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Influence of Prostatic Edema on 131Cs Permanent Prostate Seed Implants: A Dosimetric and Radiobiological Study
Int. J. Radiation Oncology Biol. Phys., Vol. 80, No. 2, pp. 621–627, 2011 Copyright Ó 2011 Elsevier Inc. Printed in the USA. All rights reserved 0360-3016/$–see front matter
doi:10.1016/j.ijrobp.2010.07.001
PHYSICS CONTRIBUTION
INFLUENCE OF PROSTATIC EDEMA ON 131CS PERMANENT PROSTATE SEED IMPLANTS: A DOSIMETRIC AND RADIOBIOLOGICAL STUDY THAN S. KEHWAR, PH.D., D.SC., HEATHER A. JONES, M.D., PH.D., M. SAIFUL HUQ, PH.D., AND RYAN P. SMITH, M.D. Department of Radiation Oncology, University of Pittsburgh Cancer Institute, UPMC Cancer Centers, Pittsburgh, Pennsylvania Purpose: To study the influence of prostatic edema on postimplant physical and radiobiological parameters using 131Cs permanent prostate seed implants. Methods and Materials: Thirty-one patients with early prostate cancer who underwent 131Cs permanent seed implantation were evaluated. Dose-volume histograms were generated for each set of prostate volumes obtained at preimplantation and postimplantion days 0, 14, and 28 to compute quality indices (QIs) and fractional doses at level x (FDx). A set of equations for QI, FDx, and biologically effective doses at dose level Dx (BEDx) were defined to account for edema changes with time after implant. Results: There were statistically significant differences found between QIs of pre- and postimplant plans at day 0, except for the overdose index (ODI). QIs correlated with postimplant time, and FDx was found to increase with increasing postimplant time. With the effect of edema, BED at different dose levels showed less improvement due to the short half-life of 131Cs, which delivers about 85% of the prescribed dose before the prostate reaches its original volume due to dissipation of edema. Conclusions: Results of the study show that QIs, FDx, and BEDs at the level of Dx changed from preneedle plans to postimplant plans and have statistically significant differences (p < 0.05), except for the ODI (p = 0.106), which suggests that at the time of 131C seed implantation, the effect of edema must be accounted for when defining the seed positions, to avoid the possibility of poor dosimetric and radiobiologic results for 131Cs seed implants. Ó 2011 Elsevier Inc. Quality indices, Biologically effective dose, Effective treatment time, Prostatic edema, Fractional doses.
In this study, we present the results of our investigation of the potential effects of edema on various quality indices (QIs), which were defined previously (16–20) for low-dose-rate interstitial seed implants and biologically effective doses (BED) at D80, D90 and D100.
INTRODUCTION Iodine-125 (125I) and palladium-103 (103Pd) seed implants are used routinely as a monotherapy or a boost to a course of external beam radiation therapy (EBRT) (1 – 3) for the treatment of localized prostate cancer. Recently, cesium-131 (131Cs) seeds have been introduced (IsoRay, Inc., Richmond,WA) for permanent prostate implants. The dosimetric characteristics of 131 Cs seeds are similar to those of 125I and 103Pd seeds, with the exception that 131Cs seeds have a short half-life of 9.7 days (4, 5). Many studies have suggested that shorter-halflife radioactive seeds offer better tumor control than longerhalf-life radioactive seeds (6, 7). Published reports of 125I and 103Pd prostate implants are based on an evaluation of preimplant volumes or postimplant volumes of the prostate obtained after 1 month of implantation (2, 6–8). The effect of prostatic edema on dosimetric quantities has been studied by many investigators (9–13). However, few studies (11, 12, 14, 15) have been reported for 131Cs implants. Details about the effect of edema on these study patients have been described previously (15).
METHODS AND MATERIALS Patients Thirty-one prostate cancer patients who underwent permanent Cs seed implantation were included in this study. Patient data, implantation techniques, procedures, dose prescriptions, and dose limits to the urethra have been previously described in detail (14). Briefly, 131 Cs seeds were implanted using a real-time procedure and peripheral loading, with central seeds placed no closer than 0.5 cm to the urethra to ensure the urethral dose was less than 150% of the prescribed dose. The complete procedure took approximately 45 minutes to 1.0 hour, which included insertion of the needles, postneedle planning, and source implantation. At 2.0 hr after implantation, computed tomography (CT) images were obtained, with which postimplant plans were generated at day 0. Transrectal ultrasound (US) was used to measure preimplant volume (volume measured prior to the implant 131
Reprint requests to: T. S. Kehwar, Ph.D., D.Sc., Department of Radiation Oncology, University of Pittsburgh Cancer Institute, Pittsburgh, PA 15232. Tel: (412)784-4915; Fax: (412)784-4905; E-mail: [email protected]
Conflict of interest: none. Received July 7, 2009, and in revised form June 28, 2010. Accepted for publication July 2, 2010. 621
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procedure was called volume study) and pre- and postneedle volumes (volumes measured before and after needle insertion in the operating room), and postimplant CT images were used to obtain postimplant prostate volumes at days 0, 14, and 28 for all patients. The magnitude of edema was determined by comparing preneedle and postimplant volumes. Dose–volume histograms (DVHs) were generated for preneedle and postimplant volumes, to compute various indices describing the quality of the implant. Preneedle plans were generated using preneedle US volumes. The same number of 131Cs seeds was used in preplanning as in real-time implants to determine changes that occurred from preimplant to postimplant QIs. Seed positions on preneedle images were defined by using a manual back-projection method.
QIs of an implant To assess the quality of interstitial implants, many investigators have introduced a number of QIs (16–20), including the coverage index (CI), the relative dose–homogeneity index (DHI), the dose nonuniformity ratio (DNR), and the overdose index (ODI), which are defined as the fraction of the target volume that receives a dose equal to or greater than the prescribed dose in the range of 1.0 to 1.5 times the prescribed dose; equal to or greater than 1.5 times the prescribed dose; and equal to or greater than 2.0 times the prescribed dose, respectively. QI values were calculated from the DVH of each implant, generated from preneedle US, postneedle US, and postimplant CT volumes on day 0, day 14, and day 28. Equations 1 to 3 give expressions for first-order differential equations for CI, DNR, and ODI with time: CIðtÞ ¼ CIð0Þ þ ½1 CIð0Þ½1 expðlCI tÞ
(1)
DNRðtÞ ¼ DNRð0Þ þ ½1 DNRð0Þ½1 expðlDNR tÞ
(2)
ODIðtÞ ¼ ODIð0Þ þ ½1 ODIð0Þ½1 expð lODI tÞ
(3)
and
Due to the exponential form of DHI, its dependence on time (t) may be expressed by the relationship DHIðtÞ ¼ DHIð0ÞexpðlDHI tÞ
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q(T) is a dose protraction factor accounting for sublethal damage repair (23) and is given by h 2 i qðTÞ ¼ 2ðlTÞ2 ={ðmTÞ2 1 l2 =m2 1 elT } eðlþmÞT þ {mT 1 e2lT ð2lTÞ} { 1 þ e2lT 2} (7) where l and m are the decay constants of the radioactive source and the repair constant of sublethal damage, respectively, and can be defined as l = ln(2)/t1/2 and m = ln(2)/trep, where t1/2 and trep are the half-life of radionuclide used in implantation and half-repair time of sublethal damage, respectively. For permanent seed implantation, where treatment time, T, approaches infinity, the term T of Eq. 6 becomes unrealistic and hence so does the value of the BED. On the other hand, when the dose rate reaches below the value at which the instantaneous tumor cell proliferation rate exceeds the cell kill rate, this dose rate is called the critical dose rate. Below the critical dose rate, at any point in the implant, the delivered dose is effectively a wasted dose. The time interval between implantation and the point at which the dose rate reaches the critical value is called the effective treatment time (Teff) (24). Teff provides a measure of the time over which tumor cell kill is ensured and is given by Teff x ¼ ð1=lÞln{0:693= aR0 x Tp } (8) where R0_x is the initial dose rate for the implant at x level of dose. In Eqs. 6 and 7, replacing T with Teff, the expressions of BED and q(T) can be written as BEDðtÞ ¼ DðtÞ þ ½qðtÞ=ða=bÞD2 ðtÞ gTeff
(9)
and h 2 2 2 i qðtÞ ¼ 2 lTeff ={ mTeff 1 l2 =m2 1 elTeff } ðlþmÞTeff þ {mTeff 1 e2lTeff 2lTeff } e { 1 þ e2lTeff 2}
(10)
In the calculation of g in Eq. 9, it is assumed that tumor cell proliferation starts on day 0.
(4)
where lCI, lDNR, lODI, and lDHI are time constants of CI, DNR, ODI, and DHI, respectively, whereas, CI(0), DNR(0), ODI(0), and DHI(0) are values of CI, DNR, ODI, and DHI at day 0, respectively.
Physical dose In permanent implants of decaying sources, the dose rate R(t) at a point in the implant at time t can be given by RðtÞ ¼ R0 expðltÞ
Biological Model
(11)
With permanent implants, tumor cells are continuously irradiated with decaying dose rates of low-energy photons. Treatment delivery times with these implants are theoretically infinite, and sublethal damage repair and tumor cell repopulation occur simultaneously. Therefore, during dose delivery, the survival fraction (SF) of the tumor cells (6,7,9,21–23) can be given by
where D0 is the prescribed dose. The dose received at a point in any time, t, can be written as
SF ¼ exp½aBED
DðtÞ ¼ ðR0 =lÞ½1 expðltÞ
where R0 is the initial dose rate. The instantaneous dose, Din(t), at any time, t, can be written as Din ðtÞ ¼ D0 expðltÞ
(5)
where the BED can be written as 2
BED ¼ DðTÞ þ ½qðTÞ=ða=bÞD ðTÞ gT
(6)
where a/b is the a b ratio of radiosensitivity constants of the linearquadratic model. The g (= 0.693/aTp; here Tp is the potential doubling time of tumor cells) and T are the tumor cell repopulation constant and treatment time of the implant in days, respectively. The
Using Teff from Eq. 8 fitted into Eqs. 12 and 13, we have Din ðtÞ ¼ D0 exp lTeff
(12)
(13)
(14)
and DðtÞ ¼ ðR0 =lÞ 1 exp lTeff
(15)
131Cs permanent seed implants–>Prostatic edema in 131Cs permanent seed implants d T. S. KEHWAR et al.
Kehwar et al. (15) derived a relationship between fractional D90 (FD90) and postimplant time, t, as FD90 ðtÞ ¼ FD90 ð0Þ þ ½FD90 ð0Þ a½1 expðlFD tÞ
(16)
where lFD is the time constant and was replaced by the edema resolution constant, le, elsewhere (15), a is an adjustable parameter, and FD90(0) is the FD90 at day 0. In this paper, it is assumed that fractional D80 (FD80) and fractional D100 (FD100) vary in the same manner as FD90 does in Eq. 16 with postimplant time. The generalized form of the relationship can be written as FDx ðtÞ ¼ FDx ð0Þ þ ½FDx ð0Þ a½1 expðlx tÞ
(17)
where x = 80, 90, 100, etc. Again, lx = le = ln(2)/T1/2_edema. FD80 and FD100 data from the patients were fitted into Eq. 17 by using the method of least-square-fit to get the values of a and correlation coefficients. FD90 was defined by Kehwar et al. (15) as the ratio of D90 at time t to the total prescribed dose at that time. In terms of dose rate, it can also be defined as the ratio of R90 at time t to the instantaneous prescribed dose rate at that time: FD90 ðtÞ ¼ D90 ðtÞ=TDðtÞ ¼ R90 ðtÞ=Rp ðtÞ or the generalized form FDx ðtÞ ¼ Dx ðtÞ=TDðtÞ ¼ Rx ðtÞ=Rp ðtÞ
(18)
Using Eqs. 12, 17, and 18, dose rate, Rx (R80, R90, R100, etc.), at time t can be written as Rx ðtÞ ¼ R0 expðltÞ½FDx ð0Þ þ {FDx ð0Þ a} {1 expðlx tÞ}
(19)
where R0 is the initial prescribed dose rate. The Dx value received at time t for a decaying source can be written as ð Teff Dx ðtÞ ¼ R0 expðltÞ½FDx ð0Þ þ {FDx ð0Þ a}{1 0
expðlx tÞ}dt The solution for this equation is Dx ðtÞ ¼ R0 {FDx ð0Þ=l}{1 exp lTeff } þ{ðFDx ð0Þ aÞ=l}{1 exp lTeff } {ðFDx ð0Þ aÞ=ðl þ lx Þ}{1 exp ðl þ lx ÞTeff
(20)
(21)
By replacing D(t) in Eq. 5 with Dx(t), BED can be written as BEDx ðtÞ ¼ Dx ðtÞ þ ½qðtÞ=ða=bÞD2x ðtÞ gTeff
(22)
The values of Teff are calculated based on the corresponding initial dose rates, i.e., R80(0), R90(0), and R100(0) at D80, D90, and D100. For BED calculations, a = 0.15 Gy1; a/b = 3.1 Gy; m = 62.38/ day[i.e. m = ln(2)/trep, where trep = 16 min]; and Tp = 42 days (25,26). In this work, the value of T1/2_edema was 9.72 days (15) and was used to calculate lx and Teff.
RESULTS The values for CI, DNR, ODI, DHI, FD80, FD90, and FD100 obtained using the DVHs of the plans of preneedle volumes and postimplant volumes at day 0 are listed in Table 1. There were statistically significant differences between the
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QIs for preneedle plans and same-day postimplant plans (p < 0.05), except for the ODI (p = 0.106). Figure 1 shows plots of mean values of CI, DNR, ODI, and DHI as functions of postimplant time. The CI, DNR, and ODI values increased from the mean values of 0.91 0.05 (range, 0.76–0.98), 0.46 0.14 (range, 0.24–0.81), and 0.17 0.07 (range, 0.08–0.37) on postimplant day 0 to 0.96 0.03 (range, 0.88–1.00), 0.64 0.15 (range, 0.33–0.84), and 0.28 0.28 (range, 0.11–0.43) on postimplant day 28, respectively. On the other hand, the DHI value had decreased from a mean value of 0.45 0.11 (range, 0.17-0.66) on postimplant day 0 to 0.32 0.13 (range, 0.15–0.61) on postimplant day 28. The correlation coefficients and time constants of corresponding best-fit regression lines, obtained by fitting the mean values of CI, DNR, ODI, and DHI to Eqs. 1, 2, 3, and 4, using the method of least-square-fit, were found to be 0.9867 and 0.0316 for CI; 0.9988 and 0.0148 for DNR; 0.9958 and 0.0053 for ODI; and 0.9983 and 0.0125 for DHI, respectively. Figure 2 shows plots of FDx versus postimplant time along with best-fit regression lines. The value of the time constant in Eq. 17 was set to be equal to the time constant of edema. The values of a and correlation coefficients of best-fit regression lines were computed by fitting FD80, FD90, and FD100 data into Eq. 17, using the least-square-fit method and were found to be 0.9695 and 1.0000 for FD80; 0.881 and 0.9895 for FD90; and 0.3893 and 0.9999 for FD100. Table 2 lists values of different dosimetric and radiobiological parameters calculated for each patient for the plans of preneedle volumes and postimplant volumes at day 0. There were statistically significant differences between parameters for preneedle plans and same-day postimplant plans (p<0.02). The initial dose rates, Rx(0), at D80, D90, and D100 were used to calculate respective values of Teff_x, using Eq. 8, and were found to be 63.66 0.43 days, 61.83 0.43 days, and 57.53 0.65 days, respectively, for preneedle/implant plans; and 62.71 0.96 days, 60.86 1.40 days, and 51.91 2.03 days, respectively, for postimplant plans at day 0. Dx(0) decay to Teff_x and Dx(Teff_x) are the doses calculated using Eqs. 15 and 21, to be delivered in Teff_x time with and without accounting for edema effect, respectively, at D80, D90 and D100. For each patient, the BEDs at D80, D90, and D100 were also calculated using Eqs. 9 and 10 for corresponding Teff_x values with and without edema resolution correction for preneedle/implant plans and postimplant plans at day 0. There is an improvement in the BED with the consideration of the edema effect compared to the BED without considering the edema effect. Figures 3 and 4 show the plots between TDin(t), 1.5 TDin(t), 2.0 TDin(t), CI(t), DNR(t), and ODI(t), versus postimplant time in days, for 131Cs and 125I prostate seed implants, respectively. The TDin(t) value was calculated using Eq. 12 for different postimplant times. The 1.5 TDin(t) and 2.0 TDin(t) values are the 1.5 and 2.0 times values of TDin(t), respectively. CI(t), DNR(t), and ODI(t) were calculated using Eqs. 1, 2, and 3, respectively. In the calculations of CI(t), DNR(t), and ODI(t) for 125I implants, it is assumed that the values of the respective parameters, lCI, lDNR, and lODI,
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Table 1. Mean parameter value change from preimplant to postimplant plan
FDx(t) vs post implant time 1.6
Postimplant plan Parameter Preneedle/preimplant plan at day 0 p value 0.99 0.01 0.40 0.05 0.15 0.03 0.59 0.05 1.25 0.04 1.11 0.03 0.82 0.04
CI DNR ODI DHI FD80 FD90 FD100
0.91 0.05 0.46 0.14 0.17 0.07 0.45 0.11 1.19 0.08 1.04 0.11 0.55 0.08
< 0.001 0.046 0.106 <0.001 <0.001 <0.001 <0.001
Data show changes in means 1 standard deviations (SD) of coverage index (CI), dose nonuniformity ratio (DNR), overdose index (ODI), relative dose homogeneity index (DHI), and fractional D90 (FD90) from preimplant plan to postimplant plan at day 0.
will be the same as those calculated for 131Cs implants. However, in actuality, theses values may be different because the source characteristics and the pattern of 125I seed distribution differ considerably from that of 131Cs implants.
DISCUSSION 131
Cs seeds are used in many clinics across the United States for permanent prostate seed implants. Compared to 125 I seeds, many precautions have to be taken with 131Cs seeds because of their relatively short half-life, which delivers approximately 80% of the dose in 3 weeks after implantation, with a higher initial dose rate compared to initial dose rate and 80% dose delivery time for 125I. This rapid dose delivery might prove disadvantageous due to the development of acute prostatic edema. Chen et al. (11) reported that seed implantation performed on the basis of preimplant dosimetry always overestimates the true delivered dose because it ignores the increase of interseed separation caused by acute prostatic edema. This overestimation with 131Cs implants ranges from 1.2% to 45% for a change in the magnitude of edema and its half life from 10% and 2 days to 100% and 25 days,
QIs vs Post implant time 1.00
QIs---->
0.80
CI(t)
0.60
DHI(t)
0.40
DNR(t) ODI(t)
0.20 0.00 0
5
10
15
20
25
30
Post Implant time (days)---->
Fig. 1. Plot of coverage index(CI), relative dose homogeneity index(DHI), dose non – uniformity ratio(DNR) and over dose index(ODI) with post implant time. The open square, open triangle, open circle and open diamond symbols indicate the mean values of CI, DNR, ODI, and DHI, respectively.
FD x (t)--->
Mean SD change FD80(t)
1.2
FD90(t) FD100(t)
0.8
0.4 0
5
10
15
20
25
30
Pos t implant time (days)--->
Fig. 2. Plot of FD80, FD90, and FD100 with postimplant time.
respectively. They also reported that the magnitude of preand postimplant dosimetry error for 131Cs implants was found to be similar to that of 103Pd implants for typical edema magnitudes of 100% and half-life of 17 days and was worse than 125 I implants (11). Results of our study, shown in Table 1, show that the values of CI, DHI, FD80, FD90, and FD100 have decreased, while the values of DNR and ODI have increased from preneedle plans to postimplant plans. These changes have statistically significant differences (p < 0.05), except for the values of ODI (p = 0.106). This illustrates that the quality of the implants has been significantly affected by prostatic edema. The main drawback in back-projected preplans is the use of the same number of seeds, as used in real-time implants in smaller prostates. This would have more impact with a higher pronounced magnitude of postimplant edema, and the dosimetric pattern would be different compared to real-time preplans. However, it would not be realistic to evaluate the edema effect if preplans performed with fewer seeds, to compare with real-time plans that had a higher number of seeds. Most reports of permanent prostate seed implants focused on the discussion of pre- or postimplant studies of dosimetric quantities, D90 or V100 (11, 27–30), and had neglected a discussion of other dosimetric quantities, such as D80, D100, V150, and V200 (27, 31). In contrast to these studies, we have investigated statistically significant changes in the values of FD80, FD90 and FD100 along with the derivatives of V100, V150, and V200, such as CI, DHI, DNR, and ODI for preneedle/implant plans and postimplant plans at day 0. It was also found that there are changes in the values of these quantities with postimplant time (Figs. 1 and 2) due to edema resolution. Figure 1 shows that the CI, DNR, and ODI increase with postimplant time, whereas the value of DHI decreases as postimplant time increases. For each patient, the values of QIs are found to vary with the postneedle prostate volume, implanted needle configuration, and number of radioactive seeds used, as well as postimplant time. Nearly all of the apparent improvement in QIs were observed by postimplant day 28. This improvement in the values of QIs leads to an improvement in the dosimetric outcome of the implants. The half-life of radioactive sources plays an important role in the accomplishment of this improvement. For example, due to the short half-life of 131Cs sources, the improvement in
D100
D90
625
250
1.2
200
1.0
T Din(t) 1.5T Din(t)
0.8
150
0.6 100
QIs--->
TD(Gy)---->
Cs-131 implants
0.4
50
0.2
0
0.0 1
11
21
31
41
2.0T Din(t) CI(t) D N R (t) ODI(t)
51
T ime (days)--->
Fig. 3. Plot of instantaneous doses TDin, 1.5 TDin, 2.0 TDin and coverage index(CI), dose nonuniformity ratio (DNR), overdose index(ODI) with postimplant time for 131Cs implants. The vertical axes on left and right show the values of TDin(t) and QIs, respectively.
QIs cannot be used to design a 131Cs implant with a better dosimetric outcome than that obtained with an 125I implant, with a relatively long half-life. This is because by 28 days, about 85% of the dose would have been delivered with 131 Cs implants, while only about 27% of the dose would have been delivered with 125I implants. Figure 1 also shows that as the amount of edema resolved with postimplant time, the prostate volume coverage improved. On the other hand, it was also seen that the dose distribution within the prostate implant become more heterogeneous with postimplant time, and if uniform seed loading was done throughout the prostate, the central portion would be relatively overdosed. Figure 2 shows an increase in FD80, FD90, and FD100 with postimplant time. However, when the actual doses delivered at FD80, FD90, and FD100 are calculated for 131Cs sources, using Eq. 21, at different times, the improvements in FD80, FD90 and FD100 could not improve actual dose delivery, hence, it becomes meaningless. Sahgal et al. (28) have performed replanning of previous 125 I implants for 131Cs seeds and have calculated the BED for manual and inverse planning. Other investigators (12,26,32) have studied the equivalent uniform dose of initial postimplant plans or in combination with pre- and initial postimplant plans for 125I and 103Pd implants. But no one has evaluated any biological parameters for 131Cs implants at different postimplant times. In the present study, I-125 implants 350
1.2
300
1.0
TDin(t)
0.8
1.5TDin(t)
250 200
0.6
150
0.4
100
QIs--->
TD(Gy)--->
Table data show mean 1 standard deviation (SD) values of different pre- and post implant dosimetric and radiobiologic parameters of 31 patients who underwent permanent 131Cs seed prostate implantation.
163.96 7.41 Gy 148.16 15.02 Gy 0.0144 139.98 6.40 Gy 126.69 20.04 Gy 0.0009 115.76 7.11 Gy 67.45 14.03 Gy 4.09 1010 145.20 4.90 Gy 134.73 9.97 Gy 0.0145 125.67 4.24 Gy 116.83 13.30 Gy 0.0009 89.63 4.66 Gy 57.74 9.33 Gy 4.76 1010 161.15 6.65 Gy 146.85 13.65 Gy 0.0145 139.42 5.83 Gy 127.15 18.34 Gy 0.0008 116.86 6.60 Gy 71.14 13.52 Gy 6.04 1010 63.66 0.43 days 62.71 0.96 days 0.0186 61.83 0.43 Gy 60.86 1.40 days 0.0006 57.53 0.65 days 51.91 2.03 days 2.31 1008 D80
Preneedle /preimplant plan Postimplant plan p value Preneedle/preimplant plan Postimplant plan p value Preneedle/preimplant plan Postimplant plan p value
10.43 0.32 Gy/day 9.74 0.65 Gy/day 0.0136 9.15 0.28 Gy/day 8.56 0.88 Gy/day 0.0008 6.74 0.32 Gy/day 4.54 0.64 Gy/day 6.31 1010
145.88 4.46 Gy 136.28 9.16 Gy 0.0145 127.97 3.97 Gy 119.54 12.31 Gy 0.0008 94.21 4.42 Gy 63.47 9.12 Gy 6.49 1010
144.34 4.46 Gy 134.74 9.16 Gy 0.0145 126.42 3.91 Gy 118.18 12.31 Gy 0.0008 92.67 4.42 Gy 61.93 9.12 Gy 6.50 1010
BEDx(decay to Teff_x) Dx(Teff_x)edema Dx(T)decay to Teff_x Dx(0) Teff_x Rx(0) Parameter Dx
Mean SD difference
Table 2. Differences between pre- and postimplant dosimetric and radiobiologic parameters
BEDx(Teff_x)edema
Prostatic edema in 131Cs permanent seed implants d T. S. KEHWAR et al.
2.0TDin(t) CI(t)
50
0.2
DNR(t)
0
0.0
ODI(t)
1
11
21
31
41
51
Time(days)--->
Fig. 4. Plot of instantaneous doses, TDin, 1.5 TDin, 2.0 TDin , and coverage index (CI), dose nonuniformity ratio (DNR), overdose index(ODI) with postimplant time for 125I implants. The vertical axes on left and right show the values of TDin(t) and QIs, respectively.
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we have derived a relationship that accounts for the effect of edema at different dose levels, Dx, and that is used to calculate D80, D90, and D100 for preneedle/implant plans and postimplant plans at day 0 (Table 2). In the calculations of Teff_x at D80, D90, and D100, the corresponding initial dose rates were used because different dose regions received doses with different dose rates, and hence, the cell killing rates were also different. Therefore, the same effective treatment time cannot be used for all regions of the target volume; hence, each region will receive different effective doses. In Table 2, three dose parameters are described, where Dx(0) is obtained from the DVH, while Dx(T)decay to Teff_x and Dx(Teff_x)edema are calculated by using the effect of source decay and a combined factor of source decay and edema resolution, respectively. The values of Dx(T)decay to Teff_x and Dx(Teff_x)edema are used to calculate corresponding values of BED for preneedle/implant plans and postimplant plans at day 0 at dose levels of D80, D90, and D100. For both plans, i.e., for preneedle/implant plans and postimplant plans at day 0 at dose levels of D80, D90, and D100, there is an improvement in Dx(Teff_x)edema and BEDx(Teff_x)edema compared to Dx(T)decay to Teff_x and BEDx(decay to Teff_x) due to edema resolution. It is clear from Table 2 that the dose rate, dose, and BED values are higher (p < 0.02) for preneedle/implant plans than for postimplant plans at day 0 at dose levels of D80, D90, and D100, which reveals that the development of prostatic edema has tremendous impact on these quantities in postimplant plans at day 0. Comparing the BED values of pre- and postimplant plans, it was found that there is a significant loss of BED (p < 0.02) of 15.80 11.21 Gy at D80, 13.29 13.22 Gy at D90, and 48.31 10.57 Gy at D100, respectively. The BED loss at D100 is significantly more than at D80 or D90. This reveals that if 131Cs seeds are implanted using preimplant plans there will be a significant underdosing to the prostate at D100. One potential solution to compensate for this loss in BED could be to increase the initial dose rate by increasing the number of seeds to increase implanted source activity by a factor of 1.10 0.02 at D80, 1.07 0.01 at D90, and 1.48 0.06 at D100, respectively. This solution has not been clinically tested, and hence, the impact on urethral, rectal, and bladder complications is unknown. This loss in BED can also be
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compensated by the use of EBRT, as suggested by Chen et al. (12), who calculated BED for 131Cs implants and suggested that for a prescribed dose of 120 Gy, 1, 4, 6, 7, or 9 number of fractions of 2-Gy/fraction of EBRT could be needed to compensate for a 5%, 10%, 15%, 20%, or 25% edema-induced dose reduction, respectively. Figure 3 reveals that values of CI, DNR, and ODI increase with postimplant time due to edema resolution. At the same time, as shown in Fig.4, the dose TDin(t), 1.5 TDin(t), and 2 TDin(t) decay very fast due to the short half-life of 131Cs sources compared to the corresponding doses obtained with longer-half-life 125I implants. Therefore, the effect of edema on CI, DNR, and ODI is much more pronounced with 131Cs implants than with 125I implants because three-fourths of the dose is delivered in 2 half-lives of the source with 131Cs implants. Furthermore, during this period of time, approximately three-fourths of the edema has resolved, leaving one-fourth yet to dissipate. On the other hand, with 125I implants, approximately 20% of the dose is delivered during the same period of time (2 half-lives of 131Cs), leaving 80% of the dose yet to be delivered, during which the effect of edema would have had less or negligible effect.
CONCLUSIONS Results of this study show that edema has a more pronounced effect with the use of 131Cs implants, even if a real-time implant procedure was used. Compared to 125I implants, the improvement in QIs with 131Cs implants with postimplant time cannot improve the dosimetric and radiobiologic outcome due to fast dose delivery, i.e., the short halflife of 131Cs seeds. Therefore, we conclude that 131Cs prostate seeds implanted on the basis of preimplant plans will result in poor coverage of the prostate gland and less biological effect. Hence, it is recommended that 131Cs seeds should be implanted using the real-time procedure and postneedle plans. In a postneedle plan, the coverage of the prostate gland and other dosimetric parameters should be evaluated as satisfactory before seed implantation so that the effect of edema can be minimized.
REFERENCES 1. Peschel RE, Fogel TD, Kacinski BM, et al. Iodine-125 implants for carcinoma of the prostate. Int J Radiat Oncol Biol Phys 1985;11:1777–1781. 2. Blasko JC, Grimm PD, Ragde H. Brachytherapy and organ preservation in the management of carcinoma of the prostate. Semin Radiat Oncol 1993;3:240–249. 3. Lee WR, Moughan J, Owen JB, et al. The 1999 pattern of care study of radiotherapy in localized prostate carcinoma: A comprehensive survey of prostate brachytherapy in the United States. Cancer 2003;98:1987–1994. 4. Henschke UK, Lawrence DC. Cesium –; 131 seeds for permanent implants. Radiology 1965;85:1117–1119. 5. Murphy MK, Piper RK, Greenwood LR, et al. Evaluation of the new cesium-131 seed for use in low-energy x – ray brachytherapy. Med Phys 2004;31(6):1529–1538.
6. Armpilia CI, Dale RG, Coles IP, et al. The determination of radiobiologically optimized half-lives for radionuclides used in permanent brachytherapy implants. Int J Radiat Oncol Biol Phys 2003;55:378–385. 7. Brenner DJ, Martinez AA, Edmundson GK, et al. Direct evidence that prostate tumors show high sensitivity to fractionation (low a/b ratio) similar to late responding normal tissue. Int J Radiat Oncol Biol Phys 2002;52:6–13. 8. Bice WS, Prestidge BR. A review of postimplant quality assessment in permanent transperineal interstitial prostate brachytherapy. J Brachytherapy Int 1997;13:297–313. 9. Waterman FM, Yue N, Reisinger S, et al. Effect of edema on the post-implant dosimetry of an I-125 prostate implant: a case study. Int J Radiat Oncol Biol Phys 1997;38:335– 339.
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10. Waterman FM, Yue N, Corn BW, et al. Edema associated with 125 I or 103Pd prostate brachytherapy and its impact on postimplant dosimetry: An analysis based on serial CT acquisition. Int J Radiat Oncol Biol Phys 1998;41:1069–1077. 11. Chen Z, Deng J, Roberts K, et al. Potential impact of prostate edema on the dosimetry of permanenet seed implants using the new 131Cs (model CS-1) seeds. Med Phys 2006;33:968–975. 12. Chen ZJ, Deng J, Roberts K, Nath R. On the need to compensate for edema-induced dose reductions in preplanned 131Cs prostate brachytherapy. Int J Radiat Oncol Biol Phys 2008;70:303–310. 13. Chen Z, Yue N, Wang X, et al. Dosimetric effects of edema in permanent prostate seed implants: A rigorous solution. Int J Radiat Oncol Biol Phys 2000;47:1405–1419. 14. Smith RP, Beriwal S, Komanduri K, et al. Planning based on postneedle volume with early dosimetric assessment is beneficial for Cesium-131 permanent prostate seed implantation. Brachytherapy 2008;7:237–241. 15. Kehwar TS, Jones HA, Huq MS, et al. Effect of edema associated with 131Cs prostate permanent seed implants on dosimetric quality indices. Med Phys 2009;36(8):3536–3542. 16. Anderson LL. A ‘‘natural’’ volume – Dose histogram for brachytherapy. Med Phys 1986;13(6):898–903. 17. Saw CB, Suntharalingam N. Reference dose rates for singleplane and double-plane iridium – 192 implants. Med Phys 1988;15:391–396. 18. Saw CB, Suntharalingam N. Quantitative assessment of interstitial implants. Int J Radiat Oncol Biol Phys 1990;20:135–139. 19. Wu A, Ulin K, Sternick ES. A dose homogeneity index for evaluating 192Ir interstitial breast implants. Med Phys 1988;15:104–107. 20. Kehwar TS, Akber SF, Passi K. Qualitative dosimetric and radiobiological evaluation of high-dose-rate interstitial brachytherapy implants. Int J Med Sci 2008;5:41–49. 21. Dale RG. The application of the linear-quadratic dose-effect equation to fractionated and protracted radiotherapy. Brit J Radiol 1985;58:515–528. 22. Thames HD. An incomplete-repair model for survival after fractionated and continuous irradiations. Int J Radiat Biol 1985;47: 319–339.
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23. Zaider M, Minerbo GN. Tumor control probability: A formulation applicable to any temporal protocol of dose delivery. Phys Med Biol 2000;45:279–293. 24. Antipas V, Dale RG, Coles IP. A theoretical investigation into the role of tumor radiosensitivity, clonogen repopulation, tumor shrinkage and radionuclide RBE in permanent brachytherapy implants of 125I and 103Pd. Phys Med Biol 2001;46: 2557–2569. 25. Wang JZ, Guerrero M, Li XA. How low is the alpha/beta ratio for prostate cancer? Int J Radiat Oncol Biol Phys 2003; 55:194–203. 26. Butler WM, Stewart RR, Merrick GS. A detailed radiobiological and dosimetric analysis of biochemical outcomes in a casecontrol study of permanent prostate brachytherapy patients. Med Phys 2009;36:776–787. 27. Song Y, Chan MF, Burman C, Cann D. Prostate cancer: Combined intensity modulated radiation therapy with 125I seed implant brachytherapy and 125I seed implant brachytherapy alone. J Appl Clin Med Phys 2008;9(2):1–14. 28. Sahgal A, Jabbari S, Chen J, et al. Comparison of dosimetric and biologic effective dose parameters for prostate and urethra using 131Cs and 125I for prostate permanent implant brachytherapy. Int J Radiat Oncol Biol Phys 2008;72:247–254. 29. Villeneuve M, Leclerc G, Lessard E, et al. Relationship between isotope half-life and prostate edema for optimal prostate dose coverage in permanent seed implants. Med Phys 2008;35(5): 1970–1977. 30. Van Gellekom MPR, Moerland MA, Kal HB, Battermann JJ. Biologically effective dose for permanent prostate brachytherapy taking into account postimplant edema. Int J Radiat Oncol Biol Phys 2002;53:422–433. 31. Miles EF, Nelson JW, Alkaissi AK, et al. Equivalent uniform dose, D90 and V100 correlation with biochemical control after low-dose-rate prostate brachytherapy for clinically low-risk prostate cancer. Brachytherapy 2008;7:206–211. 32. Wang JZ, Li XA. Evaluation of external beam radiotherapy and brachytherapy for localized prostate cancer using equivalent uniform dose. Med Phys 2003;30:34–40.
doi:10.1016/j.ijrobp.2010.07.001
PHYSICS CONTRIBUTION
INFLUENCE OF PROSTATIC EDEMA ON 131CS PERMANENT PROSTATE SEED IMPLANTS: A DOSIMETRIC AND RADIOBIOLOGICAL STUDY THAN S. KEHWAR, PH.D., D.SC., HEATHER A. JONES, M.D., PH.D., M. SAIFUL HUQ, PH.D., AND RYAN P. SMITH, M.D. Department of Radiation Oncology, University of Pittsburgh Cancer Institute, UPMC Cancer Centers, Pittsburgh, Pennsylvania Purpose: To study the influence of prostatic edema on postimplant physical and radiobiological parameters using 131Cs permanent prostate seed implants. Methods and Materials: Thirty-one patients with early prostate cancer who underwent 131Cs permanent seed implantation were evaluated. Dose-volume histograms were generated for each set of prostate volumes obtained at preimplantation and postimplantion days 0, 14, and 28 to compute quality indices (QIs) and fractional doses at level x (FDx). A set of equations for QI, FDx, and biologically effective doses at dose level Dx (BEDx) were defined to account for edema changes with time after implant. Results: There were statistically significant differences found between QIs of pre- and postimplant plans at day 0, except for the overdose index (ODI). QIs correlated with postimplant time, and FDx was found to increase with increasing postimplant time. With the effect of edema, BED at different dose levels showed less improvement due to the short half-life of 131Cs, which delivers about 85% of the prescribed dose before the prostate reaches its original volume due to dissipation of edema. Conclusions: Results of the study show that QIs, FDx, and BEDs at the level of Dx changed from preneedle plans to postimplant plans and have statistically significant differences (p < 0.05), except for the ODI (p = 0.106), which suggests that at the time of 131C seed implantation, the effect of edema must be accounted for when defining the seed positions, to avoid the possibility of poor dosimetric and radiobiologic results for 131Cs seed implants. Ó 2011 Elsevier Inc. Quality indices, Biologically effective dose, Effective treatment time, Prostatic edema, Fractional doses.
In this study, we present the results of our investigation of the potential effects of edema on various quality indices (QIs), which were defined previously (16–20) for low-dose-rate interstitial seed implants and biologically effective doses (BED) at D80, D90 and D100.
INTRODUCTION Iodine-125 (125I) and palladium-103 (103Pd) seed implants are used routinely as a monotherapy or a boost to a course of external beam radiation therapy (EBRT) (1 – 3) for the treatment of localized prostate cancer. Recently, cesium-131 (131Cs) seeds have been introduced (IsoRay, Inc., Richmond,WA) for permanent prostate implants. The dosimetric characteristics of 131 Cs seeds are similar to those of 125I and 103Pd seeds, with the exception that 131Cs seeds have a short half-life of 9.7 days (4, 5). Many studies have suggested that shorter-halflife radioactive seeds offer better tumor control than longerhalf-life radioactive seeds (6, 7). Published reports of 125I and 103Pd prostate implants are based on an evaluation of preimplant volumes or postimplant volumes of the prostate obtained after 1 month of implantation (2, 6–8). The effect of prostatic edema on dosimetric quantities has been studied by many investigators (9–13). However, few studies (11, 12, 14, 15) have been reported for 131Cs implants. Details about the effect of edema on these study patients have been described previously (15).
METHODS AND MATERIALS Patients Thirty-one prostate cancer patients who underwent permanent Cs seed implantation were included in this study. Patient data, implantation techniques, procedures, dose prescriptions, and dose limits to the urethra have been previously described in detail (14). Briefly, 131 Cs seeds were implanted using a real-time procedure and peripheral loading, with central seeds placed no closer than 0.5 cm to the urethra to ensure the urethral dose was less than 150% of the prescribed dose. The complete procedure took approximately 45 minutes to 1.0 hour, which included insertion of the needles, postneedle planning, and source implantation. At 2.0 hr after implantation, computed tomography (CT) images were obtained, with which postimplant plans were generated at day 0. Transrectal ultrasound (US) was used to measure preimplant volume (volume measured prior to the implant 131
Reprint requests to: T. S. Kehwar, Ph.D., D.Sc., Department of Radiation Oncology, University of Pittsburgh Cancer Institute, Pittsburgh, PA 15232. Tel: (412)784-4915; Fax: (412)784-4905; E-mail: [email protected]
Conflict of interest: none. Received July 7, 2009, and in revised form June 28, 2010. Accepted for publication July 2, 2010. 621
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procedure was called volume study) and pre- and postneedle volumes (volumes measured before and after needle insertion in the operating room), and postimplant CT images were used to obtain postimplant prostate volumes at days 0, 14, and 28 for all patients. The magnitude of edema was determined by comparing preneedle and postimplant volumes. Dose–volume histograms (DVHs) were generated for preneedle and postimplant volumes, to compute various indices describing the quality of the implant. Preneedle plans were generated using preneedle US volumes. The same number of 131Cs seeds was used in preplanning as in real-time implants to determine changes that occurred from preimplant to postimplant QIs. Seed positions on preneedle images were defined by using a manual back-projection method.
QIs of an implant To assess the quality of interstitial implants, many investigators have introduced a number of QIs (16–20), including the coverage index (CI), the relative dose–homogeneity index (DHI), the dose nonuniformity ratio (DNR), and the overdose index (ODI), which are defined as the fraction of the target volume that receives a dose equal to or greater than the prescribed dose in the range of 1.0 to 1.5 times the prescribed dose; equal to or greater than 1.5 times the prescribed dose; and equal to or greater than 2.0 times the prescribed dose, respectively. QI values were calculated from the DVH of each implant, generated from preneedle US, postneedle US, and postimplant CT volumes on day 0, day 14, and day 28. Equations 1 to 3 give expressions for first-order differential equations for CI, DNR, and ODI with time: CIðtÞ ¼ CIð0Þ þ ½1 CIð0Þ½1 expðlCI tÞ
(1)
DNRðtÞ ¼ DNRð0Þ þ ½1 DNRð0Þ½1 expðlDNR tÞ
(2)
ODIðtÞ ¼ ODIð0Þ þ ½1 ODIð0Þ½1 expð lODI tÞ
(3)
and
Due to the exponential form of DHI, its dependence on time (t) may be expressed by the relationship DHIðtÞ ¼ DHIð0ÞexpðlDHI tÞ
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q(T) is a dose protraction factor accounting for sublethal damage repair (23) and is given by h 2 i qðTÞ ¼ 2ðlTÞ2 ={ðmTÞ2 1 l2 =m2 1 elT } eðlþmÞT þ {mT 1 e2lT ð2lTÞ} { 1 þ e2lT 2} (7) where l and m are the decay constants of the radioactive source and the repair constant of sublethal damage, respectively, and can be defined as l = ln(2)/t1/2 and m = ln(2)/trep, where t1/2 and trep are the half-life of radionuclide used in implantation and half-repair time of sublethal damage, respectively. For permanent seed implantation, where treatment time, T, approaches infinity, the term T of Eq. 6 becomes unrealistic and hence so does the value of the BED. On the other hand, when the dose rate reaches below the value at which the instantaneous tumor cell proliferation rate exceeds the cell kill rate, this dose rate is called the critical dose rate. Below the critical dose rate, at any point in the implant, the delivered dose is effectively a wasted dose. The time interval between implantation and the point at which the dose rate reaches the critical value is called the effective treatment time (Teff) (24). Teff provides a measure of the time over which tumor cell kill is ensured and is given by Teff x ¼ ð1=lÞln{0:693= aR0 x Tp } (8) where R0_x is the initial dose rate for the implant at x level of dose. In Eqs. 6 and 7, replacing T with Teff, the expressions of BED and q(T) can be written as BEDðtÞ ¼ DðtÞ þ ½qðtÞ=ða=bÞD2 ðtÞ gTeff
(9)
and h 2 2 2 i qðtÞ ¼ 2 lTeff ={ mTeff 1 l2 =m2 1 elTeff } ðlþmÞTeff þ {mTeff 1 e2lTeff 2lTeff } e { 1 þ e2lTeff 2}
(10)
In the calculation of g in Eq. 9, it is assumed that tumor cell proliferation starts on day 0.
(4)
where lCI, lDNR, lODI, and lDHI are time constants of CI, DNR, ODI, and DHI, respectively, whereas, CI(0), DNR(0), ODI(0), and DHI(0) are values of CI, DNR, ODI, and DHI at day 0, respectively.
Physical dose In permanent implants of decaying sources, the dose rate R(t) at a point in the implant at time t can be given by RðtÞ ¼ R0 expðltÞ
Biological Model
(11)
With permanent implants, tumor cells are continuously irradiated with decaying dose rates of low-energy photons. Treatment delivery times with these implants are theoretically infinite, and sublethal damage repair and tumor cell repopulation occur simultaneously. Therefore, during dose delivery, the survival fraction (SF) of the tumor cells (6,7,9,21–23) can be given by
where D0 is the prescribed dose. The dose received at a point in any time, t, can be written as
SF ¼ exp½aBED
DðtÞ ¼ ðR0 =lÞ½1 expðltÞ
where R0 is the initial dose rate. The instantaneous dose, Din(t), at any time, t, can be written as Din ðtÞ ¼ D0 expðltÞ
(5)
where the BED can be written as 2
BED ¼ DðTÞ þ ½qðTÞ=ða=bÞD ðTÞ gT
(6)
where a/b is the a b ratio of radiosensitivity constants of the linearquadratic model. The g (= 0.693/aTp; here Tp is the potential doubling time of tumor cells) and T are the tumor cell repopulation constant and treatment time of the implant in days, respectively. The
Using Teff from Eq. 8 fitted into Eqs. 12 and 13, we have Din ðtÞ ¼ D0 exp lTeff
(12)
(13)
(14)
and DðtÞ ¼ ðR0 =lÞ 1 exp lTeff
(15)
131Cs permanent seed implants–>Prostatic edema in 131Cs permanent seed implants d T. S. KEHWAR et al.
Kehwar et al. (15) derived a relationship between fractional D90 (FD90) and postimplant time, t, as FD90 ðtÞ ¼ FD90 ð0Þ þ ½FD90 ð0Þ a½1 expðlFD tÞ
(16)
where lFD is the time constant and was replaced by the edema resolution constant, le, elsewhere (15), a is an adjustable parameter, and FD90(0) is the FD90 at day 0. In this paper, it is assumed that fractional D80 (FD80) and fractional D100 (FD100) vary in the same manner as FD90 does in Eq. 16 with postimplant time. The generalized form of the relationship can be written as FDx ðtÞ ¼ FDx ð0Þ þ ½FDx ð0Þ a½1 expðlx tÞ
(17)
where x = 80, 90, 100, etc. Again, lx = le = ln(2)/T1/2_edema. FD80 and FD100 data from the patients were fitted into Eq. 17 by using the method of least-square-fit to get the values of a and correlation coefficients. FD90 was defined by Kehwar et al. (15) as the ratio of D90 at time t to the total prescribed dose at that time. In terms of dose rate, it can also be defined as the ratio of R90 at time t to the instantaneous prescribed dose rate at that time: FD90 ðtÞ ¼ D90 ðtÞ=TDðtÞ ¼ R90 ðtÞ=Rp ðtÞ or the generalized form FDx ðtÞ ¼ Dx ðtÞ=TDðtÞ ¼ Rx ðtÞ=Rp ðtÞ
(18)
Using Eqs. 12, 17, and 18, dose rate, Rx (R80, R90, R100, etc.), at time t can be written as Rx ðtÞ ¼ R0 expðltÞ½FDx ð0Þ þ {FDx ð0Þ a} {1 expðlx tÞ}
(19)
where R0 is the initial prescribed dose rate. The Dx value received at time t for a decaying source can be written as ð Teff Dx ðtÞ ¼ R0 expðltÞ½FDx ð0Þ þ {FDx ð0Þ a}{1 0
expðlx tÞ}dt The solution for this equation is Dx ðtÞ ¼ R0 {FDx ð0Þ=l}{1 exp lTeff } þ{ðFDx ð0Þ aÞ=l}{1 exp lTeff } {ðFDx ð0Þ aÞ=ðl þ lx Þ}{1 exp ðl þ lx ÞTeff
(20)
(21)
By replacing D(t) in Eq. 5 with Dx(t), BED can be written as BEDx ðtÞ ¼ Dx ðtÞ þ ½qðtÞ=ða=bÞD2x ðtÞ gTeff
(22)
The values of Teff are calculated based on the corresponding initial dose rates, i.e., R80(0), R90(0), and R100(0) at D80, D90, and D100. For BED calculations, a = 0.15 Gy1; a/b = 3.1 Gy; m = 62.38/ day[i.e. m = ln(2)/trep, where trep = 16 min]; and Tp = 42 days (25,26). In this work, the value of T1/2_edema was 9.72 days (15) and was used to calculate lx and Teff.
RESULTS The values for CI, DNR, ODI, DHI, FD80, FD90, and FD100 obtained using the DVHs of the plans of preneedle volumes and postimplant volumes at day 0 are listed in Table 1. There were statistically significant differences between the
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QIs for preneedle plans and same-day postimplant plans (p < 0.05), except for the ODI (p = 0.106). Figure 1 shows plots of mean values of CI, DNR, ODI, and DHI as functions of postimplant time. The CI, DNR, and ODI values increased from the mean values of 0.91 0.05 (range, 0.76–0.98), 0.46 0.14 (range, 0.24–0.81), and 0.17 0.07 (range, 0.08–0.37) on postimplant day 0 to 0.96 0.03 (range, 0.88–1.00), 0.64 0.15 (range, 0.33–0.84), and 0.28 0.28 (range, 0.11–0.43) on postimplant day 28, respectively. On the other hand, the DHI value had decreased from a mean value of 0.45 0.11 (range, 0.17-0.66) on postimplant day 0 to 0.32 0.13 (range, 0.15–0.61) on postimplant day 28. The correlation coefficients and time constants of corresponding best-fit regression lines, obtained by fitting the mean values of CI, DNR, ODI, and DHI to Eqs. 1, 2, 3, and 4, using the method of least-square-fit, were found to be 0.9867 and 0.0316 for CI; 0.9988 and 0.0148 for DNR; 0.9958 and 0.0053 for ODI; and 0.9983 and 0.0125 for DHI, respectively. Figure 2 shows plots of FDx versus postimplant time along with best-fit regression lines. The value of the time constant in Eq. 17 was set to be equal to the time constant of edema. The values of a and correlation coefficients of best-fit regression lines were computed by fitting FD80, FD90, and FD100 data into Eq. 17, using the least-square-fit method and were found to be 0.9695 and 1.0000 for FD80; 0.881 and 0.9895 for FD90; and 0.3893 and 0.9999 for FD100. Table 2 lists values of different dosimetric and radiobiological parameters calculated for each patient for the plans of preneedle volumes and postimplant volumes at day 0. There were statistically significant differences between parameters for preneedle plans and same-day postimplant plans (p<0.02). The initial dose rates, Rx(0), at D80, D90, and D100 were used to calculate respective values of Teff_x, using Eq. 8, and were found to be 63.66 0.43 days, 61.83 0.43 days, and 57.53 0.65 days, respectively, for preneedle/implant plans; and 62.71 0.96 days, 60.86 1.40 days, and 51.91 2.03 days, respectively, for postimplant plans at day 0. Dx(0) decay to Teff_x and Dx(Teff_x) are the doses calculated using Eqs. 15 and 21, to be delivered in Teff_x time with and without accounting for edema effect, respectively, at D80, D90 and D100. For each patient, the BEDs at D80, D90, and D100 were also calculated using Eqs. 9 and 10 for corresponding Teff_x values with and without edema resolution correction for preneedle/implant plans and postimplant plans at day 0. There is an improvement in the BED with the consideration of the edema effect compared to the BED without considering the edema effect. Figures 3 and 4 show the plots between TDin(t), 1.5 TDin(t), 2.0 TDin(t), CI(t), DNR(t), and ODI(t), versus postimplant time in days, for 131Cs and 125I prostate seed implants, respectively. The TDin(t) value was calculated using Eq. 12 for different postimplant times. The 1.5 TDin(t) and 2.0 TDin(t) values are the 1.5 and 2.0 times values of TDin(t), respectively. CI(t), DNR(t), and ODI(t) were calculated using Eqs. 1, 2, and 3, respectively. In the calculations of CI(t), DNR(t), and ODI(t) for 125I implants, it is assumed that the values of the respective parameters, lCI, lDNR, and lODI,
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Table 1. Mean parameter value change from preimplant to postimplant plan
FDx(t) vs post implant time 1.6
Postimplant plan Parameter Preneedle/preimplant plan at day 0 p value 0.99 0.01 0.40 0.05 0.15 0.03 0.59 0.05 1.25 0.04 1.11 0.03 0.82 0.04
CI DNR ODI DHI FD80 FD90 FD100
0.91 0.05 0.46 0.14 0.17 0.07 0.45 0.11 1.19 0.08 1.04 0.11 0.55 0.08
< 0.001 0.046 0.106 <0.001 <0.001 <0.001 <0.001
Data show changes in means 1 standard deviations (SD) of coverage index (CI), dose nonuniformity ratio (DNR), overdose index (ODI), relative dose homogeneity index (DHI), and fractional D90 (FD90) from preimplant plan to postimplant plan at day 0.
will be the same as those calculated for 131Cs implants. However, in actuality, theses values may be different because the source characteristics and the pattern of 125I seed distribution differ considerably from that of 131Cs implants.
DISCUSSION 131
Cs seeds are used in many clinics across the United States for permanent prostate seed implants. Compared to 125 I seeds, many precautions have to be taken with 131Cs seeds because of their relatively short half-life, which delivers approximately 80% of the dose in 3 weeks after implantation, with a higher initial dose rate compared to initial dose rate and 80% dose delivery time for 125I. This rapid dose delivery might prove disadvantageous due to the development of acute prostatic edema. Chen et al. (11) reported that seed implantation performed on the basis of preimplant dosimetry always overestimates the true delivered dose because it ignores the increase of interseed separation caused by acute prostatic edema. This overestimation with 131Cs implants ranges from 1.2% to 45% for a change in the magnitude of edema and its half life from 10% and 2 days to 100% and 25 days,
QIs vs Post implant time 1.00
QIs---->
0.80
CI(t)
0.60
DHI(t)
0.40
DNR(t) ODI(t)
0.20 0.00 0
5
10
15
20
25
30
Post Implant time (days)---->
Fig. 1. Plot of coverage index(CI), relative dose homogeneity index(DHI), dose non – uniformity ratio(DNR) and over dose index(ODI) with post implant time. The open square, open triangle, open circle and open diamond symbols indicate the mean values of CI, DNR, ODI, and DHI, respectively.
FD x (t)--->
Mean SD change FD80(t)
1.2
FD90(t) FD100(t)
0.8
0.4 0
5
10
15
20
25
30
Pos t implant time (days)--->
Fig. 2. Plot of FD80, FD90, and FD100 with postimplant time.
respectively. They also reported that the magnitude of preand postimplant dosimetry error for 131Cs implants was found to be similar to that of 103Pd implants for typical edema magnitudes of 100% and half-life of 17 days and was worse than 125 I implants (11). Results of our study, shown in Table 1, show that the values of CI, DHI, FD80, FD90, and FD100 have decreased, while the values of DNR and ODI have increased from preneedle plans to postimplant plans. These changes have statistically significant differences (p < 0.05), except for the values of ODI (p = 0.106). This illustrates that the quality of the implants has been significantly affected by prostatic edema. The main drawback in back-projected preplans is the use of the same number of seeds, as used in real-time implants in smaller prostates. This would have more impact with a higher pronounced magnitude of postimplant edema, and the dosimetric pattern would be different compared to real-time preplans. However, it would not be realistic to evaluate the edema effect if preplans performed with fewer seeds, to compare with real-time plans that had a higher number of seeds. Most reports of permanent prostate seed implants focused on the discussion of pre- or postimplant studies of dosimetric quantities, D90 or V100 (11, 27–30), and had neglected a discussion of other dosimetric quantities, such as D80, D100, V150, and V200 (27, 31). In contrast to these studies, we have investigated statistically significant changes in the values of FD80, FD90 and FD100 along with the derivatives of V100, V150, and V200, such as CI, DHI, DNR, and ODI for preneedle/implant plans and postimplant plans at day 0. It was also found that there are changes in the values of these quantities with postimplant time (Figs. 1 and 2) due to edema resolution. Figure 1 shows that the CI, DNR, and ODI increase with postimplant time, whereas the value of DHI decreases as postimplant time increases. For each patient, the values of QIs are found to vary with the postneedle prostate volume, implanted needle configuration, and number of radioactive seeds used, as well as postimplant time. Nearly all of the apparent improvement in QIs were observed by postimplant day 28. This improvement in the values of QIs leads to an improvement in the dosimetric outcome of the implants. The half-life of radioactive sources plays an important role in the accomplishment of this improvement. For example, due to the short half-life of 131Cs sources, the improvement in
D100
D90
625
250
1.2
200
1.0
T Din(t) 1.5T Din(t)
0.8
150
0.6 100
QIs--->
TD(Gy)---->
Cs-131 implants
0.4
50
0.2
0
0.0 1
11
21
31
41
2.0T Din(t) CI(t) D N R (t) ODI(t)
51
T ime (days)--->
Fig. 3. Plot of instantaneous doses TDin, 1.5 TDin, 2.0 TDin and coverage index(CI), dose nonuniformity ratio (DNR), overdose index(ODI) with postimplant time for 131Cs implants. The vertical axes on left and right show the values of TDin(t) and QIs, respectively.
QIs cannot be used to design a 131Cs implant with a better dosimetric outcome than that obtained with an 125I implant, with a relatively long half-life. This is because by 28 days, about 85% of the dose would have been delivered with 131 Cs implants, while only about 27% of the dose would have been delivered with 125I implants. Figure 1 also shows that as the amount of edema resolved with postimplant time, the prostate volume coverage improved. On the other hand, it was also seen that the dose distribution within the prostate implant become more heterogeneous with postimplant time, and if uniform seed loading was done throughout the prostate, the central portion would be relatively overdosed. Figure 2 shows an increase in FD80, FD90, and FD100 with postimplant time. However, when the actual doses delivered at FD80, FD90, and FD100 are calculated for 131Cs sources, using Eq. 21, at different times, the improvements in FD80, FD90 and FD100 could not improve actual dose delivery, hence, it becomes meaningless. Sahgal et al. (28) have performed replanning of previous 125 I implants for 131Cs seeds and have calculated the BED for manual and inverse planning. Other investigators (12,26,32) have studied the equivalent uniform dose of initial postimplant plans or in combination with pre- and initial postimplant plans for 125I and 103Pd implants. But no one has evaluated any biological parameters for 131Cs implants at different postimplant times. In the present study, I-125 implants 350
1.2
300
1.0
TDin(t)
0.8
1.5TDin(t)
250 200
0.6
150
0.4
100
QIs--->
TD(Gy)--->
Table data show mean 1 standard deviation (SD) values of different pre- and post implant dosimetric and radiobiologic parameters of 31 patients who underwent permanent 131Cs seed prostate implantation.
163.96 7.41 Gy 148.16 15.02 Gy 0.0144 139.98 6.40 Gy 126.69 20.04 Gy 0.0009 115.76 7.11 Gy 67.45 14.03 Gy 4.09 1010 145.20 4.90 Gy 134.73 9.97 Gy 0.0145 125.67 4.24 Gy 116.83 13.30 Gy 0.0009 89.63 4.66 Gy 57.74 9.33 Gy 4.76 1010 161.15 6.65 Gy 146.85 13.65 Gy 0.0145 139.42 5.83 Gy 127.15 18.34 Gy 0.0008 116.86 6.60 Gy 71.14 13.52 Gy 6.04 1010 63.66 0.43 days 62.71 0.96 days 0.0186 61.83 0.43 Gy 60.86 1.40 days 0.0006 57.53 0.65 days 51.91 2.03 days 2.31 1008 D80
Preneedle /preimplant plan Postimplant plan p value Preneedle/preimplant plan Postimplant plan p value Preneedle/preimplant plan Postimplant plan p value
10.43 0.32 Gy/day 9.74 0.65 Gy/day 0.0136 9.15 0.28 Gy/day 8.56 0.88 Gy/day 0.0008 6.74 0.32 Gy/day 4.54 0.64 Gy/day 6.31 1010
145.88 4.46 Gy 136.28 9.16 Gy 0.0145 127.97 3.97 Gy 119.54 12.31 Gy 0.0008 94.21 4.42 Gy 63.47 9.12 Gy 6.49 1010
144.34 4.46 Gy 134.74 9.16 Gy 0.0145 126.42 3.91 Gy 118.18 12.31 Gy 0.0008 92.67 4.42 Gy 61.93 9.12 Gy 6.50 1010
BEDx(decay to Teff_x) Dx(Teff_x)edema Dx(T)decay to Teff_x Dx(0) Teff_x Rx(0) Parameter Dx
Mean SD difference
Table 2. Differences between pre- and postimplant dosimetric and radiobiologic parameters
BEDx(Teff_x)edema
Prostatic edema in 131Cs permanent seed implants d T. S. KEHWAR et al.
2.0TDin(t) CI(t)
50
0.2
DNR(t)
0
0.0
ODI(t)
1
11
21
31
41
51
Time(days)--->
Fig. 4. Plot of instantaneous doses, TDin, 1.5 TDin, 2.0 TDin , and coverage index (CI), dose nonuniformity ratio (DNR), overdose index(ODI) with postimplant time for 125I implants. The vertical axes on left and right show the values of TDin(t) and QIs, respectively.
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I. J. Radiation Oncology d Biology d Physics
we have derived a relationship that accounts for the effect of edema at different dose levels, Dx, and that is used to calculate D80, D90, and D100 for preneedle/implant plans and postimplant plans at day 0 (Table 2). In the calculations of Teff_x at D80, D90, and D100, the corresponding initial dose rates were used because different dose regions received doses with different dose rates, and hence, the cell killing rates were also different. Therefore, the same effective treatment time cannot be used for all regions of the target volume; hence, each region will receive different effective doses. In Table 2, three dose parameters are described, where Dx(0) is obtained from the DVH, while Dx(T)decay to Teff_x and Dx(Teff_x)edema are calculated by using the effect of source decay and a combined factor of source decay and edema resolution, respectively. The values of Dx(T)decay to Teff_x and Dx(Teff_x)edema are used to calculate corresponding values of BED for preneedle/implant plans and postimplant plans at day 0 at dose levels of D80, D90, and D100. For both plans, i.e., for preneedle/implant plans and postimplant plans at day 0 at dose levels of D80, D90, and D100, there is an improvement in Dx(Teff_x)edema and BEDx(Teff_x)edema compared to Dx(T)decay to Teff_x and BEDx(decay to Teff_x) due to edema resolution. It is clear from Table 2 that the dose rate, dose, and BED values are higher (p < 0.02) for preneedle/implant plans than for postimplant plans at day 0 at dose levels of D80, D90, and D100, which reveals that the development of prostatic edema has tremendous impact on these quantities in postimplant plans at day 0. Comparing the BED values of pre- and postimplant plans, it was found that there is a significant loss of BED (p < 0.02) of 15.80 11.21 Gy at D80, 13.29 13.22 Gy at D90, and 48.31 10.57 Gy at D100, respectively. The BED loss at D100 is significantly more than at D80 or D90. This reveals that if 131Cs seeds are implanted using preimplant plans there will be a significant underdosing to the prostate at D100. One potential solution to compensate for this loss in BED could be to increase the initial dose rate by increasing the number of seeds to increase implanted source activity by a factor of 1.10 0.02 at D80, 1.07 0.01 at D90, and 1.48 0.06 at D100, respectively. This solution has not been clinically tested, and hence, the impact on urethral, rectal, and bladder complications is unknown. This loss in BED can also be
Volume 80, Number 2, 2011
compensated by the use of EBRT, as suggested by Chen et al. (12), who calculated BED for 131Cs implants and suggested that for a prescribed dose of 120 Gy, 1, 4, 6, 7, or 9 number of fractions of 2-Gy/fraction of EBRT could be needed to compensate for a 5%, 10%, 15%, 20%, or 25% edema-induced dose reduction, respectively. Figure 3 reveals that values of CI, DNR, and ODI increase with postimplant time due to edema resolution. At the same time, as shown in Fig.4, the dose TDin(t), 1.5 TDin(t), and 2 TDin(t) decay very fast due to the short half-life of 131Cs sources compared to the corresponding doses obtained with longer-half-life 125I implants. Therefore, the effect of edema on CI, DNR, and ODI is much more pronounced with 131Cs implants than with 125I implants because three-fourths of the dose is delivered in 2 half-lives of the source with 131Cs implants. Furthermore, during this period of time, approximately three-fourths of the edema has resolved, leaving one-fourth yet to dissipate. On the other hand, with 125I implants, approximately 20% of the dose is delivered during the same period of time (2 half-lives of 131Cs), leaving 80% of the dose yet to be delivered, during which the effect of edema would have had less or negligible effect.
CONCLUSIONS Results of this study show that edema has a more pronounced effect with the use of 131Cs implants, even if a real-time implant procedure was used. Compared to 125I implants, the improvement in QIs with 131Cs implants with postimplant time cannot improve the dosimetric and radiobiologic outcome due to fast dose delivery, i.e., the short halflife of 131Cs seeds. Therefore, we conclude that 131Cs prostate seeds implanted on the basis of preimplant plans will result in poor coverage of the prostate gland and less biological effect. Hence, it is recommended that 131Cs seeds should be implanted using the real-time procedure and postneedle plans. In a postneedle plan, the coverage of the prostate gland and other dosimetric parameters should be evaluated as satisfactory before seed implantation so that the effect of edema can be minimized.
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