- Email: [email protected]
Ionization profiles of conformed therapeutic electron beams
Beam Interactions withWaterials&Atoms
ELSEVIER
Nuclear
Instruments and Methods in Physics Research B 13’2( 1997) 326-330
Ionization profiles of conformed therapeutic electron beams M.E. Galassi ‘**, G.H. Olivera ‘, R.D. Rivarola ’ Institute
‘, P.J. Meoli b
de fisica
dr Rosario ( Consejo Nucionrrl de I~tl;rstiguc,iorIP.vCientificus y TPcnicas und Urticersidud Nucionul de Rosurio), Prllegrini ,750. 3000 Rosurio. Argentina ’ Depurtunwnto de Radioturupiu. lnstituto Akwnder Fierning. Crumrr 1180. 1426 Buenos Aires. Argrntinu
Ac.
Abstract Ionization profiles of conformed therapeutic electron beams were oblique incidence it appears that the air gap produces a competition the loss of intensity of the beam both of which depend upon the size of 0 1997 with simple multiple-scattering calculations are performed
measured at normal and oblique incidence. At between the coulombic multiple-scattering and the conformed beam. Comparisons of our results Elsevier Science B.V. _
-
1. Introduction Nowadays the use of electron beams on radiotherapy is a common technique. Therapeutic electron beams are very useful for the treatment of superficial or not very deep tumors. The information on the volume to irradiate generally comes from analysis of the anatomic data of the patient. Often, the beam has an irregular form, and due to the curvature of the patient the beam reaches the body at oblique angles. Several works deal with conformed electron beams from the theoretical and experimental point of view [l-6]. However, to the best knowledge of the authors, information about conformed therapeutic electron beams at
‘Corresponding author. Also at: Departamento de Fisica, Escuela de Ciencias Exactas y Naturales. Facultad de Ciencias Exactas. Ingenieria y Agrimensura. Universidad National de Rosario. 0168-583X/97/$17.00 Q 1997 Elsevier Science B.V. All rights reserved PIISO168-583X(97)00451-7
oblique incidence does not presently exist. The aim of the present work is to present some of the main features of the ionization profiles for this type of incidence, comparing the experimental results with simple approximations based on coulombic multiple-scattering processes. This work is the first in a comprehensive study on the topic that will be developed by the authors.
2. Experimental
setup and theoretical description
We have measured ionization profiles as functions of the depth on the axis and out of the axis of the beam for incidence angles of 0”. 20”, 40” and 60”, using a standard applicator for a 10 x 10 cm’ field. The beams were also conformed as rectangular fields using cut-out of cerrobend and lead on the treatment head. The surface nominal electron energies analyzed were 6, 10 and 15 MeV.
M.E. Galassi et al. I Nucl. Instr. and Meth
CENTRAL AXIS
L
cut-out 1 block 27
1 _ Aplicator
in Phys. Rex
B 132 (19971 326-330
327
The measurements were performed on a Siemens KDS-2 accelerator, using an ionization plane-parallel chamber type MARKUS PTW 23343. We have used a water phantom ACCUSCAN II of two dimensions. We performed a modification that has permitted us to obtain the ionization profiles at different angles (Fig. 1). The electron beam reaches the ionization chamber in a direction normal to the window entrance, which is a necessary condition for using this type of chamber. Our measurements are compared with those calculations obtained using the method proposed by Hogstrom et al. [7]. This method employs some reference field as input data (in our case the central ionization profile on the axis of a 10 x 10 cm? field at normal incidence) and the multiple coulomb scattering is described with the Fermi-Eyges theory [8,9]. The effect of high-energy secondary electrons produced by electron-electron Moller scattering [lo] is included in the experimentally determined reference depth-dose curve. Geometrical contours and air gaps are included in the model.
Angle: 0 degrees
Depth(cm) Fig. 2. Ionization profiles at normal incidence as a function of the depth for the treatment Ibrmation. The references about the different curves are shown in the figure.
head of 10 x 10 cm’ with and without
con-
3. Results and discussions In this work we prefer to analyze ionization profiles instead of dose profiles. The dosimetry of electron beams is well developed under calibrations conditions [I 1.121. but for the case of conformed beams with air gaps, the water to air stopping power ratio is not well known. Moreover. Ding et al. [13] have shown that the stopping power ratios depend on the machine used even under calibration conditions. In Fig. 2 we present ionization profiles on the axis for different conformed electron beams at normal incidence with 6 and 15 MeV nominal energies at the surface (without conformation). To understand the behavior of an oblique therapeutic electron beam it is instructive to use a schema similar to the one proposed by Ekstrand and Dixon [14]. A broad beam can be considered as the addition of a large number of electron pencil beams. In Fig. 3 a schema of these idealized beams each of small initial width (plotted is one isodose curve for each of these beams) is represented. Two of the features that can be interpreted with this simple schema are: ( I) The lack of symmetry on the transversal ionization profiles and (3) the shift of the maximum of the ionization profiles toward the surface due to the overlap of the pencils at shallow depths. However, we note this shifting
depends critically on the particular shape of the isodose, and here we have only indicated how the shifting comes about. We observe the first of these effects in Fig. 4, where a measured three-dimensional ionization profile and the corresponding iso-ionization curves are represented. It must be noted that the zero of the X-coordinate is taken in the crossing point between the central axis of the beam and the water surface for any depth. In Fig. 5. transversal ionization measurements at oblique incidence are shown. For this case, the origin of the X-coordinate is moved to the crossing between the beam axis and the line parallel to the water surface (see Fig. 1). In Fig. 5(a) we observe that for a fixed depth, the ionization is always larger for the negative X-coordinate. However, in Fig. 5(b) we see that at depths near the maximum of ionization the values are larger for positive Xvalues. This effect is possibly due to a competition
a)
ELECTRONS
W S-Coordinate (cm) -2CO
Water
Fig. 3. Schema
of pencil beams at oblique
incidence.
-1.OO
000
100
2.00
Fig. 4. (a) Experimental three-dimensional nizatlon profiles and (b) iso-ionization Z A IO cm2 beam at an incidence angle of nominal energy. The number in the curves tage of ionization.
3.00
representation of iocurves. both for I 40” and for 6 MeV indicate the percen-
M. E. Gulussi el ul. I Nwl.
329
Instr-. u?lti Meth. in Pllps. Rr.r. B 132 ( 1997) 326-330
80
0 -10
-8
-6
-4
-2
0
2
4
6
8
10 -4
-3
X- ccwdhnate
t ig. 5. Transversal about the ditrerent
ionization scanning for different curves are shown in the figure.
conformed
between the coulombic multiple-scattering of the beam and the loss of intensity of the beam in the air gap (which depends approximately with the inverse of the square of the source-surface distance), plus the contribution of scattered electrons at the cut out material. The air gap produces also a dispersion of the pencils before reaching the water surface. This dispersion depends on the X-coordinate and it is approximately linear with the traversed distance. For the smaller field size, the air gap does not produce an important intensity attenuation but, for the 10 x 10 cm’ field size the loss of intensity of the beam is more important than the corresponding coulombic multiple scatlering dispersion of the beam. These considerations may explain the different behavior for the two fields considered. Theoretical calculations will help us to quantify the contribution of each effect. Finally, in Fig. 6. we compare measured and calculated iso-ionization curves for normal incidence when a 10 x 3 cm2 field is used. The nominal energy at the surface is 6 MeV. We observe that the experimental results are reasonably reproduced by the theoretical model for the iso-ionization curves of 90% or smaller percentage for
-2
-1
0
1
2
3
4
(cm)
beams
at oblique
incidence
and at different
depths.
The references
depths larger than that corresponding to the maximum of ionization. The disagreement at depths smaller than that corresponding to the maximum are evidently due to the fact that the theoretical model does not consider the effect of the treatment head. On the other hand, the width of the experimental region of ionization is larger than the calculated one. These facts could be improved using the information obtained by codes such as BEAM [15] or the calculations performed by Ebert and Hoban [16.17].
Fig. 6. Iso-ionization curves for a 3 x IO cm2 conformed beam at normal incidence for a 6 MeV nominal energy. Theory: full line; experiments: dashed line. The iso-ionization curves are varled by intervals of 10%.
330
M.E. Galassi et al. I Nud. Instr. unti Met/t.
4. Conclusions Some of the main features of the ionization profiles of conformed electron beams have been studied. We observe a probable competition between the coulombic multiple-scattering of the beam in the air gap and the corresponding loss of intensity of the beam. Comparison of our experimental results and those obtained with a simple multiple-scattering theory, shows that they agree only for depths larger than that corresponding to the maximum ionization. More work is in progress to compare our experimental results for conformed oblique electron beams with more elaborated models such as the one of Jette and coworkers, including the effect of the treatment head [18-211.
Acknowledgements The authors wish to acknowledge the assistance of the Departamento de Radioterapia of the Instituto Alexander Fleming of Buenos Aires in providing use of its equipment facilities. This work has been developed as a part of the Proyecto de Investigation Anual N” 6909/96 of the Consejo National de Investigaciones Cientificas y Tecnicas (CONICET). One of us (G.H.O.) thanks Dr. David Jette and Dr. David Rogers for fruitful discussions.
in Plays. Rex
B 132 (1997) 326-330
References Sl PI [31 [41 [51 Fl [71 PI [91 UOI [ill
[121 [I31 1141 [I51
WI [I*1
B.J. McParland. Med. Phys. 16 (1989) 88. I.A.D. Bruinvis. A. Van Amstel. A.J., A.J. Elevelt, R. Van der Laarse, Phys. in Med. Biol. 28 (1983) 667. M. Mills. K. Hogstrom, P.R. Almond, Med. Phys. 9 (1982) 60. B.J. McParland, Med. Phys. 19 (1992) 901. B.J. McParland, Med. Phys. 15 (1988) 489. P.J. Biggs, Phys. in Med. Biol. 29 (1984) 1089. K. Hogstrom, M. Mills. A.J. Elevelt, P.R. Almond, Phys. in Med. Biol. 26 (1981) 445. L. Eyges. Phys. Rev. 74 (1948) 1534. B. Rossi. K. Greisen. Rev. Mod. Phys. 74 (1948) 1534. E.J. Williams, Phys. Rev. 58 (1940) 292. Absorbed dose determination in photon and electron beams: international Atomic Energy Agency, Technical Report 277, Viena, 1987. AAPM-TG2l. Med. Phys. 10 (1983) 741. G.X. Ding, D.W.O. Rogers. T.R. Mackie. Med. Phys. 22 (1995) 489. K. Ekstrand, R.L. Dixon, Med. Phys. 9 (1982) 278. D.W.O. Rogers, B.A. Faddegon. G.X. Ding. C.M. Ma, J. We, T.R. Mackie, Med. Phys. 2 (1995) 503. M.A. Ebert, P.W. Hoban, Med. Phys. 22 (1995) 1419. M.A. Ebert. P.W. Hoban. Med. Phys. 22 (1995) 1431. D. Jette, Med. Phys. 23 (1996) 459. D. Jette. in: A.R. Smith (Ed.). Medica Radiology, Radiation Therapy. Springer, Berlin. 1995, p. 95 and references therein. H. Neuenschwander, T.R. Mackie, P.J. Reckwerdt, Phys. in Med. Biol. 40 (1995) 543. H. Huizenga. P.R.M. Storchi. Phys. in Med. Biol. 34 (1989) 1371.
ELSEVIER
Nuclear
Instruments and Methods in Physics Research B 13’2( 1997) 326-330
Ionization profiles of conformed therapeutic electron beams M.E. Galassi ‘**, G.H. Olivera ‘, R.D. Rivarola ’ Institute
‘, P.J. Meoli b
de fisica
dr Rosario ( Consejo Nucionrrl de I~tl;rstiguc,iorIP.vCientificus y TPcnicas und Urticersidud Nucionul de Rosurio), Prllegrini ,750. 3000 Rosurio. Argentina ’ Depurtunwnto de Radioturupiu. lnstituto Akwnder Fierning. Crumrr 1180. 1426 Buenos Aires. Argrntinu
Ac.
Abstract Ionization profiles of conformed therapeutic electron beams were oblique incidence it appears that the air gap produces a competition the loss of intensity of the beam both of which depend upon the size of 0 1997 with simple multiple-scattering calculations are performed
measured at normal and oblique incidence. At between the coulombic multiple-scattering and the conformed beam. Comparisons of our results Elsevier Science B.V. _
-
1. Introduction Nowadays the use of electron beams on radiotherapy is a common technique. Therapeutic electron beams are very useful for the treatment of superficial or not very deep tumors. The information on the volume to irradiate generally comes from analysis of the anatomic data of the patient. Often, the beam has an irregular form, and due to the curvature of the patient the beam reaches the body at oblique angles. Several works deal with conformed electron beams from the theoretical and experimental point of view [l-6]. However, to the best knowledge of the authors, information about conformed therapeutic electron beams at
‘Corresponding author. Also at: Departamento de Fisica, Escuela de Ciencias Exactas y Naturales. Facultad de Ciencias Exactas. Ingenieria y Agrimensura. Universidad National de Rosario. 0168-583X/97/$17.00 Q 1997 Elsevier Science B.V. All rights reserved PIISO168-583X(97)00451-7
oblique incidence does not presently exist. The aim of the present work is to present some of the main features of the ionization profiles for this type of incidence, comparing the experimental results with simple approximations based on coulombic multiple-scattering processes. This work is the first in a comprehensive study on the topic that will be developed by the authors.
2. Experimental
setup and theoretical description
We have measured ionization profiles as functions of the depth on the axis and out of the axis of the beam for incidence angles of 0”. 20”, 40” and 60”, using a standard applicator for a 10 x 10 cm’ field. The beams were also conformed as rectangular fields using cut-out of cerrobend and lead on the treatment head. The surface nominal electron energies analyzed were 6, 10 and 15 MeV.
M.E. Galassi et al. I Nucl. Instr. and Meth
CENTRAL AXIS
L
cut-out 1 block 27
1 _ Aplicator
in Phys. Rex
B 132 (19971 326-330
327
The measurements were performed on a Siemens KDS-2 accelerator, using an ionization plane-parallel chamber type MARKUS PTW 23343. We have used a water phantom ACCUSCAN II of two dimensions. We performed a modification that has permitted us to obtain the ionization profiles at different angles (Fig. 1). The electron beam reaches the ionization chamber in a direction normal to the window entrance, which is a necessary condition for using this type of chamber. Our measurements are compared with those calculations obtained using the method proposed by Hogstrom et al. [7]. This method employs some reference field as input data (in our case the central ionization profile on the axis of a 10 x 10 cm? field at normal incidence) and the multiple coulomb scattering is described with the Fermi-Eyges theory [8,9]. The effect of high-energy secondary electrons produced by electron-electron Moller scattering [lo] is included in the experimentally determined reference depth-dose curve. Geometrical contours and air gaps are included in the model.
Angle: 0 degrees
Depth(cm) Fig. 2. Ionization profiles at normal incidence as a function of the depth for the treatment Ibrmation. The references about the different curves are shown in the figure.
head of 10 x 10 cm’ with and without
con-
3. Results and discussions In this work we prefer to analyze ionization profiles instead of dose profiles. The dosimetry of electron beams is well developed under calibrations conditions [I 1.121. but for the case of conformed beams with air gaps, the water to air stopping power ratio is not well known. Moreover. Ding et al. [13] have shown that the stopping power ratios depend on the machine used even under calibration conditions. In Fig. 2 we present ionization profiles on the axis for different conformed electron beams at normal incidence with 6 and 15 MeV nominal energies at the surface (without conformation). To understand the behavior of an oblique therapeutic electron beam it is instructive to use a schema similar to the one proposed by Ekstrand and Dixon [14]. A broad beam can be considered as the addition of a large number of electron pencil beams. In Fig. 3 a schema of these idealized beams each of small initial width (plotted is one isodose curve for each of these beams) is represented. Two of the features that can be interpreted with this simple schema are: ( I) The lack of symmetry on the transversal ionization profiles and (3) the shift of the maximum of the ionization profiles toward the surface due to the overlap of the pencils at shallow depths. However, we note this shifting
depends critically on the particular shape of the isodose, and here we have only indicated how the shifting comes about. We observe the first of these effects in Fig. 4, where a measured three-dimensional ionization profile and the corresponding iso-ionization curves are represented. It must be noted that the zero of the X-coordinate is taken in the crossing point between the central axis of the beam and the water surface for any depth. In Fig. 5. transversal ionization measurements at oblique incidence are shown. For this case, the origin of the X-coordinate is moved to the crossing between the beam axis and the line parallel to the water surface (see Fig. 1). In Fig. 5(a) we observe that for a fixed depth, the ionization is always larger for the negative X-coordinate. However, in Fig. 5(b) we see that at depths near the maximum of ionization the values are larger for positive Xvalues. This effect is possibly due to a competition
a)
ELECTRONS
W S-Coordinate (cm) -2CO
Water
Fig. 3. Schema
of pencil beams at oblique
incidence.
-1.OO
000
100
2.00
Fig. 4. (a) Experimental three-dimensional nizatlon profiles and (b) iso-ionization Z A IO cm2 beam at an incidence angle of nominal energy. The number in the curves tage of ionization.
3.00
representation of iocurves. both for I 40” and for 6 MeV indicate the percen-
M. E. Gulussi el ul. I Nwl.
329
Instr-. u?lti Meth. in Pllps. Rr.r. B 132 ( 1997) 326-330
80
0 -10
-8
-6
-4
-2
0
2
4
6
8
10 -4
-3
X- ccwdhnate
t ig. 5. Transversal about the ditrerent
ionization scanning for different curves are shown in the figure.
conformed
between the coulombic multiple-scattering of the beam and the loss of intensity of the beam in the air gap (which depends approximately with the inverse of the square of the source-surface distance), plus the contribution of scattered electrons at the cut out material. The air gap produces also a dispersion of the pencils before reaching the water surface. This dispersion depends on the X-coordinate and it is approximately linear with the traversed distance. For the smaller field size, the air gap does not produce an important intensity attenuation but, for the 10 x 10 cm’ field size the loss of intensity of the beam is more important than the corresponding coulombic multiple scatlering dispersion of the beam. These considerations may explain the different behavior for the two fields considered. Theoretical calculations will help us to quantify the contribution of each effect. Finally, in Fig. 6. we compare measured and calculated iso-ionization curves for normal incidence when a 10 x 3 cm2 field is used. The nominal energy at the surface is 6 MeV. We observe that the experimental results are reasonably reproduced by the theoretical model for the iso-ionization curves of 90% or smaller percentage for
-2
-1
0
1
2
3
4
(cm)
beams
at oblique
incidence
and at different
depths.
The references
depths larger than that corresponding to the maximum of ionization. The disagreement at depths smaller than that corresponding to the maximum are evidently due to the fact that the theoretical model does not consider the effect of the treatment head. On the other hand, the width of the experimental region of ionization is larger than the calculated one. These facts could be improved using the information obtained by codes such as BEAM [15] or the calculations performed by Ebert and Hoban [16.17].
Fig. 6. Iso-ionization curves for a 3 x IO cm2 conformed beam at normal incidence for a 6 MeV nominal energy. Theory: full line; experiments: dashed line. The iso-ionization curves are varled by intervals of 10%.
330
M.E. Galassi et al. I Nud. Instr. unti Met/t.
4. Conclusions Some of the main features of the ionization profiles of conformed electron beams have been studied. We observe a probable competition between the coulombic multiple-scattering of the beam in the air gap and the corresponding loss of intensity of the beam. Comparison of our experimental results and those obtained with a simple multiple-scattering theory, shows that they agree only for depths larger than that corresponding to the maximum ionization. More work is in progress to compare our experimental results for conformed oblique electron beams with more elaborated models such as the one of Jette and coworkers, including the effect of the treatment head [18-211.
Acknowledgements The authors wish to acknowledge the assistance of the Departamento de Radioterapia of the Instituto Alexander Fleming of Buenos Aires in providing use of its equipment facilities. This work has been developed as a part of the Proyecto de Investigation Anual N” 6909/96 of the Consejo National de Investigaciones Cientificas y Tecnicas (CONICET). One of us (G.H.O.) thanks Dr. David Jette and Dr. David Rogers for fruitful discussions.
in Plays. Rex
B 132 (1997) 326-330
References Sl PI [31 [41 [51 Fl [71 PI [91 UOI [ill
[121 [I31 1141 [I51
WI [I*1
B.J. McParland. Med. Phys. 16 (1989) 88. I.A.D. Bruinvis. A. Van Amstel. A.J., A.J. Elevelt, R. Van der Laarse, Phys. in Med. Biol. 28 (1983) 667. M. Mills. K. Hogstrom, P.R. Almond, Med. Phys. 9 (1982) 60. B.J. McParland, Med. Phys. 19 (1992) 901. B.J. McParland, Med. Phys. 15 (1988) 489. P.J. Biggs, Phys. in Med. Biol. 29 (1984) 1089. K. Hogstrom, M. Mills. A.J. Elevelt, P.R. Almond, Phys. in Med. Biol. 26 (1981) 445. L. Eyges. Phys. Rev. 74 (1948) 1534. B. Rossi. K. Greisen. Rev. Mod. Phys. 74 (1948) 1534. E.J. Williams, Phys. Rev. 58 (1940) 292. Absorbed dose determination in photon and electron beams: international Atomic Energy Agency, Technical Report 277, Viena, 1987. AAPM-TG2l. Med. Phys. 10 (1983) 741. G.X. Ding, D.W.O. Rogers. T.R. Mackie. Med. Phys. 22 (1995) 489. K. Ekstrand, R.L. Dixon, Med. Phys. 9 (1982) 278. D.W.O. Rogers, B.A. Faddegon. G.X. Ding. C.M. Ma, J. We, T.R. Mackie, Med. Phys. 2 (1995) 503. M.A. Ebert, P.W. Hoban, Med. Phys. 22 (1995) 1419. M.A. Ebert. P.W. Hoban. Med. Phys. 22 (1995) 1431. D. Jette, Med. Phys. 23 (1996) 459. D. Jette. in: A.R. Smith (Ed.). Medica Radiology, Radiation Therapy. Springer, Berlin. 1995, p. 95 and references therein. H. Neuenschwander, T.R. Mackie, P.J. Reckwerdt, Phys. in Med. Biol. 40 (1995) 543. H. Huizenga. P.R.M. Storchi. Phys. in Med. Biol. 34 (1989) 1371.