The relationship 1/Crs = 1/CL + 1/Ccw represents which of the following?

The relationship 1/Crs = 1/CL + 1/Ccw represents which of the following?

• A. 1/Crs = 1/CL + 1/Ccw
• B. Crs = CL * Ccw
• C. Crs = CL + Ccw
• D. Crs = CL - Ccw

Answer: (A)

The key idea is how compliances combine when two elastic elements (the lungs and chest wall) are in series in the respiratory system. When you’re delivering a given tidal volume, the pressures across the lungs and chest wall add, so their compliances combine through a reciprocal sum: 1/Crs = 1/CL + 1/Ccw. This is why the expression given directly represents the relationship among Crs, CL, and Ccw. If you solve for Crs, you get Crs = (CL * Ccw) / (CL + Ccw), which shows Crs is smaller than either CL or Ccw. The other options imply Crs is simply the product, the sum, or the difference of CL and Ccw, which do not reflect how series compliances add.

The key idea is how compliances combine when two elastic elements (the lungs and chest wall) are in series in the respiratory system. When you’re delivering a given tidal volume, the pressures across the lungs and chest wall add, so their compliances combine through a reciprocal sum: 1/Crs = 1/CL + 1/Ccw. This is why the expression given directly represents the relationship among Crs, CL, and Ccw. If you solve for Crs, you get Crs = (CL * Ccw) / (CL + Ccw), which shows Crs is smaller than either CL or Ccw. The other options imply Crs is simply the product, the sum, or the difference of CL and Ccw, which do not reflect how series compliances add.