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Arterial wall tethering as a distant boundary condition
Phys. Rev. E 80, 051913 – Published 18 November, 2009
DOI: https://doi.org/10.1103/PhysRevE.80.051913
Abstract
A standing difficulty in the problem of blood vessel tethering has been that only one of the two required boundary conditions can be fully specified, namely, that at the inner (endothelial) wall surface. The other, at the outer layer of the vessel wall, is not known except in the limiting case where the wall is fully tethered such that its outer layer is prevented from any displacement. In all other cases, where the wall is either free or partially tethered, a direct boundary condition is not available. We present a method of determining this missing boundary condition by considering the limiting case of a semi-infinite wall. The result makes it possible to define the degree of tethering imposed by surrounding tissue more accurately in terms of the displacement of the outer layer of the vessel wall, rather than in terms of equivalent added mass which has been done in the past. This new approach makes it possible for the first time to describe the effect of partial tethering in its full range, from zero to full tethering. The results indicate that high tethering leads to high stresses and low displacements within the vessel wall, while low tethering leads to low stresses and high displacements. Since both extremes would be damaging to wall tissue, particularly elastin, this suggest that moderate tethering would be optimum in the physiological setting.
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References (17)
- J. D. Humphrey and S. Na, Ann. Biomed. Eng. 30, 509 (2002).
- J. R. Womersley, Oscillatory Flow in Arteries: The Constrained Elastic Tube as a Model of Arterial Flow and Pulse Transmission (Wright Air Development Center, Dayton, Ohio, 1955).
- G. W. Morgan and W. R. Ferrante, J. Acoust. Soc. Am. 27, 715 (1955).
- G. A. Holzapfel, T. C. Gasser, and M. Stadler, Eur. J. Mech. A/Solids 21, 441 (2002).
- M. Cinthio, A. R. Ahlgren, J. Bergkvist, T. Jansson, H. W. Persson, and K. Lindstrom, Am. J. Physiol. 291, H394 (2006).
- S. Cirovic, C. Walsh, and W. D. Fraser, J. Fluids Structures 16, 1029 (2002).
- D. J. Patel and D. Fry, Circ. Res. 19, 1011 (1966).
- H. B. Atabek, Biophys. J. 8, 626 (1968).
- J. C. Misra and K. R. Choudhury, Rheol. Acta 23, 548 (1984).
- J. E. Wagenseil, N. L. Nerurkar, R. H. Knutsen, R. J. Okamoto, D. Y. Li, and R. P. Mecham, Am. J. Physiol. Heart Circ. Physiol. 289, H1209 (2005).
- D. C. Gazis, J. Acoust. Soc. Am. 31, 568 (1959).
- K. Jagielska, D. Trzupek, M. Lepers, A. Pelc, and P. Zielinski, Phys. Rev. E 76, 066304 (2007).
- H. Wang and K. Williams, J. Sound Vib. 191, 955 (1996).
- S. Hodis and M. Zamir, Phys. Rev. E 78, 021914 (2008).
- D. Craiem and R. L. Armentano, Biorheology 44, 251 (2007).
- M. Zamir, The Physics of Pulsatile Flow (Springer-Verlag, New York, 2000).
- D. T. Blackstock, Fundamentals of physical acoustics (Wiley, New York, 2000).