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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.

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References

Figures

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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.

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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.

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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].

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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. 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. 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%.

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