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When becometh less more?
Int. J. Radiation
Oncology
Pergamon
Biol.
Phys., Vol. 33, No. I, pp. 235-237, 1995 Copyright 0 1995 Elsevier Science Ltd Printed in the USA. All rights reserved 0360-3016/95 $9.50 + .OO
0360-3016(95)02020-C
l
Editorial
WHEN RADHE
MOHAN,
BECOMETH PH .D. AND
LESS MORE? C. CLIFTON LING, PI-I .D.
Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, NY 1002 The paper by Soderstrom and Brahme ( 10) in this issue of the Journal (10) attempts to explore the issue of the optimum choice of the number and the directions of nonuniform (i.e., intensity-modulated) beams in coplanar radiotherapy. Their conclusions are that (a) a very small number (3-5) of intensity-modulated beams are sufficient to achieve clinically optimum treatment plans, (b) optimizing the beam angles is important when the number of beams is small, and (c) intensitymodulation can yield improvements not possible even with an infinite number of uniform beams. These considerations are significant and timely, given the rapid development in our technical ability to deliver intensity-modulated treatments. The use of the inverse method of treatment planning, pioneered by Brahme et al. (2, 5) and other developments in the field of intensity modulation that followed are likely to introduce significant advances in modem radiotherapy. This paper, and an earlier one in Medical Physics by the same authors ( 1 1 ), provide results of investigations related to the views previously expressed by Brahme (3 ) about the question of the optimum number of beams. Brahme had stated in an editorial in the Journal that three to five intensity-modulated beams are sufficient to produce optimum dose distributions, an assertion that generated an exchange of letters to the editor (4, 8). It is unlikely that the controversy will wane with the publication of the present paper. In fact, certain results in this article are likely to provoke further debate. For example, the notion that a two-field plan, albeit with optimized directions (for either uniform or intensity-modulated beams, as shown in Fig. 1 of the Soderstrom and Brahme paper), is only marginally inferior to the one with a larger number of beams seems contrary to conventional practice and belief. According to Soderstrom and B&me’s crite-
ria, three well-placed portals are nearly equivalent to a large number of fields (Figs. 1 and 2 in their paper). If this result is generally applicable and extensible to other disease sites in three-dimensional (30) geometry, the practice of radiotherapy will be greatly simplified and, indeed, revolutionized. Another notable observation is that, at least for the cervix case, three beams placed at equiangular steps are nearly as good as three optimally directed beams (Fig. 3, lo), suggesting that the former is perhaps the method of choice because it needs much less effort and resources for treatment planning. These inferences are difficult to comprehend and accept. It might have been helpful and instructive if the authors had provided the beam directions obtained or used for each of the optimized plans in Figs. 1 and 2. It seems that some of the results of Soderstrom and Brahme are constrained by the framework and methods they have employed in their investigations. For example, their analysis is confined to two-dimensional (2D), and one could question whether their conclusions would be applicable to 3D. For instances where the relative geometries of the target and critical structures are disparate at various levels, the optimum beam orientation may be different for each level. Then, would not the optimum number and directions of beams be quite different for the 3D problem than for the 2D one? One could also question whether the underlying premises and the choice of the objective function used in optimization and its parameters may affect the outcome of their investigations. The authors claim “that the present results are only marginally dependent on the precise model and model parameters used, and the conclusions would be almost identical with different clinically relevant model.” In the absence of a definitive demonstration to that effect in the paper, one is drawn to examine more
Reprint requests to: R. Mohan, Ph.D. in part by grant No. POl-CA59017 from the National Cancer Institute, National Institutes of Health, DHHS, USA. The authors thank Drs. X. H. Wang and J&g Stein for assistance in studying various aspects
of this problem. The authors also thank Drs. Samuel Hellman, Zvi Fuks, Gerald Kutcher, and members of the Medical Physics Department at MSKCC for useful discussions. Accepted for publication 7 July 1995.
Acknowledgement-Supported
235
236
I. J. Radiation Oncology 0 Biology 0 Physics
closely the fundamental optimization criteria, P+, the probability of uncomplicated control. This quantity is defined as P’ = PB - P, + 6(1 - Ps)P,, with P, = 1 II( 1 - NTCP, ) , where PBis the tumor control probability, NTCPi the normal tissue complication probabilities, and S the fraction of patients for whom Pe and P, are independent events (5). This definition assumes that the TCP and each NTCP have equal weights without regard for the different relative importance and/or severity of various end points. Another weakness of this definition is its linear dependence on NTCPs, a relationship that presupposes that one can balance an increase in NTCP with an increase in TCP. As noted by Goitein, “such a scheme implies that a 6% increase in TCP would outweigh a 5% increase in the chance of cord transection” (6). In general, the value of a treatment plan score depends nonlinearly on NTCP. In this regard, Kutcher has suggested that, at NTCP values below a clinically chosen acceptable limit, the value of the component of the score function associated with a specific end point decreases slowly and linearly with NTCP (7, 9). If the NTCP exceeds this limit, the score function should decrease rapidly to simulate the dose-limiting attribute of the critical organs. Thus, in the limited circumstance when the NTCPs of all organs are below their respective limits, the use of P+ is valid. However, if the optimization scheme is to be used in dose-limiting situations, for example, in dose-escalation studies, the use of such a score function with a purely linear dependence on NTCP may result in misleading solutions. Noting that we almost always treat tumors to the limit tolerated by the most dose-limiting normal tissue, the optimization of plans in which dose escalation is contemplated should avoid the use of P+ as an objective function. In such situations, the objective function of the type suggested by Kutcher represents more closely the clinical decision making process. It would be desirable to be assured about the authors’ claim that the conclusions of this paper are not sensitive to the choice of the objective function and the adopted values of radiobiological parameters. However, a plan considered to be superior according to the Pf criteria may be quite unacceptable by Kutcher’s criteria. As dose is escalated, the NTCP thresholds of one or more tissues may be exceeded. The score of acceptable plans in dose-limiting situations is nearly independent of NTCPs and is determined primarily by the TCP. For the same mean dose, the TCP increases with decreasing inhomogeneity ( l), which in turn improves with an increasing number of intensity-modulated beams, especially for complex situations. Thus, one can surmise that Kutcher’s criteria would lead to a larger number of beams than the P+ criteria. Furthermore, if the values
Volume 33, Number I, 1995
of TCP predicted by the models are already near saturation levels, as seems to be the case for the examples chosen by Soderstrom and Brahme, there is little to be gained by escalating dose, increasing target dose homogeneity, or increasing the number of beams. On the other hand, if the treatment site and/or stage were such that the TCP would rise significantly with target dose and homogeneity, a larger number of beams may be advantageous. Efforts to reduce the complexity of treatment planning and delivery are laudable. On the other hand, the treatment quality may deteriorate as the number of beams decreases. The question then is when do less beams become more beneficial? If a larger number of beams is desirable for clinical reasons, consideration of operational efficiency is less of a concern given the rapid development of automation in treatment delivery. For instance, a nine-field intensity-modulated treatment can be delivered with a dynamic MLC in 4 to 5 min, inclusive of beam-on time, gantry, and MLC motion, but not including patient setup ( 12). Likewise, the improvement in computer-assisted methods with electronic portal imaging devices may eventually lessen the burden of treatment verification. Even so, one can accept the premise that “less is more” in terms of the number of beams if the same treatment results can be achieved with a reasonable expenditure of resources. This paper by Soderstrom and Brahme (10, 11) and their previous one, however, do not provide a convincing answer to the question of the optimum number of beams. Considerable research is ongoing in computer-assisted optimization of radiotherapy treatment planning and delivery, including the use of intensity modulation. The specific question of the optimum number of beams is a highly complex one. The answer would depend upon a combination of geometrical and biological factors including the size, shape, and location of the target volume; the sizes, shapes, tolerances, architectures, and relative locations of the surrounding normal tissues; and the prescription dose. To answer this question satisfactorily would require substantial additional effort for each class of radiotherapy problems. No doubt this paper by Soderstrom and Brahme will be a reference for comparison. Whether this or any other investigation based on biological models can yield results directly applicable to and used in cancer radiotherapy will depend upon medical judgment as to the degree of departure of the new approaches from present conventions and clinical experience. Changes in small incremental steps are more likely to be accepted vis-a-vis radical alterations based primarily on the predictions of models.
When
becometh
less
more?
l MOHAN
AND LING
237
REFERENCES 1. Brahme, A. Dosimetric precision requirements in radiation therapy. Acta Radiologica Oncologica 23:379-391; 1984. 2. B&me, A. Optimization of stationary and moving beam radiation therapy techniques. Radiother. Oncol. 12: 129140; 1988. 3. Brahme, A. Optimization of radiation therapy and the development of multi-leaf collimation (editorial). Int. J. Radiat. Oncol. Biol. Phys. 25373-375; 1993. 4. Brahme, A. Optimization of radiation therapy. Int. J. Radiat. Oncol. Biol. Phys. 28:785-787; 1994. 5. B&me, A.; Roos, J.; Lax, I. Solution of an integral equation encountered in radiation therapy. Phys. Med. Biol. 27:1221-1229; 1982. 6. Goitein, M. The comparison of treatment plans. Semin. Radiat. Oncol. 2~246-256; 1992. 7. Kutcher, G. J. In AAPM Summer School, Kansas University, Lawrence, Kansas (ed. Purdy, J. A.) 998-1021 (American Institute of Physics, Woodbury, NY, 1990).
8. Mackie, R.; Deasy, J.; Holmes, T.; Fowler, J. Letter in response to “Optimization of radiation therapy and the development of multileaf collimation” by Anders Brahme. Int. J. Radiat. Oncol. Biol. Phys. 28:784-785; 1994. 9. Mohan, R.; Mageras, G. S.; Baldwin, B.; Brewster, L. J.; Kutcher, G. J.; Leibel, S.; Burman, C. M.; Ling, C. C.; Fuks, 2. Clinically Relevant Optimization of 3D Conformal Treatments. Med. Phys. 19:933-944; 1992. 10. Soderstrom, S.; Brahme, A. Which is the most suitable number of photon beam portals in coplanar radiation therapy. Int. J. Radiat. Oncol. Biol. Phys. 33: 1701- 1709; 1995. Il. SaderstrGm, S.; Gustafsson, A.; Brahme, A. Optimization of the dose delivery in few field techniques using radiobiological objective functions. Med. Phys. 20: 1201- 12 10; 1993. 12. Wang, X.; Spirou, S.; LoSasso, T.; Chui, C. S.; Mohan, R. Dosimetric verification of an intensity modulated treatment. Med. Phys. (in press).
Oncology
Pergamon
Biol.
Phys., Vol. 33, No. I, pp. 235-237, 1995 Copyright 0 1995 Elsevier Science Ltd Printed in the USA. All rights reserved 0360-3016/95 $9.50 + .OO
0360-3016(95)02020-C
l
Editorial
WHEN RADHE
MOHAN,
BECOMETH PH .D. AND
LESS MORE? C. CLIFTON LING, PI-I .D.
Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, NY 1002 The paper by Soderstrom and Brahme ( 10) in this issue of the Journal (10) attempts to explore the issue of the optimum choice of the number and the directions of nonuniform (i.e., intensity-modulated) beams in coplanar radiotherapy. Their conclusions are that (a) a very small number (3-5) of intensity-modulated beams are sufficient to achieve clinically optimum treatment plans, (b) optimizing the beam angles is important when the number of beams is small, and (c) intensitymodulation can yield improvements not possible even with an infinite number of uniform beams. These considerations are significant and timely, given the rapid development in our technical ability to deliver intensity-modulated treatments. The use of the inverse method of treatment planning, pioneered by Brahme et al. (2, 5) and other developments in the field of intensity modulation that followed are likely to introduce significant advances in modem radiotherapy. This paper, and an earlier one in Medical Physics by the same authors ( 1 1 ), provide results of investigations related to the views previously expressed by Brahme (3 ) about the question of the optimum number of beams. Brahme had stated in an editorial in the Journal that three to five intensity-modulated beams are sufficient to produce optimum dose distributions, an assertion that generated an exchange of letters to the editor (4, 8). It is unlikely that the controversy will wane with the publication of the present paper. In fact, certain results in this article are likely to provoke further debate. For example, the notion that a two-field plan, albeit with optimized directions (for either uniform or intensity-modulated beams, as shown in Fig. 1 of the Soderstrom and Brahme paper), is only marginally inferior to the one with a larger number of beams seems contrary to conventional practice and belief. According to Soderstrom and B&me’s crite-
ria, three well-placed portals are nearly equivalent to a large number of fields (Figs. 1 and 2 in their paper). If this result is generally applicable and extensible to other disease sites in three-dimensional (30) geometry, the practice of radiotherapy will be greatly simplified and, indeed, revolutionized. Another notable observation is that, at least for the cervix case, three beams placed at equiangular steps are nearly as good as three optimally directed beams (Fig. 3, lo), suggesting that the former is perhaps the method of choice because it needs much less effort and resources for treatment planning. These inferences are difficult to comprehend and accept. It might have been helpful and instructive if the authors had provided the beam directions obtained or used for each of the optimized plans in Figs. 1 and 2. It seems that some of the results of Soderstrom and Brahme are constrained by the framework and methods they have employed in their investigations. For example, their analysis is confined to two-dimensional (2D), and one could question whether their conclusions would be applicable to 3D. For instances where the relative geometries of the target and critical structures are disparate at various levels, the optimum beam orientation may be different for each level. Then, would not the optimum number and directions of beams be quite different for the 3D problem than for the 2D one? One could also question whether the underlying premises and the choice of the objective function used in optimization and its parameters may affect the outcome of their investigations. The authors claim “that the present results are only marginally dependent on the precise model and model parameters used, and the conclusions would be almost identical with different clinically relevant model.” In the absence of a definitive demonstration to that effect in the paper, one is drawn to examine more
Reprint requests to: R. Mohan, Ph.D. in part by grant No. POl-CA59017 from the National Cancer Institute, National Institutes of Health, DHHS, USA. The authors thank Drs. X. H. Wang and J&g Stein for assistance in studying various aspects
of this problem. The authors also thank Drs. Samuel Hellman, Zvi Fuks, Gerald Kutcher, and members of the Medical Physics Department at MSKCC for useful discussions. Accepted for publication 7 July 1995.
Acknowledgement-Supported
235
236
I. J. Radiation Oncology 0 Biology 0 Physics
closely the fundamental optimization criteria, P+, the probability of uncomplicated control. This quantity is defined as P’ = PB - P, + 6(1 - Ps)P,, with P, = 1 II( 1 - NTCP, ) , where PBis the tumor control probability, NTCPi the normal tissue complication probabilities, and S the fraction of patients for whom Pe and P, are independent events (5). This definition assumes that the TCP and each NTCP have equal weights without regard for the different relative importance and/or severity of various end points. Another weakness of this definition is its linear dependence on NTCPs, a relationship that presupposes that one can balance an increase in NTCP with an increase in TCP. As noted by Goitein, “such a scheme implies that a 6% increase in TCP would outweigh a 5% increase in the chance of cord transection” (6). In general, the value of a treatment plan score depends nonlinearly on NTCP. In this regard, Kutcher has suggested that, at NTCP values below a clinically chosen acceptable limit, the value of the component of the score function associated with a specific end point decreases slowly and linearly with NTCP (7, 9). If the NTCP exceeds this limit, the score function should decrease rapidly to simulate the dose-limiting attribute of the critical organs. Thus, in the limited circumstance when the NTCPs of all organs are below their respective limits, the use of P+ is valid. However, if the optimization scheme is to be used in dose-limiting situations, for example, in dose-escalation studies, the use of such a score function with a purely linear dependence on NTCP may result in misleading solutions. Noting that we almost always treat tumors to the limit tolerated by the most dose-limiting normal tissue, the optimization of plans in which dose escalation is contemplated should avoid the use of P+ as an objective function. In such situations, the objective function of the type suggested by Kutcher represents more closely the clinical decision making process. It would be desirable to be assured about the authors’ claim that the conclusions of this paper are not sensitive to the choice of the objective function and the adopted values of radiobiological parameters. However, a plan considered to be superior according to the Pf criteria may be quite unacceptable by Kutcher’s criteria. As dose is escalated, the NTCP thresholds of one or more tissues may be exceeded. The score of acceptable plans in dose-limiting situations is nearly independent of NTCPs and is determined primarily by the TCP. For the same mean dose, the TCP increases with decreasing inhomogeneity ( l), which in turn improves with an increasing number of intensity-modulated beams, especially for complex situations. Thus, one can surmise that Kutcher’s criteria would lead to a larger number of beams than the P+ criteria. Furthermore, if the values
Volume 33, Number I, 1995
of TCP predicted by the models are already near saturation levels, as seems to be the case for the examples chosen by Soderstrom and Brahme, there is little to be gained by escalating dose, increasing target dose homogeneity, or increasing the number of beams. On the other hand, if the treatment site and/or stage were such that the TCP would rise significantly with target dose and homogeneity, a larger number of beams may be advantageous. Efforts to reduce the complexity of treatment planning and delivery are laudable. On the other hand, the treatment quality may deteriorate as the number of beams decreases. The question then is when do less beams become more beneficial? If a larger number of beams is desirable for clinical reasons, consideration of operational efficiency is less of a concern given the rapid development of automation in treatment delivery. For instance, a nine-field intensity-modulated treatment can be delivered with a dynamic MLC in 4 to 5 min, inclusive of beam-on time, gantry, and MLC motion, but not including patient setup ( 12). Likewise, the improvement in computer-assisted methods with electronic portal imaging devices may eventually lessen the burden of treatment verification. Even so, one can accept the premise that “less is more” in terms of the number of beams if the same treatment results can be achieved with a reasonable expenditure of resources. This paper by Soderstrom and Brahme (10, 11) and their previous one, however, do not provide a convincing answer to the question of the optimum number of beams. Considerable research is ongoing in computer-assisted optimization of radiotherapy treatment planning and delivery, including the use of intensity modulation. The specific question of the optimum number of beams is a highly complex one. The answer would depend upon a combination of geometrical and biological factors including the size, shape, and location of the target volume; the sizes, shapes, tolerances, architectures, and relative locations of the surrounding normal tissues; and the prescription dose. To answer this question satisfactorily would require substantial additional effort for each class of radiotherapy problems. No doubt this paper by Soderstrom and Brahme will be a reference for comparison. Whether this or any other investigation based on biological models can yield results directly applicable to and used in cancer radiotherapy will depend upon medical judgment as to the degree of departure of the new approaches from present conventions and clinical experience. Changes in small incremental steps are more likely to be accepted vis-a-vis radical alterations based primarily on the predictions of models.
When
becometh
less
more?
l MOHAN
AND LING
237
REFERENCES 1. Brahme, A. Dosimetric precision requirements in radiation therapy. Acta Radiologica Oncologica 23:379-391; 1984. 2. B&me, A. Optimization of stationary and moving beam radiation therapy techniques. Radiother. Oncol. 12: 129140; 1988. 3. Brahme, A. Optimization of radiation therapy and the development of multi-leaf collimation (editorial). Int. J. Radiat. Oncol. Biol. Phys. 25373-375; 1993. 4. Brahme, A. Optimization of radiation therapy. Int. J. Radiat. Oncol. Biol. Phys. 28:785-787; 1994. 5. B&me, A.; Roos, J.; Lax, I. Solution of an integral equation encountered in radiation therapy. Phys. Med. Biol. 27:1221-1229; 1982. 6. Goitein, M. The comparison of treatment plans. Semin. Radiat. Oncol. 2~246-256; 1992. 7. Kutcher, G. J. In AAPM Summer School, Kansas University, Lawrence, Kansas (ed. Purdy, J. A.) 998-1021 (American Institute of Physics, Woodbury, NY, 1990).
8. Mackie, R.; Deasy, J.; Holmes, T.; Fowler, J. Letter in response to “Optimization of radiation therapy and the development of multileaf collimation” by Anders Brahme. Int. J. Radiat. Oncol. Biol. Phys. 28:784-785; 1994. 9. Mohan, R.; Mageras, G. S.; Baldwin, B.; Brewster, L. J.; Kutcher, G. J.; Leibel, S.; Burman, C. M.; Ling, C. C.; Fuks, 2. Clinically Relevant Optimization of 3D Conformal Treatments. Med. Phys. 19:933-944; 1992. 10. Soderstrom, S.; Brahme, A. Which is the most suitable number of photon beam portals in coplanar radiation therapy. Int. J. Radiat. Oncol. Biol. Phys. 33: 1701- 1709; 1995. Il. SaderstrGm, S.; Gustafsson, A.; Brahme, A. Optimization of the dose delivery in few field techniques using radiobiological objective functions. Med. Phys. 20: 1201- 12 10; 1993. 12. Wang, X.; Spirou, S.; LoSasso, T.; Chui, C. S.; Mohan, R. Dosimetric verification of an intensity modulated treatment. Med. Phys. (in press).