lnf. J Radiation Oncology tlwl Phys.. Vol. 18. pp. 1495-1501 Printed in the U.S.A. All rights reserved.
0360.3016/90 $3.00 + .oO Copyright 0 1990 Pergamon Press plc
??Technical Innovations and Notes
TREATMENT
PLANNING FOR GAMMA KNIFE RADIOSURGERY WITH MULTIPLE ISOCENTERS
JOHN C. FLICKINGER, M.D.,* L. DADE LUNSFORD, M.D.,+ ANDREW Wu, PH.D.,* ANN H. MAITZ, M.S.* AND ANDRE M. KALEND, PH.D.* University of Pittsburgh School of Medicine, and the Pittsburgh Cancer Institute, Pittsburgh, PA 152 13 Many arteriovenous malformations and tumors suitable for radiosurgicaltreatmenthave non-sphericalor irregular shapes. Forty-eight percentof the first 156 patients treatedwith the gammaunit at the Universityof Pittsburgh requiredtreatmentwith two or more isocenters to optimize dose distributions. Dose distributions for combining gamma knife treatments to two or more isocenters were systematically investigated. High speed computerized dosimetry was performed using specially developed software and dose distributions were confirmed with film densitometry. We have developed guidelines for treatmentto two or more isocenters which help reduce treatment planning time, and facilitate selection of treatment doses and optimum dose distributions. These guidelines include maintaining an account of the distances between all isocenters, using a catalogue of sample two-isocenter isodose plans, comparing dose volume histograms, and calculating complication probabilities using the integrated logistic formula. Radiosurgery, Gamma knife, Dosimetry, Integrated logistic formula, Dose volume histogram.
INTRODUCTION
unit equipped with 18 mm diameter collimators in addition to the standard 4, 8, and 14 mm diameter collimator helmets. Details of dosimetry for each of the different collimator sizes have been reported (18, 3 1). Since many target volumes are irregularly shaped or slightly larger in one or two dimensions than the 50% isodose volume for the 18 mm diameter collimator helmet, it is often necessary to consider treatment with two isocenters. The effects on the dose distribution of varying the distance between two isocenters are presented in this paper along with guidelines for choosing treatment doses and dose distributions for radiosurgery with multiple isocenters.
The concept of radiosurgery was introduced by Leksell in 195 1 ( 16). After initial work with orthovoltage irradiation and proton beam irradiation, the first Leksell gamma unit or gamma knife was constructed by Leksell and coworkers in 1968 ( 13-17). Impressive results have been reported not only for the treatment of arteriovenous malformations and acoustic neurinomas but also for craniopharyngiomas, pituitary adenomas, and other uses (l-3, 15, 27-29) Steiner (27, 28) reported an 84% complete obliteration rate at 2 years for arteriovenous malformations treated with the gamma knife which has been maintained with only a 3% permanent complication rate in over 600 treated patients (Steiner-oral communications, May 1988). These results have stimulated interest in radiosurgery with the gamma knife, charged particle irradiation, and in adapting linear accelerators for radiosurgery (4, 5, 7, 18, 19, 21, 23, 30, 31). The gamma unit at the University of Pittsburgh began treating patients in August 1987 (18). It is the first gamma
METHODS
AND MATERIALS
The gamma unit at the Presbyterian University Hospital of Pittsburgh contains 20 1 6oC0 sources arranged in an array that is approximately hemispherical. Each source has an effective focal size of 1 mm. Any number of the sources can be blocked to prevent the entry of beams
Acknowledgements-Supported
Presented in part at the 30th Annual Meeting of the American Society for Therapeutic Radiology and Oncology, New Orleans, LA, Oct. 11, 1988. Reprint requests to: John C. Flickinger, M.D., Joint Radiation Oncology Center, Presbyterian University Hospital, 230 Lothrop St., Pittsburgh, PA 15213.
in part by a grant from the Claude Worthington Benedum Foundation. * Department of Radiation Oncology. + Departments of Neurological Surgery and Radiology. Accepted for publication 5 January 1989.
1495
1496
I. J. Radiation Oncology 0 Biology 0 Physics
through the orbit and/or to modify the shape of the dose distribution. Three dimensional dose distributions are then calculated using a microcomputer with software developed at the University of Uppsala which summates the dose distributions from individually measured beam profiles. Two dimensional xy, yz or xz plots through any point in the dose distribution can be printed. Dose distributions are integrated with and superimposed on the corresponding image from computed tomography (CT), magnetic resonance imaging (MRI) and/or angiography. Composite isodose distributions are normalized with respect to the maximum dose. For two isocenter plans, this is usually located in the overlap region. Treatment is prescribed to the maximum dose (which is required to be within the target volume) with the minimum dose to the target volume specified. Prior to treatment, the patient’s skull contour is outlined by measuring the radius from the isocenter to 24 different points on the scalp. Dosimetry studies of single isocenter dose distributions with the 4, 8, 14, and 18 mm diameter collimator helmets have shown good agreement between the computer generated treatment plans and measurements with film densitometry as well as lithium fluoride thermoluminescence dosimetry (18, 31). The dose distributions generated by the treatment planning computer software for two isocenters with different separations were verified by film densitometry. The film densitometry was performed with contact film placed in the center of a polystyrene tissue equivalent spherical phantom with an 80 mm radius. Densitometry measurements were made using a film densitometer with a 0.8 mm apperture. The probability of complications was estimated using the exponential and linear quadratic versions of the integrated logistic formula (8). The derivation of the integrated logistic formula is discussed in a separate paper (8). The integrated logistic formula has the following form: 1 - P = fl {[NTD,(i)/NTD,(D50)]k
+ 1}v(i)‘v
(1)
June 1990, Volume 18,Number 6
tions per week NTD) that produces an equivalent biological endpoint (probability of complication or tumor control), predicted by a specific dose-time-fractionation formula (e.g. Neuret) (9, 20, 26, 32). The exponential version of the integrated logistic formula uses NTD (Neuret) calculated with exponents from the Neuret equation of Sheline et al. (26) converted to a TDF form (8, 22) as in the following equation: NTD2(Neuret) = 2 .5206 nid’(ti/ni)-.‘2
where n is the number of fractions, d is the dose per fraction in Gy, t is the time in days and the subscript 2 in NTD2 indicates a reference dose of 2 Gy per fraction. For the linear quadratic factor (22) version of the integrated logistic equation, NTD is calculated using the following equation utilizing constants derived for an alpha/beta ratio of .33 for brain tissue (22) and the same days per fraction (t/n) exponent of -. 12 calculated from the Neuret equation (8, 26). NTD,(LQF)
= C ni(.6226d + .1887d’)(ti/ni)-.‘2.
(3)
Values of k and DSoused in the integrated logistic formula were estimated using data for fractionated large field irradiation, split field irradiation in animals and gamma knife irradiation (6, 8, 24). The value used for NTD2DS0 is 72.19 Gy. A value of k = 12.2 is used with the exponential version of the integrated logistic equation and k = 18.5 for the linear quadratic version (8). RESULTS lsodose distributions fbr two isocenter radiosurgery
When two or more isocenters are treated, an account of the distance between all isocenters should be maintained during treatment planning as calculated using the following equation: WI, 2) = [(XI
where 1 - P is the probability that radiation necrosis will not develop (integrated over the entire volume of brain tissue, excluding tumor), V is the total volume of brain tissue, k is a constant, v(i) is a volume increment that has received an normalized total dose at 2 Gy per fraction of NTD,(i) and NTD2(D5J is the normalized total dose at 2 Gy per fraction administered to the whole brain that produces a 50% probability of complications. Published tables listing average brain weights and volumes according to age, sex, and race are available (11). For the calculations in this paper, an average brain volume of 1136 cm3 was used. The normalized total dose (NTD) is a convenient way of expressing radiation dose effect that has been defined as the total dose of radiation in Gy administered with conventional fractionation (e.g. 2 Gy per fraction, 5 frac-
(2)
-
%I2
+ (YI
-
Y2J2 + (Zl
-
z2)21”2.
(4)
Figure 1 shows the dose distribution in the xy plane for a treatment using 18 mm diameter collimator helmets with the isocenter separated by 12 mm along the x axis. As shown in Figure 1, film densitometry dose profiles shown reasonable agreement with the computer generated dose profiles for the 30%, 50%, and 90% isodose lines. There is significant underestimation by the computer of the 10% and 70% isodose volumes where the dose fall off is less steep. A series of computer generated isodose distributions were calculated for treatment with 18 mm diameter collimators with two isocenters separated by different distances to provide a guide for treatment planning. The catalogue of isodose distributions produced is now used as a guide for making an initial estimate of the treatment
Multiple isocenter radiosurgery 0 J. C.
z=
100.0
100
1497
FLICKINGERet al
2400
FRONT
ANTERKIP
120
X
Y= 100.0
80
100 n
CRAN
120
\I
Xlmml
Fig. 1. Comparison of computer generated (left) and film densitometry (right) isodoses in the xy or transverse plane (tvp), and in the XZ or coronal plane for radiosurgery with 18 mm collimators with two isocenters separated by 10 mm along the x-axis.
plan. Individual treatment plans are then generated for each patient prior to treatment and modified as needed. Figure 2 shows the change in the x, y and z diameters of the 50% isodose volume measured through the mid-point between the two isocenters as the separation increases along the x-axis. The length along the x axis of the initially ellipsoid shaped 50% isodose volume gradually increases with increasing separation of the two isocenters, while the y and z diameters of the width decrease. Figure 3 demonstrates the change in volumes enclosed by the 30%, 50%, and 90% isodoses for two 18 mm gamma knife treatments with varying isocenter separations. With increasing separation, the volumes encompassed by the different isodoses remain relatively constant (30%, 50%) or decrease (90%) until the isocenters are separated so much that the volumes encompassed by these isodoses are no longer predominantly in the overlap region. Complication risk calculations To effectively plan multiple isocenter radiosurgery treatments, one must be able to make a reasonable estimation of brain tolerance as a function of the dose distribution. In Figure 4 for example, an ellipsoid shaped tumor or malformation measuring 2 1 X 14 X 14 mm in the x, y, and z diameters, respectively, could be enclosed within the 50% isodose volume of either a single isocenter
treatment with 18 mm collimators or a two isocenter treatment with 14 mm collimators where the isocenters are separated in the x axis by 9 mm. For purposes of this example, it is assumed that the tumor is located in the center of a 16 cm diameter spherical skull containing 1136
41
i
I 0.0
0.5
I 1.0 SEPARATION
1.5
210
(cm)
Fig. 2. Diameters of the 50% isodose volume measured along the x, y and z axis for radiosurgery with 18 mm collimators and two isocenters with varied separation along the x-axis.
1498
I. J. Radiation Oncology 0 Biology 0 Physics
-0.0
0.5
1.0
1.5
2.0
SEPARATION (cm) Fig. 3. Volume enclosed by the 30%, 50%, and 90% isodoses for radiosurgery with 18 mm collimators and two isocenters with varied separation along the x-axis.
cm3 of brain tissue and that the tumor volume can be excluded from the risk calculation. Which dose distribution should be used? Figures 5 and 6 compare the tumor dose volume histograms in normal brain and tumor for these two treatments. Both the treatment isodose plans and the dose volume histograms show that the two isocenter plan is better but do not answer the question of whether it is better enough to justify the added trouble and additional uncertainty in the dose distribution from treating with two isocenters. Table 1 compares the probabilities of complications calculated over 5% dose intervals from 1% to 100% isodose for a dose of 20 Gy to the 50% isodose volume (maximum dose 40Gy). With the exponential version of the integrated logistic model, the risk
z= 100.0
June 1990, Volume 18, Number 6
of complications is 2.5% for the two 14 mm treatments and 8.8% for the single 18 mm treatment. The risks calculated with the linear quadratic version of the integrated logistic formula are lower, 0.5% with the two 14 mm treatments and 4.1% with the single 18 mm treatment. These differences are clearly enough to justify using the two isocenter treatment plan. Table 2 compares the complication probabilities predicted using a similar spherical skull model for the treatment of different sized tumors using 1 to 4 treatments with the 18 mm collimator and separations of 12 mm along the x axis between each adjacent isocenter. The first four rows show the risks for administering 20 Gy to the 50% isodose with 1 to 4 isocenters and the second four rows show the dose reductions needed to maintain the same 3.4% complication risk for each different multiple isocenter treatment. The exponential version of the integrated logistic equation was used for the complication predictions listed in Table 1 since the risks predicted were higher (i.e. more conservative) and called for slightly greater dose reductions to maintain the same 3.4% risk when the treatment volume was increased by adding a second, third or fourth shot.
Acoustic neurinomas Acoustic neurinomas are tumors that are usually very nonspherical in shape and ideally treated with two isocenters. From August 14, 1987, to September 13, 1988, 27 patients with acoustic neurinomas were treated with the Leksell gamma unit at the Presbyterian University Hospital of the University of Pittsburgh. Eighteen (67%) were treated with two isocenters and 6 (22%) with three isocenters. Figure 7 shows a commonly used isodose distribution for the treatment of acoustic neurinoma with two isocenters. The treatment with 14 mm collimators covers the intracerebral portion of the tumor and the treatment with 8 mm collimators covers the intracanali-
FRONT
80
80 80
100
X
120
80
100
120
X
Fig. 4. Isodose distributions in the xy plane used to treat a 2 1 X 14 X 14 cm ellipsoid shaped tumor. The dose profile for single isocenter radiosurgery with I8 mm collimators is shown on the left and that for radiosurgery with 14 mm isocenters separated by 9 mm is shown on the right.
Multiple isocenter radiosurgery 0 J. C.
-
IO
BRAIN
18 mm
100
FLICKINGER
1499
et al.
Table 1. Complication risk predictions of the exponential and linear quadratic versions of the integrated logistic formula for treatment of a 21 X 14 X 14 mm tumor to a dose of 20 Gy to
the 50% isodose volume with either one or two isocenters
i
I10 1
t
18 1 8.8% 4.1%
14 2 2.5% 0.5%
Collimator size (mm) No. isocenters Risk, exponential Risk, linear quadratic
Cl
.Ol
.OOl 7
.ooolo~-
20
40
60
60
100
% ISODOSE
Fig. 5. Dose volumes histograms for brain tissue comparing treatment of a 2 1 X 14 X 14 mm tumor with either 18 mm collimators and a single isocenter or two isocenters separated by 9 mm treated with 14 mm diameter collimators.
cular portion
of the tumor.
A dose of 16.67 Gy was pre-
scribed to the 50% isodose volume. DISCUSSION Planning photon radiosurgery of small irregularly shaped target volumes is a complex process that is different from the usual treatment planning problems encountered in conventional, fractionated radiotherapy of large target volumes. Guidelines for choosing treatment doses with respect to treatment volume are based on minimal data (8, 12). The optimal isodose volume for encompassing a target volume, somewhere between the 50 and 90% isodose, is a matter of debate. When two or more isocenters 100
1000 -
T"MOR14rnrn
-
TUMORtremm 100
10 r
7
are treated, one must also choose the separation between isocenters, as well as the weighting of the dose administered to each of the different isocenters. We have found the techniques discussed in this paper to be helpful in facilitating treatment planning, particularly maintaining an account of the distances between all isocenters, estimating the isodose distribution using a catalog of sample
isodose plots with different separations, comparing dose volume histograms, and estimating complications with the integrated logistic formula. The difference between the positions of the computer generated and film densitomitry depictions of the 10% and 70% isodoses in Figures 1 and 2 give some cause for concern. These differences probably do not effect the choice of the treatment isodose or lead to a choice of one plan over another since the 50% isodose volume, which agrees with the computer plan, is normally used for treatment with two isocenters, the 70% isodose volume should be within the tumor volume and the 10% isodose volume (where the dose is 4 Gy in the example) does not have a very great effect on the tolerance. There is however reason to be concerned about misrepresentations of isodose distributions for treatment with three or more isocenters with the dose planning system presently in use with the gamma knife from further magnification of any errors with more isocenters. The integrated logistic formula is the only model presently available that describes the tolerance of small volumes of brain tissue to the high dose, single fraction, inhomogeneous dose distributions used in photon radiosurgery. In comparison to choosing doses according to
Table 2. Complication risks predicted with the exponential version of the integrated logistic formula for gamma
.o,:i , ;{ 0
20
40
60
knife radiosurgery with one to four isocenters and 18 mm collimators
I.01
No. isocenters
80
100
% ISODOSE
Fig. 6. Dose volume histograms within a 2 1 X 14 X 14 mm tumor treated by the gamma knife to a maximum dose of 40 Gy in a single fraction with either a single isocenter and 18 mm diameter collimators or with two isocenters and 14 mm diameter collimators.
Tumor size (mm)
Dose to 50% (Gy)
Risk %
1 2 3 4
21 27 37 47
x x x x
21 18 18 18
x X X X
21 18 18 18
20.00 20.00 20.00 20.00
3.4 5.1 9.3 12.9
1 2 3 4
21 27 37 47
x X x x
21 18 18 18
x X X x
21 18 18 18
20.00 17.75 15.11 14.23
3.4 3.4 3.4 3.4
1500
I. J. Radiation
Oncology
0 Biology 0 Physics
June 1990. Volume
18, Number
6
Fig. 7. Axial MRI image (left side) with axial (xy) and coronal (xz) isodose plots (middle and right side) for treatment of an acoustic neurinoma using two isocenters. The intracanalicular portion of the tumor was treated with 8 mm collimators and the intracerebral portion with 14 mm collimators.
the 1% and 99% tolerance isoeffect lines of Kjellberg e/ al. (12), the integrated logistic formula has the advantage of accounting for tolerance through the entire dose distribution and can therefore be used for different beam energies, different dose distributions shapes, as well as combinations of fractionated external beam irradiation and radiosurgical boosts. In addition, the exponential dose volume relationship implied by the 1% dose volume isoeffect line of Kjellberg et al. ( 12), is a valid approximation only when applied to doses that are lower than the 50% tolerance dose for the whole organ (8, 22, 25). It is often preferable to treat an irregular shaped tumor using two or more isocenters and smaller diameter collimators rather than using a single isocenter with larger collimators. This technique is used for most of the gamma knife radiosurgery administered to patients with acoustic neurinomas because of the irregular shape of their tumors. The ellipsoid tumor volume in Figure 4 was also better treated with two isocenters than one. The dose volume histogram shown in Figure 5 showed the better dose distribution within surrounding normal brain obtained with treatment to two isocenters with 14 mm collimators compared to one isocenter with 18 mm collimators. The integrated logistic formula predicted a dramatic lowering of the complication risks by a factor of 3.5 to 8.0 when the
2 1 X 14 X 14 mm target volume was treated with two isocenters instead of one. This clearly justifies the additional efforts needed to treat two isocenters as well as the additional uncertainty accepted in the dose distribution with two isocenters. This example also illustrated the usefulness of comparing both the dose volume histograms and integrated logistic formula complication predictions. In addition to using multiple isocenters to shape the radiation dose distributions, minor changes in the shape of the treatment isodose can be made by blocking individual beams. This is the subject of a forthcoming paper. The treatment of relatively large irregularly shaped tumors could be further improved if multiple field shaping blocks could be used. The guidelines for facilitating treatment planning and for choosing optimum treatment plans outlined in this paper can be used for radiosurgical treatment with either the gamma knife or with treatment techniques using linear accelerators. Using two or more isocenters when necessary to match the treatment isodose volume to the tumor as closely as possible is presently a useful and necessary technique in radiosurgery. Comparison of dose volume histograms and risk estimations with the integrated logistic formula appear to be the two most useful techniques for deciding between different radiosurgical treatment plans.
REFERENCES Backlund, E. 0.; Johansson, L.; Sarby, B. Studies on craniopharyngiomas. II. Treatment by stereotactic radiosurgery. Acta Chir. Stand. 138:749-759; 1972. Backlund, E. 0.; Rahn, T.; Sarby, B. Treatment of pinealomas by stereotactic radiation surgery. Acta Radiol. [Ther.] (Stockh.) 13:368-376: 1974. Backlund, E. 0.; Rahn, T.; Sarby, B.; de Schryver. A.; Wennerstrand, J. Closed stereotactic hypophysectomy by means of 60 CO gamma radiation. Acta Radio]. (Ther. Phys. Biol.) 11:545-555; 1972. Betti, 0. 0.; Derechinsky, Y. E. Hyperselective encephalit irradiation with linear accelerator. Acta Neurochir. 339(Suppi.):385-390; 1984.
5. Betti, 0.0.; Munari, C.; Rosier, R. Stereotactic radiosurgery with the linear accelerator: treatment of arteriovenous malformations. Neurosurgery 24:3 11-32 1; 1989. 6. Berg, N. 0.; Lindgren, M. Relation between field size and tolerance of rabbit’s brain to roentgen irradiation (200 kv) via a slit-shaped field. Acta Radiol. 1: 147; 1963. 7. Colombo, F.; Benedetti, A.; Possa, F.; Avanzo, R. C.; Marchetti, C.; Chierego, G.; Zanardo, A. External stereotactic irradiation by linear accelerator. Neurosurgery 16: 154- 160; 1985. 8. Flickinger, J. C. The integrated logistic formula and prediction of complications from radiosurgery. Int. J. Radiat. Oncol. Biol. Phys. 17:879-885; 1989.
Multiple isocenter radiosurgery 0 J. C. FLICKINGER et al. 9. Flickinger, J. C.; Lunsford, L. D.; Deutsch, M. Retreatment megavoltage irradiation of suprasellar and pituitary tumors. Int. J. Radiat. Oncol. Biol. Phys. 17:171-175; 1989. 10. Hartman, G. H.; Schlegel, W.; Sturm, V.; Kober, B.; Pastryr, 0.; Lorenz, W. J. Cerebral radiation surgery using moving field irradiation at a linear accelerator facility. Int. J. Radiat. Oncol. Biol. Phys. 11:1185-l 192; 1985. H.; Roessmand, U.; Straumfjord, J. V.; 11. Khang-cheng, Monroe, G. Analysis of brain weight. I. Adult brain weight in relation to sex, race and age. Arch. Pathol. Lab. Med. 104:635-639; 1980. T.; Davis, K. R.; Lyons, S.; 12. Kjellberg, R. N.; Hanamura, Butler, W.; Adams, R. Bragg peak proton beam therapy for arteriovenous malformation of the brain. N. Engl. J. Med. 309:269-274; 1983. 13. Larsson, B.; Leksell, L.; Rexed, B. The high energy proton beam as a neurological tool. Nature 182: 1222- 1223; 1958. 14. Larsson, B.; Liden, K.; Sarby, B. Irradiation of small structures through the intact skull. Acta. Radiol. Oncol. Radiat. Phys. Biol. 13:5 12-534; 1974. 15. Leksell, D. G. Stereotactic radiosurgery, present status and future trends. Neurol. Res. 9:60-68; 1987. 16. Leksell, L. The stereotactic method and radiosurgery of the brain. Acta. Chr. Stand. 102:316-319; 1951. 17. Leksell, L. Stereotactic radiosurgery. J. Neurosurg. Psych. 46:797-803; 1983. 18. Lunsford, L. D.; Flickinger, J. C.; Lindner, G.; Maitz, A.; Deutsch, M. Stereotactic radiosurgery of the brain using the first United States 201 Cobalt 60 source gamma knife. Neurosurgery 24:151-159; 1989. 19. Lutz, W.; Winston, K. R.; Maleki, P. V. A system for stereotactic radiosurgery with a linear accelerator. Int. J. Radiat. Oncol. Biol. Phys. 14:373-381; 1988. 20. Maciejewski. B.; Taylor, J. M.; Withers, H. R. Alpha/beta value and the importance of size of dose per fraction for later complications in the supraglottic larynx. Radiother. Oncol. 7:322-326; 1986. 21. Marks, M. P.; Delapaz, R. L.; Fabrikant, J. I.; Frankel, K. A.; Phillips, M. H.; Levy, R. P.; Enzmann, D. R. Intracranial vascular malformations: imaging of charged particle
22.
23.
24.
25. 26.
27.
28.
29.
30.
1501
radiosurgery, part I. Results of therapy. Radiology 168:445447; 1988. Orton, C. G.; Cohen, L. A unified approach to dose-effect relationships in radiotherapy. I: modified TDF and linear quadratic equations. Int. J. Radiat. Oncol. Biol. Phys. 14: 549-556; 1988. Podgorsak, E. B.; Olivier, A.; Pla, M.; Lefebvre, P.; Hazel, J. Dynamic stereotactic radiosurgery. Int. J. Radiat. Oncol. Biol. Phys. 14:115-126; 1988. Rubin, P.; Cooper, R. A.; Phillips, T. L., eds. Radiation biology and radiation therapy pathology syllubus. Chicago: Am. College of Radiology, Publication; 1978. Schultheiss, T. E.; Orton, C. G.; Peck, R. A. Models in radiotherapy: volume effects. Med. Phys. 10:410-415; 1983. Sheline, G.; Wara, W.; Smith, V. Therapeutic irradiation and brain injury. Int. J. Radiat. Oncol. Biol. Phys. 6: 12 151228; 1980. Steiner, L. Treatment of arteriovenous malformations by radiosurgery. In: Wilson, C. B., Stein, B. M., eds. Intracranial arteriovenous malformations. Baltimore: Williams and Wilkins; 1984:295-3 13. Steiner, L. Radiosurgery in cerebral arteriovenous malformations. In: Flamm, E., Fein, J., eds. Textbook of cerebrovascular surgery Vol. 4. New York: Springer Verlag; 1986: 1161-1215. Steiner, L.; Forester, D.; Leksell, L.; Meyerson, B. A.; Boethius, J. Gammathalamotomy in intractable pain. Acta. Neuro. Chir. (Wien) 52: 173-184; 1980. Sturm, V.; Kober, B.; Hover, K. H.; Schelgel, W.; Boesecke, R.: Pastyr, 0.; Hartmann, G. H.; Schabbert, S.; Winkel, K.; Kunze, S.; Lorenz, W. J. Stereotactic percutaneous single dose irradiation of brain metastases with a linear accelerator. Int. J. Radiat. Oncol. Biol. Phys. 13:279-282; 1987.
31. Walton, L.; Bomford, C. K.; Ramsden, D. The Sheffield stereotactic radiosurgery unit: physical characteristics and principles of operation. Br. J. Radiol. 60:897-906; 1987. 32. Withers, H. R.; Thames, H.; Peters, L. A new isoeffect curve for change in dose per fraction. Radiother. Oncol. 1: 187191: 1983.
0360.3016/90 $3.00 + .oO Copyright 0 1990 Pergamon Press plc
??Technical Innovations and Notes
TREATMENT
PLANNING FOR GAMMA KNIFE RADIOSURGERY WITH MULTIPLE ISOCENTERS
JOHN C. FLICKINGER, M.D.,* L. DADE LUNSFORD, M.D.,+ ANDREW Wu, PH.D.,* ANN H. MAITZ, M.S.* AND ANDRE M. KALEND, PH.D.* University of Pittsburgh School of Medicine, and the Pittsburgh Cancer Institute, Pittsburgh, PA 152 13 Many arteriovenous malformations and tumors suitable for radiosurgicaltreatmenthave non-sphericalor irregular shapes. Forty-eight percentof the first 156 patients treatedwith the gammaunit at the Universityof Pittsburgh requiredtreatmentwith two or more isocenters to optimize dose distributions. Dose distributions for combining gamma knife treatments to two or more isocenters were systematically investigated. High speed computerized dosimetry was performed using specially developed software and dose distributions were confirmed with film densitometry. We have developed guidelines for treatmentto two or more isocenters which help reduce treatment planning time, and facilitate selection of treatment doses and optimum dose distributions. These guidelines include maintaining an account of the distances between all isocenters, using a catalogue of sample two-isocenter isodose plans, comparing dose volume histograms, and calculating complication probabilities using the integrated logistic formula. Radiosurgery, Gamma knife, Dosimetry, Integrated logistic formula, Dose volume histogram.
INTRODUCTION
unit equipped with 18 mm diameter collimators in addition to the standard 4, 8, and 14 mm diameter collimator helmets. Details of dosimetry for each of the different collimator sizes have been reported (18, 3 1). Since many target volumes are irregularly shaped or slightly larger in one or two dimensions than the 50% isodose volume for the 18 mm diameter collimator helmet, it is often necessary to consider treatment with two isocenters. The effects on the dose distribution of varying the distance between two isocenters are presented in this paper along with guidelines for choosing treatment doses and dose distributions for radiosurgery with multiple isocenters.
The concept of radiosurgery was introduced by Leksell in 195 1 ( 16). After initial work with orthovoltage irradiation and proton beam irradiation, the first Leksell gamma unit or gamma knife was constructed by Leksell and coworkers in 1968 ( 13-17). Impressive results have been reported not only for the treatment of arteriovenous malformations and acoustic neurinomas but also for craniopharyngiomas, pituitary adenomas, and other uses (l-3, 15, 27-29) Steiner (27, 28) reported an 84% complete obliteration rate at 2 years for arteriovenous malformations treated with the gamma knife which has been maintained with only a 3% permanent complication rate in over 600 treated patients (Steiner-oral communications, May 1988). These results have stimulated interest in radiosurgery with the gamma knife, charged particle irradiation, and in adapting linear accelerators for radiosurgery (4, 5, 7, 18, 19, 21, 23, 30, 31). The gamma unit at the University of Pittsburgh began treating patients in August 1987 (18). It is the first gamma
METHODS
AND MATERIALS
The gamma unit at the Presbyterian University Hospital of Pittsburgh contains 20 1 6oC0 sources arranged in an array that is approximately hemispherical. Each source has an effective focal size of 1 mm. Any number of the sources can be blocked to prevent the entry of beams
Acknowledgements-Supported
Presented in part at the 30th Annual Meeting of the American Society for Therapeutic Radiology and Oncology, New Orleans, LA, Oct. 11, 1988. Reprint requests to: John C. Flickinger, M.D., Joint Radiation Oncology Center, Presbyterian University Hospital, 230 Lothrop St., Pittsburgh, PA 15213.
in part by a grant from the Claude Worthington Benedum Foundation. * Department of Radiation Oncology. + Departments of Neurological Surgery and Radiology. Accepted for publication 5 January 1989.
1495
1496
I. J. Radiation Oncology 0 Biology 0 Physics
through the orbit and/or to modify the shape of the dose distribution. Three dimensional dose distributions are then calculated using a microcomputer with software developed at the University of Uppsala which summates the dose distributions from individually measured beam profiles. Two dimensional xy, yz or xz plots through any point in the dose distribution can be printed. Dose distributions are integrated with and superimposed on the corresponding image from computed tomography (CT), magnetic resonance imaging (MRI) and/or angiography. Composite isodose distributions are normalized with respect to the maximum dose. For two isocenter plans, this is usually located in the overlap region. Treatment is prescribed to the maximum dose (which is required to be within the target volume) with the minimum dose to the target volume specified. Prior to treatment, the patient’s skull contour is outlined by measuring the radius from the isocenter to 24 different points on the scalp. Dosimetry studies of single isocenter dose distributions with the 4, 8, 14, and 18 mm diameter collimator helmets have shown good agreement between the computer generated treatment plans and measurements with film densitometry as well as lithium fluoride thermoluminescence dosimetry (18, 31). The dose distributions generated by the treatment planning computer software for two isocenters with different separations were verified by film densitometry. The film densitometry was performed with contact film placed in the center of a polystyrene tissue equivalent spherical phantom with an 80 mm radius. Densitometry measurements were made using a film densitometer with a 0.8 mm apperture. The probability of complications was estimated using the exponential and linear quadratic versions of the integrated logistic formula (8). The derivation of the integrated logistic formula is discussed in a separate paper (8). The integrated logistic formula has the following form: 1 - P = fl {[NTD,(i)/NTD,(D50)]k
+ 1}v(i)‘v
(1)
June 1990, Volume 18,Number 6
tions per week NTD) that produces an equivalent biological endpoint (probability of complication or tumor control), predicted by a specific dose-time-fractionation formula (e.g. Neuret) (9, 20, 26, 32). The exponential version of the integrated logistic formula uses NTD (Neuret) calculated with exponents from the Neuret equation of Sheline et al. (26) converted to a TDF form (8, 22) as in the following equation: NTD2(Neuret) = 2 .5206 nid’(ti/ni)-.‘2
where n is the number of fractions, d is the dose per fraction in Gy, t is the time in days and the subscript 2 in NTD2 indicates a reference dose of 2 Gy per fraction. For the linear quadratic factor (22) version of the integrated logistic equation, NTD is calculated using the following equation utilizing constants derived for an alpha/beta ratio of .33 for brain tissue (22) and the same days per fraction (t/n) exponent of -. 12 calculated from the Neuret equation (8, 26). NTD,(LQF)
= C ni(.6226d + .1887d’)(ti/ni)-.‘2.
(3)
Values of k and DSoused in the integrated logistic formula were estimated using data for fractionated large field irradiation, split field irradiation in animals and gamma knife irradiation (6, 8, 24). The value used for NTD2DS0 is 72.19 Gy. A value of k = 12.2 is used with the exponential version of the integrated logistic equation and k = 18.5 for the linear quadratic version (8). RESULTS lsodose distributions fbr two isocenter radiosurgery
When two or more isocenters are treated, an account of the distance between all isocenters should be maintained during treatment planning as calculated using the following equation: WI, 2) = [(XI
where 1 - P is the probability that radiation necrosis will not develop (integrated over the entire volume of brain tissue, excluding tumor), V is the total volume of brain tissue, k is a constant, v(i) is a volume increment that has received an normalized total dose at 2 Gy per fraction of NTD,(i) and NTD2(D5J is the normalized total dose at 2 Gy per fraction administered to the whole brain that produces a 50% probability of complications. Published tables listing average brain weights and volumes according to age, sex, and race are available (11). For the calculations in this paper, an average brain volume of 1136 cm3 was used. The normalized total dose (NTD) is a convenient way of expressing radiation dose effect that has been defined as the total dose of radiation in Gy administered with conventional fractionation (e.g. 2 Gy per fraction, 5 frac-
(2)
-
%I2
+ (YI
-
Y2J2 + (Zl
-
z2)21”2.
(4)
Figure 1 shows the dose distribution in the xy plane for a treatment using 18 mm diameter collimator helmets with the isocenter separated by 12 mm along the x axis. As shown in Figure 1, film densitometry dose profiles shown reasonable agreement with the computer generated dose profiles for the 30%, 50%, and 90% isodose lines. There is significant underestimation by the computer of the 10% and 70% isodose volumes where the dose fall off is less steep. A series of computer generated isodose distributions were calculated for treatment with 18 mm diameter collimators with two isocenters separated by different distances to provide a guide for treatment planning. The catalogue of isodose distributions produced is now used as a guide for making an initial estimate of the treatment
Multiple isocenter radiosurgery 0 J. C.
z=
100.0
100
1497
FLICKINGERet al
2400
FRONT
ANTERKIP
120
X
Y= 100.0
80
100 n
CRAN
120
\I
Xlmml
Fig. 1. Comparison of computer generated (left) and film densitometry (right) isodoses in the xy or transverse plane (tvp), and in the XZ or coronal plane for radiosurgery with 18 mm collimators with two isocenters separated by 10 mm along the x-axis.
plan. Individual treatment plans are then generated for each patient prior to treatment and modified as needed. Figure 2 shows the change in the x, y and z diameters of the 50% isodose volume measured through the mid-point between the two isocenters as the separation increases along the x-axis. The length along the x axis of the initially ellipsoid shaped 50% isodose volume gradually increases with increasing separation of the two isocenters, while the y and z diameters of the width decrease. Figure 3 demonstrates the change in volumes enclosed by the 30%, 50%, and 90% isodoses for two 18 mm gamma knife treatments with varying isocenter separations. With increasing separation, the volumes encompassed by the different isodoses remain relatively constant (30%, 50%) or decrease (90%) until the isocenters are separated so much that the volumes encompassed by these isodoses are no longer predominantly in the overlap region. Complication risk calculations To effectively plan multiple isocenter radiosurgery treatments, one must be able to make a reasonable estimation of brain tolerance as a function of the dose distribution. In Figure 4 for example, an ellipsoid shaped tumor or malformation measuring 2 1 X 14 X 14 mm in the x, y, and z diameters, respectively, could be enclosed within the 50% isodose volume of either a single isocenter
treatment with 18 mm collimators or a two isocenter treatment with 14 mm collimators where the isocenters are separated in the x axis by 9 mm. For purposes of this example, it is assumed that the tumor is located in the center of a 16 cm diameter spherical skull containing 1136
41
i
I 0.0
0.5
I 1.0 SEPARATION
1.5
210
(cm)
Fig. 2. Diameters of the 50% isodose volume measured along the x, y and z axis for radiosurgery with 18 mm collimators and two isocenters with varied separation along the x-axis.
1498
I. J. Radiation Oncology 0 Biology 0 Physics
-0.0
0.5
1.0
1.5
2.0
SEPARATION (cm) Fig. 3. Volume enclosed by the 30%, 50%, and 90% isodoses for radiosurgery with 18 mm collimators and two isocenters with varied separation along the x-axis.
cm3 of brain tissue and that the tumor volume can be excluded from the risk calculation. Which dose distribution should be used? Figures 5 and 6 compare the tumor dose volume histograms in normal brain and tumor for these two treatments. Both the treatment isodose plans and the dose volume histograms show that the two isocenter plan is better but do not answer the question of whether it is better enough to justify the added trouble and additional uncertainty in the dose distribution from treating with two isocenters. Table 1 compares the probabilities of complications calculated over 5% dose intervals from 1% to 100% isodose for a dose of 20 Gy to the 50% isodose volume (maximum dose 40Gy). With the exponential version of the integrated logistic model, the risk
z= 100.0
June 1990, Volume 18, Number 6
of complications is 2.5% for the two 14 mm treatments and 8.8% for the single 18 mm treatment. The risks calculated with the linear quadratic version of the integrated logistic formula are lower, 0.5% with the two 14 mm treatments and 4.1% with the single 18 mm treatment. These differences are clearly enough to justify using the two isocenter treatment plan. Table 2 compares the complication probabilities predicted using a similar spherical skull model for the treatment of different sized tumors using 1 to 4 treatments with the 18 mm collimator and separations of 12 mm along the x axis between each adjacent isocenter. The first four rows show the risks for administering 20 Gy to the 50% isodose with 1 to 4 isocenters and the second four rows show the dose reductions needed to maintain the same 3.4% complication risk for each different multiple isocenter treatment. The exponential version of the integrated logistic equation was used for the complication predictions listed in Table 1 since the risks predicted were higher (i.e. more conservative) and called for slightly greater dose reductions to maintain the same 3.4% risk when the treatment volume was increased by adding a second, third or fourth shot.
Acoustic neurinomas Acoustic neurinomas are tumors that are usually very nonspherical in shape and ideally treated with two isocenters. From August 14, 1987, to September 13, 1988, 27 patients with acoustic neurinomas were treated with the Leksell gamma unit at the Presbyterian University Hospital of the University of Pittsburgh. Eighteen (67%) were treated with two isocenters and 6 (22%) with three isocenters. Figure 7 shows a commonly used isodose distribution for the treatment of acoustic neurinoma with two isocenters. The treatment with 14 mm collimators covers the intracerebral portion of the tumor and the treatment with 8 mm collimators covers the intracanali-
FRONT
80
80 80
100
X
120
80
100
120
X
Fig. 4. Isodose distributions in the xy plane used to treat a 2 1 X 14 X 14 cm ellipsoid shaped tumor. The dose profile for single isocenter radiosurgery with I8 mm collimators is shown on the left and that for radiosurgery with 14 mm isocenters separated by 9 mm is shown on the right.
Multiple isocenter radiosurgery 0 J. C.
-
IO
BRAIN
18 mm
100
FLICKINGER
1499
et al.
Table 1. Complication risk predictions of the exponential and linear quadratic versions of the integrated logistic formula for treatment of a 21 X 14 X 14 mm tumor to a dose of 20 Gy to
the 50% isodose volume with either one or two isocenters
i
I10 1
t
18 1 8.8% 4.1%
14 2 2.5% 0.5%
Collimator size (mm) No. isocenters Risk, exponential Risk, linear quadratic
Cl
.Ol
.OOl 7
.ooolo~-
20
40
60
60
100
% ISODOSE
Fig. 5. Dose volumes histograms for brain tissue comparing treatment of a 2 1 X 14 X 14 mm tumor with either 18 mm collimators and a single isocenter or two isocenters separated by 9 mm treated with 14 mm diameter collimators.
cular portion
of the tumor.
A dose of 16.67 Gy was pre-
scribed to the 50% isodose volume. DISCUSSION Planning photon radiosurgery of small irregularly shaped target volumes is a complex process that is different from the usual treatment planning problems encountered in conventional, fractionated radiotherapy of large target volumes. Guidelines for choosing treatment doses with respect to treatment volume are based on minimal data (8, 12). The optimal isodose volume for encompassing a target volume, somewhere between the 50 and 90% isodose, is a matter of debate. When two or more isocenters 100
1000 -
T"MOR14rnrn
-
TUMORtremm 100
10 r
7
are treated, one must also choose the separation between isocenters, as well as the weighting of the dose administered to each of the different isocenters. We have found the techniques discussed in this paper to be helpful in facilitating treatment planning, particularly maintaining an account of the distances between all isocenters, estimating the isodose distribution using a catalog of sample
isodose plots with different separations, comparing dose volume histograms, and estimating complications with the integrated logistic formula. The difference between the positions of the computer generated and film densitomitry depictions of the 10% and 70% isodoses in Figures 1 and 2 give some cause for concern. These differences probably do not effect the choice of the treatment isodose or lead to a choice of one plan over another since the 50% isodose volume, which agrees with the computer plan, is normally used for treatment with two isocenters, the 70% isodose volume should be within the tumor volume and the 10% isodose volume (where the dose is 4 Gy in the example) does not have a very great effect on the tolerance. There is however reason to be concerned about misrepresentations of isodose distributions for treatment with three or more isocenters with the dose planning system presently in use with the gamma knife from further magnification of any errors with more isocenters. The integrated logistic formula is the only model presently available that describes the tolerance of small volumes of brain tissue to the high dose, single fraction, inhomogeneous dose distributions used in photon radiosurgery. In comparison to choosing doses according to
Table 2. Complication risks predicted with the exponential version of the integrated logistic formula for gamma
.o,:i , ;{ 0
20
40
60
knife radiosurgery with one to four isocenters and 18 mm collimators
I.01
No. isocenters
80
100
% ISODOSE
Fig. 6. Dose volume histograms within a 2 1 X 14 X 14 mm tumor treated by the gamma knife to a maximum dose of 40 Gy in a single fraction with either a single isocenter and 18 mm diameter collimators or with two isocenters and 14 mm diameter collimators.
Tumor size (mm)
Dose to 50% (Gy)
Risk %
1 2 3 4
21 27 37 47
x x x x
21 18 18 18
x X X X
21 18 18 18
20.00 20.00 20.00 20.00
3.4 5.1 9.3 12.9
1 2 3 4
21 27 37 47
x X x x
21 18 18 18
x X X x
21 18 18 18
20.00 17.75 15.11 14.23
3.4 3.4 3.4 3.4
1500
I. J. Radiation
Oncology
0 Biology 0 Physics
June 1990. Volume
18, Number
6
Fig. 7. Axial MRI image (left side) with axial (xy) and coronal (xz) isodose plots (middle and right side) for treatment of an acoustic neurinoma using two isocenters. The intracanalicular portion of the tumor was treated with 8 mm collimators and the intracerebral portion with 14 mm collimators.
the 1% and 99% tolerance isoeffect lines of Kjellberg e/ al. (12), the integrated logistic formula has the advantage of accounting for tolerance through the entire dose distribution and can therefore be used for different beam energies, different dose distributions shapes, as well as combinations of fractionated external beam irradiation and radiosurgical boosts. In addition, the exponential dose volume relationship implied by the 1% dose volume isoeffect line of Kjellberg et al. ( 12), is a valid approximation only when applied to doses that are lower than the 50% tolerance dose for the whole organ (8, 22, 25). It is often preferable to treat an irregular shaped tumor using two or more isocenters and smaller diameter collimators rather than using a single isocenter with larger collimators. This technique is used for most of the gamma knife radiosurgery administered to patients with acoustic neurinomas because of the irregular shape of their tumors. The ellipsoid tumor volume in Figure 4 was also better treated with two isocenters than one. The dose volume histogram shown in Figure 5 showed the better dose distribution within surrounding normal brain obtained with treatment to two isocenters with 14 mm collimators compared to one isocenter with 18 mm collimators. The integrated logistic formula predicted a dramatic lowering of the complication risks by a factor of 3.5 to 8.0 when the
2 1 X 14 X 14 mm target volume was treated with two isocenters instead of one. This clearly justifies the additional efforts needed to treat two isocenters as well as the additional uncertainty accepted in the dose distribution with two isocenters. This example also illustrated the usefulness of comparing both the dose volume histograms and integrated logistic formula complication predictions. In addition to using multiple isocenters to shape the radiation dose distributions, minor changes in the shape of the treatment isodose can be made by blocking individual beams. This is the subject of a forthcoming paper. The treatment of relatively large irregularly shaped tumors could be further improved if multiple field shaping blocks could be used. The guidelines for facilitating treatment planning and for choosing optimum treatment plans outlined in this paper can be used for radiosurgical treatment with either the gamma knife or with treatment techniques using linear accelerators. Using two or more isocenters when necessary to match the treatment isodose volume to the tumor as closely as possible is presently a useful and necessary technique in radiosurgery. Comparison of dose volume histograms and risk estimations with the integrated logistic formula appear to be the two most useful techniques for deciding between different radiosurgical treatment plans.
REFERENCES Backlund, E. 0.; Johansson, L.; Sarby, B. Studies on craniopharyngiomas. II. Treatment by stereotactic radiosurgery. Acta Chir. Stand. 138:749-759; 1972. Backlund, E. 0.; Rahn, T.; Sarby, B. Treatment of pinealomas by stereotactic radiation surgery. Acta Radiol. [Ther.] (Stockh.) 13:368-376: 1974. Backlund, E. 0.; Rahn, T.; Sarby, B.; de Schryver. A.; Wennerstrand, J. Closed stereotactic hypophysectomy by means of 60 CO gamma radiation. Acta Radio]. (Ther. Phys. Biol.) 11:545-555; 1972. Betti, 0. 0.; Derechinsky, Y. E. Hyperselective encephalit irradiation with linear accelerator. Acta Neurochir. 339(Suppi.):385-390; 1984.
5. Betti, 0.0.; Munari, C.; Rosier, R. Stereotactic radiosurgery with the linear accelerator: treatment of arteriovenous malformations. Neurosurgery 24:3 11-32 1; 1989. 6. Berg, N. 0.; Lindgren, M. Relation between field size and tolerance of rabbit’s brain to roentgen irradiation (200 kv) via a slit-shaped field. Acta Radiol. 1: 147; 1963. 7. Colombo, F.; Benedetti, A.; Possa, F.; Avanzo, R. C.; Marchetti, C.; Chierego, G.; Zanardo, A. External stereotactic irradiation by linear accelerator. Neurosurgery 16: 154- 160; 1985. 8. Flickinger, J. C. The integrated logistic formula and prediction of complications from radiosurgery. Int. J. Radiat. Oncol. Biol. Phys. 17:879-885; 1989.
Multiple isocenter radiosurgery 0 J. C. FLICKINGER et al. 9. Flickinger, J. C.; Lunsford, L. D.; Deutsch, M. Retreatment megavoltage irradiation of suprasellar and pituitary tumors. Int. J. Radiat. Oncol. Biol. Phys. 17:171-175; 1989. 10. Hartman, G. H.; Schlegel, W.; Sturm, V.; Kober, B.; Pastryr, 0.; Lorenz, W. J. Cerebral radiation surgery using moving field irradiation at a linear accelerator facility. Int. J. Radiat. Oncol. Biol. Phys. 11:1185-l 192; 1985. H.; Roessmand, U.; Straumfjord, J. V.; 11. Khang-cheng, Monroe, G. Analysis of brain weight. I. Adult brain weight in relation to sex, race and age. Arch. Pathol. Lab. Med. 104:635-639; 1980. T.; Davis, K. R.; Lyons, S.; 12. Kjellberg, R. N.; Hanamura, Butler, W.; Adams, R. Bragg peak proton beam therapy for arteriovenous malformation of the brain. N. Engl. J. Med. 309:269-274; 1983. 13. Larsson, B.; Leksell, L.; Rexed, B. The high energy proton beam as a neurological tool. Nature 182: 1222- 1223; 1958. 14. Larsson, B.; Liden, K.; Sarby, B. Irradiation of small structures through the intact skull. Acta. Radiol. Oncol. Radiat. Phys. Biol. 13:5 12-534; 1974. 15. Leksell, D. G. Stereotactic radiosurgery, present status and future trends. Neurol. Res. 9:60-68; 1987. 16. Leksell, L. The stereotactic method and radiosurgery of the brain. Acta. Chr. Stand. 102:316-319; 1951. 17. Leksell, L. Stereotactic radiosurgery. J. Neurosurg. Psych. 46:797-803; 1983. 18. Lunsford, L. D.; Flickinger, J. C.; Lindner, G.; Maitz, A.; Deutsch, M. Stereotactic radiosurgery of the brain using the first United States 201 Cobalt 60 source gamma knife. Neurosurgery 24:151-159; 1989. 19. Lutz, W.; Winston, K. R.; Maleki, P. V. A system for stereotactic radiosurgery with a linear accelerator. Int. J. Radiat. Oncol. Biol. Phys. 14:373-381; 1988. 20. Maciejewski. B.; Taylor, J. M.; Withers, H. R. Alpha/beta value and the importance of size of dose per fraction for later complications in the supraglottic larynx. Radiother. Oncol. 7:322-326; 1986. 21. Marks, M. P.; Delapaz, R. L.; Fabrikant, J. I.; Frankel, K. A.; Phillips, M. H.; Levy, R. P.; Enzmann, D. R. Intracranial vascular malformations: imaging of charged particle
22.
23.
24.
25. 26.
27.
28.
29.
30.
1501
radiosurgery, part I. Results of therapy. Radiology 168:445447; 1988. Orton, C. G.; Cohen, L. A unified approach to dose-effect relationships in radiotherapy. I: modified TDF and linear quadratic equations. Int. J. Radiat. Oncol. Biol. Phys. 14: 549-556; 1988. Podgorsak, E. B.; Olivier, A.; Pla, M.; Lefebvre, P.; Hazel, J. Dynamic stereotactic radiosurgery. Int. J. Radiat. Oncol. Biol. Phys. 14:115-126; 1988. Rubin, P.; Cooper, R. A.; Phillips, T. L., eds. Radiation biology and radiation therapy pathology syllubus. Chicago: Am. College of Radiology, Publication; 1978. Schultheiss, T. E.; Orton, C. G.; Peck, R. A. Models in radiotherapy: volume effects. Med. Phys. 10:410-415; 1983. Sheline, G.; Wara, W.; Smith, V. Therapeutic irradiation and brain injury. Int. J. Radiat. Oncol. Biol. Phys. 6: 12 151228; 1980. Steiner, L. Treatment of arteriovenous malformations by radiosurgery. In: Wilson, C. B., Stein, B. M., eds. Intracranial arteriovenous malformations. Baltimore: Williams and Wilkins; 1984:295-3 13. Steiner, L. Radiosurgery in cerebral arteriovenous malformations. In: Flamm, E., Fein, J., eds. Textbook of cerebrovascular surgery Vol. 4. New York: Springer Verlag; 1986: 1161-1215. Steiner, L.; Forester, D.; Leksell, L.; Meyerson, B. A.; Boethius, J. Gammathalamotomy in intractable pain. Acta. Neuro. Chir. (Wien) 52: 173-184; 1980. Sturm, V.; Kober, B.; Hover, K. H.; Schelgel, W.; Boesecke, R.: Pastyr, 0.; Hartmann, G. H.; Schabbert, S.; Winkel, K.; Kunze, S.; Lorenz, W. J. Stereotactic percutaneous single dose irradiation of brain metastases with a linear accelerator. Int. J. Radiat. Oncol. Biol. Phys. 13:279-282; 1987.
31. Walton, L.; Bomford, C. K.; Ramsden, D. The Sheffield stereotactic radiosurgery unit: physical characteristics and principles of operation. Br. J. Radiol. 60:897-906; 1987. 32. Withers, H. R.; Thames, H.; Peters, L. A new isoeffect curve for change in dose per fraction. Radiother. Oncol. 1: 187191: 1983.
