Pressure and Flow

Basic relation for fluid flowing in a pipe: Flow = Pressure/Resistance

Analogous to Ohm’s Law for electric current: Amperes = Volts/OhmsCurrent is flow of electrons, volts is driving force, ohms is resistance to flow.

Law relating pressure, flow and resistance for fluids flowing in pipes is sometimes referred to as Ohm’s Law for flow of fluids.

In the vasculature, pressure is the force exerted on the wall of a vessel (arises from ventricular contraction, usually expressed as mm Hg), flow is the volume moving past a given point per minute. That leaves resistance.

Poiseuille’s Law

Poiseuille was a French physician, invented the mercury sphygmomanometer for measuring arterial pressure. He also worked out the relations of the resistance to the length and diameter of a pipe: Resistance is inversely proportional to the fourth power of the radius (or diameter), directly related to the length of the pipe.

Resistance depends on the length of the pipe, but extraordinarily sensitive to the radius. Doubling the radius drops resistance to 1/16 of what it was, flow increases to 16x.

This is why you should buy slightly bigger diameter water hoses as you increase their total length.

Poiseuille’s work was later applied by the government of Paris to designing the city’s first sewer system.

Fluids always flow downhill in pressure. The pressure falls, the amount depending on the resistance. In the systemic circulation, cardiac output, about 5 L/min, is the flow. The total drop in pressure is 120 mm Hg, beginning and ending in the heart.

The pathway of systemic blood and the pressures in the vasculature are: Left Ventricle -> 120 mm Hg Aorta = 120 mm Hg -> 80 mm Hg (average around 100 mm Hg) Arteries = 100 mm Hg Arterioles = 100 mm Hg -> 50 mm Hg Capillaries = 50 mm Hg -> 20 mm Hg Venules = 20 mm Hg -> 15 mm Hg Veins = 15 mm Hg -> 10 mm Hg Left Ventricle = 0 mm Hg

This shows fall in pressure in each segment of the circulation:

Flow through each segment is identical, pressure drop in each segment must, therefore, reflect their resistances.

About half the total pressure drop occurs in the arterioles. The arterioles also have muscle in their walls that change the diameter (therefore, the resistance) in the arterioles.

Arterioles have the greatest resistance and are also most subject to changes in resistance; they are called the resistance vessels.

Autoregulation of Blood Flow

Smooth muscle has some important properties. It relaxes when local oxygen levels fall or when metabolic waste concentrations rise; contracts when oxygen levels rise or waste product concentrations fall. Since arterioles have smooth muscle in their walls, contraction or relaxation constricts or expands the vessel diameter. This has large effects on resistance; hence, on flow.

When a muscle is exercised, it’s metabolic rate increases. This relaxes arterioles in that muscle (strictly local), increasing local blood flow – providing more oxygen and removing more waste. This is autoregulation of blood flow.

Where does flow fall in order to make that extra flow possible? Noplace! It increases venous return, increasing cardiac output. Remember Starling’s Law?

Neural Regulation of Pressure and Flow

Arterial pressure is monitored by baroreceptors (stretch receptors), mostly in the atria and carotid arteries. They transmit afferent information to the brain, with effects on autonomic output. These reflexes occur within seconds, adjust pressure to postural changes.

Sympathetic output increases heart rate and cardiac contractility, increasing cardiac output. It also constricts arterioles (except in brain), decreasing flow to most tissues and increasing arterial pressure. Autoregulation increases flow to muscles that are being used.

Parasympathetic input decreases heart rate (inhibits S-A node) and dilates arterioles, decreasing arterial pressure.

These are global, not local effects.

Capillary Dynamics

The cardiovascular system role is getting stuff to cells and removing stuff from their environment. This happens in the capillaries, which have pores in their walls large enough to let most things cross but are too small to allow proteins or cells to do so.

Fluid containing goodies flows out of the proximal part of a capillary, mixes with interstitial fluid that has waste products that diffused out of the cells. Fluid containing wastes enters the distal part of the capillary. Capillary dynamics describes the forces that make this happen.

Start at proximal end. Hydrostatic pressure in capillary is about 35 mm Hg. This is pushing fluid out. Since protein can’t get out, protein inside capillary exerts colloid osmotic pressure (-25 mm Hg) in opposite direction. Thus, net driving force = 10 Hg forcing fluid out.

At distal end, resistance of capillary results in hydrostatic pressure falling to only about 15 mm Hg. Now the colloid osmotic pressure bringing fluid back in exceeds the hydrostatic pressure pushing it out. Thus, volumes entering and leaving the capillary are the same.

Why does your thumb swell when you hit it with a hammer?

This illustrates importance of colloid osmotic pressure in bringing fluid back into capillaries at their distal ends. Crush injuries damage capillaries, so they no longer prevent proteins and cells from leaving the circulation.

Therefore, colloid osmotic difference between plasma and interstitial fluid no longer exists. Therefore, fluid doesn’t re-enter capillaries – no driving force. Thus, injured area swells (size is limited by the fact that the connective tissue can withstand the pressure). When capillary repair occurs, swelling goes back down. The stages of discoloration reflect steps in the destruction and removal of hemoglobin from the tissue.

Compliance and Distensibility

Vessels have varying degrees of elasticity. The volume change per unit change in pressure is its compliance. The percentage change in volume per unit change in pressure is its distensibility.

If two vessels have identical distensibility, but one has twice the total volume of the other, it has twice the compliance.

The distensibility of the veins is about 8x than that of arteries, and about 3x as much blood is in veins as in arteries. Thus, venous compliance, about 25x that of arteries, about 95% of total compliance. Veins are, therefore, sometimes called the compliance vessels (just as arterioles are sometimes called the resistance vessels).

Since veins have about 95% of the compliance, if plasma volume increases by 100 ml, about 95 ml will wind up in the veins and 5 ml in the arteries.

Conversely, if plasma volume decreases by 100 ml, venous volume will fall by 95 ml, arterial volume by 5ml.

The veins, therefore, serve as a reservoir for blood, which can be added to or removed from it readily.

Thus, veins are also called the storage vessels.

Regulation of Arterial Pressure

Short term regulation (adjustments to postural changes, for example) work mostly by autonomic reflexes originating with stretch receptors in carotid arteries and atria.

These work in seconds: next time you pop out of bed quickly, pay attention to how long the lightheadedness lasts. The receptors adapt fairly quickly, and can’t regulate arterial pressure over long periods.

But arterial pressure is regulated over many decades. How?

Body Fluid System for Long Term Regulation of Arterial Pressure

This is the so-called renal-body fluid system for long term regulation of arterial pressure. The “+” means that the effect is in the same direction as the cause; the “-” means that the effect is in the opposite direction.

Renal Function Curve

The vertical axis is relative rate of urine production (1 = normal). Output is zero below about 60 mm Hg, increases to 1 at 100 mm Hg, and rises very rapidly as pressure increases. At 105 mm Hg, it’s 5.

You can see water loss falls to near zero with pressures around 60 mm Hg, rises steeply at pressures a little above normal. This is how arterial pressure is maintained at 100 mm Hg over very long periods.

Hypertension

Hypertension is chronic elevated arterial pressure. It’s very common, and more than 90% of time it’s essential hypertension (no known cause). The renal function curve in essential hypertension is shifted to the right. Arterial pressure is regulated at a pathologically high set point.

Why is hypertension a problem?

Your arterial pressure can exceed 150 mm Hg during exercise, causing no problems. Why is hypertension a problem?

1. We have small injuries to capillaries all the time. As pressure goes up, repair decreases and the local cells die. This can have serious consequences in the brain, heart, kidneys.

2. Deposition of plaque on arterial and arteriolar walls increases as pressure increases. Since this increases pressure by increasing resistance, hypertension is self-aggravating (positive feedback).

3. Hypertension has no externally detectable symptoms, so people don’t seek medical attention until it’s been discovered incidental to a general exam.

4. Pumping against increased pressures causes cardiac hypertrophy. Vasculature in heart increases, but fails to keep up with increased cardiac muscle mass. Result: reduced perfusion of the heart.

How is hypertension managed?

1. Diuretics, to increase urine output.2. Reduced fluid intake, to reduce plasma volume.3. Reduced salt intake, to reduce plasma volume osmotically.

Muscle Pumps

Here’s a mystery : Pressure in the veins in your feet is less than 15 mm Hg. Raising blood to your heart (50 inches or so) requires a pressure of about 100 mm Hg. How can this happen?

Veins have valves that allow blood to flow toward the heart, but not away from it. Thus, any pressure on a vein segment (region between two valves) forces its contents in the direction of the heart.

Normal muscle tone in legs pumps blood from feet to heart this way. That’s why ceremonial guards standing at attention sometimes faint.

Examples illustrating muscle pumping:1. Swelling of feet with prolonged sitting (long airplane flights; meals

in Japanese homes)2. Swelling of feet when a leg is immobilized in a cast.3. Chronic situations (driving a long distance truck for years;

repeated pregnancies) can result in varicose veins – veins stretched to the point that the valves no longer prevent backward flow.

Pulmonary Circulation

Vessels in the pulmonary circulation are much shorter than those in systemic. Hence, total resistance is only about one-third of that in the systemic. But cardiac output is the same on both sides. Flow = Pressure/Resistance Pressure = Resistance x Flow

If flow is the same but resistance is lower, pressure must be lower. It is. Pressure in pulmonary artery is only about 30 mm Hg.

One interesting consequence is that because pressure is so low, the upper parts of the lungs are relatively poorly perfused. During exercise or other conditions in which metabolic rate increases, sympathetic stimulation increases pressure. One consequence is that poorly perfused parts of the lungs get more blood than they were getting. That is, we effectively have bigger lungs when we need them.

Heart Failure

When the heart is unable to eject venous return (failure of Starling’s Law), it is said to have failed. This is usually the result of injury of one sort or another.

One result is accumulation of fluid in interstitial spaces (edema) and in the air spaces in the lungs. This reduces the volume of air that can enter the lungs.

Fluid in the lungs or pulmonary airways is congestion. Heart failure severe enough to cause it is congestive heart failure.

Circulatory Shock

When pressure falls to where tissue perfusion is inadequate to prevent damage, the condition is circulatory shock. When the tissues being damaged include the heart, a positive feedback loop exists and the condition continually worsens. This is progressive or uncompensated shock. When the heart isn’t damaged, the mechanisms for short and long term regulation of pressure can prevent long term damage. This is compensated shock. Generally, loss of 10% of blood volume is compensated, more than 40% loss drops arterial pressure to near zero.

Causes and treatment of shock:1. Hypovolemic (hemorrhagic is a subcategory of this). 2. Cardiogenic. Results from damage to heart.3. Neurogenic. Usually from massive parasympathetic output, which

results from fear and anxiety.4. Treatment: Hydration, keep victim horizontal so heart isn’t

pumping uphill, reassurance to reduce anxiety.

Cardiac Circulation

Heart’s blood supply comes from coronary artery, which branches off the aorta. It has several interesting peculiarities.

One is the compensation for the fact that the arteries closest to the endocardial surface get squeezed shut before those closest to the epicardial surface do. Those nearest the endocardial surface have larger diameters, so more blood flows through them when they are open.

Another is the so-called collateral circulation – pathways through which blood can flow between small arteries.

Notice that if one vessel is blocked (right side), the area it perfuses still has a blood supply.

Aerobic exercise promotes the development of collateral circulation in the heart. This is the basis of the protective effect it has against fatal heart attacks.

Heart Attacks (Cardiac Infarctions)

When perfusion to part of the heart isinadequate, that area will die. That’s an infarction, the affected region is an infarct. With luck, it turns into a scar. There are three main consequences to infarction.1. Fibrillation. Damaged muscle can be hyperirritable, generating

action potentials at high frequencies. This is fibrillation. A defibrillator subjects the heart to a powerful shock, making every cell simultaneously contract and be refractory. When all goes well, the region quiets down and a normal sinus rhythm resumes.

2. The scar may become elastic. When this happens, some blood is pumped into the stretchy region instead of being ejected during systole. This is systolic stretch. Cardiac output is reduced because end-systolic volume is increased.

3. A small hole may form in the wall of the heart. With each beat, a little blood is squirted into the pericardial space. This reduces cardiac output by reducing end-diastolic volume. This is cardiac tamponnade.