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
`
`PII S0360-3016(99)00125-X
`
`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 laserfilm 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
`
`INTRODUCTION
`
`Serial (axial) tomotherapy is a modality of intensity modu-
`lated radiation therapy (IMRT), which is currently in clin-
`ical 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 tomo-
`
`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, respec-
`tively), 20 cm diameter roughly cylindrical volumes. The abut-
`ment 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
`
`Reprint requests to: Daniel A. Low, Ph.D., Division of Radia-
`tion Oncology, Mallinckrodt Institute of Radiology, 510 South
`Kingshighway Blvd., St. Louis, MO 63110. Tel: (314) 362-2636;
`
`Fax: (314) 362-2682; E-mail: low@castor.wustl.edu.
`Accepted for publication 22 March 1999.
`
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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) deter-
`mined 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). Be-
`cause all patients at our institution have been treated with
`more than one index, we elected to experimentally deter-
`mine the spatial precision of the couch indexing hardware
`and the dosimetric consequences of incorrect indexing.
`Even when the couch movements are precisely con-
`ducted, the dose distribution homogeneity in the abutment
`region suffers due to beam divergence. Similar to the con-
`ventional process of abutting fields they are precisely abut-
`ted 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 com-
`mercial 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 abut-
`ments. These cold and hot spots will be termed the intrinsic
`abutment region heterogeneities. The magnitude of the het-
`erogeneities 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 iso-
`center. Little dose heterogeneity was seen lateral to iso-
`center, 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
`
`effects of random daily patient setup error on the abutment
`region dosimetry for fractionated treatments.
`Low and Mutic (7) incorrectly stated that the dose cal-
`culation algorithm applied beam divergence only in the
`transverse plane and consequently the intrinsic dose distri-
`bution 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. How-
`ever, 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 sen-
`sitivity 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-dimen-
`sional rectilinear dose matrix. When the patient was scanned
`head first and supine, the positive x, y, andz axes corre-
`sponded to the patient’s left, posterior, and superior direc-
`tions, 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 immobi-
`lization) 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 treat-
`ment. Although the digital scale on the miniCRANE has the
`same accuracy as the scale on the CRANE, there are sig-
`nificant differences between the two systems. As men-
`tioned, when using the CRANE, the movement of the pa-
`tient 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 thera-
`pist conducting the alignment procedure.
`To identify the alignment precision and conduct subse-
`quent 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 posi-
`tional 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 posi-
`tion. 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 de-
`vice, the CRANE, and miniCRANE were obtained radio-
`graphically. 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 index-
`ing 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 move-
`ments 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 poly-
`styrene 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 iso-
`center, and the length required six abutting indexes. The
`index movements were purposely conducted with position-
`ing 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 over-
`laps and underlaps.
`
`Intrinsic abutment
`Even when the index movements are precisely con-
`ducted, dose distribution heterogeneities exist in the abut-
`ment 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 pro-
`jected space within which a point can be directly irradiated
`by the DMLC at all gantry angles describes a 20 cm diam-
`eter 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 con-
`siderably 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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`197
`
`the penumbra from the last arc was obtained and used to
`model the penumbra P(x) from each abutting arc with the
`formula:
`
`(1)
`
`
`
`再 2␲ tan⫺1关␣共 x ⫺ x0兲兴 ⫹ 1冎
`
`A2
`
`P共 x兲 ⫽
`
`where an overall scatter background was initially sub-
`tracted, 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 deter-
`mine 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), werefit to the follow-
`ing form:
`
`H共 x, y兲 ⫽ a ⫹ bx2 ⫹ cy ⫹ d y2
`
`(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 corre-
`sponding to the mean of both measurement sessions. For the
`direct indexing device, the standard deviation of the differ-
`ence 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
`
`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 sup-
`port 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 approxi-
`mately 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 irradi-
`ation 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. There-
`fore, 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 longitu-
`dinal 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
`
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`I. J. Radiation Oncology ● Biology ● Physics
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`Volume 45, Number 1, 1999
`
`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 in-
`tended 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 main-
`tained. 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 re-
`gions. 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 mea-
`sured 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 differ-
`ence 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 position-
`ing variation of this magnitude would not likely be found in
`
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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, respec-
`tively. 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. 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 de-
`vice, 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 one-
`dimensional 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.
`
`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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`Volume 45, Number 1, 1999
`
`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
`
`␴ ⫽ 1
`mm
`
`␴ ⫽ 2
`mm
`
`␴ ⫽ 3
`mm
`
`mode
`
`⫹y ⫺y ⫹y ⫺y ⫹y ⫺y ⫹y ⫺y
`
`1 cm
`300°
`240°
`180°
`2 cm
`300°
`180°
`
`10
`6
`3
`
`6
`2
`
`5
`4
`3
`
`3
`1
`
`10
`10
`4
`
`10
`3
`
`7
`5
`4
`
`4
`2
`
`10
`10
`6
`
`10
`4
`
`8
`6
`5
`
`5
`3
`
`10
`10
`10
`
`10
`5
`
`10
`7
`6
`
`7
`3
`
`Unless otherwise noted, distances are in centimeters.
`
`the heterogeneities to
`to limit
`These results show that
`⫾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 homoge-
`neously irradiated cylindrical targets, and the abutment-
`region 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. 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.
`
`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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`Abutment dosimetry for serial tomotherapy ● D. A. LOW et al.
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`201
`
`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 re-
`gion 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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`202
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`I. J. Radiation Oncology ● Biology ● Physics
`
`Volume 45, Number 1, 1999
`
`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 con-
`sequently beyond the scope of this article.
`
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`Abutment dosimetry for serial