter and 0.3~mm deep in the direcfMark IV, model 1100, Radiation Detection Company, tain View, CA.
Moun-
tion of the primary beam. The TLDs were located on the surface and were centered in a slab (0.325-cm thick bone or PMMA), as depicted in Figure 3(b). The LiF powder was distributed evenly in the cavity. Approximately 27 mg of the LiF was used so that the powder formed a flat surface with the surface of the slab. The locations of the slab, and thus the depths of the TLD powders, were varied to develop a central-axis thermoluminescence (TL) versus depth curve. TL per unit mass of the irradiated LiF powder was measured using a balance and a TLD reader.+ To calibrate the TL sensitivity, a set of reference TLDs, placed at a depth of maximum dose in water, was irradiated to a dose of 200 cGy during the measurement session for a 10 x lo-cm field at lOO-cm SSD. The derived calibration factor was used to convert the TL to dose for all TLD’s. A supralinearity correction to the sensitivity, normalized to 200 cGy, was then used to correct for non-linear dose response. Linearity of TL response was measured by exposing the TLD that was placed at a depth of maximum dose using a @?o beam with a variety of doses (e.g., O-400 cGy). XTL-2 film$ was also used as a detector for the PMMA-bone-PMMA phantom. The film was sandwiched §Eastman Kodak Company,
Rochester,
NY.
Dose in bone and tissue 0 A. S. 15
MeV
Electron
SHIU AND
K. R.
699
HOGSTROM
Beam
1
I 1
0.8lcm
-
1.20om
I
PMMA
Film
I
Film
(b)
-7
1132"PMMA
(4
Fig. 4. Experimental setup for the central-axis %DD measurement in a PMMA-bone-PMMA phantom using film. 15 MeV electrons; 8 x 8-cm field; lOO-cm SSD. The film plane was aligned (a) parallel or (b) perpendicular to the central-axis of the beam and (c) the film plane was aligned similar to (a) except the film was sandwiched between two 0.8-mm thick PMMA sheets, then sandwiched by two half PMMA-bone-PMMA phantoms to simulate the makeup of the Rando phantom.
between two slabs of bone such that the film plane was aligned with either the perpendicular or the parallel direction relative to the central axis of the beam. The setup for the two orientations for the film irradiation is depicted in Figure 4(a) and 4(b), respectively. The reason for irradiating the film edge-on in a PMMA-bone-PMMA phantom is to simulate a similar study by Prasad et al. (13). They sandwiched the film between two sections of anthropromorphic Rando phantom** and evaluated the influence of mandibular bone and teeth on the dose distribution. In setup process, we noticed that each side of the Rando phantom section has a very thin layer (- 0.5 mm) of protective coating which is tissue-like material. Therefore, the protective coating layers and film, together, become a long narrow cavity with respect to bone. To simulate the protective coating in the PMMA-bone-PMMA pantom study, the film was sandwiched between two 0.8-mm thick PMMA sheets that in turn were sandwiched by two phantoms of PMMA-bone-PMMA material. The film was irradiated “edge on” with the setup illustrated in Figure 4(c).
RESULTS
AND DISCUSSION
A. Dependence on bone thickness and energy Plots of the EBF versus bone thickness for 2.0-, 5.1-, 6.9-, lO.O-, and 13.1-MeV the most probable energies, respectively, at interface (2.1 cm deep from the surface of phantom) are shown in Figure 5. It is observed that the EBF increases with thickness of bone until a full electron backscatter factor is achieved. This occurs at approximately 3.5 mm at 2 MeV and 6 mm at 13.1 MeV. The full **Alderson Research Laboratory, Stamford, CT.
EBF at the interface ranges from approximately 1 .O 18 at 13.1 MeV to 1.05 at 2 MeV. The results, as illustrated in Figure 6, demonstrate that for the given most probable energy (e.g., 5.1 MeV) at the bone interface, the full EBF increases from 1.036 to 1.046 with a respective increase in the most probable initial electron energy from 10.0 to 14.8 MeV. Similar results are seen for the most probable energy of 6.9 MeV at the bone interface. This effect is attributed to the electrons with a higher most probable initial energy experiencing more secondary electron production and more energy straggling having passed through a greater pathlength in the material; these combined effects thus result in a broader energy spectrum and more low energy electrons at the bone-PMMA interface. The results also indicate that for the given most probable energy at interface, the thickness of bone at which the full EBF occurs is not particularly dependent on the energy spectrum of the electrons. B. Penetration of backscattered electrons The EBF, as a function of distance upstream from the PMMA-bone interface, is shown in Figure 7(a) for the most probable energies at 2.25-cm depth of 1.6, 4.7, 9.7, and 12.7 MeV. The penetration, expressed in terms of the relative backscatter intensity, is illustrated in Figure 7(b). The relative backscatter intensity is defined as the ratio of the amount of backscatter in PMMA determined at distance upstream from the PMMA-bone interface to the amount of backscatter determined at the bone surface. The relative backscatter intensity at the two lower energies approximately exhibits an exponential dependence on the upstream thickness of PMMA. This normally implies that the
I. J. Radiation Oncology ??Biology ??Physics
700
1.00
’
0
’c
’
1
’
’
I
j
10
5
Bone
Thickness
’
15
August 1991, Volume 21, Number 3
2
20
ia)
(mm)
Depth Upttrclm
in PUMA (mm)
Fig. 5. Dependence of electron backscatter on bone thickness and the most probable energy of electrons (E,(z)), as determined at
bone surface. The maximum uncertainty of the data was approximately 1%. The curves represent the fit of the experimental data.
backscattered fluence consists of electrons of a wide range of energies analogous to an energy spectrum for beta decay. At the higher energies there appears to be two exponential species. The relative backscatter intensity reduces to one-half of the maximum backscatter intensity within 2-mm thickness of PMMA in the upstream direction for all energies investigated (5 12.7 MeV). In fact, the one halfvalue-backscatter thickness of PMMA in the upstream direction changes very little (1.4 to 1.6 mm) from 5 to 13 MeV. This implies that the majority of the backscattered electrons are of low energy. However, the two half-valuebackscatter thickness of PMMA in the upstream direction vary from 2.7 to 4.2 mm for 5 to 13 MeV. This implies existence of a high-energy component in the backscattered electrons. C. Dose enhancement within an inhomogeneous slab (bone) phantom All measurements and calculations are normalized such that 100% equals the maximum dose on central axis for the
1.00
0
c
b
“95
‘1
‘1, ““I 10 Bone
Thickness
15
(‘@“20I’
(mm)
Fig. 6. Dependence of electron backscatter on energy spectrum (the most probable energy of electrons at bone surface, E,(z), are the same). The maximum uncertainty of the data was approximately 1%. The curves represent the fit of the experimental data.
1”
“10 lb)
LLLU I,/, 6
Depth
/, ,,, 6
Upstream
Ii,
(1 2
4
in PYYA
h\\\\\ 0
\ 18.OBrnrn
Imm)
Fig. 7. (a) Electron backscatter factor vs depth in PMMA in the “upstream” direction of the primary beam (for different the most probable energy at interface, E,(z)). The maximum uncertainty of data was within 4%. The curves represent the fit of the experimental data. (b) Penetration of backscattered electrons in PMMA in the “upstream” direction of the primary beam (for different the most probable energy at interface, E,(z)). The curves represent the fit of the experimental data.
field size of interest in a water phantom at a lOO-cm SSD. All differences and errors are reported as a percentage of the 100% dose; for example, if a calculated value of 30% is compared to a measured value of 25%, the difference is 5%. Figure 8 illustrates the central-axis depth-dose curve for the 15 MeV, 8 X 8-cm field that was measured at a lOO-cm SSD in a PMMA-bone-PMMA slab phantom. The maximum dose enhancement in bone (actual dose to a water miniphantom at that point in the bone or PMMA medium) is approximately 7% of the maximum dose in water. The central-axis depth dose was calculated using the pencil-beam algorithm of Hogstrom (7) and compared with the measured results. The calculation indicates a maximum dose of 101% (reflecting an increase of only l%), primarily due to the inverse square correction arising from bone placing the effective depth of calculation closer to the virtual source than that in water. The remaining increase is not predicted because the pencil-beam algorithm of Hogstrom et al. does not account for the increased electron fluence due to the increased angulation of the electrons in
Dose
in
bone and tissue
??A. S.
SHIU AND
K.
120
R.
701
HW.XTROM
1/
“““““i”“/““I”“.
o LiF Powder + XTL-Z(perpendicular)
-
XTL-‘2(perallel)
“, :: 1
60 I’dMA
Hone
60
PMMA
P ,fLIA Bone
40
PUMA
40
Depth
0
,n PMMA (cm)
2
4
6 Depth
11) Fig. 8. Measured vs calculated central-axis depth-dose curves in PMMA-bone-PMMA phantom. 15MeV electrons; 8 x 8-cm field; IOO-cm SD. The uncertainty of TLD data was approximately 2%.
10 in PYUA
12
(cm)
o LiF Powder + XTL-B(perpendicular) -
XTL-B(parallel)
B B
bone and the increased number of backscattered electrons and delta rays. The increase in dose at the upstream interface is due to backscattered electrons, whereas the increase at the downstream interface is due to the increase in beam angulation of the primary electrons and in secondary electrons traveling in the forward direction. Figure 9(a) illustrates the central-axis depth-dose curve measured with film for the 15MeV electrons incident on the PMMA-bone-PMMA slab phantom. When the film plane was aligned perpendicular to the central axis of the beam, the maximum dose enhancement in bone was approximately 8%, which agrees with the TLD data. However, when the film plane was aligned parallel to the central axis of the beam, the dose in bone was greater than that predicted by the other two methods, having a maximum dose enhancement in bone of approximately 13%. These results confirm that x-ray film is not suitable to be irradiated “edge on” in an inhomogeneous phantom without making perturbation corrections resulting from the film acting as a long narrow inhomogeneous cavity within the bone. These results have significant implications for the results reported by Prasad et al. In their measurement, the film was sandwiched between the bone and polystyrene slabs and irradiated edge on. For 15MeV electrons, their film data indicated a maximum dose enhancement of 20% in hard bone with relative electron density of 1.73 to water. They also used TLD chips to verify the maximum dose enhancement in bone (only one point). However, for that setup the authors did not state how the TLD chips were orientated with respect to the direction of the beam. They stated that the TLD data indicated a similar magnitude of dose enhancement in bone (16%). However, our results indicated that the film irradiated edge on did not agree with the TLD and film data (film plane perpendicular to the direction of central axis of the beam). We suspect that the Prasad et al. TLD data may have overestimated the increased dose in bone due to the TLD chip size and the orientation of the chips with respect to the beam.
; s
60
9
Depth
m PMMA (cm)
lb)
Fig. 9. (a) Plot of central-axis depth-dose curve in a PMMAbone-PMMA phantom obtained from film aligned parallel to the central axis of the beam (solid curve). The TLD data ( 0 ) also shown for comparison. Measurements of dose within the bone obtained from film aligned perpendicular to the central axis of the beam is indicated by a ( + ) sign. (b) Plot of central-axis depthdose curve in a PMMA-bone-PMMA phantom obtained from film aligned parallel to the central axis of the beam (solid curve). The only difference of the irradiation geometry was the film sandwiched between two 0.8-mm thick PMMA sheets to simulate the coating on each section of Rando phantom.
Prasad et al. also placed film between two sections of the Rando phantom and irradiated edge on. For 15MeV electrons, they reported a maximum dose enhancement of 10% in bone with the relative electron density of 1.60 to water. However, we used computed tomography (CT) to scan sections 5 and 6 of the Rando phantom. The average electron density for the mandible and teeth is 1.37 with respect to water, instead of 1.60 reported by Prasad et al. From the CT scan, only a thin layer of outer surface of mandibular bone and teeth has the relative electron density of 1.6 - 1.7 with respect to water. We tried to simulate the Rando phantom study of Prasad et al. as we addressed previously in the measurement setup 3. Each side of a Rando phantom section has a thin layer of protective coating. A thin PMMA sheet was used to simulate the protective coating in the PMMA-bone-PMMA phantom. The maximum dose enhancement in bone was even greater (17% of the maximum dose in water), as depicted in Fig-
702
I.
J. Radiation Oncology 0 Biology 0 Physics
ure 9(b) because the width of the long, narrow cavity with respect to bone was increased from 0.2 mm to 1.8 mm.
CONCLUSION At the PMMA-bone interface, the amount of backscatter is not only dependent on the most probable energy of the electrons, but is also dependent on the energy spectrum. This is observed by both the magnitude of the EBF and the penetration of the electrons upstream. Since the lower energy electrons are easier to be scattered backward than the higher energy electrons, the electron fluence at an interface has a greater increase for the lower energy electrons. However, these backscattered electrons did not penetrate as deeply in PMMA upstream from the PMMA-bone interface. The full EBF at the interface ranges from approximately 1.018 at 13.1 MeV to 1.05 at 2 MeV. The bone thickness at which the full EBF occurs is approximately 3.5 mm at 2 MeV and 6 mm at 13.1 MeV. Clinically, when electrons are used to treat lesions near bony structure, the dose at interface is increased because of backscattered electrons. Typically this dose increase is 2 to 5% of the dose in tissue at the same point. This magnitude of dose increase should be clinically acceptable. The dose enhancement in bone was investigated using a 15-MeV irradiation of a PMMA-bone-PMMA phantom to simulate irradiation of the mandible. An increase in dose may be attributed to the increased electron fluence from: (a) an increased angulation of the electrons in bone and (b) the increasing number of backscattered electrons and delta rays. The maximum dose enhancement in a hard bone was approximately 7% of the maximum dose in water, which
August 1991,
Volume 21. Number 3
is similar to that previously reported by Laughlin er al. for magnesium. However, the bone in patients is rarely this dense and thick. Therefore, one can expect the increased dose in bone to be probably much less than 7%. Future measurements of dose in a PMMA-bone-PMMA phantom at energies other than 15-MeV electrons would allow us to have a better understanding of the relationship between the magnitude of the dose in bone and the electron beam energy. Nontheless, the results of this paper give the radiotherapist a basis to judge clinically the maximum increase in dose for bone (when electron beams are used either to treat lesions behind bone or near bony structure). In this paper, we also demonstrated an overestimation of the increased dose in bone that arises if a film is irradiated edge on in an inhomogeneous (bone) phantom. We propose that there is a need for a perturbation correction factor if film is irradiated edge on in an inhomogeneous phantom. The placement of film in this orientation appears to explain the overestimation of dose in bone reported by Prasad et al. The MDACC pencil-beam algorithm (7), which underestimates by as much as 6% the increased dose in bone, has been modified (14) to account for the increased fluence due to an increased angulation of electrons in bone. The calculation obtained from the modified algorithm indicates that an increase of 2-3% in bone is due to the increased angulation; the additional 34% increase is probably due to the increasing number of secondary electrons, which is not accounted for by this algorithm. However, the redefinition pencil-beam algorithm (15) can be made to calculate dose around bone with an accuracy of 3% or better by incorporating secondary electron transport effects.
REFERENCES 1. AAPM, Task Group 21, Radiation Therapy Committee. A protocol for the determination of absorbed dose from highenergy photon and electron beams. Med. Phys. 10: 741-771; 1983. 2. Constantiou, C.; Attix, F. H.; Paliwal, B. R. Epoxy resin based tissue substitute. Br. J. Radiol. 5: 814-821; 1977. 3. Dahler, A.; Baker, A. S.; Laughlin, J. S. Compreshensive electron beam treatment planning. Ann. NY Acad. Sci. 161: 198-213; 1969. 4. Dressel, R. W. Retrofugal electron flux from massive targets irradiated by a monoenergetic primary beam. Phys. Rev. 144: 332; 1966a. 5. Dressel, R. W. Energy spectra of the retrofugal electron flux from massive targets. Phys. Rev. 144: 344; 1966b. 6. Harder, D. Energiespektren schneller elektronen in verschiedenen tiefen. In: Zuppinger, A., Poretti, G., eds. Symposium on high-energy electrons. Berlin: Springer-Verlag; 1965: 260. Hogstrom, K. R.; Mills, M. D.; Almond, P. R. Electron beam dose calculations. Phys. Med. Biol. 26: 445-459; 1981. Klevenhagen, S. C.; Lambert, G. D.; Arbabi, A. Backscattering in electron beam therapy for energies between 3 and 35 MeV. Phys. Med. Biol. 27: 363-373; 1982. Lambert, G. D.; Klevenhagen, S. C. Penetration of back-
scattered electrons in polystyrene for energies between 25 MeV. Phys. Med. Biol. 27: 721-725; 1982.
1 and
10. Laughin, J. S.; Lundy, A.; Phillips, R.; Chu, F.; Sattar, A. Electron beam treatment planning in inhomogeneous tissue. Radiology 85: 524-531; 1965. 11. Meyer, J. A.; Palta, J. R.; Hogstrom, K. R. Demonstration of relatively new electron dosimetry measurement techniques on the mevatron 80. Med. Phys. 11: 670-677; 1984. 12. Pohlit, W. Calculated and measured dose distribution in inhomogeneous materials and patients. Ann. NY Acad. Sci. 161: 189-197; 1969. 13. Prasad, S. C.; Ames, T. E.; Howard, T. B.; Bassano, D. A.; Chung, C. T.; King, G. A.; Segerman, R. H. Dose enhancement in bone in electron beam therapy. Radiology 151: 513516; 1984. electron beam dose calcula14. Shiu, A. S. Three-dimensional tions. Ph.D. dissertation, Univ. of Texas Graduate School of Biomedical Sciences, Houston, Texas; 1988. 15. Shiu, A. S.; Hogstrom, K. R. Pencil-beam redefinition algorithm for electron dose distributions. Med. Phys. 18:7-18; 1991. 16. Tabata, T. Backscattering of electrons from 3.2 to 14 MeV. Phys. Rev. 162: 336; 1967.
