0
Research Papers

Recruitment Pattern in a Complete Cerebral Arterial Circle

[+] Author and Article Information
Christine L. de Lancea

UC High Performance Computing,
University of Canterbury,
Christchurch, Canterbury 8041, New Zealand
e-mail: christine.l.french@hotmail.com

Tim David

Professor
Mem. ASME
UC High Performance Computing,
University of Canterbury,
Christchurch, Canterbury 8041, New Zealand
e-mail: tim.david@canterbury.ac.nz

Jordi Alastruey

Department of Biomedical Engineering,
Division of Imaging Sciences
and Biomedical Engineering,
King's College London,
King's Health Partners,
St. Thomas' Hospital,
London SE1 7EH, United Kingdom
e-mail: jordi.alastruey-arimon@kcl.ac.uk

Richard G. Brown

Institute of Fundamental Sciences,
Massey University,
Palmerston North, Manawatu-Wanganui 4474,
New Zealand
e-mail: r.g.brown@massey.ac.nz

Manuscript received March 19, 2015; final manuscript received August 24, 2015; published online September 18, 2015. Assoc. Editor: Alison Marsden.

J Biomech Eng 137(11), 111004 (Sep 18, 2015) (11 pages) Paper No: BIO-15-1122; doi: 10.1115/1.4031469 History: Received March 19, 2015; Revised August 24, 2015

Blood flow through a vessel depends upon compliance and resistance. Resistance changes dynamically due to vasoconstriction and vasodilation as a result of metabolic activity, thus allowing for more or less flow to a particular area. The structure responsible for directing blood to the different areas of the brain and supplying the increase flow is the cerebral arterial circle (CAC). A series of 1D equations were utilized to model propagating flow and pressure waves from the left ventricle of the heart to the CAC. The focus of the current research was to understand the collateral capability of the circle. This was done by decreasing the peripheral resistance in each of the efferent arteries, up to 10% both unilaterally and bilaterally. The collateral patterns were then analyzed. After the initial 60 simulations, it became apparent that flow could increase beyond the scope of a 10% reduction and still be within in vivo conditions. Simulations with higher percentage decreases were performed such that the same amount of flow increase would be induced through each of the efferent arteries separately, same flow tests (SFTs), as well as those that were found to allow for the maximum flow increase through the stimulated artery, maximum flow tests (MFTs). The collateral pattern depended upon which efferent artery was stimulation and if the stimulation was unilaterally or bilaterally induced. With the same amount of flow increase through each of the efferent arteries, the MCAs (middle cerebral arteries) had the largest impact on the collateral capability of the circle, both unilaterally and bilaterally.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Moritz, A. , Koci, G. , Steinlechner, B. , Hölzenbein, T. , Nasel, C. , Grubhofer, G. , and Dworschak, M. , 2007, “ Contralateral Stroke During Carotid Endarterectomy Due to Abnormalities in the Circle of Willis,” Middle Eur. J. Med., 119(21–22), pp. 669–673.
Dormanns, K. , van Disseldorp, E. , Brown, R. , and David, T. , 2015, “ Neurovascular Coupling and the Influence of Luminal Agonists Via the Endothelium,” J. Theor. Biol., 364, pp. 49–70. [CrossRef] [PubMed]
Farr, H. , 2012, “ Autoregulation of the Human Cerebrovasculature by Neurovascular Coupling or a Collection of Stories About Mathematics and the Mind,” Ph.D. thesis, University of Canterbury, Christchurch, NZ.
Filosa, J. A. , Bonev, A. D. , and Nelson, M. T. , 2004, “ Calcium Dynamics in Cortical Astrocytes and Arterioles During Neurovascular Coupling,” Circ. Res., 95(10), pp. e73–e81. [CrossRef] [PubMed]
Iadecola, C. , 2004, “ Neurovascular Regulation in the Normal Brain and in Alzheimer's Disease,” Nat. Rev. Neurosci., 5(5), pp. 347–360. [CrossRef] [PubMed]
Willie, C. K. , Cowan, E. C. , Ainslie, P. N. , Taylor, C. E. , Smith, K. J. , Sin, P. Y. W. , and Tzeng, Y. C. , 2011, “ Neurovascular Coupling and Distribution of Cerebral Blood Flow During Exercise,” J. Neurosci. Methods, 198(2), pp. 270–273. [CrossRef] [PubMed]
Thakker, B. , and Vyas, A. L. , 2011, “ Pulse Classifier for Suppressed Dicrotic Notch Pulse,” Int. J. Mach. Comput., 1(2), pp. 148–153.
Alastruey, J. , Parker, K. H. , Peiró, J. , Byrd, S. M. , and Sherwin, S. J. , 2007, “ Modeling the Circle of Willis to Assess the Effects of Anatomical Variations and Occlusions on Cerebral Flows,” J. Biomech., 40(8), pp. 1794–1805. [CrossRef] [PubMed]
Anzola, G. P. , Gasparotti, R. , Magoni, M. , and Prandini, F. , 1995, “ Transcranial Doppler Sonography and Magnetic Resonance Angiography in the Assessment of Collateral Hemispheric Flow in Patients With Carotid Artery Disease,” Stroke, 26(2), pp. 214–217. [CrossRef] [PubMed]
Baumgartner, R. W. , Baumgartner, I. , Mattle, H. P. , and Schroth, G. , 1997, “ Transcranial Color-Coded Duplex Sonography in the Evaluation of Collateral Flow Through the Circle of Willis,” Am. J. Neuroradiol., 18(1), pp. 127–133.
Cassot, F. , Vergeur, V. , Bossuet, P. , Hillen, B. , Zagzoule, M. , and Marc-Vergnes, J.-P. , 1995, “ Effects of Anterior Communicating Artery Diameter on Cerebral Hemodynamics in Internal Carotid Artery Disease: A Model Study,” Circulation, 92(10), pp. 3122–3131. [CrossRef] [PubMed]
Derdeyn, C. P. , Videen, T. O. , Fritsch, S. M. , Carpenter, D. A. , Grubb, R. L. , and Powers, W. J. , 1999, “ Compensatory Mechanisms for Chronic Cerebral Hypoperfusion in Patients With Carotid Occlusion,” Stroke, 30(5), pp. 1019–1024. [CrossRef] [PubMed]
Fahy, P. , Malone, F. , McCarthy, E. , McCarthy, P. , Thornton, J. , Brennan, P. , O'Hare, A. , Looby, S. , Sultan, S. , Hynes, N. , and Morris, L. , 2015, “ An In Vitro Evaluation of Emboli Trajectories Within a Three-Dimensional Physical Model of the Circle of Willis Under Cerebral Blood Flow Conditions,” Ann. Biomed. Eng., 43(9), pp. 2265–2278. [CrossRef] [PubMed]
Haripriya, M. , and Melani, R. S. , 2010, “ A Study of the Anatomical Variations of the Circle of Willis Using Magnetic Resonance Imaging,” Int. J. Anat. Sci., 1, pp. 21–25.
Sherwin, S. J. , Willemet, M. , and Alastruey, J. , 2014, Nektar1D Reference Manual, Department of Aeronautics, Imperial College, London.
Xiao, N. , Alastruey, J. , and Figueroa, A. C. , 2014, “ A Systematic Comparison Between 1-D and 3-D Hemodynamics in Compliant Arterial Models,” Int. J. Numer. Methods Biomed. Eng., 30(2), pp. 204–231. [CrossRef]
Alastruey, J. , Khir, A. W. , Matthys, K. S. , Segers, P. , Sherwin, S. J. , Verdonck, P. R. , Parker, K. H. , and Peiró, J. , 2011, “ Pulse Wave Propagation in a Model Human Arterial Network: Assessment of 1-D Visco-Elastic Simulations Against In Vitro Measurements,” J. Biomech., 44(12), pp. 2250–2258. [CrossRef] [PubMed]
Alastruey, J. , Parker, K. H. , Peir, J. , and Sherwin, S. J. , 2009, “ Analysing the Pattern of Pulse Waves in Arterial Networks: A Time-Domain Study,” J. Eng. Math., 64(4), pp. 331–351. [CrossRef]
Sherwin, S. J. , Formaggia, L. , Peiro, J. , and Franke, V. , 2003, “ Computational Modelling of 1D Blood Flow With Variable Mechanical Properties and Its Application to the Simulation of Wave Propagation in the Human Arterial System,” Int. J. Numer. Methods Fluids, 43(6–7), pp. 673–700. [CrossRef]
Stergiopulos, N. , Young, D. F. , and Rogge, T. R. , 1992, “ Computer Simulation of Arterial Flow With Applications to Arterial and Aortic Stenoses,” J. Biomech., 25(12), pp. 1477–1488. [CrossRef] [PubMed]
Fahrig, R. , Nikolov, H. , Fox, A. J. , and Holdsworth, D. W. , 1999, “ A Three-Dimensional Cerebrovascular Flow Phantom,” Med. Phys., 26(8), pp. 1589–1599. [CrossRef] [PubMed]
Moore, S. M. , Moorhead, K. T. , Chase, J. G. , David, T. , and Fink, J. , 2005, “ One-Dimensional and Three-Dimensional Models of Cerebrovascular Flow,” ASME J. Biomech. Eng., 127(3), pp. 440–449. [CrossRef]
Kelley, R. E. , Chang, J. Y. , Scheinman, N. J. , Levin, B. E. , Duncan, R. C. , and Lee, S. C. , 1992, “ Transcranial Doppler Assessment of Cerebral Flow Velocity During Cognitive Tasks,” Stroke, 23(1), pp. 9–14. [CrossRef] [PubMed]
Linkis, P. , Jorgensen, L. G. , Olesen, H. L. , Madsen, P. L. , Lassen, N. A. , and Secher, N. H. , 1994, “ Dynamic Exercise Enhances Regional Cerebral Artery Mean Flow Velocity,” J. Appl. Physiol., 78(1), pp. 12–16.
Madsen, P. L. , Sperling, B. K. , Warming, T. , Schmidt, J. F. , Secher, N. H. , Wildschiødtz, G. , Holm, S. , and Lassen, N. A. , 1993, “ Middle Cerebral Artery Blood Velocity and Cerebral Blood Flow and O2 Uptake During Dynamic Exercise,” J. Appl. Physiol., 74(1), pp. 245–250. [PubMed]
Spelsberg, B. , Bohning, A. , Kompf, D. , and Kessler, C. , 1998, “ Visually Induced Reactivity in Posterior Cerebral Artery Blood Flow,” J. Neuro-Ophthalmol., 18(4), pp. 263–267. [CrossRef]
Urban, P. P. , Allardt, A. , Tettenborn, B. , Hopf, H. C. , Pfennigsdorf, S. , and Lieb, W. , 1995, “ Photoreactive Flow Changes in the Posterior Cerebral Artery in Control Subjects and Patients With Occipital Lobe Infarction,” Stroke, 26(10), pp. 1817–1819. [CrossRef] [PubMed]
Devault, K. , Gremaud, P. A. , Novak, V. , Olufsen, M. S. , Vernieres, G. , and Zhao, P. , 2008, “ Blood Flow in the Circle of Willis: Modeling and Calibration,” Multiscale Model. Simul., 7(2), pp. 888–909. [CrossRef] [PubMed]
Hartkamp, M. J. , van Der Grond, J. , van Everdingen, K. J. , Hillen, B. , and Mali, W. P. , 1999, “ Circle of Willis Collateral Flow Investigated by Magnetic Resonance Angiography,” Stroke, 30(12), pp. 2671–2678. [CrossRef] [PubMed]
Hoksbergen, A. W. J. , Majoie, C. B. L. , Hulsmans, F.-J. H. , and Legemate, D. A. , 2003, “ Assessment of the Collateral Function of the Circle of Willis: Three-Dimensional Time-of-Flight MR Angiography Compared With Transcranial Color-Coded Duplex Sonography,” Am. J. Neuroradiol., 24(3), pp. 456–462.
Kim, C. S. , 2007, “ Numerical Simulation of Auto-Regulation and Collateral Circulation in the Human Brain,” J. Mech. Sci. Technol., 21(3), pp. 525–535. [CrossRef]
Sushma, R. K. , D'Souza, A. S. , and Bhat, K. M. R. , 2014, “ Fetal and Primitive Type of Circle of Willis With Unilateral Trifurcation of Internal Carotid Artery,” Med. Science, 3(3), pp. 1530–1537.
Razavi, S. E. , and Sahebjam, R. , 2014, “ Numerical Simulation of the Blood Flow Behavior in the Circle of Willis,” Bioimpacts, 4(2), pp. 89–94. [PubMed]
Viedma, A. , Jimenez-Ortiz, C. , and Marco, V. , 1997, “ Extended Willis Circle Model to Explain Clinical Observations in Periorbital Arterial Flow,” J. Biomech., 30(3), pp. 265–272. [CrossRef] [PubMed]
Amini, R. , Gornik, H. L. , Gilbert, L. , Whitelaw, S. , and Shishehbor, M. , 2011, “ Bilateral Subclavian Steal Syndrome,” Case Reports Cardiol., 2011, p. 146267. [CrossRef]

Figures

Grahic Jump Location
Fig. 3

Depicts the vessels used in the simulations. Numbers correlate with Table 1. Arrows indicate positive flow in the communicating arteries. Based on the work by Alastruey et al. [8].

Grahic Jump Location
Fig. 6

Percentages of flow increase are shown at each decrease of the peripheral resistance values, indicated by the percentage in the boxes. Since a 1% did not yield notable flow, the schematic was used to denote the vessel with the decreasing R2, highlighted by the circle, and collateral pathways. R—right, L—left, solid line—vessels that express notable flow change with a R2 decrease of up to 5%, rounded dashed line up to a 10% decrease.

Grahic Jump Location
Fig. 7

Percentages of flow increase are shown at each decrease of the peripheral resistance values, indicated by the percentage in the boxes. Since a 1% did not yield notable flow, the schematic was used to denote the vessels with the decreasing R2, highlighted by the circles, and collateral pathways. R—right, L—left, solid line—vessels that express notable flow change with a R2 decrease of up to 5%, rounded dashed line up to a 10% decrease.

Grahic Jump Location
Fig. 2

A three-element Windkessel utilized in Eq. (9), where the pressure at the terminal end of an artery—p1D—is used to match that of the pressure of the truncated vessels. Q1D—volumetric flow, pv—venous pressure, R1—characteristic impedance, C—compliance, R2—peripheral resistance, top arrows—flow.

Grahic Jump Location
Fig. 1

Demonstrates an example of the flow (top four figures) and pressure (bottom four) wave profiles. These are from a unilateral R2 decrease of 10% in the right ACA shown by dashed line against the control with no reductions, solid line. A dicrotic notch indicated by arrow.

Grahic Jump Location
Fig. 4

Percentages of flow increase are shown at each decrease of the peripheral resistance values, indicated by the percentage in the boxes. Since a 1% did not yield notable flow, the schematic was used to denote the vessel with the decreasing R2, highlighted by the circle, and collateral pathways. R—right, L—left, solid line—vessels that express notable flow change with a R2 decrease of up to 5%, rounded dashed line up to a 10% decrease.

Grahic Jump Location
Fig. 5

Percentages of flow increase are shown at each decrease of the peripheral resistance values, indicated by the percentage in the boxes. Since a 1% did not yield notable flow, the schematic was used to denote the vessels with the decreasing R2, highlighted by the circles, and collateral pathways. R—right, L—left, solid line—vessels that express notable flow change with a R2 decrease of up to 5%, rounded dashed line up to a 10% decrease.

Grahic Jump Location
Fig. 8

Percentages of flow increase are shown at each decrease of the peripheral resistance values, indicated by the percentage in the boxes. Since a 1% did not yield notable flow, the schematic was used to denote the vessel with the decreasing R2, highlighted by the circle, and collateral pathways. R—right, L—left, solid line—vessels that express notable flow change with a R2 decrease of up to 5%, rounded dashed line up to a 10% decrease.

Grahic Jump Location
Fig. 9

Percentages of flow increase are shown at each decrease of the peripheral resistance values, indicated by the percentage in the boxes. Since a 1% did not yield notable flow, the schematic was used to denote the vessels with the decreasing R2, highlighted by the circles, and collateral pathways. R—right, L—left, solid line—vessels that express notable flow change with a R2 decrease of up to 5%.

Grahic Jump Location
Fig. 10

Top shows the unilateral results and bottom shows the bilateral. The far left was used to denote the stimulated vessel, indicated by the circles, and collateral pathways. The middle indicates results from the SFTs: 0.27 cm3/s increase unilaterally and 0.49 cm3/s increase bilaterally. The right indicates the results from the MFTs: 0.28 cm3/s unilaterally and 0.54 cm3/s bilaterally. Percentages of R2 decrease are located in the boxes. R–right, L–left, solid line—vessels that express notable flow change with an R2 decrease of up to 5%, rounded dashed line up to a 10% decrease, squared dashed line decrease greater than 10%.

Grahic Jump Location
Fig. 11

Top shows the unilateral results and bottom shows the bilateral. The far left was used to denote the stimulated vessel, indicated by the circles, and collateral pathways. The middle indicates results from the SFTs: 0.27 cm3/s increase unilaterally and 0.49 cm3/s increase bilaterally. The right indicates the results from the MFTs: 0.36 cm3/s unilaterally and 0.62 cm3/s bilaterally. Percentages of R2 decrease are located in the boxes. R—right, L—left, solid line—vessels that express notable flow change with an R2 decrease of up to 5%, rounded dashed line up to a 10% decrease, squared dashed line decrease greater than 10%.

Grahic Jump Location
Fig. 12

Top shows the unilateral results and bottom shows the bilateral. The left was used to denote the stimulated vessel, indicated by the circles, and collateral pathways. The right indicates the results for the MFT, as this was used as the baseline for the SFT in the ACAs and MCAs reductions, 0.27 cm3/s unilaterally and 0.49 cm3/s bilaterally. Percentages of R2 decrease are located in the boxes. R—right, L—left, solid line—vessels that express notable flow change with an R2 decrease of up to 5%, rounded dashed line up to a 10% decrease, squared dashed line decrease greater than 10%.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In