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Flow in large blood vessels. (English) Zbl 0788.76102

Cheer, Angela Y. (ed.) et al., Fluid dynamics in biology. Proceedings of an AMS-IMS-SIAM joint summer research conference held July 6-12, 1991 at the University of Washington, Seattle, USA, with support from the National Science Foundation and NASA Headquarters. Providence, RI: American Mathematical Society. Contemp. Math. 141, 479-518 (1993).
The starting point for most treatments of pulsatile flow in complex branching system is the analysis of the flow in an individual arterial segment considered as an infinitely long, cylindrical, thin elastic tube through which flows a viscous fluid, usually taken to be Newtonian. The mathematical statement of the problem consists of coupled nonlinear partial differential equations (in space and time) governing the fluid and vessel wall motions, which satisfy appropriate matching conditions at the wall. The original Womersley model will be discussed, as well as subsequent modifications. These include wall loading and constraint, more complex wall behavior (viscoelasticity, anisotropy, etc.), thick-tube walls, nonlinear fluid and wall effects.
For the entire collection see [Zbl 0773.00015].

MSC:

76Z05 Physiological flows
92C10 Biomechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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