7.1: Partial Pressures
- Page ID
- 34488
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The lung is well designed to perform its function of gas exchange with the atmosphere, and in this chapter we will look at some of the factors that allow the lung to perform this function and how these factors might change in disease.
Before we do that though, we need to be able to calculate the units of measurement we use when describing gas exchange. When referring to gas exchange we are really referring to diffusion of gases down their concentration gradient, but rather than use concentrations, we use partial pressures.
Partial pressures describe what proportion of the total pressure is exerted by a particular component of a mixed gas. Let us look at the specific situation we are interested in to illustrate this description.
Atmospheric pressure at sea level is 760 mmHg. This pressure is generated by the collisions of all the molecules with each other and other objects. At high altitude there are fewer molecules, so fewer collisions, and hence atmospheric pressure is lower.
Now looking at the composition of our atmosphere we know that 79 percent is nitrogen, 20.9 percent is oxygen, and some trace gases collectively get us to 100 percent. Now let us calculate a partial pressure. If 79 percent of the atmosphere is nitrogen, then 79 percent of our atmospheric pressure is generated by the collisions by nitrogen molecules. Likewise 20.9 percent of the atmospheric pressure is due to oxygen, so to calculate the partial pressure of oxygen (PO2) we simply multiply atmospheric pressure (PB) by the percentage of oxygen, which means our atmosphere has a partial pressure of oxygen of 159 mmHg.
\[PO_2 = \%O_2 \times P_B \nonumber \]
\[PO_2 = 20.9\% \times 760\,mmHg = 159\,mmHg \nonumber \]
Alveolar PO2
Although related, we are more interested in the PO2 at the gas exchange surface—that is the alveolar PO2 denoted as PAO2 (note the uppercase A; lowercase refers to arterial PO2 (i.e., PaO2)). This value differs significantly from atmospheric PO2 at about 100 mmHg. So why the drop of nearly 60 mmHg from atmospheric PO2?
To calculate alveolar PO2 we need to account for the water vapor that is added to the inspired air as it enters the airways. This is equivalent to adding another gas and must be accounted for. Water vapor exerts a pressure of 47 mmHg. Subtracting this from our atmospheric pressure, our total gaseous pressure is 713 mmHg; multiplying this by our fraction of inspired O2 (FiO2 is merely the percentage (fraction) of oxygen inspired), we see our alveolar PO2 is theoretically 149.7 mmHg (i.e., ~150 mmHg).
\[P_AO_2 = FiO_2 \times (P_B - P_{H_2O}) \nonumber \]
\[P_AO_2 = 20.9\% \times (760-47) = 149.7\,mmHg \,or \sim150\,mmHg \nonumber \]
If we understand that there will be mixing with air remaining from the previous breath, the real PAO2 is 100 mmHg (however, we will see this varies across the regions of the lung).
So how does this value relate to gas exchange in the lung? The venous blood PO2 (PVO2), returning from the systemic tissue where oxygen has been consumed, is 40 mmHg (see figure 7.1). This blood passes the gas exchange surface, and a pressure gradient of 60 mmHg allows oxygen to move into the pulmonary blood. By the time the blood has passed the alveolus, arterial PO2 will have equilibrated with the alveolar PO2 and will also be 100 mmHg. These numbers are well worth committing to memory.
Figure 7.1: Oxygen tensions around the alveolus.
The other critical values we need to address here are the partial pressures of CO2 (see figure 7.2). Venous blood returning from the tissue has a PCO2 of 45 mmHg, compared to alveolar PCO2 that is 40 mmHg. This pressure gradient of 5 mmHg is enough to allow blood to equilibrate with the alveolus, and so arterial PCO2 is 40 mmHg. Again, these numbers are worth remembering.
Figure 7.2: Carbon dioxide tensions around the alveolus.
A much smaller diffusion gradient is needed for CO2 because CO2 is much more soluble than oxygen, a factor among others that is included in Fick’s law of diffusion.
Figures
Figure 7.1: Oxygen tensions around the alveolus. Grey, Kindred. 2022. CC BY 4.0. Added red blood cells by Lucas Helle from Noun Project. https://archive.org/details/7.1_20220125
Figure 7.2: Carbon dioxide tensions around the alveolus. Grey, Kindred. 2022. CC BY 4.0. Added red blood cells by Lucas Helle from Noun Project. https://archive.org/details/7.2_2022012