Research Papers

Endothelial Nitric Oxide Synthase and Calcium Production in Arterial Geometries: An Integrated Fluid Mechanics/Cell Model

[+] Author and Article Information
A. Comerford

Centre for Bioengineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

M. J. Plank

Centre for Bioengineering, University of Canterbury, Christchurch, New Zealand; Department of Mathematics, University of Canterbury, Christchurch, New Zealand

T. David

Centre for Bioengineering, University of Canterbury, Christchurch, New Zealandtim.david@canterbury.ac.nz

J Biomech Eng 130(1), 011010 (Feb 11, 2008) (13 pages) doi:10.1115/1.2838026 History: Received April 10, 2006; Revised May 14, 2007; Published February 11, 2008

It is well known that atherosclerosis occurs at very specific locations throughout the human vasculature, such as arterial bifurcations and bends, all of which are subjected to low wall shear stress. A key player in the pathology of atherosclerosis is the endothelium, controlling the passage of material to and from the artery wall. Endothelial dysfunction refers to the condition where the normal regulation of processes by the endothelium is diminished. In this paper, the blood flow and transport of the low diffusion coefficient species adenosine triphosphate (ATP) are investigated in a variety of arterial geometries: a bifurcation with varying inner angle, and an artery bend. A mathematical model of endothelial calcium and endothelial nitric oxide synthase cellular dynamics is used to investigate spatial variations in the physiology of the endothelium. This model allows assessment of regions of the artery wall deficient in nitric oxide (NO). The models here aim to determine whether 3D flow fields are important in determining ATP concentration and endothelial function. For ATP transport, the effects of a coronary and carotid wave form on mass transport is investigated for low Womersley number. For the carotid, the Womersley number is then increased to determine whether this is an important factor. The results show that regions of low wall shear stress correspond with regions of impaired endothetial nitric oxide synthase signaling, therefore reduced availability of NO. However, experimental work is required to determine if this level is significant. The results also suggest that bifurcation angle is an important factor and acute angle bifurcations are more susceptible to disease than large angle bifurcations. It has been evidenced that complex 3D flow fields play an important role in determining signaling within endothelial cells. Furthermore, the distribution of ATP in blood is highly dependent on secondary flow features. The models here use ATP concentration simulated under steady conditions. This has been evidenced to reproduce essential features of time-averaged ATP concentration over a cardiac cycle for small Womersley numbers. However, when the Womersley number is increased, some differences are observed. Transient variations are overall insignificant, suggesting that spatial variation is more important than temporal. It has been determined that acute angle bifurcations are potentially more susceptible to atherogenesis and steady-state ATP transport reproduces essential features of time-averaged pulsatile transport for small Womersley number. Larger Womersley numbers appear to be an important factor in time-dependent mass transfer.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Example geometries with mesh overlain: (a) bifurcation, (b) bend, and (c) mesh slice

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Figure 2

Comparison of the numerical solution of low diffusion coefficient species against the classic Graetz–Nusselt analytical solution (developing mass transfer boundary layer in a pipe)

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Figure 3

Pulsatile inlet wave forms, carotid wave form given by Ku (25), and coronary wave form given by Matsuo (26)

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Figure 4

WSS plotted along a cut plane through the outer wall of the bifurcation; (a) Re=200 and (b) Re=500. The minimum WSS decreases as θ decreases.

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Figure 5

ATP contours with limiting streamlines overlain, θ=75deg, Re=500. This is a perspective view looking at the outer wall where the streamlines converge on the outer wall corresponds with minimum ATP concentration (hence mass transfer); as the bifurcation angle is reduced, this region expands undergoing further depletion (data not shown).

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Figure 6

Nucleotide concentration along the outer wall of the 75deg bifurcation, Re=500: (a) ATP, ADP, and ATP+ADP concentration for τ0=3.16. (b) ATP+ADP concentration for different ATP release rates. It is clear that the outer wall of the bifurcation is subject to reduced combined nucleotide concentration relative to other regions.

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Figure 7

Contours of eNOS concentration, Re=500: (a) θ=37.5deg, (b) θ=75deg, and (c) θ=135deg regions of impaired eNOS signaling increase with decreasing θ

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Figure 8

Endothelial NOS concentration plotted along a cut plane through the outer wall of the bifurcation, Re=500. As the bifurcation angle reduces, the region of depleted eNOS concentration is more sustained. The small rise in the reduced eNOS region at θ=37.5deg results from the flow recirculation occurring in this area.

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Figure 9

WSS plotted along a cut plane through the walls of the bend, Re=300 and 500: (a) inner wall and (b) outer wall. Essentially, the elevated Reynolds number provides for amplified responses.

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Figure 10

Nucleotide concentration under slow release conditions plotted along the inner wall of the arterial bend, Re=500. The location of minimum nucleotide concentration corresponds to the flow reattachment point.

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Figure 11

Contours of eNOS concentration: (a) Re=300 and (b) Re=500. Reduced eNOS signaling is observed at the inner and outer walls, which will result in reduced production of NO. The regions of reduced signaling are more significant at the lower Reynolds number.

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Figure 12

Endothelial NOS concentration plotted along the central axis of the arterial bend walls, Re=300 and 500: (a) inner wall and (b) outer wall. Endothelial NOS concentration is low in the regions corresponding to low WSS.

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Figure 13

ATP concentration in steady flow and time-averaged concentration in pulsatile flow plotted along medial planes of the inner wall of the bend and the outer wall of the bifurcation: (a) outer wall bifurcation, (b) outer wall bifurcation with ATP release, and (c) bend. Evidently, the steady state exhibits essential features of the time-averaged profile.

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Figure 14

Comparison of Wo for carotid wave form. For the larger Wo, the ATP concentration plateaus in the daughter artery and then increases in the streamwise direction.

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Figure 15

Time variations in ATP concentration for different flow wave forms: (a) sampling locations on the bifurcation and the bend (looking at the inner wall), (b) bifurcation with carotid wave form, (c) bifurcation with coronary wave form, and (d) bend with coronary wave form

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Figure 16

Time variation of over (a) ATP and (b) WSS plotted along the inner wall varying over time. Data record every five time steps.



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