- Email: [email protected]
High doses per fraction and the linear-quadratic model
121
Letters to the Editor / Radiotherapy and Oncology 94 (2010) 117–124
own than in contrast to them. We also recommend that T and IMC radiotherapy should be used concurrently with caution until longterm toxicity results are available. We are puzzled by their statement that they ‘‘do not share the authors’ conclusion”, given that we both carefully qualified that the key issue will be the long-term toxicity and that our papers addressed only acute toxicity. In fact, our final conclusions are in the end very similar. Dr Belkacemi et al. advised clinicians ‘‘to balance the role of each therapeutic agent and their potential toxic effects when used concurrently” and that ‘‘it is important to spare the maximum heart volume during RT and select the patients who will really benefit from IMC irradiation” [1]. We similarly concluded that ‘‘the use of IMC RT concurrent with trastuzumab may continue with caution and attention to cardiac volumes when it is felt to be clinically indicated” [2]. With respect to the comment that our paper was the first to address the issue of cardiotoxicity and the use of IMC RT concurrently with T, in our defence we would state that at the time our manuscript was submitted for review, their study had not yet been published. Furthermore, we also note that the initial presentation of our data in the abstract form predated that of Belkacemi et al. [3,4]. We are nonetheless delighted that Dr Belkacemi et al. have published their important findings and conclusions, which describe an experience larger than our own, and is the first full publication on the subject as far as we are aware [1]. Dr Belkacemi and colleagues assert that long-term toxicity data are clearly needed to know the risks and benefits of concurrent IMC RT and T. We agree and concede that long-term cardiotoxicity was not addressed in our study, as clearly stated in our paper. With respect to IMC coverage in our series, the ipsilateral upper three internal costal spaces were covered with minimum 80% isodose lines in all cases in our study. Our colleagues also point out that the doses and dose fractionation varied, which is true given that this is a population-based study, rather than a prospective study with specific dose and techniques. They also raised concerns in regard to the partially wide tangent technique compared to ‘‘standard mixed photons–electrons fields”, suggesting that the latter technique may give better dose coverage. We would direct Dr Belkacemi and colleagues to Dr Pierce’s review comparing these techniques – including mixed photon–electron and partially wide tangent fields (PWTFs) – in which she concluded that ‘‘PWTFs as the most appropriate balance of target coverage and normal tissue sparing when irradiating the CW and IMN” [5]. With respect to the concern that our study is ‘‘not sufficient to draw conclusions about the safety of late consequences”, we very much agree and stated in our paper that: ‘‘the question of longterm cardiac toxicity is not addressed in this study”. They also quoted a very useful paper by Dr Borger et al., but unfortunately misquoted the findings [6]. Dr Belkacemi et al. stated that the values for CHD in our study (10 and 6 mm on average for IMC RT and non-IMC RT) are ‘‘in the range that was associated with higher rates of late cardiovascular events in the Borger et al. study”. In fact Dr Borger et al.’s study concluded that ‘‘the risk of CVD did not significantly increase with increasing MHD” (Maximum Heart Distance) [6]. Furthermore, the Hazard Ratios Dr Borger et al. reported were 1.51 (0.84–2.73) and 1.36 (0.85–2.19) for patients with MHD’s in the range of 0–10 mm and in the range of 10– 20 mm, respectively, which were not significantly different. They also had a concern that the rate of T discontinuation was higher than that seen in the initial randomized trials on the subject. Firstly we would point out that our analysis was a population-based study reflecting a broad application to the population at risk, and applied the T stopping rules equivalent to those in the randomized trial protocols. It does not seem surprising that the tolerance may differ in a population-based sample (with ages ranging up to 81) from that found in a randomized trial with stric-
ter eligibility criteria. Furthermore, they implied that the higher rates of discontinuation are related to the concurrent use of IMC RT and T, without pointing out that the discontinuation rate in the patients who had IMC RT and T in our study was in fact only 7.7%, which is lower than that found in the HERA trial at 8.5%. They also pointed out that the acute changes in LVEF may not be a useful indicator of late cardiotoxicity. We agree, although we are puzzled as to why they raised this as a critique of our study as we had not stated that it was. We echo the concerns raised by Belkacemi et al. regarding the concurrent use of IMC RT and T, and reiterate that the IMC RT and T should be continued with caution until larger studies including long-term toxicity are available. References [1] Belkacelmi Y, Gligorov J, Ozsahin M, et al. Concurrent trastuzumab with adjuvant radiotherapy in HER2-positive breast cancer patients: acute toxicity analyses from the French multicentric study. Ann Oncol 2008;19:1110–6. [2] Shaffer R, Tyldesley S, Rolles M, et al. Acute cardiotoxicity with concurrent trastuzumab and radiotherapy including internal mammary chain nodes: a retrospective single-institution study. Radiother Oncol 2009;90:122–6. [3] Rolles M, Tyldesley S, Chia S, et al. Cardiac tolerance with concurrent trastuzumab and internal mammary chain irradiation. Radiother Oncol 2006;80:S19. [4] Balkacemi Y, Gligorov J, Laharie-Mineur H, et al. Acute toxicities after concurrent administration of trastuzumab (T) and loco-regional radiation therapy (RT): a multicenter French study. Breast Cancer Res Treat 2006;100:S199. [5] Pierce L, Butler J, Martel M, et al. Post mastectomy radiotherapy of the chest wall: dosimetric comparison of common techniques. In J Rad Oncol Biol Phys 2002;52:1220–30. [6] Borger J, Hoonig M, Boersma L, et al. Cardiotoxic effects of tangential breast irradiation in early breast cancer patients: the role of irradiated heart volume. Int J Rad Oncol Biol Phys 2007;69:1131–8.
Scott Tyldesley Richard Shaffer Islam Mohamed Stephen Chia Martin Rolles BC Cancer Agency, Vancouver, Canada E-mail address: [email protected] (S. Tyldesley) Received 20 March 2009 Accepted 10 April 2009 0167-8140/$ - see front matter Ó 2009 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.radonc.2009.04.008
High doses per fraction and the linear-quadratic model
The paper by Gay et al. is a useful and well documented contribution, aiming at drawing attention to the effects of high doses per fraction on normal tissue response, and provides useful guidelines to minimize late effects by formulating normal tissue isodose constraints [1]. Yet the authors have assumed that the linear-quadratic (LQ) model is valid up to a dose per fraction (d/f) of 28 Gy. They cited a previous review and a letter in which the LQ model was considered as the best model «at present» for fitting at high d/f [2,3]. However, the review was published more than 15 years ago and the letter referred to data in the seventies and eighties. Nowadays it can hardly be assumed that the LQ model is appropriate to estimate the effect at a d/f of 28 Gy. Experimental data suggest that at high doses the survival curve asymptotically approaches the straight line [4]. An extrapolation beyond a dose as low as 6 Gy
122
Letters to the Editor / Radiotherapy and Oncology 94 (2010) 117–124
would lack clinically useful precision. Moreover, a recent report demonstrates that the two-component (TC) model is likely to better fit the effect at high d/f [5]. The TC model predicts higher tolerance doses at high d/f; in other words, the LQ model underestimates normal tissue tolerance at high d/f. Indeed the authors admit that the LQ model would give a conservative estimation, with the resulting selected constraints being more stringent than necessary. However, those values may be far from those expected, and those actually applied. According to the LQ model, a single dose of 28 Gy would be equivalent to 210 Gy on nervous tissue and to 174 Gy on bronchial tissue, if converted to conventional fractionation, a too high equivalent dose. A common fractionation schedule in lung tumours treated with stereotactic radiotherapy using the Cyberknife is 3 fractions of 20 Gy, with acceptable toxicity [6–8]. With an a/b ratio of 3 Gy for bronchial stenosis, the LQ model predicts in that case an equivalence of 276 Gy given conventionally, much exceeding the 70 Gy carrying 5% risk of bronchial stenosis as the authors correctly emphasized. Gay et al. stated: «it is unlikely that there will be any statistically significant definitive dose volume data for these endpoints in the near future». On the contrary, results with very high d/f, hypofractionated schedules using these new modalities will highly contribute refining the dose–effect relationship at these high d/f and high total doses. Finally, the authors made an incorrect sentence, that may confuse some readers. They stated on p 370 that a BED of 80 Gy4 means a biologically equivalent dose of 80 Gy using an a/b ratio of 4. They should have written : an EQD2 of 80 Gy4, that is an equivalent dose given with 2 Gy/f. The BED or biologically effective dose for such a scheme is 120 Gy4, not 80 Gy4.
References [1] Gay HA, Sibata CH, Allison RR, Jeremic B. Isodose-based methodology for minimizing the morbidity and mortality of thoracic hypofractionated radiotherapy. Radiother Oncol 2009;91:369–78. [2] Hall EJ, Brenner DJ. The radiobiology of radiosurgery: rationale for different treatment regimes for AVMs and malignancies. Int J Radiat Oncol Biol Phys 1993;25:381–5. [3] Hall EJ, Brenner DJ. In response to Dr. Marks. Int J Radiat Oncol Biol Phys 1995;32:275–6. [4] Joiner MC, Bentzen SM. Fractionation: the linear-quadratic approach. In: Joiner M, van der Kogel A, editors. Basic clinical radiobiology. Hodder Arnolds; 2009, p.102–19. [5] Joiner M. Is the LQ model applicable for brachytherapy with large doses per fraction? Radiother Oncol 2008;88:S9 [abstract 20]. [6] Castelli J, Thariat J, Benezery K, et al. Feasibility and efficacy of cyberknife radiotherapy for lung cancer: early results. Cancer Radiother 2008;12:793–9. [7] Collins BT, Vahdat S, Erickson K, et al. Radical cyberknife radiosurgery with tumor tracking: an effective treatment for inoperable small peripheral stage I non-small cell lung cancer. J Hematol Oncol 2009;2:1 (in process). [8] van Zyp NC, Prévost J-B, Hoogeman MS, et al. Stereotactic radiotherapy with real-time tumor tracking for non-small cell lung cancer: clinical outcome. Radiother Oncol 2009;91:296–300.
Adel Courdi Centre Antoine-Lacassagne, Radiotherapy, Nice, France E-mail address: [email protected] Received 1 July 2009 Accepted 12 August 2009
0167-8140/$ - see front matter Ó 2009 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.radonc.2009.08.019
Role of the linear-quadratic model in high doses per fraction
We thank Dr. Courdi for his comments, and he correctly points that the sentence on page 370 should have said: ‘‘. . .a biologically effective dose of 80 Gy. . .”. The assumption that the linear-quadratic (LQ) model is valid up to 28 Gy was arbitrarily chosen for consistency because in Table 2 the largest dose per fraction obtained with the model was ‘‘27.79 Gy”. Fowler et al. have made similar assumptions for theoretical analyses [1]. Our assumption should not be misinterpreted that we endorse this as fact. Quite the opposite, regarding tumor control we cannot emphasize enough that the clinicians should select hypofractionated regimens based on the published results showing efficacy and safety or as part of a clinical trial. This is because the LQ model could overestimate the effectiveness of the calculated regimen resulting in suboptimal local control. This does not mean that the LQ model has no use in generating preliminary normal tissue dose constraints. Recently Brenner [2] and Kirkpatrick et al. [3] eloquently discussed the virtues and shortcomings of the LQ model. At present, I agree with Brenner that the model is well validated up to 10 Gy per fraction, and reasonable for use up to about 18 Gy per fraction for the design of clinical trials. For the sake of argument, let us put the LQ model and brachial plexopathy (BP) constraints to the test. Forquer et al. recently reported BP as a dose-limiting toxicity in stereotactic body radiotherapy in early-stage NSCLC patients receiving a median total dose of 57 Gy (30–72) [4] in 3–4 fractions. To limit BP to <1% we suggested an EQD2 of 50 Gy22 , which in absolute dose terms translates to 24.5 Gy in 4 fractions or 21.6 Gy in 3 fractions. The authors concluded that ‘‘brachial plexus maximum dose should be kept <26 Gy in 3 or 4 fractions”. Could our constraints have prevented all BP? Arguably no, because despite our conservative estimates, still 1 of 7 patients with a maximum dose of 18 Gy to the brachial plexus developed BP. On the other hand, one could also argue that potentially 6 of 7 cases of BP could have been prevented. How will this change when the median follow-up is longer than 13 months? We should be cautious before we dismiss the LQ model, because when used appropriately it could help us avoid causing undue misery to our patients. Until we have definitive answers, the alternative is to ignore the LQ model and hope for the best. I have yet to regret spending a few extra minutes using the isodose-based methodology to review a treatment plan. The constraints and equations given in the article [5] have been implemented as a spreadsheet that may be downloaded at: http://www.ecu.edu/ radiationoncology/downloads.htm. The isodose% equation has been modified to allow prescriptions to isodoses other than 100% and the isodose constraints are also shown as absolute doses. References [1] Fowler JF, Tome WA, Fenwick JD, et al. A challenge to traditional radiation oncology. Int J Radiat Oncol Biol Phys 2004;60:1241–56. [2] Brenner DJ. The linear-quadratic model is an appropriate methodology for determining isoeffective doses at large doses per fraction. Semin Radiat Oncol 2008;18:234–9. [3] Kirkpatrick JP, Meyer JJ, Marks LB. The linear-quadratic model is inappropriate to model high dose per fraction effects in radiosurgery. Semin Radiat Oncol 2008;18:240–3. [4] Forquer JA, Fakiris AJ, Timmerman RD, et al. Brachial plexopathy from stereotactic body radiotherapy in early-stage NSCLC: dose-limiting toxicity in apical tumor sites. Radiother Oncol 2009;93:408–13. [5] Gay HA, Sibata CH, Allison RR, et al. Isodose-based methodology for minimizing the morbidity and mortality of thoracic hypofractionated radiotherapy. Radiother Oncol 2009;91:369–78.
Letters to the Editor / Radiotherapy and Oncology 94 (2010) 117–124
own than in contrast to them. We also recommend that T and IMC radiotherapy should be used concurrently with caution until longterm toxicity results are available. We are puzzled by their statement that they ‘‘do not share the authors’ conclusion”, given that we both carefully qualified that the key issue will be the long-term toxicity and that our papers addressed only acute toxicity. In fact, our final conclusions are in the end very similar. Dr Belkacemi et al. advised clinicians ‘‘to balance the role of each therapeutic agent and their potential toxic effects when used concurrently” and that ‘‘it is important to spare the maximum heart volume during RT and select the patients who will really benefit from IMC irradiation” [1]. We similarly concluded that ‘‘the use of IMC RT concurrent with trastuzumab may continue with caution and attention to cardiac volumes when it is felt to be clinically indicated” [2]. With respect to the comment that our paper was the first to address the issue of cardiotoxicity and the use of IMC RT concurrently with T, in our defence we would state that at the time our manuscript was submitted for review, their study had not yet been published. Furthermore, we also note that the initial presentation of our data in the abstract form predated that of Belkacemi et al. [3,4]. We are nonetheless delighted that Dr Belkacemi et al. have published their important findings and conclusions, which describe an experience larger than our own, and is the first full publication on the subject as far as we are aware [1]. Dr Belkacemi and colleagues assert that long-term toxicity data are clearly needed to know the risks and benefits of concurrent IMC RT and T. We agree and concede that long-term cardiotoxicity was not addressed in our study, as clearly stated in our paper. With respect to IMC coverage in our series, the ipsilateral upper three internal costal spaces were covered with minimum 80% isodose lines in all cases in our study. Our colleagues also point out that the doses and dose fractionation varied, which is true given that this is a population-based study, rather than a prospective study with specific dose and techniques. They also raised concerns in regard to the partially wide tangent technique compared to ‘‘standard mixed photons–electrons fields”, suggesting that the latter technique may give better dose coverage. We would direct Dr Belkacemi and colleagues to Dr Pierce’s review comparing these techniques – including mixed photon–electron and partially wide tangent fields (PWTFs) – in which she concluded that ‘‘PWTFs as the most appropriate balance of target coverage and normal tissue sparing when irradiating the CW and IMN” [5]. With respect to the concern that our study is ‘‘not sufficient to draw conclusions about the safety of late consequences”, we very much agree and stated in our paper that: ‘‘the question of longterm cardiac toxicity is not addressed in this study”. They also quoted a very useful paper by Dr Borger et al., but unfortunately misquoted the findings [6]. Dr Belkacemi et al. stated that the values for CHD in our study (10 and 6 mm on average for IMC RT and non-IMC RT) are ‘‘in the range that was associated with higher rates of late cardiovascular events in the Borger et al. study”. In fact Dr Borger et al.’s study concluded that ‘‘the risk of CVD did not significantly increase with increasing MHD” (Maximum Heart Distance) [6]. Furthermore, the Hazard Ratios Dr Borger et al. reported were 1.51 (0.84–2.73) and 1.36 (0.85–2.19) for patients with MHD’s in the range of 0–10 mm and in the range of 10– 20 mm, respectively, which were not significantly different. They also had a concern that the rate of T discontinuation was higher than that seen in the initial randomized trials on the subject. Firstly we would point out that our analysis was a population-based study reflecting a broad application to the population at risk, and applied the T stopping rules equivalent to those in the randomized trial protocols. It does not seem surprising that the tolerance may differ in a population-based sample (with ages ranging up to 81) from that found in a randomized trial with stric-
ter eligibility criteria. Furthermore, they implied that the higher rates of discontinuation are related to the concurrent use of IMC RT and T, without pointing out that the discontinuation rate in the patients who had IMC RT and T in our study was in fact only 7.7%, which is lower than that found in the HERA trial at 8.5%. They also pointed out that the acute changes in LVEF may not be a useful indicator of late cardiotoxicity. We agree, although we are puzzled as to why they raised this as a critique of our study as we had not stated that it was. We echo the concerns raised by Belkacemi et al. regarding the concurrent use of IMC RT and T, and reiterate that the IMC RT and T should be continued with caution until larger studies including long-term toxicity are available. References [1] Belkacelmi Y, Gligorov J, Ozsahin M, et al. Concurrent trastuzumab with adjuvant radiotherapy in HER2-positive breast cancer patients: acute toxicity analyses from the French multicentric study. Ann Oncol 2008;19:1110–6. [2] Shaffer R, Tyldesley S, Rolles M, et al. Acute cardiotoxicity with concurrent trastuzumab and radiotherapy including internal mammary chain nodes: a retrospective single-institution study. Radiother Oncol 2009;90:122–6. [3] Rolles M, Tyldesley S, Chia S, et al. Cardiac tolerance with concurrent trastuzumab and internal mammary chain irradiation. Radiother Oncol 2006;80:S19. [4] Balkacemi Y, Gligorov J, Laharie-Mineur H, et al. Acute toxicities after concurrent administration of trastuzumab (T) and loco-regional radiation therapy (RT): a multicenter French study. Breast Cancer Res Treat 2006;100:S199. [5] Pierce L, Butler J, Martel M, et al. Post mastectomy radiotherapy of the chest wall: dosimetric comparison of common techniques. In J Rad Oncol Biol Phys 2002;52:1220–30. [6] Borger J, Hoonig M, Boersma L, et al. Cardiotoxic effects of tangential breast irradiation in early breast cancer patients: the role of irradiated heart volume. Int J Rad Oncol Biol Phys 2007;69:1131–8.
Scott Tyldesley Richard Shaffer Islam Mohamed Stephen Chia Martin Rolles BC Cancer Agency, Vancouver, Canada E-mail address: [email protected] (S. Tyldesley) Received 20 March 2009 Accepted 10 April 2009 0167-8140/$ - see front matter Ó 2009 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.radonc.2009.04.008
High doses per fraction and the linear-quadratic model
The paper by Gay et al. is a useful and well documented contribution, aiming at drawing attention to the effects of high doses per fraction on normal tissue response, and provides useful guidelines to minimize late effects by formulating normal tissue isodose constraints [1]. Yet the authors have assumed that the linear-quadratic (LQ) model is valid up to a dose per fraction (d/f) of 28 Gy. They cited a previous review and a letter in which the LQ model was considered as the best model «at present» for fitting at high d/f [2,3]. However, the review was published more than 15 years ago and the letter referred to data in the seventies and eighties. Nowadays it can hardly be assumed that the LQ model is appropriate to estimate the effect at a d/f of 28 Gy. Experimental data suggest that at high doses the survival curve asymptotically approaches the straight line [4]. An extrapolation beyond a dose as low as 6 Gy
122
Letters to the Editor / Radiotherapy and Oncology 94 (2010) 117–124
would lack clinically useful precision. Moreover, a recent report demonstrates that the two-component (TC) model is likely to better fit the effect at high d/f [5]. The TC model predicts higher tolerance doses at high d/f; in other words, the LQ model underestimates normal tissue tolerance at high d/f. Indeed the authors admit that the LQ model would give a conservative estimation, with the resulting selected constraints being more stringent than necessary. However, those values may be far from those expected, and those actually applied. According to the LQ model, a single dose of 28 Gy would be equivalent to 210 Gy on nervous tissue and to 174 Gy on bronchial tissue, if converted to conventional fractionation, a too high equivalent dose. A common fractionation schedule in lung tumours treated with stereotactic radiotherapy using the Cyberknife is 3 fractions of 20 Gy, with acceptable toxicity [6–8]. With an a/b ratio of 3 Gy for bronchial stenosis, the LQ model predicts in that case an equivalence of 276 Gy given conventionally, much exceeding the 70 Gy carrying 5% risk of bronchial stenosis as the authors correctly emphasized. Gay et al. stated: «it is unlikely that there will be any statistically significant definitive dose volume data for these endpoints in the near future». On the contrary, results with very high d/f, hypofractionated schedules using these new modalities will highly contribute refining the dose–effect relationship at these high d/f and high total doses. Finally, the authors made an incorrect sentence, that may confuse some readers. They stated on p 370 that a BED of 80 Gy4 means a biologically equivalent dose of 80 Gy using an a/b ratio of 4. They should have written : an EQD2 of 80 Gy4, that is an equivalent dose given with 2 Gy/f. The BED or biologically effective dose for such a scheme is 120 Gy4, not 80 Gy4.
References [1] Gay HA, Sibata CH, Allison RR, Jeremic B. Isodose-based methodology for minimizing the morbidity and mortality of thoracic hypofractionated radiotherapy. Radiother Oncol 2009;91:369–78. [2] Hall EJ, Brenner DJ. The radiobiology of radiosurgery: rationale for different treatment regimes for AVMs and malignancies. Int J Radiat Oncol Biol Phys 1993;25:381–5. [3] Hall EJ, Brenner DJ. In response to Dr. Marks. Int J Radiat Oncol Biol Phys 1995;32:275–6. [4] Joiner MC, Bentzen SM. Fractionation: the linear-quadratic approach. In: Joiner M, van der Kogel A, editors. Basic clinical radiobiology. Hodder Arnolds; 2009, p.102–19. [5] Joiner M. Is the LQ model applicable for brachytherapy with large doses per fraction? Radiother Oncol 2008;88:S9 [abstract 20]. [6] Castelli J, Thariat J, Benezery K, et al. Feasibility and efficacy of cyberknife radiotherapy for lung cancer: early results. Cancer Radiother 2008;12:793–9. [7] Collins BT, Vahdat S, Erickson K, et al. Radical cyberknife radiosurgery with tumor tracking: an effective treatment for inoperable small peripheral stage I non-small cell lung cancer. J Hematol Oncol 2009;2:1 (in process). [8] van Zyp NC, Prévost J-B, Hoogeman MS, et al. Stereotactic radiotherapy with real-time tumor tracking for non-small cell lung cancer: clinical outcome. Radiother Oncol 2009;91:296–300.
Adel Courdi Centre Antoine-Lacassagne, Radiotherapy, Nice, France E-mail address: [email protected] Received 1 July 2009 Accepted 12 August 2009
0167-8140/$ - see front matter Ó 2009 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.radonc.2009.08.019
Role of the linear-quadratic model in high doses per fraction
We thank Dr. Courdi for his comments, and he correctly points that the sentence on page 370 should have said: ‘‘. . .a biologically effective dose of 80 Gy. . .”. The assumption that the linear-quadratic (LQ) model is valid up to 28 Gy was arbitrarily chosen for consistency because in Table 2 the largest dose per fraction obtained with the model was ‘‘27.79 Gy”. Fowler et al. have made similar assumptions for theoretical analyses [1]. Our assumption should not be misinterpreted that we endorse this as fact. Quite the opposite, regarding tumor control we cannot emphasize enough that the clinicians should select hypofractionated regimens based on the published results showing efficacy and safety or as part of a clinical trial. This is because the LQ model could overestimate the effectiveness of the calculated regimen resulting in suboptimal local control. This does not mean that the LQ model has no use in generating preliminary normal tissue dose constraints. Recently Brenner [2] and Kirkpatrick et al. [3] eloquently discussed the virtues and shortcomings of the LQ model. At present, I agree with Brenner that the model is well validated up to 10 Gy per fraction, and reasonable for use up to about 18 Gy per fraction for the design of clinical trials. For the sake of argument, let us put the LQ model and brachial plexopathy (BP) constraints to the test. Forquer et al. recently reported BP as a dose-limiting toxicity in stereotactic body radiotherapy in early-stage NSCLC patients receiving a median total dose of 57 Gy (30–72) [4] in 3–4 fractions. To limit BP to <1% we suggested an EQD2 of 50 Gy22 , which in absolute dose terms translates to 24.5 Gy in 4 fractions or 21.6 Gy in 3 fractions. The authors concluded that ‘‘brachial plexus maximum dose should be kept <26 Gy in 3 or 4 fractions”. Could our constraints have prevented all BP? Arguably no, because despite our conservative estimates, still 1 of 7 patients with a maximum dose of 18 Gy to the brachial plexus developed BP. On the other hand, one could also argue that potentially 6 of 7 cases of BP could have been prevented. How will this change when the median follow-up is longer than 13 months? We should be cautious before we dismiss the LQ model, because when used appropriately it could help us avoid causing undue misery to our patients. Until we have definitive answers, the alternative is to ignore the LQ model and hope for the best. I have yet to regret spending a few extra minutes using the isodose-based methodology to review a treatment plan. The constraints and equations given in the article [5] have been implemented as a spreadsheet that may be downloaded at: http://www.ecu.edu/ radiationoncology/downloads.htm. The isodose% equation has been modified to allow prescriptions to isodoses other than 100% and the isodose constraints are also shown as absolute doses. References [1] Fowler JF, Tome WA, Fenwick JD, et al. A challenge to traditional radiation oncology. Int J Radiat Oncol Biol Phys 2004;60:1241–56. [2] Brenner DJ. The linear-quadratic model is an appropriate methodology for determining isoeffective doses at large doses per fraction. Semin Radiat Oncol 2008;18:234–9. [3] Kirkpatrick JP, Meyer JJ, Marks LB. The linear-quadratic model is inappropriate to model high dose per fraction effects in radiosurgery. Semin Radiat Oncol 2008;18:240–3. [4] Forquer JA, Fakiris AJ, Timmerman RD, et al. Brachial plexopathy from stereotactic body radiotherapy in early-stage NSCLC: dose-limiting toxicity in apical tumor sites. Radiother Oncol 2009;93:408–13. [5] Gay HA, Sibata CH, Allison RR, et al. Isodose-based methodology for minimizing the morbidity and mortality of thoracic hypofractionated radiotherapy. Radiother Oncol 2009;91:369–78.