Predicting aneurysm rupture probabilities

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Predicting aneurysm rupture probabilities

  1. 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 CHARLES J. PRESTIGIACOMO, M.D.,1–3 WENZHUAN HE, M.D.,1 JEFFREY CATRAMBONE, M.D.,1 STEPHANIE CHUNG, B.S.,1 LYDIA KASPER, B.A.,1 LATHA PASUPULETI, B.S.,1 AND NEELESH MITTAL, M.D.1 Departments of 1Neurological Surgery and 2Radiology, and 3Neurological 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 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 re- gression 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 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. 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: 10.3171/2008.5.17558) KEY WORDSS UBARACHNOID hemorrhage secondary to the rupture Previous studies have suggested that the shape and of an intracranial aneurysm is a life-threatening size of the aneurysm are parameters that can be used and debilitating event with an overall morbidity to predict the risk of rupture.2 However, these studiesand mortality rate of 50–60%.2,15,20 With modern imag- only compared differences in size between unruptureding techniques, unruptured intracranial aneurysms can and ruptured intracranial aneurysms. Other studies havebe detected more reliably, but the management of these compared the size of the aneurysms between unrupturedlesions remains controversial.10 In part, the controversy versus ruptured groups, attempting to quantitatively as-revolves around the fact that microsurgical and endovas- sign a critical number to aneurysm size (that is, the sizecular treatment modalities are invasive and carry some just prior to or at the time of rupture).6,9,18 However, esti-risk to the patient.14 Consequently, the natural history of mated values of the critical size for aneurysmal ruptureany aneurysm of a given size, shape, and location must have ranged from 4.0 mm to > 10.0 mm.6,9,18 Therefore,be balanced against the risk of complications secondaryto the treatment of the aneurysm. Of import would be the the rupture of cerebral aneurysms remains an importantability to accurately predict the likelihood of aneurysm component of clinical decision-making in neurosurgery.rupture such that only those patients with aneurysms thatare likely to rupture would be appropriately exposed to morbidity and mortality of intracranial aneurysms wasthe risks of treatment. introduced by Richardson et al. in 1966.16 The authors presented a discriminative function by which mortal- Abbreviations used in this paper: ACoA = anterior communi-cating artery; BA = basilar artery; ICA = internal carotid artery; This article contains some figures that are displayed in colorMCA = middle cerebral artery; PCoA = posterior communicating online but in black and white in the print edition.artery; SAH = subarachnoid hemorrhage.J. Neurosurg. / Vol 110 / January, 2009 1
  2. 2. C. J. Prestigiacomo et al.ity could be predicted in a type of operative approachto ACoA aneurysms. Subsequently, they used the samefunction to evaluate the prognostic factors in a series ofPCoA aneurysms.17 Since the publication of their work,mathematical modeling of aneurysms has been used tounderstand the biophysical phenomena that contribute toaneurysm growth and rupture. Biomathematical modelscan incorporate various physical and dynamic phenom-ena that may provide insight into the potential for ruptureand possibly help predict the probability of aneurysmalrupture.4 Our present study describes the biomorphomet-ric properties of aneurysms in a clinical prospective se-ries. By performing binary logistic regression analysis, astatistical technique similar to the previously describeddiscriminative analysis method,16 we have derived a rela-tional equation that describes the rupture potential for ce-rebral aneurysms within this cohort. To assess the stabil-ity of this equation, we then applied it to an independentcohort of aneurysm patients to determine the rupture sta-tus of a patient’s aneurysm. To our knowledge, this repre-applicable mathematical formula that describes aneurysmrupture in an independent patient population. This study represents a retrospective review of aprospectively maintained database of patients presentingto the University Hospital of the University of Medicineand Dentistry of New Jersey with SAH due to aneurysmrupture. Between 2002 and 2005, a total of 217 patientswith 279 aneurysms (156 ruptured and 123 unruptured)presented to our institution. Multiple aneurysms wereruptured and unruptured aneurysms by location as well 1A and B). (The variables Y1, X1, and N1 represent mea-as patient age and sex is summarized in Table 1. In thesetting of aneurysmal SAH in patients with multiple an- and Y2, X2, and N2 represent measurements obtained ineurysms, the ruptured aneurysm (the index aneurysm) such as measured and calculated aneurysmal volume, lo-and correlated with the hemorrhage pattern on the initial cation of aneurysm, and rupture status were included inCT scan and repeated CT scans obtained 24 hours after this initial database. This data set was used as the ini-the initial ictus (that is, the hemorrhage), when available. tial data to generate a stepwise binary logistic regressionCerebral aneurysms were diagnosed and evaluated with model. After having completed the registration of patientsCT angiography using a GE Systems LightSpeed 16-slice to the current study, we prospectively collected a data setCT scanner. A total of 150 ml of contrast medium was from an independent cohort of 49 aneurysms in 37 pa-injected intravenously via the antecubital vein at a rate tients who presented between November 2005 and Juneof 4 ml/second. Images were then obtained at 0.625-mm 2006. The model was then applied to this independent co-slice-thickness with no overlap following an 18-second hort by one of the authors who was blinded to the ruptureacquisition delay. Source images were transferred to the status of the aneurysms. The log-odds risk of rupture forGE Advantix 3D workstation where maximal-intensity -projections and 3D reconstructions were generated. All ity and sensitivity to predict the aneurysm status usingangiograms were analyzed by 2 investigators who were our binary logistic regression model were calculated.clinical information including rupture status of aneu- Statistical Analysis - The statistical software used in this analysis waseral biomorphometric parameters were obtained in planes SPSS version 12.0 (SPSS, Inc.) for Windows. Indepen- dent t-tests and chi-square tests were used to compare thethe parent vessel. mean for continuous data and categorical data, respec- Maximum aneurysm height (Y), width (X), and neck tively. Forward binary logistic regression was then usedsize (N) were obtained in these orthogonal planes (Fig. to generate the model.2 J. Neurosurg. / Vol 110 / January, 2009
  3. 3. Significance of binary logistic regression in cerebral aneurysms * ** Demographic characteristics of the patients and thelocation of aneurysms in the cases used to generate theinitial binary logistic regression model are demonstratedin Table 1. The results of comparison of the mean val-observed for the number of ruptured versus unrupturedaneurysms between men and women (p = 0.538). How-of ruptured versus unruptured aneurysms were found4 of the 6 biomorphometric parameters obtained in this *maximum width [X1] divided by the neck size [N1]), andthe N1/N2 and X1/X2 ratios (Table 2). A stepwise binary logistic regression model was gen-erated that incorporated the aneurysm location in addi-tion to volume and the biomorphometric parameters. Inthis equation, aneurysm location was represented as a ue of the height of the aneurysm in the plane that is per- -est correlation with the initial database is expressed as of the aneurysm is represented by 1 of the 4 binary “loca-follows: tion variables” (Table 3). A value of 1 for “Location (2)” Logit = 1.127–0.457*volume + 0.254*Y2–1.214*Location would represent a patient with an aneurysm of the BA. Of (4) – 2.262*Location (3) – 1.184*Location (2) – 0.334* note, patients with aneurysms of the PCoA would have all Location (1) – 0.023*patient’s age “location variables” set at 0. Note: Location (1) = ACoA; Location (2) = BA; Location (3) = ICA; Location (4) = MCA. Y2 = the height of the aneu- tested by chi-square analysis, which generated a probabil- rysm. Volume represents the measured volume as calculated by - the system’s software package. cation were independently correlated to rupture risk (each The volume in this model represents the measuredvolume as calculated by the system’s proprietary software in this model. Using our model, we were able to predictpackage. The variable “Y2” represents the measured val- the rupture status of the 279 aneurysms with a sensitivityJ. Neurosurg. / Vol 110 / January, 2009 3
  4. 4. C. J. Prestigiacomo et al. * ** -age accuracy of the model for correctly classifying theaneurysm status was found to be 70%. Most importantly, this model was then used prospec-tively to predict aneurysm rupture in a new, independentcohort of 49 patients. Image analysis and interrogation ofthe mathematical model were performed independently *by 2 of the investigators, each blinded to the patient’sclinical status. The model was able to correctly pre-dict rupture status in 39 of 49 aneurysms. The sensitivity 78%, and an overall accuracy of 80%. The results of thisto be 83 and 78%, respectively, with an accuracy of 80% mathematical analysis are in accordance with those of a(Table 4). previous study by Hademos et al.,9 in which the correla- tion of anatomical and morphological factors with rup-Illustrative Example ture of intracranial aneurysms was studied in 74 patients In the cohort of 49 patients, a 65-year-old man pre-sented with an aneurysm located at the ACoA. After 3D and overall accuracy were 76.3% (as compared with 81%reconstructions, we calculated the aneurysm volume at in our initial data), 61.8% (55% in our initial data), and0.124 cm3 and measured its height in the plane perpen- 69.4% (70% in our initial data), respectively. The pub- lished data from the International Study of Unrupturedinto the equation: Intracranial Aneurysms10 has suggested that the cumula- Log (odds of rupture of the aneurysm) = 1.127–0.457* - Volume + 0.254*Y2–0.334*Location (1) – 0.023*Age no history of SAH (Group 1). However, the cumulative Log (odds of rupture of the aneurysm) = 1.127–0.457* 0.124 + 0.254*6.9–0.334*1–0.023*65 rupture rate of aneurysms of the same size was ~ 11 times higher per year in patients who present with a history of Log (odds of rupture of the aneurysm) = 0.9939 SAH (Group 2). The rupture rate per year in aneurysms The probability of rupture of the aneurysm = (Odds of rupture) / (1 + Odds of rupture) = Exp (0.9939) / (1 + Exp regardless of the SAH history. To date, our model has not [0.9939]) = 2.702 / (1 + 2.702) = 0.7299 been used as a means of longitudinally predicting future Thus, the probability of rupture of the aneurysm in rupture of an unruptured aneurysm. Further analysis ofthis example is 0.7299. Establishing the likelihood of an- additional, more complex parameters will be forthcom-eurysm rupture to be > 0.5, in this example, the predic- ing.tion would be that the aneurysm had ruptured. Clinical Our study revealed that aneurysm location is one of -aneurysm. eurysm, 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 The results of the present study indicate that our been established to date. By using this logistic regressionbinary logistic regression model generated from an in- model, we were able to correlate the likelihood of rup-dependent cohort of patients accurately determined the ture of an aneurysm with different locations as well asrupture status of aneurysms within a second prospective with other parameters. For instance, careful analysis of the equation demonstrates that, when keeping all other4 J. Neurosurg. / Vol 110 / January, 2009
  5. 5. Significance of binary logistic regression in cerebral aneurysmsparameters unchanged, the odds ratio of an aneurysmrupture at the ACoA to that of an aneurysm rupture at theBA would be 2.34. In other words, if all parameters wereequal except the location, an ACoA aneurysm has a prob-ability of rupture 2.34 times greater than an aneurysm ofthe BA of equal size. Similarly, the model suggests thatan aneurysm has the least probability of rupture when itis located at the ICA, while the same aneurysm locatedat the PCoA has the greatest probability of rupture. This -miological study of aneurysm size and location.3 Otherstudies have demonstrated similar results indicating thatPCoA and ACoA aneurysms are more prone to rupturethan aneurysms in other sites.1,8,9was found to be the measured height of the aneurysm in -fully analyzing the algorithm above, one can note that,for every unit of increasing height of the aneurysm, theodds of rupture increase by a factor of 1.29, suggesting increase in volume. Thus, the function of the odds risk tothat a positive correlation exists between aneurysm size the volume may be written as a segment function. In ourand the risk of rupture. Many studies have advocated the -importance of the size of aneurysms in association withrupture and have suggested a linear relationship between groups based on aneurysm rupture status. We next intro-aneurysm size and rupture.9,11,23 Several studies have at- duced additional categorical data to stratify volume intempted to determine the threshold or critical size at 3 levels. During logistic regression analysis, the volumewhich an aneurysm becomes likely to rupture. 5,10,15,21,24Nevertheless, results to date have been extremely variable some volume ranges, the odds of rupture increases withwith a wide range of critical sizes from 4 mm to > 10 the volume increase, while in other ranges, it decreasesmm.9 Beck et al.2 studied the size and location of ruptured as the volume increases (Fig. 2 plots the rupture prob-and unruptured aneurysms and concluded that a critical ability of aneurysms versus volumes of aneurysms). This -and Heros22 suggested in a review that rupture can and esis, although we were unable to demonstrate enhanceddoes occur at any size. Taken together, these studies indi- - - An additional interesting observation in our study was the revelation of patient age as a factor in predict-were observed between ruptured and unruptured aneu- ing the risk of aneurysm rupture. When we comparedrysm groups in several measurements (Table 2), includingmeasured heights and widths (Y1, Y2, X1, and X2) in both between-group differences were observed, in agreementplanes that are parallel and planes that are perpendicular with previous reports.23 Our logistic regression model, however, suggests that patient age at diagnosis is inverse-by the authors of previous studies.9,19 Based on our model, ly correlated with the risk of rupture (p = 0.031), which isthe odds of rupture of an aneurysm are positively corre- also consistent with previously published data.12 For ev-lated with the height of the aneurysm measured in a plane ery 1 year of additional age, the statistical odds of rupture decrease by a factor of 1.023. These results suggest that Prior studies have also suggested that there is a sig- age should not be treated as an isolated predictive fac- - tor for the risk of rupture, but rather should be combinedrysms and those of unruptured aneurysms. Although we with factors like aneurysm location and size.hypothesized that larger volumes correlated with higherrisk of rupture, our binary logistic regression model dem-onstrated a negative relationship between aneurysm vol-ume and the odds of rupture. One explanation for this may Using a new binary logistic regression model ofbe that the likelihood of aneurysm rupture is not linearly aneurysm rupture and basic biomorphometric data andrelated to the volume of the aneurysm; there may be a relationships obtained from CT angiography in orthogo-critical volume for which rupture risk begins to decrease. nal dimensions, we were able to accurately identify theSome early observational data and recent biomathemati- status of an aneurysm with a sensitivity of 83% and ancal modeling lend support to this hypothesis.10,13 Interest- overall accuracy of 80% in a prospectively obtained in-ingly, however, within the largest range of aneurysm vol- dependently derived cohort of 37 patients with 49 aneu-umes, the odds of rupture once again increases with an rysms. This cohort was distinct from the original cohortJ. Neurosurg. / Vol 110 / January, 2009 5
  6. 6. C. J. Prestigiacomo et al.of 217 patients with 279 aneurysms used for generation of 11. Janardhan V, Friedlander R, Riina H, Stieg PE: Identifyingthe mathematical model. Our binary logistic regression patients at risk for postprocedural morbidity after treatment of incidental intracranial aneurysms: the role of aneurysm size and location. 13(3):E1, 2002been applied and validated for use in predicting aneurysm 12. Juvela S, Porras M, Poussa K: Natural history of unrupturedrupture. Although at the present sensitivity and accuracy intracranial aneurysms: probability of and risk factors for an-this model is not robust enough for clinical evaluation, it eurysm rupture. J Neurosurg 93:379–387, 2000 13. Meng H, Feng Y, Woodward SH, Bendok BR, Hanel RA,accurate, and complex models may be derived. Future Guterman LR, et al: Mathematical model of the rupture mech- anism of intracranial saccular aneurysms through daughterbioelastic properties of tissue may further enhance these aneurysm formation and growth. 27:459–465, 2005models. 14. Mizoi K, Yoshimoto T, Nagamine Y, Kayama T, Koshu K: How to treat incidental cerebral aneurysms: a review of 139 consecutive cases. 44:114–121, 1995 15. Orz Y, Kobayashi S, Osawa M, Tanaka Y: Aneurysm size: a The authors report no conflict of interest concerning the mate- prognostic factor for rupture. 11:144–149,rials or methods used in this study or the findings specified in this 1997paper. 16. Richardson AE, Jane JA, Payne PM: The prediction of mor- bidity and mortality in anterior communicating aneurysms treated by proximal anterior cerebral ligation. J Neurosurg 25:280–283, 1966 17. Richardson AE, Jane JA, Yashon D: Prognostic factors in the 1. Asari S, Ohmoto T: Natural history and risk factors of unrup- untreated course of posterior communicating aneurysms. tured cerebral aneurysms. 95:205– 14:172–176, 1966 214, 1993 18. Rogers LA: Intracranial aneurysm size and potential for rup- 2. Beck J, Rohde S, Berkefeld J, Seifert V, Raabe A: Size and ture. J Neurosurg 67:475–476, 1987 location of ruptured and unruptured intracranial aneurysms 19. Rohde S, Lahmann K, Beck J, Nafe R, Yan B, Raabe A, et al: measured by 3-dimensional rotational angiography. Surg Fourier analysis of intracranial aneurysms: towards an objec- 65:18–27, 2006 tive and quantitative evaluation of the shape of aneurysms. 3. Carter BS, Sheth S, Chang E, Sethl M, Ogilvy CS: Epidemiol- 47:121–126, 2005 ogy of the size distribution of intracranial bifurcation aneu- 20. Rosenorn J, Eskesen V, Schmidt K, Espersen JO, Haase J, rysms: smaller size of distal aneurysms and increasing size of Harmsen A, et al: Clinical features and outcome in 1076 pa- unruptured aneurysms with age. 58:217–223, tients with ruptured intracranial saccular aneurysms: a pro- 2006 spective consecutive study. 1:33–45, 1987 4. Chaudhry HR, Lott DA, Prestigiacomo CJ, Findley TW: 21. Schievink WI, Piepgras DG, Wirth FP: Rupture of previously Mathematical model for the rupture of cerebral saccular an- documented small asymptomatic saccular intracranial aneu- eurysms through three-dimensional stress distribution in the rysms. Report of three cases. J Neurosurg 76:1019–1024, aneurysm wall. 6:325–335, 2006 1992 5. Dickey P, Nunes J, Bautista C, Goodrich I: Intracranial aneu- 22. Sekhar LN, Heros RC: Origin, growth, and rupture of saccu- rysms: size, risk of rupture, and prophylactic surgical treat- lar aneurysms: a review. 8:248–260, 1981 ment. 58:583–586, 1994 23. Weir B, Disney L, Karrison T: Sizes of ruptured and unrup- 6. Fernandez Zubillaga A, Guglielmi G, Viñuela F, Duckwiler tured aneurysms in relation to their sites and the ages of pa- GR: Endovascular occlusion of intracranial aneurysms with tients. J Neurosurg 96:64–70, 2002 electrically detachable coils: correlation of aneurysm neck 24. Yasui N, Magarisawa S, Suzuki A, Nishimura H, Okudera T, size and treatment results. 15:815– Abe T: Subarachnoid hemorrhage caused by previously diag- 820, 1994 nosed, previously unruptured intracranial aneurysms: a retro- 7. Forget TR Jr, Benitez R, Veznedaroglu E, Sharan A, Mitchell spective analysis of 25 cases. 39:1096–1101, W, Silva M, et al: A review of size and location of ruptured 1996 intracranial aneurysms. 49:1322–1326, 2001 8. Freytag E: Fatal rupture of intracranial aneurysms. Survey of 250 medicolegal cases. 81:418–424, 1966 Manuscript submitted September 28, 2007. 9. Hademenos GJ, Massoud TF, Turjman F, Sayre JW: Ana- Accepted May 8, 2008. tomical and morphological factors correlating with rupture of Please include this information when citing this paper: published intracranial aneurysms in patients referred for endovascular online October 17, 2008; DOI: 10.3171/2008.5.17558. treatment. 40:755–760, 1998 Address correspondence to: Charles J. Prestigiacomo, M.D.,10. International Study of Unruptured Intracranial Aneurysms Departments of Neurological Surgery and Radiology, New Jersey Investigators: Unruptured intracranial aneurysms—risk of Medical School, University of Medicine and Dentistry of New rupture and risks of surgical intervention. 339: Jersey, 90 Bergen Street, Suite 8100, Newark, New Jersey, 07101. 1725–1733, 1998 email: c.prestigiacomo@umdnj.edu.6 J. Neurosurg. / Vol 110 / January, 2009

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