Dose–volume conundrum for response of prostate cancer to brachytherapy: summary dosimetric measures and their relationship to tumor control probability

Int. J. Radiation Oncology Biol. Phys., Vol. 58, No. 5, pp. 1540 –1548, 2004 Copyright © 2004 Elsevier Inc. Printed in the USA. All rights reserved 0360-3016/04/$–see front matter

doi:10.1016/j.ijrobp.2003.09.016

CLINICAL INVESTIGATION

Prostate

DOSE–VOLUME CONUNDRUM FOR RESPONSE OF PROSTATE CANCER TO BRACHYTHERAPY: SUMMARY DOSIMETRIC MEASURES AND THEIR RELATIONSHIP TO TUMOR CONTROL PROBABILITY WARREN D. D’SOUZA, PH.D.,* HOWARD D. THAMES, PH.D.,†

AND

DEBORAH A. KUBAN, M.D.‡

Departments of *Radiation Physics, †Biomathematics, and ‡Radiation Oncology, The University of Texas M. D. Anderson Cancer Center, Houston, TX Purpose: Although it is known that brachytherapy dose distributions are highly heterogeneous, the effect of particular dose distribution patterns on tumor control probability (TCP) is unknown. It is unlikely that clinical results will throw light on the question in the near future, given the long follow-up and detailed dosimetry required for each patient. We used detailed dose distribution data from 50 patients combined with radiobiologic parameters consistent with what is known about TCP curves for prostate cancer to study the changes in TCP that accompany gross dosimetric measures and particular dosing irregularities (e.g., moderate underdosing of large volumes vs. extreme underdosing of small volumes). Methods and Materials: For each of the 50 patients with organ-confined prostate cancer who had undergone 125I prostate implants alone at our clinic, postimplant CT scans were obtained approximately 1 month after implantation. Dose distribution information was obtained from postimplant dosimetry. The percentage of the prostate volume receiving a specified dose was recorded from the respective differential dose–volume histograms in 10-Gy bins. In addition, the percentage of prostate volume underdosed at varying fractions of the prescription dose were determined, as was the minimal prostate dose. The log-normal distributions of the radiobiologic parameters [ln(initial clonogen number), ␣, and ␣/␤] were adjusted so that the predicted population parameters (steepness and location) of the dose–response curves for external beam radiotherapy agreed with the published estimates. The variability in the dose–volume details was increased by scaling the dose distributions by factors ranging from 0.7 to 1.5, thereby simulating, for each of the patients, nine new patients with different total doses but identical relative distributions of the dose over the voxels. Radiobiologic variability between the selected dose distributions was then removed by averaging >50 randomly chosen sets of radiobiologic parameters from the log-normal distributions to estimate the TCP for each of the dose distributions, giving some insight into the TCP variations with conventional dosimetric indexes and different patterns of underdosing. Results: Using the 450 dose distributions created by expanding the 50-patient data set, the volume of the prostate that was extremely underdosed (between 50% and 70% of the prescription dose) was related to the volume that was moderately underdosed (between 80% and 100% of the prescription dose). We found that the individual TCP is greatly dependent on the inhomogeneous dose distribution and the dosimetric indexes, such as the volume of prostate receiving 100% of the prescribed dose (V100) and the maximal dose received by 90% of the prostate volume (D90), which, by themselves, are not always accurate predictors of control probabilities. In a multivariate analysis of the dependence of TCP on these parameters (V100, D90, minimal dose, and moderately and severely underdosed volumes), only D90 and the minimal dose were statistically significant. Generally speaking, however, a lower minimal dose means a lower TCP. Conclusion: The work described here was an hypothesis-generating study. Our results showed that even if the V100 and D90 are nearly identical for 2 patients, there can be (and frequently are) significant differences in the dose distributions in the subvolumes of the prostate. Under simulated dose–response conditions (i.e., with variations in the dose distribution), the D90 and minimal dose significantly affected the TCP but the V100 and the volumes moderately or severely underdosed did not. In general, one must consider the totality of the dose distribution to evaluate the dosimetric quality of a low-dose-rate prostate implant. TCP is not a monotonic function of extreme or moderate underdosing. In some instances, extreme underdosing of relatively small volumes may result in a greater TCP than moderate underdosing of relatively large volumes and vice versa. © 2004 Elsevier Inc. Brachytherapy, Inhomogeneity, Prostate implant, Tumor control probability, Radiobiologic parameters.

Reprint requests to: Warren D. D’Souza, Ph.D., Department of Radiation Oncology, University of Maryland Medical Center, 22 S. Greene St., Baltimore, MD 21201. Tel: (410) 328-7159; Fax:

(410) 328-2618. E-mail: [email protected] Received May 5, 2003, and in revised form Aug 27, 2003. Accepted for publication Sep 3, 2003. 1540

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INTRODUCTION Transrectal ultrasound-guided low-dose-rate implants (1– 4) have become increasingly popular in the treatment of earlystage (T1-T2) prostate carcinoma. The use of CT scans done after implantation to evaluate the quality of the implant has been widely discussed in the literature (5– 8). The dose distribution resulting from such implants is inevitably highly inhomogeneous. Although the prescription minimal dose for such implants administered with 125I is 145 Gy, the protracted dose to subvolumes of the prostate can vary from 60 Gy to ⬎500 Gy. A sample differential dose–volume histogram (DVH) based on a dose distribution obtained from a postimplant CT scan is provided in Fig. 1a and highlights the inhomogeneity of the prostate implant dose distribution. Several authors have quoted various dosimetric indexes as indicators of implant quality. Willins and Wallner (5) reported that postimplant target volume coverage of ⱖ80% by the prescription isodose was adequate. An extensive review of postimplant dosimetry has cited several indexes, such as volume of the prostate receiving a specific dose and the isodose level that covers a specific fraction of the prostate, that may qualify as indicators of treatment efficacy (6, 7). In a study of 134 patients, Stock et al. (8) found that the dose was the most significant predictor of biochemical failure in a multivariate analysis using dose, prostate-specific antigen level, Gleason score, and stage. They found from postimplant CT-based dosimetric analysis that, patients in whom the maximal dose received by 90% of the prostate (D90) was ⬍140 Gy had a 4-year biochemical failure-free rate of 68% compared with a rate of 92% in patients in whom the D90 was ⱖ140 Gy. Another study by Vijverberg et al. (9) showed a statistically significant correlation between biopsy findings and the minimal dose delivered to the prostate. In most studies, the primary index used for evaluating the dosimetric quality of the prostate implants is the volume of the prostate receiving 100% of the prescribed dose (V100) or the D90. These indexes, by themselves, do not take into account differences in the dose distributions between subvolumes of different prostates. Consider for example, Fig. 1b, which shows a differential DVH obtained from postimplant dosimetry for 2 patients who underwent 125I implantation of the prostate. The V100 for Patients 1 and 2 was 91.8% and 91.9%, respectively. Additionally, the corresponding D90 for these patients was 147.9 Gy and 148.8 Gy. By the aforementioned broad criteria, these implants would be considered more or less equivalent. However, striking differences exist between the dose distributions in the subvolumes of the prostate, as is evident from the differential DVH shown in Fig. 1b. It is possible then to have dose distributions with almost identical gross descriptive parameters such as the V100 and D90 but with different subvolume dosing details. This could lead to dose distributions in which a large volume could be moderately underdosed (doses

Fig. 1. Differential dose–volume histogram (DVH) for 2 patients who underwent permanent 125I prostate implants with similar postimplant V100 and D90 values. V100 for Patients 1 and 2 was 91.8% and 91.9%, respectively. D90 for Patients 1 and 2 was 147.9 Gy and 148.8 Gy, respectively.

between 80% and 100% of the prescribed dose) or in which a small volume could be severely underdosed (doses between 50% and 70% of the prescribed dose). In this work, we used simulation techniques to study the impact of dosing differences in prostate subvolumes on the TCP. Our approach was to use real patient and simulated dose distributions in the subvolumes of the prostate and the radiobiologically predicted theoretical TCP to see how the former impacted the latter. In addition, the goal of this work was to determine whether moderate underdosing of a large volume or extreme underdosing of a small volume led to a

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greater theoretical TCP and to evaluate the validity of the conventional gross dosimetric parameters in predicting the theoretical TCP.

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for permanent brachytherapy implants. Assuming that subvolumes of the primary tumor survive independently of one another and that the number of surviving tumor clonogens is Poisson distributed, the TCP would be

METHODS AND MATERIALS

写 {e n

Assuming the validity of the linear-quadratic model for cell kill, the biologically effective dose for conventional external beam radiotherapy (BEDEBRT) delivered in n fractions with a fraction size d is given by BEDEBRT ⫽ nd共1 ⫹ d/(␣/␤) ⫺ 0.693(t-td)/(␣ Tp) where ␣ and ␤ are the radiosensitivity parameters for a given tumor associated with the linear and quadratic terms in the linear-quadratic model, respectively, t is the duration of treatment, td is the time delay after radiotherapy begins before cell proliferation, and Tp is the tumor potential doubling time. The BED for decaying low-dose-rate permanent implants (BEDBT) has been previously derived (11, 12): BEDBT ⫽ D{1 ⫹ R0/((␮ ⫹ ␭)(␣/␤))} ⫺ 0.693t/(␣ Tp) where D is the dose delivered with decaying low-doserate implants, Ro is the initial dose rate, ␮ is the sublethal damage repair constant, and ␭ is the isotope decay constant. td was assumed to be 0. Several competing phenomena are at play during a decaying low-dose-rate implant: cell killing by the protracted irradiation with a decaying dose rate, sublethal damage repair, and cell repopulation. The combination of these effects is such that there occurs a time beyond which no further increase in BED (or decrease in the surviving fraction) occurs (i.e., tumor repopulation is balanced by the instantaneous dose rate). The derivation of this time (Teff) has been previously discussed (13) and its incorporation into the linear-quadratic model to account for tumor repopulation described (14): Teff ⫽ 共1/ ␭ 兲 ln{Ro ␣ Tp/0.693} The dose delivered after this time, Teff, may be considered wasted dose and does not contribute to cell kill. Thus, the effective dose (Deff) delivered in a permanent implant with the consideration of repopulations effects is reduced: Deff ⫽ Ro/␭ ⫺ 0.693/(␣ ␭ Tp) Although the effect of the delay in repopulation, td was ignored (td ⫽ 0) in this work, the effect of it would be to increase the effective dose. If we assume a Poisson distribution of surviving tumor clonogens after treatment completion and uniform clonogen density, the TCP would equal e⫺KS, where K is the initial number of clonogens and S is the surviving fraction. In consideration of the above, this leads to the TCP

TCP ⫽

⫺Ke⫺r␣ viDi

冋

R oi 1⫹

(␮⫹␭)(␣/␤)

册}

i⫽1

where r is a multiplicative factor that approximates the relative biological effectiveness (RBE) effects of high linear energy transfer 125I radiation, vi is the fractional volume of the prostate receiving dose Di, Roi is the initial dose rate in subvolume (tumorlet) I, and n is the number of subvolumes in the prostate. The value of r assumed in our calculations was 1.2, in consideration of the published RBE data (15, 16). Note that Di is the effective dose to the ith tumorlet. Furthermore, for permanent implants, Roi ⫽ ␭Di. Fifty patients with organ-confined disease who had previously undergone ultrasound-guided 125I implants alone at our clinic between April 2000 and March 2001 were selected for this study. Each patient underwent a CT scan approximately 1 month after the implant. Postimplant dosimetry was performed after the scan. The prostate was contoured on each CT slice, and the seeds were identified in the Variseed (Varian Medical Systems, Milpitas, CA) planning system. Dosimetry data for this study were acquired from the CT scan at 1 month after implant, because edema is generally believed to be mostly resolved by 1 month after implantation (17–19). Although some variability existed in the dose–volume distributions for the 50 selected patients, this variability was still limited for purposes of studying the dependencies of moderately vs. severely underdosed volumes on the TCP (the entire dose–response curve). It would be unethical to alter the volumes of moderately or severely underdosed regions on purpose during an implant to obtain a wide range of variability in the dose distribution details in the subvolumes. For these reasons, the dose distributions for the 50 considered patients were scaled by factors ranging from 0.7 to 1.5 (in increments of 0.1) to simulate 400 additional dose distributions. This generated a total of 450 dose distributions (50 real dose distributions and 400 simulated dose distributions) with doses ranging from a minimum of approximately 45 Gy to a maximum of ⬎500 Gy. For each of the 450 dose distributions, fractional volumes of the prostate receiving doses in 10-Gy intervals (bins) were recorded from the differential DVH. Although the maximal dose received by the prostate was as great as 500 Gy or greater (the accuracy may depend on the dose calculation algorithm; note that the Variseed planning system uses a point source model in the dose calculation), doses ⬎275 Gy were found to result in ⬍0.5% change in the overall surviving fraction for the 450 dose distributions. A similar result has been previously described by Ling et al. (20) in which no improvement in TCP was noted with doses

Brachytherapy dosimetric measures and tumor-control probability

Fig. 2. Variation of tumor control probability (TCP) for 50-patient 125 I low-dose-rate dose distributions with the distribution of randomly selected radiobiologic parameters (a) ln(K), (b) ␣, and (c) ␣/␤ randomly selected from a log-normal distribution. Mean values of ln(K), ␣, and ␣/␤ in log-normal distribution were 20, 0.15 Gy⫺1, and 1.5 Gy, respectively. Corresponding standard deviations for ln(K), ␣, and ␣/␤ were 4.4, 0.25 Gy⫺1, and 0.1 Gy, respectively.

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Fig. 3. Dose–volume histogram distribution of tumor control probability (TCP) for dose distributions with (a) V100 ⱖ80% (median TCP, 0.53), (b) V100 ⱖ90% (median TCP, 0.62), and (c) D90 ⱖ140 Gy (median TCP, 0.60).

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Table 1. Summary of TCP obtained from analysis of 450 125I permanent implant dose distributions with V100 ⱖ80%, V100 ⱖ90%, and D90 ⱖ140 Gy

25th percentile Median 75th percentile

V100 ⱖ80%

V100 ⱖ90%

D90 ⱖ140 Gy

0.37 0.53 0.75

0.47 0.62 0.81

0.46 0.60 0.80

Abbreviations: TCP ⫽ tumor control probability; V100 ⫽ percentage of tumor receiving ⱖ100% of prescribed dose; D90 ⫽ maximal dose received by 90% of tumor.

greater than two times the prescription dose for tumors with low control probability and tumors with high control probability displayed no additional improvement with doses ⬎1.2 times the prescription dose. Hence, we only extended the abscissa in Fig. 1b up to 275 Gy. The minimal dose was defined as the maximal dose received by a volume of 99% of the prostate. Clinical outcomes with dose–volume data of the detail required for this study were unavailable, and we, therefore, resorted to simulating the TCP using radiobiologic models and the available dose–volume data. The TCP is strongly dependent on radiobiologic parameters such as the clonogen number (K) and the radiosensitivity parameters ␣ and ␤. Although the normally ascribed value for the tumor ␣/␤ ratio is 10 Gy, Brenner and Hall (21) reported a low ␣/␤ ratio of 1.5 Gy for the prostate, along with an estimate for the population ␣ ⫽ 0.036 Gy⫺1. Their initial publication has been supported by the conclusions of later articles (22–24). These are, however, population values, and individual radiobiologic parameters are needed when individual dose– volume data are used. The question was what distributions of individual parameters will lead to observed population dose–response curves? We constructed a dose–response curve by simulating the effect of total doses ranging from 56 to 78 Gy delivered with conventional external beam radiotherapy in 2-Gy fractions for a large number (20,000) of individual patients (to remove variability). Log-normal distributions for ln(K), ␣, and ␣/␤ and the mean values and standard deviations for these parameters were adjusted iteratively in the dose–response curve to obtain a control probability of approximately 70%. The individual and population tumor ␣/␤ values were assumed to be identical in the dose–response curve (25). By trial and error, we arrived at a mean value for the distribution of ln(K), ␣, and ␣/␤ of 20, 0.15 Gy⫺1, and 1.5 Gy, respectively. The corresponding standard deviations were 4.4, 0.25 Gy⫺1, and 0.1 Gy, respectively. These choices led to the population ␣ estimate of 0.026 Gy⫺1 (using maximal likelihood methods), close to the published estimate of Brenner and Hall of 0.036 Gy⫺1. Fifty random sets of ln(K), ␣, and ␣/␤ values were selected from these distributions and applied to each of the 450 dose distributions, and the TCP was calculated. The dependence of the TCP on the individual parameters is shown in Fig. 2.

Fig. 4. Variation of tumor control probability (TCP) as a function of (a) moderately and extremely underdosed subvolumes of prostate in 125I permanent implants. Moderately underdosed volumes were those that received between 0.8D and D, where D was the prescribed dose. Extremely underdosed subvolumes of prostate refer to those receiving between 0.5D and 0.7D. Each point represents a dose distribution with specific volumes receiving 80 –100% and 50 –70% of dose. A color code is provided such that blue dose distributions would have a TCP of 0.9 and red dose distributions would have a TCP of 0.1. (b) Left-most part of Fig. 4a (focus on smallest regions of underdose).

Because our goal was to explore the effect of dose heterogeneity on the TCP, radiobiologic variability between the selected dose distributions was removed by averaging over the 50 randomly chosen sets of parameters. Linear regression was applied to the TCP data on the basis of the averaged radiobi-

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Table 2. TCP for five selected dose distributions

Category 1 Category 2

Dose distribution 1

Dose distribution 2

Dose distribution 3

Dose distribution 4

Dose distribution 5

0.05 —

0.27 —

— 0.02

— 0.30

— 0.22

Abbreviation: TCP ⫽ tumor control probability. Dose distributions 1 and 2 comprise category 1 in which ⱕ10% of the prostate is moderately underdosed (80 –100% of prescribed dose) and ⱖ8.5% of the prostate is extremely underdosed (50 –70% of prescribed dose). Dose distributions 3, 4, and 5 comprise category 2 in which ⱖ20% of the prostate is moderately underdosed and ⱕ5% of the prostate is extremely underdosed.

ologic parameters to estimate the relative importance of V100, D90, and other dose–volume measures. RESULTS In Fig. 3, we present DVH distributions of the TCP for dose distributions in which the V100 was ⱖ80% and ⱖ90% and in which the D90 was ⱖ140 Gy. These values were selected in light of published implant quality results (5– 8, 10). Table 1 summarizes the results. The median TCP obtained from our analysis for a V100 of ⱖ 80%, V100 of ⱖ 90%, and D90 of ⱖ140 Gy was 0.53, 0.62, and 0.60, respectively. Figure 4 shows the variation in TCP as a function of the volume of the prostate receiving 80 –100% of the prescribed dose (moderate underdose) and 50 –70% of the prescribed dose (extreme underdose). Each point in Fig. 4 represents a dose distribution with specific volumes receiving 80 –100% and 50 –70% of the dose. The discreteness of Fig. 4 is the result of interpolation in regions in which data points exist (no interpolation was attempted in regions outside the range of the extreme and moderate underdosed volumes in all the dose distributions that we considered). The left bottom of Fig. 4 represents dose distributions that have relatively smaller volumes moderately and extremely underdosed. The right upper part of Fig. 4 represents dose distributions that have relatively larger volumes extremely and moderately underdosed. A color code is provided such that blue dose distributions would have a TCP of 0.9 and red dose distributions would have a TCP of 0.1. As expected, dose distributions with relatively smaller volumes extremely and moderately underdosed resulted in a greater theoretical TCP than dose distributions with relatively larger volumes extremely and moderately underdosed. The upper left of Fig. 4a represents dose distributions with relatively small volumes of moderate underdosing and relatively larger volumes of extreme underdosing. The bottom right represents dose distributions with relatively small volumes of extreme underdosing and relatively large volumes of moderate underdosing. It is not conclusive as to which of these scenarios might be preferable, because both regions display relatively moderate to low TCP values. Thus, TCP is not a monotonic function of either moderate or extreme underdosing (Fig. 4). Although moderate underdosing of a small volume may result in better TCPs in some

instances, extreme underdosing of small volumes may result in better TCPs in other instances. To illustrate this point further, we selected five sample dose distributions. Three of these dose distributions resulted in ⱕ10% of the prostate being moderately underdosed and ⱖ8.5% of the prostate being extremely underdosed. The other two dose distributions resulted in ⱖ20% of the prostate being moderately underdosed and ⱕ5% of the prostate being extremely underdosed. The TCP for each of these dose distributions is summarized in Table 2. The variation in TCP with commonly cited indexes of implant efficacy (e.g., V100 and D90) is presented in Fig. 5. The TCP decreased in a nonlinear (almost exponential) manner as a function of the volume of prostate receiving less than the prescribed dose (100 ⫺ V100). As a function of the D90, TCP displayed a nearly sigmoidal relationship. A similar relationship was found between the TCP and the minimal dose to the prostate (Fig. 6). However, the TCP values were more tightly bunched together with the minimal dose as the abscissa in the plot than with the D90. These relationships were explored further by linear regression model analysis of TCP with the covariates V100, D90, and minimal dose. Also included in the fit were volumes receiving between 80% and 100% of the prescribed dose (moderately underdosed) and volumes receiving between 50% and 70% of the prescribed dose (severely underdosed). The best-fitting model is shown in Table 3. Neither V100 nor the extremely or moderately underdosed volumes were statistically significant in any of the fits attempted; the minimal dose and D90 were statistically significant. Figure 7 displays the TCP for five dose distributions that resulted in V100 and D90 values within 1% and 1.75%, respectively, of each other. Despite the proximity in the equivalence of these indexes, these dose distributions showed marked variations in the differential DVHs (Fig. 7a). In addition, the variation in TCP is apparent (Figs. 7b,c). The dose distribution represented by the triangle marker (Fig. 7) had the second highest TCP despite having the lowest V100 value of the five dose distributions in question. The dose distribution represented by the diamond marker had the lowest TCP despite not having either the lowest V100 or D90 value. This was due to the relatively substantial fraction of the prostate receiving low doses.

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Fig. 6. Variation of tumor control probability (TCP) as a function of minimal prostate dose (maximal dose received by 99% of prostate volume) in low-dose-rate permanent 125I implants.

Fig. 5. Tumor control probability (TCP) as a function of (a) volume of prostate receiving ⬍100% of prescribed dose (100 ⫺ V100) and (b) D90 for 450 (50 real and 400 simulated) dose distributions. A series of 50 ␣ (Gy⫺1), ␣/␤ (Gy), and ln(K) values (obtained from log-normal distribution) were randomly assigned to each dose distribution. Tp was assumed to be 30 days for each prostate. Note that TCP values are not to be interpreted absolutely but rather relatively.

DISCUSSION The goal of this work was to study the impact of dose– volume dosimetric measures on the theoretically predicted TCP in low-dose-rate prostate brachytherapy. TCP was calculated by considering the doses to subvolumes of the prostate and the linear-quadratic model, along with modeling of the radiobiologic parameters. TCP was determined to be a nonmonotonic function of both moderate and severe underdosing of the prostate volume. Although a relationship between TCP and the conventional dosimetric indexes was found, linear regression model analysis showed that TCP

was only significant with the D90 and minimal dose. These results are consistent with the published clinical data of Stock et al. (8) and Vijverberg et al. (9). Although it is clear that dose distributions in which relatively small volumes are extremely and moderately underdosed lead to a greater TCP than those in which relatively large volumes are extremely and moderately underdosed, our data in Fig. 4 suggest that it cannot be generalized as to whether extremely underdosing a small fraction of the prostate leads to a lower TCP than moderately underdosing a relatively larger fraction. We used a relatively coarse definition for moderate (i.e., 80 –100%) and extreme (i.e., 50 –70%) underdosing. With finer resolution (e.g., 5% intervals), more definitive results might be possible. However, this would require consideration of significant number of dose distributions and differences in prostate subvolumes. This may only be possible by considering multi-institution pooled data with a variety of implantation techniques and seed activities. The data in the bottom right of the Fig. 4 represent dose distributions with large volumes moderately underdosed

Table 3. Multivariate analysis of TCP by dose–volume measures Quantity

Estimate

p

V100 D90 Minimal dose* Volume moderately underdosed† Volume severely underdosed‡ Constant

0.031 0.00053 0.0064 ⫺0.0032 ⫺0.00072 ⫺0.46

0.241 0.008 ⬍0.0005 0.382 0.881 0.085

Abbreviations as in Table 1. * Maximal dose received by 1% of tumor † Volume receiving 80 –100% of prescribed dose. ‡ Volume receiving 50 –70% of prescribed dose.

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(small volumes extremely underdosed), and the data in the top left represent dose distributions with volumes extremely underdosed. If it were always preferable to moderately underdose a relatively larger fraction of the prostate, the lower right portion of Fig. 4 would consistently display a greater TCP than the top left part of Fig. 4. This was further corroborated by the selective dose distributions identified in Table 2. The calculated TCP was comparable for dose distributions 1 and 3 (0.05 and 0.02) and for dose distributions 2, 4, and 5 (0.27, 0.30, and 0.22). Furthermore, it is possible to estimate one dose–volume index (e.g., target volume coverage of 80%) from another dose–volume index (e.g., V100; Fig. 7). For example, if 10% of the overall prostate volume receives less than the prescribed dose, at least 2% of the overall prostate volume will receive ⬍80% of the prescribed dose (i.e., if V100 id ⱖ90%, the target volume coverage of 80% will be ⱖ98%). We must state, however, that these values are peculiar to treatment planning (seed activity, planning involving seed and needle loading patterns) and delivery (Mick applicator). Our data in Fig. 5 suggest that the decrease in TCP is greatest for the first 10% of the prostate that is underdosed. This implies a greater drop in the TCP for a V100 decreasing from 100% to 90% than for a V100 decreasing from 90% to 80%. In addition, the TCP is an almost linear function of the D90 between approximately 120 Gy and 210 Gy. Increasing the D90 beyond 210 Gy did not result in proportionately linear gains in the TCP. The TCP displays a similar linear relationship with a minimal prostate dose between approximately 60 and 120 Gy (Fig. 6). The TCP shows marked differences between dose distributions that have V100 and D90 parameters within 2% of one another (Fig. 7). Even though these dosimetric indexes may be similar, the differential DVHs showed remarkable differences. The reliance on single dosimetric indexes is further complicated by the “crossing-over” of the differential DVHs. However, in the multivariate analysis of the dependence of TCP on these parameters (minimal dose, V100, D90, and moderately and severely underdosed volumes), only V100, and minimal dose, and moderately underdosed volume were statistically significant (25).

CONCLUSION

Fig. 7. (a) Differential dose–volume histograms of 5 patients whose postimplant dosimetry revealed V100 values within 1% of one another and D90 values within 1.75% of one another. TCP for 5 patients as a function of respective (b) V100 and (c) D90 values. Squares indicate Patient 1; circles, Patient 2; triangles, Patient 3; diamonds, Patient 4; and asterisks, Patient 5.

The work described here was an hypothesis-generating study. Our results showed that even if V100 and D90 are nearly identical for 2 patients, there can be (and frequently are) statistically significant differences in the dose distributions in the subvolumes of the prostate. Under simulated dose–response conditions (i.e., with wide variations in the prescribed dose), D90 and the minimal dose significantly affected the TCP but V100 and the volumes moderately or severely underdosed did not. One must consider the totality of the dose distribution to evaluate the dosimetric quality of

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a low-dose-rate prostate implant. TCP is not a monotonic function of extreme or moderately underdosed volume magnitudes. In some instances, extreme underdosing of rela-

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tively small volumes may result in a greater TCP than moderate underdosing of relatively large volumes and vice versa (26).

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