The Use of Photogrammetry in Tissue Compensator Design
Radiation Physics
Part II: Experimental Verification of Compensator Design 1 Wendel Dean Renner, M.S., Thomas P. O'Connor, M.D., Sharad R. Amtey, Ph.D., P. Raghunath Reddi, M.D., Gustave K. Bahr, Ph.D., and James G. Kereiakes, Ph.D. A computeralgorithmfor designing sheetleadtissuecompensators is described. Corrections are madefor scatter within the radiation fieldas well as the shape of the patientfor the mantle fields used in treating Hodgkin's disease. The method was tested experimentally with a phantomand foundto be clinically acceptable. The advantages of employing this technique with parallel opposed fields are emphasized. INDEX TERM: Treatment planning
Radiology 125:511-516, November 1977
SING THE photogrammetric technique as explained
U
in Part I, compensating filters can be designed to fit the individual patient. Figure 1 shows a patient whose anterior chest surface was sloping and was treated with an anterior as well as a posterior radiation field. An interpolating polynomial was used to obtain additional data points, thus producing a finer mesh, and a contour map showing surface elevations was plotted as shown in Figure 2. These contour lines represent boundaries between sheets of lead, while the finished compensator makes up for regions which do not contain tissue. To determine which elevations should be plotted, the thickness of the lead sheet and the amount of lead required to replace one centimeter of tissue (both given in millimeters) are fed into the computer. Beginning at the highest elevation (or at a point specified by the user), the computer plots the contours at intervals determined by the equation Fig. 1. Photograph taken with a Polaroid 450 camera andtype 107 film. Positioning is the same as the treatment setup except for a change in SSD. The x and y axes are indicated.
Distance between elevations (ern)
=
thickness of lead (mm) mm lead per cm of missing tissue
(1) however, when taking pictures this is easily corrected by realigning the patient after inserting the grid pattern. In order to standardize patient setup and calculation, the compensator is treated like a conventional wedge. The central-axis attenuation of the compensator is used to calculate the machine setting by counting the layers of lead covering the axis and referring to a chart of attenuation values . Effects of field size on attenuation were found to be negligible. The technician sets up the patient with the SSD measured on the central axis in the usual manner.
The z coordinate of the location of the compensator in the radiation beam must be specified for proper minification. The boundaries between the patient and the table top as well as small areas at the edge of the field (penumbrae) may be ignored. The compensator design is traced onto a lead sheet 0.794 mm (l/32 in.) thick and the individual pieces are cut out and soldered together. The compensator is then mounted on a plastic tray and inserted into the wedge slot of the therapy unit. It is aligned by marking the tray at the location of the cross hairs: since they were plotted as part of the original design (Fig. 2) and redrawn on the finished compensator, it can be readily aligned and taped in place . We found it necessary to shift the grid pattern slightly so that the cross hairs would not block the x and y axes;
Substituting Lead for Tissue with the Compensator
When using parallel opposed fields, it is desirable to achieve a uniform dose throughout the volume in spite of varying body thickness. With this setup the uniformity of
1 From Community Hospital, Indianapolis, Ind. (W.D.R., T.P.O.), West Virginia Medical Center, Morgantown, W. Va. (S.R.A., P.R.R .), and the Universityof Cincinnati Medical School, Cincinnati, Ohio (G.K.B., J.G.K.). Presented at the Sixty-secondScientific Assemblyand AnnualMeeting sjh of the Radiological Society of North America, Chicago, III., Nov. 14-19, 1976.
511
512
WENDEL DEAN RENNER AND OTHERS
November 1977
y
x
Fig. 2. A. Compensator designed by the computer from the photograph shown in Figure 1. The design is basically a contour map of the patient's surface in the treatment field. The elevations between contour lines correspond to layers of sheet lead 0.794 mm thick. The tick marks indicate increasing lead. B. Lead compensator made from the design shown in Figure 2, A. The compensator is mounted on a plastic tray that fits into the wedge slot of the therapy machine.
TABLE I: DEPTH (CM)
1 5 10 15 20 30
PER CENT OF TOTAL 60Co DOSE ATTRIBUTABLE TOSCATIER' FIELD SIZE (eM) O XO
4 X4
a xa
0.0 0.0 0.0 0.0 0.0 0.0
2.7 10.2 13.5 14.6 16.0 18.2
5.1 16.1 21.6 24.9 28.0 31.4
12
x
12
6.9 19.2 26.6 28.4 32 .0 36 .8
20 X 20
30 X 30
8.7 22.1 32.1 38.6 44.5 52.8
10.6 24.9 36.2 43.8 50.4 59.8
• Calculated from Johns and Cunningham (19)
the dose distribution with depth will increase as the thickness of the body section decreases regardless of the method of compensation employed. As shown below , if compensation for each field is adjusted so that the midplane receives a uniform dose, then doses above the midplane will be overcompensated and doses below the midplane will be undercompensated, so that these errors will cancel out when parallel opposed fields are used. For this reason, we wanted to achieve optimal uniformity at
the midplane (as determined on the central axis) to minimize dose heterogeneity in other relevant locations. Though this could be done by using a smaller radiation field, tissue compensators have two distinct advantages: (a) the time/dose relationship is more nearly constant throughout the treated volume and (b) treating the same field each day with a compensator is simpler than changing the field periodically to match the body topography. Previous discussions of tissue compensators (2, 11-13) have shown that compensation depends on both depth and field size, since the scattered radiations which comprise a significant portion of the dose are dependent on both of these factors (TABLE I). The amount of compensation required may be approximated by the ratio of the respective tissue/air ratios (TAR) (7, 12, 13); for example, for 5 cm of compensation, the attenuation requirement at a depth of 5, 10, and 15 cm is 0.825,0 .801, and 0.793, respectively, for a 20 X 20-cm field [as determined from the TAR table given by Johns for GOCo (19)]. In general, the greater the depth, the more attenuation required, since scatter
20 ",'"
I I
",'"
-
10
,'"
20
,
"
I
"
, -
,"--' \
".~--,
•
I
I
0
Q
.-
".".""
\
,, I,
1
.- /'"
"
0
4
o
--
1 2 •• ,.
10
11 . I '
em
Cent ime'."
0.....L..~r-.......,r-1--r~~---r
8
Radiation Physics
'"
20
0
10
10.1 0
A
513
THE USE OF PHOTOGRAMMETRY IN TISSUE COMPENSATOR DESIGN
Vol. 12S
4
8
0 -1-- r-.---r-r-r- r--....-"-'r-T- r- . 10 10 o
B
O -;--.--,....,r--T-.-....-r-r-r-.--,..-,,....,-.-...-..--r-r--r-..o C 20 10 10 20
Fig. 3. A-C. Scans along the bottom of the water phantom for field sizes of 10 X 10 (A), 18 X 18 (B), and 28 X 28 cm (C) at a SO-cmSSD. Dashed line = scan without compensator; solid line = scan with compensator . A value of 0.721 mm lead per centimeter of missing tissue was used for all three compensators.
increases with depth. This can be illustrated by considering a volume 30 cm thick which drops off to 20 cm with 5 cm of tissue missing on each opposing surface. Using the 60CO TAR table for a 20 X 20-cm field, we find that the attenuation requirement for compensation of the 20-cm portion is 0.801 at the midplane. If the compensated midplane is treated with 100 rads at a 100-cm source-axis distance (SAD) using parallel opposed fields, the dose at 1 cm from the surface in the 20-cm portion is 109 rads, compared to 116 rads at the same level in the 3D-cm portion (6 cm from the surface), i.e., the dose is actually more uniform with depth in the thinner (compensated) portion than in the thicker (uncompensated) portion. Similarly, the dose at 1 cm depth in the thick portion is 133 rads. Thus the skin dose overlying the thicker parts of the body is necessarily higher than that to the thinner portions if the midplane is to be treated uniformly. The degree of attenuation is dependent on the proportion of the field which must be compensated; for example, compensation from 5 to 10 cm for a 30 X 30-cm field may require an attenuation factor ranging from 0.847 for full compensation to 0.795 for only a small area, since scatter in turn depends on the amount of adjacent tissue which does not need compensation. Because precise compensation for varying patient thicknesses is difficult if not impossible, we will attempt to show only that this technique can facilitate dose uniformity to a plane at depth for selected phantoms. Before one can construct a surface tissue compensator , it is necessary to know how much lead is needed to replace the missing tissue. This can be determined by solving the following equation for t, assuming that tissue is missing over the entire surface: TAR pO-cm depth) TAR (5-cm depth)
= e-Silt
(2)
where J.1 cm- 1 is the linear attenuation coefficient of lead, TAR is the tissue/air ratio for the specific depths and field size used, and tis mm lead per centimeter of missing tissue; depths of 5 and 10 cm were chosen arbitrarily. To see whether this equation would hold for all field sizes, we
Fig. 4.
Phantom representing the head and chest, made from tissue-equivalent silicone rubber.
conducted a series of experiments using a sloping plywood phantom filled with water so that the depth changed from 15 to 5 cm over a distance of 15 cm. The central axis of the therapy unit (an EMI 4-MeV linear accelerator) was aligned with the slope at a 90-cm SSD and compensators were made using the technique described in Part I. Profile scans were made with a 0.6-cm 3 ionization chamber by taking measurements at t-ern intervals along a major axis of the radiation field underneath the slope. Since scatter tends to decrease the discontinuity introduced by using discrete steps, a smooth curve was drawn through the data points. These experiments showed that a single value of t can give good results for all field sizes , at least for this particular phantom. Profile scans for 10 X 10, 18 X 18, and 28 X 28-cm fields are shown in Figure 3. A single value of t 0.721 mm lead per cm of missing tissue (determined from equation 2 with a field size of 10 X 10 cm) was used to make the compensators for all three fields . The relative flatness of the profiles indicates that the size of the field had little effect on compensation . To test the compensator under clinical conditions, we made a plaster cast of the head and chest of the Rando phantom and used it as a mold to fabricate the silicone
=
514
WENDEL DEAN RENNER AND OTHERS
November 1977
Fig. 5. A. Polaroid print used in making a compensator for the silicone rubber phantom (11 X 11-cm field size, aO-cm SSD). B. Isodose plot at the midplane for a value of 0.721 mm lead per centimeter of tissue . The distance between the central axis and the film is 6 cm . C. Isodose plot at the midplane without the compensator.
rubber- phantom shown in Figure 4. Attenuation was identical to that of water . When Kodak RPIV film was placed under the phantom at a depth corresponding to the midplane of the Rando phantom and the dose to various thicknesses was checked, it was found to be the same as that determined with an ionization chamber. Isodose levels were plotted by converting film density to dose using the Artronix system." Plots made with and without the compensator showed improved dose uniformity (Fig. 5). Compensation of a Large Blocked Field The mantle field used in the treatment of Hodgkin's disease deserves special cons ideration . Various techniques have been used to achieve a uniform dose throughout the treated volume. A common practice is to reduce the field size as thinner volumes reach the target dose level ; however, the time/dose effect will vary throughoutthe volume with this method. Leung (8) designed a surface tissue compensator from a plaster cast of the patient and then made a separate compensator to offset the effect of the different amounts of scatter in the field , using a computer to plot isodose levels in a plane normal to the central axis at depth for a flat surface and irregular field. He then used both compensators in treat ing the patient. By this means he was able to achieve a uniform dose (± 5 %) over 90 % of the field. Using the technique described here, it would seem advantageous to combine the two compensators described by Leung into a single unit which we call a dose compensator. This was done in the following manner. Each of the array points of the 35 X 35 matrix which defines the surface of the patient is projected onto a plane at a depth normal to the central axis. The dose to each matrix point is then computed using the equation 2 GE RTV 602; specific gravity 0.995, electron density 3.25 X 1023 e/cm" , effective atomic number 10.5. 3 Artronix Corp., St. Louis, Mo.
B0
so
Fig. 6. Isodose plot of a plane normal to the central axis for a mantle field , using the silicone rubber phantom without a compensator. The film is located approximately where the midplane of the Rando phantom would be. Adequate backscatter mater ial was placed under the film .
SAD2
Dose
= (p. TAR + scatter)· x 2 + y2 + SAD2
(3)
where P is a penumbra parameter computed using Wilkinson's source model (20) ; it defines field flatness and penumbrae accurately but does not account for the high doses seen near the edges of large fields with many accelerators at shallow depths. TAR is the zero field size tissue/air ratio measured using the slant depth from the surface of the patient to the plane. Scatter is the scatter/air ratio computed using Clarkson's method (21) and the field size at depth. The last term corrects for slant, with x and y representing the x and y coordinates of the matrix point at depth (the origin is at the central ray) and SAD repre-
THE USE OF PHOTOGRAMMETRY IN TISSUE COMPENSATOR DESIGN
Vol. 125
515
Radiation Physics
50
Fig. 7.
Surface tissue compensator plotted for the silicone rubber phantom at the position of the mantle field, shown together with the isodose plot. This compensator corrects only for the shape of the patient.
Fig. 8. Dose compensator designed for a mantle field, together with the isodose plot. This compensator corrects for both the shape of the patient and the irregularity of the field. The plane of computation was 10 cm below the compensating point, corresponding to the level at which film was placed for dosimetry. The compensating point was chosen to be near the lower central border of the field. Most of the field is flat to within ± 5 % .
senting the source/axis distance (from the source to the plane). Since this computation requires a great deal of computer time, the dose to every other matrix point is actually computed and the others are interpolated. Even so, it takes about 3 hours using the Rad 8. The above algorithm permits the use of the same beam data employed in an irregular-field program. The user must select a point in the field as the "compensation point": in the mantle field under consideration, we chose a point near the lower central border. For doses greater than that to the
compensation point, the appropriate thickness of lead is determined such that higher doses are reduced to that at the compensation point by shielding the beam with sheet lead. In so doing, we assumed that the lead covers a wide enough area around the matrix point that both primary radiations and scatter would be reduced by the same factor (which is not completely true). To test this assumption, we conducted a series of experiments with the silicone rubber phantom (Fig. 4). First we treated the mantle field without a compensator and plotted field flatness on film as de-
516
WENDEL DEAN RENNER AND OTHERS
scribed above (Fig. 6). In order that the difference between surface and dose compensators might be appreciated, the phantom was treated with a surface compensator as shown in Figure 7. We then treated the phantom again using the dose compensator, giving the results shown in Figure 8. When the dose compensator was used, flatness was improved and dose uniformity achieved over most of the field, giving values of ± 5 % with a few small areas of 110%. CONCLUSION
A tissue compensator designed from a photograph is accurate within the limitations of the singlEHtepth concept. Leung (8) has shown that appreciable errors in dose may result when large amounts of tissue are missing and there are great differences in depth; however, if compensation is achieved at the midplane, these errors tend to cancel out when parallel opposed fields are used. The amount of lead required for compensation is known to vary with depth, field size, and the volume of missing tissue, since the scatter contribution varies with these factors. A first-order algorithm involving a simple substitution of lead for missing tissue seems appropriate for clinical purposes; however, the parameters involved must be verified experimentally. Further work is perhaps needed in arriving at a mathematical algorithm whose parameters would not need experimental verification and which would correct for all scatter conditions. Some of the techniques suggested by Johns and Cunningham (19) for computing scatter dose in a three-dimensional volume may prove useful in future developments. In the technique presented here, it takes only a few minutes to photograph the patient, which is of particular advantage in the extremely ill person. Entering the data into the computer via a graphics terminal is very efficient for small fields (about 5 minutes) and not much more difficult for a large field such as the mantle (45 minutes to an hour for anterior and posterior compensators). The only complex factor involved is the computer software; however, the FORTRAN program should be readily adaptable to other available computer systems.
ACKNOWLEDGMENT: We wish to thank Dr. Richard Horn for his help in producing the isodose plots.
REFERENCES 1. Ellis F, Hall EJ, Oliver R: A compensator for variations in tissue thickness for high energy beams. Br J RadioI32:421-422, Jun 1959
November 1977
2. Hall EJ, Oliver R: The use of standard isodose distributions with high energy radiation beams-the accuracy of a compensator technique in correcting for body contours. Br J Radiol 34:43-52, Jan 1961 3. Khan FM, Moore VC, Burns OJ: An apparatus for the construction of irregular surface compensators for use in radiotherapy. Radiology 90:593-594, Mar 1968 4. Watkins DMB: A proposed method for making reduced wax compensators for use with high-energy radiation beams. Br J Radiol 48:760-762, Sep 1975 5. Beck GG, McGonnagle WJ, Sullivan CA: Use of a Styrofoam block cutter to make tissue-equivalent compensators. Radiology 100:694-696, Sep 1971 6. Boge RJ, Edland RW, Matthes DC: Tissue compensators for megavoltage radiotherapy fabricated from hollowed Styrofoam filled with wax. Radiology 111:193-198, Apr 1974 7. Cunningham JR, Wright OJ, Webb HP,et al: A semi-automatic cutter for compensating filters. Int J Radiat Oncol BioI Phys 1:355-360, Jan-Feb 1976 8. Leung PMK, Van Dyk J, Robins J: A method of large irregular field compensation. Br J RadioI47:805-810, Nov 1974 9. Clemens J, Bjarngard B, Boyer A, et al: Computer automation of compensating filter design. Presented at the Fifth International Conference on the Use of Computers in Radiation Therapy, Dartmouth College, Hanover, N. H., Aug. 18-23, 1974 10. S\&rensen NE: A simple method for the construction of compensators for 'missing tissue.' Phys Med Bioi 13: 113-115, Jan 1968 11. Khan FM, Moore VC, Burns OJ: The construction of compensators for cobalt teletherapy. Radiology 96: 187-192, Jul 1970 12. Wilks R, Casebow MP: Tissue compensation with lead for 60Co therapy. Br J RadioI42:452-456, Jun 1969 13. van de Geijn J: The construction of individualised intensity modifying filters in cobalt 60 teletherapy. Br J Radiol 38:865-870, Nov 1965 14. Herron RE: Biostereometric measurement of body form. Year Book Phys AnthropoI16:80-121, 1972 15. Biostereometrics '74. Proceedings of the Symposium of Commission V, International Society for Photogrammetry, Washington DC, Sept. 10-13, 1974. Falls Church, Va., Am Soc Photogrammetry, 1974 16. Proceedings of the Symposium on Close-Range Photogrammetric Systems, Champaign, 111., July 28-Aug. 1, 1975. Falls Church, Va., Am Soc Photogrammetry, 1975 17. Faig W: Precision plotting of non-metric photography. [In] Biostereometrics 74. Proceedings of the Symposium of Commission V, International Society for Photogrammetry, Washington DC, Sept. 10-13, 1974. Falls Church, Va., Am Soc Photogrammetry, 1974, pp 54-64 18. Bevington PR: Data Reduction and Error Analysis for the Physical Sciences. New York, McGraw-Hili, 1969, pp 259-267 19. Johns HE, Cunningham JR: The Physics of Radiology. Springfield, 111., Thomas, 3d Ed, 1969, pp 362-363 and 749-750 20. Wilkinson JM, Rawlinson JA, Cunningham JR: An extended source model for the calculation of the primary component of a cobalt-60 radiation beam in penumbral regions. [In] Dosimetry Workshop, Hodgkin's Disease,Chicago, 111., Sept. 17, 1970. Washington DC, AAPM, 1970, pp C 1-16 21. Clarkson JR: A note on depth doses in fields of irregularshape. Br J Radiol 14:265-268, Aug 1941 Department of Radiation Oncology Community Hospital of Indianapolis 1500 N. Ritter Ave. Indianapolis, Ind. 46219
Radiation Physics
Part II: Experimental Verification of Compensator Design 1 Wendel Dean Renner, M.S., Thomas P. O'Connor, M.D., Sharad R. Amtey, Ph.D., P. Raghunath Reddi, M.D., Gustave K. Bahr, Ph.D., and James G. Kereiakes, Ph.D. A computeralgorithmfor designing sheetleadtissuecompensators is described. Corrections are madefor scatter within the radiation fieldas well as the shape of the patientfor the mantle fields used in treating Hodgkin's disease. The method was tested experimentally with a phantomand foundto be clinically acceptable. The advantages of employing this technique with parallel opposed fields are emphasized. INDEX TERM: Treatment planning
Radiology 125:511-516, November 1977
SING THE photogrammetric technique as explained
U
in Part I, compensating filters can be designed to fit the individual patient. Figure 1 shows a patient whose anterior chest surface was sloping and was treated with an anterior as well as a posterior radiation field. An interpolating polynomial was used to obtain additional data points, thus producing a finer mesh, and a contour map showing surface elevations was plotted as shown in Figure 2. These contour lines represent boundaries between sheets of lead, while the finished compensator makes up for regions which do not contain tissue. To determine which elevations should be plotted, the thickness of the lead sheet and the amount of lead required to replace one centimeter of tissue (both given in millimeters) are fed into the computer. Beginning at the highest elevation (or at a point specified by the user), the computer plots the contours at intervals determined by the equation Fig. 1. Photograph taken with a Polaroid 450 camera andtype 107 film. Positioning is the same as the treatment setup except for a change in SSD. The x and y axes are indicated.
Distance between elevations (ern)
=
thickness of lead (mm) mm lead per cm of missing tissue
(1) however, when taking pictures this is easily corrected by realigning the patient after inserting the grid pattern. In order to standardize patient setup and calculation, the compensator is treated like a conventional wedge. The central-axis attenuation of the compensator is used to calculate the machine setting by counting the layers of lead covering the axis and referring to a chart of attenuation values . Effects of field size on attenuation were found to be negligible. The technician sets up the patient with the SSD measured on the central axis in the usual manner.
The z coordinate of the location of the compensator in the radiation beam must be specified for proper minification. The boundaries between the patient and the table top as well as small areas at the edge of the field (penumbrae) may be ignored. The compensator design is traced onto a lead sheet 0.794 mm (l/32 in.) thick and the individual pieces are cut out and soldered together. The compensator is then mounted on a plastic tray and inserted into the wedge slot of the therapy unit. It is aligned by marking the tray at the location of the cross hairs: since they were plotted as part of the original design (Fig. 2) and redrawn on the finished compensator, it can be readily aligned and taped in place . We found it necessary to shift the grid pattern slightly so that the cross hairs would not block the x and y axes;
Substituting Lead for Tissue with the Compensator
When using parallel opposed fields, it is desirable to achieve a uniform dose throughout the volume in spite of varying body thickness. With this setup the uniformity of
1 From Community Hospital, Indianapolis, Ind. (W.D.R., T.P.O.), West Virginia Medical Center, Morgantown, W. Va. (S.R.A., P.R.R .), and the Universityof Cincinnati Medical School, Cincinnati, Ohio (G.K.B., J.G.K.). Presented at the Sixty-secondScientific Assemblyand AnnualMeeting sjh of the Radiological Society of North America, Chicago, III., Nov. 14-19, 1976.
511
512
WENDEL DEAN RENNER AND OTHERS
November 1977
y
x
Fig. 2. A. Compensator designed by the computer from the photograph shown in Figure 1. The design is basically a contour map of the patient's surface in the treatment field. The elevations between contour lines correspond to layers of sheet lead 0.794 mm thick. The tick marks indicate increasing lead. B. Lead compensator made from the design shown in Figure 2, A. The compensator is mounted on a plastic tray that fits into the wedge slot of the therapy machine.
TABLE I: DEPTH (CM)
1 5 10 15 20 30
PER CENT OF TOTAL 60Co DOSE ATTRIBUTABLE TOSCATIER' FIELD SIZE (eM) O XO
4 X4
a xa
0.0 0.0 0.0 0.0 0.0 0.0
2.7 10.2 13.5 14.6 16.0 18.2
5.1 16.1 21.6 24.9 28.0 31.4
12
x
12
6.9 19.2 26.6 28.4 32 .0 36 .8
20 X 20
30 X 30
8.7 22.1 32.1 38.6 44.5 52.8
10.6 24.9 36.2 43.8 50.4 59.8
• Calculated from Johns and Cunningham (19)
the dose distribution with depth will increase as the thickness of the body section decreases regardless of the method of compensation employed. As shown below , if compensation for each field is adjusted so that the midplane receives a uniform dose, then doses above the midplane will be overcompensated and doses below the midplane will be undercompensated, so that these errors will cancel out when parallel opposed fields are used. For this reason, we wanted to achieve optimal uniformity at
the midplane (as determined on the central axis) to minimize dose heterogeneity in other relevant locations. Though this could be done by using a smaller radiation field, tissue compensators have two distinct advantages: (a) the time/dose relationship is more nearly constant throughout the treated volume and (b) treating the same field each day with a compensator is simpler than changing the field periodically to match the body topography. Previous discussions of tissue compensators (2, 11-13) have shown that compensation depends on both depth and field size, since the scattered radiations which comprise a significant portion of the dose are dependent on both of these factors (TABLE I). The amount of compensation required may be approximated by the ratio of the respective tissue/air ratios (TAR) (7, 12, 13); for example, for 5 cm of compensation, the attenuation requirement at a depth of 5, 10, and 15 cm is 0.825,0 .801, and 0.793, respectively, for a 20 X 20-cm field [as determined from the TAR table given by Johns for GOCo (19)]. In general, the greater the depth, the more attenuation required, since scatter
20 ",'"
I I
",'"
-
10
,'"
20
,
"
I
"
, -
,"--' \
".~--,
•
I
I
0
Q
.-
".".""
\
,, I,
1
.- /'"
"
0
4
o
--
1 2 •• ,.
10
11 . I '
em
Cent ime'."
0.....L..~r-.......,r-1--r~~---r
8
Radiation Physics
'"
20
0
10
10.1 0
A
513
THE USE OF PHOTOGRAMMETRY IN TISSUE COMPENSATOR DESIGN
Vol. 12S
4
8
0 -1-- r-.---r-r-r- r--....-"-'r-T- r- . 10 10 o
B
O -;--.--,....,r--T-.-....-r-r-r-.--,..-,,....,-.-...-..--r-r--r-..o C 20 10 10 20
Fig. 3. A-C. Scans along the bottom of the water phantom for field sizes of 10 X 10 (A), 18 X 18 (B), and 28 X 28 cm (C) at a SO-cmSSD. Dashed line = scan without compensator; solid line = scan with compensator . A value of 0.721 mm lead per centimeter of missing tissue was used for all three compensators.
increases with depth. This can be illustrated by considering a volume 30 cm thick which drops off to 20 cm with 5 cm of tissue missing on each opposing surface. Using the 60CO TAR table for a 20 X 20-cm field, we find that the attenuation requirement for compensation of the 20-cm portion is 0.801 at the midplane. If the compensated midplane is treated with 100 rads at a 100-cm source-axis distance (SAD) using parallel opposed fields, the dose at 1 cm from the surface in the 20-cm portion is 109 rads, compared to 116 rads at the same level in the 3D-cm portion (6 cm from the surface), i.e., the dose is actually more uniform with depth in the thinner (compensated) portion than in the thicker (uncompensated) portion. Similarly, the dose at 1 cm depth in the thick portion is 133 rads. Thus the skin dose overlying the thicker parts of the body is necessarily higher than that to the thinner portions if the midplane is to be treated uniformly. The degree of attenuation is dependent on the proportion of the field which must be compensated; for example, compensation from 5 to 10 cm for a 30 X 30-cm field may require an attenuation factor ranging from 0.847 for full compensation to 0.795 for only a small area, since scatter in turn depends on the amount of adjacent tissue which does not need compensation. Because precise compensation for varying patient thicknesses is difficult if not impossible, we will attempt to show only that this technique can facilitate dose uniformity to a plane at depth for selected phantoms. Before one can construct a surface tissue compensator , it is necessary to know how much lead is needed to replace the missing tissue. This can be determined by solving the following equation for t, assuming that tissue is missing over the entire surface: TAR pO-cm depth) TAR (5-cm depth)
= e-Silt
(2)
where J.1 cm- 1 is the linear attenuation coefficient of lead, TAR is the tissue/air ratio for the specific depths and field size used, and tis mm lead per centimeter of missing tissue; depths of 5 and 10 cm were chosen arbitrarily. To see whether this equation would hold for all field sizes, we
Fig. 4.
Phantom representing the head and chest, made from tissue-equivalent silicone rubber.
conducted a series of experiments using a sloping plywood phantom filled with water so that the depth changed from 15 to 5 cm over a distance of 15 cm. The central axis of the therapy unit (an EMI 4-MeV linear accelerator) was aligned with the slope at a 90-cm SSD and compensators were made using the technique described in Part I. Profile scans were made with a 0.6-cm 3 ionization chamber by taking measurements at t-ern intervals along a major axis of the radiation field underneath the slope. Since scatter tends to decrease the discontinuity introduced by using discrete steps, a smooth curve was drawn through the data points. These experiments showed that a single value of t can give good results for all field sizes , at least for this particular phantom. Profile scans for 10 X 10, 18 X 18, and 28 X 28-cm fields are shown in Figure 3. A single value of t 0.721 mm lead per cm of missing tissue (determined from equation 2 with a field size of 10 X 10 cm) was used to make the compensators for all three fields . The relative flatness of the profiles indicates that the size of the field had little effect on compensation . To test the compensator under clinical conditions, we made a plaster cast of the head and chest of the Rando phantom and used it as a mold to fabricate the silicone
=
514
WENDEL DEAN RENNER AND OTHERS
November 1977
Fig. 5. A. Polaroid print used in making a compensator for the silicone rubber phantom (11 X 11-cm field size, aO-cm SSD). B. Isodose plot at the midplane for a value of 0.721 mm lead per centimeter of tissue . The distance between the central axis and the film is 6 cm . C. Isodose plot at the midplane without the compensator.
rubber- phantom shown in Figure 4. Attenuation was identical to that of water . When Kodak RPIV film was placed under the phantom at a depth corresponding to the midplane of the Rando phantom and the dose to various thicknesses was checked, it was found to be the same as that determined with an ionization chamber. Isodose levels were plotted by converting film density to dose using the Artronix system." Plots made with and without the compensator showed improved dose uniformity (Fig. 5). Compensation of a Large Blocked Field The mantle field used in the treatment of Hodgkin's disease deserves special cons ideration . Various techniques have been used to achieve a uniform dose throughout the treated volume. A common practice is to reduce the field size as thinner volumes reach the target dose level ; however, the time/dose effect will vary throughoutthe volume with this method. Leung (8) designed a surface tissue compensator from a plaster cast of the patient and then made a separate compensator to offset the effect of the different amounts of scatter in the field , using a computer to plot isodose levels in a plane normal to the central axis at depth for a flat surface and irregular field. He then used both compensators in treat ing the patient. By this means he was able to achieve a uniform dose (± 5 %) over 90 % of the field. Using the technique described here, it would seem advantageous to combine the two compensators described by Leung into a single unit which we call a dose compensator. This was done in the following manner. Each of the array points of the 35 X 35 matrix which defines the surface of the patient is projected onto a plane at a depth normal to the central axis. The dose to each matrix point is then computed using the equation 2 GE RTV 602; specific gravity 0.995, electron density 3.25 X 1023 e/cm" , effective atomic number 10.5. 3 Artronix Corp., St. Louis, Mo.
B0
so
Fig. 6. Isodose plot of a plane normal to the central axis for a mantle field , using the silicone rubber phantom without a compensator. The film is located approximately where the midplane of the Rando phantom would be. Adequate backscatter mater ial was placed under the film .
SAD2
Dose
= (p. TAR + scatter)· x 2 + y2 + SAD2
(3)
where P is a penumbra parameter computed using Wilkinson's source model (20) ; it defines field flatness and penumbrae accurately but does not account for the high doses seen near the edges of large fields with many accelerators at shallow depths. TAR is the zero field size tissue/air ratio measured using the slant depth from the surface of the patient to the plane. Scatter is the scatter/air ratio computed using Clarkson's method (21) and the field size at depth. The last term corrects for slant, with x and y representing the x and y coordinates of the matrix point at depth (the origin is at the central ray) and SAD repre-
THE USE OF PHOTOGRAMMETRY IN TISSUE COMPENSATOR DESIGN
Vol. 125
515
Radiation Physics
50
Fig. 7.
Surface tissue compensator plotted for the silicone rubber phantom at the position of the mantle field, shown together with the isodose plot. This compensator corrects only for the shape of the patient.
Fig. 8. Dose compensator designed for a mantle field, together with the isodose plot. This compensator corrects for both the shape of the patient and the irregularity of the field. The plane of computation was 10 cm below the compensating point, corresponding to the level at which film was placed for dosimetry. The compensating point was chosen to be near the lower central border of the field. Most of the field is flat to within ± 5 % .
senting the source/axis distance (from the source to the plane). Since this computation requires a great deal of computer time, the dose to every other matrix point is actually computed and the others are interpolated. Even so, it takes about 3 hours using the Rad 8. The above algorithm permits the use of the same beam data employed in an irregular-field program. The user must select a point in the field as the "compensation point": in the mantle field under consideration, we chose a point near the lower central border. For doses greater than that to the
compensation point, the appropriate thickness of lead is determined such that higher doses are reduced to that at the compensation point by shielding the beam with sheet lead. In so doing, we assumed that the lead covers a wide enough area around the matrix point that both primary radiations and scatter would be reduced by the same factor (which is not completely true). To test this assumption, we conducted a series of experiments with the silicone rubber phantom (Fig. 4). First we treated the mantle field without a compensator and plotted field flatness on film as de-
516
WENDEL DEAN RENNER AND OTHERS
scribed above (Fig. 6). In order that the difference between surface and dose compensators might be appreciated, the phantom was treated with a surface compensator as shown in Figure 7. We then treated the phantom again using the dose compensator, giving the results shown in Figure 8. When the dose compensator was used, flatness was improved and dose uniformity achieved over most of the field, giving values of ± 5 % with a few small areas of 110%. CONCLUSION
A tissue compensator designed from a photograph is accurate within the limitations of the singlEHtepth concept. Leung (8) has shown that appreciable errors in dose may result when large amounts of tissue are missing and there are great differences in depth; however, if compensation is achieved at the midplane, these errors tend to cancel out when parallel opposed fields are used. The amount of lead required for compensation is known to vary with depth, field size, and the volume of missing tissue, since the scatter contribution varies with these factors. A first-order algorithm involving a simple substitution of lead for missing tissue seems appropriate for clinical purposes; however, the parameters involved must be verified experimentally. Further work is perhaps needed in arriving at a mathematical algorithm whose parameters would not need experimental verification and which would correct for all scatter conditions. Some of the techniques suggested by Johns and Cunningham (19) for computing scatter dose in a three-dimensional volume may prove useful in future developments. In the technique presented here, it takes only a few minutes to photograph the patient, which is of particular advantage in the extremely ill person. Entering the data into the computer via a graphics terminal is very efficient for small fields (about 5 minutes) and not much more difficult for a large field such as the mantle (45 minutes to an hour for anterior and posterior compensators). The only complex factor involved is the computer software; however, the FORTRAN program should be readily adaptable to other available computer systems.
ACKNOWLEDGMENT: We wish to thank Dr. Richard Horn for his help in producing the isodose plots.
REFERENCES 1. Ellis F, Hall EJ, Oliver R: A compensator for variations in tissue thickness for high energy beams. Br J RadioI32:421-422, Jun 1959
November 1977
2. Hall EJ, Oliver R: The use of standard isodose distributions with high energy radiation beams-the accuracy of a compensator technique in correcting for body contours. Br J Radiol 34:43-52, Jan 1961 3. Khan FM, Moore VC, Burns OJ: An apparatus for the construction of irregular surface compensators for use in radiotherapy. Radiology 90:593-594, Mar 1968 4. Watkins DMB: A proposed method for making reduced wax compensators for use with high-energy radiation beams. Br J Radiol 48:760-762, Sep 1975 5. Beck GG, McGonnagle WJ, Sullivan CA: Use of a Styrofoam block cutter to make tissue-equivalent compensators. Radiology 100:694-696, Sep 1971 6. Boge RJ, Edland RW, Matthes DC: Tissue compensators for megavoltage radiotherapy fabricated from hollowed Styrofoam filled with wax. Radiology 111:193-198, Apr 1974 7. Cunningham JR, Wright OJ, Webb HP,et al: A semi-automatic cutter for compensating filters. Int J Radiat Oncol BioI Phys 1:355-360, Jan-Feb 1976 8. Leung PMK, Van Dyk J, Robins J: A method of large irregular field compensation. Br J RadioI47:805-810, Nov 1974 9. Clemens J, Bjarngard B, Boyer A, et al: Computer automation of compensating filter design. Presented at the Fifth International Conference on the Use of Computers in Radiation Therapy, Dartmouth College, Hanover, N. H., Aug. 18-23, 1974 10. S\&rensen NE: A simple method for the construction of compensators for 'missing tissue.' Phys Med Bioi 13: 113-115, Jan 1968 11. Khan FM, Moore VC, Burns OJ: The construction of compensators for cobalt teletherapy. Radiology 96: 187-192, Jul 1970 12. Wilks R, Casebow MP: Tissue compensation with lead for 60Co therapy. Br J RadioI42:452-456, Jun 1969 13. van de Geijn J: The construction of individualised intensity modifying filters in cobalt 60 teletherapy. Br J Radiol 38:865-870, Nov 1965 14. Herron RE: Biostereometric measurement of body form. Year Book Phys AnthropoI16:80-121, 1972 15. Biostereometrics '74. Proceedings of the Symposium of Commission V, International Society for Photogrammetry, Washington DC, Sept. 10-13, 1974. Falls Church, Va., Am Soc Photogrammetry, 1974 16. Proceedings of the Symposium on Close-Range Photogrammetric Systems, Champaign, 111., July 28-Aug. 1, 1975. Falls Church, Va., Am Soc Photogrammetry, 1975 17. Faig W: Precision plotting of non-metric photography. [In] Biostereometrics 74. Proceedings of the Symposium of Commission V, International Society for Photogrammetry, Washington DC, Sept. 10-13, 1974. Falls Church, Va., Am Soc Photogrammetry, 1974, pp 54-64 18. Bevington PR: Data Reduction and Error Analysis for the Physical Sciences. New York, McGraw-Hili, 1969, pp 259-267 19. Johns HE, Cunningham JR: The Physics of Radiology. Springfield, 111., Thomas, 3d Ed, 1969, pp 362-363 and 749-750 20. Wilkinson JM, Rawlinson JA, Cunningham JR: An extended source model for the calculation of the primary component of a cobalt-60 radiation beam in penumbral regions. [In] Dosimetry Workshop, Hodgkin's Disease,Chicago, 111., Sept. 17, 1970. Washington DC, AAPM, 1970, pp C 1-16 21. Clarkson JR: A note on depth doses in fields of irregularshape. Br J Radiol 14:265-268, Aug 1941 Department of Radiation Oncology Community Hospital of Indianapolis 1500 N. Ritter Ave. Indianapolis, Ind. 46219
