Potential and Kinetic Energy

The main form of energy present in flowing blood is the pressure distending the vessels (a form of potential energy), which is created by the pumping action of the heart. However, some of the energy of the blood is kinetic; namely, the ability of flowing blood to do work as a result of its velocity. Usually, the kinetic energy component is small compared with the pressure energy, and under normal resting conditions, it is equivalent to only a few millimeters of mercury or less. The kinetic energy of blood is proportional to its density (which is stable in normal circumstances) and to the square of its velocity. In essence, over relatively straight arterial segments, this balance of kinetic (blood flow) and potential (blood pressure) energy is maintained. The equation that summarizes this relationship is Bernoulli’s equation (Figure 1-2). If the artery lumen increases, kinetic energy is converted back into pressure (potential energy) when velocity is decreased. Conversely, if the artery lumen narrows, the potential energy is converted into kinetic energy. Therefore, within certain limits, important increases in kinetic energy occur in the systemic circulation when blood flow is high (e.g., during exercise) and in mildly stenotic lesions where luminal narrowing leads to increases in blood flow velocities. The effects of gravity due to differences in height of the blood vessel are normally neglected over short arterial segments.

FIGURE 1-2 This diagram represents the complementary changes in potential and kinetic energy taking place at an idealized stenosis. Bernoulli’s equation indicates that as velocity increases, the potential energy (pressure) of blood decreases. This idealized representation is not to scale and neglects viscous and inertial forces.

Energy Differences Related to Differences in the Levels of Body Parts

There is also variation in the energy of the blood associated with differences in the levels of body parts. For example, the pressure in the vessels in the dependent parts of the body, such as the lower portions of the legs, increases by an amount that depends on the weight of the column of blood resting on the blood in the legs. This hydrostatic pressure increases the transmural pressure and the distention of the vessels. Gravitational potential energy (potential for doing work related to the effect of gravity on a free-falling body), however, is reduced in the dependent parts of the body by the same amount as the increase resulting from hydrostatic pressure. Therefore, differences in the level of the body parts usually do not lead to changes in the driving pressure along the vascular tree unless the column of blood is interrupted, as may be the case when the venous valves close. Changes in energy and pressure associated with differences in level are important under certain conditions, such as with changes in posture or when the venous pump is activated because of muscular action during walking.

During Laminar Flow

In most vessels, blood moves in concentric layers, or laminae; hence the flow is said to be laminar. Each infinitesimal layer flows with a different velocity. In theory, a thin layer of blood is held stationary next to the vessel wall at zero velocity because of an adhesive force between the blood and the inner surface of the vessel. The next layer flows with a certain velocity, but its movement is delayed by the stationary layer because of friction between the layers, generated by the viscous properties of the fluid. The second layer, in turn, delays the next layer, which flows at a greater velocity. The layers in the middle of the vessel flow with the highest velocity, and the basic physics underlying this effect are such that the mean velocity averaged across the vessel is half of the maximal velocity measured in the center. Because the rate of change of velocity is greatest near the walls and decreases toward the center of the vessel, a velocity profile in the shape of a parabola exists along the vessel diameter, and this type of blood flow is typically referred to as laminar flow (Figure 1-3).

FIGURE 1-3 Blood flow velocity profiles across a normal arterial lumen. A, Parabolic profile of laminar flow. B, Flattened profile with a central core of relatively uniform velocity encountered in the proximal portion (inlet length) of arterial branches or with turbulent flow.

Loss of energy during blood flow occurs because of friction, and the amount of friction and energy loss is determined in large part by the dimensions of the vessels. In a small-diameter vessel, especially in the microcirculation, even the layers in the middle of the lumen are relatively close to the wall and are thus delayed considerably, resulting in a significant opposition or resistance to flow in that vessel segment. In large vessels, by contrast, a large central core of blood is far from the walls, and the frictional energy losses are less important. As indicated later, friction and energy losses increase if laminar flow is disturbed.

During Nonlaminar Flow

Various degrees of deviation from orderly laminar flow occur in the circulation under both normal and abnormal conditions. Minor factors responsible for these deviations include changes in blood flow velocity during the cardiac cycle as a result of acceleration during systole and deceleration in diastole and alterations of the lines of flow due to small changes in the diameter of the vessel. Alterations in the blood flow profiles occur at curves (Figure 1-4), at bifurcations, in branches that take off at various angles, and at stenotic lesions. Once altered, the laminar (parabolic) velocity profile is often not reestablished for a considerable distance. Instead, the velocity distributions can remain skewed after curves and branches or flattened within and just distal to stenotic lesions (plug flow) (see Figure 1-3, B).

FIGURE 1-4 Alteration in the velocity distribution of red cells in a curving arterial segment. The velocity distribution becomes asymmetric as red cells enter a curve. A laminar pattern is reestablished downstream over a distance that is mostly dependent on the velocity of blood and the diameter of the artery.

In certain circumstance, laminar flow can evolve into a blood flow pattern that is mixed: a flow profile that has both forward and backward flow velocity components across the diameter of the artery. The transition zone where the lamina reach zero velocity is then referred to as the site of boundary layer separation. This phenomenon can occur at branch points and is classically described at the carotid artery bifurcation (Figure 1-5). Another situation is distal to stenotic lesions.

FIGURE 1-5 This representation of the carotid artery bifurcation displays the principal alterations that take place in a normal bifurcation. The flow profile in the distal common carotid artery (CCA) starts to deviate from a laminar pattern to one favoring the internal carotid artery (ICA). As the red cells enter the carotid sinus, a zone of boundary layer separation (where the effective velocity is zero) forms. To one side, blood flow is reversed, whereas blood continues forward on the other side. Blood flow reestablishes itself toward a laminar one more distally in the ICA. For purposes of illustration, the actual effects of the external carotid artery (ECA) on blood flow are neglected.

At the carotid bifurcation, the blood flow profile in the distal common carotid artery tends to diverge toward the internal carotid artery and then to evolve a zone of boundary layer separation in the proximal internal carotid artery (see Figure 1-5).

Laminar flow may be altered or become disturbed or fully turbulent, even in a uniform tube. The factors that affect the development of turbulence are expressed by the dimensionless Reynolds number (Re):

    (1-5)

where v is the velocity, ρ is the density of the fluid, r is the radius of the tube, and η is the viscosity of the fluid. Because the density (ρ) and viscosity (η) of the blood are relatively constant at 1.04 to 1.05 g/cm³ and 0.03 to 0.05 poise (g/[cm sec]), respectively, the development of turbulence depends mainly on the size of the vessel and on the velocity of blood flow. In a tube model, laminar flow tends to be present if the Reynolds number is less than 2000, is considered in transition between 2000 and 4000, and is absent as turbulence is established at values above 4000. However, in the circulatory system, disturbances and various degrees of turbulence are likely to occur at lower values because of body movements, the pulsatile nature of blood flow, changes in vessel dimensions, roughness of the endothelial surface, and other factors. Turbulence develops more readily in large vessels under conditions of high flow and can be detected clinically by the finding of bruits or thrills. This would typically be seen in dialysis access fistulas. Bruits may sometimes be heard over the ascending aorta during systolic acceleration in normal individuals at rest and are frequently heard in states of high cardiac output and blood flow, even in more distal arteries, such as the femoral artery.¹ Distortion of laminar flow velocity profiles can be assessed using Doppler ultrasound, and such assessments can be applied for diagnostic purposes. For example, in arteries with severe stenosis, pronounced turbulence is a diagnostic feature observed in the poststenotic zone. This is typically associated with soft tissue vibrations in the range of 100 to 300 Hz.²

Turbulence occurs because a jet of blood with high velocity and high kinetic energy suddenly encounters a normal-diameter lumen or a lumen of increased diameter (because of poststenotic dilatation), where both the velocity and energy level are lower than in the stenotic region. During turbulent flow, the loss of pressure energy between two points in a vessel is greater than that which would be expected from the factors in Poiseuille’s equation and Bernoulli’s equation (see Figure 1-2), and the parabolic velocity profile is flattened (see Figure 1-3, B).