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# Pressure regulation and fluid dynamics of the respiratory system

## Problem

During breathing, the body directs the flow of oxygen and nitrogen via coordinated motion of the diaphragm and lungs. In particular, during inhalation the diaphragm muscles are used to increase the volume of the lungs, leading to air intake in a manner analogous to the operation of a piston. During exhalation, the diaphragm muscles undergo an almost-reverse process, decreasing the volume of the lungs and pushing air back out of the body. A simple schematic of the respiratory system is shown in Figure 1.
During inhalation, the alveoli, capillary-rich terminals of pulmonary veins, expand as well, increasing the surface area of the capillary-air interface in order to more effectively accept oxygen into the bloodstream. The key mechanism by which this process occurs is gaseous diffusion, in which carbon dioxide diffuses out of de-oxygenated blood through a thin membrane, while oxygen diffuses into the blood. This process is aided by the high solubility of carbon dioxide in blood, which is nearly 20 times that of oxygen.
The dynamics of the repeated expansion and contraction of the alveoli during respiration are governed by the control of pressure provided by the diaphragm and the elastic response of the alveoli, which passively contract during exhalation without the need for active muscle stimulation. Rather, the diaphragm serves to actively modulate the pressure within the respiratory system, the lungs serve to transmit these pressure differences to the alveoli, and the alveoli respond to these pressure changes in a manner analogous to balloons. Chronic emphysema occurs when the tissues comprising the alveoli lose their elasticity, resulting in incomplete re-compression during exhalation that manifests as labored breathing.
Figure 1: A simplified diagram of the respiratory system.
Which of the following calculations gives the most accurate ratio of the diffusion rates of carbon dioxide molecules to oxygen molecules in the alveoli?