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Abutment region dosimetry for serial tomotherapy
Int. J. Radiation Oncology Biol. Phys., Vol. 45, No. 1, pp. 193–203, 1999 Copyright © 1999 Elsevier Science Inc. Printed in the USA. All rights reserved 0360-3016/99/$–see front matter
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ABUTMENT REGION DOSIMETRY FOR SERIAL TOMOTHERAPY DANIEL A. LOW, PH.D., SASA MUTIC, M.S., JAMES F. DEMPSEY, PH.D., JERRY MARKMAN, SC.D., S. MURTY GODDU, PH.D., AND JAMES A. PURDY, PH.D. Division of Radiation Oncology, Mallinckrodt Institute of Radiology, Washington University Medical Center, St. Louis, MO, Purpose: A commercial intensity modulated radiation therapy system (Corvus, NOMOS Corp.) is presently used in our clinic to generate optimized dose distributions delivered using a proprietary dynamic multileaf collimator (DMLC) (MIMiC) composed of 20 opposed leaf pairs. On our accelerator (Clinac 600C/D, Varian Associates, Inc.) each MIMiC leaf projects to either 1.00 ⴛ 0.84 or 1.00 ⴛ 1.70 cm2 (depending on the treatment plan and termed 1 cm or 2 cm mode, respectively). The MIMiC is used to deliver serial (axial) tomotherapy treatment plans, in which the beam is delivered to a nearly cylindrical volume as the DMLC is rotated about the patient. For longer targets, the patient is moved (indexed) between treatments a distance corresponding to the projected leaf width. The treatment relies on precise indexing and a method was developed to measure the precision of indexing devices. A treatment planning study of the dosimetric effects of incorrect patient indexing and concluded that a dose heterogeneity of 10% mm-1 resulted. Because the results may be sensitive to the dose model accuracy, we conducted a measurement-based investigation of the consequences of incorrect indexing using our accelerator. Although the indexing provides an accurate field abutment along the isocenter, due to beam divergence, hot and cold spots will be produced below and above isocenter, respectively, when less than 300° arcs were used. A preliminary study recently determined that for a 290° rotation in 1 cm mode, 15% cold and 7% hot spots were delivered to 7 cm above and below isocenter, respectively. This study completes the earlier work by investigating the dose heterogeneity as a function of position relative to the axis of rotation, arc length, and leaf width. The influence of random daily patient positioning errors is also investigated. Methods and Materials: Treatment plans were generated using 8.0 cm diameter cylindrical target volumes within a homogeneous rectilinear film phantom. The plans included both 1 and 2 cm mode, optimized for 300°, 240°, and 180° gantry rotations. Coronal-oriented films were irradiated throughout the target volumes and scanned using a laser film digitizer. The central target irradiated in 1 cm mode was also used to investigate the effects of incorrect couch indexing. Results: The dose error as a function of couch index error was 25% mm-1, significantly greater than previously reported. The clinically provided indexing system yielded 0.10 mm indexing precision. The intrinsic dose distributions indicated that more heterogeneous dose distributions resulted from the use of smaller gantry angle ranges and larger leaf projections. Using 300° gantry angle and 1 cm mode yielded 7% hot and 15% cold spots 7 cm below and above isocenter, respectively. When a 180° gantry angle was used, the values changed to 22% hot and 27% cold spots for the same locations. The heterogeneities for the 2 cm mode were 70% greater than the corresponding 1 cm values. Conclusions: While serial tomotherapy is used to deliver highly conformal dose distributions, significant dosimetric factors must be considered before treatment. The patient must be immobilized during treatment to avoid dose heterogeneities caused by incorrect indexing due to patient movement. Even under ideal conditions, beam divergence can cause significant abutment-region dose heterogeneities. The use of larger gantry angle ranges, smaller leaf widths, and appropriate locations of the gantry rotation axis can minimize these effects. © 1999 Elsevier Science Inc. Intensity modulated radiation therapy, Radiation therapy quality assurance, Serial tomotherapy
therapy uses a dynamic multileaf collimator (DMLC) with independently driven parallel-opposed leaf banks, simultaneously delivering dose to anywhere within two 0.84 cm or 1.70 cm thick (on our linear accelerator, termed 1 cm or 2 cm modes, respectively), 20 cm diameter roughly cylindrical volumes. The abutment region between the two leaf banks passes through the central axis and lies within the gantry rotation plane. The abutment between these two delivered slices is, therefore, ideal, and no
INTRODUCTION Serial (axial) tomotherapy is a modality of intensity modulated radiation therapy (IMRT), which is currently in clinical use throughout the world. The process of treatment planning and delivery of IMRT using serial tomotherapy has been described by Verellen et al. (1), Tsai et al. (2), and Low et al. (3). The commercial implementation of tomoReprint requests to: Daniel A. Low, Ph.D., Division of Radiation Oncology, Mallinckrodt Institute of Radiology, 510 South Kingshighway Blvd., St. Louis, MO 63110. Tel: (314) 362-2636;
Fax: (314) 362-2682; E-mail: [email protected]. Accepted for publication 22 March 1999. 193
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significant dose distribution heterogeneities result in that region. However, when the target volume is longer than 1.68 cm, multiple abutting regions must be irradiated. The individually delivered cylinder pairs are termed indexes by the manufacturer, and we will use that terminology throughout this article. When multiple indexes are used, the patient is moved by an amount corresponding to twice the leaf width projected to isocenter. The process requires a highly precise couch movement, or an unintended overlap or underlap will result. A couch immobilization and indexing device (CRANE, NOMOS Corp., Pittsburgh, PA, USA) is furnished by the manufacturer and is used to provide the precise motion required for accurate dose delivery. Carol et al. (4) determined that the heterogeneity caused by such an indexing error is 10% mm-1. However, that study was conducted using only a treatment planning system, and the actual value may differ because of limitations in the dose-calculation model or because of the finite spatial resolution of the treatment planning system commissioning data (5,6). Because all patients at our institution have been treated with more than one index, we elected to experimentally determine the spatial precision of the couch indexing hardware and the dosimetric consequences of incorrect indexing. Even when the couch movements are precisely conducted, the dose distribution homogeneity in the abutment region suffers due to beam divergence. Similar to the conventional process of abutting fields they are precisely abutted along a single distance from the radiation source. Cold and hot spots are found upstream and downstream from this distance, respectively and in this case, the abutment distance is selected to be at the isocenter. When parallel-opposed fields of the same field sizes are used, the hot and cold spots nearly compensate. For most clinical applications, the commercial tomotherapy system uses arcs of less than 360°, with an arc angle range that is symmetric about the vertical axis. For example, when the Varian gantry angle convention is used, a common clinical angle range is 60° to 300°. A large portion of the beams from above (120° to 240°) do not have corresponding opposed beams and will consequently yield dose heterogeneities due to the divergent beam abutments. These cold and hot spots will be termed the intrinsic abutment region heterogeneities. The magnitude of the heterogeneities will depend on the total arc angle range, the projected leaf size, and the distance from gantry rotation axis. Low and Mutic (7) recently described a preliminary measurement of the abutment region dosimetry for the 1 cm mode and for a total arc angle of 290°. They measured the dose heterogeneity only along the vertical and horizontal axes and found that the dose heterogeneity varied from 6% at 7.0 cm below isocenter to ⫺15% at 7.0 cm above isocenter. Little dose heterogeneity was seen lateral to isocenter, but no attempt was made to map the heterogeneity in two dimensions. In this article, we describe measurements to characterize the heterogeneity as a function of gantry angle, leaf width, and position relative to the gantry rotation axis. In addition, a model is presented to determine the
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effects of random daily patient setup error on the abutment region dosimetry for fractionated treatments. Low and Mutic (7) incorrectly stated that the dose calculation algorithm applied beam divergence only in the transverse plane and consequently the intrinsic dose distribution heterogeneities were not correctly modeled. The treatment planning system considers divergence in all three dimensions and the calculated dose distributions exhibit the characteristics of intrinsic abutment region dosimetry. However, the magnitude of the dose distribution heterogeneities may be influenced by the finite size pencil beams used in the model and by the dose calculation resolution in the direction parallel to the couch index movement. Because of the sensitivity of the results on these parameters, we have not included calculated dose distributions in this article. We feel that it is important for each user to independently determine the accuracy of the calculated intrinsic abutment region dose heterogeneities. METHODS AND MATERIALS Index devices The dose distributions were calculated on a three-dimensional rectilinear dose matrix. When the patient was scanned head first and supine, the positive x, y, and z axes corresponded to the patient’s left, posterior, and superior directions, respectively. The investigated treatment setup used the couch placed parallel to the gantry axis of rotation, and the couch immobilization and indexing system placed such that the couch was moved along the same direction. Because of the potentially large dose errors introduced by incorrect indexing, a method was developed to measure the longitudinal indexing error made by the commercial device. The CRANE is shown in Fig. 1; it consists of orthogonal rack-and-pinion drive mechanisms and corresponding linear digital position readouts with 0.01 mm readout resolution. After an arc delivery is complete, the therapist disengages the motion locks and turns a hand crank, which activates the pinion gear. The readout mechanism is directly attached to the movement system, and the therapist stops moving the crank when the digital readout reaches the desired value. Ideally, this indicates that the couch, and, consequently, the patient has been moved the appropriate amount, and a perfect abutment will take place. However, some friction may occur in the couch bearings causing a torque to be applied to the indexing mechanism, slightly twisting it about the vertical axis, and the patient will not be placed in the appropriate location. Qualitative evidence of this has been reported by Low et al. (3). Another device was developed by the manufacturer (miniCRANE; NOMOS Corp.) that does not rely on the correspondence between the rack-and-pinion and patient position. The miniCRANE (Fig. 2) also uses a precision linear readout scale, but it is attached directly to the couch rail, closer to the radiation beam. An anodized aluminum plate with two vertical reflective white stripes is attached to the movable portion of the digital scale. The therapist first
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Fig. 1. Commercial indexing and couch immobilization device (CRANE).
positions the patient at the nominal origin position (using traditional laser alignment marks for noninvasive immobilization) and aligns the reflective stripes to intercept the vertical alignment lasers. The longitudinal couch position readout is then set to 0.00, and the movable portion of the digital scale is set to the first treatment position. The couch is moved so the reflective marks once again intercept the positioning lasers, positioning the patient for the first treatment. Although the digital scale on the miniCRANE has the same accuracy as the scale on the CRANE, there are significant differences between the two systems. As mentioned, when using the CRANE, the movement of the patient may not be the same as the digital scale due to friction in the couch support bearings. However, the miniCRANE
relies on optical alignment of the lasers and scribe lines. The precision of that alignment relies on the skills of the therapist conducting the alignment procedure. To identify the alignment precision and conduct subsequent studies requiring precision phantom movement, a direct indexing device (Fig. 3) was developed that also used a digital position scale. The phantoms were positioned on a stage riding on an optical rail system (selected for its positional stability) that was bolted to an optical bench. The bench was placed on the treatment couch and aligned so that the rail lay parallel to the gantry axis of rotation. The position scale was bolted directly between the stage and the optical bench, providing a direct reading of the stand position. During most experiments, both the couch longitudinal
Fig. 2. Commercial indexing device (miniCRANE) that relies on manual alignment of the room patient-positioning lasers and white scribe marks positioned on the device.
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Fig. 3. Direct indexing device developed for precision abutment-region measurements.
lock and the CRANE were used to immobilize the couch while the stage and, correspondingly, the film phantoms were being moved. The CRANE was detached during the miniCRANE indexing precision test. Index accuracy Index precision measurements of the direct indexing device, the CRANE, and miniCRANE were obtained radiographically. A sheet of radiographic film (XV, Kodak, Rochester, NY, USA), oriented horizontally, was placed between two 4 cm thick sheets of Lucite and the assembly placed on the stage at a height passing through isocenter. The multileaf collimator leaves were opened to 0.84 cm (for a total field size of 1.68 cm), and the film was exposed to a net optical density of approximately 1.5. The couch was moved and the exposure repeated. The distance moved was adjusted to between 1.72 cm and 1.64 cm in increments of 0.01 cm. The resulting exposures exhibited corresponding underlaps and overlaps between successive abutments. A confocal scanning laser digitizer (Dynascan, Computerized Medical Systems, St. Louis, MO, USA) was used to obtain the dose profile (after suitable dose calibration) across the film and passing through the central axis projections. The digitizer has a spatial resolution and position spacing of 0.25 mm. The relationship between the hot and cold spots and the intended movement was determined using the direct indexing device results. A third-order polynomial fit was used to model this relationship, and the physical distance of film movement was determined by the measured hot and cold spots. Precision of the CRANE and miniCRANE movements was also determined using the same fit and the measurements were repeated to ensure reproducible results. Index error The hot and cold spots measured using the fixed fields may not represent the dose heterogeneities when arc treat-
ments are used. The hot and cold spots for arc treatments resulting from incorrect indexing were measured using a fluence distribution generated to irradiate a centrally located 8 cm diameter cylindrical target volume. A rectilinear polystyrene film phantom (8) was used with a radiographic film placed in the horizontal orientation. The cylindrical target volume was oriented such that the axis of symmetry lay parallel to the gantry axis of rotation, passing through isocenter, and the length required six abutting indexes. The index movements were purposely conducted with positioning errors of ⫺2, ⫺1, 0, ⫹1, and ⫹2 mm, resulting in overlaps and underlaps. The radiographic films were scanned using the densitometer, and the magnitudes of the hot and cold spots were determined for the associated overlaps and underlaps.
Intrinsic abutment Even when the index movements are precisely conducted, dose distribution heterogeneities exist in the abutment regions. To characterize these heterogeneities, the same 8 cm diameter cylindrical target volume was used and the Peacock (Corvus 1.0) optimization and dose calculation software used to generate the DMLC instructions. The projected space within which a point can be directly irradiated by the DMLC at all gantry angles describes a 20 cm diameter cylinder. Points outside this cylinder can be irradiated for only a subset of gantry angles, limiting the ability of the system to modulate the beam. The target volume was considerably smaller than the 20 cm diameter, so to determine the heterogeneity distribution throughout the volume, five treatment plan geometries were used, each with the target volume positioned in a different location throughout the 20 cm diameter circle, similar to the technique by Low and Mutic (7). Figure 4 shows the relative geometry of the treatment plans and the 20 cm diameter cylinder. To deter-
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the penumbra from the last arc was obtained and used to model the penumbra P(x) from each abutting arc with the formula:
P共 x兲 ⫽
Fig. 4. Relative geometry of the 8 cm diameter target volumes used to measure the intrinsic abutment region dosimetry. Also shown are the three investigated gantry angle ranges.
mine the sensitivity of the dose heterogeneities on gantry angle, three gantry rotation angles were investigated: 180°, 240°, and 300°. Because of the interference of patient support hardware, few facilities have used gantry rotations in excess of 300°, and couch or patient interference has rarely limited the gantry rotation angle to less than 180°. In each case, the angle refers to the total arc angle the gantry is rotated during delivery, but the leaves do not open on our system until the gantry has rotated 7.5°, and they close 7.5° before the end. Therefore, the irradiated arc range was 15° less than the overall rotation angle. The experiments were repeated for the 2-cm leaf mode using the 180° and 300° rotation angles. In all cases, the direct indexing device was used. Radiographic films were placed at positions approximately 1.3 cm apart along the y axis. Dose contours were obtained by scanning the films in the z direction using 0.025 cm spacing; obtaining profiles spaced each 0.5 cm along the x direction throughout the target volume. In the 1 cm mode, each target required six couch indexes, so the first two positions were irradiated using the 180° arc plan, and the second and third pairs using the 240° and 300° plans, respectively. While five abutments resulted with this irradiation pattern, only the first, third, and fifth provided useful data. Because of limitations in the dose optimization engine, the doses delivered to the four leaf patterns within each pair of abutting fields were not precisely homogeneous. Therefore, it was not possible to use a simple peak extraction method to obtain the value of the hot and cold spots in the abutment region. Instead, it was assumed that the longitudinal dose distribution at the abutment region from each index could be modeled as a penumbra, with the abutment region dose as the sum of two opposing penumbrae. A fit to
再
A 2 tan⫺1关 ␣ 共 x ⫺ x 0兲兴 ⫹ 1 2
冎
(1)
where an overall scatter background was initially subtracted, A was the asymptotic dose, ␣ was a parameter that fit the penumbra slope, and x0 provided the penumbra offset. For each case, the relative dose and penumbra separations were fit as free parameters to the measured distributions. The locations of the abutment region centers were obtained directly from the film scans. After the data were fit, the two adjoining penumbrae were renormalized to an asymptotic magnitude of 1.0, and the sum was recalculated to determine the peak height. The precision of this technique was estimated to have a standard deviation of 2%. Similar data analyses were conducted for the 2 cm mode where only two abutment region doses were acquired for each scan. The results of the data analysis provided a matrix of measured points within the 20 cm diameter treatment circle. To characterize the dose heterogeneities throughout the circle, the hot and cold spots, H(x,y), were fit to the following form: H共 x, y兲 ⫽ a ⫹ bx 2 ⫹ cy ⫹ d y 2
(2)
and the coefficients were determined for each gantry angle range and leaf width. To model the effects of random intrafraction longitudinal patient positioning variation, the extracted hot and cold spot peaks were convolved with Gaussian distributions with standard deviations of 1, 2, and 3 mm. The analytical fits to the overlap data were used for the convolution, and the resulting peak heights were used to define the reduced hot and cold spots. RESULTS Index devices Figure 5 shows an example of the radiographic fixed-field abutment film obtained using the direct indexing device. The relationship between the intended abutment shift and the effect on the abutment hot or cold spot is clear. The hot and cold spots (defined as the difference between the peak dose and the nominal dose values) of the first measurement session are shown as a function of the intended index movement in Fig. 6. A third-order fit is also shown corresponding to the mean of both measurement sessions. For the direct indexing device, the standard deviation of the difference between the intended and measured index distance was 0.002 cm. The hot and cold spots as a function of the intended index distance using the CRANE are also shown in Fig. 6. There is a clear difference between the precision of
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Fig. 5. Index test abutment film obtained using the direct indexing device.
the CRANE and the direct indexing device, reflecting the standard deviation of the difference between the intended and measured distance of 0.010 cm. For the miniCRANE, the standard deviation of the difference between the intended and measured distance was 0.008 cm, slightly better than with the CRANE. Index error A dose profile taken through the index error test is shown in Fig. 7a, with the resulting hot and cold spots presented as a function of the index error shown in Fig. 7b. A linear fit is also shown. The slope is equal to 25% mm-1, indicating the dose error rate for small overlap errors. This is considerably larger than the 10% mm-1 value quoted by Carol et al. (4) and indicates that great care must be taken to ensure that both indexing accuracy and longitudinal patient stability are maintained. Because the index accuracy was measured along the central axis (the region with the sharpest penumbra), it will exhibit the greatest sensitivity to index errors. Intrinsic abutment The measured beam edge penumbra and corresponding fit are shown in Fig. 8 and indicate that the arctangent function adequately described the penumbra shape. An example of
one of the profiles taken through an abutment region is shown in Fig. 9a. The profile clearly shows the complex shape and differences of dose between the abutment regions. One of the abutment regions (180° arc, 1 cm mode) is highlighted for additional examination in Fig. 9b. The raw data are shown, as well as the individual penumbra fits and the resulting sum. For this example, the hot spot was measured to be 21.7% ⫾ 2%. Figure 10a shows a two-dimensional contour plot of the two-dimensional fit (Eqn. 2) to the 180° arc, 1 cm mode data. The fit was limited to the 20 cm diameter circle subtended by the DMLC and the standard deviation difference between the fit and the measured data was 2%, which was typical of the measurements. The relationship between the dose heterogeneity and the y position is significant and expected, with cold and hot spots found at negative and positive values of y, respectively. A dependence on the x position also exists, with off-axis positions exhibiting 10% lower doses than along x ⫽ 0. Fig. 10(b– d) shows the effects of random patient setup errors on intrinsic dose heterogeneities. The peak values are significantly reduced when the standard deviation reaches 3 mm. Daily positioning variation of this magnitude would not likely be found in
Abutment dosimetry for serial tomotherapy
Fig. 6. Hot and cold spot doses as a function of intended indexing for the profile obtained using the direct indexing device (squares), CRANE (circles), and miniCRANE (triangles). A third-order fit, determined with all measurements using the direct indexing device, is also shown.
treatments of the head and neck or brain, but could be found in treatments of other sites. Because two-dimensional graphs are not conducive to quantitative evaluation and because the spatial dependence of the abutment region heterogeneity lies principally along the y axis, the remaining results are presented using onedimensional graphs taken along the x ⫽ 0 axis. Figure 11(a– c) shows the dose heterogeneity for the 300°, 240°, and 180° arc angles using the 1 cm mode. Fig. 11(d,e) shows the 300° and 180° arc angles for the 2 cm mode. Also shown are the results convolved with the random patient setup errors of 1, 2, and 3 mm.
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The effect of selecting an increased gantry angle range can be clearly seen by comparing the three 1 cm mode experiments. At 10 cm below isocenter, the 300°, 240°, and 180° gantry angle ranges yield 5%, 12%, and 27% hot spots, respectively, while at 10 cm above isocenter, the same measurements yield 24%, 33%, and 44% cold spots, respectively. When the 2 cm data are examined, at 10 cm below isocenter, the results for the 300° and 180° gantry angle measurements yield 12% and 48% hot spots, respectively, while at 10 cm above isocenter, the same measurements yield 38% and 71% cold spots, respectively. Even when random patient setup errors are considered, the dose errors for the 180° arc and 2 cm mode are considerably greater than for the 300° arcs and the 1 cm mode. To determine the clinical impact of these data, Table 1 shows the range in y that provides a ⫾10% dose heterogeneity for all tested modes and random setup errors. Entries that contain 10 cm indicate that the dose heterogeneities did not reach the 10% level for that case. The available space is clearly reduced when shorter gantry angle ranges are used, as well as for the 2 cm mode. DISCUSSION The difference between the index precision using the CRANE and miniCRANE was small, and the results may have been a strong function of the quality of the accelerator couch and the skills of the operator. Therefore, they were not intended as a definitive statement of the general index quality of these systems, but were representative of the values found in our clinic. Based on the measured dose heterogeneity as a function of incorrect indexing, the direct indexing device would produce an error of 0.5%, the CRANE would yield an error of 2.5%, and the miniCRANE an error of 2.0%.
Fig. 7. (a) Dose profile for the index error test showing the over- and underdoses for the tested under- and overlaps, respectively. (b) Measured dose errors as a function of the indexing error with the line corresponding to a linear fit with a slope of 25% mm-1.
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Table 1. Distance available to place target volume to ensure less than 10% dose heterogeneity for 0 through 3 mm standard deviation longitudinal random patient setup error Setup error
⫽0 mm mode 1 cm 300° 240° 180° 2 cm 300° 180°
⫽1 mm
⫽2 mm
⫽3 mm
⫹y
⫺y
⫹y
⫺y
⫹y
⫺y
⫹y
⫺y
10 6 3
5 4 3
10 10 4
7 5 4
10 10 6
8 6 5
10 10 10
10 7 6
6 2
3 1
10 3
4 2
10 4
5 3
10 5
7 3
Unless otherwise noted, distances are in centimeters. Fig. 8. Beam-edge profile used to determine the cylindrical target penumbra edge. Also shown is the fit of the formula shown in Eqn. 1.
The intrinsic abutment dosimetry showed considerable dose errors that were not completely removed even after redistribution by relatively large random setup errors. As expected, the worst case occurred when using the 2 cm mode with the 180° gantry angle. In this case, the dose heterogeneity changed 6% cm-1 with respect to the y axis and near the central axis, which is considerable for all but the smallest lesions when aligned with the rotation axis. Even with a random longitudinal motion of 3 mm, the heterogeneity was 2% cm-1. The heterogeneity was roughly one-half when using the 1 cm mode with the 180° gantry angle, but was still larger than with the 240° or 300° angles.
These results show that to limit the heterogeneities to ⫾10%, small leaf settings, large angle range, and proper positioning of the target relative to isocenter limits are needed. Note that these data were obtained using homogeneously irradiated cylindrical targets, and the abutmentregion heterogeneity for other targets will be a function of their shape and neighboring critical structures. The results compared well with those found by Low and Mutic (7), who used a 290° arc and 1 cm mode. They found 6% and 15% hot and cold spots at off-axis positions of 7 cm and ⫺7 cm, respectively, agreeing almost exactly with the findings using a 300° gantry angle range. The patient positioning variation model was conducted in only the longitudinal direction. The setup errors in the vertical and lateral directions would not affect the dose heterogeneity in the abutment region as significantly as movement in the lon-
Fig. 9. (a) Example of a dose profile (arbitrarily normalized) taken through the 1 cm intrinsic abutment region measurement film at x ⫽ ⫺1.5 cm and y ⫽ 7.3 cm. The penumbra for the 180° arc angle experiments is highlighted. (b) Enlarged view of the abutment region highlighted in (a), also showing the fits using the mathematical form of Eqn. 1. The fits normalized to asymptotic values of 1.0 are shown to illustrate the method used to determine the dose heterogeneity.
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Fig. 10. Two-dimensional contour plots of the intrinsic dose heterogeneity (in percent) for the experiment shown in Fig. 9 (180° arc, 1 cm mode). (a) Intrinsic dose heterogeneity obtained using the two-dimensional fit shown in Eqn. 2. (b) Results shown in (a) modified to model the effects of a 1 mm standard deviation longitudinal random daily setup variation. (c) Same as in (b) with a 2 mm standard deviation. (d) Same as in (b) with a 3 mm standard deviation.
gitudinal direction. While the magnitude of the abutment region dosimetry would change somewhat due to that motion, distances required to significantly affect it were on the order of centimeters. For example, as shown in Fig. 10, a 3 cm vertical
(y) shift is required to change the dose heterogeneity by 15% (with 0 cm random longitudinal fluctuations), while only a 2 mm standard deviation random position fluctuation is required in the longitudinal direction. Of course, local gradients caused
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Fig. 11. Fit to intrinsic dose heterogeneity results as a function of the y position and along the x ⫽ 0 axis. The data shown are for the measured points along the x ⫽ 0 axis. Also shown are the fits modified to model the effects of longitudinal random daily setup variations of 1, 2, and 3 mm standard deviation: (a) 300° arc angle, 1 cm mode; (b) 240° arc angle, 1 cm mode; (c) 180° arc angle, 1 cm mode; (d) 300° arc angle, 2 cm mode; (e) 180° arc angle, 2 cm mode. Note that the dose axis limits vary significantly from figure to figure.
by dose optimization might be as significant as the abutment dosimetry gradients, and in these cases, significant dose errors would occur due to movement in the lateral and vertical
directions. However, these are clinical issues that would be dealt with by the proper application of margins, and are consequently beyond the scope of this article.
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A simple remedy could be developed by the manufacturer to reduce the intrinsic heterogeneity by one-half. If the leaf fluence distributions were delivered using alternate leaf banks, the heterogeneity would be redistributed throughout the patient. For example, on odd-numbered days, the treatment would be delivered as currently planned. On evennumbered days, rather than treat the first two leaf banks using the first index, only the first leaf bank would be treated using an index offset by 0.84 cm. The other leaf bank would remain closed, as it intercepted the patient outside (generally superior to) the treated volume. The patient would then be moved by the nominal index of 1.68 cm, and the fluences corresponding to the second and third leaf banks would be
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delivered. On odd-numbered days, the region between the second and third leaf banks would correspond to an abutment region, rather than lying along the beam central axis. The abutment region dosimetry would, therefore, be distributed throughout the patient and reduced in magnitude. This remedy would ideally be implemented in conjunction with a fully automated system for indexing the couch. As an alternative, if the couch motion was remotely automated to high precision (⫾0.1 mm), the couch could be moved in concert with the gantry. This would enable the delivery of spiral tomotherapy, distributing the abutment dosimetry throughout the patient and correspondingly reducing its magnitude.
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Biol Phys 1996;34:183–187. 5. Wu A, Johnson M, Chen ASJ, et al. Evaluation of dose calculation algorithm of the peacock system for multileaf intensity modulation collimator. Int J Radiat Oncol Biol Phys 1996; 36:1225–1231. 6. Low DA, Mutic S. A commercial IMRT treatment planning dose calculation algorithm. Int J Radiat Oncol Biol Phys 1998;41:933–937. 7. Low DA, Mutic S. Abutment region dosimetry for sequential arc IMRT delivery. Phys Med Biol 1997;42:1465–1470. 8. Low DA, Gerber RL, Mutic S, et al. Phantoms for IMRT dose distribution measurement and treatment verification. Int J Radiat Oncol Biol Phys 1998;40:1465–1470.
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PHYSICS CONTRIBUTION
ABUTMENT REGION DOSIMETRY FOR SERIAL TOMOTHERAPY DANIEL A. LOW, PH.D., SASA MUTIC, M.S., JAMES F. DEMPSEY, PH.D., JERRY MARKMAN, SC.D., S. MURTY GODDU, PH.D., AND JAMES A. PURDY, PH.D. Division of Radiation Oncology, Mallinckrodt Institute of Radiology, Washington University Medical Center, St. Louis, MO, Purpose: A commercial intensity modulated radiation therapy system (Corvus, NOMOS Corp.) is presently used in our clinic to generate optimized dose distributions delivered using a proprietary dynamic multileaf collimator (DMLC) (MIMiC) composed of 20 opposed leaf pairs. On our accelerator (Clinac 600C/D, Varian Associates, Inc.) each MIMiC leaf projects to either 1.00 ⴛ 0.84 or 1.00 ⴛ 1.70 cm2 (depending on the treatment plan and termed 1 cm or 2 cm mode, respectively). The MIMiC is used to deliver serial (axial) tomotherapy treatment plans, in which the beam is delivered to a nearly cylindrical volume as the DMLC is rotated about the patient. For longer targets, the patient is moved (indexed) between treatments a distance corresponding to the projected leaf width. The treatment relies on precise indexing and a method was developed to measure the precision of indexing devices. A treatment planning study of the dosimetric effects of incorrect patient indexing and concluded that a dose heterogeneity of 10% mm-1 resulted. Because the results may be sensitive to the dose model accuracy, we conducted a measurement-based investigation of the consequences of incorrect indexing using our accelerator. Although the indexing provides an accurate field abutment along the isocenter, due to beam divergence, hot and cold spots will be produced below and above isocenter, respectively, when less than 300° arcs were used. A preliminary study recently determined that for a 290° rotation in 1 cm mode, 15% cold and 7% hot spots were delivered to 7 cm above and below isocenter, respectively. This study completes the earlier work by investigating the dose heterogeneity as a function of position relative to the axis of rotation, arc length, and leaf width. The influence of random daily patient positioning errors is also investigated. Methods and Materials: Treatment plans were generated using 8.0 cm diameter cylindrical target volumes within a homogeneous rectilinear film phantom. The plans included both 1 and 2 cm mode, optimized for 300°, 240°, and 180° gantry rotations. Coronal-oriented films were irradiated throughout the target volumes and scanned using a laser film digitizer. The central target irradiated in 1 cm mode was also used to investigate the effects of incorrect couch indexing. Results: The dose error as a function of couch index error was 25% mm-1, significantly greater than previously reported. The clinically provided indexing system yielded 0.10 mm indexing precision. The intrinsic dose distributions indicated that more heterogeneous dose distributions resulted from the use of smaller gantry angle ranges and larger leaf projections. Using 300° gantry angle and 1 cm mode yielded 7% hot and 15% cold spots 7 cm below and above isocenter, respectively. When a 180° gantry angle was used, the values changed to 22% hot and 27% cold spots for the same locations. The heterogeneities for the 2 cm mode were 70% greater than the corresponding 1 cm values. Conclusions: While serial tomotherapy is used to deliver highly conformal dose distributions, significant dosimetric factors must be considered before treatment. The patient must be immobilized during treatment to avoid dose heterogeneities caused by incorrect indexing due to patient movement. Even under ideal conditions, beam divergence can cause significant abutment-region dose heterogeneities. The use of larger gantry angle ranges, smaller leaf widths, and appropriate locations of the gantry rotation axis can minimize these effects. © 1999 Elsevier Science Inc. Intensity modulated radiation therapy, Radiation therapy quality assurance, Serial tomotherapy
therapy uses a dynamic multileaf collimator (DMLC) with independently driven parallel-opposed leaf banks, simultaneously delivering dose to anywhere within two 0.84 cm or 1.70 cm thick (on our linear accelerator, termed 1 cm or 2 cm modes, respectively), 20 cm diameter roughly cylindrical volumes. The abutment region between the two leaf banks passes through the central axis and lies within the gantry rotation plane. The abutment between these two delivered slices is, therefore, ideal, and no
INTRODUCTION Serial (axial) tomotherapy is a modality of intensity modulated radiation therapy (IMRT), which is currently in clinical use throughout the world. The process of treatment planning and delivery of IMRT using serial tomotherapy has been described by Verellen et al. (1), Tsai et al. (2), and Low et al. (3). The commercial implementation of tomoReprint requests to: Daniel A. Low, Ph.D., Division of Radiation Oncology, Mallinckrodt Institute of Radiology, 510 South Kingshighway Blvd., St. Louis, MO 63110. Tel: (314) 362-2636;
Fax: (314) 362-2682; E-mail: [email protected]. Accepted for publication 22 March 1999. 193
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significant dose distribution heterogeneities result in that region. However, when the target volume is longer than 1.68 cm, multiple abutting regions must be irradiated. The individually delivered cylinder pairs are termed indexes by the manufacturer, and we will use that terminology throughout this article. When multiple indexes are used, the patient is moved by an amount corresponding to twice the leaf width projected to isocenter. The process requires a highly precise couch movement, or an unintended overlap or underlap will result. A couch immobilization and indexing device (CRANE, NOMOS Corp., Pittsburgh, PA, USA) is furnished by the manufacturer and is used to provide the precise motion required for accurate dose delivery. Carol et al. (4) determined that the heterogeneity caused by such an indexing error is 10% mm-1. However, that study was conducted using only a treatment planning system, and the actual value may differ because of limitations in the dose-calculation model or because of the finite spatial resolution of the treatment planning system commissioning data (5,6). Because all patients at our institution have been treated with more than one index, we elected to experimentally determine the spatial precision of the couch indexing hardware and the dosimetric consequences of incorrect indexing. Even when the couch movements are precisely conducted, the dose distribution homogeneity in the abutment region suffers due to beam divergence. Similar to the conventional process of abutting fields they are precisely abutted along a single distance from the radiation source. Cold and hot spots are found upstream and downstream from this distance, respectively and in this case, the abutment distance is selected to be at the isocenter. When parallel-opposed fields of the same field sizes are used, the hot and cold spots nearly compensate. For most clinical applications, the commercial tomotherapy system uses arcs of less than 360°, with an arc angle range that is symmetric about the vertical axis. For example, when the Varian gantry angle convention is used, a common clinical angle range is 60° to 300°. A large portion of the beams from above (120° to 240°) do not have corresponding opposed beams and will consequently yield dose heterogeneities due to the divergent beam abutments. These cold and hot spots will be termed the intrinsic abutment region heterogeneities. The magnitude of the heterogeneities will depend on the total arc angle range, the projected leaf size, and the distance from gantry rotation axis. Low and Mutic (7) recently described a preliminary measurement of the abutment region dosimetry for the 1 cm mode and for a total arc angle of 290°. They measured the dose heterogeneity only along the vertical and horizontal axes and found that the dose heterogeneity varied from 6% at 7.0 cm below isocenter to ⫺15% at 7.0 cm above isocenter. Little dose heterogeneity was seen lateral to isocenter, but no attempt was made to map the heterogeneity in two dimensions. In this article, we describe measurements to characterize the heterogeneity as a function of gantry angle, leaf width, and position relative to the gantry rotation axis. In addition, a model is presented to determine the
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effects of random daily patient setup error on the abutment region dosimetry for fractionated treatments. Low and Mutic (7) incorrectly stated that the dose calculation algorithm applied beam divergence only in the transverse plane and consequently the intrinsic dose distribution heterogeneities were not correctly modeled. The treatment planning system considers divergence in all three dimensions and the calculated dose distributions exhibit the characteristics of intrinsic abutment region dosimetry. However, the magnitude of the dose distribution heterogeneities may be influenced by the finite size pencil beams used in the model and by the dose calculation resolution in the direction parallel to the couch index movement. Because of the sensitivity of the results on these parameters, we have not included calculated dose distributions in this article. We feel that it is important for each user to independently determine the accuracy of the calculated intrinsic abutment region dose heterogeneities. METHODS AND MATERIALS Index devices The dose distributions were calculated on a three-dimensional rectilinear dose matrix. When the patient was scanned head first and supine, the positive x, y, and z axes corresponded to the patient’s left, posterior, and superior directions, respectively. The investigated treatment setup used the couch placed parallel to the gantry axis of rotation, and the couch immobilization and indexing system placed such that the couch was moved along the same direction. Because of the potentially large dose errors introduced by incorrect indexing, a method was developed to measure the longitudinal indexing error made by the commercial device. The CRANE is shown in Fig. 1; it consists of orthogonal rack-and-pinion drive mechanisms and corresponding linear digital position readouts with 0.01 mm readout resolution. After an arc delivery is complete, the therapist disengages the motion locks and turns a hand crank, which activates the pinion gear. The readout mechanism is directly attached to the movement system, and the therapist stops moving the crank when the digital readout reaches the desired value. Ideally, this indicates that the couch, and, consequently, the patient has been moved the appropriate amount, and a perfect abutment will take place. However, some friction may occur in the couch bearings causing a torque to be applied to the indexing mechanism, slightly twisting it about the vertical axis, and the patient will not be placed in the appropriate location. Qualitative evidence of this has been reported by Low et al. (3). Another device was developed by the manufacturer (miniCRANE; NOMOS Corp.) that does not rely on the correspondence between the rack-and-pinion and patient position. The miniCRANE (Fig. 2) also uses a precision linear readout scale, but it is attached directly to the couch rail, closer to the radiation beam. An anodized aluminum plate with two vertical reflective white stripes is attached to the movable portion of the digital scale. The therapist first
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Fig. 1. Commercial indexing and couch immobilization device (CRANE).
positions the patient at the nominal origin position (using traditional laser alignment marks for noninvasive immobilization) and aligns the reflective stripes to intercept the vertical alignment lasers. The longitudinal couch position readout is then set to 0.00, and the movable portion of the digital scale is set to the first treatment position. The couch is moved so the reflective marks once again intercept the positioning lasers, positioning the patient for the first treatment. Although the digital scale on the miniCRANE has the same accuracy as the scale on the CRANE, there are significant differences between the two systems. As mentioned, when using the CRANE, the movement of the patient may not be the same as the digital scale due to friction in the couch support bearings. However, the miniCRANE
relies on optical alignment of the lasers and scribe lines. The precision of that alignment relies on the skills of the therapist conducting the alignment procedure. To identify the alignment precision and conduct subsequent studies requiring precision phantom movement, a direct indexing device (Fig. 3) was developed that also used a digital position scale. The phantoms were positioned on a stage riding on an optical rail system (selected for its positional stability) that was bolted to an optical bench. The bench was placed on the treatment couch and aligned so that the rail lay parallel to the gantry axis of rotation. The position scale was bolted directly between the stage and the optical bench, providing a direct reading of the stand position. During most experiments, both the couch longitudinal
Fig. 2. Commercial indexing device (miniCRANE) that relies on manual alignment of the room patient-positioning lasers and white scribe marks positioned on the device.
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Fig. 3. Direct indexing device developed for precision abutment-region measurements.
lock and the CRANE were used to immobilize the couch while the stage and, correspondingly, the film phantoms were being moved. The CRANE was detached during the miniCRANE indexing precision test. Index accuracy Index precision measurements of the direct indexing device, the CRANE, and miniCRANE were obtained radiographically. A sheet of radiographic film (XV, Kodak, Rochester, NY, USA), oriented horizontally, was placed between two 4 cm thick sheets of Lucite and the assembly placed on the stage at a height passing through isocenter. The multileaf collimator leaves were opened to 0.84 cm (for a total field size of 1.68 cm), and the film was exposed to a net optical density of approximately 1.5. The couch was moved and the exposure repeated. The distance moved was adjusted to between 1.72 cm and 1.64 cm in increments of 0.01 cm. The resulting exposures exhibited corresponding underlaps and overlaps between successive abutments. A confocal scanning laser digitizer (Dynascan, Computerized Medical Systems, St. Louis, MO, USA) was used to obtain the dose profile (after suitable dose calibration) across the film and passing through the central axis projections. The digitizer has a spatial resolution and position spacing of 0.25 mm. The relationship between the hot and cold spots and the intended movement was determined using the direct indexing device results. A third-order polynomial fit was used to model this relationship, and the physical distance of film movement was determined by the measured hot and cold spots. Precision of the CRANE and miniCRANE movements was also determined using the same fit and the measurements were repeated to ensure reproducible results. Index error The hot and cold spots measured using the fixed fields may not represent the dose heterogeneities when arc treat-
ments are used. The hot and cold spots for arc treatments resulting from incorrect indexing were measured using a fluence distribution generated to irradiate a centrally located 8 cm diameter cylindrical target volume. A rectilinear polystyrene film phantom (8) was used with a radiographic film placed in the horizontal orientation. The cylindrical target volume was oriented such that the axis of symmetry lay parallel to the gantry axis of rotation, passing through isocenter, and the length required six abutting indexes. The index movements were purposely conducted with positioning errors of ⫺2, ⫺1, 0, ⫹1, and ⫹2 mm, resulting in overlaps and underlaps. The radiographic films were scanned using the densitometer, and the magnitudes of the hot and cold spots were determined for the associated overlaps and underlaps.
Intrinsic abutment Even when the index movements are precisely conducted, dose distribution heterogeneities exist in the abutment regions. To characterize these heterogeneities, the same 8 cm diameter cylindrical target volume was used and the Peacock (Corvus 1.0) optimization and dose calculation software used to generate the DMLC instructions. The projected space within which a point can be directly irradiated by the DMLC at all gantry angles describes a 20 cm diameter cylinder. Points outside this cylinder can be irradiated for only a subset of gantry angles, limiting the ability of the system to modulate the beam. The target volume was considerably smaller than the 20 cm diameter, so to determine the heterogeneity distribution throughout the volume, five treatment plan geometries were used, each with the target volume positioned in a different location throughout the 20 cm diameter circle, similar to the technique by Low and Mutic (7). Figure 4 shows the relative geometry of the treatment plans and the 20 cm diameter cylinder. To deter-
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the penumbra from the last arc was obtained and used to model the penumbra P(x) from each abutting arc with the formula:
P共 x兲 ⫽
Fig. 4. Relative geometry of the 8 cm diameter target volumes used to measure the intrinsic abutment region dosimetry. Also shown are the three investigated gantry angle ranges.
mine the sensitivity of the dose heterogeneities on gantry angle, three gantry rotation angles were investigated: 180°, 240°, and 300°. Because of the interference of patient support hardware, few facilities have used gantry rotations in excess of 300°, and couch or patient interference has rarely limited the gantry rotation angle to less than 180°. In each case, the angle refers to the total arc angle the gantry is rotated during delivery, but the leaves do not open on our system until the gantry has rotated 7.5°, and they close 7.5° before the end. Therefore, the irradiated arc range was 15° less than the overall rotation angle. The experiments were repeated for the 2-cm leaf mode using the 180° and 300° rotation angles. In all cases, the direct indexing device was used. Radiographic films were placed at positions approximately 1.3 cm apart along the y axis. Dose contours were obtained by scanning the films in the z direction using 0.025 cm spacing; obtaining profiles spaced each 0.5 cm along the x direction throughout the target volume. In the 1 cm mode, each target required six couch indexes, so the first two positions were irradiated using the 180° arc plan, and the second and third pairs using the 240° and 300° plans, respectively. While five abutments resulted with this irradiation pattern, only the first, third, and fifth provided useful data. Because of limitations in the dose optimization engine, the doses delivered to the four leaf patterns within each pair of abutting fields were not precisely homogeneous. Therefore, it was not possible to use a simple peak extraction method to obtain the value of the hot and cold spots in the abutment region. Instead, it was assumed that the longitudinal dose distribution at the abutment region from each index could be modeled as a penumbra, with the abutment region dose as the sum of two opposing penumbrae. A fit to
再
A 2 tan⫺1关 ␣ 共 x ⫺ x 0兲兴 ⫹ 1 2
冎
(1)
where an overall scatter background was initially subtracted, A was the asymptotic dose, ␣ was a parameter that fit the penumbra slope, and x0 provided the penumbra offset. For each case, the relative dose and penumbra separations were fit as free parameters to the measured distributions. The locations of the abutment region centers were obtained directly from the film scans. After the data were fit, the two adjoining penumbrae were renormalized to an asymptotic magnitude of 1.0, and the sum was recalculated to determine the peak height. The precision of this technique was estimated to have a standard deviation of 2%. Similar data analyses were conducted for the 2 cm mode where only two abutment region doses were acquired for each scan. The results of the data analysis provided a matrix of measured points within the 20 cm diameter treatment circle. To characterize the dose heterogeneities throughout the circle, the hot and cold spots, H(x,y), were fit to the following form: H共 x, y兲 ⫽ a ⫹ bx 2 ⫹ cy ⫹ d y 2
(2)
and the coefficients were determined for each gantry angle range and leaf width. To model the effects of random intrafraction longitudinal patient positioning variation, the extracted hot and cold spot peaks were convolved with Gaussian distributions with standard deviations of 1, 2, and 3 mm. The analytical fits to the overlap data were used for the convolution, and the resulting peak heights were used to define the reduced hot and cold spots. RESULTS Index devices Figure 5 shows an example of the radiographic fixed-field abutment film obtained using the direct indexing device. The relationship between the intended abutment shift and the effect on the abutment hot or cold spot is clear. The hot and cold spots (defined as the difference between the peak dose and the nominal dose values) of the first measurement session are shown as a function of the intended index movement in Fig. 6. A third-order fit is also shown corresponding to the mean of both measurement sessions. For the direct indexing device, the standard deviation of the difference between the intended and measured index distance was 0.002 cm. The hot and cold spots as a function of the intended index distance using the CRANE are also shown in Fig. 6. There is a clear difference between the precision of
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Fig. 5. Index test abutment film obtained using the direct indexing device.
the CRANE and the direct indexing device, reflecting the standard deviation of the difference between the intended and measured distance of 0.010 cm. For the miniCRANE, the standard deviation of the difference between the intended and measured distance was 0.008 cm, slightly better than with the CRANE. Index error A dose profile taken through the index error test is shown in Fig. 7a, with the resulting hot and cold spots presented as a function of the index error shown in Fig. 7b. A linear fit is also shown. The slope is equal to 25% mm-1, indicating the dose error rate for small overlap errors. This is considerably larger than the 10% mm-1 value quoted by Carol et al. (4) and indicates that great care must be taken to ensure that both indexing accuracy and longitudinal patient stability are maintained. Because the index accuracy was measured along the central axis (the region with the sharpest penumbra), it will exhibit the greatest sensitivity to index errors. Intrinsic abutment The measured beam edge penumbra and corresponding fit are shown in Fig. 8 and indicate that the arctangent function adequately described the penumbra shape. An example of
one of the profiles taken through an abutment region is shown in Fig. 9a. The profile clearly shows the complex shape and differences of dose between the abutment regions. One of the abutment regions (180° arc, 1 cm mode) is highlighted for additional examination in Fig. 9b. The raw data are shown, as well as the individual penumbra fits and the resulting sum. For this example, the hot spot was measured to be 21.7% ⫾ 2%. Figure 10a shows a two-dimensional contour plot of the two-dimensional fit (Eqn. 2) to the 180° arc, 1 cm mode data. The fit was limited to the 20 cm diameter circle subtended by the DMLC and the standard deviation difference between the fit and the measured data was 2%, which was typical of the measurements. The relationship between the dose heterogeneity and the y position is significant and expected, with cold and hot spots found at negative and positive values of y, respectively. A dependence on the x position also exists, with off-axis positions exhibiting 10% lower doses than along x ⫽ 0. Fig. 10(b– d) shows the effects of random patient setup errors on intrinsic dose heterogeneities. The peak values are significantly reduced when the standard deviation reaches 3 mm. Daily positioning variation of this magnitude would not likely be found in
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Fig. 6. Hot and cold spot doses as a function of intended indexing for the profile obtained using the direct indexing device (squares), CRANE (circles), and miniCRANE (triangles). A third-order fit, determined with all measurements using the direct indexing device, is also shown.
treatments of the head and neck or brain, but could be found in treatments of other sites. Because two-dimensional graphs are not conducive to quantitative evaluation and because the spatial dependence of the abutment region heterogeneity lies principally along the y axis, the remaining results are presented using onedimensional graphs taken along the x ⫽ 0 axis. Figure 11(a– c) shows the dose heterogeneity for the 300°, 240°, and 180° arc angles using the 1 cm mode. Fig. 11(d,e) shows the 300° and 180° arc angles for the 2 cm mode. Also shown are the results convolved with the random patient setup errors of 1, 2, and 3 mm.
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The effect of selecting an increased gantry angle range can be clearly seen by comparing the three 1 cm mode experiments. At 10 cm below isocenter, the 300°, 240°, and 180° gantry angle ranges yield 5%, 12%, and 27% hot spots, respectively, while at 10 cm above isocenter, the same measurements yield 24%, 33%, and 44% cold spots, respectively. When the 2 cm data are examined, at 10 cm below isocenter, the results for the 300° and 180° gantry angle measurements yield 12% and 48% hot spots, respectively, while at 10 cm above isocenter, the same measurements yield 38% and 71% cold spots, respectively. Even when random patient setup errors are considered, the dose errors for the 180° arc and 2 cm mode are considerably greater than for the 300° arcs and the 1 cm mode. To determine the clinical impact of these data, Table 1 shows the range in y that provides a ⫾10% dose heterogeneity for all tested modes and random setup errors. Entries that contain 10 cm indicate that the dose heterogeneities did not reach the 10% level for that case. The available space is clearly reduced when shorter gantry angle ranges are used, as well as for the 2 cm mode. DISCUSSION The difference between the index precision using the CRANE and miniCRANE was small, and the results may have been a strong function of the quality of the accelerator couch and the skills of the operator. Therefore, they were not intended as a definitive statement of the general index quality of these systems, but were representative of the values found in our clinic. Based on the measured dose heterogeneity as a function of incorrect indexing, the direct indexing device would produce an error of 0.5%, the CRANE would yield an error of 2.5%, and the miniCRANE an error of 2.0%.
Fig. 7. (a) Dose profile for the index error test showing the over- and underdoses for the tested under- and overlaps, respectively. (b) Measured dose errors as a function of the indexing error with the line corresponding to a linear fit with a slope of 25% mm-1.
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Table 1. Distance available to place target volume to ensure less than 10% dose heterogeneity for 0 through 3 mm standard deviation longitudinal random patient setup error Setup error
⫽0 mm mode 1 cm 300° 240° 180° 2 cm 300° 180°
⫽1 mm
⫽2 mm
⫽3 mm
⫹y
⫺y
⫹y
⫺y
⫹y
⫺y
⫹y
⫺y
10 6 3
5 4 3
10 10 4
7 5 4
10 10 6
8 6 5
10 10 10
10 7 6
6 2
3 1
10 3
4 2
10 4
5 3
10 5
7 3
Unless otherwise noted, distances are in centimeters. Fig. 8. Beam-edge profile used to determine the cylindrical target penumbra edge. Also shown is the fit of the formula shown in Eqn. 1.
The intrinsic abutment dosimetry showed considerable dose errors that were not completely removed even after redistribution by relatively large random setup errors. As expected, the worst case occurred when using the 2 cm mode with the 180° gantry angle. In this case, the dose heterogeneity changed 6% cm-1 with respect to the y axis and near the central axis, which is considerable for all but the smallest lesions when aligned with the rotation axis. Even with a random longitudinal motion of 3 mm, the heterogeneity was 2% cm-1. The heterogeneity was roughly one-half when using the 1 cm mode with the 180° gantry angle, but was still larger than with the 240° or 300° angles.
These results show that to limit the heterogeneities to ⫾10%, small leaf settings, large angle range, and proper positioning of the target relative to isocenter limits are needed. Note that these data were obtained using homogeneously irradiated cylindrical targets, and the abutmentregion heterogeneity for other targets will be a function of their shape and neighboring critical structures. The results compared well with those found by Low and Mutic (7), who used a 290° arc and 1 cm mode. They found 6% and 15% hot and cold spots at off-axis positions of 7 cm and ⫺7 cm, respectively, agreeing almost exactly with the findings using a 300° gantry angle range. The patient positioning variation model was conducted in only the longitudinal direction. The setup errors in the vertical and lateral directions would not affect the dose heterogeneity in the abutment region as significantly as movement in the lon-
Fig. 9. (a) Example of a dose profile (arbitrarily normalized) taken through the 1 cm intrinsic abutment region measurement film at x ⫽ ⫺1.5 cm and y ⫽ 7.3 cm. The penumbra for the 180° arc angle experiments is highlighted. (b) Enlarged view of the abutment region highlighted in (a), also showing the fits using the mathematical form of Eqn. 1. The fits normalized to asymptotic values of 1.0 are shown to illustrate the method used to determine the dose heterogeneity.
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Fig. 10. Two-dimensional contour plots of the intrinsic dose heterogeneity (in percent) for the experiment shown in Fig. 9 (180° arc, 1 cm mode). (a) Intrinsic dose heterogeneity obtained using the two-dimensional fit shown in Eqn. 2. (b) Results shown in (a) modified to model the effects of a 1 mm standard deviation longitudinal random daily setup variation. (c) Same as in (b) with a 2 mm standard deviation. (d) Same as in (b) with a 3 mm standard deviation.
gitudinal direction. While the magnitude of the abutment region dosimetry would change somewhat due to that motion, distances required to significantly affect it were on the order of centimeters. For example, as shown in Fig. 10, a 3 cm vertical
(y) shift is required to change the dose heterogeneity by 15% (with 0 cm random longitudinal fluctuations), while only a 2 mm standard deviation random position fluctuation is required in the longitudinal direction. Of course, local gradients caused
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Fig. 11. Fit to intrinsic dose heterogeneity results as a function of the y position and along the x ⫽ 0 axis. The data shown are for the measured points along the x ⫽ 0 axis. Also shown are the fits modified to model the effects of longitudinal random daily setup variations of 1, 2, and 3 mm standard deviation: (a) 300° arc angle, 1 cm mode; (b) 240° arc angle, 1 cm mode; (c) 180° arc angle, 1 cm mode; (d) 300° arc angle, 2 cm mode; (e) 180° arc angle, 2 cm mode. Note that the dose axis limits vary significantly from figure to figure.
by dose optimization might be as significant as the abutment dosimetry gradients, and in these cases, significant dose errors would occur due to movement in the lateral and vertical
directions. However, these are clinical issues that would be dealt with by the proper application of margins, and are consequently beyond the scope of this article.
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A simple remedy could be developed by the manufacturer to reduce the intrinsic heterogeneity by one-half. If the leaf fluence distributions were delivered using alternate leaf banks, the heterogeneity would be redistributed throughout the patient. For example, on odd-numbered days, the treatment would be delivered as currently planned. On evennumbered days, rather than treat the first two leaf banks using the first index, only the first leaf bank would be treated using an index offset by 0.84 cm. The other leaf bank would remain closed, as it intercepted the patient outside (generally superior to) the treated volume. The patient would then be moved by the nominal index of 1.68 cm, and the fluences corresponding to the second and third leaf banks would be
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delivered. On odd-numbered days, the region between the second and third leaf banks would correspond to an abutment region, rather than lying along the beam central axis. The abutment region dosimetry would, therefore, be distributed throughout the patient and reduced in magnitude. This remedy would ideally be implemented in conjunction with a fully automated system for indexing the couch. As an alternative, if the couch motion was remotely automated to high precision (⫾0.1 mm), the couch could be moved in concert with the gantry. This would enable the delivery of spiral tomotherapy, distributing the abutment dosimetry throughout the patient and correspondingly reducing its magnitude.
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Biol Phys 1996;34:183–187. 5. Wu A, Johnson M, Chen ASJ, et al. Evaluation of dose calculation algorithm of the peacock system for multileaf intensity modulation collimator. Int J Radiat Oncol Biol Phys 1996; 36:1225–1231. 6. Low DA, Mutic S. A commercial IMRT treatment planning dose calculation algorithm. Int J Radiat Oncol Biol Phys 1998;41:933–937. 7. Low DA, Mutic S. Abutment region dosimetry for sequential arc IMRT delivery. Phys Med Biol 1997;42:1465–1470. 8. Low DA, Gerber RL, Mutic S, et al. Phantoms for IMRT dose distribution measurement and treatment verification. Int J Radiat Oncol Biol Phys 1998;40:1465–1470.