Bifurcation geometry and the presence of cerebral artery aneurysms

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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 2.9 ± 1.2 (mean ± standard deviation [SD]), which is close to the theoretical optimum of 3, but it was significantly smaller (p < 0.001; 1.7 ± 0.8, 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 (1.02–11.74) 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 48.06 (9.7–238.2).

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.

Article Information

Address reprint requests to: Tor Ingebrigtsen, Ph.D., Department of Neurosurgery, University Hospital of North Norway, N-9038 Tromsø, Norway. email: tor.ingebrigtsen@unn.no.

© AANS, except where prohibited by US copyright law.

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Figures

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    Schematic drawing showing the measurements obtained from each arterial bifurcation: the radii from the parent vessel (r0), the largest branch (r1), and the smallest branch (r2); and the angles ϕ1 and ϕ2 formed between the parent vessel and the largest and smallest branch, respectively.

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    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).

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    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.

References

  • 1.

    Anxionnat RBracard SDucrocq Xet al: Intracranial aneurysms: clinical value of 3D digital subtraction angiography in the therapeutic decision and endovascular treatment. Radiology 218:7998082001Anxionnat R Bracard S Ducrocq X et al: Intracranial aneurysms: clinical value of 3D digital subtraction angiography in the therapeutic decision and endovascular treatment. Radiology 218:799–808 2001

    • Search Google Scholar
    • Export Citation
  • 2.

    Bridcut RRWinder RJWorkman Aet al: Assessment of distortion in a three-dimensional rotational angiography system. Br J Radiol 75:2662702002Bridcut RR Winder RJ Workman A et al: Assessment of distortion in a three-dimensional rotational angiography system. Br J Radiol 75:266–270 2002

    • Search Google Scholar
    • Export Citation
  • 3.

    Ferguson GG: Physical factors in the initiation, growth, and rupture of human intracranial saccular aneurysms. J Neurosurg 37:6666771972Ferguson GG: Physical factors in the initiation growth and rupture of human intracranial saccular aneurysms. J Neurosurg 37:666–677 1972

    • Search Google Scholar
    • Export Citation
  • 4.

    Forbus WD: On the origin of miliary aneurysms of the superficial cerebral arteries. Bull Johns Hopkins Hosp 47:2392841930Forbus WD: On the origin of miliary aneurysms of the superficial cerebral arteries. Bull Johns Hopkins Hosp 47:239–284 1930

    • Search Google Scholar
    • Export Citation
  • 5.

    Hutchins GMMiner MMBoitnott JK: Vessel caliber and branch-angle of human coronary artery branch-points. Circ Res 38:5725761976Hutchins GM Miner MM Boitnott JK: Vessel caliber and branch-angle of human coronary artery branch-points. Circ Res 38:572–576 1976

    • Search Google Scholar
    • Export Citation
  • 6.

    Kasuya HShimizu TNakaya Ket 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 45:89941999Kasuya 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 1999

    • Search Google Scholar
    • Export Citation
  • 7.

    Kerber CWHecht STKnox Ket al: Flow dynamics in a fatal aneurysm of the basilar artery. AJNR 17:141714211996Kerber CW Hecht ST Knox K et al: Flow dynamics in a fatal aneurysm of the basilar artery. AJNR 17:1417–1421 1996

    • Search Google Scholar
    • Export Citation
  • 8.

    Murray CD: The physiological principle of minimum work applied to the angle of branching of arteries. J Gen Physiol 9:8358411926Murray CD: The physiological principle of minimum work applied to the angle of branching of arteries. J Gen Physiol 9:835–841 1926

    • Search Google Scholar
    • Export Citation
  • 9.

    Roach MRScott SFerguson GG: The hemodynamic importance of the geometry of bifurcations in the circle of Willis (glass model studies). Stroke 3:2552671972Roach MR Scott S Ferguson GG: The hemodynamic importance of the geometry of bifurcations in the circle of Willis (glass model studies). Stroke 3:255–267 1972

    • Search Google Scholar
    • Export Citation
  • 10.

    Rosen R: Optimality Principles in Biology. London: Butterworths1967 pp 4159Rosen R: Optimality Principles in Biology. London: Butterworths 1967 pp 41–59

    • Search Google Scholar
    • Export Citation
  • 11.

    Rossitti S: Shear stress in cerebral arteries carrying saccular aneurysms. A preliminary study. Acta Radiol 39:7117171998Rossitti S: Shear stress in cerebral arteries carrying saccular aneurysms. A preliminary study. Acta Radiol 39:711–717 1998

    • Search Google Scholar
    • Export Citation
  • 12.

    Rossitti SLöfgren J: Optimality principles and flow orderliness at the branching points of cerebral arteries. Stroke 24:102910321993Rossitti S Löfgren J: Optimality principles and flow orderliness at the branching points of cerebral arteries. Stroke 24:1029–1032 1993

    • Search Google Scholar
    • Export Citation
  • 13.

    Rossitti SLöfgren J: Vascular dimensions of the cerebral arteries follow the principle of minimum work. Stroke 24:3713771993Rossitti S Löfgren J: Vascular dimensions of the cerebral arteries follow the principle of minimum work. Stroke 24:371–377 1993

    • Search Google Scholar
    • Export Citation
  • 14.

    Schueler BASen AHsiung HHet al: Three-dimensional vascular reconstruction with a clinical x-ray angiography system. Acad Radiol 4:6936991997Schueler BA Sen A Hsiung HH et al: Three-dimensional vascular reconstruction with a clinical x-ray angiography system. Acad Radiol 4:693–699 1997

    • Search Google Scholar
    • Export Citation
  • 15.

    Smith DBSacks MSVorp DAet al: Surface geometric analysis of anatomic structures using biquintic finite element interpolation. Ann Biomed Eng 28:5986112000Smith DB Sacks MS Vorp DA et al: Surface geometric analysis of anatomic structures using biquintic finite element interpolation. Ann Biomed Eng 28:598–611 2000

    • Search Google Scholar
    • Export Citation
  • 16.

    Stehbens WE: Etiology of intracranial berry aneurysms. J Neurosurg 70:8238311989Stehbens WE: Etiology of intracranial berry aneurysms. J Neurosurg 70:823–831 1989

    • Search Google Scholar
    • Export Citation
  • 17.

    Steinman DAMilner JSNorley CJet al: Image-based computational simulation of flow dynamics in a giant intracranial aneurysm. AJNR 24:5595662003Steinman DA Milner JS Norley CJ et al: Image-based computational simulation of flow dynamics in a giant intracranial aneurysm. AJNR 24:559–566 2003

    • Search Google Scholar
    • Export Citation
  • 18.

    Sugahara TKorogi YNakashima Ket al: Comparison of 2D and 3D digital subtraction angiography in evaluation of intracranial aneurysms. AJNR 23:154515522002Sugahara T Korogi Y Nakashima K et al: Comparison of 2D and 3D digital subtraction angiography in evaluation of intracranial aneurysms. AJNR 23:1545–1552 2002

    • Search Google Scholar
    • Export Citation
  • 19.

    Ujiie HLiepsch DWGoetz Met al: Hemodynamic study of the anterior communicating artery. Stroke 27:208620931996Ujiie H Liepsch DW Goetz M et al: Hemodynamic study of the anterior communicating artery. Stroke 27:2086–2093 1996

    • Search Google Scholar
    • Export Citation
  • 20.

    Zamir MBigelow DC: Cost of departure from optimality in arterial branching. J Theor Biol 109:4014091984Zamir M Bigelow DC: Cost of departure from optimality in arterial branching. J Theor Biol 109:401–409 1984

    • Search Google Scholar
    • Export Citation

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