Advanced Haemodynamics

ABC of Vascular Disease

Arterial Haemodynamics

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Haemodynamics is the branch of science that describes how blood flows.  The physical principles of haemodynamics is a specific example of the general principles of fluid dynamics and the equations of blood flow and general fluid flow are identical.  Blood is a liquid tissue: it has both physical and biological properties.  For the purposes of haemodynamics it is the physical properties that are of specific interest.  The two fundamental properties of a fluid are its density and its viscosity. The density is the mass per unit volume and blood is slightly denser than water.  The viscosity is the resistance of the fluid to being moved.  Blood is nearly four times more viscid than water.

In order for a fluid to move something must push it.  This something is pressure. To be more accurate, the fluid will move from a region of higher pressure towards a region of lower pressure.  The greater the difference in the pressure, the quicker the flow.  The properties of the fluid also play a part.  The more viscid the fluid the more it will resist the movement and the more pressure difference will be required to achieve the same flow.

Steady flow in a straight tube
The simplest analogy to blood flowing in an artery or vein is steady fluid flow through a tube.  The relationship between the pressure difference, the flow, the viscosity of the fluid and the area of the tube was determined experimentally by J.L.M.Poiseuille in the mid 1800's.  Poiseuille found that:

bulletThe flow was proportional to the pressure difference between the ends of the tube.
bulletThe flow was inversely proportional to the area of the tube squared.

This means that the bigger the tube and the greater the pressure difference the more blood can flow.  It also means that the smaller the tube the more difficult it is to push a given flow of blood through.

The circulation of the blood
In the body is a network of blood vessels which are of two types.  Arteries carry blood from the heart to all the organs of the body to keep them supplied with oxygen.  Veins carry the blood back from the organs to the heart and the heart then pumps the blood through the blood vessels in the lungs.  In the lungs the waste product from the body called carbon dioxide is released from the blood and replaced with oxygen from the air.  The blood goes around and around this loop hundreds of times a day, delivering oxygen to the body and removing the waste carbon dioxide.

Blood pressure and the heart
Just as for fluid flow in a tube, for blood to flow from the heart along an artery there must be a pressure difference to push the blood through.  The heart is a muscle: as the heart muscle contracts it squeezes the blood inside and increases the blood pressure.  When the pressure reaches a certain point the blood will be squeezed out of the heart into the arteries.  This sudden increase in blood pressure in an artery caused by the heart squeezing the blood out can be easily felt as the pulse.  Arteries are not rigid tubes, they have elastic walls.  Arteries are not closed, they connect with the network of microscopic vessels called capillaries that join the arteries to the veins.

The action of the heart is very similar to someone trying to pump up a leaky tyre.  As you pump the pressure in the tyre increases but so does the size of the leak.  Eventually as you keep pumping the pressure reaches a point where what goes in is equal to what leaks out and, although the pressure is going up and down with each stroke, the average pressure stays the same.  To increase the pressure you have to pump faster.  If the leak gets bigger then the pressure will fall unless you pump faster to compensate.

In order to make sure the heart pumps at the correct rate, the brain measures the blood pressure in the arteries near to the heart.  If the pressure is too low the brain tells the heart to speed up; if the pressure is too high the brain tells the heart to slow down.

Effect of exercise
When you walk the muscles in the body move the legs and also prevent you from falling over.  When muscles contract they need more oxygen and this oxygen has to be delivered to the muscles by the blood.  So, as you walk, or do any form of muscular exertion, the blood flow to the muscles increases.  In fact the muscles control this change in flow themselves by altering the size of the small arteries inside the muscles.  To increase the flow they allow the artery to widen and this allows a greater flow (see Poiseuille above).  The increase in flow means that the blood pressure in the arteries will tend to fall (just as with a leaky tyre).  The body detects this fall in pressure and makes the heart beat faster to compensate.  So, as you exercise, the blood flow through the arteries to the muscles increases, the heart beats faster but the blood pressure stays about the same.  Normal arteries are large enough to handle the extra blood flow that is needed during exercise and the muscles are not starved of oxygen.  Blood flow to the legs can easily increase by ten fold during exercise! 

Flow in an artery with a narrowing
If an artery is narrowed (stenosis), then the blood must squeeze through the narrow part and as it does so it has to move more quickly.  When the blood squirts from the narrowing it forms a jet that catches up with the slower moving blood in the normal artery beyond the narrowing.  The mixing of the jet and the slower moving blood downstream causes the blood to swirl.  Swirling flow is not as efficient as a smooth flow and a greater pressure is needed to force the blood to flow through a narrowing.  In other words, for a given pressure difference, the flow of blood is less if it is swirling than if it is moving smoothly.

Leg pain on exercise and arterial disease
The most common form of arterial disease is where the inside of the artery becomes "furred up" and the artery becomes narrowed.  When this happens the amount that the blood flow can increase during exercise becomes limited.  Eventually a point is reached where the muscles do not get enough blood and become starved of oxygen and they start to "complain" by producing pain.  This pain in the leg muscles brought on by exercise is called intermittent claudication and is a warning sign that there is arterial disease in the leg arteries.  The distance a person can walk before claudication starts depends on several factors

bulletthe severity of the arterial disease
bulletthe walking speed
bulletthe slope of the path
bulletthe person's weight

Many people with claudication quickly learn that walking up hill is more difficult and to reduce the pain they walk more slowly.

Treating claudication
The obvious way to treat claudication is to unblock the narrowed artery and allow more blood to reach the muscles during exercise.  This is much easier said than done.  By the time the arterial narrowing causes symptoms the arterial disease is usually quite advanced and extensive.  Unblocking all the affected arteries is usually not possible and other strategies have to be used (see Intermittent Claudication).

To explore how this works using a computer simulation see Advanced Haemodynamics

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S.R.Dodds 2001