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TECHNICAL PAPERS

Stress-Modulated Growth, Residual Stress, and Vascular Heterogeneity

[+] Author and Article Information
Larry A. Taber

Department of Biomedical Engineering, Washington University, St. Louis, MO 63130e-mail: lat@biomed.wustl.edu

Jay D. Humphrey

Biomedical Engineering Program, Texas A&M University, College Station, TX 77843e-mail: jhumphrey@tamu.edu

J Biomech Eng 123(6), 528-535 (Jul 25, 2001) (8 pages) doi:10.1115/1.1412451 History: Received March 09, 2000; Revised July 25, 2001
Copyright © 2001 by ASME
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References

Figures

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Schematic of a residual stress experiment. An arterial section first is cut circumferentially to produce two rings. Then, each ring is cut transmurally and the opening angle ϕ of each is measured.
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Configurations for a growing artery. B0(0): unstressed reference state at the time of the first heartbeat in the embryo; B1(t): zero-stress state after growth (divided into an infinite number of parts); B2(t) unloaded artery with finite number of cuts; b(t): intact pressurized artery after growth.
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Computed pressure-radius curves for mature bovine carotid artery. With growth included, the model (dashed curve) gives reasonable agreement with the results based on the measurements of von Maltzahn et al. 24 (solid curve). (r1: loaded inner radius; r10: unloaded inner radius)
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Transmural residual circumferential (hoop) stress distributions in mature rat aorta for case 1(homogeneous properties). Intact (P=0) and one-cut states are shown. The residual stresses in the intact artery generate a bending moment M. A single radial cut relieves almost all residual stress.
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Transmural residual circumferential (hoop) stress distributions in mature rat aorta for case 2 (bilayer wall). (a) Intact (P=0) and one-cut states: residual stress changes little due to the radial cut. (b) Two-cut state with circumferential cut A in inner layer: most stress is relieved in inner ring. (c) Two-cut state with circumferential cut B between layers: most stress is relieved in both rings. (d) Two-cut state with circumferential cut C in outer layer: most stress is relieved in outer ring. The locations of cuts A, B, and C are shown in Fig. 7(b).
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Transmural residual circumferential (hoop) stress distributions in mature rat aorta for case 3 (continuous variation). (a) Intact (P=0) and one-cut states: significant residual stress remains after cut. (b) Two-cut state with circumferential cut A: most stress is relieved in inner ring. (c) Two-cut state with circumferential cut B: both rings still contain residual stress. (d) Two-cut state with circumferential cut C: most stress is relieved in outer ring. The locations of cuts A, B, and C are shown in Fig. 7(c).
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Computed opening angles for inner and outer rings of mature rat aorta as functions of Eulerian location h of the circumferential cut. In contrast to case 1, the angles for cases 2 and 3 show strong dependence on circumferential cut location. Insert shows transmural distribution of the material coefficient C for the three studied cases.
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Theoretical and experimental opening angles for inner and outer rings of mature bovine carotid artery as functions of Eulerian location h of the circumferential cut. The model results agree well with the experimental measurements of Greenwald et al. 16 Reprinted with permission, from the Annual Review of Biomedical Engineering, Vol. 3, © 2001, by Annual Reviews www.annualreviews.org.
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Computed distributions of circumferential stretch ratio (λΘ) and Cauchy stress (σθ) across the wall of a pressurized rat aorta without residual stress. Results are shown for each studied case with P=16 kPa. Although λΘ decreases monotonically across the wall for all cases, the distribution of σθ is generally more complex and depends on the material properties of the vessel. When growth and residual stress are included, however, the homeostatic stress at maturity is uniform for all cases.
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Schematic of stress distribution in rat aorta for case 2 after a single radial cut (see Fig. 5(a)). The bending moments M1 and M2 are due to stresses on each side of a prospective circumferential cut at the three locations shown in Fig. 7(b). After cuts A, B, and C are made, the inner and outer rings bend in the directions opposite to M1 and M2, respectively, hence reducing these moments to zero.

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