Chapter 7

### INTRODUCTION

This chapter mainly deals with the physiology of the arterial system and the hemodynamic analysis of pressure and flow in the arterial tree. Although most of the topics covered are generic and applicable to the systemic and pulmonary circulation, there is no doubt that the main focus is on the systemic circulation because it is the most studied, and also the most accessible, certainly for noninvasive measurement technology.

Before tackling arterial system physiology, we first provide the reader with a concise overview of some elementary laws of flow dynamics that are frequently used and cited in clinical literature, but without going in detail on the mathematical derivation.

The chapter first provides the "classic" analysis of hemodynamic data in the frequency domain, which is based on the parallelism between flow dynamics and electric system analysis. Input and characteristic impedance are defined and discussed, and it is demonstrated how arterial wave reflection can be assessed and quantified from pressure and flow. In addition to this classic view, we also consider wave intensity analysis, which is an alternative method of analyzing arterial hemodynamic data and wave reflection, but in what is perhaps a more intuitive way in the time domain.

A subsequent section is dedicated to the analysis of "arterial function" and "arterial stiffness," which is a new emerging domain of clinical research. Different methods are described, ranging from local measurement of arterial properties to parameters describing the complete arterial tree, most of them emerging from an electrical analog representation of the arterial tree. The clinical applicability of the methods, their strong and weak points, and the relevance of measuring arterial stiffness in general are discussed.

### BLOOD FLOW IN ARTERIES—GENERAL FLUID DYNAMIC LAWS

Blood flow in the arterial tree is of a relatively complex nature, for many different reasons. First of all, blood in itself is a complex liquid.1,2 As a suspension of biochemically active cells in plasma, it is a non-Newtonian liquid, which implies that it has a nonconstant viscosity. When not in motion, red blood cells coagulate and rouleaux formation occurs, increasing the viscosity of blood. Under the action of shear forces within the blood (see later in the chapter), these rouleaux break up when blood flows and the viscosity of the blood decreases. Blood is therefore known as a "shear thinning liquid," with viscosity at high shear rates in the order of 3 to 4 mPa s (or cPoise). Blood can be generally considered as a homogenous liquid, except at the level of the arterioles and capillaries, where the size of the red blood cells (8 μm) becomes relatively large with respect to the vessel diameter (100 μm and less). Here, more complex rheological models should be considered, or blood should be treated as a multiphase liquid.

To define "shear rate," we take the example of flow of a liquid ...

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