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Accuracy of numerically produced compensators
Medical Dosimetry, Vol. 24, No. 1, pp. 49 –52, 1999 Copyright © 1999 American Association of Medical Dosimetrists Printed in the USA. All rights reserved 0958-3947/99/$–see front matter
PII S0958-3947(98)00049-1
ACCURACY OF NUMERICALLY PRODUCED COMPENSATORS H. THOMPSON, B.SC., M. D. C. EVANS, H.SC., and B. G. FALLONE, PH.D, FCCPM Medical Physics Unit, McGill University, Montre´al, Que´bec, H3G 1A4, Canada Abstract—A feasibility study is performed to assess the utility of a computer numerically controlled (CNC) mill to produce compensating filters for conventional clinical use and for the delivery of intensity-modulated beams. A computer aided machining (CAM) software is used to assist in the design and construction of such filters. Geometric measurements of stepped and wedged surfaces are made to examine the accuracy of surface milling. Molds are milled and filled with molten alloy to produce filters, and both the molds and filters are examined for consistency and accuracy. Results show that the deviation of the filter surfaces from design does not exceed 1.5%. The effective attenuation coefficient is measured for CadFree, a cadmium-free alloy, in a 6 MV photon beam. The effective attenuation coefficients at the depth of maximum dose (1.5 cm) and at 10 cm in solid water phantom are found to be 0.546 cm21 and 0.522 cm21, respectively. Further attenuation measurements are made with Cerrobend to assess the variations of the effective attenuation coefficient with field size and source-surface distance. The ability of the CNC mill to accurately produce surfaces is verified with dose profile measurements in a 6 MV photon beam. The test phantom is composed of a 10° polystyrene wedge and a 30° polystyrene wedge, presenting both a sharp discontinuity and sloped surfaces. Dose profiles, measured at the depth of compensation (10 cm) beneath the test phantom and beneath a flat phantom, are compared to those produced by a commercial treatment planning system. Agreement between measured and predicted profiles is within 2%, indicating the viability of the system for filter production. © 1999 American Association of Medical Dosimetrists. Key Words: Compensators, CNC mill, Intensity-modulated beams, Inverse treatment planning.
INTRODUCTION
tion, a computer numerically controlled (CNC) mill and a computer aided machining (CAM) software package can be used. The use of a CAM program rather than a dedicated compensator producing software allows the user greater flexibility and control. Compensator data from virtually any treatment planning system or any radiological imaging modality can be imported into the CAM program and discrete data is converted into smooth, continuous surfaces. Parameters for the toolpath, which describes the path the cutting tool follows to mill a surface, are user-defined, providing the operator with control over the accuracy with which each surface is produced. The automated milling system is able to produce complex surfaces with more speed and accuracy than traditional manual techniques. In this work, the effective attenuation coefficient is measured for a low melting point alloy. Compensator test surfaces are designed using a CAM program and CNC milled to be verified with both geometric measurements and measured dose profiles.
Since the advent of megavoltage radiotherapy in the late 1950’s, compensating filters have been used to correct for factors such as variations in body contour, oblique beam incidence and inhomogeneities.1 Of late, there has been increasing interest in the use of beam modulating filters for conformal therapy.2,3 Although dynamic techniques of intensity modulations are in use, static filters retain the advantages of being well documented and relatively easy to implement. In fact, many clinics already possess the equipment and the expertise to produce beam-modulating filters. A compensating filter modulates the intensity of a photon beam through the process of exponential attenuation. The attenuating properties of a material depend to some degree on the depth of measurement, field size, attenuator thickness, off-axis position and beam energy.4,5,6 An effective attenuation coefficient is defined to account for these variations. Ideally, effective attenuation coefficients would be tabulated for all combinations of field size, depth of measurement and energy. It has been observed that variations with field size are small enough that a single effective attenuation coefficient can be used without significant error.4,5 In addition, the effective attenuation coefficient does not vary significantly with filter thickness.5,7 In order to improve the efficiency of filter produc-
METHODS AND MATERIALS Geometric surface measurements. Prior to testing the performance of any compensators, it was necessary to determine whether any gross errors were being made in the construction process. There are two possible sources of error: the toolpath generation and the milling itself. Two test surfaces were designed and milled following the same procedure that would be used to mill a clinical compensator. Each
Reprint requests to: B. G. Fallone, PhD, FCCPM, Medical Physics Unit, Montreal General Hospital, 1650 Avenue Ce´dar, Montre´al, Que´bec, H3G 1A4, Canada. 49
50
Medical Dosimetry
Fig. 1. (a) Stepped test surface, (b) wedge test surface, (c) phantom for compensator testing.
surface was entered into the MasterCam (CNC Software, Tolland, Connecticut) software as a point cloud with 2 mm spacing which was converted to a series of parallel splines, and then to a surface. The first surface was a square divided into four level planes, each of a different thickness (Fig. 1a). The purpose of this test was twofold: to determine whether the CNC mill (Techno ISEL, New Hyde Park, New Jersey) was producing surfaces of the correct thickness and to determine whether the centre of the surface was being properly located. Four locating markers were placed on each side of the surface to act as a reference. Within MasterCam a toolpath was created for the surface, along with the locating markers, and a mold for the test surface was milled out of styrofoam. The depth of each plane was measured in five locations with calipers and averaged. The mold was then filled with molten CadFree and cooled under running water. Both the styrofoam mold and the CadFree surface were inspected following the removal of the compensator from the mold. It was also verified that the centre of the surface coincided with the centre as defined by the markers on each of the four sides of the surface. The second test surface, a wedge (Fig. 1b), was designed to determine the offsetting of sloped surfaces by the cutting tool. The location of the maximum and minimum wedge thickness relative to the markers was used to determine the offset of the surface. Measurements of effective attenuation coefficient. Transmission measurements were taken in phantom with an ion chamber (Shonka 2581, Nuclear Enterprises Technology Ltd., Berkshire, England) and electrometer
Volume 24, Number 1, 1999
(Precision Electrometer/Dosimeter 530, Victoreen, Cleveland, Ohio) to determine the effective attenuation coefficient of CadFree (AIM Products Inc., Smithfield, Rhode Island). Since our clinic was on the verge of replacing the CadFree alloy with Cerrobend, a complete set of attenuation measurements was not taken. Instead, measurements were taken for a small number of variables in order to assess the significance of the variations of the effective attenuation coefficient with depth of measurement, field size and source-surface distance. Some of these measurements were taken with Cerrobend since a larger number of Cerrobend slabs were available. Although the attenuation coefficient of CadFree is larger than that of Cerrobend, the two materials were expected to follow similar trends. Measurements of meff for CadFree were made at the depth of maximum dose (1.5 cm) and at a depth of 10 cm in solid water for a 6 MV photon beam (Clinac 2300C/D, Varian Associates, Palo Alto, California). Thin slabs of attenuator, up to a maximum thickness of 12 mm for CadFree and 60 mm for Cerrobend, were placed in the beam at the level of the blocking tray (65 cm from the source), and transmission measurements were recorded. In order for the field area to be completely covered by the attenuator slabs, the maximum field size measured was limited to 7 3 7 cm2 at SSD 100 cm by the size of the slabs. Measurements of the effective attenuation coefficient for Cerrobend were made at depth of 10 cm in phantom for field sizes of 4 3 4 cm2 and 7 3 7 cm2 and at depth of 10 cm for source-surface distance of 100 cm and source-axis distance 100 cm. The absolute transmission data was converted to relative transmission values and the effective attenuation coefficients were determined. Dose Measurements. A compensator was designed by a commercial treatment planning system (CadPlan, Varian-Dosetek, Espoo, Finland) for the geometry of Fig. 1c. The phantom consisted of two polystyrene wedges (30° and 10°) back to back. The sharp discontinuity at the center presents a challenge that would not likely be encountered in conventional radiotherapy but could be found in intensity modulated beams for inversely planned treatments.8,9 Compensation was calculated for a plane at 10 cm depth. CadPlan provides an ASCII file describing a three dimensional point cloud that can be read by MasterCam, and from this cloud the compensator surface can be defined and a toolpath created. A styrofoam mold was milled using the effective attenuation coefficient that was measured at depth of 10 cm in phantom. The dose profile was measured at 10 cm beneath the phantom with the compensator on the blocking tray. Measurements were taken with a water tank (WP 700, Wellhofer Dosimetrie Verwaltungs GmbH, Schwarzenbruck, Germany) and a 6 MV photon beam with source-surface distance of 100 cm. The compensator was similarly tested for a flat phantom. Because the
Accuracy of numerically produced compensators ● B. G. FALLONE et al.
51
Table 1. CadFree test surface measurements: stepped test surface Design Thickness
Measured Thickness
% Difference
3 mm 5 mm 7 mm 10 mm
3.015 mm 5.004 mm 7.084 mm 10.076 amm
0.50% 0.08% 1.20% 0.76%
phantom is uniform in one direction, we studied dose profiles rather than dose distributions in a plane. Profiles were normalized to the maximum dose and matched at 50%.
Fig. 3. (a) Dose profile measured beneath double-wedge phantom with compensator, (b) dose profile measured beneath flat phantom with compensator.
RESULTS AND DISCUSSION
Fig. 2. (a) Transmission curves for CadFree in 6 MV photon beam. Field size: 7 3 7 cm2, 100 cm SSD, (b) transmission curves for Cerrobend in 6 MV photon beam. Depth (d) 5 10 cm, 100 cm SSD, (c) transmission curves for Cerrobend in 6 MV photon beam. Field size: 7 3 7 cm2, d 5 10 cm.
The maximum deviation between the designed and measured surface thickness (Fig. 1a) was found to be 1.2% (Table 1). The styrofoam mold was also measured before and after the CadFree was poured. The maximum measured change in the depth of the mold following pouring was 0.041 mm which is less than the estimated measured change in the depth of the mold due to compression of the styrofoam by the calipers and is therefore negligible. The intersection of the four planes corresponded to the center of the surface within 6 0.5 mm. Measurements of the wedge test surface (Fig. 1b) agreed with the design to within 6 1.5%. At d max (1.5 cm) for a 7 3 7 cm2 field, SSD 5 100 cm, the effective attenuation coefficient of CadFree was
52
Medical Dosimetry
determined to be 0.546 cm21 (Fig. 2a). For the same beam conditions, at a depth of 10 cm the effective attenuation coefficient was measured to be 0.522 cm21. This represents a variation of 4.4%. Measurements of the effective attenuation coefficient of Cerrobend taken for field sizes 4 3 4 cm2 and 7 3 7 cm2 determined the effective attenuation coefficients to be 0.466 cm21 and 0.464 cm21, respectively (Fig. 2b). This is a difference of only 0.4%. When the source-surface distance was changed from 100 cm to 90 cm the effective attenuation coefficient changed from 0.456 cm21 to 0.451 cm21 (Fig. 2c). Normalized dose profiles were obtained for both phantoms and are in good agreement with those predicted by CadPlan (Figs. 3a, b). The average deviation between the calculated and measured profiles for Fig. 3a is 1.69%. Similarly, the average deviation between the calculated and measured profiles of Fig. 3b is 1.78%. For each profile, the maximum deviation occurs at the discontinuity located at the central axis which is the expected result. The edge effects predicted by CadPlan at the junction of the two wedges and seen in Fig. 3a are not evident in the measured profile. Higher resolution measurements taken with film show that these edge effects are indeed present but to a lesser degree than predicted. This turns out to be a desirable property since the modulations of 6 10% seen at the discontinuity in Fig. 3a would not be tolerated within a target volume. Referring to Fig. 3b, it can be seen that beam modulations approaching vertical at depth can be accurately planned and delivered. Based on the measured effective attenuation coefficient for CadFree, it is possible to achieve intensity modulations from 100% to almost 10% with a 4 cm modulation of the filter thickness. These properties indicate that the present system is suit-
Volume 24, Number 1, 1999
able for use in the construction of filters for beam intensity modulated therapy. CONCLUSIONS These average deviations of less than 2% in the dose profiles indicate the viability of the use of MasterCam software with a CNC mill for compensator production. Numerically produced compensators have the advantage of being smooth, continuous surfaces that can be produced with little effort and time expenditure on the part of the operator. The success of this system in coping with both sharp discontinuities and gently contoured surfaces indicates that similar success should be realized with the filters presenting multiple peaks and valleys used in conformal treatments. REFERENCES 1. Ellis, F.; Hall, E.J.; Oliver, R. A compensator for variations in tissue thickness for high energy beams. Brit. J. Radiol. 32:421– 422; 1959. 2. Low, D.A.; Li, Z.; Klein, E.E. Verification of two-dimensional photon compensating filters using an electronic portal imaging device. Med. Phys. 23:929 –938; 1996. 3. Jiang, S.B.; Ayyangar, K.M. On compensator design for photon beam intensity-modulated conformal therapy. Med. Phys. 25:668 – 674; 1998. 4. Wilks, R.; Casebow, M.P. Tissue compensation with lead for 60Co therapy. Brit. J. Radiol. 42:452– 456; 1969. 5. Boyer, A.L. Compensating filters for high energy x-rays. Med. Phys. 9:429 – 433; 1982. 6. Bagne, F.R.; Samsami, N.; Hoke, S.W.; Bronn, D.G. A study of effective attenuation coefficient for calculating tissue compensator thickness. Med. Phys. 17:117–121; 1990. 7. Huang, P.; Chin, L.M.; Bja¨rngard, B.E. Scattered photons produced by beam-modifying filters. Med. Phys. 13:57– 63; 1986. 8. Hristov, D.H.; Fallone, B.G. An active set algorithm for treatment planning optimization. Med. Phys. 24:1455–1464; 1997. 9. Hristov, D.H.; Fallone, B.G. A continuous penalty function method for inverse treatment planning, Med. Phys. 25:208 –223; 1998.
PII S0958-3947(98)00049-1
ACCURACY OF NUMERICALLY PRODUCED COMPENSATORS H. THOMPSON, B.SC., M. D. C. EVANS, H.SC., and B. G. FALLONE, PH.D, FCCPM Medical Physics Unit, McGill University, Montre´al, Que´bec, H3G 1A4, Canada Abstract—A feasibility study is performed to assess the utility of a computer numerically controlled (CNC) mill to produce compensating filters for conventional clinical use and for the delivery of intensity-modulated beams. A computer aided machining (CAM) software is used to assist in the design and construction of such filters. Geometric measurements of stepped and wedged surfaces are made to examine the accuracy of surface milling. Molds are milled and filled with molten alloy to produce filters, and both the molds and filters are examined for consistency and accuracy. Results show that the deviation of the filter surfaces from design does not exceed 1.5%. The effective attenuation coefficient is measured for CadFree, a cadmium-free alloy, in a 6 MV photon beam. The effective attenuation coefficients at the depth of maximum dose (1.5 cm) and at 10 cm in solid water phantom are found to be 0.546 cm21 and 0.522 cm21, respectively. Further attenuation measurements are made with Cerrobend to assess the variations of the effective attenuation coefficient with field size and source-surface distance. The ability of the CNC mill to accurately produce surfaces is verified with dose profile measurements in a 6 MV photon beam. The test phantom is composed of a 10° polystyrene wedge and a 30° polystyrene wedge, presenting both a sharp discontinuity and sloped surfaces. Dose profiles, measured at the depth of compensation (10 cm) beneath the test phantom and beneath a flat phantom, are compared to those produced by a commercial treatment planning system. Agreement between measured and predicted profiles is within 2%, indicating the viability of the system for filter production. © 1999 American Association of Medical Dosimetrists. Key Words: Compensators, CNC mill, Intensity-modulated beams, Inverse treatment planning.
INTRODUCTION
tion, a computer numerically controlled (CNC) mill and a computer aided machining (CAM) software package can be used. The use of a CAM program rather than a dedicated compensator producing software allows the user greater flexibility and control. Compensator data from virtually any treatment planning system or any radiological imaging modality can be imported into the CAM program and discrete data is converted into smooth, continuous surfaces. Parameters for the toolpath, which describes the path the cutting tool follows to mill a surface, are user-defined, providing the operator with control over the accuracy with which each surface is produced. The automated milling system is able to produce complex surfaces with more speed and accuracy than traditional manual techniques. In this work, the effective attenuation coefficient is measured for a low melting point alloy. Compensator test surfaces are designed using a CAM program and CNC milled to be verified with both geometric measurements and measured dose profiles.
Since the advent of megavoltage radiotherapy in the late 1950’s, compensating filters have been used to correct for factors such as variations in body contour, oblique beam incidence and inhomogeneities.1 Of late, there has been increasing interest in the use of beam modulating filters for conformal therapy.2,3 Although dynamic techniques of intensity modulations are in use, static filters retain the advantages of being well documented and relatively easy to implement. In fact, many clinics already possess the equipment and the expertise to produce beam-modulating filters. A compensating filter modulates the intensity of a photon beam through the process of exponential attenuation. The attenuating properties of a material depend to some degree on the depth of measurement, field size, attenuator thickness, off-axis position and beam energy.4,5,6 An effective attenuation coefficient is defined to account for these variations. Ideally, effective attenuation coefficients would be tabulated for all combinations of field size, depth of measurement and energy. It has been observed that variations with field size are small enough that a single effective attenuation coefficient can be used without significant error.4,5 In addition, the effective attenuation coefficient does not vary significantly with filter thickness.5,7 In order to improve the efficiency of filter produc-
METHODS AND MATERIALS Geometric surface measurements. Prior to testing the performance of any compensators, it was necessary to determine whether any gross errors were being made in the construction process. There are two possible sources of error: the toolpath generation and the milling itself. Two test surfaces were designed and milled following the same procedure that would be used to mill a clinical compensator. Each
Reprint requests to: B. G. Fallone, PhD, FCCPM, Medical Physics Unit, Montreal General Hospital, 1650 Avenue Ce´dar, Montre´al, Que´bec, H3G 1A4, Canada. 49
50
Medical Dosimetry
Fig. 1. (a) Stepped test surface, (b) wedge test surface, (c) phantom for compensator testing.
surface was entered into the MasterCam (CNC Software, Tolland, Connecticut) software as a point cloud with 2 mm spacing which was converted to a series of parallel splines, and then to a surface. The first surface was a square divided into four level planes, each of a different thickness (Fig. 1a). The purpose of this test was twofold: to determine whether the CNC mill (Techno ISEL, New Hyde Park, New Jersey) was producing surfaces of the correct thickness and to determine whether the centre of the surface was being properly located. Four locating markers were placed on each side of the surface to act as a reference. Within MasterCam a toolpath was created for the surface, along with the locating markers, and a mold for the test surface was milled out of styrofoam. The depth of each plane was measured in five locations with calipers and averaged. The mold was then filled with molten CadFree and cooled under running water. Both the styrofoam mold and the CadFree surface were inspected following the removal of the compensator from the mold. It was also verified that the centre of the surface coincided with the centre as defined by the markers on each of the four sides of the surface. The second test surface, a wedge (Fig. 1b), was designed to determine the offsetting of sloped surfaces by the cutting tool. The location of the maximum and minimum wedge thickness relative to the markers was used to determine the offset of the surface. Measurements of effective attenuation coefficient. Transmission measurements were taken in phantom with an ion chamber (Shonka 2581, Nuclear Enterprises Technology Ltd., Berkshire, England) and electrometer
Volume 24, Number 1, 1999
(Precision Electrometer/Dosimeter 530, Victoreen, Cleveland, Ohio) to determine the effective attenuation coefficient of CadFree (AIM Products Inc., Smithfield, Rhode Island). Since our clinic was on the verge of replacing the CadFree alloy with Cerrobend, a complete set of attenuation measurements was not taken. Instead, measurements were taken for a small number of variables in order to assess the significance of the variations of the effective attenuation coefficient with depth of measurement, field size and source-surface distance. Some of these measurements were taken with Cerrobend since a larger number of Cerrobend slabs were available. Although the attenuation coefficient of CadFree is larger than that of Cerrobend, the two materials were expected to follow similar trends. Measurements of meff for CadFree were made at the depth of maximum dose (1.5 cm) and at a depth of 10 cm in solid water for a 6 MV photon beam (Clinac 2300C/D, Varian Associates, Palo Alto, California). Thin slabs of attenuator, up to a maximum thickness of 12 mm for CadFree and 60 mm for Cerrobend, were placed in the beam at the level of the blocking tray (65 cm from the source), and transmission measurements were recorded. In order for the field area to be completely covered by the attenuator slabs, the maximum field size measured was limited to 7 3 7 cm2 at SSD 100 cm by the size of the slabs. Measurements of the effective attenuation coefficient for Cerrobend were made at depth of 10 cm in phantom for field sizes of 4 3 4 cm2 and 7 3 7 cm2 and at depth of 10 cm for source-surface distance of 100 cm and source-axis distance 100 cm. The absolute transmission data was converted to relative transmission values and the effective attenuation coefficients were determined. Dose Measurements. A compensator was designed by a commercial treatment planning system (CadPlan, Varian-Dosetek, Espoo, Finland) for the geometry of Fig. 1c. The phantom consisted of two polystyrene wedges (30° and 10°) back to back. The sharp discontinuity at the center presents a challenge that would not likely be encountered in conventional radiotherapy but could be found in intensity modulated beams for inversely planned treatments.8,9 Compensation was calculated for a plane at 10 cm depth. CadPlan provides an ASCII file describing a three dimensional point cloud that can be read by MasterCam, and from this cloud the compensator surface can be defined and a toolpath created. A styrofoam mold was milled using the effective attenuation coefficient that was measured at depth of 10 cm in phantom. The dose profile was measured at 10 cm beneath the phantom with the compensator on the blocking tray. Measurements were taken with a water tank (WP 700, Wellhofer Dosimetrie Verwaltungs GmbH, Schwarzenbruck, Germany) and a 6 MV photon beam with source-surface distance of 100 cm. The compensator was similarly tested for a flat phantom. Because the
Accuracy of numerically produced compensators ● B. G. FALLONE et al.
51
Table 1. CadFree test surface measurements: stepped test surface Design Thickness
Measured Thickness
% Difference
3 mm 5 mm 7 mm 10 mm
3.015 mm 5.004 mm 7.084 mm 10.076 amm
0.50% 0.08% 1.20% 0.76%
phantom is uniform in one direction, we studied dose profiles rather than dose distributions in a plane. Profiles were normalized to the maximum dose and matched at 50%.
Fig. 3. (a) Dose profile measured beneath double-wedge phantom with compensator, (b) dose profile measured beneath flat phantom with compensator.
RESULTS AND DISCUSSION
Fig. 2. (a) Transmission curves for CadFree in 6 MV photon beam. Field size: 7 3 7 cm2, 100 cm SSD, (b) transmission curves for Cerrobend in 6 MV photon beam. Depth (d) 5 10 cm, 100 cm SSD, (c) transmission curves for Cerrobend in 6 MV photon beam. Field size: 7 3 7 cm2, d 5 10 cm.
The maximum deviation between the designed and measured surface thickness (Fig. 1a) was found to be 1.2% (Table 1). The styrofoam mold was also measured before and after the CadFree was poured. The maximum measured change in the depth of the mold following pouring was 0.041 mm which is less than the estimated measured change in the depth of the mold due to compression of the styrofoam by the calipers and is therefore negligible. The intersection of the four planes corresponded to the center of the surface within 6 0.5 mm. Measurements of the wedge test surface (Fig. 1b) agreed with the design to within 6 1.5%. At d max (1.5 cm) for a 7 3 7 cm2 field, SSD 5 100 cm, the effective attenuation coefficient of CadFree was
52
Medical Dosimetry
determined to be 0.546 cm21 (Fig. 2a). For the same beam conditions, at a depth of 10 cm the effective attenuation coefficient was measured to be 0.522 cm21. This represents a variation of 4.4%. Measurements of the effective attenuation coefficient of Cerrobend taken for field sizes 4 3 4 cm2 and 7 3 7 cm2 determined the effective attenuation coefficients to be 0.466 cm21 and 0.464 cm21, respectively (Fig. 2b). This is a difference of only 0.4%. When the source-surface distance was changed from 100 cm to 90 cm the effective attenuation coefficient changed from 0.456 cm21 to 0.451 cm21 (Fig. 2c). Normalized dose profiles were obtained for both phantoms and are in good agreement with those predicted by CadPlan (Figs. 3a, b). The average deviation between the calculated and measured profiles for Fig. 3a is 1.69%. Similarly, the average deviation between the calculated and measured profiles of Fig. 3b is 1.78%. For each profile, the maximum deviation occurs at the discontinuity located at the central axis which is the expected result. The edge effects predicted by CadPlan at the junction of the two wedges and seen in Fig. 3a are not evident in the measured profile. Higher resolution measurements taken with film show that these edge effects are indeed present but to a lesser degree than predicted. This turns out to be a desirable property since the modulations of 6 10% seen at the discontinuity in Fig. 3a would not be tolerated within a target volume. Referring to Fig. 3b, it can be seen that beam modulations approaching vertical at depth can be accurately planned and delivered. Based on the measured effective attenuation coefficient for CadFree, it is possible to achieve intensity modulations from 100% to almost 10% with a 4 cm modulation of the filter thickness. These properties indicate that the present system is suit-
Volume 24, Number 1, 1999
able for use in the construction of filters for beam intensity modulated therapy. CONCLUSIONS These average deviations of less than 2% in the dose profiles indicate the viability of the use of MasterCam software with a CNC mill for compensator production. Numerically produced compensators have the advantage of being smooth, continuous surfaces that can be produced with little effort and time expenditure on the part of the operator. The success of this system in coping with both sharp discontinuities and gently contoured surfaces indicates that similar success should be realized with the filters presenting multiple peaks and valleys used in conformal treatments. REFERENCES 1. Ellis, F.; Hall, E.J.; Oliver, R. A compensator for variations in tissue thickness for high energy beams. Brit. J. Radiol. 32:421– 422; 1959. 2. Low, D.A.; Li, Z.; Klein, E.E. Verification of two-dimensional photon compensating filters using an electronic portal imaging device. Med. Phys. 23:929 –938; 1996. 3. Jiang, S.B.; Ayyangar, K.M. On compensator design for photon beam intensity-modulated conformal therapy. Med. Phys. 25:668 – 674; 1998. 4. Wilks, R.; Casebow, M.P. Tissue compensation with lead for 60Co therapy. Brit. J. Radiol. 42:452– 456; 1969. 5. Boyer, A.L. Compensating filters for high energy x-rays. Med. Phys. 9:429 – 433; 1982. 6. Bagne, F.R.; Samsami, N.; Hoke, S.W.; Bronn, D.G. A study of effective attenuation coefficient for calculating tissue compensator thickness. Med. Phys. 17:117–121; 1990. 7. Huang, P.; Chin, L.M.; Bja¨rngard, B.E. Scattered photons produced by beam-modifying filters. Med. Phys. 13:57– 63; 1986. 8. Hristov, D.H.; Fallone, B.G. An active set algorithm for treatment planning optimization. Med. Phys. 24:1455–1464; 1997. 9. Hristov, D.H.; Fallone, B.G. A continuous penalty function method for inverse treatment planning, Med. Phys. 25:208 –223; 1998.