Bifurcation geometry and the presence of cerebral artery aneurysms

Transcription

1 J Neurosurg 101: , 2004 Bifurcation geometry and the presence of cerebral artery aneurysms TOR INGEBRIGTSEN, PH.D., MICHAEL K. MORGAN, M.D., KEN FAULDER, M.B.B.S., LINDA INGEBRIGTSEN, M.SC., TRYGVE SPARR, PH.D., AND HENRIK SCHIRMER, PH.D. Department of Surgery, University of Sydney and Dalcross Private Hospital; Department of Radiology, Royal North Shore Hospital, Sydney; Department of Epidemiology and Preventive Medicine, Monash University, Melbourne, Australia; Department of Neurosurgery, University Hospital of North Norway, Tromsø; Simula Research, Oslo; The Norwegian Defense Research Establishment, Kjeller; and Institute of Community Medicine, University of Tromsø, Norway Object. The angles of arterial bifurcations are governed by principles of work minimization (optimality principle). This determines the relationship between the angle of a bifurcation and the radii of the vessels. Nevertheless, the model is predicated on an absence of significant communication between these branches. The circle of Willis changes this relationship because the vessels proximal to the ring of vessels have additional factors that determine work minimization compared with more distal branches. This must have an impact on understanding of the relationship between shear stress and aneurysm formation. The authors hypothesized that normal bifurcations of cerebral arteries beyond the circle of Willis would follow optimality principles of minimum work and that the presence of aneurysms would be associated with deviations from optimum bifurcation geometry. Nevertheless, the vessels participating in (or immediately proximal to) the circle of Willis may not follow the geometric model as it is generally applied and this must also be investigated. Methods. One hundred seven bifurcations of the middle cerebral artery (MCA), distal internal carotid artery (ICA), and basilar artery (BA) were studied in 55 patients. The authors analyzed three-dimensional reconstructions of digital subtraction angiography images with respect to vessel radii and bifurcation angles. The junction exponent (that is, a calculated measure of the division of flow at the bifurcation) and the difference between the predicted optimal and observed branch angles were used as measures of deviation from the geometry thought best to minimize work. The mean junction exponent for MCA bifurcations was (mean standard deviation [SD]), which is close to the theoretical optimum of 3, but it was significantly smaller (p 0.001; , mean SD) for distal ICA bifurcations. In a multilevel multivariate logistic regression analysis, only the observed branch angles were significant independent predictors for the presence of an aneurysm. The odds ratio (OR) (95% confidence interval) for the presence of an aneurysm was 3.46 ( ) between the lowest and highest tertile of the observed angle between the parent vessel and the largest branch. The corresponding OR for the smallest branch was ( ). Conclusions. The bifurcation beyond the circle of Willis (that is, the MCA) closely approximated optimality principles, whereas the bifurcations within the circle of Willis (that is, the distal ICA and BA) did not. This indicates that the confluence of hemodynamic forces plays an important role in the distribution of work at bifurcations within the circle of Willis. In addition, the observed branch angles were predictors for the presence of aneurysms. KEY WORDS cerebral aneurysm hemodynamics risk factor digital subtraction angiography computer-assisted image processing D Abbreviations used in this paper: ACA = anterior cerebral artery; ANOVA = analysis of variance; BA = basilar artery; CI = confidence interval; DS = digital subtraction; ICA = internal carotid artery; MCA = middle cerebral artery; OR = odds ratio; SD = standard deviation; 2D = two-dimensional; 3D = three-dimensional. 108 ISRUPTION of the internal elastic lamina is a requirement for the creation of saccular aneurysms; hemodynamic factors also play an important role. Saccular aneurysms arise at the distal carina of bifurcations, where the vessel wall is exposed to maximum impact of hemodynamic shear stress. 16 The amount of shear stress depends on the geometry of the bifurcation. 3,4,9,19 Theoretically, shear stress is minimized when the relation between vessel radii and bifurcation angles follows optimality principles of minimum work. 10,13,20 In a study of cerebral angiograms demonstrating normal results, the authors concluded that the cerebral vascular network follows such principles. 12,13 Nevertheless, a concern in applying optimality principles to the cerebral circulation is that the reunification of the arteries within the circle of Willis may have an impact on the derived equation. This has not been addressed previously. Difficulties with the exact determination of bifurcation angles on 2D angiograms have limited the usefulness of previous studies. The 3D reconstruction of rotational DS angiography images is a new technique that is superior to 2D methods in clarifying relationships between aneurysms and adjacent vessels. 1,14,18 In our study, 3D DS angiography images of the cerebral circulation were analyzed with re-

2 Bifurcation geometry in cerebral artery aneurysms FIG. 2. Measurements of vessel diameters obtained using 3D DS angiography. The diameter of the parent vessel was measured midway between the last branch point and the bifurcation of interest. In the branches, the diameters were measured 5 mm beyond the apex of the bifurcation, or if a new branch arose before this, at the most distal location before the next bifurcation. These points were identified on oblique images oriented along the flow axis of the vessel (A). The diameters were measured at eight different centripetals in a plane oriented 90 on the flow axis, which is also the plane where the shape of the vessel appears to be closest to circular (B). FIG. 1. Schematic drawing showing the measurements obtained from each arterial bifurcation: the radii from the parent vessel (r 0 ), the largest branch (r 1 ), and the smallest branch (r 2 ); and the angles 1 and 2 formed between the parent vessel and the largest and smallest branch, respectively. spect to vessel radii and bifurcation angles. We hypothesized that normal bifurcations on cerebral arteries beyond the circle of Willis would follow optimality principles of minimum work and that the presence of aneurysms would be associated with deviations from optimum bifurcation geometry. Nevertheless, the vessels participating in (or immediately proximal to) the circle of Willis may not follow the geometric model as it is generally applied and this must also be investigated. Materials and Methods Patient Population Three-dimensional DS angiography was introduced at Dalcross Private Hospital in Sydney, Australia, as a routine examination for patients undergoing diagnostic cerebral angiography in February Angiograms obtained in 69 consecutive patients between February 2002 and March 2003 were considered eligible for inclusion, regardless of the indications for neuroradiological examinations. Images obtained in 55 patients, 15 with subarachnoid hemorrhage, 10 with a family history of intracranial aneurysms, nine with ischemic cerebrovascular events, five with other cerebrovascular disease, four with cranial nerve palsy, and 12 with nonspecific neurological symptoms were included, whereas images from nine patients were excluded because of movement artifacts. Three-Dimensional DS Angiography Rotational DS angiography images were obtained using an Advantx DS angiography unit (General Electric Medical Systems, Milwaukee, WI) and the images were transferred to an Advantage 4.0 workstation (General Electric Medical Systems) for postprocessing. Rotational angiography was performed with a 6-second, 200 rotation of the C-arm. Both a mask and a dynamic contrast run were obtained. The matrix size of each frame was pixels. Eighteen milliliters of iopomide 300 mg/ml (Ultravist 300; Schering AG, Berlin, Germany) was injected at 3 ml/second with the catheter positioned in the ICA or the vertebral artery, providing continuous filling of the vessels during contrast runs. We did not perform additional injections for the purpose of this study. Mask data and contrast data were individually transferred to the workstation. Reconstructed images including surface display models were obtained. Minimum density threshold processing was performed to optimize visualization of the branch points of interest. The AW Volume Analysis (General Electric Medical Systems) software package was used to display baseline axial, coronal, and sagittal views and to create reformatted oblique views at selected locations and orientations within the 3D volume. These images were used for measurements of radii and angles. Measurements of Radii and Angles We chose to study three bifurcations, as follows: 1) the terminal bifurcation of the ICA; 2) the division of the M 1 segment of the MCA into two main branches of the M 2 segment; and 3) the bifurcation of the BA. Five measurements were obtained, as follows: 1) radii from the parent vessel (r 0 ); 2) the largest branch (r 1 ); 3) the smallest branch (r 2 ); and 4) and 5) the angle formed between the parent vessel and the largest branch ( 1 ) and the smallest branch ( 2 ), respectively (Fig. 1). The diameter of the parent vessel was measured midway between the last branch point and the bifurcation of interest. In the branches, the vessel diameters were measured 5 mm beyond the apex of the bifurcation, or if a new branch arose before this, at the most distal location before the next bifurcation. These points were identified on images oriented along the flow axis of the vessel. The diameter (d) was measured on eight different axes (centripetals) in a plane oriented 90 to the flow axis. The flow axis is the plane on which the shape of the vessel appears closest to circular (Fig. 2). The radius (r) was calculated as r = mean d/2. The area ratio was calculated according 2 to the following equation: area ratio = (r 12 r 22 ) r 0. Figure 3 shows how we measured 1 and 2. These angles represent the deviation from the direction of flow in the parent vessel into the branches. They were calculated using the AW Volume Analysis software package. The principal investigator (T.I.) performed all measurements. A neuroradiologist (K.F.) who was blinded to the results obtained by the principal investigator measured 42 randomly chosen angles to estimate interobserver error. Determination of Minimum Work Optimality Arterial branch points are designed to minimize the work required for blood to flow throughout the body. The theoretical basis for this 109

3 T. Ingebrigtsen, et al. FIG. 3. Measurements of bifurcation angles obtained using 3D DS angiography. Three points were defined in the 3D volume to measure an angle: the center of the parent vessel at the point where the diameter was measured, the center of the bifurcation, and the center of the branch at the point where the diameter was measured. First, the cursor (blue circle) was placed in the parent vessel (A). Second, an oblique plane oriented along the flow axis (solid orange line) was defined (B), and the cursor (upper end of blue line) was placed in the bifurcation (C). Third, a plane oriented 90 on the flow axis of the branch (solid orange line) was defined (D) and the cursor (upper end of blue line) was placed in the branch (E). Finally, the location of the blue line depicting the bifurcation angle was inspected and eventually adjusted in several oblique planes to ensure central placement in the vessels at all locations (F). For measurement of the second angle at the same bifurcation, the defined points in the parent vessel and the bifurcation were kept fixed while the cursor was appropriately placed in the second branch. optimality principle of minimum work was initially described by Murray. 8 This theory has been developed and applied to the cerebral circulation. 10,12,13,20 The relationship between blood flow rate (f) and internal vessel radius (r) is expressed as f = kr n, where k is a constant involving blood viscosity and the metabolic cost per unit volume for maintenance of the blood and vessel wall tissue, and the junction exponent (n) is an indirect measure of the division of flow at the bifurcation. The junction exponent n is defined by the equation r 0n = r 1n r 2n. (1) According to Rosen, 10 in the theoretically optimal situation, n = 3. The optimal branch angles can also be determined. In a symmetrical situation in which both branches have the same radius and form the same angle with the parent artery, the optimal angle can be expressed as cos = (r ba /r pa ) 4, where r ba is the radius of the branches and r pa is the radius of the parent artery. In a nonsymmetrical situation (Fig. 1), the optimal branch angles 1 and 2 are calculated using the equations cos 1 = (r 04 r 14 r 24 ) (2r 02 r 12 ) 1 and (2) cos 2 = (r 04 r 24 r 14 ) (2r 02 r 22 ) 1. (3) Deviation from this optimum will increase the energy impacting on the arterial wall at this point. This can be readily understood when TABLE 1 Geometric characteristics of 107 intracranial artery bifurcations* Bifurcation of Geometric Characteristic ICA (52 vessels) BA (8 vessels) MCA (47 vessels) p Value radius (mm) parent vessel r largest branch r smallest branch r area ratio (º) (º) junction exponent * Continuous values are expressed as means SD. Probability values are calculated from one-way ANOVA for all variables except the junction exponent, which was analyzed with the Kruskal Wallis test. Abbreviations: 1 = observed angle between the parent vessel and the largest branch; 2 = observed angle between the parent vessel and the smallest branch. The junction exponent could not be calculated for four bifurcations in which r 0 was less than or equal to r

4 Bifurcation geometry in cerebral artery aneurysms TABLE 2 Characteristics of intracranial artery bifurcations in eight patients with normal results on angiograms and 47 patients with aneurysms* Patients w/ Patients w/ Aneurysms Normal Results: Variable Bifs w/o Aneurysms Bifs w/o Aneurysms Bifs w/ Aneurysms p Value no. of vessels (º) difference 1 1 (º) (º) difference 2 2 (º) junction exponent * Continuous values are expressed as means SD. Probability values are calculated from one-way ANOVA for all variables except the junction exponent, which was analyzed with the Kruskal Wallis test. Abbreviations: bifs = bifurcations; 1 = predicted optimal angle between the parent vessel and the largest branch; 2 = predicted optimal angle between the parent vessel and the smallest branch. Values are given as the means from 50 bifurcations (eight in patients with normal results on angiography, 34 without lesions in patients who had aneurysms in other locations, and eight with aneurysms) in which optimal angles could be determined. The junction exponent could not be calculated for four bifurcations in which the radius of the largest branch was larger or equal to that of the parent vessel. considering a normal cerebral angiogram with a branch point that takes off at an almost perpendicular angle to the parent artery (for example, the lenticulostriate arteries). In this case, cos (nearing cos 90 ) approaches 0, indicating that for optimal work minimization the branch arteries must have very small radii. In comparison, with continuation of a parent artery in a straight line, cos (nearing cos 180 ) approaches 1, and the branch must have nearly the same radius as the parent artery. We used MATLAB software (release 6.5; The MathWorks, Inc., Natick, MA) and solved Equation 1 for n by bisection with inverse quadratic interpolation. Equations 2 and 3 were solved for 1 and 2. The differences 1 1 and 2 2 between the predicted optimal and the observed angles and the junction exponent were used as measures of deviation from optimum bifurcation geometry. Statistical Methods The means with normal distributions were compared using t-tests or one-way ANOVA including post hoc analysis with the Gabriel test, and the means with skewed distributions were compared using the Kruskal Wallis test. Comparisons of proportions were performed using the chi-square test for trends, or the Fisher exact test for small samples (expected count in one cell 5). The relationship between continuous variables was assessed using correlation analysis. Data analysis also included backward multilevel logistic regression to analyze factors associated with the presence of aneurysms. Only factors significant in univariate analysis were allowed to enter. Probability values are two-tailed; software purchased from SPSS, Inc., Chicago, IL (SPSS release 10.0) was used for these calculations. Results Baseline Parameters We analyzed 107 bifurcations (mean 1.9 per patient). The mean range for the eight measurements of diameter at each location was 0.4 mm (95% CI mm). The mean difference in bifurcation angle between the two observers was 3 (95% CI 1 to 7 ; p = 0.147, paired samples t-test). The interobserver correlation was highly significant (p 0.001), with an intraclass correlation coefficient (Cronbachs ) of 0.94 (95% CI ). Table 1 shows significant differences between the ICA, BA, and MCA bifurcations with respect to the mean vessel radii, the mean area ratio, and observed bifurcation angles. The radii were larger, the area ratio smaller, and the angle between the parent vessel and the smallest branch was larger at the ICA bifurcations compared with the MCA bifurcations. Optimality in Relation to Anatomical Location The mean junction exponent was (mean SD) for bifurcations beyond the circle of Willis (that is, MCA bifurcations; Table 1); this is close to the theoretical optimum of 3. The mean junction exponent was and (mean SD) for bifurcations within the circle of Willis (that is, ICA and BA bifurcations, respectively; Table 1). This is significantly less than the theoretical optimum. The optimal angles could be determined according to Equations 2 and 3 in 50 (47%) of the 107 bifurcations. They clearly cannot be determined when the calculated value for cos is not between 1 and 1. This occurred in a significantly smaller proportion (p 0.001, chi-square test for trends) of the MCA bifurcations (10 [21%] of 47) compared with the ICA (41 [79%] of 52) and BA bifurcations (six [75%] of eight). The predicted angles were generally smaller than the observed ones, both for the largest (mean 31 25) and the smallest branch (mean 34 25) (mean SD) at all locations. The observed angles were scattered widely around the predicted optimal angles with no significant correlation for either the largest (r = 0.058) or the smallest branch (r = 0.129). Optimality in Bifurcations With and Without Aneurysms Aneurysms were detected in 14 (13%) of the 107 bifurcations that were analyzed with respect to geometric characteristics. Table 2 shows characteristics for bifurcations in patients with normal results on angiograms, bifurcations without aneurysms in patients with aneurysms at other locations, and bifurcations with aneurysms. There were significant differences among groups with respect to the mean observed bifurcation angles and the mean differences between predicted optimal and observed angles. The mean junction exponents and vessel radii were not significantly different among the groups. In a multilevel multivariate logistic regression analysis, only the observed angles were significant predictors for the presence of an aneurysm. Table 3 shows ORs for tertiles of 111

5 T. Ingebrigtsen, et al. TABLE 3 Independent predictors for the presence of an aneurysm in 107 intracranial artery bifurcations* Variable OR (95% CI) for an Aneurysm tertiles of 1 (º) (reference) ( ) ( ) tertiles of 2 (º) (reference) ( ) ( ) * Odds ratios are derived from three-level multivariate logistic regression with backward elimination, with probability values greater than 0.05 as exclusion criteria, adjusted for location of bifurcation. the angles. The magnitude of the ORs, but not their significance or direction, was enhanced by adjusting for location of the bifurcation, thus acknowledging the differences in branch angles among the three locations. There were no significant interactions between the variables in the model. Angles between the parent vessel and the largest branch in the middle tertile reduced the risk of aneurysms, whereas angles in the highest tertile increased the risk, implying a J-shaped relation. For the angle between the parent vessel and the smallest branch, there was a stepwise increase in the risk of aneurysms for increasing tertiles. The receiver operating characteristic area for the model was 0.8. Discussion There is no previous study in which 3D DS angiography has been used to determine geometrical characteristics of bifurcations in cerebral arteries. Theoretically, measurements of vessel dimensions obtained using 3D DS angiography multiplanar volume reconstruction are more accurate than those performed manually on regular 2D DS angiography images. The computer software allows registration with an accuracy of 0.1 mm. The effect of image distortion has recently been assessed in two studies in which measurement errors within 0.5 and 0.8 mm, respectively, were found. 1,2 Our observations indicate an intraobserver repeatability of 0.4 mm. Accordingly, the total measurement error is likely to be approximately 0.5 mm. This is unlikely to influence the mean values for vessel dimensions in our study. The main advantage of 3D DS angiography is that any angle can be measured within the 3D volume; previous studies have been restricted to vessels located approximately in the sagittal plane. 11 In addition, angle measurements may be observer dependent (for example, when there is a curved course of the vessel). Our observations indicate an interobserver variation within 3, which is much smaller than the differences that are considered significant. Previous studies indicate that vessel calibers are optimized according to the theoretical Equation 1. 5,13 Nevertheless, branch angles scatter widely around the theoretical optimum of Equations 2 and 3. The wide scatter of branch angles is confirmed in our study. Rossitti and Löfgren 13 reported that bifurcations in normal cerebral angiograms have a mean area ratio of and a mean junction exponent of (mean SD). They included bifurcations of parent and branch segments of the ICA, MCA, and ACA, but not the distal bifurcations of the ICA and BA (S Rossitti, personal communication, 2003). Our observations of the MCA correspond to those made by Rossitti and Löfgren, and are in agreement with optimality principles. The distal bifurcations of the ICA and BA showed significantly smaller area ratios and junction exponents compared with the MCA. Most (79 and 75%, respectively) of the observations for the ICA and BA bifurcations were so extreme that optimal angles could not be predicted. This indicates a deviation from established optimality principles. The unique anatomy of the circle of Willis may explain this: a confluence of hemodynamic forces with the combination of flow from three vessels (both ICAs and the BA) is anatomically significantly different from the normal branching nature addressed by the optimality principle. Accordingly, bifurcations in the circle of Willis may follow optimality principles not yet established. Kasuya, et al., 6 used 3D computerized tomography angiography to study anterior communicating artery complexes, and found that aneurysms were associated with increased angles between the directions of flow in the A 1 and A 2 segments. We also observed significantly larger branch angles in bifurcations with aneurysms compared with those with no lesion. Furthermore, the difference between predicted optimal and observed angles for the largest branch was significantly increased at bifurcations with aneurysms. Nevertheless, the logistic regression showed that only the observed angles were independent predictors for the presence of an aneurysm. These findings support the hypothesis that bifurcation geometry plays a role in the formation of saccular aneurysms. This may be considered paradoxical given the wide scatter of observed angles around the predicted angles. Studies by Zamir and Bigelow 20 indicate that considerable deviations from optimum angles involve relatively low (2 5%) increases in energy cost. Nevertheless, only a small increase in shear stress (caused by unfavorable bifurcation geometry) may be sufficient to initiate aneurysm formation once a disruption of the internal elastic lamina has occurred. The mean junction exponent did not predict aneurysms in our study. Rossitti 11 analyzed bifurcations in patients with aneurysms in the distal ACA and in those with normal results on angiographic studies. He pooled all observations for each patient and found slightly lower mean junction exponents in patients with aneurysms. This author also estimated shear stress by a mathematical method based on junction exponents and vessel radii and reported slightly increased shear stress patients with aneurysms. Analysis of our data with the same methods (not reported) revealed no such differences. Monte Carlo simulations (not reported) show that estimates of the junction exponent are critically dependent on the measurement noise. With increasing noise, the junction exponent becomes gradually more skewed, with significant bias if the measurement error for vessel radii is 0.1 mm or larger. Accordingly, attempts to estimate shear stress on the basis of analysis of angiographic studies may not be valid. More advanced methods, such as biquintic finite element interpolation, may be necessary for estimation of stress at intracranial arterial bifurcations

6 Bifurcation geometry in cerebral artery aneurysms This method can be used for exact analysis of lumen geometry and flow dynamics, which is essential for providing hemodynamic information that may predict growth and rupture of an individual aneurysm. 7,17 Conclusions The bifurcation beyond the circle of Willis (that is, the MCA) closely approximated optimality principles, whereas the bifurcations within the circle of Willis (that is, the distal ICA and BA) did not. This indicates that the confluence of hemodynamic forces plays an important role in the distribution of work at bifurcations within the circle of Willis. In addition, the observed branch angles were predictors for the presence of aneurysms. Disclaimer The authors have no financial interest in the radiological equipment or software used in this study. References 1. Anxionnat R, Bracard S, Ducrocq X, et al: Intracranial aneurysms: clinical value of 3D digital subtraction angiography in the therapeutic decision and endovascular treatment. Radiology 218: , Bridcut RR, Winder RJ, Workman A, et al: Assessment of distortion in a three-dimensional rotational angiography system. Br J Radiol 75: , Ferguson GG: Physical factors in the initiation, growth, and rupture of human intracranial saccular aneurysms. J Neurosurg 37: , Forbus WD: On the origin of miliary aneurysms of the superficial cerebral arteries. Bull Johns Hopkins Hosp 47: , Hutchins GM, Miner MM, Boitnott JK: Vessel caliber and branchangle of human coronary artery branch-points. Circ Res 38: , Kasuya H, Shimizu T, Nakaya K, et al: Angles between A1 and A2 segments of the anterior cerebral artery visualized by three-dimensional computed tomographic angiography and association of anterior communicating artery aneurysms. Neurosurgery 45: 89 94, Kerber CW, Hecht ST, Knox K, et al: Flow dynamics in a fatal aneurysm of the basilar artery. AJNR 17: , Murray CD: The physiological principle of minimum work applied to the angle of branching of arteries. J Gen Physiol 9: , Roach MR, Scott S, Ferguson GG: The hemodynamic importance of the geometry of bifurcations in the circle of Willis (glass model studies). Stroke 3: , Rosen R: Optimality Principles in Biology. London: Butterworths, 1967, pp Rossitti S: Shear stress in cerebral arteries carrying saccular aneurysms. A preliminary study. Acta Radiol 39: , Rossitti S, Löfgren J: Optimality principles and flow orderliness at the branching points of cerebral arteries. Stroke 24: , Rossitti S, Löfgren J: Vascular dimensions of the cerebral arteries follow the principle of minimum work. Stroke 24: , Schueler BA, Sen A, Hsiung HH, et al: Three-dimensional vascular reconstruction with a clinical x-ray angiography system. Acad Radiol 4: , Smith DB, Sacks MS, Vorp DA, et al: Surface geometric analysis of anatomic structures using biquintic finite element interpolation. Ann Biomed Eng 28: , Stehbens WE: Etiology of intracranial berry aneurysms. J Neurosurg 70: , Steinman DA, Milner JS, Norley CJ, et al: Image-based computational simulation of flow dynamics in a giant intracranial aneurysm. AJNR 24: , Sugahara T, Korogi Y, Nakashima K, et al: Comparison of 2D and 3D digital subtraction angiography in evaluation of intracranial aneurysms. AJNR 23: , Ujiie H, Liepsch DW, Goetz M, et al: Hemodynamic study of the anterior communicating artery. Stroke 27: , Zamir M, Bigelow DC: Cost of departure from optimality in arterial branching. J Theor Biol 109: , 1984 Manuscript received August 11, Accepted in final form March 1, Dr. T. Ingebrigtsen was supported by a research grant from the University Hospital of North Norway. Address reprint requests to: Tor Ingebrigtsen, Ph.D., Department of Neurosurgery, University Hospital of North Norway, N-9038 Tromsø, Norway. tor.ingebrigtsen@unn.no. 113