PREDICTION OF COMPLICATIONS IN GAMMA KNIFE RADIOSURGERY OF ARTERIOVENOUS MALFORMATIONS
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1 Acta Oncologica Vol. 35, No. I, pp , 1996 PREDICTION OF COMPLICATIONS IN GAMMA KNIFE RADIOSURGERY OF ARTERIOVENOUS MALFORMATIONS INGMAR LAX and BENGT KARLSSON The incidence of complications following radiosurgical treatment of arteriovenous malformations ( AVM) is presented. A simple relationship exists between average dose and risk of complications, and on this basis a model is presented that gives a qualitatively correct description of this relationship. The parameters of the model have been determined using a clinical material of 862 AVM treatments to give a quantitatively correct description of the risk of complications. The dose-response curve is described by a double-exponential function. An accurate description of the dose-response curve at high dose levels is shown to be very important in radiosurgery. Stereotatic radiosurgery was developed almost four decades ago by Leksell (1). During the 196s the first Gamma Knife (GK) was manufactured and in 1968 was introduced into clinical operation in Stockholm. The second GK was installed at the Karolinska Hospital in 1974, and was in clinical use until One year later, in the third unit was installed. The long period of clinical use is an endorsement of the value of radiosurgery in the treatment of arteriovenous malformations (AVM) (2-5), acoustic neurinomas (6-8), metastases (9-12), meningiomas (13) and other benign tumours (14-16). In large AVM materials a high percentage of totally obliterated malformations following GK radiosurgery is reported (2. 3, 5). The malformations in these published series are usually small and the incidence of complications consequently low. However, when the AVM volume for treatment increases, so does the need for an accurate estimate of the risk of complications caused by the treatment, as early as at the planning state. If this could be Received 15 November Accepted 14 July From the Departments of Hospital Physics (I. Lax) and Neurosurgery (B. Karlsson) Karolinska Hospital. Stockholm, Sweden. Correspondence to: Dr. Ingmar Lax, Department of Hospital Physics, Karolinska Hospital, Box 65, S Stockholm. Sweden. obtained, different dose plans could then be compared and the optimal dose plan chosen for each patient. Furthermore, if the risk of complications is high, microsurgery or embolization may offer a lower level of risk and, if so, GK treatment should not be performed. Models that describe the biological effect and that can be applied on the calculated dose distributions have been discussed for radiotherapy applications for more than three decades. However, their clinical introduction is still very limited. The complexity of the problem when multiple organs are involved is compounded by a lack of accurate clinical data and the fact that three-dimensional dose planning is still in the early stages of development. In radiosurgery a unique situation exists in the sense that the dose planning preceding the treatment has for more than ten years been threedimensional and that a very small volume in general is irradiated. It is thus possible to extract accurate dosevolume information from existing dose plans. This is a valuable prerequisite when clinical results are used to design models for predicting outcome of treatments. The present article deals with a model for predicting the risk of complications in radiosurgery of AVM. Furthermore, the incidence of complications in a large clinical material is presented. An important base for the suggested model is the relation observed between the incidence of complications and average dose to a specified volume. It is shown that the model qualitatively describes this relation, and that parameters in the model can be determined for a correct quantitative description of the relation. Scandinavian University Press ISSN X 49
2 5 1. LAX AND B KARLSSON Actu Oncologicu 35 ( 1996) Reference volume, V ---- equal to the volume of the brain Calculation of comdlication arobabilitv. P Serial organization of the FSU:s according to the model FSU Fig. 1. Scheme for the calculation of the complication probability according to the model. The first step is the calculation of the dose distribution in a three dimensional dose matrix, where the dose to each subvolume v, is D,. Next, the model is applied to the calculated dose distribution to determine the complication probability. It should be noted that there is no equivalence between the subvolumes in the dose calculation and the FSUs of the model. In the dose planning of GK radiosurgery, the dose distribution is calculated in a cubic volume, surrounding the target, with a maximum volume of 7.7 x 7.7 x 7.7 cm3. The three-dimensional dose matrix consists of 31 x 31 x 31 elements. To speed up the calculations in the dose planning an intcrpolation procedure is used (17). In this study a special computer program was written to read the dose matrix from the dose planning in order to calculate dosevolume histograms and average doses in different specified volumes. Method Complication probability model The complications observed following the therapeutic use of radiation have been described in terms of inactivation of functional subunits (FSU) (18, 19). They define three different types of FSU organization: 1) critical element, 2) integral response, and 3) graded response. The critical element type is a serial organization of the FSUs, in which a complication appears when any of the FSUs is inactivated. Examples of tissues in which this type of organization can be assumed are spinal cord and nerves (18). The organization of the FSUs has later been described in terms of serial, parallel and, more generally, a combination of the two (2). Schultheiss et al. (21) have provided expressions for the probability of complications using a model of the serial organization type in which the volume effect is accounted for. For a heterogeneous dose distribution, the probability of complications P( {D), v) is expressed as P( {D}, V) = 1 - n,[ 1 - P(D,, Eq. [I] where the dose to the fractional subvolume, Av, = v,/v, is D,. The reference volume is presented by V. The doseresponse function for the reference volume is expressed as P( D, 1). Fig. 1 illustrates the volumes for the dose calculation in the middle of the figure, and the model specific organization of the FSUs in the lower part. Eq. [I] has been suggested by Flickinger (22) for prediction of complications in radiosurgery using the logistic equation for the dose-response curve P(D, 1) (21). D,, is the dose which gives a complication probability of 5%. The parameters D,, and k have to be determined from clinical data. This may be a difficult task, as it is generally assumed that data is collected from homogeneous irradiated organs or functional structures. This is not the case in radiosurgery, but, instead, a very heterogeneous dose distribution inside as well as outside the target (23). Another expression that has been extensively used to describe the dose-response curve (2, 24-26) is given as P( D, 1) = exp( - N, exp( - D/Do)) Eq. [ 31 where N, and D, are parameters that have to be determined from clinical data. Equation (3) may also be expressed in terms of the parameters D,, and 'J (2). p(d, 1) ~ 2-eXp(M1-D/Dsn)) Eq. 134 where g is the maximum slope of the dose-response curve and D,, is the dose for a 5% risk of complication. By a power expansion of the outer exponential function in Eq. (3) and combined with Eq. [I], the probability of complication will be P({D}, V) = 1 ~ n[no ~XP( -DIP,) -.5N; exp( - 2Di/D,) +... Invi Eq. [41 This expression has the interesting aspect that if only the first term of the expansion is kept, the probability of complication can be written as P( {D}, v) z 1 - exp[(in N, - D,,/D,)v] Eq. [5]
3 m Thus the probability of complication, in the first approximation, is related in a simple way to the average dose D,, in the fractional volume v = Cv,/V, irrespective of the dose distribution (cf. ref. 24). Within the validity of dropping higher terms in Eq. [4], Eq. [5] can be used for determination of the coefficients N, and Do from clincial materials if the average dose in a specified volume is known. In the analysis of the clinical material in this study, average doses in different volumes have been calculated. The validity of using Eq. [5] for determination of N,, and Do in radiosurgery has been investigated. The average dose should be calculated in a volume such that the dose level circumscribing the volume is close to that given by the inequality D > ~ No exp( ~ D/Do) > 1, or explicit D,, In( 1 /N<,) = D,, In N,, = ey D,, Eq. [61 as Eq. [5] will underestimate P( {D}, v) for larger volumes (cf. Fig. 5). Using Eq. [3a], the inequality will be D > D5( /~) Eq. [6a] This means that the determination of the parameters is not deterministic but a fitting procedure has to be used. It should be noted that Eq. [5], derived from the power expansion, is generally not valid for the situation in conventional radiotherapy. In this situation the dose is usually restricted to be less than D,,, as it is often given to an extensive part of the volume of an organ. For this range of dose Eq. [5] is not valid (cf. Eq. [6]). However, in radiosurgery the situation is different. The dose is generally considerably higher than D,,, which can be tolerated because of the small fraction of the brain volume that is irradiated. Owing to the volume effect, the dose to the target can be much higher than D,, but the incidence of complications is still only a few percent (cf. also paragraph 4 of Results). The mechanism behind the radiation-induced complications observed in radiosurgery of AVM is not known. It can be assumed that it is a complex one and dependent on multiple factors. However, for the application of the model described here, as well as other models, sone kind of hypothesis regarding the relevant part of the irradiated volume for the development of complications has to be defined for the determination of No and Do. Three obvious hypotheses are: (A) All of the irradiated volume, including that of the AVM, is of importance for the genesis of complications. (B) Only the irradiated volume outside the AVM is of relevance in this context (22). (C) All of the volume outside the AVM plus a fraction of the volume of the AVM (i.e. normal brain tissue within the AVM) is of relevance. All three hypotheses can be applied equally well to the above described method. Clinicul data Two sets of clinical data were pooled. The first data set includes all 61 1 patients with an AVM visible on angiography and treated at the Karolinska Hospital from April 197 to December These trcatrnents were performed on the first and second GK treatments. Patients with cavernous angiomas were excluded from the data set. Seven of the 61 1 patients had two nidii or two residuals of an AVM. Patients who had been treated earlier with radiotherapy (n = 3), those with repeated GK treatments (n = 44), and cases where a re-evaluation of the treatment was impossible (n = 16) were excluded from the study. In 5 of the patients with two nidii, the malformations could be defined within one and the same target volume. In two cases the distance between the lesions was large and the radiation fields did not overlap and they were therefore considered as two separate treatments. Thus, this data set is based on 55 treatments. In this data set one or two isocenters were used in 92% of the treatments. The second data set consists of patients treated with the third GK installed in A new and improved threcdimensional dose-planning system ( KULA) was introduced together with this GK. Owing to the fact that more than 9% of complications following radiosurgery occur within 18 months after treatment (27), all 356 patients with 369 AVM treated at the Karolinska Hospital between March 1988 and April 1992 were included. Those excluded were patients who had received radiotherapy treatment before GK surgery (n = 8), those who received second GK treatment for retreated cases (n = 4) and those in which a re-evaluation of the treatment was impossible (n = 4). In 5 of the patients with two AVMs, the malformations were so close that, from a complication point of view, they could be considered as a single treatment. The distance between lesions in 11 cases excluded interference of the radiation fields. Thus, this data set is based on 312 treatments. In this dataset multiple isocenters per treatment were more frequent compared with those in the first dataset. Taking both materials together, we have a total material of 862 treatments. A complication was defined as radiation-induced new or aggravated neurological symptoms or signs, transitory or permanent occurring together with radiological evidence of edema or radionecrosis. Radiation-induced side effects on the cranial nerves were not considered as a complication in this study. The relation between AVM location and incidence of complications was also studied. The nidus was defined as being central when it was located in the mesencephalon, intra- or paraventricular or in the basal ganglia. Of the malformations included in this study, 456 were located centrally and 367 peripherally. AVM located in the cerebellum were not included. The x2 test was used for comparing the nominal data. A difference was considered to be statistically significant when p <.1.
4 52 1. LAX AND B. KARLSSON Actu Oncologicu 35 (1996) c * I Average dose in 2 cm3 (Gy) Fig. 2. Incidence of complications is shown by the point with 95"h confidence interval. The line is a fit to the points. The total material includes 862 treatments. L Average dose in 2 cms Fig. 3. The line shows the incidence of complications (from Fig. 2). The points show the calculated risk of complication for 1 treatments. All 862 treatments were re-evaluated by the KULA dose-planning program (ELEKTA Inc.) and the threedimensional dose distributions calculated. A dose-volume histogram was calculated using an independent program (HISTOGRAM), for each treatment from the calculated dose distribution. The program was also designed to calculate average doses in different volumes. The total data set of 862 treatments was divided into 5 groups according to the average dose in a volume of 2cm'. This volume was selected because it covers the volume of interest in this context. The number of patients in each group was roughly the same. For each group, the incidence of complications and the mean of the average dose in 2 cm3 were determined. The parameters No and Do in Eq. [3] were determined by a fitting procedure. The evaluation was made by a least-square fit of the risk of complication calculated by Eqs. [l] and [3] from the reconstructed dose distributions to a linear fit of the clinical data of risk of complication for the 5 groups described above. The independent variable was the average dose in a constant volume. The volume was selected to 2cm3. In the fitting calculations the reference volume V was assumed to be that of the brain (V = cm3, (22)). The fit was made for a volume including that of the AVM (hypothesis A). The clinical data were extrapolated down to an average dose of 5 Gy and up to 25 Gy (cf. Fig. 2). Results The results from the follow-up study of the 862 AVM treatments can be found in Fig. 2, which shows the incidence of complications vs. the average dose in a 2cm3 volume centered at the AVM. The error bars give the 95% confidence interval. The large statistical uncertainty in the data, despite the large number of patients, is dependent on the fact that the overall incidence of complications was small. The line in Fig. 2 is a linear fit to the data points. A theoretically better fit would be Eq. [5]. However, the deviation from a linear relation is very small for the incidence of complications shown in Fig. 2. Regarding the location of the AVM, 13 complications were registered in the group of 367 peripherally located AVM (4%). In the centrally located group, 32 complications out of 456 AVM were registered. This is a nonsignificant difference (p =.3), however. The results of fitting the calculated risk of complications expressed by Eqs. [l] and [3] to the clinical data are presented in Fig. 3, where the points indicate the calculated risk of complications for a subset of 1 treatments and the line is the clinical data from Fig. 2. The values of the parameters determined from the fit were N, = and D, = 3.33 Gy. For the same dose-response curve, expressed in terms of Eq. [3a], the parameters are D,, = 7.63 Gy and y =.85. The resulting dose-response curve P(D, 1) given by Eq. [3], with the parameters determined from the fit, is represented by the solid line in Fig. 4. If the dose-response curve is described by Eq. [2] with the same D,, and the same maximum slope, the parameters will be D,,= 1-8 s Y.- CI 6 ls.- 4 n Dose (Gy) Fig. 4. Doseeresponse curve for complications from Eq. [2] (---) and Eq. [3] (-).
5 Actu Oncoiogicu 35 ( 1996) GAMMA KNItE RADIOSURCFRY OF ARTERIOVENOUS MALbORMATIONS 53 1 $ 8 - C.o 6.- c1 I n Dose (Gy) 1 8 (d? (D 2 3 Fig. 5. Risk of complication calculated for one 18 mm shot and maximum dose of 5 Gy. The calculations were made for different volumes circumscribed by different dose levels. The dose- response curve is also shown. ~ Eqs. [I] and [3];--- Eq. IS]; Eqs. [I] and [21;. Eq. [ Dose (Gy) Fig. 6. Dose-response curves for the reference volume equal to that of the whole brain (left curves). The two curves to the right shows the dose-response curves for a volume equal to 1 cm. Eq. [3]; --- Eq. [2]; Eqs[l] and [3];.. E ~s. [ 11 and [Z] Gy and k = 3.4. This curve is represented by the hatched line in Fig. 4. In order to compare the result from the approximation given by Eq. [5] to that given by Eq. [I], the fractional risk of complication has been calculated for one 18 mm shot and a maximum dose of 5Gy. Fractional risk of complication is here defined as the risk of complication that is calculated for the dose distribution within the volume circumscribed by a certain dose leve. The risk is thus zero at the point of maximum dose, and increasing with increasing volumes and lower dose levels. The calculation was made with Eqs. [I] and [3] and with Eq. [5]. The parameters of No and Do given above were used. For comparison purposes, the calculation was also made with Eqs. [I] and [2] using the parameters of D,, and k given above. The results are presented in Fig. 5. The doseresponse curve (Eq. [3]) is also shown in the figure. The dose given by the inequality (6) is 6.42 Gy for the parameter values of No and Do given above. As an example the risk of complication using 18 mm collimators and a maximum dose of 5 Gy is 9.3% calculated by Eqs. [ Iland [3], 8.3% calculated by Eq. [5] at the dose given by Eq. [6] and 6.9% calculated by Eqs. [I] and [21. Discussion In the present study it has been assumed that all of the irradiated volume is of importance for the development of complications (hypothesis A). It may be argued that the volume of the AVM contains only a small fraction of normal brain tissue, and that it is the effect on the normal brain tissue that is of importance for the development of clinical complications (hypothesis C). However it has so far not been possible to draw this conclusion from the clinical data. Whether or not hypothesis A is, from a radiobiological point of view, the correct one it is, from an operational point of view, a valid hypothesis which is confirmed by the result in Fig. 3. One explanation for this could be that the irradiated volume outside the AVM will, in the first approximation, be proportional to the volume of the AVM. Another important reason for choosing hypothesis A in this study is the lack of information about the extent and density of the AVM. This is generally based on two orthogonal angiography projections, which is insufficient for reconstruction of the complete outline of the AVM and its infrastructure. Despite the extent of the patient material, we could not detect a statistically significant difference in the incidence of complications between centrally and peripherally located malformations. Owing to this fact the model does not discriminate for the location of the AVM. However, the tendency toward a higher incidence of complications in centrally located malformations may in the future, when more patients can be added to the material, prove to be statistically significant. If so, dose-response curves can be determined separately for different parts of the brain. On the other hand, if in a patient material of almost 9 treatments some significant importance of the location cannot be found, the clinical value of discriminating the risk of complications for the location would not be an important issue. In the program HISTOGRAM the average dose was calculated in a number of volumes for each treatment. Relationships qualitatively similar to those shown in Fig. 2 were found for volumes other than 2cm, though not presented in this article. For smaller volumes the curve is shifted to higher average doses, and the reverse for larger volumes. The volume 2 cm3 was selected for the determination of the parameters as this will cover the irradiated volume down to the low dose levels. The difference between the two dose- response curves shown in Fig. 4 is small, and it could be assumed that the risk of complication calculated using 18 mm collimators
6 54 I LAX AND B. KARLSSON Aria Oncologicu 35 ( 1996) and a maximum dose of 5 Gy is likely to be similar (cf. Fig. 5). However, from the dose-response curve overlaid on the results in Fig. 5, it may be concluded that the high-dose region (>D,,) of the dose-response curve will be very important for the outcome of the calculation. There is a small but significant difference between the two dose-response curves in this region. This can be clearly demonstrated if the dose- response curve is calculated for a volume smaller than the reference volume. The reference volume V was here assumed to be the whole brain, cm3. However, the volume irradiated to a high dose in radiosurgery is only a fraction of the volume of the brain. Furthermore, if complications occur, the radiological evidence of the complications is generally located in a relatively small volume surrounding the AVM. Dose-response curves have been calculated for a volume of 1cm3, using Eqs. [l] and [2] and [I] and [3]. The values of k, D,, and No, Do were as given above. The results are presented in Fig. 6. For comparison, the doseresponse curves for the reference volume are also presented. The last two are thus the same as those shown in Fig. 4. From Fig. 6 it can be seen that the steepness of the dose-response curve is considerably reduced, and the curves shifted to a higher dose for a volume of 1cm3. This is qualitatively the effect demonstrated by Withers et al. (19). The difference between the two dose-response curves (1 cm3) explains the difference shown above of the risk of complication calculated for the case in Fig. 5. It is thus, as expected, important to have an accurate description of the dose-response curve in the high-dose region. It is generally a difficult task to evaluate heterogeneous dose distributions for correlation with the clinical outcome. An instrumental concept for this is the dose-volume histogram reduction methods that have been presented earlier (28, 29). In this study, however, the dose-response curve expressed in Eq. [3] has the property that a single parameter of the dose distribution-average dose-has a high relevance when applied to dose levels that are used in radiosurgery of AVM. This is illustrated in Fig. 3. It should be pointed out that the dose-response curve presented here is valid for radiosurgery of AVM using hypothesis A, and that this dose-response curve cannot directly be applied to other applications of radiosurgery. The model presented in this study is verified by clinical data up to an incidence of complications of about 12%. When large AVM are treated, the model will be a useful tool for estimating the risk of complication. The model has been implemented in the program HISTOGRAM and is today in clinical use at the Karolinska Gamma Knife Center. ACKNOWLEDGEMENTS Valuable comments from Professor Anders Brahme are gratefully acknowledged. REFERENCES 1. Leksell L. The stereotatic method and radiosurgery of the brain. Acta Chir Scand 1951; 12: Lunsford LD, Kondziolka D, Flickinger JC, et al. Stereotactic radiosurgery for arteriovenous malformations of the brain. J Neurosurgery 1991; 75: Steiner L. Radiosurgery in cerebral arteriovenous malformations. In: Flamm Fein EJ, ed. Textbook of cerebral surgery. New York: Springer-Verlag, 1986: Steiner L. Treatment of arteriovenous malformations by radiosurgery In: Wilson CB, Stein BM, eds. Intracranial arteriovenous malformations. Baltimore: Williams and Wilkins, 1984; Steiner L. Lindquist C, Cail W, et al. Guest editorial: Microsurgery and radiosurgery in brain arteriovenous malformations. J Neurosurgery 1993; 79: Flickinger JC, Lunsford LD, Linskey M. Gamma Knife radiosurgery for acoustic tumours: multivariance analysis of four ten-years results. Radiother Oncol 1993; 27: Noren G. Stereotactic radiosurgery in acoustic neurinomas, a new therapeutic approach (Dissertation). Karolinska Institute, Stockholm, Noren G, Greitz D, Hirsch A., et al. Gamma Knife surgery in acoustic tumors. Acta Neurochir 1993; 58: Karlsson B, Kihlstrom L, Lindquist C. Medical controversy: is Gamma Knife surgery the treatment of choice for cerebral metastases? Trends in Experimental and Clinical Medicine son B, Lindquist C. Gamma Knife surgery for cerebral metastases. Implictions for survival based on 16 years experience. Stereotact and Func Neurosurg 1993; 61 (Suppl I): Kihlstrom L, Karlsson B, Lindquist C. Gamma Knife surgery for cerebral metastases. Acta Neurochir 1991; (Suppl 52): Lindquist C. Gamma Knife surgery for recurrent solitary metastasis of a cerebral hypernephroma: Case report. Neurosurgery 1989; 25: Steiner L, Lindquist C, Steiner M. Meningiomas and gamma knife radiosurgery in meningiomas. Ossama AM, ed. New York: Raven Press; 1991: Backlund EO, Axelsson B, Bergstrand CG, et al. Treatment of craniopharyngiomas- the stereotactic approach in a ten to twenty-three years perspective. I. Surgical, radiological and ophhalmological aspects. Acta Neurochir ( Wien) 1989; 99: Dempsey PK, Lunsford LD. Stereotactic radiosurgery for pineal region tumours. Neurosurg Clin N Am 1992; 3: Rahn T, Thorkn M, Werner S. Steorereotactic radiosurgery in pituitary adenomas. In pituitary adenomas. New trends in basic and clincial research. Venice: Excerpta Medica, 1991, 17. Ahnesjo A. A fast algorithm for dose planning of radiosurgery with stereotactic multi-cobolt units. Proceedings of the VII Int. Conf. on Medical Physics. Espo, Finland, 1985: p Goitein M, Niemierko A. Biologically based models for scoring treatment plans. In: Zink S, ed. Future directions of computer-aided radiotherapy. National Cancer Inst.. Bethesda, Withers HR, Taylor J, Maciejewski B. Treatment volume and tissue tolerance. Int J Oncol Biol Phys 1988; 14: Kallman P, Agren AK, Brahme A. Tumor and normal tissue responses to fractionated non-uniform dose delivery. Int J Radiat Biol 1992: 62:
7 Acta Oiicologica 35 ( 1996) GAMMA KNIFE RADIOSbRGERY OF ARTERIOVENOUS MALFORMATlOhS Schultheiss TE, Orton CG, Peck RA. Models in radiotherapy: volume effects. Med Phys 1983; 1: Flickinger JC. An integrated logistic formula for prediction of complications from radiosurgery. Int J Radiat Oncol Biol Phys 1989; 17: Lax I. Target dose versus extratarget dose in stereotactic radiosurgery. Acta Oncol 1993; 32: Brahme A. Dosimetric precision requirements in radiation therapy. Acta Radiol Oncol 1984; 23: Munro TR, Gilbert CW. The relation between tumor lethal dose and the radiosensitivity of tumor cells. Br J Radiol 1961; 34: Yeas RJ. Some implications of the linear quadratic model for tumor control probability. Int J Radiat Oncol Biol Phys 1988; 14: Guo WY. Radiological aspects of Gamma Knife radiosurgery for arteriovenous malformations and other non-tumoral disorders of the brain (Dissertation). Karolinska Institute, Stockholm, Kutcher GJ, Burman C. Calculation of complication probability factors for non-uniform normal tissue irradiation: the effective volume method. Int J Radiat Oncol Biol Phys 1989; 16: Lyman JT, Wolbarst AB. Optimisation of radiation therapy. IV: a dose-volume histogram reduction algorithm. lnt J Radiat Oncol Biol Phys 1989: 17:
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