- Email: [email protected]
In response to Dr. Patton
1426
I. J. Radiation Oncology
● Biology ● Physics
pensated (4). For these reasons, Nyandoto et al.’s report of the Finnish experience with a no-fault patient compensation system for patients experiencing adverse events from radiation therapy is noteworthy (5). Several problems exist with the analysis: The authors’ terminology is confusing. “Number of patient visits” actually refers to the number of radiation treatments administered. “Radiation treatments” equates to treatment courses that are assumed to average 20 treatments; no data are presented to justify this assumption. Actual numbers of radiation treatments during the May 1987 to January 1999 study period were not directly available but were estimated from limited data points within this period. Figure 1 coarsely illustrates the magnitude of Finnish radiation therapy. The scale of the x-axis in Fig 1 is nonlinear, and the y-axis perpetuates the authors’ confusing use of “number of treatments” when actually referring to the estimated number of radiation therapy treatment courses per year. The May 1987 to January 1999 study period is imprecisely illustrated. Although 102 patients are reported to have filed claims during the study period for radiation-related adverse events, Fig. 2 illustrates only 100 claims and 100 events. The distinction between events and claims is unexplained. Despite these problems, however, the essence of Nyandoto et al.’s report remains intact: radiation injuries in Finland are infrequently compensated and most often for nominal amounts. The authors’ conclusions that “the number of radiation therapy injuries that are financially compensated can remain low in an insurance-based judicial system” and “expenditure for compensation of adverse radiotherapy events was relatively low” hardly constitute a ringing endorsement of this system. Is patient compensation infrequent and limited because there are few true radiation-related injuries, or simply because of the impenetrability of the system? A patient’s ultimate outcome within this compensation system hinges on two inherently subjective factors, the membership of the Patients Insurance Association and the Patient Injury Board, and the “agreed-on scale” for compensation of those injured. The success of any such no-fault compensation system should be gauged by three criteria: (1) the exclusion of unworthy claims, while handling meritorious claims both (2) efficiently and (3) sufficiently. 1. Table 2 detailing the reasons for not compensating claims demonstrates a high hurdle for successful claims, namely an unexpected injury directly attributable to radiation therapy. Only 18 percent of patients submitting claims met this threshold. 2. Efficiency is questionable, with claims resolution taking up to 48 months, with a median of 12 months. Although likely faster than malpractice litigation, this pace is hardly speedy. 3. Sufficiency is altogether unclear. With a median award of less than $2000, the Finnish system seems downright stingy. The largest single compensation of $287,430 lies nearly 4 standard deviations above the mean; the next largest award is less than one quarter as much. Given the gravity of the radiation injuries detailed (including blindness, sterility, vesicovaginal fistula, and 4 cases of myelopathy), the magnitude of patient compensation seems remarkably small by U.S. standards. Herein lies the greatest problem, drawing useful parallels between the markedly different cultures and judicial systems in Finland and the United States. American culture promotes the idea that every citizen is entitled to equal protection under the law, making litigation a much more commonly used tool in this country. Although relatively little has been written about professional liability in radiation oncology, it has been reported that lawsuits are common in the field, with approximately 50% of radiation oncologists practicing in the United States having been sued after 20 years in practice (6). Could such a no-fault compensation system as that described by Nyandoto work in this country? Hypothetically, yes, but in the real world, no. The political reality in the United States is that too many factions (plaintiff attorneys, defense attorneys, insurance companies, expert witnesses, and, too infrequently patients) benefit from the current medical malpractice industry to allow it to be replaced by a no-fault system such as is used in Finland. Although an interesting perspective on an alternative dispute resolution system, radiation-related injuries in the United States will continue to be addressed by the existing inefficient system until a fundamental reshaping of the entire professional liability system emerges. There is no indication that any such change is imminent. GREGORY A. PATTON, M.D., M.S., M.S., M.B.A. Northwest Cancer Specialists Portland, OR
Volume 52, Number 5, 2002 PII S0360-3016(01)02824-3 1. Cohen L, Schultheiss TE, Kennaugh RC. A radiation overdose incident: initial data. Int J Radiat Oncol Biol Phys 1995;33:217–224. 2. Ostrom LT, Rathbun P, Cumberlin R, et al. Lessons learned from investigations of therapy misadministration events. Int J Radiat Oncol Biol Phys 1996;34:227–234. 3. Kohn LT, Corrigan JM, Donaldson MS. To err is human: building a safer health system. Washington, DC: Institute of Medicine Press 2000. 4. Localio AR, Lawthers AG, Brennan TA, et al. Relation between malpractice claims and adverse events due to negligence: Results of the Harvard Medical Practice Study III. N Engl J Med 1991;325:245–251. 5. Nyandoto P, Muhonen T, Hakala T, et al. Financial compensation for radiotherapy-related adverse events in a judicial system where proof of medical negligence is not required. Int J Radiat Oncol Biol Phys 2001;51:209 –212. 6. Sherman NE, Rich TA, Peters LJ. Professional liability in radiotherapy: experience of the Fletcher Society. Int J Radiat Oncol Biol Phys 1991;20:563–566.
IN RESPONSE TO DR. PATTON To the Editor: The purpose of our study was to examine the frequency of radiation-related adverse events that lead to financial compensation in a judicial system that is not based on litigation in court, but on statutory insurance, in which proof of medical negligence is not required for obtaining compensation. Insurance is statutory for all persons providing health care in Finland, and all insurers must belong to the Patients Insurance Association. Litigation in court has not been ruled out, and all those who are dissatisfied after receiving the Patient Injury Board recommendation, which is based on medical expert statements, may still sue in court. If Dr. Patton was right in his belief that there is a big hurdle for successful claims and that the level of compensations paid are remarkably small, one would expect many litigation cases in court, because all victims are informed about this possibility. Because no litigation regarding radiation therapy has arisen since the adoption of the no-fault system in 1987, we suspect that the number of dissatisfied patients may be small. As in the United States, the Western European societies, including Finland, promote the idea that every citizen is entitled to equal protection under the law, but we fail to understand why respect of this principle should lead to frequent litigation of the medical practitioners in court. It is possible that adoption of the no-fault system might speed up and increase the reporting of medical mishaps of the kind described by Dr. Patton. The median time of 12 months (range 1– 48) for the Patient Insurance Association to make a decision is not unreasonably long, because all cases are carefully assessed by several experts. Unfortunately, we do not know how this median time compares with malpractice litigation in the U.S. courts. The compensations paid in single cases varied widely. The appropriate levels of compensation is difficult to judge, but in many cases cancer itself causes loss of organ function, which inappropriate therapy may fail to prevent, or malpractice causes the same end result as would progressing cancer. For example, loss of vision after irradiation of a hypophysis tumor may be caused in part by tumor progression (case 12, compensated for $5130), whereas postoperative radiation-related spinal cord damage causing paralysis can only be explained by poor treatment technique (case 4, compensated for $287,430). We agree that the levels of compensations may be difficult to define and may also depend on other than purely medical factors in any system. Yet, we consider it possible that a litigationbased system may do no better, and similar injuries may not necessarily lead to similar compensations in court. Finally, we do not agree with Dr. Patton in his contention that several problems exist with the analysis. We explain in the Methods and Materials section of the paper the terminology used. Because only patient visits to the radiation therapy units are recorded in Finnish hospitals, we estimated that a single treatment course consisted of 20 visits. Knowing the clinical practice, we believe this is a reasonable estimate. This estimation had little influence on the main results and affected only the calculation for the expenditure used for compensating adverse radiation events per treated patient (we estimated it to be $4). Had we assumed one treatment course to consist of 10 visits (certainly too low a figure), the expenditure for compensation of adverse radiation events would have been about $2 per treated patient, and if we had assumed one treatment course to consist of 30 visits (likely too high a figure), the expenditure would have been about $7. Counting the actual radiation treatments for an entire nation and for a
Letters to the editor period of more than 1 decade would have been a vast task, and we are surprised that Dr. Patton is not satisfied with the counts performed at about 5-year intervals. The x-axis of Figure 1 is not intended to be linear, and, therefore, the year of measurement is given under each data point. The period under investigation (May 1987 to January 1999) is clearly stated in the text, and depicted in Fig. 1 with an arrow. We thank Dr. Patton for pointing out that 2 of the 102 cases are not shown in Fig. 2, but all cases were consistently included in the calculations performed. In sum, our study shows that the frequency of radiation therapy injuries that are financially compensated can remain low in an insurance-based system, and although the victims still have the right to sue in court, this seldom takes place. PAUL NYANDOTO, M.D. TIMO MUHONEN, M.D. HEIKKI JOENSUU, M.D. Department of Oncology Helsinki University Central Hospital Helsinki, Finland
PII S0360-3016(01)02825-5
IS THE ␣/ FOR PROSTATE TUMORS REALLY LOW? IN REGARD TO FOWLER ET AL., IJROBP 2001;50:1021–1031 To the Editor: The article by Fowler et al. (1) provides more evidence for the likelihood that ␣/ for prostate tumors is low, with the authors finding a best estimate of 1.49 Gy. The ␣/ estimates were derived using three different methods for intercomparing the 5-year bNED results observed in treatments involving external beam, I-125 implants, and Pd-103 implants. However, in their analysis, as in the earlier analysis by Brenner and Hall (2) that began investigations into prostate ␣/ values, no allowance was made for the relative biological effectiveness (RBE) of the radiation emitted by I-125 and Pd-103. While there is some debate as to what RBE values should be used for these two nuclides, there is little doubt that they are significantly greater than unity and they should therefore be considered when deducing radiobiological parameters from iso-effect comparisons. If implant RBE effects are included in the analysis of Fowler et al. (1) this will lead to yet lower estimates of the ␣/ parameter, as we demonstrate in the following simple example. As indicated by Fowler et al., (1) the relative effectiveness (RE) factor for a permanent implant employing an exponentially decaying source of radiation (Eq. 1 in their article) is:
RE ⫽ 1 ⫹
R0 共 ⫹ 兲 共␣/兲
(1)
where R0 is the initial dose-rate, is the repair constant of sublethal damage, is the decay constant of the radionuclide, and ␣ and  are the LQ radiosensitivity coefficients (3). For implants using long-lived radionuclides, such as I-125 and Pd-103, is very small in comparison with and, for the purposes of this exercise, may be neglected, [i.e., Eq. 1 simplifies to]:
RE ⫽ 1 ⫹
R0 共␣/兲
(2)
Eq. 2 represents the RE for a low-LET radiation source associated with an RBE of unity. For radiations for which the RBE is greater than unity, Eq. 2 is changed to (4, 5):
RE ⫽ RBEmax ⫹
R0 共␣/兲
(3)
where RBEmax is the maximum RBE [i.e., that determined at very low dose-rate]. The ␣/ value in Eq. 3 is the same as that which appears in Eq.
1427
2 [i.e., it is that determined for low-LET radiation]. The biologically effective dose (BED) associated with a permanent implant involving such a source is thus:
冋
BED ⫽ TDimplant RBEmax ⫹
册
R0 共␣/兲
(4)
where TDimplant is the total physical dose delivered following complete decay of the implanted sources. For an external beam treatment delivered using conventional photon radiation with an RBE of unity, the associated BED is:
冋
BED ⫽ TDext 1 ⫹
册
d 共␣/兲
(5)
where TDext is the total physical dose and d is the dose per fraction. If prostate tumor repopulation effects are neglected (as Fowler et al. (1) considered a reasonable assumption), then the external beam treatment and implant each produce the same biological result when the associated BEDs are equal. Eqs. 4 and 5 may thus be equated and then re-arranged to provide an analytical expression for determining the low-LET tumor ␣/ value [(␣/)turn]:
共␣/兲tum ⫽
dTDext ⫺ R0TDimplant 共TDimplantRBEmax ⫺ TDext)
(6)
For I-125, Scalliet and Wambersie (6) found the RBE to be approximately 1.2 when determined at high-dose rate and around 2 when measured at low-dose rate. Ling et al. (7) measured the RBE at low-dose rate to be 1.4, Wuu et al. (8) put the value at 2.1 following microdosimetric measurements, and Wuu and Zaider (9) derived a theoretical value of 1.5. For I-125, therefore, a low-dose-rate RBE working value (i.e., RBEmax) of 1.45 seems reasonable (5). For Pd-103, the last three publications derived RBE values in the range 1.6 –2.3, and an average RBEmax value of 1.75 may therefore be assumed. As the RBEmax parameter appears in the denominator of Eq. 6, it is apparent that omission of this factor will produce an overestimate of ␣/. For prostate tumors, Fowler et al. derived a repair half-time of 1.90 h corresponding to a value of 0.365h⫺1. In their first method of analysis, an I-125 implant dose of 145 Gy was found to be iso-effective to an external beam schedule consisting of 71.0 Gy in 2-Gy fractions. Using an average RBEmax value of 1.45 for I-125, the tumor (␣/)tum is calculated from Eq. 6 to be 0.82 Gy. Similarly, 124 Gy delivered via Pd-103 implants was found to be iso-effective to an external beam schedule of 73.1 Gy in 2-Gy fractions. Using this figure in conjunction with an RBE of 1.75, the ␣/ calculated from Eq. 6 drops further to 0.52 Gy. The above examples are for illustrative purposes only and these quickly calculated ␣/ values are in no way definitive. Additional sources of variation are associated with the manner in which the implant doses are defined (as discussed by Fowler et al. (1) and there is also the possibility that the RBEmax values are themselves tissue-specific. It has long been believed that RBEs are higher in slowly dividing tissues tumors, and some authors (10) have suggested that there is an inverse analytical relationship between RBEmax itself and the tissue ␣/ ratio, but this requires experimental validation. Furthermore, the doses (and dose rates) will vary within an implant, thus producing a spatial variation of RBE values. Despite these provisos, the omission of RBE from the more rigorous methods used by Fowler et al. (1) and Brenner and Hall (2) will likely have led to an overestimation of ␣/. The possibility that prostatic tumors may have an even higher fractionation and dose-rate sensitivity than is currently assumed holds many far-reaching implications for treatment strategies, and we suggest that the analyses be repeated to determine how the inclusion of a range of possible RBE values might alter their results. This discussion also highlights the need for further experimental work to determine the RBEs for I-125 and Pd-103 more precisely, especially at low-dose rates. ROGER G. DALE, PH.D., F.INST.P., F.I.P.E.M. BLEDDYN JONES, M.D., F.R.C.R., F.R.C.P. Radiation Physics and Radiobiology Charing Cross Hospital London, UK
I. J. Radiation Oncology
● Biology ● Physics
pensated (4). For these reasons, Nyandoto et al.’s report of the Finnish experience with a no-fault patient compensation system for patients experiencing adverse events from radiation therapy is noteworthy (5). Several problems exist with the analysis: The authors’ terminology is confusing. “Number of patient visits” actually refers to the number of radiation treatments administered. “Radiation treatments” equates to treatment courses that are assumed to average 20 treatments; no data are presented to justify this assumption. Actual numbers of radiation treatments during the May 1987 to January 1999 study period were not directly available but were estimated from limited data points within this period. Figure 1 coarsely illustrates the magnitude of Finnish radiation therapy. The scale of the x-axis in Fig 1 is nonlinear, and the y-axis perpetuates the authors’ confusing use of “number of treatments” when actually referring to the estimated number of radiation therapy treatment courses per year. The May 1987 to January 1999 study period is imprecisely illustrated. Although 102 patients are reported to have filed claims during the study period for radiation-related adverse events, Fig. 2 illustrates only 100 claims and 100 events. The distinction between events and claims is unexplained. Despite these problems, however, the essence of Nyandoto et al.’s report remains intact: radiation injuries in Finland are infrequently compensated and most often for nominal amounts. The authors’ conclusions that “the number of radiation therapy injuries that are financially compensated can remain low in an insurance-based judicial system” and “expenditure for compensation of adverse radiotherapy events was relatively low” hardly constitute a ringing endorsement of this system. Is patient compensation infrequent and limited because there are few true radiation-related injuries, or simply because of the impenetrability of the system? A patient’s ultimate outcome within this compensation system hinges on two inherently subjective factors, the membership of the Patients Insurance Association and the Patient Injury Board, and the “agreed-on scale” for compensation of those injured. The success of any such no-fault compensation system should be gauged by three criteria: (1) the exclusion of unworthy claims, while handling meritorious claims both (2) efficiently and (3) sufficiently. 1. Table 2 detailing the reasons for not compensating claims demonstrates a high hurdle for successful claims, namely an unexpected injury directly attributable to radiation therapy. Only 18 percent of patients submitting claims met this threshold. 2. Efficiency is questionable, with claims resolution taking up to 48 months, with a median of 12 months. Although likely faster than malpractice litigation, this pace is hardly speedy. 3. Sufficiency is altogether unclear. With a median award of less than $2000, the Finnish system seems downright stingy. The largest single compensation of $287,430 lies nearly 4 standard deviations above the mean; the next largest award is less than one quarter as much. Given the gravity of the radiation injuries detailed (including blindness, sterility, vesicovaginal fistula, and 4 cases of myelopathy), the magnitude of patient compensation seems remarkably small by U.S. standards. Herein lies the greatest problem, drawing useful parallels between the markedly different cultures and judicial systems in Finland and the United States. American culture promotes the idea that every citizen is entitled to equal protection under the law, making litigation a much more commonly used tool in this country. Although relatively little has been written about professional liability in radiation oncology, it has been reported that lawsuits are common in the field, with approximately 50% of radiation oncologists practicing in the United States having been sued after 20 years in practice (6). Could such a no-fault compensation system as that described by Nyandoto work in this country? Hypothetically, yes, but in the real world, no. The political reality in the United States is that too many factions (plaintiff attorneys, defense attorneys, insurance companies, expert witnesses, and, too infrequently patients) benefit from the current medical malpractice industry to allow it to be replaced by a no-fault system such as is used in Finland. Although an interesting perspective on an alternative dispute resolution system, radiation-related injuries in the United States will continue to be addressed by the existing inefficient system until a fundamental reshaping of the entire professional liability system emerges. There is no indication that any such change is imminent. GREGORY A. PATTON, M.D., M.S., M.S., M.B.A. Northwest Cancer Specialists Portland, OR
Volume 52, Number 5, 2002 PII S0360-3016(01)02824-3 1. Cohen L, Schultheiss TE, Kennaugh RC. A radiation overdose incident: initial data. Int J Radiat Oncol Biol Phys 1995;33:217–224. 2. Ostrom LT, Rathbun P, Cumberlin R, et al. Lessons learned from investigations of therapy misadministration events. Int J Radiat Oncol Biol Phys 1996;34:227–234. 3. Kohn LT, Corrigan JM, Donaldson MS. To err is human: building a safer health system. Washington, DC: Institute of Medicine Press 2000. 4. Localio AR, Lawthers AG, Brennan TA, et al. Relation between malpractice claims and adverse events due to negligence: Results of the Harvard Medical Practice Study III. N Engl J Med 1991;325:245–251. 5. Nyandoto P, Muhonen T, Hakala T, et al. Financial compensation for radiotherapy-related adverse events in a judicial system where proof of medical negligence is not required. Int J Radiat Oncol Biol Phys 2001;51:209 –212. 6. Sherman NE, Rich TA, Peters LJ. Professional liability in radiotherapy: experience of the Fletcher Society. Int J Radiat Oncol Biol Phys 1991;20:563–566.
IN RESPONSE TO DR. PATTON To the Editor: The purpose of our study was to examine the frequency of radiation-related adverse events that lead to financial compensation in a judicial system that is not based on litigation in court, but on statutory insurance, in which proof of medical negligence is not required for obtaining compensation. Insurance is statutory for all persons providing health care in Finland, and all insurers must belong to the Patients Insurance Association. Litigation in court has not been ruled out, and all those who are dissatisfied after receiving the Patient Injury Board recommendation, which is based on medical expert statements, may still sue in court. If Dr. Patton was right in his belief that there is a big hurdle for successful claims and that the level of compensations paid are remarkably small, one would expect many litigation cases in court, because all victims are informed about this possibility. Because no litigation regarding radiation therapy has arisen since the adoption of the no-fault system in 1987, we suspect that the number of dissatisfied patients may be small. As in the United States, the Western European societies, including Finland, promote the idea that every citizen is entitled to equal protection under the law, but we fail to understand why respect of this principle should lead to frequent litigation of the medical practitioners in court. It is possible that adoption of the no-fault system might speed up and increase the reporting of medical mishaps of the kind described by Dr. Patton. The median time of 12 months (range 1– 48) for the Patient Insurance Association to make a decision is not unreasonably long, because all cases are carefully assessed by several experts. Unfortunately, we do not know how this median time compares with malpractice litigation in the U.S. courts. The compensations paid in single cases varied widely. The appropriate levels of compensation is difficult to judge, but in many cases cancer itself causes loss of organ function, which inappropriate therapy may fail to prevent, or malpractice causes the same end result as would progressing cancer. For example, loss of vision after irradiation of a hypophysis tumor may be caused in part by tumor progression (case 12, compensated for $5130), whereas postoperative radiation-related spinal cord damage causing paralysis can only be explained by poor treatment technique (case 4, compensated for $287,430). We agree that the levels of compensations may be difficult to define and may also depend on other than purely medical factors in any system. Yet, we consider it possible that a litigationbased system may do no better, and similar injuries may not necessarily lead to similar compensations in court. Finally, we do not agree with Dr. Patton in his contention that several problems exist with the analysis. We explain in the Methods and Materials section of the paper the terminology used. Because only patient visits to the radiation therapy units are recorded in Finnish hospitals, we estimated that a single treatment course consisted of 20 visits. Knowing the clinical practice, we believe this is a reasonable estimate. This estimation had little influence on the main results and affected only the calculation for the expenditure used for compensating adverse radiation events per treated patient (we estimated it to be $4). Had we assumed one treatment course to consist of 10 visits (certainly too low a figure), the expenditure for compensation of adverse radiation events would have been about $2 per treated patient, and if we had assumed one treatment course to consist of 30 visits (likely too high a figure), the expenditure would have been about $7. Counting the actual radiation treatments for an entire nation and for a
Letters to the editor period of more than 1 decade would have been a vast task, and we are surprised that Dr. Patton is not satisfied with the counts performed at about 5-year intervals. The x-axis of Figure 1 is not intended to be linear, and, therefore, the year of measurement is given under each data point. The period under investigation (May 1987 to January 1999) is clearly stated in the text, and depicted in Fig. 1 with an arrow. We thank Dr. Patton for pointing out that 2 of the 102 cases are not shown in Fig. 2, but all cases were consistently included in the calculations performed. In sum, our study shows that the frequency of radiation therapy injuries that are financially compensated can remain low in an insurance-based system, and although the victims still have the right to sue in court, this seldom takes place. PAUL NYANDOTO, M.D. TIMO MUHONEN, M.D. HEIKKI JOENSUU, M.D. Department of Oncology Helsinki University Central Hospital Helsinki, Finland
PII S0360-3016(01)02825-5
IS THE ␣/ FOR PROSTATE TUMORS REALLY LOW? IN REGARD TO FOWLER ET AL., IJROBP 2001;50:1021–1031 To the Editor: The article by Fowler et al. (1) provides more evidence for the likelihood that ␣/ for prostate tumors is low, with the authors finding a best estimate of 1.49 Gy. The ␣/ estimates were derived using three different methods for intercomparing the 5-year bNED results observed in treatments involving external beam, I-125 implants, and Pd-103 implants. However, in their analysis, as in the earlier analysis by Brenner and Hall (2) that began investigations into prostate ␣/ values, no allowance was made for the relative biological effectiveness (RBE) of the radiation emitted by I-125 and Pd-103. While there is some debate as to what RBE values should be used for these two nuclides, there is little doubt that they are significantly greater than unity and they should therefore be considered when deducing radiobiological parameters from iso-effect comparisons. If implant RBE effects are included in the analysis of Fowler et al. (1) this will lead to yet lower estimates of the ␣/ parameter, as we demonstrate in the following simple example. As indicated by Fowler et al., (1) the relative effectiveness (RE) factor for a permanent implant employing an exponentially decaying source of radiation (Eq. 1 in their article) is:
RE ⫽ 1 ⫹
R0 共 ⫹ 兲 共␣/兲
(1)
where R0 is the initial dose-rate, is the repair constant of sublethal damage, is the decay constant of the radionuclide, and ␣ and  are the LQ radiosensitivity coefficients (3). For implants using long-lived radionuclides, such as I-125 and Pd-103, is very small in comparison with and, for the purposes of this exercise, may be neglected, [i.e., Eq. 1 simplifies to]:
RE ⫽ 1 ⫹
R0 共␣/兲
(2)
Eq. 2 represents the RE for a low-LET radiation source associated with an RBE of unity. For radiations for which the RBE is greater than unity, Eq. 2 is changed to (4, 5):
RE ⫽ RBEmax ⫹
R0 共␣/兲
(3)
where RBEmax is the maximum RBE [i.e., that determined at very low dose-rate]. The ␣/ value in Eq. 3 is the same as that which appears in Eq.
1427
2 [i.e., it is that determined for low-LET radiation]. The biologically effective dose (BED) associated with a permanent implant involving such a source is thus:
冋
BED ⫽ TDimplant RBEmax ⫹
册
R0 共␣/兲
(4)
where TDimplant is the total physical dose delivered following complete decay of the implanted sources. For an external beam treatment delivered using conventional photon radiation with an RBE of unity, the associated BED is:
冋
BED ⫽ TDext 1 ⫹
册
d 共␣/兲
(5)
where TDext is the total physical dose and d is the dose per fraction. If prostate tumor repopulation effects are neglected (as Fowler et al. (1) considered a reasonable assumption), then the external beam treatment and implant each produce the same biological result when the associated BEDs are equal. Eqs. 4 and 5 may thus be equated and then re-arranged to provide an analytical expression for determining the low-LET tumor ␣/ value [(␣/)turn]:
共␣/兲tum ⫽
dTDext ⫺ R0TDimplant 共TDimplantRBEmax ⫺ TDext)
(6)
For I-125, Scalliet and Wambersie (6) found the RBE to be approximately 1.2 when determined at high-dose rate and around 2 when measured at low-dose rate. Ling et al. (7) measured the RBE at low-dose rate to be 1.4, Wuu et al. (8) put the value at 2.1 following microdosimetric measurements, and Wuu and Zaider (9) derived a theoretical value of 1.5. For I-125, therefore, a low-dose-rate RBE working value (i.e., RBEmax) of 1.45 seems reasonable (5). For Pd-103, the last three publications derived RBE values in the range 1.6 –2.3, and an average RBEmax value of 1.75 may therefore be assumed. As the RBEmax parameter appears in the denominator of Eq. 6, it is apparent that omission of this factor will produce an overestimate of ␣/. For prostate tumors, Fowler et al. derived a repair half-time of 1.90 h corresponding to a value of 0.365h⫺1. In their first method of analysis, an I-125 implant dose of 145 Gy was found to be iso-effective to an external beam schedule consisting of 71.0 Gy in 2-Gy fractions. Using an average RBEmax value of 1.45 for I-125, the tumor (␣/)tum is calculated from Eq. 6 to be 0.82 Gy. Similarly, 124 Gy delivered via Pd-103 implants was found to be iso-effective to an external beam schedule of 73.1 Gy in 2-Gy fractions. Using this figure in conjunction with an RBE of 1.75, the ␣/ calculated from Eq. 6 drops further to 0.52 Gy. The above examples are for illustrative purposes only and these quickly calculated ␣/ values are in no way definitive. Additional sources of variation are associated with the manner in which the implant doses are defined (as discussed by Fowler et al. (1) and there is also the possibility that the RBEmax values are themselves tissue-specific. It has long been believed that RBEs are higher in slowly dividing tissues tumors, and some authors (10) have suggested that there is an inverse analytical relationship between RBEmax itself and the tissue ␣/ ratio, but this requires experimental validation. Furthermore, the doses (and dose rates) will vary within an implant, thus producing a spatial variation of RBE values. Despite these provisos, the omission of RBE from the more rigorous methods used by Fowler et al. (1) and Brenner and Hall (2) will likely have led to an overestimation of ␣/. The possibility that prostatic tumors may have an even higher fractionation and dose-rate sensitivity than is currently assumed holds many far-reaching implications for treatment strategies, and we suggest that the analyses be repeated to determine how the inclusion of a range of possible RBE values might alter their results. This discussion also highlights the need for further experimental work to determine the RBEs for I-125 and Pd-103 more precisely, especially at low-dose rates. ROGER G. DALE, PH.D., F.INST.P., F.I.P.E.M. BLEDDYN JONES, M.D., F.R.C.R., F.R.C.P. Radiation Physics and Radiobiology Charing Cross Hospital London, UK