Understanding lung function is vital for both intensivists and anaesthetists. Normal lung physiology is unfortunately extremely complex, and this complexity is further enhanced in sick lungs! Lacking smart and well-programmed supercomputers to simulate normal lung physiology, we tend to rely on gross over-simplification. The relationship between our current understanding of how lungs function, and what actually happens is perhaps similar to the relationship between counting on one's fingers and advanced matrix algebra! Unfortunately, many of the fruitful analogies that we use have been turned into dogma!
In most textbooks, you will encounter a vast array of "laws", which examination candidates in particular are encouraged to regurgitate, often with minimal understanding. For the record, here are some of them:-
| A List of Laws Note that this mildly formidable table is mainly for reference purposes. The wise reader will skip over it, and come back from time to time. All equations are discussed in a friendly fashion in the body of the text! Those we are on "first name" terms with (Henry, Charles & Graham) will be used less extensively! | ||
| Name | Equation | Meaning |
| Boyle's Law | P.V = K | In a container filled with gas, if you decrease the volume, the pressure will correspondingly increase, and vice versa. |
| Dalton's Law | In a mixture of gases, each gas behaves as if it were on its own: it exerts a partial pressure that is independent of that exerted by other gases in the mixture. | |
| Hooke's Law |  L  T | The change in length of a spring is proportional to the tension exerted on the spring. |
| Laplace's Law | P = 2.T/r | The pressure inside a bubble exceeds the pressure outside the bubble by twice the surface tension, divided by the radius. In other words, the smaller a bubble, the more the pressure inside it exceeds the pressure on the outside. |
| Poiseuille's Law | R = 8.L.eta/(pi.r4) | Where laminar flow occurs, the resistance to flow decreases with the fourth power of the radius - if you double the radius, the resistance decreases sixteen times! Resistance also depends on the eta, (the viscosity of the gas or fluid), as well as the length of the tube being assessed (L). Note that with turbulent flow, things are completely different - we can't even talk about "resistance" as the drop in pressure is not directly related to flow, but to flow squared! |
| The Fanning Equation | P 1 / r5 | With turbulent flow, for any particular flow rate, pressure drop depends on the fifth power of the radius of the tube. |
| Fick's Law | Vgas A * P / L | Gas transfer through a membrane is proportional to membrane surface area (A) and partial pressure gradient across the membrane(P), and inversely proportional to thickness (L). |
| Graham's Law | D sol / MW0.5 | Diffusion of molecules is inversely proportional to the square root of their molecular weight, and directly proportional to their solubility. |
| Henry's Law | The number of molecules of gas dissolved in solution is proportional to the partial pressure of the gas. | |
| Charles' Law | V = K'. T | As the temperature of an amount of gas increases, so does its volume (maintaining a constant pressure). We can combine this with Boyle's law to get: PV = nRT Where n is the number of moles of gas, and R is a constant, the universal gas constant. At standard temperature and pressure, a mole of gas occupies 22.4 litres. The actual value for CO2 and N2O is about 22.2 litres. |
| Reynold's number | linear gas velocity * diameter * density / viscosity | Reynold's number is dimensionless. Turbulence occurs if Reynold's number is over 1000, and flow is entirely turbulent if it exceeds 1500. |
Basic Ideas
Atmospheric oxygen arose as a toxic by-product of the very first photosynthetic organisms, which were possibly quite similar to today's blue-green algae. Smarter organisms rapidly learned to use this oxygen, and minimise its toxic effects. When they possibly unwisely decided to abandon their individual identities and co-operate to form multicellular organisms, and moved onto land, then their problems really began! They needed:
- Ways of acquiring atmospheric oxygen in large quantities;
- A method to transport this O2 to distant, oxygen- starved cells;
- Processes for removal of carbon dioxide, the principal metabolic waste product.
All of these are more-or-less adequately fulfilled by the tightly entwined cardiovascular and respiratory systems. The respiratory system is a marvellous, efficient pump for passing air over the capillary bed of the lung, where oxygen moves into the blood and CO2 is removed from the blood. The inefficient and failure-prone cardiovascular system then takes over, finally distributing oxygen to oxygen-hungry cells throughout the body. The inefficiency with which this occurs can be seen if we look at the oxygen cascade, which documents the changes in partial pressure of oxygen from inspired air down to the mitochondrion where the oxygen is actually used. Oxygen moves down a gradient, from a partial pressure of about 160mmHg in the atmosphere, down to about 4-20mmHg in the mitochondrion! The steps are:
| Inspired oxygen | 160 mmHg | |
| Alveolar oxygen | ~ 120 mmHg | |
| Oxygen in the blood | ~ 100 mmHg | |
| Oxygen at tissue level | ~ 4-20 mmHg |
- Atmospheric pressure at sea level is about 760mmHg, and the concentration of oxygen is 20.95%. Using Dalton's Lawwe calculate that in dry, inspired air, the partial pressure of oxygen is 159mmHg. Unfortunately, air within the lungs is 100% saturated with water. We need to re-think! If we know that the partial pressure of water vapour at 37 degrees Celsius is 47mmHg, we can work out that the partial pressure of the remaining gases is (760 - 47)mmHg. We'll call this barometric pressure that excludes water vapour pressure the 'dry barometric pressure', or PBdry. Applying Dalton's law yet again, we determine that the inspired PO2 is therefore actually 149mmHg, once the air has become fully hydrated in the nose. Let's abbreviate the inspired PO2 to PiO2. But wait a bit..
- Oxygen is taken up in the lung! This will decrease the amount of oxygen in the alveolar air. The decrease will be directly related to the amount of oxygen taken up, and inversely related to the alveolar ventilation. In other words, the greater the alveolar ventilation, the less the effect of this oxygen uptake on the fraction of oxygen in the alveolar air. This is an expression of the "universal alveolar air equation". We say:
alveolar PO2 ~ PBdry * (FiO2 - fractional O2 uptake)
Where the fractional O2 uptake is equal to: O2 uptake / alveolar ventilation
We may abbreviate alveolar PO2 to PAO2. Thus:
- PAO2 ~ PBdry * (FiO2 - O2 uptake / alveolar ventilation)
Note that this is only approximate - differences between inspired and expired volumes will affect the estimate. In addition, if you guessed that PAO2 fluctuated with each breath, you would be correct, but this variation is normally only about 3mmHg.
(There are more convenient ways of estimating PAO2, although many of these are fairly inaccurate!) Plugging values into the above, we might get something like:
PAO2 = (760 - 47) * ( 0.2095 - 250/5000)
Where the true barometric pressure is 760mmHg - the partial pressure of water vapour at 37 degrees is 47mmHg, the inspired oxygen concentration is 20.95%, the oxygen consumption is say 250 ml/minute, and the alveolar ventilation is 5 litres/minute. This gives us a PAO2 of about 114 mmHg. We rush on, inexorably down the oxygen cascade!
- In a healthy young adult breathing air, the gradient from alveolus to capillary is minimal - under 15mmHg. In the 'normal' elderly person, this may rise to 37mmHg! (One convenient estimate of this gradient is simply 4 + age/4 mmHg)! In the critically ill, this alveolar/arterial oxygen difference may be hundreds of millimetres of mercury. Nevertheless, even in the normal young individual we still take a small step down, to an arterial partial pressure of oxygen (PaO2) of about 100mmHg.
Another useful estimate for PaO2 at sea level (in healthy subjects breathing air) is given as:
- PaO2 = 102 - 0.33 * (age in years)
This is expressed in mmHg, and we stress that the confidence limits for this estimate are fairly wide: +- 10mmHg.
- The big drop comes at the tissue level, where the PO2 within the mitochondrion has been estimated to be as low as 4-20mmHg! In some normally functioning cells this PO2 may even drop to 1mm Hg!Perhaps this is the PO2 that our ancient unicellular ancestors first found that they could effectively use, and there has been no (heh) pressure to subsequently change, or perhaps this low PO2 is a trade-off related to the number of capillaries needed to support the tissues, but we know one thing, and that is that we could sure use a bigger tolerance margin in critically ill patients!
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