Su b a r a c h n o i d hemorrhage secondary to the rupture

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1 J Neurosurg 110:1 6, 2009 Predicting aneurysm rupture probabilities through the application of a computed tomography angiography derived binary logistic regression model Clinical article Ch a r l e s J. Pr e s t i g i a c o m o, M.D., 1 3 We n z h u a n He, M.D., 1 Jef f r ey Ca t r a m b o n e, M.D., 1 St e p h a n i e Ch u n g, B.S., 1 Ly d i a Ka s p e r, B.A., 1 La t h a Pa s u p u l e t i, B.S., 1 a n d Ne e l e s h Mi t ta l, M.D. 1 Departments of 1 Neurological Surgery and 2 Radiology, and 3 Neurological Institute of New Jersey, New Jersey Medical School, University of Medicine of Dentistry of New Jersey, Newark, New Jersey Object. The goal of this study was to establish a biomathematical model to accurately predict the probability of aneurysm rupture. Biomathematical models incorporate various physical and dynamic phenomena that provide insight into why certain aneurysms grow or rupture. Prior studies have demonstrated that regression models may determine which parameters of an aneurysm contribute to rupture. In this study, the authors derived a modified binary logistic regression model and then validated it in a distinct cohort of patients to assess the model s stability. Methods. Patients were examined with CT angiography. Three-dimensional reconstructions were generated and aneurysm height, width, and neck size were obtained in 2 orthogonal planes. Forward stepwise binary logistic regression was performed and then applied to a prospective cohort of 49 aneurysms in 37 patients (not included in the original derivation of the equation) to determine the log-odds of rupture for this aneurysm. Results. A total of 279 aneurysms (156 ruptured and 123 unruptured) were observed in 217 patients. Four of 6 linear dimensions and the aspect ratio were significantly larger (each with p < 0.01) in ruptured aneurysms than unruptured aneurysms. Calculated volume and aneurysm location were correlated with rupture risk. Binary logistic regression applied to an independent prospective cohort demonstrated the model s stability, showing 83% sensitivity and 80% accuracy. Conclusions. This binary logistic regression model of aneurysm rupture identified the status of an aneurysm with good accuracy. The use of this technique and its validation suggests that biomorphometric data and their relationships may be valuable in determining the status of an aneurysm. (DOI: / ) Ke y Wo r d s binary logistic regression cerebral aneurysm subarachnoid hemorrhage Su b a r a c h n o i d hemorrhage secondary to the rupture of an intracranial aneurysm is a life-threatening and debilitating event with an overall morbidity and mortality rate of 50 60%. 2,15,20 With modern imaging techniques, unruptured intracranial aneurysms can be detected more reliably, but the management of these lesions remains controversial. 10 In part, the controversy revolves around the fact that microsurgical and endovascular treatment modalities are invasive and carry some risk to the patient. 14 Consequently, the natural history of any aneurysm of a given size, shape, and location must be balanced against the risk of complications secondary to the treatment of the aneurysm. Of import would be the ability to accurately predict the likelihood of aneurysm rupture such that only those patients with aneurysms that are likely to rupture would be appropriately exposed to the risks of treatment. Abbreviations used in this paper: ACoA = anterior communicating artery; BA = basilar artery; ICA = internal carotid artery; MCA = middle cerebral artery; PCoA = posterior communicating artery; SAH = subarachnoid hemorrhage. J. Neurosurg. / Vol 110 / January, 2009 Previous studies have suggested that the shape and size of the aneurysm are parameters that can be used to predict the risk of rupture. 2 However, these studies only compared differences in size between unruptured and ruptured intracranial aneurysms. Other studies have compared the size of the aneurysms between unruptured versus ruptured groups, attempting to quantitatively assign a critical number to aneurysm size (that is, the size just prior to or at the time of rupture). 6,9,18 However, estimated values of the critical size for aneurysmal rupture have ranged from 4.0 mm to > 10.0 mm. 6,9,18 Therefore, the identification of factors that can be used to predict the rupture of cerebral aneurysms remains an important component of clinical decision-making in neurosurgery. The first mathematical model for predicting the morbidity and mortality of intracranial aneurysms was introduced by Richardson et al. in The authors presented a discriminative function by which mortal- This article contains some figures that are displayed in color on line but in black and white in the print edition. 1

2 C. J. Prestigiacomo et al. ity could be predicted in a type of operative approach to ACoA aneurysms. Subsequently, they used the same function to evaluate the prognostic factors in a series of PCoA aneurysms. 17 Since the publication of their work, mathematical modeling of aneurysms has been used to understand the biophysical phenomena that contribute to aneurysm growth and rupture. Biomathematical models can incorporate various physical and dynamic phenomena that may provide insight into the potential for rupture and possibly help predict the probability of aneurysmal rupture. 4 Our present study describes the biomorphometric properties of aneurysms in a clinical prospective series. By performing binary logistic regression analysis, a statistical technique similar to the previously described discriminative analysis method, 16 we have derived a relational equation that describes the rupture potential for cerebral aneurysms within this cohort. To assess the stability of this equation, we then applied it to an independent cohort of aneurysm patients to determine the rupture status of a patient s aneurysm. To our knowledge, this represents the first attempt at verifying a potentially clinically applicable mathematical formula that describes aneurysm rupture in an independent patient population. Methods This study represents a retrospective review of a prospectively maintained database of patients presenting to the University Hospital of the University of Medicine and Dentistry of New Jersey with SAH due to aneurysm rupture. Between 2002 and 2005, a total of 217 patients with 279 aneurysms (156 ruptured and 123 unruptured) presented to our institution. Multiple aneurysms were identified in 48 of these 217 patients. The distribution of ruptured and unruptured aneurysms by location as well as patient age and sex is summarized in Table 1. In the setting of aneurysmal SAH in patients with multiple aneurysms, the ruptured aneurysm (the index aneurysm) was identified at the time of surgery by direct observation and correlated with the hemorrhage pattern on the initial CT scan and repeated CT scans obtained 24 hours after the initial ictus (that is, the hemorrhage), when available. Cerebral aneurysms were diagnosed and evaluated with CT angiography using a GE Systems LightSpeed 16-slice CT scanner. A total of 150 ml of contrast medium was injected intravenously via the antecubital vein at a rate of 4 ml/second. Images were then obtained at mm slice-thickness with no overlap following an 18-second acquisition delay. Source images were transferred to the GE Advantix 3D workstation where maximal-intensity projections and 3D reconstructions were generated. All angiograms were analyzed by 2 investigators who were blinded to specific diagnoses and to all the patients clinical information including rupture status of aneurysms. The region of interest consisting of the identified aneurysm(s) and the parent vessel was identified, and several biomorphometric parameters were obtained in planes parallel and perpendicular to the direction of flow within the parent vessel. Maximum aneurysm height (Y), width (X), and neck size (N) were obtained in these orthogonal planes (Fig. Fig. 1. Three-dimensional CT reconstructions illustrating the method of measuring aneurysm height (Y), width (X), and neck size (N). Measurements were obtained in 2 orthogonal planes parallel (A) and perpendicular (B) to blood flow. 1A and B). (The variables Y1, X1, and N1 represent measurements obtained in the plane parallel to blood flow, and Y2, X2, and N2 represent measurements obtained in the plane perpendicular to blood flow.) Additional data, such as measured and calculated aneurysmal volume, location of aneurysm, and rupture status were included in this initial database. This data set was used as the initial data to generate a stepwise binary logistic regression model. After having completed the registration of patients to the current study, we prospectively collected a data set from an independent cohort of 49 aneurysms in 37 patients who presented between November 2005 and June The model was then applied to this independent cohort by one of the authors who was blinded to the rupture status of the aneurysms. The log-odds risk of rupture for each aneurysm in the cohort was then obtained. Specificity and sensitivity to predict the aneurysm status using our binary logistic regression model were calculated. Statistical Analysis The statistical software used in this analysis was SPSS version 12.0 (SPSS, Inc.) for Windows. Independent t-tests and chi-square tests were used to compare the mean for continuous data and categorical data, respectively. Forward binary logistic regression was then used to generate the model. 2 J. Neurosurg. / Vol 110 / January, 2009

3 Significance of binary logistic regression in cerebral aneurysms TABLE 1: Patient demographics and aneurysm location stratified by aneurysm rupture status* Aneurysm Rupture Status Variable Ruptured Unruptured p Value patient age in yrs < , < , < , < , < , < patient sex M F aneurysm location <0.001 AcoA BA 7 7 ICA MCA PCoA * Values represent numbers of aneurysms. Results Demographic characteristics of the patients and the location of aneurysms in the cases used to generate the initial binary logistic regression model are demonstrated in Table 1. The results of comparison of the mean values are listed in Table 2. No significant differences were observed for the number of ruptured versus unruptured aneurysms between men and women (p = 0.538). However, statistically significant differences for the number of ruptured versus unruptured aneurysms were found among different locations of the aneurysm (p < 0.001). In addition, there was a statistically significant difference in 4 of the 6 biomorphometric parameters obtained in this study (X1, Y1, X2, and Y2), aspect ratio (defined as the maximum width [X1] divided by the neck size [N1]), and the N1/N2 and X1/X2 ratios (Table 2). A stepwise binary logistic regression model was generated that incorporated the aneurysm location in addition to volume and the biomorphometric parameters. In this equation, aneurysm location was represented as a binary variable. The final equation generating the highest correlation with the initial database is expressed as follows: Logit = *volume *Y *Location (4) 2.262*Location (3) 1.184*Location (2) 0.334* Location (1) 0.023*patient s age J. Neurosurg. / Vol 110 / January, 2009 TABLE 2: Descriptive statistics for numerical data obtained in 123 unruptured and 156 ruptured aneurysms* Parameter & Aneurysm Status Mean (mm) SD (mm) p Value 95% CI (mm) X unruptured ruptured Y unruptured ruptured N unruptured ruptured X unruptured ruptured Y unruptured ruptured N unruptured ruptured N1/N unruptured ruptured X1/X unruptured ruptured aspect ratio unruptured ruptured vol unruptured ruptured * X1, Y1, and N1 are the maximum width, height, and neck diameter of the aneurysm measured in an orthogonal plane parallel to the flow of blood in the parent artery; similarly X2, Y2, and N2 are the corresponding values measured in the plane perpendicular to blood flow. Abbreviations: CI = confidence interval; SD = standard deviation. Note: Location (1) = ACoA; Location (2) = BA; Location (3) = ICA; Location (4) = MCA. Y2 = the height of the aneurysm. Volume represents the measured volume as calculated by the system s software package. The volume in this model represents the measured volume as calculated by the system s proprietary software package. The variable Y2 represents the measured value of the height of the aneurysm in the plane that is perpendicular to the blood flow. In this equation, the location of the aneurysm is represented by 1 of the 4 binary location variables (Table 3). A value of 1 for Location (2) would represent a patient with an aneurysm of the BA. Of note, patients with aneurysms of the PCoA would have all location variables set at 0. The significance of the binary logistic regression was tested by chi-square analysis, which generated a probability value of < Measured volume and aneurysm location were independently correlated to rupture risk (each with p < 0.001) and were used as predictors of outcome in this model. Using our model, we were able to predict the rupture status of the 279 aneurysms with a sensitivity 3

4 C. J. Prestigiacomo et al. TABLE 3: Coding of aneurysm location* Parameter Coding Location No. of Aneurysms Loc (1) Loc (2) Loc (3) Loc (4) ACoA BA ICA MCA PCoA * If an aneurysm is located at ACoA, then Location (1) is assigned 1 in our equation and Locations (2) through (4) are assigned 0. Similar assignments are given to other locations in our equation based on the coding shown. If an aneurysm is located at PCoA, then in the equation Locations (1) through (4) are assigned 0. Abbreviation: Loc = Location. and specificity of 81 and 55%, respectively. The percentage accuracy of the model for correctly classifying the aneurysm status was found to be 70%. Most importantly, this model was then used prospectively to predict aneurysm rupture in a new, independent cohort of 49 patients. Image analysis and interrogation of the mathematical model were performed independently by 2 of the investigators, each blinded to the patient s clinical status. The model was able to correctly predict rupture status in 39 of 49 aneurysms. The sensitivity and specificity for the model in this cohort were found to be 83 and 78%, respectively, with an accuracy of 80% (Table 4). Illustrative Example In the cohort of 49 patients, a 65-year-old man presented with an aneurysm located at the ACoA. After 3D reconstructions, we calculated the aneurysm volume at cm 3 and measured its height in the plane perpendicular to the flow (Y2) as 6.9 mm. Applying these data into the equation: Log (odds of rupture of the aneurysm) = * Volume *Y *Location (1) 0.023*Age Log (odds of rupture of the aneurysm) = * * * *65 Log (odds of rupture of the aneurysm) = The probability of rupture of the aneurysm = (Odds of rupture) / (1 + Odds of rupture) = Exp (0.9939) / (1 + Exp [0.9939]) = / ( ) = Thus, the probability of rupture of the aneurysm in this example is Establishing the likelihood of aneurysm rupture to be > 0.5, in this example, the prediction would be that the aneurysm had ruptured. Clinical data confirmed that this patient presented with a ruptured aneurysm. Discussion The results of the present study indicate that our binary logistic regression model generated from an independent cohort of patients accurately determined the rupture status of aneurysms within a second prospective cohort of patients with a sensitivity of 83%, specificity of TABLE 4: Classification of retrospective data and prospective cohort data* Data Source & Observed Predicted Status Aneurysm Status Unruptured Ruptured % Correct model generation data (279 aneurysms) unruptured (123 aneurysms) ruptured (156 aneurysms) overall % correct 70 prospective cohort study (49 aneurysms) unruptured (37 aneurysms) ruptured (12 aneurysms) overall % correct 80 combined data (328 aneurysms) unruptured (160 aneurysms) ruptured (168 aneurysms) overall % correct 71 * Values represent numbers of aneurysms unless otherwise indicated. 78%, and an overall accuracy of 80%. The results of this mathematical analysis are in accordance with those of a previous study by Hademos et al., 9 in which the correlation of anatomical and morphological factors with rupture of intracranial aneurysms was studied in 74 patients with aneurysms. In that study, the sensitivity, specificity, and overall accuracy were 76.3% (as compared with 81% in our initial data), 61.8% (55% in our initial data), and 69.4% (70% in our initial data), respectively. The published data from the International Study of Unruptured Intracranial Aneurysms 10 has suggested that the cumulative rate of rupture for aneurysms that are < 10 mm in diameter at diagnosis was < 0.05% per year in patients with no history of SAH (Group 1). However, the cumulative rupture rate of aneurysms of the same size was ~ 11 times higher per year in patients who present with a history of SAH (Group 2). The rupture rate per year in aneurysms that were 10 mm in diameter was ~ 1% in both groups regardless of the SAH history. To date, our model has not been used as a means of longitudinally predicting future rupture of an unruptured aneurysm. Further analysis of additional, more complex parameters will be forthcoming. Our study revealed that aneurysm location is one of the significant factors in predicting the rupture of the aneurysm, which is consistent with previous studies. 1,2,7,9,23 Although previous studies support that location of the aneurysm is a valid predictor of rupture, a correlation between location and rupture of the aneurysm has not been established to date. By using this logistic regression model, we were able to correlate the likelihood of rupture of an aneurysm with different locations as well as with other parameters. For instance, careful analysis of the equation demonstrates that, when keeping all other 4 J. Neurosurg. / Vol 110 / January, 2009

5 Significance of binary logistic regression in cerebral aneurysms parameters unchanged, the odds ratio of an aneurysm rupture at the ACoA to that of an aneurysm rupture at the BA would be In other words, if all parameters were equal except the location, an ACoA aneurysm has a probability of rupture 2.34 times greater than an aneurysm of the BA of equal size. Similarly, the model suggests that an aneurysm has the least probability of rupture when it is located at the ICA, while the same aneurysm located at the PCoA has the greatest probability of rupture. This result is consistent with the findings of a recent epidemiological study of aneurysm size and location. 3 Other studies have demonstrated similar results indicating that PCoA and ACoA aneurysms are more prone to rupture than aneurysms in other sites. 1,8,9 Another significant predictor of aneurysm rupture was found to be the measured height of the aneurysm in the plane perpendicular to the blood flow (Y2). By carefully analyzing the algorithm above, one can note that, for every unit of increasing height of the aneurysm, the odds of rupture increase by a factor of 1.29, suggesting that a positive correlation exists between aneurysm size and the risk of rupture. Many studies have advocated the importance of the size of aneurysms in association with rupture and have suggested a linear relationship between aneurysm size and rupture. 9,11,23 Several studies have attempted to determine the threshold or critical size at which an aneurysm becomes likely to rupture. 5,10,15,21,24 Nevertheless, results to date have been extremely variable with a wide range of critical sizes from 4 mm to > 10 mm. 9 Beck et al. 2 studied the size and location of ruptured and unruptured aneurysms and concluded that a critical size for aneurysm rupture could not be identified. Sekhar and Heros 22 suggested in a review that rupture can and does occur at any size. Taken together, these studies indicate that there is no definite size above which rupture will definitely occur. This might explain, in part, our observation that only aneurysm height of is a significant predictor of rupture. In our study, however, significant differences were observed between ruptured and unruptured aneurysm groups in several measurements (Table 2), including measured heights and widths (Y1, Y2, X1, and X2) in both planes that are parallel and planes that are perpendicular to the blood flow. These observations support those made by the authors of previous studies. 9,19 Based on our model, the odds of rupture of an aneurysm are positively correlated with the height of the aneurysm measured in a plane perpendicular to the blood flow. Prior studies have also suggested that there is a significant difference between the volumes of ruptured aneurysms and those of unruptured aneurysms. Although we hypothesized that larger volumes correlated with higher risk of rupture, our binary logistic regression model demonstrated a negative relationship between aneurysm volume and the odds of rupture. One explanation for this may be that the likelihood of aneurysm rupture is not linearly related to the volume of the aneurysm; there may be a critical volume for which rupture risk begins to decrease. Some early observational data and recent biomathematical modeling lend support to this hypothesis. 10,13 Interestingly, however, within the largest range of aneurysm volumes, the odds of rupture once again increases with an J. Neurosurg. / Vol 110 / January, 2009 Fig. 2. Scatterplot showing probability of aneurysm rupture versus volume of aneurysms. increase in volume. Thus, the function of the odds risk to the volume may be written as a segment function. In our model, we first used standard statistically based discriminant and classification functions to classify volume in 3 groups based on aneurysm rupture status. We next introduced additional categorical data to stratify volume in 3 levels. During logistic regression analysis, the volume was replaced by this stratified volume, revealing that in some volume ranges, the odds of rupture increases with the volume increase, while in other ranges, it decreases as the volume increases (Fig. 2 plots the rupture probability of aneurysms versus volumes of aneurysms). This modified model allowed us to substantiate our hypothesis, although we were unable to demonstrate enhanced sensitivity and specificity in our prospective cohort of aneurysm patients. Further work is necessary to refine the stratification of volume to adjust the model. An additional interesting observation in our study was the revelation of patient age as a factor in predicting the risk of aneurysm rupture. When we compared age in the ruptured and unruptured groups, no significant between-group differences were observed, in agreement with previous reports. 23 Our logistic regression model, however, suggests that patient age at diagnosis is inversely correlated with the risk of rupture (p = 0.031), which is also consistent with previously published data. 12 For every 1 year of additional age, the statistical odds of rupture decrease by a factor of These results suggest that age should not be treated as an isolated predictive factor for the risk of rupture, but rather should be combined with factors like aneurysm location and size. Conclusions Using a new binary logistic regression model of aneurysm rupture and basic biomorphometric data and relationships obtained from CT angiography in orthogonal dimensions, we were able to accurately identify the status of an aneurysm with a sensitivity of 83% and an overall accuracy of 80% in a prospectively obtained independently derived cohort of 37 patients with 49 aneurysms. This cohort was distinct from the original cohort 5

6 C. J. Prestigiacomo et al. of 217 patients with 279 aneurysms used for generation of the mathematical model. Our binary logistic regression model represents the first time that such a technique has been applied and validated for use in predicting aneurysm rupture. Although at the present sensitivity and accuracy this model is not robust enough for clinical evaluation, it does provide a basis from which more sensitive, specific, accurate, and complex models may be derived. Future studies combining dynamic flow characteristics and the bioelastic properties of tissue may further enhance these models. Disclaimer The authors report no conflict of interest concerning the materials or methods used in this study or the findings specified in this paper. References 1. Asari S, Ohmoto T: Natural history and risk factors of unruptured cerebral aneurysms. 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J Neurosurg 76: , Sekhar LN, Heros RC: Origin, growth, and rupture of saccular aneurysms: a review. Neurosurgery 8: , Weir B, Disney L, Karrison T: Sizes of ruptured and unruptured aneurysms in relation to their sites and the ages of patients. J Neurosurg 96:64 70, Yasui N, Magarisawa S, Suzuki A, Nishimura H, Okudera T, Abe T: Subarachnoid hemorrhage caused by previously diagnosed, previously unruptured intracranial aneurysms: a retrospective analysis of 25 cases. Neurosurgery 39: , 1996 Manuscript submitted September 28, Accepted May 8, Please include this information when citing this paper: published online October 17, 2008; DOI: / Address correspondence to: Charles J. Prestigiacomo, M.D., Departments of Neurological Surgery and Radiology, New Jersey Medical School, University of Medicine and Dentistry of New Jersey, 90 Bergen Street, Suite 8100, Newark, New Jersey, c.prestigiacomo@umdnj.edu. 6 J. Neurosurg. / Vol 110 / January, 2009