Aspects of Fluid Dynamics Applied to the Larger Arteries

A review is given of some of the ideas from fluid mechanics which are considered essential background for researchers in cardiovascular flows. The paper links the topics discussed at a fundamental level with real problems which, in the experience of the author, occur in research. In particular, approximate equations governing the principal phenomena, and which help with understanding, are introduced. A description is given of the equations of motion and the significance of similarity parameters is discussed: it is shown how Reynolds number and the Womersley parameter arise from dimensionless forms of the equations. Steady flow equations and approximations are commented on, including illustrations of their use. Unsteady flow phenomena are introduced and it is shown how Stokesʹ first and second problems illustrate key aspects of unsteady viscous diffusion and boundary layers in the circulation. Important features of pulsatile pipe flow, as analysed by both Uchida and Womersley, are discussed and linked to Stokesʹ two-dimensional results. Entrance effects in steady and unsteady pipe flow are compared and contrasted. Other phenomena discussed include the effects of bends in vessels, transition to turbulence and the different time-scales associated with unsteady flows. Computational methods, which are assuming increasing importance in biological fluid mechanics, also receive a brief description. Finally, comments are made on pressure and other measurements and the need for an understanding of various fluid flow phenomena when planning measurements and interpreting the resulting data.