Volume 40, Number 3
March 1997
Interactive Article


Prediction of Obliteration after Gamma Knife Surgery for Cerebral Arteriovenous Malformations

Bengt Karlsson, M.D., Ph.D., Christer Lindquist, M.D., Ph.D., Ladislau Steiner, M.D., Ph.D.

Department of Neurosurgery (BK, CL), Karolinska Hospital, Stockholm, Sweden, and Department of Neurological Surgery (LS), The University of Virginia School of Medicine, Charlottesville, Virginia

OBJECTIVE: To define the factors of importance for the obliteration of cerebral arteriovenous malformations (AVMs), thus making a prediction of the probability for obliteration possible.

METHODS: In 945 AVMs of a series of 1319 patients treated with the gamma knife during 1970 to 1990, the relationship between patient, AVMs, and treatment parameters on the one hand and the obliteration of the nidus on the other was analyzed.

RESULTS: The obliteration rate increased both with increased minimum (lowest periphery) and average dose and decreased with increased AVM volume. The minimum dose to the AVMs was the decisive dose factor for the treatment result. The higher the minimum dose, the higher the chance for total obliteration. The curve illustrating this relation increased logarithmically to a value of 87%. A higher average dose shortened the latency to AVM obliteration. For the obliterated cases, the larger the malformation, the lower the minimum dose used. This prompted us to relate the obliteration rate to the product minimum dose (AVM volume)1/3 (K index). The obliteration rate increased linearly with the K index up to a value of approximately 27, and for higher K values, the obliteration rate had a constant value of approximately 80%. For the group of 273 cases treated with a minimum dose of at least 25 Gy, the obliteration rate at the study end point (defined as 2-yr latency) was 80% (95% confidence interval = 75-85%). If obliterations that occurred beyond the end point are included, the obliteration rate increased to 85% (81-89%).

CONCLUSION: The probability of obliteration of AVMs after gamma knife surgery is related both to the lowest dose to the AVMs and the AVM volume, and it can be predicted using the K index.

(Neurosurgery 40:425-431, 1997)

Key words: Arteriovenous malformations, Gamma knife radiosurgery

In April 1970, a project to treat arteriovenous malformations (AVMs) of the brain using the Leksell gamma knife was started. Because single high-dose treatment had never been used for treatment of cerebral AVMs, no previous experience on which to rely existed. This shaped the rationales for the decisions, strategy, and pace of the project. A report presented by Rojas on vessel rupture and hemorrhage after radiotherapy of tumors in the neck influenced our decision concerning the dose selection in our first cases of AVMs treated by radiosurgery. Marcial-Rojas and Castro (12a) used 60 Gy in fractionated doses, and we reasoned that to avoid the complications described by him, we should never administer more than 50 Gy, which usually resulted in a periphery dose of approximately 25 Gy. We missed that Rojas treated suprainfected cancer cases. The cause of the vessel rupture was not the radiation but erosion of the vessel wall by tumor infiltration and infection. Moreover, the biological effect of the single dose of 50 Gy is significantly higher than 60 Gy in fractionated doses. Thus, the rationale for our dose selection was haphazard. Nevertheless, as sometimes happens in research, despite the false rationale, 25 Gy as the peripheral dose proved to be sufficient in most cases. Starting from "scratch" determined also the pace of the project. No new case was treated before the follow-up results of the previous case were available and carefully evaluated. This explains why until 1979, only 68 patients had been treated (14). With accumulated experience and documented therapeutic success, the number of treated cases started to increase relatively fast, and today, of the approximately 10,000 AVMs treated using the gamma knife worldwide, more than 2,400 have been treated by us.

The importance of different parameters for the angiographic and clinical outcomes has been sporadically discussed in the literature (3, 4, 12). However, a systematic study of the role of different parameters in determining the success as well as the complications after radiosurgery and an effort to predict treatment results based on patient, treatment, and AVM parameters has not been reported.

The aim of this study is to assess the parameters involved in radiosurgery and to define, quantitatively if possible, the role of each one in success and failure. In a parallel study, the role of these parameters for complications will be addressed.


The present results are based on a consecutive series of AVMs that we treated using the gamma knife between April 1, 1970, and December 31, 1990. That the study was retrospective and that the time period studied was long explains why some data were lost for some patients. Additionally, the dose plans from the first gamma knife and the gamma knife in Buenos Aires could not be reevaluated because of technical factors. This has resulted in lack of knowledge of some parameters in some patients. For example, the AVM volume could be calculated in 87%, the maximum dose in 98%, and the AVM location in 99% of the cases.

Patient population

The material includes 1319 consecutive patients with AVMs that were visible on angiograms; cryptic AVMs were excluded. All patients were treated by us at four different centers. Excluded from the study were patients who had received radiotherapy before gamma knife surgery (17 patients) and patients who underwent other treatment, including radiosurgery, within 2 years (15 patients) or who had died during that period (13 patients). Also excluded were the results of subsequent treatment in patients who were treated a second time with gamma knife surgery (91 patients) and patients with adequate angiographic follow-up still pending (306 patients). Of the latter, 43 patients had undergone magnetic resonance studies at least 2 years after the treatment, which demonstrated evidence of persisting malformations. Additionally, 10 of the 306 patients did suffer from hemorrhage later than 24 months after the treatment. These 53 cases were included as treatment failures. Of the patients included in the study, 15 had two occurrences of AVMs. Thus, 930 patients with 945 AVMs were included in the study.

The initial symptom was hemorrhage in 727 cases (78%), epilepsy in 112 (12%), migraine in 24 (3%), and neurology in 23 (2%). In 21 (2%) of the cases, the AVMs were discovered accidentally, in 10 (1%), the patients had symptoms not related to the AVMs, and in 13 (1%), the initial symptom was unknown. The mean age of the patients at the time of treatment was 30 years (4-72 yr), and the median age was 28 years. The other patient characteristics are listed in Table 1.

TABLE 1.  Patient Characteristics

Embolized prior gamma10511
Operated prior gamma9411
Children < 13 yr8910

AVM volume and location

The AVM size is usually classified according to the largest diameter of the AVM nidus (2, 5, 12). If a volume estimation is desired, the diameter can be considered to be the diameter in a sphere and the sphere volume can then be calculated. If this technique is used, the size of the AVMs in our series is comparable with that in earlier published radiosurgical series (1, 9, 12). This is illustrated in Table 2.

To avoid the flaws inherited with the method described above, we developed an indirect volume estimation technique suitable for radiosurgery. In gamma knife surgery, the aim of the dose planning is to describe the whole AVM nidus periphery with as accurate a fit as possible to an isodose line. Thus, the volume within this isodose line can be used as an approximation of the AVM nidus volume. We used this and defined the AVM volume to be equal to the volume within the best fit isodose. In this material, the mean AVM nidus volume was 3.6 cm3 (1-50 cm3). The locations of the AVMs are shown in Table 3.

Assessment of angiograms

The assessments of the follow-up imaging studies were performed by a neuroradiologist who was not directly involved in the treatment of the patients. The end point of this study was total obliteration or patency after 2 years. Total obliteration was defined as complete absence of pathological vessels in the former nidus of the malformation, disappearance or normalization of draining veins, and normal circulation time on high-quality rapid series subtracted angiograms (see Fig. 5) (10). The presence of an early filling vein only (see Fig. 6) was defined as subtotal obliteration and, for the time being, was considered an unsatisfactory result despite that some of these AVMs obliterated after the end point of the study was reached (7).

Assessment of dosimetry and treatment parameters

During the initial stage of this project, the KULA dose planning program had not yet been introduced. Therefore, in all patients treated, the dose plans were reconstructed by one of us with this program, using the original treatment protocols.

TABLE 2.  Sizes of Arteriovenous Malformations in Patients Selected for Radiosurgery
Lunsford et al., 1991 (12)Levy et al., 1989 (9)Our SeriesIsodose Technique

<1 cc22  (10%)2  (5%)112  (14%)129  (16%)
1-10 cc141  (62%)23  (57%)461  (56%)643  (78%)
>10 cc64  (28%)14  (38%)253  (31%)54  (7%)

TABLE 3.  Locations of Arteriovenous Malformations

Basal ganglia/thalamus17418
Midbrain/brain stem10511
Corpus callosum566
Parietal lobe13414
Temporal lobe13014
Frontal lobe778
Occipital lobe768

The gamma knife

Eight cases were treated with the first prototype gamma knife, which had two different sets of collimators with ellipsoid apertures (3 x 5 and 3 x 7 mm). The second prototype of the gamma knife was used for 444 cases. This device had two sets of collimators, with circular apertures of 8- and 14-mm diameters. The remaining patients were treated in units with four available collimator sizes, with circular apertures of 4-, 8-, 14-, and 18-mm diameters.

Statistical methods

For statistical analysis, the chi2 test was used for nominal data. For continuous data, the Wilcoxon two-sample test was used because it does not demand normal distribution. Multivariate analysis was performed using the proportional hazards model. A result was considered statistically significant if P < 0.01. In all graphs, the bars represent the 95% confidence intervals.


Patient and AVM parameters and AVM obliteration

Neither gender nor age had any statistically significant influence on the treatment results. There were 254 of 447 (57%) obliterated AVMs in female patients and 280 of 498 (56%) in male patients (P = 0.85). The mean patient age for the 534 obliterated AVMs and the 411 nonobliterated AVMs was the same, 31 years. If children (<13 yr at treatment) are compared with adults, the obliteration rate is almost the same (61 versus 56%).

In the cases in which a volume estimation was possible, the mean volume of the 467 obliterated cases was 2.1 cm3 and for the 285 nonobliterated cases was 5.3 cm3. The difference is statistically significant (P < 0.0001). Among the 238 optimally treated cases (K index > 27), the mean volume in the obliterated cases was 2.6 cm3 and in the nonobliterated cases was 3.2 cm3, a nonsignificant difference (P = 0.03)

Treatment parameters and AVM obliteration: collimator

In treatments using one isocenter, there were 61 of 82 AVMs (74%) obliterated with the 8-mm collimator, 263 of 383 (69%) with the 14-mm collimator, and 17 of 29 (59%) with the 18-mm collimator. When the group treated with 8-mm collimators was compared with the group treated with 14-mm collimators, no significant difference was observed (P = 0.30).

Maximum, average, minimum, and integral dose

The maximum dose was 45 Gy (mean value) in the group of obliterated and 42 Gy (mean value) in the group of nonobliterated AVMs, a nonsignificant difference (P = 0.27). The average dose in the obliterated cases was 37 Gy (mean value), whereas in the nonobliterated cases, it was 29 Gy (mean value). The difference was statistically significant (P < 0.0001). A relation was also observed between the time to obliteration (or, more accurately, the time between treatment and angiography proving obliteration) and the average dose administered to the AVMs. There was a statistically significant shorter latency at a higher average dose (P < 0.0001), and the linear correlation was excellent (R2 = 0.99), as Figure 1 illustrates.

The minimum dose in the obliterated cases was 23 Gy (mean value) and in the nonobliterated cases was 13 Gy (mean value), a statistically significant difference (P < 0.0001). Figure 2 shows the obliteration rate plotted against the minimum and average doses. The incidence of obliteration increased with the minimum dose up to 87%. The curve can be described accurately by a logarithmic function, f (x) = 3.57 ·ln (x) - 0.4 (R2 = 0.99).

Also, the integral dose to the AVMs was related to the obliteration rate. However, the relation was negative (i.e., the higher the integral dose, the lower the obliteration rate, as illustrated in Fig. 3).

K index

The observation that the incidence of obliteration increases with the minimum dose and that for the obliterated cases, the larger the AVMs the lower the periphery dose administered gave us the idea to combine the parameters of the minimum dose and AVM volume. The resulting index was named K index and defined as the product (minimum dose)·(AVM volume)1/3. Figure 4 illustrates the relation between the obliteration rate and the K index. The relation can be divided in two parts, one increasing and one constant. The intersection between the linear regressions for these two parts is (27.1; 80). Thus, a treatment was defined as optimal when the K index equaled 27.

FIGURE 1. Time between the treatment and angiography proving obliteration plotted against the average dose to the AVMs. The linear regression is also illustrated. As seen, the relation is almost linear.

FIGURE 2. Incidence of obliteration plotted against the average and lowest dose to the AVM nidus. For both parameters, the incidence of obliteration increased with the dose.

FIGURE 3. Incidence of obliteration plotted against the integral dose. Except for the beginning, the incidence of obliteration decreased with an increasing integral dose. This is most likely because a significant number of the larger malformations received insufficient doses.

FIGURE 4. Incidence of obliteration plotted against the K index. Two linear regressions are also illustrated (one for the first five points and the other for the two last points). For both regressions, the linearity is good. The curve indicates that the minimum dose needed to obliterate larger malformations is lower, as compared to smaller AVMs. It also indicates that there is a volume-dependent dose limit for optimizing the chance for obliteration.

Dose rate

Both the dose and the dose rate decreased from the center to the periphery of the target volume. The dose rate at the maximum dose was compared in obliterated and nonobliterated AVMs. No significant difference could be found (P = 0.40). Nevertheless, a number of factors, such as the homogeneity of the radiation field, affect the dose rate in a manner that could not be accounted for and thus the analysis was inconclusive.

FIGURE 5. Subtraction angiogram of basal ganglia AVMs. A and B, vertebral angiograms obtained at the time of gamma knife surgery. The nidus was also fed from the carotid, but the two vascular territories overlapped each other. C and D, vertebral and carotid angiograms obtained 2 years after gamma knife surgery, showing total obliteration of the nidus.

FIGURE 6. Subtraction angiogram of parietal AVMs. A and B, stereotactic angiograms obtained at the time of gamma knife surgery. C and D, nidus is no longer visible, but an early filling vein still persists. Hence, the case is assessed as subtotal obliteration and a treatment failure in this study.


Because the AVM treatments were started without previous reports to rely on, this material, for better or worse, is unique. Thus, the case selection process, the treatment principles, and the selection of treatment parameters remained largely unbiased by established protocols. The "trial and error" character of the activity persisted for a long time and resulted in a relatively wide gamut of parameters, which are now available for evaluation. On the other hand, the experimental character of the initial phases of the project lead to a number of failures that weigh heavily in the present statistical results. There is reason to assume that the wealth of information provided in this study will help to eliminate this "learning curve effect" in future series.

AVM volume

The result of AVM treatments is, regardless of the treatment modality, related to the AVM volume. In general, the larger the malformations the less favorable the results. The most commonly used surgical grading scale includes, therefore, AVM size, defined as the longest diameter, as one of the parameters (13). Thus, in surgical series, the size of the AVMs is expressed in length, which makes a comparison between microsurgical and radiosurgical results difficult.

To facilitate comparison, we compared the results between the volume estimation technique used in this article to what was obtained by considering the largest diameter being a diameter in a sphere after correction for the magnification factor on the film. For this comparison, the material was grouped in five groups according to the volume defined by the technique used in this article. The relation between the two methods could be described by the linear regression as follows: f (x) = 5.57 · x - 0.09 (R2 = 1.0). Thus, if the largest diameter is known, the results in other series can be compared with the findings in the present series. Because of the large standard deviation, the linear equation cannot be used to compare single cases.

AVM size and obliteration

For radiosurgery, that the results are better in direct correlation with the smaller size of the AVMs is documented in the literature (1, 4, 12). The conclusion has been drawn that it is the AVM volume itself that is important for the outcome also with radiosurgery. This is supported in that a multivariate analysis cannot detect any difference in importance between dose and volume (P < 0.0001 for AVM volume and minimum and integral doses). This may, however, be because the AVM volume and the dose administered are interdependent.

The observation that there is no significant difference in volume between optimally treated obliterated and nonobliterated AVMs indicates that the dose selection is more important than AVM volume. Additionally, a significant correlation exists between the outcome and minimum dose when a subgroup of AVMs with similar volume (<2 cm3) is studied, which indicates the same (P < 0.0001).

The findings above, together with the observation that the optimal dose is volume-dependent, indicates that not only small but also medium sized AVMs can be treated with a reasonable success rate. A caveat is that the AVM volume interval in which the K index can be used is uncertain. To date, our best guess is that the volume within the prescription isodose should rather be below than exceed 10 cm3.

One way to eliminate the uncertainty with the K index would be to administer the same minimum dose for all AVMs independent of the volume. Unfortunately, if the same minimal dose is administered to larger AVMs, the risk of complications is increased (8). Therefore, to minimize the risk for complications, the doses in this series were inversely related to size. This decrease in dose to increasing size could lead to the false conclusion that the treatment result is negatively related to AVM volume. Stereotactic radiation with a fractionation scheme may theoretically decrease the risk. However, this remains to be proven. In a series of 26 patients with AVM volumes of 7 to 107 cm3, 42 Gy was delivered during 6 weeks. This resulted in only two obliterated malformations and two obvious complications (11).

K index

The aim of introducing the K index is to make an attempt to find an optimal dose for every occurrence of AVMs. Retrospectively, a K index value of approximately 27 seems to be optimal to obtain as high a chance for cure as possible with as low a risk for complications as possible. Using the K index together with a risk estimation model makes it possible to perform a cost/benefit analysis for an individual case before the treatment is administered (6, 8). Additionally, if for larger AVMs a lower value is obtained, the K index may be used to estimate the probability for obliteration with the minimum dose administered.

Two different theories can be raised to explain the relation between the K index and the incidence of obliterations. The first is the assumption that AVMs consist of a number of subunits and that it is sufficient to obliterate only a critical part of a sufficient number of subunits to totally obliterate the malformation. If so, then for stochastic reasons, the larger the malformations, the less the important it is that the entire malformations are covered with a high dose.

The other theory is based on the assumption that the larger the malformations, the higher the probability that normal brain tissue will be included in what is defined as the AVM volume from angiographic films in two projections only. Therefore, the larger the malformations, the higher the probability that the estimated minimum dose is lower than the true minimum dose.

If the latter is true, then the K index is of limited value if also stereotactic magnetic resonance imaging (MRI) is used for the nidus definition. Therefore, the index should, as with all retrospective findings, be used with caution. However, in lack of prospectively proven predictions, it is most probably better to use the index rather than to perform no assessment of the probability of obliteration.

Dose rate

The radiation source of the gamma knife is 60Co. The half-life of 60Co is 5.3 years, which means that the dose rate is halved over this time period. For 14 years, the same gamma knife was used to treat the AVMs of the present series, and during that time, the dose rate was reduced to 16% of its original value. The other factors defining the dose rate in the target is the depth of the target, the number of isocenters used, and the collimator size. It is clear that the biological response to radiation is related to the dose rate (15). That no such relation was observed in this study may be explained by the high dose rates, 0.3 to 5.3 Gy per minute, used for the treatments of the patients in this series.

Impact of MRI findings in the present series

If an AVM nidus persists, it can be visualized using an appropriate MRI study in a high percentage of cases. This may result in a delay of performing follow-up angiography. In other words, if an MRI scan 2 years after treatment shows persistent flow void, the follow-up angiography may be postponed. The use of MRI has increased with time, and, therefore, an important bias has been introduced for selecting patients for angiographic follow-up. This is the reason we included only cases treated before 1991; the use of MRI follow-up was very sparse for patients treated until then. Still, there were patients with MRI showing evidence of persisting malformations for at least 2 years after the treatment. It is most reasonable to think that this information has contributed to postpone follow-up angiography for some of these patients. To avoid a falsely high obliteration rate in this series, we defined all 43 patients who had MRI evidence of persisting malformations for 2 years or more as having failed treatment. We did not define any patient as cured without follow-up angiography. Thus, we have deliberately introduced a bias in the study, resulting in an underestimation of the obliteration rate in the present material.


We thank all of our colleagues at the department of Neuroradiology, Karolinska Hospital, for help with interpreting the radiological follow-up material.

Received, November 2, 1995.
Accepted, October 7, 1996.
Reprint requests: Bengt Karlsson M.D., Department of Neurosurgery, Karolinska Hospital, S-104 05 Stockholm, Sweden.


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Karlsson et al. provide their analysis of the dose-response relationship in radiosurgery of arteriovenous malformations (AVMs) based on a 20-year experience in patients managed from 1970 to 1990. The compilation of such data is long overdue. Because the number of centers performing radiosurgery of AVMs has increased dramatically during the last decade, a prior evaluation and publication of this initial large experience would have been truly helpful in the management of other patients worldwide.

Although not the main thrust of this report, one of the most interesting concepts it addresses is the tremendous change in the method of dose planning since 1970. As the authors accept, the initial treatment plans of the 1970s were so crude as to not be fully suitable for analysis by modern dose-planning systems. The method of calculating the addition of two or more isocenters was not performed correctly, as current mathematical formulae now indicate. Previous multiple isocenters just superimposed the isodose configurations of each isocenter on top of one another, without integration and recalculation of the individual isodoses. This leads to overdosing at each isocenter in cases for which this was performed (before the KULA system was available). The discussion of the initial concept of dose selection for vascular malformation radiosurgery based on tumor radiotherapy is a story that few may know. That the first doses selected were beneficial was a serendipitous discovery; it is remarkable how often this happens in medicine! If lower doses had been selected and unsuccessful outcomes documented, radiosurgery of AVMs may well have died out by 1975.

AVM obliteration is achieved through proper imaging definition of the AVM nidus (via computed tomography, magnetic resonance imaging, or angiography), proper configuration of the isodose plan, and selection of an optimal dose for the desired effect. This report addresses only the latter factor. Thus, the reader cannot sort out whether poor angiographic technique led to subtotal obliteration in patients receiving higher doses or whether a low dose alone lead to subtotal obliteration in larger AVMs for which optimal techniques were used. We are left to rely on the authors' interpretation of the plans and evaluation of dose within the plans themselves. To this point, most centers performing radiosurgery choose a dose for AVM obliteration that is the highest possible as determined by AVM volume. Many use the integrated logistics formula of Flickinger to select this dose, with an approximate 3% chance for permanent radiation-induced complications. We have recently published a comprehensive analysis of the obliteration response of AVMs treated at the University of Pittsburgh (1). In this report, we provided the reader with a percentage obliteration rate that can be expected at individual doses delivered to the AVM margin. Thus, if the dose delivered to the AVM margin as calculated on the computer actually is tailored to the AVM nidus, an expected obliteration rate will be predicted by the dose selected. The authors of this report developed the "K index" which links the AVM margin dose to the cubic root of the AVM volume. Although this index has not been tested, it may prove to be another useful method for dose selection that can be evaluated in further studies.

Will this report help us to perform AVM radiosurgery better? Perhaps. The more we know about the dose-response relationship for radiosurgery of AVMs, the better, although we may have reached our current limit for obliteration based on proper dose selection alone. I think that future improvements in AVM radiosurgery will first come through better multimodality imaging, such as combined magnetic resonance angiography and conventional angiography and, possibly, computed tomography angiographic techniques. To get beyond these improvements in technique, we will have to enter an era of vascular radiosensitization or brain radioprotection to allow more effective or higher radiation doses to be delivered. There is much work to be done.

Douglas Kondziolka
Pittsburgh, Pennsylvania

  1. Flickinger JC, Pollock BE, Kondziolka D, Lunsford LD: A dose-response analysis of arteriovenous malformation obliteration after radiosurgery. Int J Radiat Oncol Biol Phys (in press).

Karlsson et al. report a series that represents a mature and very large experience treating patients with inoperable AVMs with radiosurgery. The value of their experience is demonstrated by the substantial efforts involved in the analysis of their results. The clinical data provided in this report will guide international AVM radiosurgery practice for years. The results strongly confirm what is known about the basic principles of radiosurgery for AVMs: 1) the higher the minimum dose, the higher the obliteration rate; 2) the higher the minimum dose, the more rapid complete obliteration occurs; 3) minimum doses beyond 25 Gy are unlikely to substantially improve obliteration rates and only increase complications; 4) unlike the importance of minimum doses, isocenter or maximum doses do not correlate with obliteration rates; and 5) larger lesions have lower obliteration rates not because of intrinsic radiobiological properties but because they must receive a lower dose to prevent the development of symptomatic radiation injury. For larger volume lesions, the development of more conformal radiosurgery techniques is clearly needed to reduce the dose delivered to non-AVM tissue (normal brain) that is often included within the target volume.

Jay S. Loeffler
Radiation Oncologist
Boston, Massachusetts

Karlsson et al. review a 945-patient subset of the 1319 AVMs treated with the gamma knife between 1970 and 1990 to determine which treatment factors predicted complete obliteration. They found that minimum dose was most important. The higher the minimum dose, the higher the obliteration rate, up to 25 Gy. The obliteration rate in the 268 cases that received this minimum dose was 81%. The authors then invented something they call the "K index," which is the product of the minimum dose times the cube root of the AVM volume. They suggest that the K index should always have a value of 27. The K index, as illustrated in Figure 4 of the article, seems to be an entirely arbitrary mathematical construct. The authors do not state how the K index volume was obtained (it appears for the first time in the Results section), but I assume it was from their dose-planning method. Because the volume is 4/3 pi r3, the K index is approximately equal to the equivalent spherical radius of the AVMs multiplied by the peripheral dose. Would it not be simpler to use this formulation rather than the cube root of the volume? The authors' observation that optimal obliteration rates occurred at a K index of 27, with no improvement above that number, may be of importance. It may mean, as the authors suggest, that larger AVMs, for unknown reasons, require less peripheral dose to attain thrombosis. Because dose was deliberately decreased for larger AVMs to avoid complications, however, this is by no means clear. For instance, were the higher K numbers in this series mainly in small AVMs treated with very high doses of radiation? The upper end limitations in obliteration rate may also have been caused, in part, by the crude localization and dosimetry techniques used in the early days of radiosurgery.

The authors are trying to answer a very important question: Is it dose or volume that limits our ability to thrombose AVMs with radiosurgery? They have the data to answer the question, given their huge number of patients. The technique needed is multivariate statistics. A standard statistical analysis, not the "K index," will provide the only hope of adequately addressing this complex issue.

William A. Friedman
Gainesville, Florida

Please submit your thoughts or comments to William Chandler, Internet Moderator at wchndlr@umich.edu.

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