- Email: [email protected]
Modeling prostate cancer: In regards to Nahum et al. (Int J Radiat Oncol Biol Phys 2003;57:391–401)
Letters to the Editor fibroproliferative change in rat irradiated lung using soluble transforming growth factor-beta (TGF-) receptor mediated by adenoviral vector. Int J Radiat Oncol Biol Phys 2004;58:1235–1241. 2. Rabbani ZN, Anscher MS, Zhang X, et al. Soluble TGF type II receptor gene therapy ameliorates acute radiation-induced pulmonary injury in rats. Int J Radiat Oncol Biol Phys 2003;57:563–572. 3. van Eerde MR, Kampinga HH, Szabo BG, et al. Comparison of three rat strains for development of radiation-induced lung injury after hemithoracic irradiation. Radiother Oncol 2001;58:313–316. 4. Vujaskovic Z, Feng QF, Rabbani ZN, et al. Radioprotection of lungs by amifostine is associated with reduction in profibrogenic cytokine activity. Radiat Res 2002;157:656 – 660.
309
parameters are distributed normally (standard Gaussian distribution), based on the data reported in Table 1 of ref. (1), a simple statistical calculation gives us the means and standard deviations (SD) for ␣ and  as 0.26 ⫾ 0.21 Gy⫺1 and 0.031 ⫾ 0.022 Gy⫺2, respectively. These standard deviations are much larger than the standard errors used by Nahum et al. for ␣ and  (0.21 vs. 0.06 Gy⫺1 and 0.022 vs. 0.006 Gy⫺2 for ␣ and  respectively). The heterogeneity of radiosensitivities and its intrinsic distribution is characterized by the SD, instead of the standard error (SE) of the mean. By definition, the relation between the SE and SD is
SE ⫽
SD
兹n
,
(1)
MODELING PROSTATE CANCER: IN REGARDS TO NAHUM ET AL. (INT J RADIAT ONCOL BIOL PHYS 2003;57:391– 401) To the Editor: With great interest, we read the article by Nahum et al. (1) which adressed important issues related to the ␣/ ratio for prostate cancer. The authors used information derived from in vitro studies to examine how interpatient variability in radiosensitivity and tumor hypoxia impacts on the interpretation and analysis of clinical data for prostate cancer. They reported that the ␣/ ratio for prostate cancer is 8.5 and 15.5 Gy for well-oxygenated and hypoxic clonogens, respectively. These estimates are higher than the ␣/ ratios of 1.2–3.9 Gy derived from clinical data by other investigators (2– 8). The study reported by Nahum et al. raises questions about the potential usefulness of moving toward hypofractionation for the treatment of prostate cancer. However, as we point out in this letter, the Nahum et al. study contains several inconsistencies and some of the in vitro data used in their study are reported incorrectly. Whether or not the ␣/ ratio for prostate cancer is low (1.2–3.9 Gy) or high (8.5 Gy or higher) remains open to debate. Relevance and reliability of in vitro data: The analysis presented by Nahum et al. (1) was completely based on model parameters (e.g., ␣, , OER) obtained from in vitro experiments. The response of tumors cells in vivo may be quite different from in vitro responses because of a host of microenvironmental factors. Moreover, all of the in vitro data used by Nahum et al. are for exponentially cycling cells, which may be a poor surrogate for slow-growing prostate tumors. Such in vitro cultures are known to contain cells of various radiosensitivities (9 –11). This may be one of the explanations for the large variations of radiosensitivies observed among different in vitro measurements for various prostate cancer cell lines. The relevance of in vitro data for the prediction of clinical response is controversial. In a letter to the editor, King and Mayo (12) also compiled in vitro measurements for different prostate cancer cell lines [see Table 1 of ref. (12)]. According to their compilation, one can obtained the average values of ␣ and  as 0.19 Gy⫺1 and 0.035 Gy⫺2, which gives an ␣/ ratio of 5.4 Gy. The mean ␣ value is quite different from the value 0.26 Gy⫺1 used in Nahum et al.’s study, and even out of the range specified by the standard error (0.26 ⫾ 0.06 Gy⫺1). The larger value for ␣ reported by Nahum et al. arises because of two new data points that are not included in King and Mayo’s compilation. These two points, which are based on the measured data for the LnCap cell line, correspond to very large ␣ values (0.49 and 0.68 Gy⫺1, respectively) (13, 14). The ␣/ ratios obtained from the two data sets are 34 and 128 Gy, much higher than those from the other reported measurements. Also unusual is that the  value derived from the measured data that gave the largest value for ␣ (i.e., 0.68 Gy⫺1) is negative (⫺0.0053 Gy⫺2) (14). One of the most striking aspects of the in vitro radiosensitivity parameters reported in Table 1 of Nahum et al. (1) is that the differences in the radiosensitivity parameters determined from data reported by different laboratories are as large as or larger than the differences in radiosensitivity parameters observed among the various prostate cancer cell lines. This observation suggests that the details of the experimental protocol have a significant impact on estimates of radiosensitivity parameters. Estimating interpatient variability in tumor radiosensitivity parameters by pooling the available in vitro data is a highly questionable procedure, especially because the estimated mean and standard deviation could be easily biased by one or two outliers (e.g., the measurements from LnCap cell line). However, even if we assume that the data reported in Table 1 of ref. (1) reflects the true distribution of the radiosensitivity for prostate cancer cell lines, the average ␣/ ratio calculated using the same methodology as presented in ref. (1) is about 20 Gy, which is much larger than the claimed value of 8.5 Gy for the well-oxygenated prostate tumor cells. Standard deviation vs. standard error: If we assume the radiosensitivity
where n is the number of measurements. It is clear from Eq. 1 that the SE will approach zero as n becomes large. The mean and variance of the radiosensitivity distribution used to characterize interpatient variability should not depend on the sample size. Thus the SE of the mean is not an appropriate quantity for estimating interpatient variability of radiosensitivity. The results reported by Nahum et al. will be completely different if the SD associated with the radiosentivity parameters is used instead of the SE of the mean. Normal or log-normal distribution of radiosensitivity parameters: The assumption of the intrinsic radiosensitivity as a normal distribution is, at best, a crude approximation. From Table 1 of ref. (1), the report range for ␣ is from 0.06 to 0.68 Gy⫺1. The order of magnitude difference in the estimated values for ␣ indicates that the variance in the underlying distribution must be quite large. As pointed out previously, the arithmetic mean of ␣/ ratio (20 Gy) is quite different from the value (8.4 Gy) calculated from the mean values of ␣ and . This inconsistency indirectly demonstrates the assumption that radiosensitivity parameters are normally distributed is problematic and may not be realistic. In fact, Brenner and Hall (15) have shown that radiosensitivity parameters derived from 36 in vitro experiments are distributed approximately as a log-normal distribution. If the radiosensitivity parameters for the prostate cancer cell lines are log-normally distributed, the geometric mean will provide a much better approximation to estimate the linear-quadratic model parameters than the arithmetic mean. The data shown in Table 1 of ref. (1) give the geometric mean of ␣ and  as 0.19 Gy⫺1 and 0.023 Gy⫺2 respectively. The ␣/ ratio calculated from geometric mean of ␣ and  is 8.3 Gy, which is very consistent with the geometric mean of the ␣/ ratio (8.2 Gy) directly calculated from the ␣/ values listed in Table 1 of Nahum et al. The good agreement implies that a log-normal distribution provides a better description of the in vitro radiosensitivity than a normal distribution. Very different results would be expected from the Nahum et al. study if a log-normal distribution is used instead of a normal distribution. Heterogeneity of tumor hypoxia: In their study, the authors used in vitro OER values (1.75 and 3.25 for OER␣ and OER, respectively) to model prostate cancer in vivo. However, for tumors in vivo, the degree of hypoxia depends on the individual local tumor microenvironment including tumor microvascularity and other factors (16, 17). In contrast to in vitro situation, the population for tumors in vivo always reflects a spectrum of hypoxia. Even for well-identified hypoxic tumor patient groups, hypoxic cells may exist only in subvolumes of the tumor. Therefore, the effective OER for clinical response may be much smaller than the OER determined from in vitro experiments using anoxic conditions. In addition, Zolzer and Streffer (18) argued that tumors in vivo should be dominated by chronic hypoxia and the radiosensitivity for cells under chronic hypoxia conditions would be higher than those under acute hypoxia conditions. They reported two OER measurements of human-tumor cell lines under continued/chronic hypoxia conditions (1.3 and 1.5 for MeWo and squamous carcinoma 4451, respectively), which are quite different from the OER values measured under acute hypoxia conditions. Incorrectly cited radiosensitivity parameters and calculated error bars for clinical data: Two values of ␣,  in Table 1 of Nahum et al. (1) were incorrectly cited. The value of ␣ reported by Leith et al. (13) for PC-3 cell line was 0.487 Gy⫺1 and not 0.521 Gy⫺1 as shown in Table 1 of ref. (1). One of the  values of the LnCap cell line was negative in the original literature (14), but was treated as a positive value in this article (i.e., the value of 0.0053 Gy⫺2 was used instead of ⫺0.0053 Gy⫺2). The method used to calculate the error bars for clinical data in ref. (1) was 冑n/n. In general, the clinical data are presumed to follow a binomial distribution, and the variance of bNED (no evidence of disease from rising PSA levels) is calculated as,
310
I. J. Radiation Oncology
2 bNED ⫽
np(1 ⫺ p) n
2
● Biology ● Physics
,
(2)
where n is the number of patients at a dose point, and p is the proportion of the successful outcome (bNED). In summary, we have found that the article by Dr. Nahum et al. contains several inconsistencies and some of the measured data are reported and interpreted incorrectly. Although Nahum et al. suggest that tumor hypoxia and the heterogeneity of radiosensitivity may have a significant impact on the analysis of clinical data, the reported study and data analysis does not provide a sufficient basis to address the question of whether the ␣/ ratio for prostate cancer is low or high. JIAN Z. WANG, PH.D. NINA A. MAYR, M.D. Radiation Oncology Center Department of Radiological Sciences University of Oklahoma Health Science Center Oklahoma City, Oklahoma X. ALLEN LI, PH.D. Department of Radiation Oncology Medical College of Wisconsin Milwaukee, Wisconsin ROBERT D. STEWART, PH.D. School of Health Sciences Purdue University West Lafayette, Indiana doi:10.1016/j.ijrobp.2004.08.043 1. Nahum AE, Movsas B, Horwitz EM, et al. Incorporating clinical measurements of hypoxia into tumor local control modeling of prostate cancer: Implications for the ␣/ ratio. Int J Radiat Oncol Biol Phys 2003;57:391– 401. 2. Brenner DJ, Hall EJ. Fractionation and protraction for radiotherapy of prostate carcinoma. Int J Radiat Oncol Biol Phys 1999;43:1095–1101. 3. Fowler J, Chappell R, Ritter M. Is ␣/ for prostate cancer really low? Int J Radiat Oncol Biol Phys 2001;50:1021–1031. 4. Brenner DJ, Martinez AA, Edmundson GK, et al. Direct evidence that prostate tumors show high sensitivity to fractionation (low ␣/ ratio), similar to late-responding normal tissue. Int J Radiat Oncol Biol Phys 2002;52:6 –13. 5. Wang JZ, Guerrero M, Li XA. How low is the ␣/ ratio for prostate cancer? Int J Radiat Oncol Biol Phys 2003;55:194 –203. 6. Wang JZ, Li XA, Yu CX, et al. The low ␣/ ratio for prostate cancer: What does the clinical outcome of HDR brachytherapy tell us? Int J Radiat Oncol Biol Phys 2003;57:1101–1108. 7. Kal HB, Van Gellekom MPR. How low is the ␣/ ratio for prostate cancer? Int J Radiat Oncol Biol Phys 2003;57:1116 –1121. 8. Carlone M, Wilkins D, Balazs N, et al. TCP isoeffect analysis using a heterogeneous distribution of radiosensitivity. Med Phys 2004;31: 1176 –1182. 9. Sinclair WK, Morton RA. Variation in X-ray response during the division cycle of partially synchronized Chinese hamster cells in culture. Nature 1963;199:1158 –1160. 10. Sinclair WK, Morton RA. X-ray and ultraviolet sensitivity of synchronized Chinese hamster cells at various stages of the cell cycle. Biophys J 1965;5:609 – 621. 11. Gillespie CJ, Chapman JD, Reuvers AP, et al. The inactivation of Chinese hamster cells by X-rays: Synchronized and exponential cell populations. Radiat Res 1975;64:353–364. 12. King CR, Mayo CS. Is the prostate ␣/ ratio of 1.5 from Brenner and Hall a modeling artifact [Letter]? Int J Radiat Oncol Biol Phys 2000; 47:536 –538. 13. Leith JT, Quaranto L, Padfield G, et al. Radiobiological studies of PC-3 and DU-145 human prostate cancer cells: X-ray sensitivity in vitro and hypoxic fractions of xenografted tumors in vivo. Int J Radiat Oncol Biol Phys 1993;25:283–287. 14. Leith JT. In vitro radiation sensitivity of the LNCaP prostate tumor cell line. Prostate 1994;24:119 –124. 15. Brenner DJ, Hall EJ. Conditions for the equivalence of continuous to pulsed low dose rate brachytherapy. Int J Radiat Oncol Biol Phys 1991;20:181–190. 16. Mayr NA, Hawighorst H, Yuh WTC, et al. MR microcirculation in
Volume 61, Number 1, 2005 cervical cancer; correlations with histomorphological tumor markers and clinical outcome. JMRI 1999;10:267–276. 17. Montebello JM, Mayr NA, Yuh WTC, et al. Dynamic contrastenhanced MR imaging for predicting tumor control in patients with cervical cancer. In: Jackson A, Buckley DL, Parker GJM, editors. Dynamic contrast-enhanced magnetic resonance imaging in Oncology. New York: Springer Verlag; 2005. In press. 18. Zolzer F, Streffer C. Increased radiosensitivity with chronic hypoxia in four human tumor cell lines Int J Radiat Oncol Biol Phys 2002;54:910 –920.
IN RESPONSE TO DR. WANG ET AL. To the Editor: We would like to thank Drs. Wang et al. for their recent comments and concerns about our recent article (1), which presented modeling data for human prostate cancer incorporating new information about the oxygenation status of that disease. Several of the points they raise are valid (many deal with the statistical handling of data) but, in the end, they do not dissuade us from our conviction that we have demonstrated that the ␣/ ratio need not be low to explain the clinical data. First, those of us who have devoted much of our career to the precise definition of the intrinsic radiosensitivity of tumor cell lines in vitro and tumor clonogens in vivo share the frustration of not knowing, with certainty, the radiosensitivity of prostate cancer cells in situ. A quick read of a recent review article by one of us (2) will serve to support our belief that the linear-quadratic model of radiation sensitivity strictly applies to homogeneous populations of cells only. That article describes some of the “laboratory tricks” required with cells lines in vitro to approach this ideal situation, such as cell synchronization, the use of low temperature during irradiation to inhibit the repair of the -sublesions, and the use of standard chemical environments, to name a few. When precise linear-quadratic parameters are extracted from survival curves generated with synchronized cells (3, 4), the ␣- inactivation coefficient for any one cell line was found to vary only slightly throughout the interphase of its cell cycle. Thus the large differences observed for the ␣-coefficient of different tumor cells lines reflect largely differences in the intrinsic radiosensitivity of cells in interphase. This difference is also observed when human tumor cells are irradiated as quiescent, stationary-phase populations. But at mitosis, the ␣-coefficient increases dramatically to a large value that is quite similar for different cell lines (4, 5) and equal to those of the most “repair-deficient” lines (6). For asynchronous populations of tumor cells, their ␣-inactivation coefficient is some complex average of those exhibited throughout the cell cycle weighted by their distribution frequency (3). Consequently, we chose to use the simple (arithmetic) average of the single-hit inactivation coefficients of prostate cancer cell lines that had been published. This article and previous studies indicate that the double-hit mechanism (-inactivation) contributed only a minor component of the total tumor cell kill when daily fractionated doses of 2 Gy and less and low-dose-rate brachytherapy are used. We agree with the suggestion that the elimination of the high ␣-values for LnCap cells obtained by different laboratories (or, for that matter, the low values for TSU cells) would alter the average ␣-coefficient that was employed in our study. We apologize for entering an incorrect value of ␣ for PC-3 cells (0.521 should read 0.487 Gy–1) and for omitting the negative sign from the -coefficient for one determination of radiosensitivity for LnCap cells in Table 1 (1). We can assure the readers that these errors did not affect significantly the “message” of the study because the average value for ␣ that we used would be changed negligibly, and, second, the -inactivation mechanism accounts for only a very small proportion of the total cell kill. We considered using only those inactivation parameters of human prostate cancer cells obtained in our laboratory (2, 7), which we knew had been generated by standard procedures using low temperature to inhibit the repair of the sublethal -damage during the irradiation process. This usually resulted in a larger value for the -inactivation parameter, because the repair that can occur at room temperature over 20 –30 minutes of irradiation is minimized. The average ␣-inactivation obtained from only our survival curves was 0.28 Gy–1, quite close to the average generated with data from all the different studies. And because we had no insight to suggest that some measures might be more precise than others, we included all values to obtain an average value of 0.26 Gy–1. And, yes, we did proceed to use the standard error of the mean rather than the standard deviation to give us an estimate of ␣. We surmised that a significant part of the standard deviation observed between the parameters would arise from differences in the experimental procedures used in the different
309
parameters are distributed normally (standard Gaussian distribution), based on the data reported in Table 1 of ref. (1), a simple statistical calculation gives us the means and standard deviations (SD) for ␣ and  as 0.26 ⫾ 0.21 Gy⫺1 and 0.031 ⫾ 0.022 Gy⫺2, respectively. These standard deviations are much larger than the standard errors used by Nahum et al. for ␣ and  (0.21 vs. 0.06 Gy⫺1 and 0.022 vs. 0.006 Gy⫺2 for ␣ and  respectively). The heterogeneity of radiosensitivities and its intrinsic distribution is characterized by the SD, instead of the standard error (SE) of the mean. By definition, the relation between the SE and SD is
SE ⫽
SD
兹n
,
(1)
MODELING PROSTATE CANCER: IN REGARDS TO NAHUM ET AL. (INT J RADIAT ONCOL BIOL PHYS 2003;57:391– 401) To the Editor: With great interest, we read the article by Nahum et al. (1) which adressed important issues related to the ␣/ ratio for prostate cancer. The authors used information derived from in vitro studies to examine how interpatient variability in radiosensitivity and tumor hypoxia impacts on the interpretation and analysis of clinical data for prostate cancer. They reported that the ␣/ ratio for prostate cancer is 8.5 and 15.5 Gy for well-oxygenated and hypoxic clonogens, respectively. These estimates are higher than the ␣/ ratios of 1.2–3.9 Gy derived from clinical data by other investigators (2– 8). The study reported by Nahum et al. raises questions about the potential usefulness of moving toward hypofractionation for the treatment of prostate cancer. However, as we point out in this letter, the Nahum et al. study contains several inconsistencies and some of the in vitro data used in their study are reported incorrectly. Whether or not the ␣/ ratio for prostate cancer is low (1.2–3.9 Gy) or high (8.5 Gy or higher) remains open to debate. Relevance and reliability of in vitro data: The analysis presented by Nahum et al. (1) was completely based on model parameters (e.g., ␣, , OER) obtained from in vitro experiments. The response of tumors cells in vivo may be quite different from in vitro responses because of a host of microenvironmental factors. Moreover, all of the in vitro data used by Nahum et al. are for exponentially cycling cells, which may be a poor surrogate for slow-growing prostate tumors. Such in vitro cultures are known to contain cells of various radiosensitivities (9 –11). This may be one of the explanations for the large variations of radiosensitivies observed among different in vitro measurements for various prostate cancer cell lines. The relevance of in vitro data for the prediction of clinical response is controversial. In a letter to the editor, King and Mayo (12) also compiled in vitro measurements for different prostate cancer cell lines [see Table 1 of ref. (12)]. According to their compilation, one can obtained the average values of ␣ and  as 0.19 Gy⫺1 and 0.035 Gy⫺2, which gives an ␣/ ratio of 5.4 Gy. The mean ␣ value is quite different from the value 0.26 Gy⫺1 used in Nahum et al.’s study, and even out of the range specified by the standard error (0.26 ⫾ 0.06 Gy⫺1). The larger value for ␣ reported by Nahum et al. arises because of two new data points that are not included in King and Mayo’s compilation. These two points, which are based on the measured data for the LnCap cell line, correspond to very large ␣ values (0.49 and 0.68 Gy⫺1, respectively) (13, 14). The ␣/ ratios obtained from the two data sets are 34 and 128 Gy, much higher than those from the other reported measurements. Also unusual is that the  value derived from the measured data that gave the largest value for ␣ (i.e., 0.68 Gy⫺1) is negative (⫺0.0053 Gy⫺2) (14). One of the most striking aspects of the in vitro radiosensitivity parameters reported in Table 1 of Nahum et al. (1) is that the differences in the radiosensitivity parameters determined from data reported by different laboratories are as large as or larger than the differences in radiosensitivity parameters observed among the various prostate cancer cell lines. This observation suggests that the details of the experimental protocol have a significant impact on estimates of radiosensitivity parameters. Estimating interpatient variability in tumor radiosensitivity parameters by pooling the available in vitro data is a highly questionable procedure, especially because the estimated mean and standard deviation could be easily biased by one or two outliers (e.g., the measurements from LnCap cell line). However, even if we assume that the data reported in Table 1 of ref. (1) reflects the true distribution of the radiosensitivity for prostate cancer cell lines, the average ␣/ ratio calculated using the same methodology as presented in ref. (1) is about 20 Gy, which is much larger than the claimed value of 8.5 Gy for the well-oxygenated prostate tumor cells. Standard deviation vs. standard error: If we assume the radiosensitivity
where n is the number of measurements. It is clear from Eq. 1 that the SE will approach zero as n becomes large. The mean and variance of the radiosensitivity distribution used to characterize interpatient variability should not depend on the sample size. Thus the SE of the mean is not an appropriate quantity for estimating interpatient variability of radiosensitivity. The results reported by Nahum et al. will be completely different if the SD associated with the radiosentivity parameters is used instead of the SE of the mean. Normal or log-normal distribution of radiosensitivity parameters: The assumption of the intrinsic radiosensitivity as a normal distribution is, at best, a crude approximation. From Table 1 of ref. (1), the report range for ␣ is from 0.06 to 0.68 Gy⫺1. The order of magnitude difference in the estimated values for ␣ indicates that the variance in the underlying distribution must be quite large. As pointed out previously, the arithmetic mean of ␣/ ratio (20 Gy) is quite different from the value (8.4 Gy) calculated from the mean values of ␣ and . This inconsistency indirectly demonstrates the assumption that radiosensitivity parameters are normally distributed is problematic and may not be realistic. In fact, Brenner and Hall (15) have shown that radiosensitivity parameters derived from 36 in vitro experiments are distributed approximately as a log-normal distribution. If the radiosensitivity parameters for the prostate cancer cell lines are log-normally distributed, the geometric mean will provide a much better approximation to estimate the linear-quadratic model parameters than the arithmetic mean. The data shown in Table 1 of ref. (1) give the geometric mean of ␣ and  as 0.19 Gy⫺1 and 0.023 Gy⫺2 respectively. The ␣/ ratio calculated from geometric mean of ␣ and  is 8.3 Gy, which is very consistent with the geometric mean of the ␣/ ratio (8.2 Gy) directly calculated from the ␣/ values listed in Table 1 of Nahum et al. The good agreement implies that a log-normal distribution provides a better description of the in vitro radiosensitivity than a normal distribution. Very different results would be expected from the Nahum et al. study if a log-normal distribution is used instead of a normal distribution. Heterogeneity of tumor hypoxia: In their study, the authors used in vitro OER values (1.75 and 3.25 for OER␣ and OER, respectively) to model prostate cancer in vivo. However, for tumors in vivo, the degree of hypoxia depends on the individual local tumor microenvironment including tumor microvascularity and other factors (16, 17). In contrast to in vitro situation, the population for tumors in vivo always reflects a spectrum of hypoxia. Even for well-identified hypoxic tumor patient groups, hypoxic cells may exist only in subvolumes of the tumor. Therefore, the effective OER for clinical response may be much smaller than the OER determined from in vitro experiments using anoxic conditions. In addition, Zolzer and Streffer (18) argued that tumors in vivo should be dominated by chronic hypoxia and the radiosensitivity for cells under chronic hypoxia conditions would be higher than those under acute hypoxia conditions. They reported two OER measurements of human-tumor cell lines under continued/chronic hypoxia conditions (1.3 and 1.5 for MeWo and squamous carcinoma 4451, respectively), which are quite different from the OER values measured under acute hypoxia conditions. Incorrectly cited radiosensitivity parameters and calculated error bars for clinical data: Two values of ␣,  in Table 1 of Nahum et al. (1) were incorrectly cited. The value of ␣ reported by Leith et al. (13) for PC-3 cell line was 0.487 Gy⫺1 and not 0.521 Gy⫺1 as shown in Table 1 of ref. (1). One of the  values of the LnCap cell line was negative in the original literature (14), but was treated as a positive value in this article (i.e., the value of 0.0053 Gy⫺2 was used instead of ⫺0.0053 Gy⫺2). The method used to calculate the error bars for clinical data in ref. (1) was 冑n/n. In general, the clinical data are presumed to follow a binomial distribution, and the variance of bNED (no evidence of disease from rising PSA levels) is calculated as,
310
I. J. Radiation Oncology
2 bNED ⫽
np(1 ⫺ p) n
2
● Biology ● Physics
,
(2)
where n is the number of patients at a dose point, and p is the proportion of the successful outcome (bNED). In summary, we have found that the article by Dr. Nahum et al. contains several inconsistencies and some of the measured data are reported and interpreted incorrectly. Although Nahum et al. suggest that tumor hypoxia and the heterogeneity of radiosensitivity may have a significant impact on the analysis of clinical data, the reported study and data analysis does not provide a sufficient basis to address the question of whether the ␣/ ratio for prostate cancer is low or high. JIAN Z. WANG, PH.D. NINA A. MAYR, M.D. Radiation Oncology Center Department of Radiological Sciences University of Oklahoma Health Science Center Oklahoma City, Oklahoma X. ALLEN LI, PH.D. Department of Radiation Oncology Medical College of Wisconsin Milwaukee, Wisconsin ROBERT D. STEWART, PH.D. School of Health Sciences Purdue University West Lafayette, Indiana doi:10.1016/j.ijrobp.2004.08.043 1. Nahum AE, Movsas B, Horwitz EM, et al. Incorporating clinical measurements of hypoxia into tumor local control modeling of prostate cancer: Implications for the ␣/ ratio. Int J Radiat Oncol Biol Phys 2003;57:391– 401. 2. Brenner DJ, Hall EJ. Fractionation and protraction for radiotherapy of prostate carcinoma. Int J Radiat Oncol Biol Phys 1999;43:1095–1101. 3. Fowler J, Chappell R, Ritter M. Is ␣/ for prostate cancer really low? Int J Radiat Oncol Biol Phys 2001;50:1021–1031. 4. Brenner DJ, Martinez AA, Edmundson GK, et al. Direct evidence that prostate tumors show high sensitivity to fractionation (low ␣/ ratio), similar to late-responding normal tissue. Int J Radiat Oncol Biol Phys 2002;52:6 –13. 5. Wang JZ, Guerrero M, Li XA. How low is the ␣/ ratio for prostate cancer? Int J Radiat Oncol Biol Phys 2003;55:194 –203. 6. Wang JZ, Li XA, Yu CX, et al. The low ␣/ ratio for prostate cancer: What does the clinical outcome of HDR brachytherapy tell us? Int J Radiat Oncol Biol Phys 2003;57:1101–1108. 7. Kal HB, Van Gellekom MPR. How low is the ␣/ ratio for prostate cancer? Int J Radiat Oncol Biol Phys 2003;57:1116 –1121. 8. Carlone M, Wilkins D, Balazs N, et al. TCP isoeffect analysis using a heterogeneous distribution of radiosensitivity. Med Phys 2004;31: 1176 –1182. 9. Sinclair WK, Morton RA. Variation in X-ray response during the division cycle of partially synchronized Chinese hamster cells in culture. Nature 1963;199:1158 –1160. 10. Sinclair WK, Morton RA. X-ray and ultraviolet sensitivity of synchronized Chinese hamster cells at various stages of the cell cycle. Biophys J 1965;5:609 – 621. 11. Gillespie CJ, Chapman JD, Reuvers AP, et al. The inactivation of Chinese hamster cells by X-rays: Synchronized and exponential cell populations. Radiat Res 1975;64:353–364. 12. King CR, Mayo CS. Is the prostate ␣/ ratio of 1.5 from Brenner and Hall a modeling artifact [Letter]? Int J Radiat Oncol Biol Phys 2000; 47:536 –538. 13. Leith JT, Quaranto L, Padfield G, et al. Radiobiological studies of PC-3 and DU-145 human prostate cancer cells: X-ray sensitivity in vitro and hypoxic fractions of xenografted tumors in vivo. Int J Radiat Oncol Biol Phys 1993;25:283–287. 14. Leith JT. In vitro radiation sensitivity of the LNCaP prostate tumor cell line. Prostate 1994;24:119 –124. 15. Brenner DJ, Hall EJ. Conditions for the equivalence of continuous to pulsed low dose rate brachytherapy. Int J Radiat Oncol Biol Phys 1991;20:181–190. 16. Mayr NA, Hawighorst H, Yuh WTC, et al. MR microcirculation in
Volume 61, Number 1, 2005 cervical cancer; correlations with histomorphological tumor markers and clinical outcome. JMRI 1999;10:267–276. 17. Montebello JM, Mayr NA, Yuh WTC, et al. Dynamic contrastenhanced MR imaging for predicting tumor control in patients with cervical cancer. In: Jackson A, Buckley DL, Parker GJM, editors. Dynamic contrast-enhanced magnetic resonance imaging in Oncology. New York: Springer Verlag; 2005. In press. 18. Zolzer F, Streffer C. Increased radiosensitivity with chronic hypoxia in four human tumor cell lines Int J Radiat Oncol Biol Phys 2002;54:910 –920.
IN RESPONSE TO DR. WANG ET AL. To the Editor: We would like to thank Drs. Wang et al. for their recent comments and concerns about our recent article (1), which presented modeling data for human prostate cancer incorporating new information about the oxygenation status of that disease. Several of the points they raise are valid (many deal with the statistical handling of data) but, in the end, they do not dissuade us from our conviction that we have demonstrated that the ␣/ ratio need not be low to explain the clinical data. First, those of us who have devoted much of our career to the precise definition of the intrinsic radiosensitivity of tumor cell lines in vitro and tumor clonogens in vivo share the frustration of not knowing, with certainty, the radiosensitivity of prostate cancer cells in situ. A quick read of a recent review article by one of us (2) will serve to support our belief that the linear-quadratic model of radiation sensitivity strictly applies to homogeneous populations of cells only. That article describes some of the “laboratory tricks” required with cells lines in vitro to approach this ideal situation, such as cell synchronization, the use of low temperature during irradiation to inhibit the repair of the -sublesions, and the use of standard chemical environments, to name a few. When precise linear-quadratic parameters are extracted from survival curves generated with synchronized cells (3, 4), the ␣- inactivation coefficient for any one cell line was found to vary only slightly throughout the interphase of its cell cycle. Thus the large differences observed for the ␣-coefficient of different tumor cells lines reflect largely differences in the intrinsic radiosensitivity of cells in interphase. This difference is also observed when human tumor cells are irradiated as quiescent, stationary-phase populations. But at mitosis, the ␣-coefficient increases dramatically to a large value that is quite similar for different cell lines (4, 5) and equal to those of the most “repair-deficient” lines (6). For asynchronous populations of tumor cells, their ␣-inactivation coefficient is some complex average of those exhibited throughout the cell cycle weighted by their distribution frequency (3). Consequently, we chose to use the simple (arithmetic) average of the single-hit inactivation coefficients of prostate cancer cell lines that had been published. This article and previous studies indicate that the double-hit mechanism (-inactivation) contributed only a minor component of the total tumor cell kill when daily fractionated doses of 2 Gy and less and low-dose-rate brachytherapy are used. We agree with the suggestion that the elimination of the high ␣-values for LnCap cells obtained by different laboratories (or, for that matter, the low values for TSU cells) would alter the average ␣-coefficient that was employed in our study. We apologize for entering an incorrect value of ␣ for PC-3 cells (0.521 should read 0.487 Gy–1) and for omitting the negative sign from the -coefficient for one determination of radiosensitivity for LnCap cells in Table 1 (1). We can assure the readers that these errors did not affect significantly the “message” of the study because the average value for ␣ that we used would be changed negligibly, and, second, the -inactivation mechanism accounts for only a very small proportion of the total cell kill. We considered using only those inactivation parameters of human prostate cancer cells obtained in our laboratory (2, 7), which we knew had been generated by standard procedures using low temperature to inhibit the repair of the sublethal -damage during the irradiation process. This usually resulted in a larger value for the -inactivation parameter, because the repair that can occur at room temperature over 20 –30 minutes of irradiation is minimized. The average ␣-inactivation obtained from only our survival curves was 0.28 Gy–1, quite close to the average generated with data from all the different studies. And because we had no insight to suggest that some measures might be more precise than others, we included all values to obtain an average value of 0.26 Gy–1. And, yes, we did proceed to use the standard error of the mean rather than the standard deviation to give us an estimate of ␣. We surmised that a significant part of the standard deviation observed between the parameters would arise from differences in the experimental procedures used in the different