(Stroke. 2000;31:2466.)
© 2000 American Heart Association, Inc.
Original Contributions |
Experimental Radiosurgery Simulations Using a Theoretical Model of Cerebral Arteriovenous Malformations
From the Department of Radiological Sciences (T.F.M., G.J.H.), Division of Neurosurgery (A.A.F. De S.), and Department of Radiation Oncology (T.D.S.), University of California at Los Angeles, School of Medicine and Medical Center.
Correspondence to Tarik F. Massoud, MD, Section of Neuroradiology, Department of Radiology, University of Cambridge School of Clinical Medicine, Addenbrooke’s Hospital, Hills Rd, Box 219, Cambridge CB2 2QQ, UK. E-mail tfm23{at}cam.ac.uk
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Abstract |
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 Top Abstract IntroductionMethodsResultsDiscussionAppendix 1Appendix 2ReferencesIntroduction |
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Background and Purpose—A novel biomathematical arteriovenous malformation (AVM) model based on electric network analysis was used to investigate theoretically the potential role of intranidal hemodynamic perturbations in elevating the risk of rupture after simulated brain AVM radiosurgery.
Methods—The effects of radiation on 28 interconnected
plexiform and fistulous AVM nidus vessels were simulated by predefined
random or stepwise occlusion. Electric circuit analysis
revealed the changes in intranidal flow, pressure, and risk of rupture
at intervals of 3 months during a 3-year latency period after simulated
partial/complete irradiation of the nidus using doses <25 and 
25 Gy.
An expression for risk of rupture was derived on the basis of the
functional distribution of the critical radii of component vessels. The
theoretical effects of radiation were also tested on AVM nidus vessels
with progressively increasing elastic modulus (E) and
wall thickness during the latency period, simulating their eventual
fibrosis.
Results—In an AVM with E=5.0x104
dyne/cm2, 4 (14.3%) of a total 28 sets of AVM radiosurgery
simulations revealed theoretical nidus rupture (risk of rupture
100%). Three of these were associated with partial nidus coverage
and 1 with complete treatment. All ruptures occurred after random
occlusion of nidus vessels in AVMs receiving low-dose radiosurgery.
Intranidal hemodynamic perturbations were observed in
all cases of AVM rupture; the occlusion of a fistulous component
resulted in intranidal rerouting of flow and escalation of the
intravascular pressure in adjacent plexiform components. Risk of
rupture was found to correlate with nidus vessel wall strength: a low
E of 1.9x104 dyne/cm2 resulted
in a 92.8% incidence of AVM rupture, whereas a higher E
of 7.0x104 dyne/cm2 resulted in only a 3.6%
incidence of AVM rupture. A dramatic reduction in rupture incidence was
observed when increasing fibrosis of the nidus was modeled during the
latency period.
Conclusions—It was found that the theoretical occurrence of AVM hemorrhage after radiosurgery was low, particularly when radiation-induced fibrosis of nidus vessels was considered. When rupture does occur, it would appear from a theoretical standpoint that the occlusion of intranidal fistulas or larger-caliber plexiform vessels could be a significant culprit in the generation of critical intranidal hemodynamic surges resulting in nidus rupture. The described AVM model should serve as a useful research tool for further theoretical investigations of cerebral AVM radiosurgery and its hemodynamic sequelae.
Key Words: cerebral arteriovenous malformations • hemodynamics • intracerebral hemorrhage • models, theoretical • radiosurgery
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Introduction |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1Appendix 2ReferencesIntroduction |
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Minimally invasive treatment with stereotaxic radiosurgery represents a useful adjuvant to conventional neurosurgery in selected patients with intracranial arteriovenous malformations (AVMs). Although radiosurgical techniques continue to evolve with advancing experience and technology, the risks of AVM rupture and ensuing neurological complications associated with postradiosurgery latency periods are still present and remain a concern.
Optimal stereotaxic radiosurgery would utilize the highest therapeutic radiation dose associated with the lowest incidence of possible complications. Radiation injury to the AVM vessels causes endothelial cell damage and proliferation, intimal and medial degeneration, and hyalin thickening, which leads to altered blood flow dynamics, hemostasis, and eventually thrombosis and obliteration of the AVM.1 Complete AVM obliteration is observed when blood flow through the AVM has ceased and all involved AVM nidus vessels have disappeared and is generally noted angiographically up to 3 years after radiosurgery.1 2 Thus, a latency period exists before complete obliteration, during which the irradiated nidus vessels begin to narrow, resulting in potentially dangerous intranidal hemodynamic disturbances that may predispose to AVM rupture.3 It is during this latency period that some radiosurgeons consider the risk of AVM hemorrhage to remain elevated before falling to negligible levels, particularly for partially treated AVMs. Colombo et al3 reported in a study of 180 patients with radiosurgically treated intracranial AVMs that the bleeding risk for partially treated cases (ie, the entire nidus was not irradiated) was disturbingly high at 26% per year, with the normal risk of rupture for untreated AVMs being approximately 3% per year.2 3 Concern regarding the increased likelihood of hemorrhage after partial AVM radiosurgery has also been expressed by others.4 5 Deliberate partial radiosurgery may be adopted as a management strategy for some giant AVMs,6 and in some patients partial AVM radiosurgery occurs after inadvertent incomplete obliteration.7 The risk of hemorrhage in both categories of patients may be elevated and therefore remains worrisome. In addition to these observations for partially treated AVMs, preliminary experience from large8 and smaller9 10 11 clinical series is accumulating to indicate a possible increased propensity to rupture for some completely irradiated AVMs during postradiosurgery latency periods, regardless of selection or referral biases. By contrast, a recent study by Karlsson et al12 has demonstrated a protective effect of radiation on AVMs, as evidenced by an observed decrease in the incidence of AVM hemorrhage compared with the natural course. In an attempt to shed further light on these contradictory clinical observations, we provide in this preliminary report a theoretical analysis of the intranidal hemodynamic changes and some biophysical mechanisms that affect the risk of AVM nidus rupture after radiosurgery.
A novel biomathematical model of intracranial AVMs based on electric network analysis has been developed13 14 and employed14 previously as an experimental tool capable of qualitative simulation of complex hemodynamics through a theoretical AVM nidus and of assessment of its risk of rupture before, during, and after therapy. In this preliminary study, we used this new biomathematical AVM model to simulate the hypothetical occlusive responses of nidus vessels to 2 levels of radiosurgical dosages and to investigate the resultant theoretical intranidal hemodynamic changes. In addition, we studied the intranidal stability during the latency period by theoretical quantification of the risk of nidus rupture at defined temporal intervals up to 3 years after treatment. The goals of this preliminary study were as follows: (1) to investigate the theoretical influence of radiation dosage, rate of AVM occlusion, extent of irradiated AVM volume (partial versus complete), and inherent strength of nidus vessels on the risk of nidus rupture in radiosurgically treated AVMs and (2) to examine theoretically whether intranidal hemodynamic perturbations occur after AVM radiosurgery and to what extent these may contribute to the elevation in risk of rupture during the latency period.
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Methods |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1Appendix 2ReferencesIntroduction |
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The details of this AVM model are described elsewhere,13 14 15 in Appendix 1, and in Figure 1
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AVM Model Simulations of Radiosurgery
The biomathematical AVM model was used to simulate the response
of a theoretical intracranial AVM to radiosurgery with the application
of 2 different hypothetical occlusion schemes to intranidal vessels.
The occlusion schemes (ie, the schemes by which simulated vessels of an
AVM nidus could theoretically undergo occlusion after irradiation) were
based on 3 primary factors: mechanism of vessel occlusion, radiation
dosage, and extent of irradiated AVM volume.
Although the underlying mechanisms of vessel occlusion in response to radiation are speculative, 2 mechanisms have been proposed in the literature16 17 18 and are applied individually to the AVM model simulations described herein. These 2 mechanisms of vessel occlusion are (1) stepwise circumferential vessel narrowing and eventual occlusion and (2) random immediate total vessel occlusion. In the first mechanism, the radius of each nidus vessel within the irradiated AVM volume was reduced abruptly by a uniform percentage of the initial vessel radius at discrete time intervals after simulated radiosurgery. The quantitative percentage values depended on the radiation dosage and the time lapsed after irradiation and will be discussed in detail below. The second mechanism of occlusion involves the total occlusion of nidus vessels randomly selected (using a random number generator) within the irradiated AVM volume according to the percentage of affected vessels dictated by the radiation dosage and time lapsed after irradiation.
Both stepwise and random occlusion schemes were investigated in the
biomathematical AVM model simulations according to 2 levels of
radiation dosage (D): (1) D <25 Gy and (2) D 25 Gy. The rate of
occlusion is dependent strongly on the radiation dose delivered to the
AVM volume, as evidenced by the data presented in Figure 4 of
the report by Yamamoto et al.19 In that study,
postradiation changes in angiographically determined nidus volumes were
studied quantitatively in 22 AVM cases treated by gamma-unit
radiosurgery. In the aforementioned Figure 4 of Reference
19 , the percentage of occlusion was plotted for each
dosage level at 1 year, 2 years, and 3 years. Significantly, it was the
region within 6 months after irradiation at which the propensity of the
nidus to hemorrhage reached its maximum before subsiding at
later times. Using that information from the work of Yamamoto et
al19 to determine quantitatively the rate of occlusion at
points within each year, we recorded the exact data points from the
aforementioned plots and fitted them to polynomial functions through
interpolation. These functions for each radiation dose are given
below:
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. Thus, for
each dose, the percentage of nidus vessel occlusion was determined at
3-month intervals from 0 (time of AVM irradiation) to 3 years after
irradiation. The resultant reduction in caliber of plexiform and
fistulous vessels is seen in Figure 3. In
this study, each simulated radiosurgery of the AVM model was executed
with a theoretical uniform dosage to all the area/volume being treated,
ie, no treatment isodoses were simulated (the central dose and dose to
the AVM margin were equal). This was considered a sufficient
approximation of the commonly practiced clinical prescription of a
margin dose at the 90% isodose contour.3 20
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Investigations of the effects of radiosurgery on irradiated AVM volume were performed through simulations of the occlusion schemes on the total nidus (complete treatment), the upper and lower halves of the nidus, and 4 quarters of the nidus (partial treatment). The upper and lower halves of the nidus were separated such that all 4 fistulous components were contained within the lower half of the nidus. Similarly, in the quarters of the nidus, the fistulous components were contained in the lower 2 quarters. For each of the simulations, particularly with the partially irradiated volumes, the radiosurgery occlusion schemes were applied only to the nidus vessels contained within the volume under investigation while keeping the remainder of the nidus vessels untreated, ie, patent.
It can be seen from the equation in Appendix 1, and as outlined in
previous accounts of this model,14 15 that the risk of
nidus rupture is also assumed to be dependent on the elastic modulus
(E) and the thickness (t) of nidus vessels. The
"typical" or average values assumed for these
parameters in the present and previous studies are
5.0x104 dyne/cm2 and
50 µm, respectively. In reality, our adopted value for
t is a fair approximation, as evidenced by inspection of
light microscopic sections of cerebral AVM tissue. On the other hand,
the value for E is speculative but, at least, is derived
through knowledge of values of E for normal venules
(1.0x105
dyne/cm2)21 and arteries (3.0
to 5.0x108
dyne/cm2),22 as is available in the
literature. Clearly, the value of E (and to a similar extent
that of t) assigned to nidus vessels and used in calculating
the risk of rupture after radiosurgery could have a significant/crucial
influence on whether or not an AVM is found to rupture. Since the exact
value of E for AVM nidus vessels is unknown, one might
speculate that if a high value of E is assumed, then our
calculations might yield low percentages of risk of rupture, and vice
versa. For this reason, and to study precisely the influence of
E on our results, all radiosurgical simulations were
performed in the typical AVM model using the typical value of
E at 5.0x104
dyne/cm2; these were then repeated in models
possessing values of E that varied at intervals within the
range 1.9x104 to 8.0x104
dyne/cm2. Note that the lower value of this range
was chosen because the resultant AVM was found to have a baseline risk
of rupture that remained <100% (ie, was unruptured in its natural
state before radiosurgery). The use of any lower values of E
would result in AVMs that were inherently too unstable/fragile (ie,
with a risk of rupture 100%) prior to therapy.
An additional issue with regard to investigating the risk of rupture of
AVMs after radiosurgery is the likelihood that values of E
and t do not remain static but instead increase in value (as
a result of the actual radiosurgery) during the latency period as the
nidus vessel walls get stronger and thicker with time, leading
eventually to obliterative fibrosis. Therefore, the 3 cases of rupture
occurring in the irradiated zones of the typical AVM possessing an
E of 5.0x104
dyne/cm2 were subject to a separate reassessment
of their risk of rupture as the value of E itself was
gradually increased during the latency period, to ultimately approach
the known value of E for thick sclerotic vessels, ie, 5.0 to
8.0x107
dyne/cm2.21 Furthermore, by
using the data on temporal change in vessel radius obtained from Figure 3
and by simplistically assuming that this caliber reduction
could be a direct result of progressive increase in mural thickness, we
calculated the hypothetical temporal increases in t for the
3 vessels exhibiting rupture within irradiated zones of the nidus (when
only a static t is assumed). These new progressively higher
values of t were, in turn, used in the equation in Appendix
1 to calculate the new values of risk of rupture for these 3 cases at
3-month intervals during the latency period.
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Results |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1Appendix 2ReferencesIntroduction |
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Results of the baseline AVM hemodynamics and risk of nidus rupture before simulated radiosurgery are presented in Appendix 2. A total of 364 AVM radiosurgery simulations were performed for the AVM assigned the typical value of E. The various permutations of factors (28 AVM cases at 13 time intervals) considered in arriving at this total number of simulations are outlined in Figure 4
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Risk of Nidus Rupture After Radiosurgery of the Typical
AVM
Gradual trends in the transnidal and intranidal distribution of
hemodynamics and corresponding risk of rupture were
observed for almost all radiosurgery simulations over the temporal
intervals after AVM irradiation. For the nidus vessels subjected to the
random vascular occlusion scheme, immediate pronounced surges in the
risk of rupture of vessels adjacent to the occluded vessels after
irradiation were identified before reaching a plateau and subsequent
drop to negligible values of risk of rupture. Similar patterns of
surges in the risk of rupture for nidus vessels affected by the
stepwise vascular occlusion scheme were noted. For all occluded nidus
vessels, regardless of occlusion scheme, marked increases in the risk
of rupture of adjoining nidus vessels were shown, indicating a
corresponding shift in the hemodynamic burden
originally accommodated by the occluded vessels.
For the typical AVM, definite nidus rupture was observed in a total of
4 of 28 theoretical AVM cases (14.3%) after simulated radiosurgery
with simulations of <25 Gy and random vascular occlusion (Table 1). Overall, 1 of 4 cases (25%) of total
AVM irradiation, compared with 3 of 24 cases (12.5%) of partial AVM
irradiation, resulted in nidus rupture. Figure 5A through 5D consists of schematic
diagrams of the nidus network for the 4 cases of rupture, also
displaying examples of either total or subtotal (half or quarter)
irradiation of the nidus as performed in this study. Accompanying these
figures is a graph (Figure 5E) showing the change in risk of
rupture over time for the individual intranidal vessels (those vessels
in Figure 5A through 5D depicted by thick black arrows) that
have demonstrated rupture. The remaining 24 theoretical AVM cases did
not reveal nidus rupture after simulated radiosurgery.
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Three of the 4 cases of rupture after random vascular occlusion
occurred within a simulated latency period of 9 months after
irradiation. This is in general agreement with a recent report from the
Stockholm group8 confirming that most AVM
hemorrhages occur within the first 6 months after radiosurgery.
In all these AVM cases with random vascular occlusion, rupture occurred
in a nidus vessel as a direct result of a connected high-flow vessel
(an intranidal fistula component) becoming occluded totally, which
causes a dramatic shift and escalation of the
hemodynamic burden into an already weakened adjoining
vessel leading to its rupture. For 3 cases (cases 1 to 3), the sites of
rupture within the nidus were toward the arterial portion
of the nidus, and in 1 case (case 4) this occurred toward the venous
portion of the nidus (Table 1 and Figure 5A through
5D).
Risk of AVM Rupture With Varying Biomechanical Properties of Nidus
Vessel Walls
The results of radiosurgery simulations in AVM models that possess
varying values of E for nidus vessels are shown in Table 2. The following can be seen: (1) The
weaker the nidus vessels (low E), the higher was the
percentage of AVMs that ruptured after radiosurgery, and vice versa. At
E=8.0x104
dyne/cm2, none of the AVMs ruptured during the
latency period. (2) The weaker the nidus vessels (low E),
the higher was the proportion of ruptures that occurred with partial
nidus irradiation, and the stronger the nidus vessels (high
E), the higher was the proportion of ruptures that occurred
with total nidus irradiation. However, the use of proportions or
percentages in this instance may be misleading because, overall, there
were far fewer simulations of total nidus irradiation. In fact, many
more theoretical ruptures were observed after partial nidus
irradiation, supporting to some extent knowledge of the dangers of this
particular therapeutic strategy (deliberate or
inadvertent).3 In AVMs composed of weak
nidus vessels (low E), no difference was observed in the
risk of rupture after either low-dose (<25 Gy) or high-dose (25
Gy) radiosurgery.4 Random vessel occlusion
resulted in higher percentages of nidus rupture, presumably as a
consequence of the associated sudden and complete shifts of
hemodynamic forces into adjacent nidus vessels. By
contrast, stepwise vessel occlusion was associated with lesser
incidence of nidus rupture.
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Influence of Increasing Nidus Vessel Fibrosis on Risk of AVM
Rupture
At present, there is no documentation in the literature of the
rate at which nidus vessels change their mechanical properties during
the latency period to eventually become fibrotic. Simplistically and
speculatively, if it is assumed, for example, that the typical AVM
might change its value of E from
5x104 dyne/cm2 to that of
1x107 dyne/cm2 (that of a
fibrotic vessel) in a linear fashion, it can be seen from Figure 6 that the 3 cases of rupture that
occurred within irradiated zones of the nidus originally at 6, 9, and
15 months after irradiation (when the value of E was assumed
static) would all have considerably higher values of E at
these specific times. From Table 2, it can be appreciated that
no AVM ruptures at E=8.0x104
dyne/cm2. These higher values of E due
to progressive fibrosis would result in a 0% rate of rupture instead
of the 14.3% previously obtained in the presence of a static
E. The use of this typical AVM as a single example of
implementing the possible effects of additional fibrosis after
irradiation shows that, in reality, all the figures obtained for
percentages of rupture after radiosurgery (seen in Table 2) are
likely to be artifactually elevated. This assertion is further
supported by the absence of rupture observed when increasing thickness
of vessels during the latency period is also accounted for. Figure 7 exemplifies this in case 1, in which
rupture occurs with a static t but the risk falls below the
rupture threshold when increasing mural thickness and eventual luminal
occlusion are modeled after simulated radiosurgery.
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Discussion |
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The salient findings of this preliminary study are as follows: (1) The occurrence of theoretical AVM hemorrhage after simulated radiosurgery in this model is infrequent; this provides some indirect support for the likelihood that irradiation does not change or even lowers the propensity of AVMs to rupture, rather than actually increasing it. This appears to be the case particularly because of the effects of irradiation on strengthening and thickening nidus vessel walls and promoting their eventual fibrosis. (2) The risk of AVM rupture was found to be highly dependent on the biomechanical properties assigned to nidus vessels during theoretical simulations. More accurate and informative modeling of radiosurgery is unlikely to be possible unless laboratory-based determination of such key biomechanical factors (including the elastic modulus of nidus vessels) can be made in future studies on human AVM specimens. Significantly, this study highlights an important need for comprehensive biomechanical investigations of human AVM vessels obtained at surgery or autopsy to further our basic understanding of these complex and challenging lesions. The elastic modulus of other cerebral vasculopathies (eg, saccular aneurysms) has been determined previously,24 25 and it should be possible to establish this for specimens of AVM tissue as well. (3) As seen theoretically in this model, intranidal hemodynamic perturbations appear to play a significant role in the generation of hemorrhage when this occurs during the latency period. (4) As seen theoretically in this model, partial and/or low-dose radiosurgery are found to be of particular danger when treating AVMs. The implications of these findings are discussed below.
Biomathematical Modeling of AVM Radiosurgery
Models are necessary to achieve reproducibility, which is an
essential component of scientific experimentation. The many advantages
of biomathematical modeling and the rationale behind using this
experimental approach have been described previously.13 26
Biomathematical models offer a way to theoretically understand AVM
physiology under normal hemodynamic conditions and
during various types and stages of therapy, particularly in a region of
an AVM (the nidus) that is otherwise inaccessible to detailed
investigations by any other current technique. The biomathematical
modeling of AVM radiosurgery will always be limited by the lack of
biological and biovariability traits and is therefore best used in
combination with other experimental techniques, eg, recently developed
animal models,27 and in concert may provide the potential
to enhance dramatically our understanding of AVM radiosurgery and
create a forum for research and exploration of new
ideas.28 Generally, the results of biomathematical
modeling are not intended to be extrapolated directly to the clinical
setting but instead are to be used as a framework within which clinical
phenomena can be better understood and possible implications
suggested.28 The advantages and disadvantages of the
specific AVM model used in this study have been discussed
previously.13 14 15 In addition, the general principles and
philosophical premises of modeling in biomedical research have been
reviewed in detail recently by the authors29 ; the
present modeling study was conducted within a framework provided by
these previously presented guidelines. Importantly, no
quantitative extrapolation to a human AVM setting is possible with this
model (at least, as presented in this preliminary study) in
assessing the risk of hemorrhage after treatment; instead, a
qualitative appreciation can be obtained for the ability of irradiation
to induce hemodynamic and biomechanical alterations in
the stability of the nidus vessels and to induce rupture.
A biomathematical model was used previously by Lo and colleagues16 17 18 to analyze the theoretical hemodynamic perturbations in and around abnormal AVM shunts in response to radiosurgery. This important work has provided some support and a theoretical basis to clinical observations that partial volume irradiation of AVMs may lead to transient increases in pressure gradients and a propensity to hemorrhage within persistent AVM shunts. In the present study we have expanded on this subject by performing a more detailed theoretical analysis of the hemodynamic changes and risks of vessel rupture within a much more complex and realistically simulated AVM nidus in a model based on electric network analysis.
The 2 simplistic approaches to occlusion of intranidal vessels used in this study have been used previously in theoretical modeling of radiosurgery.16 17 18 It is acknowledged, however, that random occlusion of vessels is the less likely of the 2 mechanisms to occur in vivo. In reality, a third more complex vessel occlusion mechanism would more likely replicate in vivo events within an AVM nidus after radiosurgery. This may be described as a "gradual" circumferential vessel occlusion scheme, in which intranidal vessels are reduced continuously and systematically in diameter as the time after irradiation increases. The difference between this and the stepwise mechanism arises by virtue of the latter’s inability to consider temporal/dynamic phenomena. The introduction of this gradual mechanism of occlusion would have increased greatly the complexity of our model simulations and the necessary mathematical calculations in this preliminary study. By adopting this third mechanism in future simulations, it may be possible for the model to account for the rate of increase in pressure gradients within nidus vessels and to study how a nidus responds to and accommodates dynamically the resultant hemodynamic surges after radiosurgery. We speculate that this may translate into even lower risks of nidus rupture than predicted by the results of the present study.
Risk of AVM Nidus Rupture
The results of the AVM model simulations demonstrate that as the
nidus vessels becomes occluded after irradiation, the risk of rupture
changes as the intranidal pressure redistributes itself to compensate
for the radiosurgically induced occlusion. Generally, increases in risk
of AVM nidus rupture were observed particularly in close proximity to
the sites of ingress of arterial feeders and egress of
draining veins. In the event of nidus rupture, those intranidal vessels
adjacent to either the arterial feeders or draining veins
were shown to exhibit an unsafe increase in the risk of rupture. The
theoretical occurrence of more ruptured vessels at the boundaries of
the nidus, as opposed to the center of the nidus, was interesting and
due presumably to the already relatively high pretreatment
intravascular pressures found at the arterial end of the
nidus and the already relatively high pretreatment risks of vessel
rupture at the venous end of the nidus.14
The observed lack of difference between the hemorrhage risks
after optimal and suboptimal dosages in AVMs composed of inherently
weak nidus vessels (low E) (Table 2) was presumably
because in these vessels, any additional stresses after irradiation
(regardless of dosage) might result in hemorrhage.
Interestingly, this interpretation might hold true for a similarly
encountered clinical observation by Lindquist8 in the
radiosurgical management of some brain AVMs. On the other hand, our
results suggest that in the majority of AVM models (with higher values
of E), a lower dose was associated with higher percentages
of nidus rupture in the latency period. This dependence of the
obliterative process (and, therefore, AVM protection) on the delivery
of an appropriate amount of radiation energy was demonstrated in
previous clinical series to be of statistical
significance.12
The values for risk of AVM nidus rupture used in this study are not intended to duplicate figures that represent the annual risk of AVM hemorrhage as expressed commonly in clinical practice, such as the 3% annual hemorrhage rate for untreated AVMs. Nor are these values for risk of rupture intended to match other methods of assessing lifetime risk of AVM hemorrhage, such as that involving the multiplicative law of probability formula, which requires knowledge of the patient’s age and annual hemorrhage risk.30 Instead, the expression used in this study does not take into account age or time factors but provides results that are static and fixed at one time only, ie, at the time the intervening therapy or its effect takes place. This is another reason why the results of the model, although numerical in nature, can only be interpreted qualitatively with a view to appreciating the underlying or portrayed principles.
Several clinical (eg, AVM hemorrhage within a year before radiosurgery11 and the patient’s age8 ), morphological (eg, AVM size8 ), and angioarchitectural (eg, the presence of aneurysms related to the AVM11 ) factors other than those examined in this study are thought to influence the risk of nidus rupture after AVM radiosurgery as well. Our preliminary study was not intended to investigate all possible factors that could affect the risk of AVM hemorrhage during the latency period. Nevertheless, when possible, these additional influences will be examined in future studies. The results of this preliminary study show that, based on theoretical grounds, the risk of AVM nidus rupture is influenced by the extent of nidus volume undergoing irradiation and that perturbed hemodynamics resulting from occlusions of intranidal vessels represents a significant culprit among possible mechanisms of nidus rupture after radiosurgery.
Intranidal Hemodynamic Changes After AVM
Radiosurgery
Several reports in the literature3 4 31 32 33 indicate
the likelihood that incomplete AVM radiosurgery induces intranidal
hemodynamic perturbations that ultimately contribute to
hemorrhage during the latency period. The rationale for this
hypothesis is indirect and relies on (1) generalized angiographic
observations after AVM radiosurgery and (2) knowledge of intranidal
hemodynamic changes consequent to other forms of
partial AVM nidus occlusion (at embolotherapy) or resection (at
surgery).
Angiographic changes in patients undergoing partial irradiation of AVMs and who have bled subsequently have been reported by Colombo.34 A high frequency of increase in blood flow rates through patent portions of AVMs, increased tortuosity of draining veins, and the appearance of aneurysms (all suggesting increased hemodynamic stresses) were recorded in these patients during the latency period. Therefore, with documentation of such changes consequent to radiosurgery, it has been speculated that partial thrombosis of the malformed nidus vessels may increase their outflow resistance, resulting in the creation of high-flow shunting within the remaining unoccluded portions of the nidus and predisposing it to rupture. Levy et al4 have suggested that this is a potential hazard of most treatments that obliterate only a portion of an AVM, occurring also with partial embolization35 or subtotal surgical resection of large AVMs.
The concept of intranidal surges in hazardous hemodynamics as a cause of nidus rupture during the latency period appears intuitively sound; however, this is not accepted universally because of the lack of concrete evidence to support it.36 One goal of this preliminary study was to attempt to investigate this controversial issue further. Our findings demonstrate, at least on theoretical grounds, that the generation of intranidal hemodynamic disturbances could represent a significant (perhaps, the main) cause of increased risk of AVM rupture when this occurs during the latency period after radiosurgery. Furthermore, the use of our novel theoretical model, which displays distinct intranidal components and simulates the presence of both fistulous and plexiform vessels, has enabled for the first time the qualitative investigation and appreciation of these theoretical intranidal hemodynamic and biophysical events leading to rupture. Thus, in all simulated cases in which AVM rupture occurred, it was found that rupture in the implicated intranidal vessel was due to a connecting intranidal vessel becoming occluded totally, which causes a shift/escalation of the hemodynamic burden (the intravascular pressure) into an already weakened adjacent vessel, leading to its rupture.
As noted above, the presence of dangerous intranidal shifts in hemodynamic forces leading to AVM rupture after radiosurgery may be appreciated intuitively by some clinicians, but this is an idea not embraced by others. Three useful analogies in favor of this concept might be drawn through knowledge of hemodynamic events from other observations upstream, within, and downstream from an AVM: (1) It is well accepted that partial embolization of an AVM nidus raises the intravascular pressure within feeders situated proximal to the site of occlusion.37 38 (2) Viñuela et al39 have reported that intranidal rerouting of flow to plexiform portions of the nidus after abrupt endovascular obliteration of an intranidal fistula (ie, a scenario similar to that depicted by our simulations) may result in AVM rupture. (3) A previous study using this same AVM model has demonstrated a propensity of the nidus vessels to rupture consequent to simulated stenoses or occlusions more distally in the draining veins.14 It is not inconceivable for similar luminal narrowing and prestenotic buildup of hemodynamic forces to take place intranidally. Therefore, such surges in intravascular pressures may occur (and the results of this study demonstrate this) in delicate nidus microvessels after irradiation; the rerouting of these pressure elevations may also occur on a microscopic level intranidally, and in some cases the buildup could lead to rises above the threshold for rupture. As also observed in a prior study pertaining to luminal narrowing more distally in the draining veins,14 that occurring within nidus vessels raises the risk of rupture to values >100% before a subsequent decline to values below the pretreatment state. Therefore, our theoretical hemodynamic observations possibly unravel the reason for another apparent "enigma," as expressed by Lindquist,8 as to why radiosurgical obliteration of an AVM (with its known histological effects of progressive vessel wall thickening) does not simply (and only) decrease the hemorrhage risk before complete obliteration.
Although quantitative extrapolation to the setting of human AVMs is not possible, the results of theoretical simulations using our biomathematical AVM model suggest and allow the qualitative appreciation of these intranidal hemodynamic perturbations. Moreover, the model simulations have demonstrated a difference in hemodynamic consequences to irradiation of the plexiform vis-à-vis the fistulous intranidal vessels. Occlusion of a fistulous component leads to greater hemodynamic shifts to adjacent vessels, and consequent increased risk of rupture, than for occlusion of plexiform components. This is similar to the mechanism speculated on by Viñuela et al39 (as mentioned above) for rupture after endovascular embolization of AVMs. In our simulations, this occurred in all cases demonstrating nidus rupture. This hazardous rise in risk of rupture occurs regardless of the extent of nidus radiosurgery, ie, this danger is present theoretically for total as well as subtotal irradiation of a nidus, although in our simulations, an increased risk of rupture for completely irradiated AVMs that results in a risk >100% was quite infrequent.
In clinical practice, large multifistulous AVMs are not considered optimal lesions for radiosurgical treatment40 or are first subjected to embolization (or even surgical resection in some cases) before radiosurgery for the purpose of volume reduction (down to the optimal <3 cm in size).11 With regard to treatment of large AVMs (which commonly contain fistulas), Pollock et al7 state that "unlike embolization before microsurgical resection, in which flow reduction is the goal, volume reduction is the goal of preradiosurgical embolization." The results of this theoretical study are at variance with this assertion because if an intranidal fistula is present within an AVM of optimal size for radiosurgery (however uncommonly), then it may still predispose the nidus to rupture because of the induction of critical intranidal hemodynamic perturbations. Therefore, 2 clinically relevant ramifications to the results of this study are as follows: (1) the procurement of objective hemodynamic data and detailed angiomorphological information would be desirable in the evaluation of AVMs before their radiosurgical treatment; and (2) preradiosurgical embolotherapy should be regarded as (and efforts be made toward making it) a flow-reductive as well as a volume-reductive technique. Toward both aims, it may be desirable to perform superselective angiography on AVMs, at least those that show subjectively a suspiciously high flow (intimating, perhaps, the presence of a fistula/s) when delineated by less selective angiograms. It has been demonstrated previously that superselective angiography is of paramount importance in the accurate delineation of intranidal AVM angioarchitecture.41 This may also be accompanied by more objective hemodynamic characterization of AVMs through intravascular pressure measurements, and/or Doppler ultrasound, and/or MR angiography, with a view to establishing the presence of an intranidal fistula. For instance, the discovery of a transcatheter mean arterial feeder pressure >40 mm Hg below the mean systemic blood pressure is in itself highly indicative of the presence of a downstream intranidal fistula.42 Once a fistula is discovered after superselective angiography and hemodynamic assessment, it may be necessary to occlude it endovascularly (eg, under systemic hypotension, to reduce the possibility of rupture during the procedure43 ) before radiosurgery. It is speculated that future adoption of these measures may allow a more precise and objective means of selecting/screening those AVMs that are hemodynamically amenable to safe and effective radiosurgical treatment and may perhaps help in reducing the hemorrhage rates in those AVMs that are partially irradiated or those that are completely irradiated (such as some larger AVMs or those in older patients8 ). In addition, the future procurement of accurate hemodynamic data from human AVMs before and during the radiosurgical latency period may help considerably in further understanding and analysis of the basic mechanisms revealed by this preliminary theoretical study and in the promotion of newer and potentially more useful and safer strategies for radiosurgical treatment of AVMs.
In conclusion, this preliminary theoretical study supports the general consensus that radiosurgery does not increase the risk of rupture in AVMs and, if anything, may have a "protective" effect, as suggested by the Stockholm group.12 In the few cases in which rupture was observed, it was found that a larger number occurred after subtotal and low-dose radiosurgery, supporting theoretically the clinical observation that these are dangerous strategies. The radiosurgical occlusion of intranidal fistulas or larger-caliber plexiform vessels appears to be a major culprit in the generation of dangerous intranidal hemodynamic surges that lead to critical elevations in the risk of nidus rupture. Future studies directed at the detailed histometric and biomechanical characterization of human nidus vessels are required to further advance our understanding of cerebral AVMs, both before and after their radiosurgical treatment. The described novel AVM model should serve as a useful research tool for further theoretical studies of radiosurgical strategies (eg, we are currently studying the theoretical effects on the AVM nidus of dose inhomogeneity due to multiple isocenter irradiation) and in investigating the hemodynamic sequelae of treatment.
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Appendix 1 |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1Appendix 2ReferencesIntroduction |
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Biomathematical AVM Model
The AVM theoretical electric network, nestled within a simulated circulatory network of the head and neck, consisted of 4 arterial feeders (AFs), 2 draining veins (DVs), and a nidus angioarchitecture with a randomly distributed array of 28 interconnected plexiform and fistulous components, as shown in Figure 1
. Twenty-four of the nidus vessels were plexiform, and 4 nidus
vessels were fistulous. Two AFs (AF1 and AF2) were considered major
feeders, while AF3 and AF4 (a simulated transdural supply) were minor
feeders. Both DVs drained into the simulated intracranial venous
sinuses. The pressure values implemented into the radiosurgical simulations were as follows: mean systemic blood pressure, 74 mm Hg; mean AF pressure (for major AFs), 47 mm Hg; mean AF pressure (for minor AFs), 50 mm Hg; mean DV pressure, 17 mm Hg; and mean central venous pressure, 5 mm Hg. All the above values (and those of the nidus vessel elastic modulus [E] and wall thickness [t], used in calculating the risk of nidus vessel rupture14 15 [see below]) were considered for the purpose of this study to be "typical" or average ones. A separate parameter optimization study to further characterize the functioning of this AVM model had revealed that the adoption of all the aforementioned values results in an acceptable representation of a typical high-flow large intracranial AVM on the basis of its total volumetric blood flow and its baseline risk of rupture.15
With the use of an electric analogy of Ohm’s law, flow rate was determined on the basis of Poiseuille’s law given the aforementioned pressures and resistance of each nidus vessel. To determine the hemodynamic quantities within each vessel of the vascular array during each simulation, network analysis of the loops and nodes constituting the AVM model circuit was performed to yield 41 linear equations corresponding to the 41 vessels and distinct values of volumetric flow rate.13 The 41 derived linear equations were solved simultaneously by expanding Poiseuille’s formula into matrix form.13 The matrices corresponding to pressure and resistance were created with the use of a spreadsheet application (Microsoft Excel) and transported to an advanced mathematical computation program (Mathematica, Champaign, Ill) for solution of the flow rate values for all 41 vessels.13 Once the volumetric flow rate was determined for each simulation, it was then possible to calculate the risk of rupture for each nidus vessel.
Risk of Nidus Rupture
The highly tortuous, structurally weak intranidal vessels
subjected to the continual impingement of large
hemodynamic forces make AVMs highly susceptible to
hemorrhage. The precise location or region of rupture is
extremely difficult to observe angiographically and to detect
histologically and remains a source of speculation in
the study of AVMs. It is believed commonly that, based on the
biomechanical properties of the intranidal vessels, rupture occurs when
the cumulative hemodynamic stresses of the vessel wall
exceed its elastic modulus. An expression for the risk of rupture has
been derived previously14 15 on the basis of the
functional distribution of the critical radius over a range of
intravascular pressures experienced by a cylindrical vessel during a
normal cardiac cycle and is given as follows:
 |
100%) that is of paramount
importance. |
Appendix 2 |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1Appendix 2ReferencesIntroduction |
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Baseline AVM Hemodynamics and Risk of Nidus Rupture
The simulated total volumetric blood flow through the normal AVM model before any treatment was 814 mL/min, akin to values of flow through large intracranial AVMs.23 The intranidal flow rate varied from an average of 31.3 mL/min for the plexiform vessels and a substantially increased flow rate with an average of 617 mL/min within the intranidal fistula. For the "typical" AVM (with E=5.0x104 dyne/cm2), the risk of rupture for individual AVM vessels within the nidus before radiosurgery ranged from 4.4% to 91.2%.
Received April 25, 2000; revision received June 28, 2000; accepted July 12, 2000.
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References |
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Editorial Comment
Department of Neurological Surgery, University of California, Davis, Sacramento, California
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Introduction |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1Appendix 2ReferencesIntroduction |
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The authors use a biomathematical model to evaluate the factors involved in an intracranial AVM rupture after a radiosurgery. This model uses electric network analysis whereby various anatomic characteristics of AVM are represented by a circuit analog. The most important factor in determining the validity of a biomathematical model is its ability to duplicate the real physiological situation.
One significant limitation of this model is the assumption made by the authors that a nidal vessel occlusion occurs by either of the 2 mechanisms: what they refer to as a stepwise occlusion and a random occlusion. In reality, as correctly pointed out by the authors, the nidal vessel occlusion after radiosurgery is more likely to be gradual and continuous. Thus, a sudden change in an intranidal flow hemodynamics is unlikely to be the main cause of AVM rupture. The authors, however, should be commended for their innovative approach in evaluating the different variables involved with the AVM rupture after a radiosurgical treatment.
Received April 25, 2000; revision received June 28, 2000; accepted July 12, 2000.
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