5.7.12

P1 P2 P3

R1 R2 R3

P= P1 + P2 + P3

=QR1+QR2+QR3

=QRR=R1+R2+R3

R1,Q1

R2,Q2

Q=Q1+Q2

=P/R1+P/R2

=P/RR=1/R1+1/R2

The slow velocity of blood through capillaries has the beneficial effect of allowing more time for the exchange of molecules between the cardiovascular system and extracellular fluid

Bernoulli’s principle states that when the fluid flow through a tube is constant, the total fluid energy –the sum of kinetic energy and potential energy-remains constant

It explains why fluid pressure is low in blood vessels at places where its radius is less

Proximal to the structure of stenosis, blood flow is laminar. Blood passing through stenotic orifice also remains laminar, but its velocity increases to maintain the volumetric rate of flow. Here the pressure against the walls is least and hence there is a pressure drop across the narrower area of a vessel

The volume of blood contained within a flexible blood vessel depends on

1.Transmural Pressure: 2.Degree of flexibility within the vessel

wall

Transmural pressure is always defined as the difference in pressure inside versus outside a hollow structure

Vasscular distensibility is expressed as the fractional increase in volume for each mmHg rise of pressure

All the vessels though the extent varies are distensible (flexible)

Distensibility depends onVessel wall tensionElastic properties of vessel constituent materials

Vessels which are highly elastic are called Windkessel vessels such as aorta and its large branches.

Conducting arteries (conducting because they offer much less resistance to blood flow due to large diameter) i. e. aorta and its major branches are most elastic vessels because they contain more elastin than any other vessel type

These vessels store part of the energy produced by cardiac ejection as potential energy and in doing so their walls are distended during systole. During diastole recoil of the walls converts stored energy into kinetic energy for circulation

Elastic recoil of the arterial system helped by the resistance to outflow offered by peripheral arterioles convert the pulsatile ejection of heart into a steady flow

The heart generates high pressure within the ventricles when it contracts during systole which then drops to near zero during a diastole

During diastole, elastic recoil of arteries pushes blood forward against the downstream vascular resistance generating a significant diastolic pressure

For this reason diastolic pressure drops to only about 80mmHg in the aorta as compared with near zero in ventricles

Veins are most distensible vessels. Veins by changing their luminal configuration i.e. from elliptical to circular cross sectional profiles adjust the capacity of vascular system

Any transmural pressure within a vessel exerts a force on the vessel wall that would tend to rip the wall apart were it not for the opposing force supplied by the muscle and connective tissue of the vessel wall

This opposing force is called the wall tension The tension T is roughly proportional to

transmural pressure i.e. pressure difference on the inside and outside of the wall and the radius r of the vessel. ThusT = a P r Here ‘a’ is a constant. This is Laplace law

More precisely T= P r /w where w is the thickness of the vessel wall

Small vessels are able to withstand higher pressures than vessels of larger diameter

Capillaries with small diameter can withstand relatively high intravascular pressures even though they are composed of a single layer of endothelial cells

In arteries and veins, vessels with thick walls relative to their radius are able to withstand high pressure than vessels with small r/w rato

Large transmural pressure within flexible vessels create large intravascular volumes

Small transmural pressure in stiff walled vessels produce small intravascular volumes

Although arteries are quite distensible because they are most elastic but elastic recoil of arterial wall decreases he amount of blood contained within them

Vascular compliance is given by

The compliance of vein is about 24 times that of its corresponding artery

Fahreus-Lindqvist Effect: Relative viscosity of water, serum or plasma is not altered

when they are made to flow through tubes of different sizes But the relative viscosity of blood is altered when it passes

through tubes of different sizes i.e. blood flow in very minute vessels exhibit far less viscous effect than it does in large vessels. This is called Fahreus-Lindqvist Effect

• in particular there's a decrease of viscosity of blood as it moves from larger vessels to smaller ones (only if the vessel diameter is between 10 and 300 micrometers).

• The viscosity decreases with decreasing capillary radius r. This decrease was most pronounced for capillary diameters < 0.5mm

• Reasons for Fahreus-Lindqvist Effect:

Segre–Silberberg effect, Plasma Skimming

Change in haematocrit

For deformable particles (such as red blood cells) flowing in a tube, there is a net hydrodynamic force that tends to force the particles towards the center of the vessels with diameter between 10 and 300 micrometers This is known as the Segre–Silberberg effect.

On average, there will be more red blood cells near the center of the capillary than very near the wall, leaving plasma at the wall of the vessel

There is a cell free layer near the vessel wall. This redistribution is known as “plasma skimming”

In larger vessels such as aorta and its major branches, the cell free layer is only a small % of complete blood stream, so it does not effect the viscosity of blood much

However in arterioles (<300µm) and capillaries, this layer becomes a great % of the total volume contained within the vessel, so fluid velocity as a whole decreases in these vessels

Newtons law of motion under translational and rotational motion

If the red blood cell is not located directly within the flow centerline (assuming that the flow is fully developed and parabolic, then the forces induced by the fluid velocity will be different on each end of the red blood cell. Due to this influence of forces, the red blood cell will tend to rotate towards the higher flow region

Recall that the higher fluid velocity has a lower shear stress and therefore higher shear stress would be localized closer to the vessel wall

This continues until the

forces acting o the red cell

are balanced and do not

cause rotation

Therefore red cells move to

the lower shear stress region

which have high velocities in

order to balance forces.

Another reason for Fahreus-Lindqvist Effect is change in haematocrit as the vessel diameter decreases

The haematocrit in capillaries e.g. is lower than in the arteries. This is because red blood cells are fairly restricted to the centerline (higher velocity flow) in capillaries and plasma is slowest at the vessel wall

With an inflow haematocrit of 40-50%, capillary haematocrit is about 10-20%

Red blood cells in the capillaries tend to plug the capillary preventing the plasma to flow freely as it does in large blood vessels

While the red blood cells flow fairly steadily, the plasma in between the cells experiences turbulent eddies and recirculation zones

These eddies helps to move materials from the centerline of the plasma towards the vessel wall, potentially helping in the transfer of materials across the capillary wall

These turbulent eddies tend to move compounds to the endothelial cell wall, so that they can diffuse across the wall, instead of convect across the blood and then diffuse across the wall

There is a very small layer of plasma along the blood vessel wall that experiences very high shear stresses, because it is being squeezed between a red blood cell and an endothelial cell. Here the shear stress increases significantly

Effect of gravity on pressureDistance heart-head~ 0.4 mHeart-feet ~ 1.4 m P = gh

55 mm Hg

100 mm Hg

195 mm Hg

100 mmHg95 mmHg 95 mm Hg

-35 mm Hg

1 mm Hg

105 mm Hg

Venous pressures

Arterial pressures

The pressure in any vessel above heart level is decreased by the effect of gravity

The arterial pressure is increased by 0.77mmHg for every centimeter below the right atrium and similarly decreased for each cm above the right atrium