Vascular Haemodynamics

Abstract

Vascular interventions have developed rapidly since the first aortic replacement with Dacron by Dubois in 1952 (Lawrence-Brown et al., How is durability related to patient selection and graft design with endoluminal grafting for abdominal aortic aneurysm. In: Durability of vascular and endovascular surgery, London, pp. 375–385, 1999, Harris et al., The need for clinical trials of endovascular abdominal aortic aneurysm stent-graft repair: the EUROSTAR project, Los Angeles, 1997). An appreciation of vascular haemodynamics is important for understanding vascular disease, improving existing vascular interventions and in the development of new medical devices and procedures.

The various laws and governing equations that describe the behaviour of fluids in conduits play a critical role in our understanding of aneurysms, arterial dissections and atherosclerotic occlusive disease. Models that include non-Newtonian flow, pulsatile flow, compliance and elastic walls are complex and difficult to describe.

Therefore, to firstly understand Newtonian fluid dynamics, (essentially water, in which the viscosity is independent of velocity and the strain to stress ratio is constant), is fundamental, and takes us some way towards answering simple vascular dynamic questions where it is easier to simplify a model to that with Newtonian fluid and non-pulsatile flow. However, we must always bear in mind that blood is non-Newtonian and the influence of pulsatility and complex (non-Newtonian) fluids on haemodynamics can then be investigated further. It is important to appreciate that a better understanding of haemodynamics can help correct mistaken clinical assumptions and answer important questions regarding the pathophysiology of vascular diseases. In this chapter, we will examine a series of questions and explain:

• How Laplace’s law explains why an aneurysm grows when it is exposed to relative constant pressure;

• How Poiseuille’s flow equation explains why flow is driven by a pressure gradient, but is also affected by the length of the artery;

• How Bernoulli’s equation explains why velocity is higher and pressure falls in a stenosis;

• How Young’s modulus increases with age when the arteries become stiffer and this has effects on pulsatile flow;

• How the Momentum Conservation equation describes

  • The forces on an endovascular graft;

  • Why the forces acting on a thoracic graft are not necessarily greater than those on an abdominal graft; and

  • Why forces change with curves, changes in diameter and tortuosity.