INTRODUCTION

Arterial blood flow is complex and consists of pulsatile flow of an inhomogeneous fluid through viscoelastic arteries that branch, curve, and taper. However, a useful understanding of hemodynamics can be gained by first considering simple models, such as steady flow in a rigid tube. Factors affecting venous flow will also be considered. This will allow us to interpret spectral Doppler and color Doppler images of blood flow more easily. However, when interpreting color flow images it is important to remember that the color represents the mean velocity of flow obtained from the sample volumes and that this will depend on the angle between the ultrasound beam and blood flow. The pulse repetition frequency (PRF) and filter setting used and the length of time over which the image is created may also affect the appearance of the image. Artifactual effects also have to be considered carefully before drawing conclusions about the blood flow.

STRUCTURE OF VESSEL WALLS

The arterial and venous systems are often thought of as a series of tubes that transport blood to and from organs and tissues. In reality, blood vessels are highly complex structures that respond to nervous stimulation and interact with chemicals in the blood stream to regulate the flow of blood throughout the body. Changes in cardiac output and the tone of the smooth-muscle cells in the arterial walls are crucial factors that affect blood flow. The structure of a blood vessel wall varies considerably depending on its position within the vascular system.

Arteries and veins are composed of three layers of tissue, with veins having thinner walls than arteries. The outer layer is called the adventitia and is predominantly composed of connective tissue with collagen and elastin. The middle layer, the media, is the thickest layer and is composed of smooth-muscle fibers and elastic tissue. The intima is the inner layer and consists of a thin layer of endothelium overlying an elastic membrane. The capillaries, by contrast, consist of a single layer of endothelium, which allows for the exchange of molecules through the capillary wall. It is possible to image the structure of larger vessel walls using ultrasound and to identify the early stages of arterial disease, such as intimal thickening.

The arterial tree consists of elastic arteries, muscular arteries, and arterioles. The aorta and subclavian arteries are examples of elastic or conducting arteries and contain elastic fibers and a large amount of collagen fibers to limit the degree of stretch. Elastic arteries function as a pressure reservoir, as the elastic tissue in the vessel wall is able to absorb a proportion of the large amount of energy generated by the heart during systole. This maintains the end-diastolic pressure and decreases the load on the left side of the heart. Muscular or distributing arteries, such as the radial artery, contain a large proportion of smooth-muscle cells in the media. These arteries are innervated by nerves and can dilate or constrict. The muscular arteries are responsible for regional distribution of blood flow. Arterioles are the smallest arteries, and their media is composed almost entirely of smooth-muscle cells. Arterioles have an important role in controlling blood pressure and flow, and they can constrict or dilate after sympathetic nerve or chemical stimulation. The arterioles distribute blood to specific capillary beds and can dilate or constrict selectively around the body depending on the requirements of organs or tissues.

WHY DOES BLOOD FLOW?

Energy created by the contraction of the heart forces blood around the body. Blood flow in the arteries depends on two factors: (1) the energy available to drive the blood flow, and (2) the resistance to flow presented by the vascular system.

A scientist named Daniel Bernoulli (1700–1782) showed that the total fluid energy, which gives rise to the flow, is made up of three parts:

Gravitational potential energy (ρgh) is equivalent to hydrostatic pressure but has an opposite sign (i.e.−ρgh). For example, when a person is standing, there is a column of blood – the height of the heart above the feet – resting on the blood in the vessels in the foot (Fig. 5.1A) causing a higher pressure, due to the hydrostatic pressure, than that seen when the person is lying down (Fig. 5.1B). As the heart is taken as the reference point, and the feet are below the heart, the hydrostatic pressure is positive. If the arm is raised so that it is above the heart, the hydrostatic pressure is negative, causing the veins to collapse and the pressure in the arteries in the arm to be lower than the pressure at the level of the heart. The total fluid energy is given by:

Figure 5.1 Schematic diagram showing typical pressures in arteries and veins with the subject standing (A) and lying (B). The component due to hydrostatic pressure when the subject is vertical is shown alongside A.

     (5.2)

Figure 5.2 gives a graphical display of how the total energy, kinetic energy, and pressure alter with continuous flow through an idealized narrowing. Usually the kinetic energy component of the total energy is small compared with the pressure energy. When fluid flows through a tube with a narrowing, the fluid travels faster as it passes through the narrowed section. As the velocity of the fluid increases in a narrowed portion of the vessel, the kinetic energy increases and the potential energy (i.e., the pressure) falls. The pressure within the narrowing is therefore lower than the pressure in the portion of the vessel before the narrowing. As the fluid passes beyond the narrowing, the velocity drops again and the kinetic energy is converted back to potential energy (the pressure), which increases. Energy is lost as the fluid passes through the narrowing (Fig. 5.2), with the extent of the entrance and exit losses depending on the geometry and degree of the narrowing (Oates 2008). In normal arteries, very little energy is lost as the blood flows away from the heart toward the limbs and organs, and the mean pressure in the small distal vessels is only slightly lower than in the aorta. However, in the presence of significant arterial disease, energy may be lost from the blood as it passes through tight narrowings or small collateral vessels around occlusions, leading to a drop in the pressure greater than that which would be expected in a normal artery; this can lead to reduced blood flow and tissue perfusion distally. Because the entrance and exit losses account for a large proportion of the pressure loss, it is likely that two adjacent stenoses will have a more significant effect than one long one (Oates 2008).

Figure 5.2 Diagram showing how energy losses can occur across a narrowing. KE, kinetic energy.

(Oates (ed), Cardiovascular Haemodynamics and Doppler Waveforms Explained. 2008. Cambridge University Press)

RESISTANCE TO FLOW

In 1840, a physician named Poiseuille established a relationship between flow, the pressure gradient along a tube, and the dimensions of a tube. The relationship can simply be understood as:

     (5.3)

     (5.4)

Viscosity causes friction between the moving layers of the fluid. Treacle, for example, is a highly viscous fluid, whereas water has a low viscosity and therefore offers less resistance to flow when traveling through a small tube. Poiseuille’s law shows that the resistance to flow is highly dependent on changes in the radius (r⁴). In the normal circulation, the greatest proportion of the resistance is thought to occur at the arteriole level. Tissue perfusion is controlled by changes in the diameter of the arterioles. The presence of arterial disease in the arteries, such as stenoses or occlusions, can significantly alter the resistance to flow, with the reduction in vessel diameter having a major effect on the change in resistance seen. In severe disease, the arterioles distal to the disease may become maximally dilated in order to reduce the peripheral resistance, thus increasing blood flow in an attempt to maintain tissue perfusion. Poiseuille described nonpulsatile flow in a rigid tube, so his equation does not completely represent arterial blood flow; however, it gives us some understanding of the relationship between pressure drop, resistance, and flow.

VELOCITY CHANGES WITHIN STENOSES

We have already seen that fluid travels faster through a narrowed section of tube. The theory to determine these changes in velocity is described below. The volume flow through the tube is given by:

     (5.5)

where V is the mean velocity across the whole of the vessel, averaged over time, and A is the cross-sectional area of the tube. If the tube has no outlets or branches through which fluid can be lost, the flow along the tube remains constant. Therefore, the velocity at any point along the tube depends on the cross-sectional area of the tube. Figure 5.3 shows a tube of changing cross-sectional area (A₁, A₂); now, as the flow (Q) along the tube is constant:

Figure 5.3 Change in cross-sectional area. As the flow is constant through the tube, the velocity of the fluid increases from V₁ to V₂ as the cross-sectional area decreases from A₁ to A₂.

     (5.6)

     (5.7)

     (5.8)

Figure 5.4 shows how the flow and velocity within an idealized stenosis vary with the degree of diameter reduction caused by the stenosis, based on the predictions from a simplified theoretical model. On the right-hand side of the graph, where the diameter reduction is less than 70–80%, the flow remains relatively unchanged as the diameter of the vessel is reduced. This is because the proportion of the resistance to flow due to the stenosis is small compared with the overall resistance of the vascular bed that the vessel is supplying. However, as the diameter reduces farther, the resistance offered by the stenosis becomes a significant proportion of the total resistance, and the stenosis begins to limit the flow. This is known as a hemodynamically significant stenosis. At this point, the flow decreases quickly as the diameter is reduced.

Figure 5.4 Changes in flow and velocity as the degree of stenosis alters, predicted by a simple theoretical model of a smooth, symmetrical stenosis.

(Spencer & Reid, Quantitation of carotid stenosis with continuous-wave (C-W), Doppler Ultrasound. Stroke 10:326-330, 1979)

The graph also predicts the behavior of the velocity as the vessel diameter is reduced and shows that the velocity increases with diameter reduction. Noticeable changes in velocity begin to occur at much smaller diameter reductions than would produce a flow reduction. Therefore, measurement of velocity changes is a more sensitive method of detecting small-vessel lumen reductions than measurement of flow. Measurements of velocity made using Doppler ultrasound are also more accurate than measurement of flow, as will be discussed later (see Ch. 6). Therefore, it is usually the change in velocity of blood within a diseased artery that is used to quantify the degree of narrowing. Eventually, there comes a point at which the resistance to flow produced by the narrowing is so great that the flow drops to such an extent that the velocity begins to decrease, as shown on the left side of the graph. This is seen as ‘trickle flow’ within the vessel. It is especially important to be able to identify trickle flow within a stenosis as the peak velocities seen may be similar to those seen in healthy vessels, but the color image and waveform shapes will not appear normal.

As blood flow is pulsatile and arteries are nonrigid vessels, it is difficult to predict theoretically the velocity increase that would be seen for a particular diameter reduction. Instead, velocity criteria used to quantify the degree of narrowing are produced by comparing Doppler velocity measurements with arteriogram results, as arteriography has been considered to be the ‘gold standard’ for the diagnosis of arterial disease.

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