external and Iodine-125 ('âI) therapy, whereas the summated t-ad doses are by no means representative of the biological effectiveness of the combination ...
hr.
0
J. Radiation
Oncology
Biol. Phys.,
1977, Vol. 2, pp. 55-60.
Pergamon
Press.
Printed
in the U.S.A
Original Contribution
TIME-DOSE EFFECTS
FACTOR (TDF) ANALYSIS OF DOSE RATE IN PERMANENT IMPLANT DOSIMETRY
COLIN G. ORTON, Ph.D. Department
of Radiation
and BANICE M. WEBBER, M.D.
Oncology, Rhode Island Hospital Medicine, Brown University
and, Section
on Radiation
The Time-Dose Factor (TDF) concept has been applied to the “biological dosbnetry” of permanent interstitial implants. The theory is derived by extrapolation to low dose rates of temporary implant data at dose rates above 25 rad/br. This extrapolation is supported by a retrospective analysis of published techniques and results of permanent implantation, and now is being used for planning such implants. Since TDFs from various modalities are additive, the TDF theory is particularly valuable for the analysis (and planning) of combined external and Iodine-125 (‘“I) therapy, whereas the summated t-ad doses are by no means representative of the biological effectiveness of the combination because of the low dose rates of 9 implants. Bracbytberapy,
Radiotherapy,
and NSD.
INTRODUCTION
In a recent paper, Kim and Hilaris’ reported data concerning tissue tolerance with permanent implants. They showed that tissues tolerated 16,000 rad from low dose rate “‘1 seed implants about as well as they tolerated only 8000rad from Radon-222 (222Rn) implants. For example, for the treatment of unresectable carcinoma of the lung, they report complication rates of 11% for 16,000 rad ‘*‘I and 13% for 8000 rad *‘*Rn implants. It is clear that defining the dose in rad is not entirely satisfactory and what is required is a statement of dose in terms of “biologically effective” units. This paper describes the use of Time-Dose Factors (TDFs) for the “biological” dosimetry of permanent interstitial implants. METHODS
The use of TDF factors both in fractionated radiotherapy and in brachytherapy has been described in detail elsewhere.“’ For the development of the brachytherapy TDF Reprint requests to: Department of Radiation Oncology, Rhode Island Hospital, 593 Eddy Street, Providence, RI 02902, U.S.A. Acknowledgements-We gratefully acknowledge the helpful advice and assistance of Drs. A. S.
theory,’ the dose rate effect was derived from an analysis of the iso-effect data of Paterson,” Green (as cited by Ellis),4 McWhirter,8 and CowelL3 and normal tissue tolerance was found to be represented by the expression: T = 2.10
x 104. r-‘.35
(1)
where T is the “iso-effect” time (hr) at dose rate r (rad/hr). This equation was derived from data at dose rates between about 25 and 150 rad/hr. However, with permanent implants, even if the initial dose rate is within this range, much of the dose will be delivered at dose rates below 25 rad/hr. The problem is clear. From the Memorial Hospital experience,’ it is known that there is a dose-rate effect at these low dose rates, but there is not sufficient data from which to derive a time-dose relationship. Therefore, it is proposed that the little data that is available be used to test a time-dose theory derived from an extrapolation of equation (1) to dose rates below 25 rad/hr. Glicksman, D. McShan and L. Reinstein and the cooperation of Drs. J. S. Laughlin and R. Mohan for providing us with the computer software for our ‘*‘I implant analysis.
55
56
Radiation Oncology 0 Biology 0 Physics
THEORY
TDF = (4.76 x 1O-3- ro’.35)/1.35h
(2)
T,,is the initial dose rate in rad/hr, and h decay constant (per hr) for the isotope. r,, is related to the total dose to complete by: ro = (TOTAL DOSE).
Substituting expression:
1977, Volume 2, No. 1 and No. 2
Table 1. TDF values for permanent implants
The use of equation (1) to derive an expression for the TDF of a permanent implant has been described elsewhere.’ The resulting equation is:
where is the Also, decay
January-February
A.
for r. in equation (2) leads to the
TDF = 3.53 x 1O-3 x (A)‘.” ’(TOTAL DOSE)‘.=.
RESULTS
the be are the
Equivalent doses of temporary and permanent implants Temporary implants. For small volumes
(less than 4 cm average dimension), typically quoted normal tissue tolerance doses for temporary implants are: 5000 rad Radium (Ra) in 3 days14(TDF = (TDF = 7000 rad Ra in 7 days6.14 6500 rad Iridium-192 (?r) in 6.5 days6 (TDF = (TDF = 7000 rad lg21rin 7 days6
TDF (“‘Rn)
TDF (19’Au)
TDF (1251)
1000 2000 3000 4000 5000
7 18 32 46 63
8 21 36 53 71
3 7 12 24
6000 7000 8000 9000 10,000
80 99 118 139 160
91 112 134 1.57 181
31 38 45 53 61
12,000 14,000 16;OOO 18,000
205
232
t
t
:
:
78 96 115
18
135
20,000
t
t
24,000 22,000 26,006
:
I
t
t
156 177 199 222
(3)
Using equation (3), a table of TDFs for various values of the total dose has been constructed for permanent implants of the three isotopes ‘**Rn, gold-198 (‘%Au), and “‘1 (Table 1). In this table, no correction has been made to account for any RBE differences between the radiations. If required, a method for correcting TDFs for relative biological effectiveness (RBE) changes has been published elsewhere.’
In order to demonstrate the validity of theory presented in this paper, it must shown that the TDF values in Table 1 realistic. This evidence is presented in following sections.
Total dose (rad)
105) 123) 114) 123)
tTDFs greater than 250 far exceed tolerance and are omitted from this table. 7000 Paterson-Parker
Roentgens (TDF = 110) (or 6440 rad)13 in 7 days’*
The above TDF of 115.
tolerance
doses
average
to a
Permanent implants. According to Kim and Hilaris,’ the equivalent tolerance dose with an 125I implant is 16,00Orad, and for a ‘*‘Rn implant it is 8000 rad, the TDFs being 115 and 118 respectively (from Table 1). These figures are clearly consistent with the above TDF values for temporary implants, and hence support the extrapolation of the use of equation (1) to low dose rates. Combined therapy
lz51 and
fractionated
external
With temporary (removable) implants, the time of application is variable, and hence the total dose delivered may be controlled. The required number of sources, their strength, and their distribution, is pre-calculated prior to implantation. Once implanted, any deviation from the planned dose (or dose distribution) can be corrected by changing the time of
TDF analysis of dose rate effects in permanent implant dosimetry 0 C. G. ORTONand B. M. WEBBER
removal of some or all of the sources. Typically, such decisions would be based upon an analysis of the computerized dose distribution of the actual implant. However, in the case of permanent implants, the time factor is fixed, and correction for implantation is not as simple. For example, if the dose is too high, one might wish to remove the offending sources. Since this is virtually impossible in most instances, experienced radiotherapists tend to implant seeds conservatively. On the other hand, if the dose is too low, the time factor cannot be increased, since this is infinity. However, a modest underdosing of the tumor may, if necessary, be rectified later, either by an additional implant, or by adding a boost of local external radiotherapy to the volume of tissue inadequately treated. This has been the policy with ‘zsI implantation at Memorial Hospital.5 This one example provides of a combined fractionated/permanent implant regime. An alternative example is the practice of preceeding a permanent implant with fractionated radiotherapy.5,7 If total dose alone were important, the dosimetry would be elementary. However, the biological effectiveness of an implant is dose-rate dependent, and the effectiveness of external radiotherapy depends on time, dose, and fractionation. Clearly, a simple addition of internal and external “rad” is unsuitable unless this is supported by the experience of the radiotherapist. This is analogous to the long-time use of mg hr in radium therapy. This was a suitable unit of dose only until experience was gained with a more representative unit (the rad). In the Memorial Technique,5 a boost of external irradiation is applied if the total minimum tumor dose from small (average dimension less than or equal to 4 cm) “‘1 implants is less than 16,000 rad. The amount of boost is determined by the difference between 8000 rad and the minimum dose to the tumor from the implant after one half-life? (60.2 days). For example, if it is determined (by computerized dosimetry or other calculation) tNote. An implant designed to deliver 16,000 to complete decay will have deposited 8000rad
rad of
57
that an ‘*‘I implant will deliver, say, 12,000 rad to complete decay, the dose after one half-life will be 6000rad, and therefore, a boost of external irradiation to a dose of 8000-6000 = 2000 rad is required. Assuming this is delivered in a conventional manner with 200rad fractions over 2 weeks,’ the total TDF is (Table 1, and Orton and Ellis, 1973):” TDF = TDF (Y) + TDF (external) =78+33 = 111. This is close to the planned TDF of 115 for a 16,000 rad implant. In fact, it is easily shown that for total l*‘I doses between 4000 and 16,000 rad, the TDF range is from 110 to 117. In contrast, the rad range is from 10,000 to 16,000. Clearly, the TDF concept presented in this paper is consistent with the Memorial Hospital experience with combined “‘1 and external fractionated radiotherapy, and represents isoeffect doses far better than the summated rad doses. Patient dosimetry
The data reported above refers to a retrospective analysis of cases. The TDF method is now being used in this Department to plan treatments. Following is a typical application of its use in the planning of a combined ‘*‘I implant/external beam course of radiotherapy. Patient:
D.C. The patient was a 68 year old male, who presented in November 1975, with a carcinoma in the left tonsillar fossa. The patient previously had undergone a course of radiation therapy between February and April 1974, for a supraglottic carcinoma of the larynx (T&Jo). The patient had tolerated this course of treatment well, and had shown complete tumor regression. Examination in October 1975, however, revealed a suspicious area in the left tonsillar fossa. A biopsy was taken and a report of squamous cell carcinoma was obtained. It was planned to treat the tonsillar area this dose after one half-life.
Radiation Oncology 0 Biology 0 Physics
58
with 4 MeV X-rays to a dose of 6500 rad in 7 weeks. Examination during the first week of treatment, however, revealed that the tumor obviously extended down the lateral pharyngeal wall on the left side (the same side as the supraglottic lesion), and it was assumed that the lesion represented extension along the pharyngeal wall and along the posterior tonsillar pillar from the original laryngeal lesion. It was necessary, therefore, to alter the patient’s field to cover the extent of tumor. This resulted in some overlap with the previously irradiated area. In view of this, it was felt that external irradiation should be terminated after 25 fractions and the remaining treatment given by a permanent lzsI seed implant. The patient received external radiotherapy to the appropriately adjusted field at the rate of 186 rad/day to a total dose of 4650 rad in 5 weeks. This was followed by a lo-day rest I---‘-
!l-
January-February 1977, Volume 2, No. 1 and No. 2
period. The residual tumor was then to be implanted with lz51seeds of strength 0.50 mCi. The problem was to determine how many seeds to use, and at what average spacing, in order to achieve the equivalent to a 16,000 rad I*? implant (TDF = 115). From the fractionated radiotherapy TDF tables and the decay factor table,” the given TDF was 73 x 0.97 = 71. Hence, the implant had to deliver a TDF of 115-71=44. From the ‘*‘I TDF table (Table l), this corresponds to a total I*‘1 dose of 7860 rad. The residual tumor was roughly ellipsoidal, of dimensions 6 cm x 4 cm x 2 cm, the average dimension being 4 cm and the elongation factor 3. The equation for calculating required seed spacing (u, cm)‘** is?:
-T
--
,...
tThe seed spacing and number of seeds can be determined with less mathematics by reference to
the “‘1 spacing
nomograph.‘.’
TDF analysis of dose rate effects in permanent implant dosimetry
U, = 0.47 lf,d,2’3u 1’3
(4)
where “fe” is the elongation correction factor (in this case 0.88), “d,” is the average dimension (in this case 4.0 cm), and “a” is the seed strength in mCi per seed. If the correct seed strength of 0.50 mCi is inserted into this equation (or the nomograph) the calculated spacing will correspond to a total lz51dose of 16,00Orad, whereas, in this case, only 7860 rad is required. The correct spacing can, however, be determined by inserting into the equation an “effective activity” in the ratio of the required doses, i.e. Put a =
0.5 x
o7860 =
1.018
mci.
0 C. G. ORTON and B. M. WEBBER
Substitution
59
into equation (4) gives u, = 1.05 cm.
The number of seeds repuired can be calculated using the relationship’~*.’ total effective activity = = :. number of seeds = i.e. 19 or 20 seeds are
5 x average dimension 20 mCi 2O/l.Olg = 19.6 needed
Twenty 0.50 mCi seeds were spaced as close to 1.05 cm apart as possible, and the resultant isodose distributions, determined from the tube shift films of the actual implant, are shown in frontal and sagittal projections in
Fig. l(b). Fig. 1. Computer generated isodose plots for the permanent “‘1 implant in patient D.C. The solid contours represent the 8000 rad isodose lines in (a) the frontal projection and (b) the sagittal projection. The grid lines are 1 cm apart and the contours outside the 8000 (D) rad line representdosesof5000(E),3000(F),2000(G)and lOOO(H)rad.
60
Radiation
Oncology
0 Biology
0 Physics
Fig. 1. Calculations were performed on a PDP 1l/45 computer using a modification of Cunningham’s NEEDLES program, with “‘1 depth-dose data from Memorial Hospital. The 8000rad isodose line closely corresponds to the desired treatment volume. DISCUSSION AND CONCLUSIONS Since clinical experience with permanent implant dosimetry supports the concept that tissue tolerance is a function of dose rate as well as of total dose,7 the dosimetry of such implants should be expressed in “biologically effective” dose units rather than in rud. However, there is not sufficient clinical data at very low dose rates from which to derive a
January-February
1977, Volume
2, No. 1 and No. 2
time-dose theory. Consequently, the TDF theory for brachytherapy at dose rates above 25 rad/hr, has been extrapolated to lower dose rates and then tested with existing clinical data. All tests support the TDF theory presented in this paper. The principal advantage of the TDF method, is that it can be applied to the analysis of different combinations of radiotherapy, such as combined fractionated and interstitial modalities. This is particularly valuable with combined external and “‘1 therapy, since the summated rad doses are by no means representative of the biological effectiveness of the combination because of the low dose rates of ‘*‘I implants.
REFERENCES 1. Anderson, L.L.: Spacing nomograph for interstitial implants of ‘*‘I seeds. Med. Phys. 3: 48-51, 1976. 2. Anderson, L.L.: Dosimetry for interstitial radiation therapy. In Handbook of Interstitial Radiotherapy, ed. by Hilaris, B.S. Acton, Publishing Sciences Group, 1975, pp. 87-115. 3. Cowell, M.A.C.: 15th Annual Report of the British Empire Cancer Campaign, London, British Empire Cancer Campaign, 1938, p. 162. 4. Ellis, F.: In Time and Dose Relationships in Radiation Biology as Applied to Radiotherapy.
Upton, Brookhaven National Laboratory, BNL50203 (C-57), 1969, p. 313. 5. Hilaris, B.S.: Interstitial radiation using Iodine 125 encapsulated sources. In Afterloading in Radiotherapy. Rockville USDHEW, Publ. No. (FDA) 72-8024, 1971, pp. 370-387. 6. Hilaris, B.S., Vallejo, A.: Head and neck cancer. In Handbook of Interstitial Radiotherapy, ed. by Hilaris, B.S. Acton, Publishing Sciences Group, 1975, pp. 127-153.
7. Kim, J.H., Hilaris, B.S.: Iodine-125 source in interstitial tumor therapy. Am. J. Roentgenol. 123: 163-169, 1975. 8. McWhirter, R.: 13th Annual Report of the British Empire Cancer Campaign, London, British Empire Cancer Campaign, 1936, p. 154. 9. Orton, C.G.: Time-dose factors (TDFs) in brachytherapy. Br. J. Radiol. 47: 603-607,1974. 10. Orton, C.G.: Errors in applying the NSD concept. Radiology 115: 233-235, 1975. 11. Orton, C.G., Ellis, F.: A simplification in the use of the NSD concept in practical radiotherapy. Br. J. Radiol. 46: 529-537,1973. 12. Paterson, R.: The Treatment of Malignant Disease by Radiotherapy, Baltimore, Williams & Wilkins, 1963, p. 210. 13. Porter, E.H.: How many rads per PatersonParker roentgen? Br. J. Radiol. 43: 629-637, 1970. 14. Von Essen, C.F.: Skin and lip. In Textbook of Radiotherapy, ed. by Fletcher G.H., 2nd Edn. Philadelphia, Lea & Febiger, 1975, p. 209.
