general principles of circulation

Arteries are strong, elasticvessels adapted for carryingblood away from the heartunder high pressure.

Three distinct layers:Endothelium – Inner mostlayer. Rich in elastic andcollagenous fibers. Called thetunica interna.

Middle layer – Tunica media.Smooth muscle fibers, thicklayer of elastic connectivetissue.

Outer layer – Tunica externa.Attaches the artery to tissues. Contains vasa vasorum that givesRise to capillaries

Hagen-Poisseuille LawTM

Poiseuille's LawThe biggest surprise in the application of Poiseuille's law to fluid flow is the dramatic effect of changing the radius.A decrease in radius has an equally dramatic effect, as shown in blood flow examples.

Blood Flow Examples

Suppose you have an emergency requirement for a five-fold increase in blood volume flowrate (like being chased by a big dog)? How does your body supply it?According to Poiseuille's law, a five-fold increase in blood pressure would be required if the increase were supplied by blood pressure alone!But the body has a much more potent method for increasing volume flowrate in the vasodilation of the small vessels called arterioles.Since the smaller vessels provide most of the resistance to flow, the arterioles in their position just prior to the capillaries can provide a major controlling influence on the volume flowrate. This system of small vessels can constrict flow to one part of the body while enhancing the flow to another to meet changing demands for oxygen and nutrient

Blood Flow Examples

But how do we know which way a fluid will flow?

We use an Engineering Trick:

Dimensionless Numbers

Invented by an Engineer: Predicts Laminar flow versus Turbulent

flow

Low Number means Laminar Flow

High Number means Turbulent Flow

Reynold’s Number is: The ratio of Inertial forces to Viscous

forces

Reynold’s Number = vpL/u

Reynold’s Number = vpL/u

p is the weight-density of the fluid u is the dynamic viscosity of the fluid v is the velocity of the fluid flow L the Characteristic Length

Maintains fairly constant blood flow despite BP variation

Myogenic control mechanisms occur in some tissues because vascular smooth muscle contracts when stretched & relaxes when not stretched E.g. decreased arterial pressure causes

cerebral vessels to dilate & vice versa

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Metabolic control mechanism matches blood flow to local tissue needs

Low O2 or pH or high CO2, adenosine, or K+ from high metabolism cause vasodilation which increases blood flow (= active hyperemia)

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Wall Tension Pascal's principle requires that the pressure is everywhere the same inside the balloon at equilibrium. But examination immediately reveals that there are great differences in wall tension on different parts of the balloon. The variation is described by Laplace's Law.

LaPlace's Law The larger the vessel radius, the larger the wall tension required to withstand a given internal fluid pressure.

For a given vessel radius and internal pressure, a spherical vessel will have half the wall tension of a cylindrical vessel.

Why does the wall tension increase with radius?

Why does wall tension increase with radius?

If the upward part of the fluid pressure remains the same, then the downward component of the wall tension must remain the same. But if the curvature is less, then the total tension must be greater in order to get that same downward component of tension.

Tension in Arterial Walls The tension in the walls of arteries and veins in the human body is a classic example of LaPlace's law. This geometrical law applied to a tube or pipe says that for a given internal fluid pressure, the wall tension will be proportional to the radius of the vessel.

The implication of this law for the large arteries, which have comparable blood pressures, is that the larger arteries must have stronger walls since an artery of twice the radius must be able to withstand twice the wall tension. Arteries are reinforced by fibrous bands to strengthen them against the risks of an aneurysm. The tiny capillaries rely on their small size.

Capillary Walls

The walls of the capillaries of the human circulatory system are so thin as to appear transparent under a microscope, yet they withstand a pressure up to about half of the full blood pressure. LaPlace's law gives insight into how they are able to withstand such pressures: their small size implies that the wall tension for a given internal pressure is much smaller than that of the larger arteries. Given a peak blood pressure of about 120 mmHg at the left ventricle, the pressure at the beginning of the capillary system may be on the order of 50 mmHg. The large radii of the large arteries imply that for pressures in that range they must have strong walls to withstand the large resulting wall tension. The larger arteries provide much less resistance to flow than the smaller vessels according to Poiseuille's law, and thus the drop in pressure across them is only about half the total drop. The capillaries offer large resistances to flow,but don’t required much strength in their walls