Pressure and Flow in the Vascular System Flow and Flow Velocity

Function of the organ systems depends on the volume of blood flowing per unit time through them, or the volume flow rate. This is often shortened to the term 'flow'. Flow can be measured in ml/s (or l/min). The total flow through the systemic circulation or the lungs is equal to the cardiac output.

Figure CR.2

Blood vessel structure

Figure CR.2

Blood vessel structure

FUNCTIONAL ASPECTS OF BLOOD VESSEL WALL CHARACTERISTICS

Characteristic

Functional aspect

Wall thickness

Thick walls provide tensile strength to withstand pressure in arteries

Thin walls in capillaries allow exchange with interstitial fluid

Elastic component in walls

Smoothing of pulsations, storage of energy to maintain flow in diastole

Smooth muscle component in walls

Control of vessel diameter by autonomic reflex and humoral activity

Fibrous component in walls

Mechanical strength

Figure CR.3

BLOOD VESSEL DIAMETERS AND MEAN PRESSURES

Vessel

Diameter

Wall thickness

Mean pressure (mmHg)

Aorta

25 mm

2 mm

100

Artery

4 mm

1 mm

95

Arteriole

20

|m

6 |m50

Terminal arteriole

10 |m

2 |m

45

Capillary

8 |m

0.5 |m

30

Venules

20 |m

1 |m

20

Veins

5 mm

0.5 mm

8

Vena cava

30 mm

1.5 mm

3

Figure CR.4

BLOOD VESSELS AND THEIR FUNCTIONS

Vessel

Function

Aorta

Storage of energy to maintain delivery in diastole, and damping of pressure pulses

Arteries

Delivery, distribution and damping of pressure waveform

Arterioles

Resistance to control pressure and distribution to capillaries

Capillaries

Microcirculation and exchange

Venules and small veins

Collection

Large veins and vena cava

Collection, storage capacitance and delivery of venous return (or portal circulations)

Figure CR.5

Figure CR.5

Flow should be differentiated from flow velocity. Flow velocity defines how fast fluid is moving at any given point and has units of cm/s. In a blood vessel the flow velocity of blood varies between the centre of the vessel and the vessel wall. If the flow pattern of the blood is described as laminar (i.e. without turbulence) the blood moves smoothly in the direction of the axis of the vessel. The velocity of the blood varies in a predictable pattern with maximum velocity in the centre of the vessel and minimum velocity next to the wall, as if the blood is moving in concentric layers (Figure CR.6).

Figure CR.6 Physics of laminar flow

Consider a vessel with cross sectional area A. The mean flow velocity (v) can be taken across the cross section. The flow (Q) is then related to the mean flow velocity (v) by:

This relationship can be applied to the vascular system as a whole since the number and diameter of any type of blood vessel determines the total cross sectional area presented to flow at that stage in the vascular system. The greater the total cross sectional area of any given generation of vessels, the slower the velocity of blood flow through those vessels. The cross sectional area of the aorta is about 4.5 cm2 with peak flow velocities of > 120 cm/s. In contrast, the flow velocity in the several billion capillaries of the vascular system is usually between 0 and 1 cm/s due to a total capillary cross sectional area of > 4500 cm2 (Figure CR.7). These flow velocities reflect the functions of delivery and distribution in the aorta and arteries, as opposed to perfusion and exchange in the capillaries.

Figure CR.7 Flow velocity in different vessels

In an individual vessel if the cross sectional area is reduced by a constriction such as a valve or an atheromatous plaque, the flow velocity increases through the constriction. Such increases in flow velocity can affect the characteristics of the blood flow making it turbulent and leading to an increased tendency towards thrombus formation. The motion of blood across the stationary surface of the vessel wall produces a viscous drag or shear stress along the surface of the vessel wall. This shear stress is increased with increased flow velocity producing a force that tends to pull endothelium and plaques away from the wall, leading to dissection or emboli. Increased flow velocity also produces bruits or murmurs (Figure CR.8).

Figure CR.8 Turbulent flow and drag in vessels

Flow Through the Systemic Circulation

The energy imparted to blood within the circulation by the heart and the elastic recoil of the great vessels causes it flow through the systemic and pulmonary circulations. There are additional contributions of energy to flow from skeletal muscle contraction and negative intrathoracic pressure during inspiration. These mechanisms create a pressure difference across the vascular system that produces the total flow (cardiac output) through the vascular system. A simple electrical analogy lies in Ohm's law where a potential difference (V) produces an electrical current (I) through a resistance (R). In this case:

Thus the pressure difference between mean arterial pressure (MAP) and central venous pressure (CVP) is related to cardiac output (CO) and systemic vascular (SVR) by:

This is often approximated to: (MAP) = (CO) x (SVR)

Vascular Resistance

"Vascular resistance' is a clinical term used to represent the effect of all the forces opposing blood flow through a vascular bed. It may be applied to the systemic vascular circulation, the pulmonary circulation or a given visceral circulation. The forces opposing blood flow through a vascular system are composed of two main components. First, those which dissipate energy due to frictional effects. This resistance arises as a result of drag between fluid layers and friction between fluid and vessel walls. The viscosity of the blood is a major determinant of this component of resistance.

The second component of opposing forces arises from the conversion of pump work into stored energy. This occurs when potential energy is stored by the elasticity of distended vessel walls or by gravity as blood is pumped to a greater height within the body. In addition, inertial effects store kinetic energy when blood is accelerated. This component is referred to as the "reactive' component and is dependent on the pulsatile component of the pressure waveform. If the pressure difference applied across a vascular bed were constant the reactive component would be minimal.

In vivo the systemic vascular resistance (SVR) and the pulmonary vascular resistance (PVR) can be estimated using pulmonary artery catheterization.

Flow in a Single Vessel

Blood flow through larger vessels (> 0.5 mm diameter) can be approximated to the case of an idealized or Newtonian fluid (such as water) flowing though a tube. Under laminar flow conditions with a steady pressure gradient, the flow (Q) between any two points, Pi and P2, is dependent on the pressure difference, AP, between the points, and inversely dependent on the resistance to flow (R) (Figure CR.9).

4-

--*■

Lo minor

flow

P,

*-

-p.

Pressure difference = AP

Figure CR.9 Poiseuille's law

Pressure difference = AP

Figure CR.9 Poiseuille's law

According to the Hagen-Poiseuille law, which describes laminar flow in tubes, the flow resistance, R, is dependent on the length of the tube and the viscosity of the fluid, but inversely related to the fourth power of the radius. The real situation of blood flowing through a vessel differs from this ideal model in the following respects:

• Blood vessels are not uniform in cross section

• Blood vessel walls are elastic

• Pressure gradients pushing blood through vessels have a pulsatile component

• Blood as a fluid behaves differently from a Newtonian fluid due to the cellular components and its flow properties are not solely determined by viscosity

Blood Viscosity

The rheological properties of blood describe its flow resistive properties. In a Newtonian fluid these resistive properties are dependent on a constant, the coefficient of viscosity. Blood, however, is a suspension of cells, and although the viscosity can be determined to give an apparent value, this value varies significantly with blood composition and flow conditions. The factors causing this variation in apparent viscosity include:

• Haematocrit—an increase in haematocrit to 0.7 (normal haematocrit = 0.45) can double the apparent viscosity (Figure CR.10)

• Diameter of the vessel—apparent blood viscosity can be measured in vitro using a capillary tube viscometer, and decreases as tube diameter decreases < about 0.3 mm

• Red blood cell streaming—in smaller diameter vessels red blood cells stream centrally along the axis of the vessel. This effectively reduces the haematocrit in these vessels. The haematocrit in capillaries may be 25% of the value in larger vessels (Figure CR.11)

Figure CR.10 Haematocrit related to viscosity
Figure CR.11 Haematocrit related to blood vessel size

• In vivo—apparent blood viscosity is lower in vivo than in vitro. At normal haematocrit the in vivo blood viscosity may only be half of the equivalent in vitro value

• Flow velocity—apparent viscosity decreases at higher flow velocities and increases at low flow velocities. This is due to increased red cell aggregation and leucocyte adherence to vessel walls at low flow velocities

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