Introduction

   Identifying indication of impending cerebral aneurysm rupture has been an area of considerable interest for many years. Among the many variables considered, aneurysm size is the best studied, and a correlation between lesion size and risk of rupture has been documented. The International Study of Unruptured Intracranial Aneurysm (ISUIA) studies have indicated that the size of an intracranial aneurysm may be a primary determinant of rupture probability.^4)14)20) Nevertheless, it is well known that many small aneurysms rupture and that many aneurysms reach a large size without causing subarchnoidal hemorrhage. Other factors may also have value in predicting which intact aneurysm is likely subsequently to rupture.
   Ujiie and colleagues^13)16)17) hypothesized that flow stagnation might precipitate aneurysm rupture. Such condition is more likely to occur in aneurysms having a long depth in relation to a small orifice. These authors proposed that the aspect ratio (AR: ratio of depth to neck width) of the aneurysm may be a risk factor for rupture.
   The AR (referred to as the dome/neck ratio) has gained the attention of interventional radiologist because a low ratio is generally associated with greater technical difficulty and poorer result from coil application.³⁾ The present retrospective study was undertaken to prove the reliability of the AR (dome/neck ratio) for predicting aneurysmal rupture.

Clinical Material and Methods

Patient population
   Patients were retrospectively selected for this study based on the availability of angiograms and a clear diagnosis of an unruptured or ruptured aneurysm. All patients undergone digital subtraction angiography. We measured the aspect ratios and sizes of aneurysms, as determined by examining angiographic films. Patient age and sex, and the location of the aneurysm were also recorded. 106 patients with 140 aneurysms were included. 19 patients harbored only unruptured lesions, 70 patients only ruptured lesions, and 17 both ruptured and unruptured lesions. Of 106 patients, 25.0% were male and 75.0% female. The mean age of the patients was 54.23 3.24 years and the median age was 53 years. The number of aneurysms per patient were one in 89, two in 8, three in 6, four in 3 patients, and five in one patients.
   In patients with multiple aneurysms, the aneurysm that ruptured was determined using standard radiological and clinical methods such as the following: the pattern of blood on a computerized tomography scan; the relative size, site, and loculations on an angiogram; and the operative findings.

Statistical analysis
   A spreadsheet with statistical functions (Microsoft Excel; Microsoft Corp., Redmond, WA) was used for preliminary calculations; all other analysis were performed using a statistical software package (SPSS for Windows version 10.0: SPSS INC., Chicago, IL). Logistic regression analysis of the influence of size and AR on ruptured status, adjusted for patient sex and age, and aneurysm location, were performed. The probability of an aneurysm being a ruptured one was calculated by first categorizing aneurysms by size or AR into four groups according to the 25th, 50th, and 75th percentiles of the respective distribution.
   To compare the utility of aneurysm size and AR more fully for discriminating between ruptured and unruptured aneurysms, we performed receiver operating characteristic(ROC) analysis. The ROC curve is used to plot sensitivity against 1 - specificity, as the cut-point is varied continuously from larger to smaller values. Thus, for large values of the cut-point, the sensitivity will be low, but the specificity will be high. As the cut-point is progressively decreased, the sensitivity increases and the specificity decreases.

Results

   Descriptive statistics for aneurysm size and AR are shown in Table 1. The ruptured aneurysms were larger and had greater ARs.
   In univariate analysis, in which logistic regression was used to model the probability that an aneurysm is ruptured, we analysis the effect of patient age and sex, and aneurysm location, size, and AR. Patient age had no statistically significant effect on the risk of rupture, but sex did(p<0.001). On average the odds of finding a ruptured aneurysm in a female patient was 48.0% that in a male patient. Different locations had different odds of rupture. Using the cavernous internal carotid artery (ICA) as a reference, because the relative chance of aneurysm rupture in cavernous ICA was lower than other sites, the odds were 6.2-fold greater for aneurysms of the posterior circulation(p=0.002), 4.8-fold greater for those on the posterior communicating artery (PCoA) (p=0.005), 4.5-fold greater for those on the anterior communicating artery (ACoA)(p=0.007), 3.2-fold greater for those on the middle cerebral artery (MCA) (p=0.021), and 2.4-fold greater for those on the ophthalmic segment of the carotid artery (OphA)(p=0.120).
   The risk of rupture increase with the size of an aneurysm. The probability of an aneurysm being a ruptured one was calculated by first categorizing aneurysms by size or AR into four groups according to the 25th, 50th, and 75th percentiles of the respective distribution. Aneurysms with sizes in the three higher percentile groups had a significantly (p<0.001) greater chance of being ruptured lesions than those with size in the 0 to 25 percentile group. This was also true for the corresponding AR groups (Table 2). For size, however, the risk of rupture was similar in the three higher percentile groups, whereas for the AR there was a steady increase in risk with increasing AR. Only 8(9.3%) of 86 ruptured aneurysms had ARs equal to or less than 1.30 compared with 26(48.1%) of 54 unruptured ones.
   Multivariate analysis of the effects of aneurysm size and other factors produced similar results to the univariate analysis, Adjusted for patient sex and the location and size of the aneurysm, patient age did not have a significant effect on the risk of aneurysm rupture (p=0.240). Age was therefore dropped from the model and the results of fitting the final model, including patient sex and location and size of the aneurysm, are shown in Table 3. The odds of rupture were nearly threefold greater for the second quartile of size relative to the first, but the odds ratio (OR) increased only slightly for the third and fourth quartiles (Fig. 1A).
   In the multivariate analysis of the effects of the AR and other factors, patient age again did not reach statistical significance (p=0.120) and was subsequently dropped from the model. In the final model (Table 4) the effects of location were somewhat less than those shown in Table 3, with the only significant contrasts noted when the PCoA was compared with the cavernous ICA and when the posterior circulation was compared with the cavernous ICA. The AR exhibited a rather strong gradient effect; the odds of rupture increased steadily with the AR(Fig. 1B).
   The number of ruptured and unruptured aneurysms, as classified by their size and rupture rate (number of ruptured lesions/total number of aneurysms) in each size group(> or 7 mm), is given in Table 5. The cutpoint for size (7 mm) was cited by prospective arm of ISUIA study. The chance that an aneurysm 7 mm or smaller was not ruptured(negative predictive value) was 40.0%, whereas the chance that an aneurysm larger than 7 mm was ruptured was 65.7% (positive predictive value). The negative predictive value for an AR of 1.80 or less was 55.0% and the positive predictive value for an AR greater than 1.80 was 79.0%. Among aneurysms 7 mm or smaller with and AR higher than 1.80, 81.8% were ruptured; however, among similar lesions with a smaller AR only 44.2% were ruptured. Among aneurysms larger than 7 mm with an AR of 1.80 or less, only 50.0% were ruptured; at a higher AR, however, 73.9% of these lesions were ruptured (Table 6).
   The results of the ROC analysis are depicted in Fig. 2. It is apparent that the curve for the AR dominates that for maximum size. The area under the ROC curve for the AR is 0.773 (95% CI 0.691-0.854), whereas that for aneurysm size is 0.554 (95% CI 0.453-0.656). The difference between these area is highly statistically significant (p<0.001). At a cut-point of 1.80 for the AR, the specificity is approximately 76.0%, but the sensitivity is 61.0%.

Discussion

   The treatment of asymptomatic unruptured intracranial aneurysms has been the subject of a great deal of debate in neurosurgical community. Because of the development of increasingly advanced methods for intracranial vascular imaging, the identification of unruptured intracranial aneurysms is becoming more common. Unruptured aneurysms may affect from 2 to 10% of the general population,^1)7)8)9)15) whereas the incidence of subarachnoid hemorrhage is relatively low, with an annual rupture rate of approximately 1 to 2% per year.^{5)7)10)21)22)} Because most intracranial aneurysms do not rupture,¹⁰⁾ their identification creats a serious dilemma for neurosurgeons with regard to whether to operate on patients with incidentally discovered unruptured aneurysms, becasue a rupture of such an aneurysm can lead to catastrophic results.⁴⁾¹⁸⁾ Therefore, the decision to perform preventive surgery for an unruptured aneurysms must be based on a prediction of which aneurysms are most likely to develop a rupture. So, identifying reliable indicators of risk for rupture of an intact lesion could vastly improve clinical management of intracranial aneurysm. Aneurysm size is a well-recognized risk factor in predicting aneurysm rupture. However, there is little consensus regarding a threshold value at which to treat these aneurysm.^6)11)12) Other factors, such as cigarette smoking, the morphology of the aneurysm, and other underlying conditions, are important risk factors in predicting aneurysm rupture. The retrospective result differed from epidemiological data, however, indicating that most ruptured aneurysms had diameters less than 10 mm.²⁾¹⁹⁾
   On the basis of experimental studies showing an increased tendency for bleb formation and dumbbell shapes in aneurysms having sluggish flow, Ujiie and colleagues^13)16)17) proposed that the AR of the aneurysm (ratio of depth to neck width) may be a risk factor for rupture. These authors considered that this ratio might be a better geometric index than maximum size alone in determining intra-arterial flow and, thus the tendency to rupture. In their retrospective study of angiographic data, 103(79.8%) of 129 ruptured aneurysms had an AR greater than 1.60, whereas 70(89.7%) of 78 unruptured aneurysms had an AR less than 1.60.¹⁷⁾
   In this retrospective study the authors examined the aspect ratio (AR: the maximum dimension of the dome/width of the neck of an aneurysm). The AR initially has gained the attention of interventional radiologist because a low ratio is generally associated with greater technical difficulty and poorer result from coil application. We compared the distribution of this ratio in a group of ruptured and unruptured aneurysms. A similar comparison was performed in relation to the maximum dimension of the aneurysm
alone.
   What seems to separate unruptured from ruptured aneurysms most effectively? A size smaller than or equal to 7 mm is associated with a rupture rate of 60.0% and an AR smaller than or equal to 1.80 with a rupture rate of 45.0%. A size greater than 7 mm is associated with a rupture rate of 65.7% and an AR ratio greater than 1.80 with a rupture rate of 79.0%. The cutoff AR of 1.80 has higher negative(55.0%) and positive(79.0%) predictive value than the size cutoff of 7 mm, for which the negative and positive predictive values are 40.0% and 65.7%, respectively.
   Our data show that 61.6% of ruptured aneurysms had greater than 1.80 and that of 74.0% of unruptured aneurysms had an AR of 1.8 or less. This compares with rates of 88.1% and 56.3%, respectively, in the study by Weir et al.¹⁹⁾ In that study, the negative and positive predicted values were 81.5% and 69.2%, respectively, and high AR was more frequently associated with an unruptured aneurysm (lower specificity and positive predictive value). In our study, however, a low AR was more frequently associated with an ruptured aneurysm (low specificity and negative predictive value), and a high AR was more likely to be useful in predicting aneurysm rupture(higher specificity and positive predictive value).
   However, we found that a fairly high percentage of ruptured aneurysms had a low AR. Will these be more prone to unrupture in the future compared with unruptured aneurysms with a high AR? Prospective studies are required to determine whether unruptured aneurysm with a low AR are more likely unrupture than lesions that have the same size but a high AR.
   To reach a decision regarding the treatment of an asymptomatic unruptured aneurysm, other contributing factors such as the patient's age and average number of years of life remaining for different age groups, the patient's history of smoking and familial aneurysms, an association with autosomal dominant polycystic kidney disease, and aneurysm morphology, especially loculation (daughter aneurysms), should be taken into account.
   The limitation of this study include its retrospective nature, subjective bias in determining aneurysm dimension, and the special patient population resulting from the selection and referral bias. A common limitation in using aneurysm shape as predictor of aneurysm rupture is the use of 2D angiographic data for determining and calculating shape feature such as AR. Standard cerebral angiographic projections are 2D images. Cerebral aneurysm are often asymmetrical structures that do not allow for simple extrapolation of 3D morphology from 2D data. Thus the measurements of geometric features can vary with the angiographic projection used, resulting in multiple findings for the same aneurysm. This phenomenon may partially explain the contradictory findings of different reports in regard to the effect of AR and risk of aneurysm rupture.²⁾¹⁷⁾ Another potential source of bias is that a relatively large percentage of patients harbored multiple aneurysm and in patients with multiple aneurysms, it is not always possible to identify with certainty which aneurysm has ruptured.

Conclusions

   Selecting the optimal treatment for incidentally found unruptured aneurysms remains difficult, and individual factors such as family history, patient's age, aneurysm size, and medical risk factors must be weighted carefully. As described in this article, however, the difference in aspect between ruptured and unruptured aneurysms is statistically significant, and a high AR was more likely to be useful in predicting aneurysm rupture (higher specificity and positive predictive value). The aspect ratio therefore may become a reliable index for predicting aneurysmal rupture and it should be made routinely. It may assist in the difficult decision making regarding whether to treat unruptured aneurysms.

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