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Intensity modulation with the “step and shoot” technique using a commercial mlc: a planning study
Int. J. Radiation Oncology Biol. Phys., Vol. 45, No. 5, pp. 1315–1324, 1999 Copyright © 1999 Elsevier Science Inc. Printed in the USA. All rights reserved 0360-3016/99/$–see front matter
PII S0360-3016(99)00324-7
PHYSICS CONTRIBUTION
INTENSITY MODULATION WITH THE “STEP AND SHOOT” TECHNIQUE USING A COMMERCIAL MLC: A PLANNING STUDY MARK-ALEKSI KELLER-REICHENBECHER, PH.D.,* THOMAS BORTFELD, PH.D.,* SABINE LEVEGRU¨ N, PH.D.,* JO¨ RG STEIN, PH.D.,† KONRAD PREISER, PH.D.,* AND WOLFGANG SCHLEGEL, PH.D.* *Deutsches Krebsforschungszentrum (DKFZ), Department of Medical Physics, Heidelberg, Germany; and †MRC Systems, Heidelberg, Germany Purpose/Objective: For complex planning situations where organs at risk (OAR) surrounding the target volume place stringent constraints, intensity-modulated treatments with photons provide a promising solution to improve tumor control and/or reduce side effects. One approach for the clinical implementation of intensity-modulated treatments is the use of a multileaf collimator (MLC) in the “step and shoot” mode, in which multiple subfields are superimposed for each beam direction to generate stratified intensity distributions with a discrete number of intensity levels. In this paper, we examine the interrelation between the number of intensity levels per beam for various numbers of beams, the conformity of the resulting dose distribution, and the treatment time on a commercial accelerator (Siemens Mevatron KD2) with built-in MLC. Methods and Materials: Two typical, clinically relevant cases of patients with head and neck tumors were selected for this study. Using the inverse planning technique, optimized treatment plans are generated for 3–25 evenly distributed coplanar beams as well as noncoplanar beams. An iterative gradient method is used to optimize a physical treatment objective that is based on the specified target dose and individual dose constraints assigned to each organ at risk (brain stem, eyes, optic nerves) by the radiation oncologist. The intensity distribution of each beam is discretized within the inverse planning program into three to infinitely many intensity levels or strata. These stratified intensity distributions are converted into MLC leaf position sequences, which can be subsequently transferred via computer link to the linac console, and can be delivered without user intervention. The quality of the plan is determined by comparing the values of the objective function, dosevolume histograms (DVHs), and isodose distributions. Results: Highly conformal dose distributions can be achieved with five intensity levels in each of seven beams. The merit of using more intensity levels or more beams is relatively small. Acceptable results are achievable even with three levels only. On average, the number of subfields per beam is about 2–2.5 times the number of intensity levels. The average treatment time per subfield is about 20 s. The total treatment time for the three-level and seven-beam case with a total of 39 subfields is 13 min. Conclusion: Optimizing stratified intensity distributions in the inverse planning process allows us to achieve close to optimum results with a surprisingly small number of intensity levels. This finding may help to facilitate and accelerate the delivery of intensity-modulated treatments with the “step and shoot” technique. © 1999 Elsevier Science Inc. Conformal radiotherapy, Multileaf collimators, Optimization, Inverse problem, “Step and shoot” technique.
INTRODUCTION Intensity-modulated radiotherapy (IMRT) has the potential to improve the conformity of dose distributions to target volumes significantly, especially for very complex cases. It is anticipated that this capability will improve local tumor control and/or reduce side effects. Several techniques have been developed and applied for the practical delivery of IMRT in recent years. Among the most frequently used in
clinical practice are the slice-by-slice or tomotherapy concept, which uses continuous gantry rotations, as well as the fixed-beam multileaf modulation technique (MLM). The reader is referred to the book of Webb (1) for a detailed review of these approaches. In this paper, we will focus on the MLM technique. This technique can either be realized in a fully dynamic mode, in which the MLC leaves are moving while the beam is on, or in the so-called “step and shoot” or multisegmental mode, in
Presented at the ASTRO Annual Meeting, Orlando, FL, 1997. Reprint requests to: Mark-Aleksi Keller-Reichenbecher, Deutsches Krebsforschungszentrum, FS Radiologische Diagnostik und Therapie, Abt. Medizinische Physik (E0401), Im Neuenheimer Feld 280, D-69120 Heidelberg, Germany. Tel: (⫹49) 6221-
42-2579; Fax: (⫹49) 6221-42-2561; E-mail: m.keller@ dkfzheidelberg.de. Acknowledgments—Financial and technical support by SIEMENS Oncology Care Systems (OCS), CA, is gratefully acknowledged. Accepted for publication 3 June 1999. 1315
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Fig. 1. Discretization of the intensity profiles with method 1.
which a sequence of subfields with different MLC shapes is delivered from each direction of incidence, and the beam is switched off while the leaves are moving. Both techniques are in clinical use (2– 4), and both of them have specific pros and cons (1, p. 130). According to our initial experience, the “step and shoot” technique has the advantage of being more readily verified, while the dynamic technique is potentially faster. With current technology, the overall treatment time in “step and shoot” or multisegmental MLM is mainly determined by the total number of subfields used. This is because the actual beam-on time in each subfield is often only a fraction of the considerable time overhead for the start-up procedure and the record and verify system. Obviously, the number of subfields is given by the product of the number of beams and the number of subfields per beam. In “step and shoot” MLM, the latter is governed by the number of intensity levels in the modulation profiles. From a point of view of minimizing the treatment time it is therefore important to reduce the number of intensity levels to the smallest number that is compatible with the objective of achieving a highly conformal dose distribution. In a previous approach to “step and shoot” MLM we used an inverse planning program to calculate continuous intensity profiles, which were subsequently approximated by stratified intensity profiles. The number of evenly spaced intensity levels in the stratified profiles was varied until the minimum number was found that allowed for an approxi-
Fig. 2. Change in the values of the physical objective as a function of the number of iterations for a seven-beam plan of case 1 with different discretization methods: (a) method 1, (b) method 2 and method 3.
mation within a given RMS deviation (5). However, it is not obvious how small the RMS deviation of the intensity profiles has to be in order to achieve clinically acceptable dose distributions. Consequently, in this work we attempt to determine to which degree the stratification of the intensity profiles translates into a deterioration of the treatment plans. For this purpose, we investigate simple approaches for the optimization of intensity distributions with a given number of levels. For two clinical cases and different numbers of beams, we estimate the minimum number of levels that
Fig. 3. Sequence of MLC-generated field shapes producing the three-level intensity distribution of Fig. 4c.
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Fig. 4. Intensity distribution for the first of seven fields for the treatment of case 1 with: (a) continuous modulation, (b) five levels, and (c) three levels.
yield (a) acceptable and (b) close to optimum results. The resulting treatment times on a commercial linear accelerator (linac) with built-in MLC are also determined. A related investigation was published before in (6). There, however, only a single two-dimensional model case was considered, and the focus was on the comparison of tomotherapy and stratified MLM, not on the comparison of different numbers of strata in MLM. METHODS Inverse planning The inverse planning program KonRad (MRC Systems, Heidelberg, Germany), which was developed at DKFZ, is used to calculate the optimized intensity distributions for different numbers and directions of incident beams (7). The algorithm minimizes a physical objective function (F) considering the mean square deviation between calculated and prescribed dose values in the target volume, as well as any dose values beyond tolerance in critical structures (8). Dosevolume constraints (9) are not included because all relevant organs are assumed to have negligible volume effect. The optimization procedure is based on a gradient-type algorithm, which allows us to do the optimization within a few minutes on a Pentium II processor or below 1 min on a DEC ALPHA Station 500 (Digital Equipment Corporation, May-
nard, MA). The dose calculation engine used in KonRad is a pencil beam convolution algorithm (10) adapted for 15 MV radiation from a SIEMENS KD2 (SIEMENS Oncology Care Systems (OCS), Concord, CA) with built-in MLC. The resolution of the intensity matrices is set to 10 mm in the in-plane direction, which corresponds with the leafwidth of the MLC. In the cross-plane direction, the resolution is 5.5 mm. The MLC is not rotated. The voxel size of the dose calculation cube is 2.5 ⫻ 2.5 ⫻ 4.5 mm3. Stratification of the intensity profiles A simple and practical way of stratification can be achieved when the optimization process is completed as schematically shown in Fig. 1. After n steps of the optimization the intensity values of each profile are subdivided into x equidistant levels (method 1). The level size is calculated by dividing the maximum fluence in each profile by the number of levels. Figure 2a shows the values of the objective function F which were obtained for different numbers of intensity levels if method 1 is applied after 10 steps of the optimization compared to the value of F without stratification. Because the investigation shows that use of the stratified intensity profiles for additional steps of the optimization affects the gradient-type algorithm in a negative way, only the first result after stratification is used. Another strategy would be to enable the stratification from
Fig. 5. Transversal, sagittal, and frontal CT reconstructions of case 1 (clivus chordoma) in the isocenter. Shown are the outlines of the target volume (T), the brainstem (B), and the patient contour. The grey line indicates a beam with gantry angle 0.
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Fig. 6. Transversal, sagittal, and frontal CT reconstructions of case 2 (schwannoma) in the isocenter. Shown are the outlines of the target volume (T), the brainstem (B), the left and right optic nerve (N), the optic chiasm (C), and the patient contour. The grey line indicates a beam with gantry angle 0.
the beginning of the optimization process (method 2). Figure 2b shows the corresponding values of F obtained with method 2. Compared to Fig. 2a, no stratification level could achieve as low values of F as gained with method 1 described above. A third method of optimization was investigated where only in every second step the stratification was enabled (method 3). This results in better objectives than obtained with method 2 but not better than the ones achieved with method 1 (Fig. 2b). Therefore, method 1 is used for the following investigations. Calculation of leaf trajectories The leaf trajectories necessary for the delivery of the discrete intensity profiles are determined by the discrete sweep technique (5). More specifically, an algorithm for dynamic multileaf modulation (11) is modified to calculate the discrete leaf positions in this case. This results in a number of subfields of about 1.5–2 times the number of intensity levels. The tongue-and-groove effect is avoided by means of synchronization of the positions of neighboring leaf pairs (12, 13). We find that by fully synchronizing the leaf trajectories, leaf collision problems are also automatically avoided. However, the price to be paid is that the required number of subfields increases by about 50% through synchronization. As an illustrative example we show in Fig. 3 the six subfields calculated with the methods just described for the first of seven beams of the first clinical case (described
below). The superposition of these six subfields yields the three-level intensity distribution of Fig. 4c. Delivery of the sequences The sequences of subfields with their corresponding MLC leaf positions are transferred via computer link to the linac console. The delivery is done with the SIMTEC (Siemens Intensity Modulation TEChnology) module without user intervention. Clinical cases The study is performed for two cases of different complexity with target localizations in the head. The first case (case 1, Fig. 5), a clivus chordoma close to the brainstem, is planned with evenly distributed coplanar beams only. The transversal CT reconstruction in Fig. 5 shows the target volume (T) surrounding the brainstem (B). The difficulties here are to get a very steep dose gradient between the target volume and the OAR. For verification purposes the outlines from case 1 are transferred to a spherical phantom which is used for further investigations. The second and more complex case is a head and neck tumor (schwannoma), where the target volume is surrounded or even overlapped by different types of organs at risk (OARs) (case 2, Fig. 6). Here, noncoplanar beams are used in addition, which were selected on the basis of 3DCRT by an experienced planner. The goal of the treatment was to exclude the eyes (E), the optic nerves (N), and
Table 1. Parameters of the physical objective for case 1 (clivus chordoma) Parameter
Target
Right eye
Left eye
Brainstem
Right optic nerve
Left optic nerve
Optic chiasm
Phantom
Overlap priority Min dose Max dose Penalty min dose Penalty max dose
2 68.00 71.50 99.00 20.00
4 0.00 30.00 0.00 3.00
3 0.00 30.00 0.00 3.00
1 0.00 35.00 0.00 100.0
7 0.00 40.00 0.00 3.00
6 0.00 0.00 0.00 6.00
8 0.00 60.00 0.00 3.00
5 0.00 60.00 0.00 3.00
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Table 2. Parameters of the physical objective for case 2 (schwannoma) Parameter
Target
Right eye
Left eye
Brainstem
Right optic nerve
Left optic nerve
Optic chiasm
Head
Spinal cord
Overlap priority Min dose Max dose Penalty min dose Penalty max dose
2 65.00 70.00 5.00 5.00
5 0.00 10.00 0.00 1.00
4 0.00 10.00 0.00 1.00
3 0.00 60.00 0.00 1.00
1 0.00 50.00 0.00 5.00
6 0.00 45.00 0.00 1.00
7 0.00 50.00 0.00 1.00
9 0.00 45.00 0.00 4.00
8 0.00 55.00 0.00 1.00
the optic chiasm (C) from damage even if they lie partially inside or close to the target volume (T) (Fig. 6). Each case is first planned and optimized by an experienced planner without reducing the number of strata. The optimization parameters such as the number and angle of beams, dose constraints, and the resolution of the underlying intensity profiles are saved for further evaluation. The resulting dose distributions are chosen as a reference for comparison with the alternatively generated results. In Tables 1 and 2, the parameters of the physical objective assigned to the target volume and OARs for case 1 and case 2 are listed. The parameters for each volume of interest (VOI) are the overlap priority, maximum and minimum doses, and penalties for violation of the specified dose constraints. The overlap priority is used by the inverse planning program to determine which volumes belong to which organ if two or more organs are overlapping. In both head and neck cases, the volumes surrounding the target volumes (“phantom” in case 1 and “head” in case 2) are included to reduce the overall irradiation both outside the target volume and the various OARs. Differences in the minimum and maximum dose values of the physical objectives are a result of adaptations made during optimization and due to the different localizations of the target volumes. As for the example in case 1, the brainstem is much closer to the target volume compared to case 2, the specified maximum dose value is defined lower to achieve the desired results. The same holds true for the other OAR. The investigation is performed by reducing the number of strata from initially infinitely many to 15, and to numbers between 10 and 2 in case 1, and to numbers between 9 and 3 in case 2. Furthermore, the number of beams is modified in case 1 from initially 5 to 25, 13, 9, 7, 5, and 3 evenly distributed beams. In case 2, the initially five noncoplanar beams are modified to five and seven evenly distributed coplanar beams. To achieve the results, the inverse planning program KonRad is stopped for each of the different optimization runs after 20 iterations in case 1 and 30 iterations in case 2. In both cases, the change of the objective F from one iteration step to another is below 0.2%. Depending on the clinical case and the number of beams, the optimization times ranges between 5 s and 45 s on a DEC ALPHA Station 500. Time calculation The time calculation for the delivery is based on preliminary measurements for the SIMTEC module, which results
in an average of about 20 s per subfield including the time for gantry/couch movement, beam-on time, and verification. This measurement is performed for case 1 with seven beams and three fluence levels in the profiles. The anticipated delivery times are calculated as the product of the number of beams times the number of subfields per beam times 20 s. RESULTS Case 1 Figure 7 shows as an example the resulting transversal dose distributions in the isocenter plane where the intensity profiles of a 7 beam plan are stratified from initially infinitely many (Fig. 7a) to five (Fig. 7b) and three (Fig. 7c) fluence levels. The gray area indicates the target volume and the dark gray area indicates the brainstem. The absolute doses are displayed as isodose curves in the following order: 100%/69.8 Gy, 90%/62.8 Gy, 80%/55.8 Gy, 60%/41.8 Gy, and 40%/27.9 Gy. All three figures show good conformation of the calculated dose distribution to the target, while the brainstem is sufficiently spared (below 41.8 Gy). The isodose curves show only minor differences from each other. However, stratification to five levels (Fig. 7b) results in a better sparing of the brainstem compared to continuous modulation. Here, even doses below 40%/27.9 Gy are achievable in the selected plane. If stratification to three levels is applied (Fig. 7c), the area of the 60%/41.8 Gy isodose curve is slightly smaller than with continuous modulation or stratification to five levels. The resulting dose-volume histograms (DVH) of the dose distributions of these seven beam plans for the target volume and the brainstem can be seen in Fig. 8. As expected, the best dose homogeneity in the target volume is achieved with the unstratified plan (Fig. 8, black line). Slightly larger inhomogeneities can be found when the stratification to 5, 4, or 3 levels is applied. The DVH of the brainstem shows no significant differences between infinite and five intensity levels. Further reduction of the number of intensity levels to four and three intensity levels results in slightly higher doses in this OAR. Of the vast number of investigated beam/stratification combinations, the five-beam configuration is selected for a further DVH comparison. Compared to the seven-beam plans above, stratification of the five-beam plans (Fig. 9) results in a higher dose inhomogeneity in the target volume. The worst underdosage can be seen with four intensity levels. A larger overdosage due to a shift of the DVH can be
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Fig. 8. DVH of target volume and brainstem of case 1: Plans with seven beams and reduced number of strata.
observed if stratification to three levels is applied. If renormalized downward, the three-levels curve may have comparable homogeneity as the four- or five-levels curve, but a better sparing of the OAR brainstem. However, a good sparing of the brainstem is possible with all of the stratification approaches. Another effect of the stratification to the dose distribution which occur in both Figs. 8 and 9 are the steps in the DVH. These are best visible in the DVH of the brainstem for four and three intensity levels. To demonstrate the effects of stratification as a function of the number of beams, DVHs are generated for five intensity levels (Fig. 10). Figure 10 shows that the dose homogeneity rises continuously in the target volume with the use of additional beams. Minor effects can be observed in the DVH of the brainstem. Only the use of 3–5 beams results in slightly higher doses to the OAR. As already observed in Figs. 8 and 9, the major differences between stratification and the use of infinitely many levels for different numbers of beams are the steps in the DVH that occur if less beams are used. The investigated effects are summarized in Fig. 11, where the relative values of the physical objective F for different beam/stratification combinations are plotted. The change in
Fig. 7. Transversal dose distributions of case 1 in the isocenter plane for a seven-beam plan with: (a) continuous modulation, (b) five, and (c) three levels. The following isodose lines are shown: 100%/69.8 Gy, 90%/62.8 Gy, 80%/55.8 Gy, 60%/41.8 Gy, and 40%/27 Gy.
Fig. 9. DVH of target volume and brainstem of case 1: Plans with seven beams and reduced number of strata.
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Fig. 10. DVH of target volume and brainstem for plans of case 1 with different number of beams and with stratification to five levels.
the objective is nearly independent from the number of beams. The highest benefit of adding intensity levels can be seen between 3 and 5 levels, where F changes by about 30% per additional level, although in one case (5 beams), the value of F is worst with 4 levels. The reduction decreases if more levels are used. Compared to infinitely many levels, the reduction is about 30% if 5 levels are used and about 20% if 10 levels are used. The differences between 15 and infinitely many levels are about 5–10%. However, the selection of a suitable beam/stratification combination depends on the delivery time of a complete sequence of subfields. Figure 12 shows the values of F for the investigated beam/stratification combinations as a function of the delivery time of the calculated sequences compared to different numbers of beams without stratification. Assuming a time limit of approximately 20 –25 min per fraction, the lowest value of F can be achieved in this case with seven beams and five levels of intensity. According to the objective function, a faster delivery below 15 min could only be realized with seven beams and three levels or five beams and five levels.
Fig. 11. Relative values of the physical objective as a function of the number of intensity levels for different number of beams for case 1 compared to infinite levels.
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Fig. 12. Physical objective versus delivery time for different beam/ stratification combinations compared to different number of beams without stratification for case 1. The first part denotes the number of beams and the second part the number of intensity levels. The delivery time is calculated with 20 s per subfield, which includes the time for gantry/couch movement, beam on time, and verification.
Case 2 If stratification method 1 is applied to a seven-beam plan of case 2 (Fig. 13), quite similar effects as in case 1 can be demonstrated. Figure 13a shows the dose distribution obtained with continuous modulation. Figures 13b and 13c show the results if stratification to five and three intensity levels is applied, respectively. The absolute doses are displayed as isodose curves in the following order: 100%/67.5 Gy, 90%/60.8 Gy, 80%/54 Gy, 70%/47.3 Gy, 60%/40.5 Gy, and 40%/27 Gy. Large dose inhomogeneities in the target volume can be observed, especially in the region of the right optic nerve, which is basically independent from the level of stratification. This is of course the desired result of the optimization parameter definition of the right optic nerve which should be spared (overlap priority 1, see Table 2). Only minor differences in the dose distribution can be seen if infinite and five intensity levels are compared to this. The 100%– 40% isodose curves remain almost at the same position in each figure, except for some minor deviations if stratification to three intensity levels is applied. Here we can observe a greater inhomogeneity in the target volume compared to infinitely many and five levels (Fig. 13c). On the other hand, the best sparing of the optic chiasm (Fig. 13c, 70%/47.3 Gy isodose curve) is possible with only three intensity levels. Figure 14a shows the related DVH of the seven-coplanar beam plan for the selected OAR brainstem, right optic nerve, and the target volume. As a comparison, the DVH of the five noncoplanar beam plan is shown in Fig. 14b. Apart from the slightly higher doses to the OAR and the target volume for stratification to three levels, continuous modulation and stratification to five levels show only significant differences in the right optic nerve for the seven-beam plan (Fig. 14a). The effects of stratification on the target volume dose homogeneity are smaller for the seven-coplanar plan
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Fig. 14. DVH of brainstem, right optic nerve, and target (from left to right) of case 2 with reduced number of strata: Plans with: (a) seven coplanar beams and (b) five noncoplanar beams.
(Fig. 14a) than for the five-beam noncoplanar plan (Fig. 14b). Larger effects to the OAR can also be observed for the five noncoplanar beams in Fig. 14b if stratification to five or three levels is used compared to the seven coplanar beams. The major differences between seven coplanar beams and five noncoplanar beams can be seen in the brainstem, where
Fig. 13. Transversal dose distributions of case 2 in the isocenter plane for a seven-beam plan with: (a) continuous modulation, (b) five, and (c) three levels. The following isodose lines are shown: 100%/67.5 Gy, 90%/60.8 Gy, 80%/54 Gy, 70%/47.3 Gy, 60%/ 40.5 Gy, and 40%/27 Gy.
Fig. 15. Relative values of the physical objective as a function of the number of intensity levels for different beam configurations for case 2 compared to infinite levels.
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Fig. 16. Physical objective versus delivery time for different beam/ stratification combinations compared to different number of beams without stratification for case 2. The first part denotes the beam configuration (number of beams, (c)oplanar, (n)oncoplanar), the second part, the number of intensity levels. The delivery time is calculated with 20 s per subfield, which includes the time for gantry/couch movement, beam on time, and verification.
seven coplanar beams reduce the maximum dose in that OAR, but irradiate a larger volume with lower doses. Figure 15 shows the comparison of the relative values of F as a function of the number of intensity levels (3–7) compared to an infinite number of levels for the investigated beam configurations. The smallest change in F can be seen if five or seven coplanar beams are used. Here the objective F changes only by about 20% between three and infinitely many levels. An artifact can be observed if six or seven intensity levels are used for the five and seven coplanar beams. In the five-beam case, F rises again until it decreases at seven or more intensity levels. In the seven-beam case, F rises with both the six and seven intensity levels and decreases above. The reasons for this effect are given in the Discussion. The values of F for different beam/stratification combinations are plotted in Fig. 16 as a function of the delivery time. According to the indicated values, five noncoplanar beams with five or six, or even four intensity levels would be selected if delivery time should be less than approximately 20 –25 min. Of course, no significant differences in the absolute height of F can be seen between five and six levels. The use of five noncoplanar beams with four intensity levels has about the same value as seven coplanar beams with five intensity levels or five coplanar beams with seven intensity levels. In all cases, there is no significant advantage to use more than 5–7 intensity levels compared to continuous modulation. DISCUSSION In the delivery of intensity modulated treatments using the “step and shoot” technique on some commercial linacs equipped with MLCs, the treatment time is roughly proportional to the number of subfields, while the actual irradiation
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time is only a small fraction of the treatment time. The use of more subfields generally allows better treatment plans. However, the number of subfields is limited by the total treatment time (including patient setup) acceptable in clinical practice (i.e., 15–25 min for complex treatments). For the machine used in this investigation (Siemens KD2), it takes about 20 s to deliver one subfield (including couch/gantry movement, beam-on time, and verification), and the delivery of a sequence of subfields is done without user intervention. Consequently, around 50 subfields can be delivered in a single treatment. In principle, this number of subfields can now be distributed freely among different numbers of beams. Extreme cases would be the use of all 50 subfields within a single beam from one direction of incidence, or the use of 50 uniform beams with one “subfield” each. Both of these extremes are obviously inadequate for most cases; the optimum distribution is somewhere in the middle. This investigation has shown that the use of about five intensity levels per beam gives results that are close to the optimum solution, which is obtained with infinitely many levels. The 5 intensity levels translate into 10 –15 subfields per beam. These findings are almost independent of the number of beams. Our findings demonstrate, on the other hand, that with additional beams and more intensity levels, it is possible to gain more homogeneity in the target volume, but not automatically a better sparing of the OARs. In general, for intensity modulation, it can be stated that it is easier to reduce dose to OARs than to irradiate target volumes with the same homogeneity as with open fields. Due to the fact that around seven coplanar beams are sufficient in most cases, the total number of subfields needed to achieve results that are close to optimum is 70 –100. This number is too high to be delivered efficiently with the equipment available to us. Hence, further reduction of the time overhead in the delivery of subfields would be desirable. On the other hand, we have found that acceptable results are achievable even with only three intensity levels, resulting in about 40 – 60 subfields. Therefore, intensity modulated treatments can be performed with existing technology within acceptable times. Because the resolution in the intensity maps (here 10 ⫻ 5.5 mm) corresponds directly to the number of subfields, a reduction to a resolution of 10 ⫻ 10 mm could help to reduce the delivery time even more. Of course, this will also reduce the homogeneity of the dose in the target volume. However, further investigations should be done on this topic. Although only two clinical cases have been investigated in this study, we believe that the numbers of subfields given can be generalized at least as an upper limit, because the cases are highly complex. It may be surprising that such a relatively coarse discretization of the intensity distributions compromises the quality of dose distributions only slightly, although this finding is in line with a previous result based on biologically based optimization (14). A possible explanation is the known non-uniqueness of the solution of the inverse problem (15): Different intensity distributions (e.g., discretized and continuous ones) can produce very similar
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dose distributions. Our findings do not agree with another study on this problem (6), from which one might conclude that even 10 intensity levels are insufficient in some cases. The reasons for this discrepancy cannot be fully understood because this study is only a short contribution with a limited amount of data (6). A possible explanation is that the discrepancy is due to the obvious differences in the planning and evaluation strategies between our work and (6). A further advantage of the use of fewer subfields (in addition to the reduced treatment time) is that the number of monitor units (MU) per subfield increases proportionally, such that linac instability problems, which may exist at very small MU values, do not play an important role. One problem we saw in the practical delivery of “step and shoot” MLM with very few subfields is the existence of split fields within the sequence. This can be seen in subfields 4 and 6 of Fig. 3, for example. As a consequence, a matchline problem may occur, which shows up as a narrow region of underdose along the abutment line. This problem can be solved by means of a small adjustment of the leaf positions in those regions. However, further investigations are necessary in this context. In general, the value of the objective function F decreases with increasing number of intensity levels. However, we saw some small-scale deviations from this trend. The most likely explanation for such artifacts is our rather crude way of doing the stratification. Because the height of each intensity level depends on the maximum fluence in the specific profile, already one single “hot spot” can shift the levels to unrepresen-
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tative heights. On the other hand, the value of F is very sensitive to small changes in the intensity profiles. This holds true especially if, due to stratification, an OAR with a small volume but high penalty for overdosage (such as the right optic nerve in case 2) receives higher doses in some regions. The approaches presented in this work for the reduction of the number of subfields are based on the stratification of continuous intensity matrices (with an infinite number of intensity levels) into relatively few levels. This is by far not the only possible method to achieve practical values for the number of subfields, and probably not an optimal one. Further reduction without compromising the quality of the treatment plan might be possible with more sophisticated methods. An alternative approach is the beam segmentation technique (16, 17), which starts from uniform beams, and segments the beams into sub-beams. The weights of these sub-beams are then optimized. It seems that both alternatives converge to a practical solution somewhere between uniform beam treatments and full intensity modulation. CONCLUSION Optimizing stratified intensity distributions in the inverse planning process allows close to optimum results with a surprisingly small number of intensity levels. This finding allows the delivery of intensity-modulated treatments with the “step and shoot” technique in clinically acceptable time using commercial equipment.
REFERENCES 1. Webb S. The physics of conformal radiotherapy—advances in technology. Bristol: IOP Publishing; 1997. 2. Derycke S, De Gersem WR, Van Duyse BB, et al. Conformal radiotherapy of Stage III non-small cell lung cancer: A class solution involving non-coplanar intensity-modulated beams. Int J Radiat Oncol Biol Phys 1998; 41:771–777. 3. Eisbruch A, Marsh LH, Martel MK, et al. Comprehensive irradiation of head and neck cancer using conformal multisegmental fields: Assessment of target coverage and noninvolved tissue sparing. Int J Radiat Oncol Biol Phys 1998; 41:559 –568. 4. Ling CC, Burman C, Chui CS, et al. Conformal radiation treatment of prostate cancer using inversely-planned intensitymodulated photon beams produced with dynamic multileaf collimation. Int J Radiat Oncol Biol Phys 1996; 35:721–730. 5. Bortfeld TR, Kahler DL, Waldron TJ, et al. X-ray field compensation with multileaf collimators. Int J Radiat Oncol Biol Phys 1994; 28:723–730. 6. Webb S. Tomotherapy and beamweight stratification. In: Hounsell, AR, et al., editors. XIIth International Conference on the Use of Computers in Radiation Therapy. Stockport, United Kingdom: Handley Printers Limited; 1994. p. 58 –59. 7. Preiser K, Bortfeld T, Hartwig K, et al. A new program for inverse radiotherapy planning. In: Leavitt DD, Starkschall G, editors. XIIth International Conference on the Use of Computers in Radiation Therapy. Madison, WI: Medical Physics Publishing; 1997. p. 425– 428. 8. Bortfeld T, Bu¨rkelbach J, Boesecke R, et al. Methods of image reconstruction from projections applied to conformation radiotherapy. Phys Med Biol 1990; 35:1423–1434. 9. Bortfeld T, Stein J, Preiser K. Clinically relevant intensity
10. 11. 12. 13.
14. 15. 16.
17.
modulation optimization using physical criteria. In: Leavitt DD, Starkschall G, editors. XIIth International Conference on the Use of Computers in Radiation Therapy. Madison, WI: Medical Physics Publishing; 1997. p. 1– 4. Bortfeld T, Schlegel W, Rhein B. Decomposition of pencil beam kernels for fast dose calculations in three-dimensional treatment planning. Med Phys 1993; 20:311–318. Stein J, Bortfeld T, Do¨rschel B, et al. Dynamic x-ray compensation for conformal radiotherapy by means of multi-leaf collimation. Radiother Oncol 1994; 32:163–173. Van Santvoort JPC, Heijmen BJM. Dynamic multileaf collimation without “tongue and groove” underdosage effects. Phys Med Biol 1996; 41:2091–2105. Webb S, Bortfeld T, Stein J, et al. The effect of stair-step leaf transmission on the “tongue-and-groove problem” in dynamic radiotherapy with a multileaf collimator. Phys Med Biol 1997; 42:595– 602. Gustafsson A, Lind BK, Brahme A. A generalized pencil beam algorithm for optimization of radiation therapy. Med Phys 1994; 21:343–356. Cormack AM. A problem in rotation therapy with X rays. Int J Radiat Oncol Biol Phys 1987; 13:623– 630. De Neve W, De Wagter C, De Jaeger K, et al. Planning and delivering high doses to targets surrounding the spinal cord at the lower neck and upper mediastinal levels: Static beamsegmentation technique executed with a multileaf collimator. Radiother Oncol 1996; 40:271–279. Webb S. Optimization by simulated annealing of three-dimensional, conformal treatment planning for radiation fields defined by a multileaf collimator. Phys Med Biol 1991; 36:1201–1226.
PII S0360-3016(99)00324-7
PHYSICS CONTRIBUTION
INTENSITY MODULATION WITH THE “STEP AND SHOOT” TECHNIQUE USING A COMMERCIAL MLC: A PLANNING STUDY MARK-ALEKSI KELLER-REICHENBECHER, PH.D.,* THOMAS BORTFELD, PH.D.,* SABINE LEVEGRU¨ N, PH.D.,* JO¨ RG STEIN, PH.D.,† KONRAD PREISER, PH.D.,* AND WOLFGANG SCHLEGEL, PH.D.* *Deutsches Krebsforschungszentrum (DKFZ), Department of Medical Physics, Heidelberg, Germany; and †MRC Systems, Heidelberg, Germany Purpose/Objective: For complex planning situations where organs at risk (OAR) surrounding the target volume place stringent constraints, intensity-modulated treatments with photons provide a promising solution to improve tumor control and/or reduce side effects. One approach for the clinical implementation of intensity-modulated treatments is the use of a multileaf collimator (MLC) in the “step and shoot” mode, in which multiple subfields are superimposed for each beam direction to generate stratified intensity distributions with a discrete number of intensity levels. In this paper, we examine the interrelation between the number of intensity levels per beam for various numbers of beams, the conformity of the resulting dose distribution, and the treatment time on a commercial accelerator (Siemens Mevatron KD2) with built-in MLC. Methods and Materials: Two typical, clinically relevant cases of patients with head and neck tumors were selected for this study. Using the inverse planning technique, optimized treatment plans are generated for 3–25 evenly distributed coplanar beams as well as noncoplanar beams. An iterative gradient method is used to optimize a physical treatment objective that is based on the specified target dose and individual dose constraints assigned to each organ at risk (brain stem, eyes, optic nerves) by the radiation oncologist. The intensity distribution of each beam is discretized within the inverse planning program into three to infinitely many intensity levels or strata. These stratified intensity distributions are converted into MLC leaf position sequences, which can be subsequently transferred via computer link to the linac console, and can be delivered without user intervention. The quality of the plan is determined by comparing the values of the objective function, dosevolume histograms (DVHs), and isodose distributions. Results: Highly conformal dose distributions can be achieved with five intensity levels in each of seven beams. The merit of using more intensity levels or more beams is relatively small. Acceptable results are achievable even with three levels only. On average, the number of subfields per beam is about 2–2.5 times the number of intensity levels. The average treatment time per subfield is about 20 s. The total treatment time for the three-level and seven-beam case with a total of 39 subfields is 13 min. Conclusion: Optimizing stratified intensity distributions in the inverse planning process allows us to achieve close to optimum results with a surprisingly small number of intensity levels. This finding may help to facilitate and accelerate the delivery of intensity-modulated treatments with the “step and shoot” technique. © 1999 Elsevier Science Inc. Conformal radiotherapy, Multileaf collimators, Optimization, Inverse problem, “Step and shoot” technique.
INTRODUCTION Intensity-modulated radiotherapy (IMRT) has the potential to improve the conformity of dose distributions to target volumes significantly, especially for very complex cases. It is anticipated that this capability will improve local tumor control and/or reduce side effects. Several techniques have been developed and applied for the practical delivery of IMRT in recent years. Among the most frequently used in
clinical practice are the slice-by-slice or tomotherapy concept, which uses continuous gantry rotations, as well as the fixed-beam multileaf modulation technique (MLM). The reader is referred to the book of Webb (1) for a detailed review of these approaches. In this paper, we will focus on the MLM technique. This technique can either be realized in a fully dynamic mode, in which the MLC leaves are moving while the beam is on, or in the so-called “step and shoot” or multisegmental mode, in
Presented at the ASTRO Annual Meeting, Orlando, FL, 1997. Reprint requests to: Mark-Aleksi Keller-Reichenbecher, Deutsches Krebsforschungszentrum, FS Radiologische Diagnostik und Therapie, Abt. Medizinische Physik (E0401), Im Neuenheimer Feld 280, D-69120 Heidelberg, Germany. Tel: (⫹49) 6221-
42-2579; Fax: (⫹49) 6221-42-2561; E-mail: m.keller@ dkfzheidelberg.de. Acknowledgments—Financial and technical support by SIEMENS Oncology Care Systems (OCS), CA, is gratefully acknowledged. Accepted for publication 3 June 1999. 1315
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Fig. 1. Discretization of the intensity profiles with method 1.
which a sequence of subfields with different MLC shapes is delivered from each direction of incidence, and the beam is switched off while the leaves are moving. Both techniques are in clinical use (2– 4), and both of them have specific pros and cons (1, p. 130). According to our initial experience, the “step and shoot” technique has the advantage of being more readily verified, while the dynamic technique is potentially faster. With current technology, the overall treatment time in “step and shoot” or multisegmental MLM is mainly determined by the total number of subfields used. This is because the actual beam-on time in each subfield is often only a fraction of the considerable time overhead for the start-up procedure and the record and verify system. Obviously, the number of subfields is given by the product of the number of beams and the number of subfields per beam. In “step and shoot” MLM, the latter is governed by the number of intensity levels in the modulation profiles. From a point of view of minimizing the treatment time it is therefore important to reduce the number of intensity levels to the smallest number that is compatible with the objective of achieving a highly conformal dose distribution. In a previous approach to “step and shoot” MLM we used an inverse planning program to calculate continuous intensity profiles, which were subsequently approximated by stratified intensity profiles. The number of evenly spaced intensity levels in the stratified profiles was varied until the minimum number was found that allowed for an approxi-
Fig. 2. Change in the values of the physical objective as a function of the number of iterations for a seven-beam plan of case 1 with different discretization methods: (a) method 1, (b) method 2 and method 3.
mation within a given RMS deviation (5). However, it is not obvious how small the RMS deviation of the intensity profiles has to be in order to achieve clinically acceptable dose distributions. Consequently, in this work we attempt to determine to which degree the stratification of the intensity profiles translates into a deterioration of the treatment plans. For this purpose, we investigate simple approaches for the optimization of intensity distributions with a given number of levels. For two clinical cases and different numbers of beams, we estimate the minimum number of levels that
Fig. 3. Sequence of MLC-generated field shapes producing the three-level intensity distribution of Fig. 4c.
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Fig. 4. Intensity distribution for the first of seven fields for the treatment of case 1 with: (a) continuous modulation, (b) five levels, and (c) three levels.
yield (a) acceptable and (b) close to optimum results. The resulting treatment times on a commercial linear accelerator (linac) with built-in MLC are also determined. A related investigation was published before in (6). There, however, only a single two-dimensional model case was considered, and the focus was on the comparison of tomotherapy and stratified MLM, not on the comparison of different numbers of strata in MLM. METHODS Inverse planning The inverse planning program KonRad (MRC Systems, Heidelberg, Germany), which was developed at DKFZ, is used to calculate the optimized intensity distributions for different numbers and directions of incident beams (7). The algorithm minimizes a physical objective function (F) considering the mean square deviation between calculated and prescribed dose values in the target volume, as well as any dose values beyond tolerance in critical structures (8). Dosevolume constraints (9) are not included because all relevant organs are assumed to have negligible volume effect. The optimization procedure is based on a gradient-type algorithm, which allows us to do the optimization within a few minutes on a Pentium II processor or below 1 min on a DEC ALPHA Station 500 (Digital Equipment Corporation, May-
nard, MA). The dose calculation engine used in KonRad is a pencil beam convolution algorithm (10) adapted for 15 MV radiation from a SIEMENS KD2 (SIEMENS Oncology Care Systems (OCS), Concord, CA) with built-in MLC. The resolution of the intensity matrices is set to 10 mm in the in-plane direction, which corresponds with the leafwidth of the MLC. In the cross-plane direction, the resolution is 5.5 mm. The MLC is not rotated. The voxel size of the dose calculation cube is 2.5 ⫻ 2.5 ⫻ 4.5 mm3. Stratification of the intensity profiles A simple and practical way of stratification can be achieved when the optimization process is completed as schematically shown in Fig. 1. After n steps of the optimization the intensity values of each profile are subdivided into x equidistant levels (method 1). The level size is calculated by dividing the maximum fluence in each profile by the number of levels. Figure 2a shows the values of the objective function F which were obtained for different numbers of intensity levels if method 1 is applied after 10 steps of the optimization compared to the value of F without stratification. Because the investigation shows that use of the stratified intensity profiles for additional steps of the optimization affects the gradient-type algorithm in a negative way, only the first result after stratification is used. Another strategy would be to enable the stratification from
Fig. 5. Transversal, sagittal, and frontal CT reconstructions of case 1 (clivus chordoma) in the isocenter. Shown are the outlines of the target volume (T), the brainstem (B), and the patient contour. The grey line indicates a beam with gantry angle 0.
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Fig. 6. Transversal, sagittal, and frontal CT reconstructions of case 2 (schwannoma) in the isocenter. Shown are the outlines of the target volume (T), the brainstem (B), the left and right optic nerve (N), the optic chiasm (C), and the patient contour. The grey line indicates a beam with gantry angle 0.
the beginning of the optimization process (method 2). Figure 2b shows the corresponding values of F obtained with method 2. Compared to Fig. 2a, no stratification level could achieve as low values of F as gained with method 1 described above. A third method of optimization was investigated where only in every second step the stratification was enabled (method 3). This results in better objectives than obtained with method 2 but not better than the ones achieved with method 1 (Fig. 2b). Therefore, method 1 is used for the following investigations. Calculation of leaf trajectories The leaf trajectories necessary for the delivery of the discrete intensity profiles are determined by the discrete sweep technique (5). More specifically, an algorithm for dynamic multileaf modulation (11) is modified to calculate the discrete leaf positions in this case. This results in a number of subfields of about 1.5–2 times the number of intensity levels. The tongue-and-groove effect is avoided by means of synchronization of the positions of neighboring leaf pairs (12, 13). We find that by fully synchronizing the leaf trajectories, leaf collision problems are also automatically avoided. However, the price to be paid is that the required number of subfields increases by about 50% through synchronization. As an illustrative example we show in Fig. 3 the six subfields calculated with the methods just described for the first of seven beams of the first clinical case (described
below). The superposition of these six subfields yields the three-level intensity distribution of Fig. 4c. Delivery of the sequences The sequences of subfields with their corresponding MLC leaf positions are transferred via computer link to the linac console. The delivery is done with the SIMTEC (Siemens Intensity Modulation TEChnology) module without user intervention. Clinical cases The study is performed for two cases of different complexity with target localizations in the head. The first case (case 1, Fig. 5), a clivus chordoma close to the brainstem, is planned with evenly distributed coplanar beams only. The transversal CT reconstruction in Fig. 5 shows the target volume (T) surrounding the brainstem (B). The difficulties here are to get a very steep dose gradient between the target volume and the OAR. For verification purposes the outlines from case 1 are transferred to a spherical phantom which is used for further investigations. The second and more complex case is a head and neck tumor (schwannoma), where the target volume is surrounded or even overlapped by different types of organs at risk (OARs) (case 2, Fig. 6). Here, noncoplanar beams are used in addition, which were selected on the basis of 3DCRT by an experienced planner. The goal of the treatment was to exclude the eyes (E), the optic nerves (N), and
Table 1. Parameters of the physical objective for case 1 (clivus chordoma) Parameter
Target
Right eye
Left eye
Brainstem
Right optic nerve
Left optic nerve
Optic chiasm
Phantom
Overlap priority Min dose Max dose Penalty min dose Penalty max dose
2 68.00 71.50 99.00 20.00
4 0.00 30.00 0.00 3.00
3 0.00 30.00 0.00 3.00
1 0.00 35.00 0.00 100.0
7 0.00 40.00 0.00 3.00
6 0.00 0.00 0.00 6.00
8 0.00 60.00 0.00 3.00
5 0.00 60.00 0.00 3.00
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Table 2. Parameters of the physical objective for case 2 (schwannoma) Parameter
Target
Right eye
Left eye
Brainstem
Right optic nerve
Left optic nerve
Optic chiasm
Head
Spinal cord
Overlap priority Min dose Max dose Penalty min dose Penalty max dose
2 65.00 70.00 5.00 5.00
5 0.00 10.00 0.00 1.00
4 0.00 10.00 0.00 1.00
3 0.00 60.00 0.00 1.00
1 0.00 50.00 0.00 5.00
6 0.00 45.00 0.00 1.00
7 0.00 50.00 0.00 1.00
9 0.00 45.00 0.00 4.00
8 0.00 55.00 0.00 1.00
the optic chiasm (C) from damage even if they lie partially inside or close to the target volume (T) (Fig. 6). Each case is first planned and optimized by an experienced planner without reducing the number of strata. The optimization parameters such as the number and angle of beams, dose constraints, and the resolution of the underlying intensity profiles are saved for further evaluation. The resulting dose distributions are chosen as a reference for comparison with the alternatively generated results. In Tables 1 and 2, the parameters of the physical objective assigned to the target volume and OARs for case 1 and case 2 are listed. The parameters for each volume of interest (VOI) are the overlap priority, maximum and minimum doses, and penalties for violation of the specified dose constraints. The overlap priority is used by the inverse planning program to determine which volumes belong to which organ if two or more organs are overlapping. In both head and neck cases, the volumes surrounding the target volumes (“phantom” in case 1 and “head” in case 2) are included to reduce the overall irradiation both outside the target volume and the various OARs. Differences in the minimum and maximum dose values of the physical objectives are a result of adaptations made during optimization and due to the different localizations of the target volumes. As for the example in case 1, the brainstem is much closer to the target volume compared to case 2, the specified maximum dose value is defined lower to achieve the desired results. The same holds true for the other OAR. The investigation is performed by reducing the number of strata from initially infinitely many to 15, and to numbers between 10 and 2 in case 1, and to numbers between 9 and 3 in case 2. Furthermore, the number of beams is modified in case 1 from initially 5 to 25, 13, 9, 7, 5, and 3 evenly distributed beams. In case 2, the initially five noncoplanar beams are modified to five and seven evenly distributed coplanar beams. To achieve the results, the inverse planning program KonRad is stopped for each of the different optimization runs after 20 iterations in case 1 and 30 iterations in case 2. In both cases, the change of the objective F from one iteration step to another is below 0.2%. Depending on the clinical case and the number of beams, the optimization times ranges between 5 s and 45 s on a DEC ALPHA Station 500. Time calculation The time calculation for the delivery is based on preliminary measurements for the SIMTEC module, which results
in an average of about 20 s per subfield including the time for gantry/couch movement, beam-on time, and verification. This measurement is performed for case 1 with seven beams and three fluence levels in the profiles. The anticipated delivery times are calculated as the product of the number of beams times the number of subfields per beam times 20 s. RESULTS Case 1 Figure 7 shows as an example the resulting transversal dose distributions in the isocenter plane where the intensity profiles of a 7 beam plan are stratified from initially infinitely many (Fig. 7a) to five (Fig. 7b) and three (Fig. 7c) fluence levels. The gray area indicates the target volume and the dark gray area indicates the brainstem. The absolute doses are displayed as isodose curves in the following order: 100%/69.8 Gy, 90%/62.8 Gy, 80%/55.8 Gy, 60%/41.8 Gy, and 40%/27.9 Gy. All three figures show good conformation of the calculated dose distribution to the target, while the brainstem is sufficiently spared (below 41.8 Gy). The isodose curves show only minor differences from each other. However, stratification to five levels (Fig. 7b) results in a better sparing of the brainstem compared to continuous modulation. Here, even doses below 40%/27.9 Gy are achievable in the selected plane. If stratification to three levels is applied (Fig. 7c), the area of the 60%/41.8 Gy isodose curve is slightly smaller than with continuous modulation or stratification to five levels. The resulting dose-volume histograms (DVH) of the dose distributions of these seven beam plans for the target volume and the brainstem can be seen in Fig. 8. As expected, the best dose homogeneity in the target volume is achieved with the unstratified plan (Fig. 8, black line). Slightly larger inhomogeneities can be found when the stratification to 5, 4, or 3 levels is applied. The DVH of the brainstem shows no significant differences between infinite and five intensity levels. Further reduction of the number of intensity levels to four and three intensity levels results in slightly higher doses in this OAR. Of the vast number of investigated beam/stratification combinations, the five-beam configuration is selected for a further DVH comparison. Compared to the seven-beam plans above, stratification of the five-beam plans (Fig. 9) results in a higher dose inhomogeneity in the target volume. The worst underdosage can be seen with four intensity levels. A larger overdosage due to a shift of the DVH can be
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Fig. 8. DVH of target volume and brainstem of case 1: Plans with seven beams and reduced number of strata.
observed if stratification to three levels is applied. If renormalized downward, the three-levels curve may have comparable homogeneity as the four- or five-levels curve, but a better sparing of the OAR brainstem. However, a good sparing of the brainstem is possible with all of the stratification approaches. Another effect of the stratification to the dose distribution which occur in both Figs. 8 and 9 are the steps in the DVH. These are best visible in the DVH of the brainstem for four and three intensity levels. To demonstrate the effects of stratification as a function of the number of beams, DVHs are generated for five intensity levels (Fig. 10). Figure 10 shows that the dose homogeneity rises continuously in the target volume with the use of additional beams. Minor effects can be observed in the DVH of the brainstem. Only the use of 3–5 beams results in slightly higher doses to the OAR. As already observed in Figs. 8 and 9, the major differences between stratification and the use of infinitely many levels for different numbers of beams are the steps in the DVH that occur if less beams are used. The investigated effects are summarized in Fig. 11, where the relative values of the physical objective F for different beam/stratification combinations are plotted. The change in
Fig. 7. Transversal dose distributions of case 1 in the isocenter plane for a seven-beam plan with: (a) continuous modulation, (b) five, and (c) three levels. The following isodose lines are shown: 100%/69.8 Gy, 90%/62.8 Gy, 80%/55.8 Gy, 60%/41.8 Gy, and 40%/27 Gy.
Fig. 9. DVH of target volume and brainstem of case 1: Plans with seven beams and reduced number of strata.
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Fig. 10. DVH of target volume and brainstem for plans of case 1 with different number of beams and with stratification to five levels.
the objective is nearly independent from the number of beams. The highest benefit of adding intensity levels can be seen between 3 and 5 levels, where F changes by about 30% per additional level, although in one case (5 beams), the value of F is worst with 4 levels. The reduction decreases if more levels are used. Compared to infinitely many levels, the reduction is about 30% if 5 levels are used and about 20% if 10 levels are used. The differences between 15 and infinitely many levels are about 5–10%. However, the selection of a suitable beam/stratification combination depends on the delivery time of a complete sequence of subfields. Figure 12 shows the values of F for the investigated beam/stratification combinations as a function of the delivery time of the calculated sequences compared to different numbers of beams without stratification. Assuming a time limit of approximately 20 –25 min per fraction, the lowest value of F can be achieved in this case with seven beams and five levels of intensity. According to the objective function, a faster delivery below 15 min could only be realized with seven beams and three levels or five beams and five levels.
Fig. 11. Relative values of the physical objective as a function of the number of intensity levels for different number of beams for case 1 compared to infinite levels.
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Fig. 12. Physical objective versus delivery time for different beam/ stratification combinations compared to different number of beams without stratification for case 1. The first part denotes the number of beams and the second part the number of intensity levels. The delivery time is calculated with 20 s per subfield, which includes the time for gantry/couch movement, beam on time, and verification.
Case 2 If stratification method 1 is applied to a seven-beam plan of case 2 (Fig. 13), quite similar effects as in case 1 can be demonstrated. Figure 13a shows the dose distribution obtained with continuous modulation. Figures 13b and 13c show the results if stratification to five and three intensity levels is applied, respectively. The absolute doses are displayed as isodose curves in the following order: 100%/67.5 Gy, 90%/60.8 Gy, 80%/54 Gy, 70%/47.3 Gy, 60%/40.5 Gy, and 40%/27 Gy. Large dose inhomogeneities in the target volume can be observed, especially in the region of the right optic nerve, which is basically independent from the level of stratification. This is of course the desired result of the optimization parameter definition of the right optic nerve which should be spared (overlap priority 1, see Table 2). Only minor differences in the dose distribution can be seen if infinite and five intensity levels are compared to this. The 100%– 40% isodose curves remain almost at the same position in each figure, except for some minor deviations if stratification to three intensity levels is applied. Here we can observe a greater inhomogeneity in the target volume compared to infinitely many and five levels (Fig. 13c). On the other hand, the best sparing of the optic chiasm (Fig. 13c, 70%/47.3 Gy isodose curve) is possible with only three intensity levels. Figure 14a shows the related DVH of the seven-coplanar beam plan for the selected OAR brainstem, right optic nerve, and the target volume. As a comparison, the DVH of the five noncoplanar beam plan is shown in Fig. 14b. Apart from the slightly higher doses to the OAR and the target volume for stratification to three levels, continuous modulation and stratification to five levels show only significant differences in the right optic nerve for the seven-beam plan (Fig. 14a). The effects of stratification on the target volume dose homogeneity are smaller for the seven-coplanar plan
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Fig. 14. DVH of brainstem, right optic nerve, and target (from left to right) of case 2 with reduced number of strata: Plans with: (a) seven coplanar beams and (b) five noncoplanar beams.
(Fig. 14a) than for the five-beam noncoplanar plan (Fig. 14b). Larger effects to the OAR can also be observed for the five noncoplanar beams in Fig. 14b if stratification to five or three levels is used compared to the seven coplanar beams. The major differences between seven coplanar beams and five noncoplanar beams can be seen in the brainstem, where
Fig. 13. Transversal dose distributions of case 2 in the isocenter plane for a seven-beam plan with: (a) continuous modulation, (b) five, and (c) three levels. The following isodose lines are shown: 100%/67.5 Gy, 90%/60.8 Gy, 80%/54 Gy, 70%/47.3 Gy, 60%/ 40.5 Gy, and 40%/27 Gy.
Fig. 15. Relative values of the physical objective as a function of the number of intensity levels for different beam configurations for case 2 compared to infinite levels.
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Fig. 16. Physical objective versus delivery time for different beam/ stratification combinations compared to different number of beams without stratification for case 2. The first part denotes the beam configuration (number of beams, (c)oplanar, (n)oncoplanar), the second part, the number of intensity levels. The delivery time is calculated with 20 s per subfield, which includes the time for gantry/couch movement, beam on time, and verification.
seven coplanar beams reduce the maximum dose in that OAR, but irradiate a larger volume with lower doses. Figure 15 shows the comparison of the relative values of F as a function of the number of intensity levels (3–7) compared to an infinite number of levels for the investigated beam configurations. The smallest change in F can be seen if five or seven coplanar beams are used. Here the objective F changes only by about 20% between three and infinitely many levels. An artifact can be observed if six or seven intensity levels are used for the five and seven coplanar beams. In the five-beam case, F rises again until it decreases at seven or more intensity levels. In the seven-beam case, F rises with both the six and seven intensity levels and decreases above. The reasons for this effect are given in the Discussion. The values of F for different beam/stratification combinations are plotted in Fig. 16 as a function of the delivery time. According to the indicated values, five noncoplanar beams with five or six, or even four intensity levels would be selected if delivery time should be less than approximately 20 –25 min. Of course, no significant differences in the absolute height of F can be seen between five and six levels. The use of five noncoplanar beams with four intensity levels has about the same value as seven coplanar beams with five intensity levels or five coplanar beams with seven intensity levels. In all cases, there is no significant advantage to use more than 5–7 intensity levels compared to continuous modulation. DISCUSSION In the delivery of intensity modulated treatments using the “step and shoot” technique on some commercial linacs equipped with MLCs, the treatment time is roughly proportional to the number of subfields, while the actual irradiation
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time is only a small fraction of the treatment time. The use of more subfields generally allows better treatment plans. However, the number of subfields is limited by the total treatment time (including patient setup) acceptable in clinical practice (i.e., 15–25 min for complex treatments). For the machine used in this investigation (Siemens KD2), it takes about 20 s to deliver one subfield (including couch/gantry movement, beam-on time, and verification), and the delivery of a sequence of subfields is done without user intervention. Consequently, around 50 subfields can be delivered in a single treatment. In principle, this number of subfields can now be distributed freely among different numbers of beams. Extreme cases would be the use of all 50 subfields within a single beam from one direction of incidence, or the use of 50 uniform beams with one “subfield” each. Both of these extremes are obviously inadequate for most cases; the optimum distribution is somewhere in the middle. This investigation has shown that the use of about five intensity levels per beam gives results that are close to the optimum solution, which is obtained with infinitely many levels. The 5 intensity levels translate into 10 –15 subfields per beam. These findings are almost independent of the number of beams. Our findings demonstrate, on the other hand, that with additional beams and more intensity levels, it is possible to gain more homogeneity in the target volume, but not automatically a better sparing of the OARs. In general, for intensity modulation, it can be stated that it is easier to reduce dose to OARs than to irradiate target volumes with the same homogeneity as with open fields. Due to the fact that around seven coplanar beams are sufficient in most cases, the total number of subfields needed to achieve results that are close to optimum is 70 –100. This number is too high to be delivered efficiently with the equipment available to us. Hence, further reduction of the time overhead in the delivery of subfields would be desirable. On the other hand, we have found that acceptable results are achievable even with only three intensity levels, resulting in about 40 – 60 subfields. Therefore, intensity modulated treatments can be performed with existing technology within acceptable times. Because the resolution in the intensity maps (here 10 ⫻ 5.5 mm) corresponds directly to the number of subfields, a reduction to a resolution of 10 ⫻ 10 mm could help to reduce the delivery time even more. Of course, this will also reduce the homogeneity of the dose in the target volume. However, further investigations should be done on this topic. Although only two clinical cases have been investigated in this study, we believe that the numbers of subfields given can be generalized at least as an upper limit, because the cases are highly complex. It may be surprising that such a relatively coarse discretization of the intensity distributions compromises the quality of dose distributions only slightly, although this finding is in line with a previous result based on biologically based optimization (14). A possible explanation is the known non-uniqueness of the solution of the inverse problem (15): Different intensity distributions (e.g., discretized and continuous ones) can produce very similar
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I. J. Radiation Oncology
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Biology
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Physics
dose distributions. Our findings do not agree with another study on this problem (6), from which one might conclude that even 10 intensity levels are insufficient in some cases. The reasons for this discrepancy cannot be fully understood because this study is only a short contribution with a limited amount of data (6). A possible explanation is that the discrepancy is due to the obvious differences in the planning and evaluation strategies between our work and (6). A further advantage of the use of fewer subfields (in addition to the reduced treatment time) is that the number of monitor units (MU) per subfield increases proportionally, such that linac instability problems, which may exist at very small MU values, do not play an important role. One problem we saw in the practical delivery of “step and shoot” MLM with very few subfields is the existence of split fields within the sequence. This can be seen in subfields 4 and 6 of Fig. 3, for example. As a consequence, a matchline problem may occur, which shows up as a narrow region of underdose along the abutment line. This problem can be solved by means of a small adjustment of the leaf positions in those regions. However, further investigations are necessary in this context. In general, the value of the objective function F decreases with increasing number of intensity levels. However, we saw some small-scale deviations from this trend. The most likely explanation for such artifacts is our rather crude way of doing the stratification. Because the height of each intensity level depends on the maximum fluence in the specific profile, already one single “hot spot” can shift the levels to unrepresen-
Volume 45, Number 5, 1999
tative heights. On the other hand, the value of F is very sensitive to small changes in the intensity profiles. This holds true especially if, due to stratification, an OAR with a small volume but high penalty for overdosage (such as the right optic nerve in case 2) receives higher doses in some regions. The approaches presented in this work for the reduction of the number of subfields are based on the stratification of continuous intensity matrices (with an infinite number of intensity levels) into relatively few levels. This is by far not the only possible method to achieve practical values for the number of subfields, and probably not an optimal one. Further reduction without compromising the quality of the treatment plan might be possible with more sophisticated methods. An alternative approach is the beam segmentation technique (16, 17), which starts from uniform beams, and segments the beams into sub-beams. The weights of these sub-beams are then optimized. It seems that both alternatives converge to a practical solution somewhere between uniform beam treatments and full intensity modulation. CONCLUSION Optimizing stratified intensity distributions in the inverse planning process allows close to optimum results with a surprisingly small number of intensity levels. This finding allows the delivery of intensity-modulated treatments with the “step and shoot” technique in clinically acceptable time using commercial equipment.
REFERENCES 1. Webb S. The physics of conformal radiotherapy—advances in technology. Bristol: IOP Publishing; 1997. 2. Derycke S, De Gersem WR, Van Duyse BB, et al. Conformal radiotherapy of Stage III non-small cell lung cancer: A class solution involving non-coplanar intensity-modulated beams. Int J Radiat Oncol Biol Phys 1998; 41:771–777. 3. Eisbruch A, Marsh LH, Martel MK, et al. Comprehensive irradiation of head and neck cancer using conformal multisegmental fields: Assessment of target coverage and noninvolved tissue sparing. Int J Radiat Oncol Biol Phys 1998; 41:559 –568. 4. Ling CC, Burman C, Chui CS, et al. Conformal radiation treatment of prostate cancer using inversely-planned intensitymodulated photon beams produced with dynamic multileaf collimation. Int J Radiat Oncol Biol Phys 1996; 35:721–730. 5. Bortfeld TR, Kahler DL, Waldron TJ, et al. X-ray field compensation with multileaf collimators. Int J Radiat Oncol Biol Phys 1994; 28:723–730. 6. Webb S. Tomotherapy and beamweight stratification. In: Hounsell, AR, et al., editors. XIIth International Conference on the Use of Computers in Radiation Therapy. Stockport, United Kingdom: Handley Printers Limited; 1994. p. 58 –59. 7. Preiser K, Bortfeld T, Hartwig K, et al. A new program for inverse radiotherapy planning. In: Leavitt DD, Starkschall G, editors. XIIth International Conference on the Use of Computers in Radiation Therapy. Madison, WI: Medical Physics Publishing; 1997. p. 425– 428. 8. Bortfeld T, Bu¨rkelbach J, Boesecke R, et al. Methods of image reconstruction from projections applied to conformation radiotherapy. Phys Med Biol 1990; 35:1423–1434. 9. Bortfeld T, Stein J, Preiser K. Clinically relevant intensity
10. 11. 12. 13.
14. 15. 16.
17.
modulation optimization using physical criteria. In: Leavitt DD, Starkschall G, editors. XIIth International Conference on the Use of Computers in Radiation Therapy. Madison, WI: Medical Physics Publishing; 1997. p. 1– 4. Bortfeld T, Schlegel W, Rhein B. Decomposition of pencil beam kernels for fast dose calculations in three-dimensional treatment planning. Med Phys 1993; 20:311–318. Stein J, Bortfeld T, Do¨rschel B, et al. Dynamic x-ray compensation for conformal radiotherapy by means of multi-leaf collimation. Radiother Oncol 1994; 32:163–173. Van Santvoort JPC, Heijmen BJM. Dynamic multileaf collimation without “tongue and groove” underdosage effects. Phys Med Biol 1996; 41:2091–2105. Webb S, Bortfeld T, Stein J, et al. The effect of stair-step leaf transmission on the “tongue-and-groove problem” in dynamic radiotherapy with a multileaf collimator. Phys Med Biol 1997; 42:595– 602. Gustafsson A, Lind BK, Brahme A. A generalized pencil beam algorithm for optimization of radiation therapy. Med Phys 1994; 21:343–356. Cormack AM. A problem in rotation therapy with X rays. Int J Radiat Oncol Biol Phys 1987; 13:623– 630. De Neve W, De Wagter C, De Jaeger K, et al. Planning and delivering high doses to targets surrounding the spinal cord at the lower neck and upper mediastinal levels: Static beamsegmentation technique executed with a multileaf collimator. Radiother Oncol 1996; 40:271–279. Webb S. Optimization by simulated annealing of three-dimensional, conformal treatment planning for radiation fields defined by a multileaf collimator. Phys Med Biol 1991; 36:1201–1226.