Clinical helical tomotherapy commissioning dosimetry

Transcription

1 Clinical helical tomotherapy commissioning dosimetry John Balog and Gustavo Olivera TomoTherapy Incorporated, Madison, Wisconsin and Department of Medical Physics, University of Wisconsin at Madison, Madison, Wisconsin Jeff Kapatoes TomoTherapy Incorporated, Madison, Wisconsin Received 6 May 2003; revised 20 September 2003; accepted for publication 22 September 2003; published 18 November 2003 Helical tomotherapy presented many unique dosimetric challenges and solutions during the initial commissioning process, and some of them are presented. The dose calculation algorithm is convolution/superposition based. This requires that the energy fluence spectrum and magnitude be quantified. The methodology for doing so is described. Aspects of the energy fluence characterization that are unique to tomotherapy are highlighted. Many beam characteristics can be measured automatically by an included megavoltage computed tomography imaging system. This greatly improves data collection efficiency American Association of Physicists in Medicine. DOI: / Key words: tomotherapy, treatment planning commissioning, convolution/superposition, IMRT, end-of-planning I. INTRODUCTION Helical tomotherapy represents a new approach to intensity modulated radiation therapy IMRT. 1,2 Most commercial forms of IMRT evolved from standard linear accelerators equipped with field shaping multileaf collimators MLC. However, helical tomotherapy was designed specifically as an IMRT machine, and it has many unique features. This has resulted in some novel dosimetric characteristics that were studied during commissioning of the first clinical tomotherapy machine at the University of Wisconsin. Those results are presented here. The dose calculation algorithm is convolution/ superposition C/S based. A more detailed discussion is presented elsewhere. 3 This requires that the energy fluence magnitude and spectrum be quantified. This is common for many commercially available systems, but some distinctive aspects for helical tomotherapy are presented. Helical tomotherapy constantly superimposes a rectangular beam that is up to 40-cm wide in the transverse direction and up to 5 cm wide in the longitudinal direction. The beam superimposition is along the longitudinal direction of the patient. 4,5 This is the direction of couch travel. This mandates that the dose calculation be extremely accurate in this direction as small errors in the longitudinal dose profile quickly add to significant amounts. The helical tomotherapy accelerator is mounted on a slip ring gantry. This allowed a CT detector array Xenon filled linear array to be mounted opposite the source. The primary purpose of this detector is for megavoltage computed tomography MVCT, delivery verification, and dose reconstruction. 6 8 This on-board linear array of ion chambers also has demonstrated its advantage for quality assurance and beam alignment commissioning. 9 Additionally, it has also proved useful for quantifying required dose planning system parameters. A figure illustrating the geometry of helical tomotherapy is shown in Fig. 1. More extensive geometrical references have been published. 9 The International Electro technical Standards IEC coordinate system is followed. The X axis is the transverse direction, the Z axis is the vertical axis, and the Y axis is the inferior superior or longitudinal axis. A moveable set of tungsten jaws defines the field width in the inferior superior direction. The presentation is divided into three sections: energyfluence modeling, beam spectrum uniformity, and end-ofplanning measurements EOP. The energy fluence is modeled from static beam measurements and verified by helical delivery measurements early in the commissioning process. EOP considerations occur, by definition, after and independent from treatment optimization. The data can be collected anytime the final beam parameters are set, but typically are measured at the end of commissioning. Beam spectrum uniformity does not require specific commissioning measurements, but rather is presented to demonstrate dosimetric differences of helical tomotherapy. II. MATERIALS AND METHODS Two ion chambers and one film type were used for all measurements, as well as the on-board MVCT imaging detectors. The Standard Imaging A14SL and A12S ion chamber were used Middleton, WI. The collector lengths and collecting volumes were 2.0 mm and 7.4 mm long and cm 3, and 0.25 cm 3 wide, respectively. Kodak EDR2 film was used Rochester, NY. The Howtek MultiRad 450 film digitizer Hudson, NH digitized the films. Separate calibration exposures were used to convert the optical density values to dose values Med. Phys , December Õ2003Õ30 12 Õ3097Õ10Õ$ Am. Assoc. Phys. Med. 3097

2 3098 Balog, Olivera, and Kapatoes: Clinical helical tomotherapy commissioning dosimetry 3098 FIG. 1. This is an illustration of the helical tomotherapy coordinate system. A. Energy-fluence modeling 1. Static measurement Helical tomotherapy C/S is similar to many other C/Sbased planning systems in that the spectrum of the incident photons must be quantified. 10,11 Each Y -axis field width is modeled and commissioned separately, but a single spectrum is modeled for all Y -axis field widths. 3 However, a complete data set is collected for each Y -axis field width for verification. The spectrum along the central axis must be quantified first. 12 This is done iteratively until the percent depth dose PDD, which is calculated from an assumed incident energy fluence sufficiently matches the measured PDD. The source to surface distance used was 85 cm, which is the isocenter of the slip ring gantry. The helical tomotherapy central axis spectrum has also been studied via Monte Carlo analysis. 13 The next step is to estimate the off-axis energy-fluence intensity decrease. Helical tomotherapy does not employ a flattening filter, and therefore, there is a significant decrease in intensity away from the central axis. The off-axis intensity model is varied until the predicted transverse dose profiles match those measured at various depths. EDR2 film has proven useful for this Transverse dose profiles were recorded on the film. A static delivery was used, which is defined as having the gantry and couch stationary during delivery. All leaves were open, and the moveable jaws were set to a produce a 1.12 cm field width in the Y direction. The depths used were 1.5 cm, 5.0 cm, 10.0 cm, 15 cm, and 20 cm. Various thicknesses of custom-made Virtual Water Med-Cal, Verona, WI were fabricated specifically for these measurements. These had dimensions of 15 cm by 55 cm. Each treatment lasted long enough to deliver approximately 300 cgy to the film. The films were digitized, and transverse dose profiles were measured and converted to dose. The longitudinal dose profiles had to be measured as well for accurate dose modeling. The static films used for the transverse profiles can be used to model the energy fluence along the Y -axis direction as well. However, Kodak EDR2 film dosimetry demonstrates inadequacies for helical tomotherapy, which will be shown later. The film-measured longitudinal profile was compared to a longitudinal profile measured by an ion chamber via a topographic scan. A topographic scan is one in which the gantry is stationary and the couch moves. This technique has proved useful for tomotherapy dosimetry. 17 An A14Sl ion chamber Standard Imaging, Middleton, WI with a collecting volume of cm 3 was placed in the rectangular Virtual Water at a depth of 1.5 cm and an SSD of 85 cm. The gantry was placed at 0, where the beam points straight down. All leaves were opened and the ion chamber moved past the beam with a speed of 0.5 mm per second. The readings were read every 0.5 seconds by the PTW Unidos electrometer Hicksville, New York. The accelerator-head monitor ion chambers that automatically record the output for each treatment procedure were used to normalize the individual PTW readings. The accelerator-head monitor ion chambers report an updated reading every accelerator pulse, which is at a frequency of 296 Hz, but the reported signal is a running average over 15 pulses. The signals were then down sampled to 2 Hz for comparison. The PTW signal is correlated with the accelerator-head monitor ion chambers signal by inspecting when the first PTW signal jumps above previous leakage values. That value is compared to subsequent PTW signals. The ratio of the first PTW value above leakage to the second represents the percentage of time that the accelerator was on during the first 5 second sample pulse. This method works well providing the initial PTW readings are not within a high dose gradient and the beam is stable. The PTW readings were then divided by the down sampled and correlated accelerator-head monitor ion chamber signal. The same gantry angle, couch speed, electrometer readout rate, and normalization method were used for all topographic measurements presented. 2. Helical verification The energy-fluence output is set to the level necessary for the dose computation to reproduce the dose measured for the 6-rotation uniform helical delivery. This is considered more clinically relevant as treatments are delivered helically. 3 The accuracy of the beam modeling is tested by all other helical rotational deliveries. A series of measurements was recorded in a specially fabricated cylindrically symmetric Virtual Water phantom Med- Cal. This was designed specifically for helical tomotherapy energy-fluence commissioning. The phantom is 30 cm in diameter and 18 cm long. The phantom is divided into two halves such that film may be placed between them. Additionally, a row of ion chamber holes was drilled in the phantom along a radial line perpendicular to the film plane. This allows for subsequent verification of film measurement by rotating the phantom 90. The holes are separated 1 cm away from each other, starting 5 cm from the center of the phantom. Virtual Water sticks are inserted into holes that do not hold ion chambers. This phantom is illustrated in Fig. 2. This

3 3099 Balog, Olivera, and Kapatoes: Clinical helical tomotherapy commissioning dosimetry 3099 FIG. 2. This is a picture of the cylindrical Virtual Water phantom used to measure the axial and helical treatment procedures. The rectangular sheet extending between the two halves shows the EDR film in place. An ion chamber is shown above and below the film. phantom was placed on a specially designed base not shown. This base supported the phantom from two hollow aluminum rods that extended from the end of the couch. This allowed sufficient support with minimum attenuating material. Therefore, the center of the phantom had almost the same radiological path at all gantry angles. EDR2 film was placed between the phantom halves. A 1.12 cm Y-axis field width beam with the central 32-leaves open was delivered axially. 18 The gantry rotated and the couch was stationary. Two gantry rotations of 20 seconds each were used. The resultant film image was digitized and converted into dose. A Y -axis dose profile was obtained. Next, the A14Sl ion chamber measured the longitudinal dose profile topographically in the cylindrically symmetric Virtual Water phantom. The chamber was placed at the most central ion chamber position, 0.5 cm below the isocenter. The magnitude of this topographic dose profile was multiplied by an experimentally determined correction factor of This factor accounts for the ion chamber being 0.5 cm lower than the center of the phantom, which is where the film was. It also accounts for inherent rotation output variations that would be present for the axial delivery, but not present for the rotational delivery. The topographic profile distance axis was scaled by the ratio of 85.0/85.5 as well. Both Y-axis dose profiles are referred to as the impulse functions as they are effectively convolved with the couch translation distance. Next a series of helical treatment procedures from 1 to 10 rotations were used to irradiate other films. The same central 32 leaves were opened for all deliveries. The gantry rotation period for all deliveries was 20 seconds. Two rotations were used for the axial delivery to increase the dose. The pitch, the distance the couch travels per rotation divided by the field width, was set to 0.5 for all helical deliveries, so the couch traveled 0.56 cm per gantry rotation. The films were digitized and the longitudinal dose profiles were recorded. The A14SL ion chamber was inserted 0.5 cm below the phantom center, and adjusted longitudinally to read the maximum dose point for each of the helical deliveries to film described above. The maximum central dose values and the longitudinal dose-profile shapes were predicted for each helical delivery by convolving both film/axial and ion-chamber/topographic impulse functions. The two digitized impulse functions were passed to the PV-Wave function convol VNI Inc. Boulder, Colorado. The mathematical details are specified in the appendix. The results were compared to the film-measured helical dose profiles. The longitudinal dose profile for the 6-rotation delivery was measured, over multiple treatment deliveries, by the A14SL ion chamber. The chamber starting position was offset for each separate delivery. The offset distance varied based on the dose gradient. This was to verify the accuracy of the ion chamber-measured impulse function and its convolution, for that one 6-rotation example. B. Beam spectrum uniformity The absence of the flattening filter produces a beam spectrum that is more uniform for the entire field than one that undergoes flattening filter-induced beam hardening. 13 This is beneficial for the tomotherapy model-based dose calculation, as fewer corrections are required. The beam can be modulated flat if a uniform dose distribution is desired. Inverting the cone profile as measured at a depth of 1.5 cm and applying those weights to the leaf intensity pattern for a static delivery demonstrated this. A film was placed at the isocenter at a depth of 1.5 cm. The central leaf was open for 20 seconds. Off-axis leaves were open for this time divided by their relative off-axis intensity decrease. The transverse dose profile across the film was measured, and normalized to its central dose value. The leaf-open weights were modified by the inverse of the ratio of their corresponding measured dose value to unity. A new film was exposed and the process continued for three iterations until the profile flatness remained unchanged by qualitative comparison. A dose profile was also measured at a depth of 10 cm for the final leaf-modulation pattern. C. End of planning EOP considerations occur after the optimized energyfluence pattern or sinogram has been determined for a particular patient. This accounts for machine specific modifications to the optimized treatment. Accurate energy-fluence modeling requires that the tongue-and-groove, penumbralblur effect TAG-P be well modeled. 17,19,20 The actual energy fluence transmitted to a point under the direct path of a leaf of interest LOI is dependent on the state of its adjacent leaves. 17 The state of neighbor leaves is not considered during optimization. The leaf fluence output factor LFOF refers to the relative energy-fluence increase to a point under an LOI when adjacent leaves are open. The magnitude of this effect and the degree to which it extends to adjacent leaves had to be determined. The A12S ion chamber was used with a 3 mm aluminum build-up cap, which was placed within the trajectory of a

4 3100 Balog, Olivera, and Kapatoes: Clinical helical tomotherapy commissioning dosimetry 3100 FIG. 3. This shows normalized transverse dose profiles for a helical tomotherapy unit. central MLC leaf leaf 32 at the gantry isocenter. A series of static treatments was delivered and measured. This was done for the 1.12 cm field width. Leaf 32 was open by itself for 30 seconds. Next leaves 31 and 33 were opened followed by Then leaves 30 and 34 were opened, followed by leaves This process continued out to five leaves on each side of leaf 32. Then all leaves were opened. The charge collected by the A12S ion chamber was measured for each case. Pairs of leaves equidistant from the center were always opened simultaneously, e.g., 31 and 33 together, or 30 and 34, since the combined signal would be more forgiving to small lateral misalignment of the ion chamber. The total charge collected for a set of all-open leaves divided by the sum of the odd-open and even-open leaves for the same number of leaves is the LFOF for that set of leaves. Leaves 31, 32, and 33 would be opened sequentially, and the total charge collected would be summed. Then, those leaves would be opened simultaneously and a new charge collected. The ratio of the simultaneously collected charge to the sequentially collected charge is the LFOF for leaf 32 when both adjacent leaves are opened, for example. The LFOFs need to be determined for each leaf for maximum accuracy. It was hypothesized that the MVCT detector arrays could perform the same energy-fluence measurement for the various open-leaf combinations much more efficiently. A single treatment procedure was devised that had the same open-leaf combination as that used for the external ion chamber measurement. A single treatment procedure was created that cycled through the LOIs in sets of two simultaneously, i.e., leaf 1 and leaf 32 would be the leaves for which LFOF data were collected. Each set would cycle the LOI and its adjacent neighbors individually and together. Then this would switch for leaves 2 and 33. Having 2 LOIs at once sped the delivery process. The leaves were sufficiently separated that interference between them was negligible. Another EOP consideration is the actual or effective open time of the MLC leaves versus the programmed MLC open time. These are differences due to motion delay times and transit time effects. Again the MVCT detectors were employed. Ion chamber vs MVCT detector measurements were again performed to verify this methodology, but the results are not shown since this concept is a repeat of that described in the LFOF section above. Two factors were known to affect leaf motion of pneumatically driven leaves, the rapidity of the motion and the number of leaves commanded to move. 21 First, the effect of the motion timing for simultaneously moving leaves was studied for the 1.12 cm field width. An 800-projection treatment plan was created. Each projection was 200 ms. All leaves were closed for the first 50 projections. Leaves 2, 12, 22, 32, 33, 43, 53, and 63 were programmed to be open for 100% of the time for the next 30 projections. Those leaves were programmed to be open 2.5% of the time for the next 30 projections. This was repeated for increasing percent open times of 4%, 5%, 6.0%, 10%, 15%, 20%...80%, 85%, 90%, 94%, 95%, 96%, 97.5% and 100%. The effective open time was calculated for each leaf for each programmed percent-open time. This was defined as the sum of the corresponding leaf MVCT detector signal for a particular programmed set by the average sum measured for the 100%-open sets at the beginning and the end. This experiment was repeated for projection times of 400, 600, 800, and 1000 ms. Second, the effect of the number of moving leaves on the effective open time was considered. All leaves were programmed to simultaneously open and close. The same opentime percentages were used. Only the results for the previously studied leaves 2, 12, 22, 32, 33, 43, 53, and 63 were investigated for consistency and clarity. The 200 ms projection time was used, as the shortest projection time would be the worst case. III. RESULTSÕDISCUSSION A. Energy-fluence modeling The static transverse dose profiles of the un-flattened beam recorded on film are shown in Fig. 3. They demonstrate a pronounced peak in the center of the slit beam. The central-axis intensity value is more than double that at the lateral edges of the beam. Figure 4 illustrates the differences between the ion cham- FIG. 4. This shows a comparison of the normalized dose profile for the 1.12 cm longitudinal field width measured by film for an axial delivery and by ion chamber for a topographic deliver. This un-normalized profile represents the impulse function used to predict the longitudinal dose profile at the center of the phantom resultant from a series of helical deliveries.

5 3101 Balog, Olivera, and Kapatoes: Clinical helical tomotherapy commissioning dosimetry 3101 FIG. 5. This shows the Y-axis dose profiles measured by film along the line that passed through the isocenter for 1, 2, 3, 4, 6, and 10 helical rotations. ber and film-measured Y axis axially delivered dose profiles for the narrow clinical beam. The difference is most pronounced in the penumbral regions between the 5 50 % dose levels. The value of the integral of each normalized dose profile was 8.0% higher for the ion chamber measurement. The film-measured helical dose profiles along the isocenter shown in Fig. 5 demonstrate an increase in dose output for each additional helical rotation 1, 2, 3, 4, 6, and 10 rotations shown. The number of rotations required for a uniform dose profile is equal to the inverse of the pitch, due to the dose ramp up and ramp down associated with helical tomotherapy. Therefore, the longitudinal dose profile does not begin to plateau until the third rotation for these results (pitch 0.5). Due to the relatively narrow Y -axis field width, it is not until the fourth rotation that a uniform region is readily observable. The comparisons of measurement with ion chamber and film-based convolution are shown in Fig. 6, for 1 and 10 helical rotations. The longitudinal dose profile shape predicted for 1 helical rotation from the film-measured impulse function matches the actual film measurement much closer than does the profile predicted from the ion chamber measured impulse function. All longitudinal dose profiles converge by the tenth helical rotation, and upon very close inspection, the ion chamber-based prediction better matches film. The convolution-predicted dose values in the center of each helical delivery are compared to all those measured by film and by ion chamber, and are shown in Table I. There was excellent agreement between the dose predicted via the ion-chamber impulse function and the ion chamber measured dose value in the center of each helical delivery column 1. The agreement was not as good for the ion chamber impulse function prediction and that measured by film column 2. However, the differences were not outside the accuracy that can be expected from film dosimetry. 22,23 There is significant divergence for the magnitude of the dose values predicted from the two impulse functions column 3. The divergence increases with increasing number of rotations, but it starts to plateau after 5 or 6 rotations. EDR film was adequate for measuring the transverse dose profiles because the penumbral region only contributes once FIG. 6. a This shows longitudinal dose profile for a 1-helical rotation treatment procedure as measured by EDR2 film, and predicted by convolving the film and ion chamber measured impulse functions. b shows the same results for a 10 helical rotation treatment procedure. to the dose. However, the film-measured Y -axis dose profile incorrectly represented the integral of the dose. This filmmeasured axial dose profile, when convolved with distances representing many gantry rotation distances, can adequately predict the shape of the film-measured longitudinal dose profiles Figs. 6 a and 6 b. This is as expected as all would exhibit the same dose under response at the penumbral region. Conversely, the magnitude of the measured dose in the center of the longitudinal dose profile deviates from the value predicted from convolution of the film-measured impulse function for increasing rotations Table I. This deviation leveled off at a value of 8% near 10 rotations. Therefore measurement and prediction only deviate when prediction is convolved over a range wide enough to include the under responding penumbral region. That 8% dose difference is equal to the difference in magnitude between the film and ion chamber measured axial dose profiles the impulse functions. The ion chamber-measured impulse dose profile proved to be an excellent way to derive the total integral dose. That is shown by the agreement between the ion chamber-predicted and measured dose in the longitudinal center of each helical delivery Table I. It was also demonstrated by the excellent agreement for the multiple helical measurements and the ion chamber measured impulse function prediction for 6 rotations, as shown in Fig. 7. Those results may seem obvious, but only if both measurements are correct. Any significant

6 3102 Balog, Olivera, and Kapatoes: Clinical helical tomotherapy commissioning dosimetry 3102 TABLE I. A comparison of the maximum central dose measured by ion chamber and film and predicted from a convolution of the impulse function for a series of helical deliveries. Number of helical rotations Ion chamber impulse convolution/ion chamber measurement Ion chamber impulse convolution/film measurement Ion chamber impulse convolution/film impulse convolution error present in the measurement of the impulse function, i.e., leakage, would result in an erroneous prediction when convolved a distance equal to 6 rotations. Even if the same leakage were present for the multiple helical measurements, that error would not match that predicted, as the error in the impulse function will be multiplied. The ion chamber-measured impulse function was only about 1 mm wider than the film measurement. The under response of the EDR film is interesting, but the more significant point is how that feature demonstrates the convolving nature of tomotherapy dose deposition. Seemingly small measurement errors become appreciable when continuously superimposed. The actual tomotherapy C/S dose calculation is, of course, not a simple convolution of the measured impulse function. However, the effect is the same, and the specific Y -axis dose profile calculated from the C/S code must match the measurement. B. Beam spectrum uniformity The relative flattened static tomotherapy beam dose profile for the 1.5 cm depth is shown in Fig. 8, as well as the relative dose profile at 10 cm depth and the final relative leaf intensity pattern. The 1.5 cm depth dose profile had a standard deviation of 0.4% of the mean over the central 80% ( 16 cm) of the transverse beam width. The standard deviation of the mean was also 0.4% over the central 90% ( 18 cm) of the transverse beam width. The standard deviation of the mean at a depth of 10 cm was 0.8% and 1.1% over the central 80% and 90%, respectively, of the transverse beam width. The intensity-modulating abilities inherent in a tomotherapy unit are capable of modulating the beam exceptionally flat. The intensity modulation pattern designed to produce a uniform dose profile at a depth of 1.5 cm produced a dose profile at a depth of 10 cm depth that is more uniform than is the definition of a flat beam, which is 3% over the central 80% of the beam width. 24 This was due to the more uniform beam spectrum across the transverse width of the beam that exists when there is no flattening filter. The flattening filter is also seen to reduce the beam output at the central axis by more than 50%, as seen in Fig. 3. The beam spectrum uniformity simplifies the C/S dose calculation because the same dose deposition kernels can be used for offaxis beams. 3 C. End of planning A comparison of the LFOFs as determined by the A12S ion chamber and the MVCT detectors is shown in Table II. FIG. 7. This shows the comparison between the longitudinal dose profile at the isocenter for a 6-rotation helical delivery as calculated by the ion chamber-measured impulse function and several discrete ion chamber measurements. FIG. 8. This shows a transverse dose profile where the beam was modulated to produce a uniform dose distribution at a depth of 1.5 cm. The dose profile measured at a depth of 10 cm for the same intensity modulation is shown for comparison. The relative leaf open time across the transverse width of the MLC is also shown.

7 3103 Balog, Olivera, and Kapatoes: Clinical helical tomotherapy commissioning dosimetry 3103 TABLE II. This shows the leaf fluence output factors for a series of open-leaf combinations as measured by an external ion chamber and by the MVCT detectors for leaf 32. Leaf 32 and number of open adjacent leaves Ion chamber measured fluence output factor MVCT-detector measuredfluence output factor The MVCT detector-measured LFOFs agreed with the A12Smeasured LFOFs within 1% for all open-leaf combinations except for the case with 4, 20, and 32 adjacent leaves where the difference was 2%. This validated using the MVCT detectors for quantitative dosimetry. Table II. shows that the LFOFs do not increase significantly as leaves are opened beyond the two adjacent leaves, and the dose calculation code does not account for LFOFs beyond them. This is another benefit of not having a flattening filter, as it has been shown to be the main source of extra-focal radiation or collimator scatter. 25 By definition, extra-focal radiation is what passes through the opening from multiple open adjacent leaves. 17 Not having a flattening filter greatly simplifies a C/S-based dose calculation. The MVCT detector computed LFOFs are shown in Table III for select sets of leaves. The extra-focal radiation that could contribute to an LOI was categorized for each open adjacent leaf and for both open adjacent leaves. The dose calculation code does not assume that each adjacent leaf produces identical LFOFs. The LFOF value when both adjacent leaves are open is not equal to the sum of the left and right LFOF value. Opening one adjacent leaf allows much of the TABLE III. This shows sample of the leaf fluence output factors obtained automatically in a single treatment procedure by the MVCT detectors. Leaf of interest Left leaf FOF Right leaf FOF Both Adj FOF FIG. 9. This illustrates why the LFOF for both adjacent leaves open is not twice that for a single adjacent leaf open. The solid lines show the projection of the source viewable at the measurement plane when only the LOI is open. The dashed lines show the increase in viewable source when one adjacent leaf is open. This increase is on both sides of the source, and therefore opening the other does not add as much. missing source to be seen, and the viewable projection back to the source plane is only slightly increased by opening both adjacent leaves. This is illustrated in Fig. 9. As can be seen, one adjacent leaf allows more of both sides of the source plane to be seen, and not as much energy fluence is gained by opening the other adjacent leaf. The LFOF values are a little larger for the outer leaves than for the central leaves, for a properly aligned MLC. This is because the MLC leaves are focused just behind the physical source location. Central leaves point directly at the source. Outer leaves do not, and therefore more energy fluence is gained by opening the adjacent leaves. The MLC leaf-latency results are shown in Figs. 10 a 10 d. Figure 10 a shows the effective leaf-open times as a function of programmed leaf-open times for the programmed leaves for the 200 ms projection time. The response is linear over a range from 25% to 80% of the time. Figure 10 b is the same thing for the 400 ms projection time. The linear region is extended to approximately from 10% to 90% of the programmed open-time. The MLC leaf latency is modeled in the end-of-planning for the dose calculation as a linear line where the effective leaf open time is equal to some constant,

8 3104 Balog, Olivera, and Kapatoes: Clinical helical tomotherapy commissioning dosimetry 3104 FIG. 10. Plot a shows the effective leaf open time as a function of the programmed leaf open time for eight individual moving leaves for a 200 millisecond projection time. Plot b is the same as a, but with a 400 ms projection time. Plot c shows the curve fits for different projection times. Plot d shows the effective computed leaf response for those eight individual leaves when only those leaves moved vs when all the leaves moved for a 200 ms projection time. or the slope, multiplied by the programmed open time plus another constant, or offset. The leaf responses are very similar within a projection time. This allows a single linear effective open time model to be used per projection time. Those linear models are shown in Fig. 10 c for the 200, 400, and 600 ms projection times. As evident from that graph, the linear model is very similar for the 400 and 600 ms projection times. This was similar for greater projection times as well. The EOP code stores constants for 200, 300, 400, 600, 800, and 1000 ms projection times. A greater projection time would use the 1000 ms model. The actual projection time used for a patient treatment procedure will be some floating-type value equal to the gantry rotation period divided by the number of projections per rotation. The linear equation used to predict the leaf response is interpolated between those stored projection-time models. The typical projection time for treatments at University of Wisconsin so far has been around 400 ms for prescriptions ranging from 1 Gy to 10 Gy. The programmed open time for a particular patient plan is then calculated from the interpolated effective response equation and the optimized open times. Any leaf open time that is calculated to open below a low threshold open time of 20 ms will be set closed for the projection. The lowest projection time allowed is 294 ms. This projection time results when a 15 second gantry period has 51 projections per rotation. Figure 10 d shows the comparison between the linear model for effective open times for the 8 leaves studied when only those 8 leaves moved versus when all MLC leaves moved 200 ms projection time. The similarity between these two curves for the worst-case projection time is another useful simplification, as only one model is needed regardless of the number of leaves programmed to open. The LFOF and MLC latency experiments were repeated for varying field widths up to 5 cm. The MVCT detector is 2.0 cm wide, projected at isocenter. Therefore it might not properly measure differences due to field widths beyond 2.0 cm. However, the results were so similar it is doubtful that field width appreciably affects the EOP values. Typically most ( 75%) of the LFOF values were identical across jaw settings. The differences when they occurred were usually 1% larger LFOF values for the wider jaw settings i.e., 1.08 vs The MLC latency results were remarkably consistent across field widths. A sample comparison of effective open times vs programmed open times for a 1 cm field width anda5cmfield width is shown in Table IV. The independence of EOP results vs field width simplifies measurement and modeling.

9 3105 Balog, Olivera, and Kapatoes: Clinical helical tomotherapy commissioning dosimetry 3105 TABLE IV. This shows the MLC latency results as a function of field width for the 400 ms projection time. Programmed Actual open time ms open time ms 1.0 cm field width 5.0 cm field width IV. CONCLUSION Helical tomotherapy treatment beam commissioning dosimetry differs from other treatment planning versions for a variety of reasons. Helical tomotherapy machines do not have a flattening filter and this results in a treatment beam with a strong triangular shape across the transverse direction. This shape has to be explicitly modeled in the dose optimization and calculation process. Helical delivery continuously superimposes the inferiorsuperior dose contribution with slight translation offsets. A modeling error of the Y -axis dose profile can become significant over increasing translation offsets, associated with more patient slices treated. The lack of a flattening filter is beneficial for a variety of reasons. The beam output is more than twice what it would be along the central axis without the filter. This reduces the treatment time, as every prescription point must lie along the central axis for some fraction of the rotational delivery. The beam spectrum is also more uniform across the field. This simplifies beam modeling, and can produce some advantageous dosimetric characteristics, such as a flat beam at multiple depths if so desired. The lack of a flattening filter reduces the extra-focal radiation, and minimizes LFOFs. This further simplifies beam modeling. The extra-focal radiation that is present when leaves adjacent to an LOI are open simultaneously with the LOI is accounted for in the end-ofplanning calculation of the C/S-based dose calculation code. The LFOFs are only calculated for each adjacent leaf to an LOI. The effective response on the MLC leaves is another endof-planning consideration. A series of linear response equations based on calculated treatment projection time is used to model the effective leaf opening time. The data for both effective MLC leaf latency and LFOF are collected automatically via the on-board MVCT detectors. This greatly expedites the collection process. APPENDIX The Y -axis dose profile impulse function measured by film for an axial delivery and by ion chamber for a topographical delivery was convolved to predict what that dose should be for helical deliveries. This was for dose points only along the center of the phantom, which was at the isocenter, because only those points were rotationally invariant with respect to radiation delivery. The convolution function was included in the software programming and analysis package PV-Wave 7.0, sold by Visual Numerics Inc., Boulder, CO. The convolution function used is shown below: result CONVOL array,kernel,scale factor. The corresponding algorithm is shown below: m 1 Result t 1/Scale * i 0 Array t i Kernel i, where Result is the predicted dose profile along the isocenter for the number of helical rotations corresponding to a couch translation distance described by the kernel, and Array is an n-element vector representing the impulse function. Scale is the scale factor. 1 T. R. Mackie, T. Holmes, S. Swerdloff, P. Reckwerdt, J. Deasy, J. Yang, B. Paliwal, and T. Kinsella, Tomotherapy: A new concept for the delivery of conformal radiotherapy, Med. Phys. 20, T. R. Mackie, J. Balog, K. Ruchala, D. Shepard, S. Aldridge, E. Fitchard, P. Reckwerdt, G. Olivera, and T. McNutt, Tomotherapy, Semin Radiat. Oncol. 9, G. H. Olivera, J. Balog, R. McDonald, W. Lu, J. Kapatoes, P. J. Reckwerdt, R. Jeraj, and K. Ruchala, Commissioning of collapsed cone convolution-superposition dose calculation for use in IMRT rotational deliveries, Med. Phys. submitted. 4 J. N. Yang, T. R. Mackie, P. Reckwerdt, J. O. Deasy, and B. R. Thomadsen, An investigation of tomotherapy beam delivery, Med. Phys. 24, J. Balog, Tomotherapy dosimetry and the tomotherapy workbench, University of Wisconsin, Madison, thesis, Chap. 8, J. Ruchala, G. H. Olivera, E. A. Schloesser, and T. R. Mackie, Megavoltage CT on a tomotherapy system, Phys. Med. Biol. 44, K. J. Ruchala, G. H. Olivera, J. M. Kapatoes, J. B. Smilowitz, E. A. Schloesser, D. W. Pearson, J. P. Balog, P. J. Reckwerdt, and T. R. Mackie, Tomographic verification of tomotherapy before, during and after treatment, in Proceedings of the 13th International Conference on Computers in Radiotherapy Heidelberg, Germany, 2000, edited by W. Schlegel and T. Bortfeld Springer-Verlag, Berlin, 2000, pp M. Kapatoes, G. H. Olivera, K. J. Ruchala, P. J. Reckwerdt, J. S. Smilowitz, J. P. Balog, H. Keller, and T. R. Mackie, A feasible method for clinical delivery verification and dose reconstruction in tomotherapy, Med. Phys. 28, J. Balog, T. R. Mackie, D. Pearson, S. Hui, B. Paliwal, and R. Jeraj, Benchmarking beam alignment for a clinical helical tomotherapy device, Med. Phys. 30,

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