Questions: Airway Resistance and Breathing Mechanics

Question 1

During an asthma attack, smooth muscle contraction halves the radius of the conducting airways. According to Poiseuille's law, airway resistance:

• A. Doubles, since resistance is inversely proportional to radius
• B. Quadruples, since resistance is inversely proportional to radius squared
• C. Increases 8-fold, since resistance is inversely proportional to radius cubed
• D. Increases 16-fold, since resistance is inversely proportional to the fourth power of radius

Answer: (D)

Poiseuille's law: R ∝ 1/r⁴. If r is halved, resistance changes by 1/(r/2)⁴ = 16/r⁴ — a 16-fold increase. This fourth-power dependence is why asthma can rapidly become life-threatening: what appears to be modest bronchospasm produces catastrophic increases in resistance, and the work of breathing (proportional to resistance × flow) quickly exhausts respiratory muscles. Options A, B, and C reflect the common misconceptions that resistance scales as 1/r, 1/r², or 1/r³.

Question 2

In a healthy adult lung at rest, where does the majority of airway resistance reside?

• A. The trachea and mainstem bronchi, since they carry the entire airflow through a single tube
• B. The smallest bronchioles (< 2 mm), since they have the narrowest individual lumens
• C. The medium-sized bronchi (generations 3–7), where tube number and individual resistance balance to produce the highest total resistance
• D. The alveolar ducts, since precise laminar flow is required for gas exchange

Answer: (C)

Despite being narrowest individually, the smallest bronchioles contribute little to total resistance under normal conditions because there are thousands of them arranged in parallel — parallel resistances add reciprocally, so thousands of tiny tubes present far less combined resistance than fewer larger ones. Most resistance resides in the medium-sized bronchi, where the number of airways is still relatively small but caliber is already substantially reduced. This is the 'quiet zone': small-airway disease can progress silently before measurable increases in total airway resistance appear.

Question 3

Because the smallest bronchioles have the narrowest individual lumens, they contribute more total airway resistance than medium-sized bronchi in a healthy lung.

• T. True
• F. False

Answer: False

Paradoxically, the smallest bronchioles contribute relatively little to total resistance in a healthy lung. There are thousands of them arranged in parallel, and parallel resistances add reciprocally — the combined resistance of all small bronchioles is far less than that of the fewer medium-sized bronchi. This 'quiet zone' means small-airway obstruction can be severe before total airway resistance measurably increases. In disease states like asthma, however, small airways become the primary obstruction site because they lack cartilaginous support and are prone to collapse.

Question 4

β₂-agonist inhalers (like albuterol) relieve asthma symptoms by relaxing bronchial smooth muscle, increasing airway radius and dramatically reducing resistance.

• T. True
• F. False

Answer: True

β₂-adrenergic receptors on bronchial smooth muscle, when activated by albuterol, trigger relaxation via cAMP-mediated pathways. Because R ∝ 1/r⁴, even a modest radius increase substantially reduces resistance — a 20% radius increase reduces resistance by roughly half (1/1.2⁴ ≈ 0.48). This rapid bronchodilation directly reverses the bronchoconstriction causing obstruction, making β₂-agonists the first-line rescue treatment for acute asthma.

Question 5

Why does Poiseuille's fourth-power law make even a modest reduction in airway radius clinically dangerous in asthma, when the same fractional radius reduction in a pipe would seem like a minor engineering concern?

Model answer: The physics is the same in both cases — R ∝ 1/r⁴ governs any tube. The difference is that the body cannot compensate indefinitely by increasing the pressure driving airflow: the respiratory muscles have a finite maximum effort. A 30% reduction in airway radius increases resistance roughly 4-fold (1/0.7⁴ ≈ 4.2), which may exceed the respiratory muscles' capacity to maintain adequate ventilation, causing rapid fatigue and hypoxemia. Unlike an engineer who can simply use a higher-pressure pump, a patient in status asthmaticus is doing enormous muscular work but cannot maintain airflow — the fourth-power dependence turns modest anatomical changes into physiologically catastrophic resistance increases.

This is also why even small improvements in airway radius from a bronchodilator provide dramatic relief: a 20% radius increase reduces resistance by half. The fourth-power law works in the patient's favor during treatment just as powerfully as it works against them during bronchospasm.