A 2-D Model of Flow-Induced Alterations in the Geometry, Structure, and Properties of Carotid Arteries

[+] Author and Article Information
R. L. Gleason

Department of Biomedical Engineering, Texas A&M University, College Station, TX

L. A. Taber

Department of Biomedical Engineering, Washington University, St. Louis, MO

J. D. Humphrey

Department of Biomedical Engineering and M.E. DeBakey Institute, Texas A&M University, College Station, TX

J Biomech Eng 126(3), 371-381 (Jun 24, 2004) (11 pages) doi:10.1115/1.1762899 History: Received May 03, 2003; Revised December 03, 2003; Online June 24, 2004
Copyright © 2004 by ASME
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Grahic Jump Location
Primary states of interest in unloaded (traction-free) βo and physiologically-loaded (in vivo) βt configurations. Times s=0,sv,s∊(sv,sh), and sh respectively denote the original homeostatic state, initial vaso-altered state in response to an increase in flow to εQh, states during G&R at the sustained flow rate, and a final state wherein a homeostatic state is recovered. The λθ and λz denote total circumferential and axial stretches, respectively.
Grahic Jump Location
Illustration of the constrained mixture approach. βo represents the unloaded configuration of the mixture whereas βok represent the natural configurations of the individual constituents, each of which may differ. Similarly, βt and βtk represent the loaded configurations of the mixture and individual constituents, respectively.
Grahic Jump Location
Stress-stretch curve in the (a) θ-direction (λz=1.50), (b) z-direction (λθ=1.50), and (c) θ-direction (λz=1.00) for each constituent: elastin, collagen, and smooth muscle (active and passive), and the mixture (active and passive). Note: Ae/A=Le/L=0.85,Ac/A=1.192,Lc/L=1.125,Am/A=Lm/L=0.95,TB=550 kPa,λM=1.8,λ0=0.8,ϕf=0.70,ϕe=0.06,ϕc=0.15, and ϕm=0.09.
Grahic Jump Location
Example 1. Panel (a) circumferential stress and panel (b) axial stress versus G&R time for individual constituents and mixture (presented as differences from the initial baseline values). Panel (c) normalized wall thickness h(s)/ho, loaded radius a(s)/ao, unloaded radius A(s)/A(0), and unloaded length L(s)/L(0) versus G&R time, s/sh. Note: ε=1.33,Ae/A=Le/L=0.85,Ac/A=1.192,Lc/L=1.125,Am/A=Lm/L=0.95,TB=550 kPa,λM=1.8,λ0=0.8,ϕf=0.70,ϕe=0.06,ϕc=0.15,ϕm=0.09, and kij=6.9.
Grahic Jump Location
Example 2. Panel (a) Circumferential stress and panel (b) axial stress versus G&R time for individual constituents and mixture (presented as differences from the initial baseline values). Panel (c) Normalized wall thickness h(s)/ho, loaded radius a(s)/ao, unloaded radius A(s)/A(0), and unloaded length L(s)/L(0) versus G&R time, s/sh. Parameter values are the same as in Figure 4.
Grahic Jump Location
Passive (a) stress-stretch and (b) pressure-diameter curves for ε=1.33 and ε=0.73, for G&R times s=0 and s=sh (Case 1 and Case 2) for λz=1.5. The normalized outer diameter is scaled such that A(0)=1 length unit.




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