Blood pressure, flow and resistance

Flow is the pressure gradient divided by resistance. Dividing by twice the resistance gives half the flow.

• Flow doubles:
• Correct: Flow halves:
• Flow does not change:

Arterioles have a thick layer of smooth muscle relative to their size. Constricting or relaxing it changes their radius and so their resistance.

• Capillaries:
• Correct: Arterioles:
• Large veins:

The brachial artery runs down the inner arm beside the humerus to the front of the elbow, where the stethoscope is placed during a cuff reading.

• Correct: On the inner side of the upper arm, down to the front of the elbow:
• On the thumb side of the wrist:
• Behind the knee:

Pulse pressure = 110 − 68 = 42 mm Hg. One-third of it is 14 mm Hg. MAP ≈ 68 + 14 = 82 mm Hg.

• 89 mm Hg: 89 mm Hg is halfway between the two numbers. At rest, the arteries spend more time near diastolic pressure, so the mean is lower than halfway.
• 96 mm Hg: 96 mm Hg adds two-thirds of the pulse pressure to the diastolic value, weighting the peak too heavily.
• Correct: 82 mm Hg: Correct. 68 + 42 ÷ 3 = 82 mm Hg.
• 42 mm Hg: 42 mm Hg is the pulse pressure, not the mean pressure.

A stiff aorta cannot stretch to absorb each ejection, so systolic pressure climbs higher. It also stores less stretch, so it recoils less during diastole, and diastolic pressure falls lower. Pulse pressure widens from 40 to 90 mm Hg.

• His heart now ejects twice the stroke volume: A much larger stroke volume would raise systolic pressure, but it would not by itself lower the diastolic pressure. Stroke volume usually does not rise with age.
• Correct: His stiff aorta stretches and recoils less: Correct. Loss of elastic stretch and recoil raises the peak and lowers the trough.
• His arterioles have dilated widely: Wider arterioles would lower resistance and tend to lower both numbers, not raise systolic pressure by 40 mm Hg.
• His veins now push blood back into his arteries: Veins carry blood toward the heart, and valves in the heart and veins prevent it being pushed back into arteries.

Resistance depends on 1 ÷ radius⁴. Halving the radius makes radius⁴ one-sixteenth as large, so resistance becomes 16 times larger. With the same pressure difference, flow becomes one-sixteenth: 200 ÷ 16 = 12.5 mL/min.

• 100 mL/min: Halving flow would treat resistance as depending on the radius alone, not its fourth power.
• 50 mL/min: One-quarter of the flow would treat resistance as depending on radius squared.
• 25 mL/min: One-eighth of the flow would treat resistance as depending on radius cubed.
• Correct: 12.5 mL/min: Correct. (½)⁴ = 1/16, so flow falls to 200 ÷ 16 = 12.5 mL/min.

Vasodilation widens the arterioles, and through the fourth-power rule resistance falls sharply. With the same driving pressure, flow to the muscle rises. Less pressure is lost across the arterioles, so capillary pressure in that bed rises, and total peripheral resistance falls slightly because the bed is in parallel with all the others.

• Radius of the calf muscle's arterioles: up. Relaxed smooth muscle in the arteriole wall lets the vessel widen: vasodilation.
• Resistance of the calf muscle's vascular bed: down. Resistance depends on 1 ÷ radius⁴, so a wider radius lowers resistance steeply.
• Blood flow through the calf muscle: up. By F = ΔP / R, with the pressure difference unchanged and resistance lower, flow rises.
• Pressure in the calf muscle's capillaries: up. Less pressure is used up across the wider arterioles, so more of the arterial pressure reaches the capillaries downstream.
• Total peripheral resistance: down. The calf bed is one of many beds in parallel. Lowering the resistance of one lowers the total a little.

The steepest drop, from about 85 to about 35 mm Hg, is across the arterioles. The same flow passes every level, and by F = ΔP / R the level with the largest resistance uses up the largest pressure difference. Arterioles hold the largest share of the resistance.

• The capillaries: Single capillaries are narrow, but billions of them lie in parallel, so their combined resistance is smaller than that of the arterioles. The graph shows a smaller drop across them.
• Correct: The arterioles: Correct. Arterioles are the resistance vessels, so the pressure falls most across them.
• The medium and large veins: The graph shows a slow, gentle fall through the veins. Valves stop backflow; they do not create a large resistance to forward flow.
• The aorta and elastic arteries: The mean pressure in the aorta is almost flat on the graph. Stretching stores energy that is returned during diastole.

Velocity = flow ÷ total cross-sectional area. The same total flow passes through every level each minute, and the capillaries together have the greatest total area, so blood moves slowest there. The velocity curve is the mirror image of the area curve.

• Correct: Their combined cross-sectional area is the largest of any level: Correct. Largest total area means lowest velocity for the same flow.
• Each capillary is narrow enough to squeeze the blood: A narrow single tube would speed blood up, not slow it, if it were the only path. What matters is the total area of all the capillaries side by side.
• The heart's push has run out by the time blood gets there: Pressure is still about 35 mm Hg entering the capillaries, and velocity rises again in the veins where pressure is even lower. Low velocity is not caused by the push running out.
• Less blood flows through the capillaries than through the aorta: In a closed circuit, the same total volume per minute flows through all the capillaries together as through the aorta.

The first Korotkoff sound appears when cuff pressure just falls below the peak of the arterial wave, at about 120 mm Hg, so that is systolic pressure. The sounds stop when cuff pressure falls below the trough, at about 80 mm Hg: the artery then stays open and flow is smooth, so that is diastolic pressure.

• Systolic 130, diastolic 80: 130 is where the cuff pressure starts, above the peaks of the wave, when no sound is heard yet. The first sound comes at about 120.
• Systolic 120, diastolic 70: The sounds stop when cuff pressure reaches about 80. Cuff pressures near 70 come after the last sound, when the artery is already open all the time.
• Correct: Systolic 120, diastolic 80: Correct. First sound = systolic, about 120; last sound = diastolic, about 80.
• Systolic 80, diastolic 120: This reverses the two. Cuff pressure falls during the reading, so the first sound is at the higher, systolic pressure.

A cuff that is too small cannot spread its pressure over the whole artery, so it needs extra pressure to squeeze the artery shut. Both the first and last sounds occur at a higher cuff pressure than the true arterial pressure, so the reading is too high.

• It will read too low: A cuff that is too large tends to read low. A too-small cuff has the opposite effect.
• It will read accurately: The gauge measures the cuff's pressure, not the artery's. The two match only when the cuff transmits its pressure fully to the artery, which a small cuff does not.
• Correct: It will read too high: Correct. An undersized cuff overestimates blood pressure.
• Only the diastolic value will be wrong: The same error affects both sounds, because both depend on the cuff squeezing the artery closed.