Flow in the Lungs - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 265

under disease conditions, the rate of diffusion will decrease significantly. The surface area
for diffusion determines the available regions for gases to be exchanged. As the surface
area for exchange decreases, which again is common during disease conditions, the rate of
diffusion will also decrease. Lastly, the diffusion coefficient is directly related to the molec-
ular properties of the gas. With a greater solubility and a lower molecular mass the diffu-
sion coefficient will be larger, which in turn leads to a higher rate of diffusion. The
changes in the rate of diffusion for gases across the respiratory boundary follow the same
principles as discussed for diffusion through a fluid.
The same factors that regulate the diffusion of gases through fluids regulate the diffu-
sion of gases through the respiratory boundary. The diffusing capacity is the ability for a
boundary to exchange gas and is defined as the volume of gas that diffuses across a mem-
brane at a pressure difference of 1 mmHg in 1 minute. Under normal resting conditions,
the diffusing capacity of oxygen is 21 mL/min/mmHg. As blood enters the alveolar
capillaries the pressure difference for oxygen is approximately 64 mmHg, but this reduces
to approximately 4 mmHg at the venous (oxygenated) side of the capillary. If we approxi-
mate this to an average of 30 mmHg, this suggests that under normal conditions 630 mL
of oxygen diffuses across the respiratory boundary, every minute. During strenuous exer-
cise, the diffusing capacity of oxygen can increase to 65 mL/min/mmHg. The diffusing
capacity of carbon dioxide is approximately 20 times greater than oxygen because it is
directly related to the diffusion coefficients (see Table 9.1 ). Therefore, the diffusing capac-
ity of carbon dioxide is approximately 425 mL/min/mmHg under normal conditions or
approximately 1300 mL/min/mmHg during strenuous exercise.

Example
Imagine standing on the top of a mountain where the atmospheric pressure is 480 mmHg and
the ambient temperature is 10 C. Assume that the percent composition of air is the same as
described in Table 9.2 (although the exact partial pressures will be different). Calculate the respi-
ration rate needed to maintain the body's oxygen requirements of 270 mL/min at standard body
temperature and pressure (i.e., 760 mmHg, 37 C). Assume that your tidal volume increases to
750 mL and that 35% of the inspired oxygen enters the blood and that all of this would meet the
body's oxygen requirements.

Solution
First let us determine the partial pressures of each of the major gases that are in air:

TABLE 9.3

Gas Percent Composition Partial Pressure

N 2 78% 374.4 mmHg

O 2 21% 100.8 mmHg

CO 2 0.04% 0.2 mmHg

H 2 O 0.5% 2.4 mmHg