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Specific integral dose: A reconsideration of the integral dose concept
Radiotherapyand Oncology, 5 (1986) 215-221 Elsevier
215
RTO 00208
Specific integral dose: A reconsideration of the integral dose concept J. R o t h 1, R. Hfinig 2 and J. K u r t z 2 1Department of Radiological Physics and 2Department of Radiation Oncology, University Hospital, Basel, Switzerland
(Received 17 May 1985, revisionreceived26 August 1985,accepted 30 October 1985)
Key words: Integraldose; Absorbedenergy
Summary The integral dose represents the total energy deposited by ionizing radiation within a body. Its distribution within normal tissues can be quite variable, depending upon beam energy and radiation technique. A close look at the concept of integral dose in its various forms should be helpful in quantifying the radiation burden borne by healthy tissues outside of the target volume. The integral dose, integral target dose and relative integral target dose will be reviewed, and the concept of specific integral dose will be introduced, using as examples the external irradiation of the urinary bladder employing various energies and techniques, as well as the intracavitary therapy of gynecological cancer using an afterloading apparatus.
Introduction Both the acute and chronic toxicities associated with a course of radiotherapy are determined by a multiplicity of factors. Among the most important of these include the volume of normal tissue irradiated, the dose deposited within this volume, and the relationship between the energy absorbed within the target volume to that absorbed by healthy tissues without [4,12,13]. Since the ability of cells and tissues to recover from radiation injury might be an inverse function of dose, it appears likely that the irradiation of a large mass of healthy tissue with a small energy per unit mass would be better tolerated than the irradiation of a small mass Of normal tissue with a large energy per unit mass.
Such an argument can have particular importance when the radiotherapy is employed in combination with substances which sensitize the normal tissues or, representing a biologically similar effect, inhibit their ability to repair radiation damage. This would mean that the optimization of radiation treatment planning would also have to take such aspects into consideration. However, parameters have not yet been firmly established to guide us in determining which concepts might be most useful for approaching this problem. This will only become possible after we have developed ways to describe dose distributions according to clearly defined and uniformly applied criteria. We hope that this paper will provide at least a modest stimulus in this direction.
0167-8140/86/$03.50 9 1986ElsevierSciencePublishers B.V. (BiomedicalDivision)
216
Definition of integral dose The integral dose represents the total radiation energy absorbed by the irradiated body [5]. This is determined from the product of the mass of the irradiated material and the dose applied within this mass. Since the absorbed dose D can generally be considered constant only within a small elemental mass din, the integral dose WD must be calculated by integrating over the entire irradiated volume:
concept of specific integral dose was thus introduced to represent the integral dose determined within a particular isodose interval. Examination of the distribution of the integral doses within different isodose intervals might allow judgement as to whether a large amount of healthy tissue is being irradiated with a low dose, or a small amount of normal tissue with a high radiation dose.
Determination of integral doses
WD = f D " dm = f D " p " d V v
V
Its units are those of energy, and are therefore expressed in Joules (J = Gy 9 kg). The determination of integral dose is complicated and time-consuming, since it requires an exact knowledge of the dose distribution as well as the distribution in space of the different types of tissues and their densities. Moreover, the dose distribution outside the primary radiation beam must also be taken into consideration. The volume dose is calculated from the product of the irradiated volume and the dose applied therein. Volume dose, therefore, does not take into consideration the variable densities within the irradiated body. The concept of volume dose arose from the assumption that a patient's chances of being cured might be improved if a smaller volume of healthy tissue were irradiated [6,11]. The integral .target dose is the product of mass and dose absorbed within the target volume [2]. The integral target dose is thus a measure of the intensity with which the target volume is irradiated. The relative integral target dose indicates the relationship between the energy absorbed within the target volume to the total energy absorbed by the irradiated body. This quantity is in practice always much smaller than the ideal value of 100%. The relative integral dose by itself, however, does not suffice to quantify the radiation burden borne by the irradiated normal tissues. This would require taking into consideration the distribution of energy absorbed within the irradiated body. The proposed
The determination of integral doses requires the use of treatment plans, preferably employing the largest possible number of body cross-sections, including some outside of the primary radiation beam [8]. Integral doses can in practice be calculated using the following formula:
WD = Z ~ s
l
(D~ + D, 1)/2. (Ft,g -- Ft.~_ 1)" & " ds i
Where: s = number of cross-section, l = number of tissue type, i = number o f isodose, Di = dose corresponding to isodose i, F~ - Fi 1 = area between isodose i - 1 and i, p~ = density of tissue type l and ds = thickness of cross-sectional slice s. For this study we employed a Philips Treatment Planning System (TPS I) for the planning of photon therapy. This allows the simultaneous determination of isodoses in nine parallel cross-sectional planes. Electron dose distributions were determined using film irradiated in a Rando-Alderson Phantom. The determination of the area between two isodose curves within a given cross-sectional plane can be tedious and time-consuming. At first this was done manually using a planimeter. Later a F O R T R A N program was developed for the TPS, allowing the calculation of the area contained within any isodose curve pointwise entered into the computer. The determination of integral dose for intraeavitary afterloading therapy can be treated as a special case. The geometric relationships are simpler, since
217 the dose distributions are often rotationally symmetric. The dose distribution in a single plane perpendicular to the axis of rotation (i.e. the axis of the applicator) suffices as the basis for the calculation. For the volumetric calculation one employs Guldin's second rule [3]: ~=
2.n.a~.~
where: ai = the center o f gravity of the surface Fi as measured from the axis of rotation, F, = rotational area within the isodose curve i. The TPS computer program which we developed for determining surface areas can also be used to calculate the distance (a) of the center o f gravity from the axis of rotation, which can be represented by two points. The integral dose for afterloading therapy can thus be calculated from the following formula:
WD = ~ (Di + Di-x)/2 9 (Vi -- V i - 1 ) ' p i
The specific integral dose is obtained as an interval result in the calculation described above. This represents the integral dose between the corresponding two isodose curves. The specific integral dose, the integral dose, and the relative integral target dose can be determined in a relatively simple fashion using the program for the three-dimensional determination of dose distributions in a treatment planning system.
Examples External irradiation of the bladder Different radiation techniques and beam energies were compared, employing the urinary bladder as standard target volume [9,10]. The maximum dose within the irradiated volume was always designated as 100%. The dose distributions were determined in nine transverse body cross-sections as well as in a sagittal section. All isodose curves down to 0.5% of the maximum dose were taken into considera-
tion. The total irradiated volume was 11.2 dm a, the target volume 0.11 dm 3. Table I displays the integral doses within the irradiated volume as well as within the target volume for each of the different radiation techniques. The integral doses range from 3.33 to 8.14 J. There is little difference among the values for integral dose within the target volume (range 0.28 to 0.24 J). The relative integral target dose varies between 2.8 and 6.6%, the remaining 93.4 to 97.2% of the radiation energy being deposited within normal tissues outside the target volume. We also calculated the integral doses according to the well-known method of Mayneord [7]. Expressed relative to the values presented in Table I, this calculation resulted in ratios of 0.85 for Cobalt-60, 1.32 for 4 MV photons and 1.08 for 40 MeV electrons. It is of course desirable that the dose distribution within the target volume be as homogeneous as possible. That is, the isodose encompassing the target volume should have the highest possible value, and the range of doses within this volume should be minimized. For example, if the target volume can only be encompassed by the 80% isodose curve (as might be the case for parallel opposed fields) a dose range of + I 1.1% within this volume must be accepted. On the other hand, encompassing the target volume with the 90% isodose results in a 4- 5.2% dose variation, the 95% isodose only + 2.6%. Using the accelerators currently available, optimal treatment planning should employ techniques which allow the 85 or 90% isodose to be chosen as the reference isodose in most cases. As mentioned previously, it should be possible to consider the radiation energy absorbed within a body in a much more discriminating fashion than the previous integral dose concepts will allow (Fig. 1). Figure la presents the variation in mass per unit isodose interval as a function of the relative dose, determined for different techniques using 8 MV photons. It is apparent that the mass of tissue absorbing high, low, or moderate doses varies as a function of radiation technique. For example, certain techniques result in an equal or even greater mass of normal tissue being irradiated with the
218 TABLE I Integral doses and relative integral target doses for different energies, beam qualities for radiation techniques for irradiation of the urinary bladder (2 Gy at the edge of the target volume). No.
Energy beam quality
Radiation technique
Integral dose (J)
Relative integral target dose (%)
Body
Target volume
1 2 3 4
60Co
~
2 Fields 3 Fields 4 Fields Arc therapy
(SSD = 80) (SSD = 80) (SSD = 80) (260~
5.13 6.42 6.33 4.90
0.20 0.21 0.21 0.24
4.0 3.3 3.4 4.8
5 6 7 8 9 10 11
4 MV
X
2 Fields
(SSD (SAD (SSD (SAD (SSD (SAD (260*)
= = = = = =
100) I00) 100) 100) 100) 100)
3.82 3.33 4.38 3.93 5.14 4.22 4.04
0.22 0.22 0.21 0.23 0.23 0.22 0.24
5.8 6.6 4.8 5.7 4.4 5.2 6.0
12 13 14 15 16 17 18
8 MV
= = = = = =
100) 100) I00) 100) 100) 100)
Arc therapy
(SSD (SAD (SSD (SAD (SSD (SAD (260~)
3.75 3.59 4.49 3.54 4.23 3.66 3.77
0.21 0.23 0.22 0.22 0.21 0.22 0.22
5.6 6.5 4.8 6.3 5.1 5.9 5.9
19 20
40 MeV
2 Fields Arc therapy
(SSD = 100) (180~)
4.82 8.14
0.22 0.23
4.6 2.8
3 Fields 4 Fields Arc therapy X
2 Fields 3 Fields 4 Fields
e-
same d o s e as t h a t a b s o r b e d w i t h i n the t a r g e t volume. This is the case with b o t h t e c h n i q u e s e m p l o y ing o p p o s e d fields (technique n u m b e r 12 a n d 13 in Fig. 1a). It is r e a d i l y a p p a r e n t t h a t there will a l w a y s be a large v o l u m e o f n o r m a l tissue r a d i a t e d with relatively low doses. T h e v a r i a t i o n in energy a b s o r p t i o n within h e a l t h y tissues as a f u n c t i o n o f r a d i a t i o n q u a l i t y a n d techniques b e c o m e s even m o r e striking w h e n the specific i n t e g r a l d o s e is t a k e n i n t o c o n s i d e r a tion. F i g u r e 2 d i s p l a y s circle d i a g r a m s o f the integral doses ( b o t h for the t a r g e t v o l u m e a n d for n o r m a l tissues) w i t h i n the 7 0 % i s o d o s e curve, b e t w e e n the 50 a n d 7 0 % isodose, a n d o u t s i d e the 50% isodose line. M a n y techniques result in a similar distrib u t i o n o f specific integral doses. H o w e v e r , c e r t a i n techniques are a s s o c i a t e d w i t h a large specific integral d o s e w i t h i n the 70% i s o d o s e line, for e x a m ple, t r e a t m e n t p l a n s 12 a n d 13 in Fig. 2a. This, o f
course, r e p r e s e n t s excessive i r r a d i a t i o n o f h e a l t h y tissues. I n c o n t r a s t , t r e a t m e n t p l a n s 4 a n d 18 (Fig. 2a,b) result in the p r e p o n d e r a n c e o f the i n t e g r a l d o s e d i s t r i b u t e d o u t s i d e in the 5 0 % i s o d o s e curve, r e p r e s e n t i n g a relatively f a v o r a b l e n o r m a l tissue radiation burden.
Gynecologic intracavitary irradiation using afterloading technique T h e integral d o s e s a s s o c i a t e d w i t h i n t r a c a v i t a r y t h e r a p y (Buchler a f t e r l o a d i n g a p p a r a t u s o u t f i t t e d with a 137Cs source) are p r e s e n t e d briefly as a further e x a m p l e . D i f f e r e n t t a r g e t v o l u m e s a r e c o m p a r e d : cervix, e n d o m e t r i a l , a n d v a g i n a l cancers. T h e t a r g e t v o l u m e s v a r i e d b e t w e e n 0.05 a n d 0.35 d m 3, t a k i n g i n t o c o n s i d e r a t i o n a b o d y v o l u m e o f a p p r o x i m a t e l y 12.9 d m 3. O n c e a g a i n t h e i s o d o s e s were d e t e r m i n e d using the Philips TPS. T h e m a x i -
219
Technique No. 12 2 fields (SSD)
13 2 fields (isocentric)
-
-
-
-
15 3 fields (isocentric)
1OOOO
"6
~
~
-
16 4 fields (SSD)
i
17 18 4 fields (isocentric) arc therapy (260*)
i
t
2"0o0 1000
t9--
&
.~0 0 9~ tO
500
200
J
-L
I-
100 50
-.j-
,-
20
-~ _ l
$
Lj
.__
!
[31
|
N!
B 20 40 60 8O 100 %
0
20 40 60 80 100 %
!1 0
-L -I_
L
II
N
E
]~j-
20 40 60 80 100 0
f~
I
I
20 40 60 80 100 0
%
%
20 40 60 80 100 0 %
20
40 60
,I
80 100
percentage value of absorbed dose (b)
Technique No. 4 60C o .~ sooo
11 4MVX
18 8 MV X
20 20MeVe-
"6 2o00 ,>
rooo
O;
.-i
500
o ~D o
200
.~
loo
~ .___
50
~
20
E
-L
S
,0
N
5
0
L
3 .........,
0
20 40 60 80 100 0 %
20 40 60 80 100 0 %
20 40 60 80 100 0 %
20 40 60 80 100 %
percentage value of absorbed dose Fig. 1. Distribution of absorbed energy in the whole body and in the target volume (hatched). The arrows indicate the absorbed dose of 2 Gy. Note the logarithmic scale. (a) For different techniques with 8 MV photons; (b) for arc therapy with different radiation qualities.
220
TECHNIQUE NO 12 20PP' FIELDS (SSD ~ i00)
TECH~HQIJE NO. 13 20PP. FIELDS (SA~ ~ i00)
TECHNIQUE ~I0. 15 3 FIE~.DS (SAD : i00}
TECHN[QUE co r
~[o.
TECHNIQUE NO, =16100) 4 ~[ELDS (SSD
TECHNIQUE NO, l l 4 Ft~.COS ~SAB = lot?)
TECHNIQUE NO , 15 ~C "~,~Y ~259 ~)
TEEHN[QUE 5 "~v x
NO
z4
18
TECHtHQUE a MV x
NO. 11
TfCHNtaUE 20 MEV e
"~0. ~0
Fig. 2. Specific integral doses for irradiation of the urinary bladder. (a) For different techniques with 8 MV photons; (b) for arc therapy with different qualities. II, Target volumes; [II],normal tissues within the 70% isodose (> 70%); IZI,normal tissues between the 50 and the 70% isodoses; I-q, normal tissues outside the 50% isodose (< 50%).
m u m dose was l o c a t e d on the a p p l i c a t o r surface. T a b l e II illustrates the expected v a r i a t i o n in the i n t e g r a l t a r g e t doses (between 14.0 a n d 34.3 J), as a f u n c t i o n o f the distinctly different t a r g e t volumes. T h e relative integral t a r g e t doses v a r i e d b e t w e e n 13.0 a n d 23.9% as expected c o n s i d e r a b l y g r e a t e r t h a n for e x t e r n a l b e a m t h e r a p y .
D i s c u s s i o n
It is the t a s k o f t r e a t m e n t p l a n n i n g , t h r o u g h a p p r o p r i a t e choice o f r a d i a t i o n p a r a m e t e r s , to strive for the fulfillment o f the following c o n d i t i o n s :
- highest p o s s i b l e relative d o s e w i t h i n the t a r g e t volume smallest p o s s i b l e difference b e t w e e n the m a x i m u m a n d m i n i m u m d o s e s w i t h i n the t a r g e t volume greatest p o s s i b l e relative i n t e g r a l t a r g e t d o s e smallest p o s s i b l e f r a c t i o n o f i r r a d i a t e d n o r m a l tissues a b s o r b i n g h i g h e r doses.
-
-
-
T h e relative i n t e g r a l t a r g e t d o s e c a n n o t b y itself a l w a y s lead to the o p t i m a l choice o f b e a m q u a l i t y a n d r a d i a t i o n technique, b u t it m a y p r o v i d e useful hints a n d reference criteria. A l t h o u g h the relative integral t a r g e t doses are a p p r o x i m a t e l y the s a m e for
TABLE II Integral doses and relative integral target doses for different target volumes for intracavitary therapy (137Cs, Buchler afterloading apparatus). 500 Gy on the surface of the applicator. No.
1 2 3 4 5 6
Target volume
Carcinoma of the cervix or endometrial Carcinoma of the vagina Carcinoma of the endometrial Carcinoma of the cervix Carcinoma of the cervix Carcinoma of the cervix
Disk for movement of the source [11
No. No. No. No. No. No.
1 2 9 10 2 and 10 (1:1) 2 and 10 (1:2)
Integral dose (J) Body
Target volume
14.01 34.31 23.54 24.63 29.47 27.85
1.97 4.47 3.67 5.54 6.82 6.39
Relative integral target dose (%)
14.1 13.0 15.6 22.5 23.1 23.9
221 treatment plans 12 and 18 in Table I, the specific integral dose calculation represented in Fig. 2a results in quite dissimilar values. This c o m p a r i s o n illustrates h o w the dose distribution within n o r m a l tissues can be strikingly different, despite equivalent target doses and similar integral doses. T r e a t m e n t plan 18 represents a significantly smaller radiation burden for the healthy tissues than plan 12 (see Fig. 2a). The differential representation o f tissue mass as function o f dose (as in Fig. 1) m a y lead to better m e t h o d s of quantifying energy a b s o r p t i o n b y normal tissues, thus contributing to i m p r o v e d treatment planning. Obviously m u c h additional experience will be required to achieve this goal. The partition o f the integral dose into different dose ranges (as in Fig. 2) provides a clear, objective means o f j u d g i n g the radiation b u r d e n u p o n the healthy tissues. This furnishes a basis for c o m p a r ison, which should facilitate the choice o f optimal b e a m quality and radiation technique. O f course it is possible that organ-specific biological factors could have an equally i m p o r t a n t role in the optimalisation o f radiation treatment planning. However, such differences in n o r m a l tissue tolerances have thus far not routinely been incorporated into integral dose concepts.
Acknowledgments The authors would like to express their appreciation to Ms. I. V o g t ( D e p a r t m e n t o f R a d i a t i o n Oncology) for her help in preparing the isodose plans, as well as to Ms. R. Blauenstein ( D e p a r t m e n t o f Radiological Physics) and the personnel in the treatment planning section for the planimetric integral dose determinations.
References 1 Arcovito, G., Piermattei, A., D'Abrarno, G. and Bassi, F. A. Intracavitary dosimetry of a high-~ctivity remote loading device with oscillating source. Br. J. Radio1. 57:1119-1130, 1984. 2 Becker, J. and Schubert, G. Die Supervolttherapie. Thieme, Stuttgart, p. 161, 1961. 3 Erwe, F. Differential- und Integralrechnung. 2. Band Hochschultaschenbficher Nr. 31/31a. Bibliographisches Institut, Mannheim, p. 181, 1964. 4 Gremmel, H., Hebbinghaus, D. and Wendhausen, H. An optimisation criteria for dose distributions, minimising the radiation effect in healthy tissue. Proceedings of the VIth Int. Conference on the Use of Computers in Radiation Therapy, G6ttingen, p. 199, 1977. 5 Johns, H. E. and Cunningham, J. R. The Physics of Radiology, 4th edn, pp. 402-407. Charles C. Thomas, Springfield, 1983. 6 Jfingling, O. Zur Frage der Raumdosis in der R6ntgentiefentherapie. M/inchener med. Wochenschr. 71: 123, 1924. 7 Mayneord, W. V. Measurement of radiation for medical purposes. Proc. Phys. Soc. 54: 405, 1942. 8 Roth, J. and Hfinig, R. Die Bestimmung der Integraldosen in der Strahlentherapie. Tagungsberichte Schweiz. Ges. Strahlenbiol. Strahlenphys. Bern, pp. 150-157, 1980. 9 Roth, J. and Hfinig, R. Determination and comparison of specific integral doses in radiation therapy. World Congress on Medical Physics and Biomedical Engineering 1982, Hamburg, No. 27.84, 1982. 10 Roth, J. and Hiinig, R. Experimental study of integral doses in radiation therapy. Tagungsberichte Schweiz. Ges. Strahlenbiol. Strahlenphys. Epalinges/Lausanne, pp. 41-47, 1982. 11 Sch6n, D. Systematische Untersuchungen fiber die tats~ichliche Strahlenbelastung des Kranken bei der therapeutischen Anwendung schneller Elektronen, konventioneller und ultraharter R6ntgenstrahlen. Strahlentherapie 120: 108, 135, 335, 533, 1963. 12 Schultheiss, T. E., Orton, C. G. and Peck, R. A. Models in radiotherapy: volume effects. Med. Physics 10: 410, 1983. 13 Wolbarst, A. B., Chin, L. M. and Svensson, G. K. Optimization of radiation therapy: integral-response of a model biological system. Int. J. Radiat. Oncol. Biol. Phys. 8: 1761, 1982.
215
RTO 00208
Specific integral dose: A reconsideration of the integral dose concept J. R o t h 1, R. Hfinig 2 and J. K u r t z 2 1Department of Radiological Physics and 2Department of Radiation Oncology, University Hospital, Basel, Switzerland
(Received 17 May 1985, revisionreceived26 August 1985,accepted 30 October 1985)
Key words: Integraldose; Absorbedenergy
Summary The integral dose represents the total energy deposited by ionizing radiation within a body. Its distribution within normal tissues can be quite variable, depending upon beam energy and radiation technique. A close look at the concept of integral dose in its various forms should be helpful in quantifying the radiation burden borne by healthy tissues outside of the target volume. The integral dose, integral target dose and relative integral target dose will be reviewed, and the concept of specific integral dose will be introduced, using as examples the external irradiation of the urinary bladder employing various energies and techniques, as well as the intracavitary therapy of gynecological cancer using an afterloading apparatus.
Introduction Both the acute and chronic toxicities associated with a course of radiotherapy are determined by a multiplicity of factors. Among the most important of these include the volume of normal tissue irradiated, the dose deposited within this volume, and the relationship between the energy absorbed within the target volume to that absorbed by healthy tissues without [4,12,13]. Since the ability of cells and tissues to recover from radiation injury might be an inverse function of dose, it appears likely that the irradiation of a large mass of healthy tissue with a small energy per unit mass would be better tolerated than the irradiation of a small mass Of normal tissue with a large energy per unit mass.
Such an argument can have particular importance when the radiotherapy is employed in combination with substances which sensitize the normal tissues or, representing a biologically similar effect, inhibit their ability to repair radiation damage. This would mean that the optimization of radiation treatment planning would also have to take such aspects into consideration. However, parameters have not yet been firmly established to guide us in determining which concepts might be most useful for approaching this problem. This will only become possible after we have developed ways to describe dose distributions according to clearly defined and uniformly applied criteria. We hope that this paper will provide at least a modest stimulus in this direction.
0167-8140/86/$03.50 9 1986ElsevierSciencePublishers B.V. (BiomedicalDivision)
216
Definition of integral dose The integral dose represents the total radiation energy absorbed by the irradiated body [5]. This is determined from the product of the mass of the irradiated material and the dose applied within this mass. Since the absorbed dose D can generally be considered constant only within a small elemental mass din, the integral dose WD must be calculated by integrating over the entire irradiated volume:
concept of specific integral dose was thus introduced to represent the integral dose determined within a particular isodose interval. Examination of the distribution of the integral doses within different isodose intervals might allow judgement as to whether a large amount of healthy tissue is being irradiated with a low dose, or a small amount of normal tissue with a high radiation dose.
Determination of integral doses
WD = f D " dm = f D " p " d V v
V
Its units are those of energy, and are therefore expressed in Joules (J = Gy 9 kg). The determination of integral dose is complicated and time-consuming, since it requires an exact knowledge of the dose distribution as well as the distribution in space of the different types of tissues and their densities. Moreover, the dose distribution outside the primary radiation beam must also be taken into consideration. The volume dose is calculated from the product of the irradiated volume and the dose applied therein. Volume dose, therefore, does not take into consideration the variable densities within the irradiated body. The concept of volume dose arose from the assumption that a patient's chances of being cured might be improved if a smaller volume of healthy tissue were irradiated [6,11]. The integral .target dose is the product of mass and dose absorbed within the target volume [2]. The integral target dose is thus a measure of the intensity with which the target volume is irradiated. The relative integral target dose indicates the relationship between the energy absorbed within the target volume to the total energy absorbed by the irradiated body. This quantity is in practice always much smaller than the ideal value of 100%. The relative integral dose by itself, however, does not suffice to quantify the radiation burden borne by the irradiated normal tissues. This would require taking into consideration the distribution of energy absorbed within the irradiated body. The proposed
The determination of integral doses requires the use of treatment plans, preferably employing the largest possible number of body cross-sections, including some outside of the primary radiation beam [8]. Integral doses can in practice be calculated using the following formula:
WD = Z ~ s
l
(D~ + D, 1)/2. (Ft,g -- Ft.~_ 1)" & " ds i
Where: s = number of cross-section, l = number of tissue type, i = number o f isodose, Di = dose corresponding to isodose i, F~ - Fi 1 = area between isodose i - 1 and i, p~ = density of tissue type l and ds = thickness of cross-sectional slice s. For this study we employed a Philips Treatment Planning System (TPS I) for the planning of photon therapy. This allows the simultaneous determination of isodoses in nine parallel cross-sectional planes. Electron dose distributions were determined using film irradiated in a Rando-Alderson Phantom. The determination of the area between two isodose curves within a given cross-sectional plane can be tedious and time-consuming. At first this was done manually using a planimeter. Later a F O R T R A N program was developed for the TPS, allowing the calculation of the area contained within any isodose curve pointwise entered into the computer. The determination of integral dose for intraeavitary afterloading therapy can be treated as a special case. The geometric relationships are simpler, since
217 the dose distributions are often rotationally symmetric. The dose distribution in a single plane perpendicular to the axis of rotation (i.e. the axis of the applicator) suffices as the basis for the calculation. For the volumetric calculation one employs Guldin's second rule [3]: ~=
2.n.a~.~
where: ai = the center o f gravity of the surface Fi as measured from the axis of rotation, F, = rotational area within the isodose curve i. The TPS computer program which we developed for determining surface areas can also be used to calculate the distance (a) of the center o f gravity from the axis of rotation, which can be represented by two points. The integral dose for afterloading therapy can thus be calculated from the following formula:
WD = ~ (Di + Di-x)/2 9 (Vi -- V i - 1 ) ' p i
The specific integral dose is obtained as an interval result in the calculation described above. This represents the integral dose between the corresponding two isodose curves. The specific integral dose, the integral dose, and the relative integral target dose can be determined in a relatively simple fashion using the program for the three-dimensional determination of dose distributions in a treatment planning system.
Examples External irradiation of the bladder Different radiation techniques and beam energies were compared, employing the urinary bladder as standard target volume [9,10]. The maximum dose within the irradiated volume was always designated as 100%. The dose distributions were determined in nine transverse body cross-sections as well as in a sagittal section. All isodose curves down to 0.5% of the maximum dose were taken into considera-
tion. The total irradiated volume was 11.2 dm a, the target volume 0.11 dm 3. Table I displays the integral doses within the irradiated volume as well as within the target volume for each of the different radiation techniques. The integral doses range from 3.33 to 8.14 J. There is little difference among the values for integral dose within the target volume (range 0.28 to 0.24 J). The relative integral target dose varies between 2.8 and 6.6%, the remaining 93.4 to 97.2% of the radiation energy being deposited within normal tissues outside the target volume. We also calculated the integral doses according to the well-known method of Mayneord [7]. Expressed relative to the values presented in Table I, this calculation resulted in ratios of 0.85 for Cobalt-60, 1.32 for 4 MV photons and 1.08 for 40 MeV electrons. It is of course desirable that the dose distribution within the target volume be as homogeneous as possible. That is, the isodose encompassing the target volume should have the highest possible value, and the range of doses within this volume should be minimized. For example, if the target volume can only be encompassed by the 80% isodose curve (as might be the case for parallel opposed fields) a dose range of + I 1.1% within this volume must be accepted. On the other hand, encompassing the target volume with the 90% isodose results in a 4- 5.2% dose variation, the 95% isodose only + 2.6%. Using the accelerators currently available, optimal treatment planning should employ techniques which allow the 85 or 90% isodose to be chosen as the reference isodose in most cases. As mentioned previously, it should be possible to consider the radiation energy absorbed within a body in a much more discriminating fashion than the previous integral dose concepts will allow (Fig. 1). Figure la presents the variation in mass per unit isodose interval as a function of the relative dose, determined for different techniques using 8 MV photons. It is apparent that the mass of tissue absorbing high, low, or moderate doses varies as a function of radiation technique. For example, certain techniques result in an equal or even greater mass of normal tissue being irradiated with the
218 TABLE I Integral doses and relative integral target doses for different energies, beam qualities for radiation techniques for irradiation of the urinary bladder (2 Gy at the edge of the target volume). No.
Energy beam quality
Radiation technique
Integral dose (J)
Relative integral target dose (%)
Body
Target volume
1 2 3 4
60Co
~
2 Fields 3 Fields 4 Fields Arc therapy
(SSD = 80) (SSD = 80) (SSD = 80) (260~
5.13 6.42 6.33 4.90
0.20 0.21 0.21 0.24
4.0 3.3 3.4 4.8
5 6 7 8 9 10 11
4 MV
X
2 Fields
(SSD (SAD (SSD (SAD (SSD (SAD (260*)
= = = = = =
100) I00) 100) 100) 100) 100)
3.82 3.33 4.38 3.93 5.14 4.22 4.04
0.22 0.22 0.21 0.23 0.23 0.22 0.24
5.8 6.6 4.8 5.7 4.4 5.2 6.0
12 13 14 15 16 17 18
8 MV
= = = = = =
100) 100) I00) 100) 100) 100)
Arc therapy
(SSD (SAD (SSD (SAD (SSD (SAD (260~)
3.75 3.59 4.49 3.54 4.23 3.66 3.77
0.21 0.23 0.22 0.22 0.21 0.22 0.22
5.6 6.5 4.8 6.3 5.1 5.9 5.9
19 20
40 MeV
2 Fields Arc therapy
(SSD = 100) (180~)
4.82 8.14
0.22 0.23
4.6 2.8
3 Fields 4 Fields Arc therapy X
2 Fields 3 Fields 4 Fields
e-
same d o s e as t h a t a b s o r b e d w i t h i n the t a r g e t volume. This is the case with b o t h t e c h n i q u e s e m p l o y ing o p p o s e d fields (technique n u m b e r 12 a n d 13 in Fig. 1a). It is r e a d i l y a p p a r e n t t h a t there will a l w a y s be a large v o l u m e o f n o r m a l tissue r a d i a t e d with relatively low doses. T h e v a r i a t i o n in energy a b s o r p t i o n within h e a l t h y tissues as a f u n c t i o n o f r a d i a t i o n q u a l i t y a n d techniques b e c o m e s even m o r e striking w h e n the specific i n t e g r a l d o s e is t a k e n i n t o c o n s i d e r a tion. F i g u r e 2 d i s p l a y s circle d i a g r a m s o f the integral doses ( b o t h for the t a r g e t v o l u m e a n d for n o r m a l tissues) w i t h i n the 7 0 % i s o d o s e curve, b e t w e e n the 50 a n d 7 0 % isodose, a n d o u t s i d e the 50% isodose line. M a n y techniques result in a similar distrib u t i o n o f specific integral doses. H o w e v e r , c e r t a i n techniques are a s s o c i a t e d w i t h a large specific integral d o s e w i t h i n the 70% i s o d o s e line, for e x a m ple, t r e a t m e n t p l a n s 12 a n d 13 in Fig. 2a. This, o f
course, r e p r e s e n t s excessive i r r a d i a t i o n o f h e a l t h y tissues. I n c o n t r a s t , t r e a t m e n t p l a n s 4 a n d 18 (Fig. 2a,b) result in the p r e p o n d e r a n c e o f the i n t e g r a l d o s e d i s t r i b u t e d o u t s i d e in the 5 0 % i s o d o s e curve, r e p r e s e n t i n g a relatively f a v o r a b l e n o r m a l tissue radiation burden.
Gynecologic intracavitary irradiation using afterloading technique T h e integral d o s e s a s s o c i a t e d w i t h i n t r a c a v i t a r y t h e r a p y (Buchler a f t e r l o a d i n g a p p a r a t u s o u t f i t t e d with a 137Cs source) are p r e s e n t e d briefly as a further e x a m p l e . D i f f e r e n t t a r g e t v o l u m e s a r e c o m p a r e d : cervix, e n d o m e t r i a l , a n d v a g i n a l cancers. T h e t a r g e t v o l u m e s v a r i e d b e t w e e n 0.05 a n d 0.35 d m 3, t a k i n g i n t o c o n s i d e r a t i o n a b o d y v o l u m e o f a p p r o x i m a t e l y 12.9 d m 3. O n c e a g a i n t h e i s o d o s e s were d e t e r m i n e d using the Philips TPS. T h e m a x i -
219
Technique No. 12 2 fields (SSD)
13 2 fields (isocentric)
-
-
-
-
15 3 fields (isocentric)
1OOOO
"6
~
~
-
16 4 fields (SSD)
i
17 18 4 fields (isocentric) arc therapy (260*)
i
t
2"0o0 1000
t9--
&
.~0 0 9~ tO
500
200
J
-L
I-
100 50
-.j-
,-
20
-~ _ l
$
Lj
.__
!
[31
|
N!
B 20 40 60 8O 100 %
0
20 40 60 80 100 %
!1 0
-L -I_
L
II
N
E
]~j-
20 40 60 80 100 0
f~
I
I
20 40 60 80 100 0
%
%
20 40 60 80 100 0 %
20
40 60
,I
80 100
percentage value of absorbed dose (b)
Technique No. 4 60C o .~ sooo
11 4MVX
18 8 MV X
20 20MeVe-
"6 2o00 ,>
rooo
O;
.-i
500
o ~D o
200
.~
loo
~ .___
50
~
20
E
-L
S
,0
N
5
0
L
3 .........,
0
20 40 60 80 100 0 %
20 40 60 80 100 0 %
20 40 60 80 100 0 %
20 40 60 80 100 %
percentage value of absorbed dose Fig. 1. Distribution of absorbed energy in the whole body and in the target volume (hatched). The arrows indicate the absorbed dose of 2 Gy. Note the logarithmic scale. (a) For different techniques with 8 MV photons; (b) for arc therapy with different radiation qualities.
220
TECHNIQUE NO 12 20PP' FIELDS (SSD ~ i00)
TECH~HQIJE NO. 13 20PP. FIELDS (SA~ ~ i00)
TECHNIQUE ~I0. 15 3 FIE~.DS (SAD : i00}
TECHN[QUE co r
~[o.
TECHNIQUE NO, =16100) 4 ~[ELDS (SSD
TECHNIQUE NO, l l 4 Ft~.COS ~SAB = lot?)
TECHNIQUE NO , 15 ~C "~,~Y ~259 ~)
TEEHN[QUE 5 "~v x
NO
z4
18
TECHtHQUE a MV x
NO. 11
TfCHNtaUE 20 MEV e
"~0. ~0
Fig. 2. Specific integral doses for irradiation of the urinary bladder. (a) For different techniques with 8 MV photons; (b) for arc therapy with different qualities. II, Target volumes; [II],normal tissues within the 70% isodose (> 70%); IZI,normal tissues between the 50 and the 70% isodoses; I-q, normal tissues outside the 50% isodose (< 50%).
m u m dose was l o c a t e d on the a p p l i c a t o r surface. T a b l e II illustrates the expected v a r i a t i o n in the i n t e g r a l t a r g e t doses (between 14.0 a n d 34.3 J), as a f u n c t i o n o f the distinctly different t a r g e t volumes. T h e relative integral t a r g e t doses v a r i e d b e t w e e n 13.0 a n d 23.9% as expected c o n s i d e r a b l y g r e a t e r t h a n for e x t e r n a l b e a m t h e r a p y .
D i s c u s s i o n
It is the t a s k o f t r e a t m e n t p l a n n i n g , t h r o u g h a p p r o p r i a t e choice o f r a d i a t i o n p a r a m e t e r s , to strive for the fulfillment o f the following c o n d i t i o n s :
- highest p o s s i b l e relative d o s e w i t h i n the t a r g e t volume smallest p o s s i b l e difference b e t w e e n the m a x i m u m a n d m i n i m u m d o s e s w i t h i n the t a r g e t volume greatest p o s s i b l e relative i n t e g r a l t a r g e t d o s e smallest p o s s i b l e f r a c t i o n o f i r r a d i a t e d n o r m a l tissues a b s o r b i n g h i g h e r doses.
-
-
-
T h e relative i n t e g r a l t a r g e t d o s e c a n n o t b y itself a l w a y s lead to the o p t i m a l choice o f b e a m q u a l i t y a n d r a d i a t i o n technique, b u t it m a y p r o v i d e useful hints a n d reference criteria. A l t h o u g h the relative integral t a r g e t doses are a p p r o x i m a t e l y the s a m e for
TABLE II Integral doses and relative integral target doses for different target volumes for intracavitary therapy (137Cs, Buchler afterloading apparatus). 500 Gy on the surface of the applicator. No.
1 2 3 4 5 6
Target volume
Carcinoma of the cervix or endometrial Carcinoma of the vagina Carcinoma of the endometrial Carcinoma of the cervix Carcinoma of the cervix Carcinoma of the cervix
Disk for movement of the source [11
No. No. No. No. No. No.
1 2 9 10 2 and 10 (1:1) 2 and 10 (1:2)
Integral dose (J) Body
Target volume
14.01 34.31 23.54 24.63 29.47 27.85
1.97 4.47 3.67 5.54 6.82 6.39
Relative integral target dose (%)
14.1 13.0 15.6 22.5 23.1 23.9
221 treatment plans 12 and 18 in Table I, the specific integral dose calculation represented in Fig. 2a results in quite dissimilar values. This c o m p a r i s o n illustrates h o w the dose distribution within n o r m a l tissues can be strikingly different, despite equivalent target doses and similar integral doses. T r e a t m e n t plan 18 represents a significantly smaller radiation burden for the healthy tissues than plan 12 (see Fig. 2a). The differential representation o f tissue mass as function o f dose (as in Fig. 1) m a y lead to better m e t h o d s of quantifying energy a b s o r p t i o n b y normal tissues, thus contributing to i m p r o v e d treatment planning. Obviously m u c h additional experience will be required to achieve this goal. The partition o f the integral dose into different dose ranges (as in Fig. 2) provides a clear, objective means o f j u d g i n g the radiation b u r d e n u p o n the healthy tissues. This furnishes a basis for c o m p a r ison, which should facilitate the choice o f optimal b e a m quality and radiation technique. O f course it is possible that organ-specific biological factors could have an equally i m p o r t a n t role in the optimalisation o f radiation treatment planning. However, such differences in n o r m a l tissue tolerances have thus far not routinely been incorporated into integral dose concepts.
Acknowledgments The authors would like to express their appreciation to Ms. I. V o g t ( D e p a r t m e n t o f R a d i a t i o n Oncology) for her help in preparing the isodose plans, as well as to Ms. R. Blauenstein ( D e p a r t m e n t o f Radiological Physics) and the personnel in the treatment planning section for the planimetric integral dose determinations.
References 1 Arcovito, G., Piermattei, A., D'Abrarno, G. and Bassi, F. A. Intracavitary dosimetry of a high-~ctivity remote loading device with oscillating source. Br. J. Radio1. 57:1119-1130, 1984. 2 Becker, J. and Schubert, G. Die Supervolttherapie. Thieme, Stuttgart, p. 161, 1961. 3 Erwe, F. Differential- und Integralrechnung. 2. Band Hochschultaschenbficher Nr. 31/31a. Bibliographisches Institut, Mannheim, p. 181, 1964. 4 Gremmel, H., Hebbinghaus, D. and Wendhausen, H. An optimisation criteria for dose distributions, minimising the radiation effect in healthy tissue. Proceedings of the VIth Int. Conference on the Use of Computers in Radiation Therapy, G6ttingen, p. 199, 1977. 5 Johns, H. E. and Cunningham, J. R. The Physics of Radiology, 4th edn, pp. 402-407. Charles C. Thomas, Springfield, 1983. 6 Jfingling, O. Zur Frage der Raumdosis in der R6ntgentiefentherapie. M/inchener med. Wochenschr. 71: 123, 1924. 7 Mayneord, W. V. Measurement of radiation for medical purposes. Proc. Phys. Soc. 54: 405, 1942. 8 Roth, J. and Hfinig, R. Die Bestimmung der Integraldosen in der Strahlentherapie. Tagungsberichte Schweiz. Ges. Strahlenbiol. Strahlenphys. Bern, pp. 150-157, 1980. 9 Roth, J. and Hfinig, R. Determination and comparison of specific integral doses in radiation therapy. World Congress on Medical Physics and Biomedical Engineering 1982, Hamburg, No. 27.84, 1982. 10 Roth, J. and Hiinig, R. Experimental study of integral doses in radiation therapy. Tagungsberichte Schweiz. Ges. Strahlenbiol. Strahlenphys. Epalinges/Lausanne, pp. 41-47, 1982. 11 Sch6n, D. Systematische Untersuchungen fiber die tats~ichliche Strahlenbelastung des Kranken bei der therapeutischen Anwendung schneller Elektronen, konventioneller und ultraharter R6ntgenstrahlen. Strahlentherapie 120: 108, 135, 335, 533, 1963. 12 Schultheiss, T. E., Orton, C. G. and Peck, R. A. Models in radiotherapy: volume effects. Med. Physics 10: 410, 1983. 13 Wolbarst, A. B., Chin, L. M. and Svensson, G. K. Optimization of radiation therapy: integral-response of a model biological system. Int. J. Radiat. Oncol. Biol. Phys. 8: 1761, 1982.