Ventilation:Perfusion Ac mismatch
Normal breathing A simple obstructionFetch the oxygen? ◦ Obstructive lung diseases

You might want to read O2 Transport and CO2 Transport if you’re not familiar with them already.

Mismatch of blood perfusion of alveoli and alveolar ventilation occurs in many lung diseases. It is important to understand how mismatch affects the arterial partial pressures of O2 and CO2 (PaO2 and PaCO2), because these effects differ between the two gases. Some obstructive lung problems respond to supplemental O2, while others do not. Understanding Ac mismatch helps identify when this might be the case, and why.

Most of what is confusing about A:c mismatch comes down to O2 transport being a carrier-mediated process that can be saturated and that O2 is entering the body, while the opposite is true of CO2 in every respect.

Normal Breathing
During normal quiet breathing, cardiac output is about 5 L/min and alveolar ventilation is much the same. Similar volumes of blood and air meet at the alveolar surface to exchange gases. When this doesn’t happen – because blood flow or airflow is disturbed – we have alveolar ventilation (A):perfusion (c) mismatch. Most respiratory diseases have a component of such mismatch, whether it is on a large scale, or spread diffusely through the lung. A tumour can occlude a bronchus and limit airflow to an entire lobe, or bronchoconstriction can limit ventilation of many or all alveoli to varying extents.

Now, recall the relationship between alveolar ventilation A) and the partial pressure of CO2 in the alveoli (PaCO2). CO2 equilibrates pretty easily at the alveolar surface, so PaCO2 is going to be very close to the partial pressure of CO2 in the alveoli (PACO2).

Figure 1: The relationship between alveolar minute ventilation (A), the partial pressure of CO2 in the alveoli (PACO2) and actual CO2 content in blood (PaCO2). (A) Shows how changing alveolar ventilation flow rates influences the PACO2 in the alveoli. Doubling the rate of A halves the PACO2; halving Ahas the opposite effect.  (B) Depicts the relationship between the PaCO2 and the CO2 content of blood. Dashed lines show the typical values.

At a typical A of 5 L/min, PACO2 should be around 5 kPa, corresponding to about 450 mL of CO2 per litre of blood. If you double A, PACO2 will halve, and there will be a change in CO2 content that reflects the relationship between PaCO2 and CO2 content – i.e. it’s not a linear relationship. At a A of 10 L/min, CO2 content will be 337 ml/L, not 225 ml/L. Read the numbers off the curves above yourself (Figure 1).

The situation for O2 is a little different, because we are trying to take it in, not get rid of it. As you increase A, PAO2 increases, but of course it can’t get any higher than 21 kPa unless you change the air that you are breathing (Figure 2). In fact, by the time air is humidified and reaches the bronchioles, water vapour takes up enough "room" to limit this to 20 kPa. Finally, when you factor in the CO2 that is continuously excreted into the alveoli, it becomes clear that PAO2 can't be much higher than 16-17 kPa at maximal A.

Figure 2:The relationship between alveolar ventilation (A), the alveolar partial pressure of O2 (PAO2), the partial pressure (PaO2), actual O2 content of arterial blood and haemoglobin saturation.  (A) Shows how increasing A> causes an increase in PAO2 .  Note that this is very different to the relationship between A and PACO2 (Figure 1). (B) Illustrates the normal relationship between the amount of O2 dissolved in plasma (PaO2), the actual full content of O2 in blood and the degree of O2 saturation of haemoglobin.  Remember, the O2 content is dependent on the amount of haemoglobin present; if haemoglobin is half of what it should be it will still be saturated, but O2 content will be halved.  Dashed lines show the typical values.

The A-PACO2 relationship doesn’t pass through zero, because the body is burning 300 ml/min at rest. If you don’t breathe enough, you ventilate the lungs below the body’s demands for O2 and die. If A is 5 L/min then PaO2 is around 14 kPa (air has a PO2 of 21 kPa, but alveolar air also contains CO2 excreted by the body and water vapour). We define hypoxeamia as a P2 < 9 kPa, so when A is under about 3 l/min, we are in that territory (at rest). We generally accept that PaO2 should be within 2 kPa of PAO2 – as it’s less soluble in water than CO2 and might not be equilibrated fully – and for our purposes here we’ll assume that they are always equal. Under these conditions, haemogloblin saturation (“sats”) is close to 100%.

A simple obstruction
Say you accidently inhaled a peanut and it jammed in the right bronchus, completely obstructing it. It tends to be the right bronchus that things get jammed in because it sits a little more vertically than the left one. The effect of the peanut is to halve ventilation.

VQ mismatch

Figure 3: How blocking an entire side of the lung with a peanut affects A:C. Blood to the right lung returns to the heart without having equilibrated with freshly ventilated alveolar air. Alveolar air in this side of the lung will equilibrate with venous blood and have the same Pa>O2 and PaCO2. If we take the average of the O2 content of blood returning from each lobe, we can determine what the that PaO2 of blood returning to the heart will be. Because of the steep nature of the haemoglobin dissociation curve, the impact of losing ventilation of one side of the lung is profound.

Now we have a nice example of shunt: when blood leaves the heart and returns without meeting with alveolar air to exchange gases. It's also something of an emergency, since a little number-crunching (see below) shows that with this degree of shunt – half the lungs – serious hypoxaemia is inevitable and untreatable until the peanut is removed. Adding supplemental O2 won't help at all – that's one definition of a shunt (although definitions of shunts vary; check your local rules!) If you can't see why supplemental O2 won't help in this situation, you will soon.

In this situation, the blood from the heart to the right lung is venous blood, there and back. It will have PaO2 of 5 kPa. The other lung is working well, though, returning blood to the heart with a PaO2 of 14 kPa. We can read off the corresponding O2 contents of the two (Figure 3) and work out what the O2 content (and equivalent PaO2 that will show up on an arterial blood gas analysis) of the mixture will be:


Because the PaO2 content relationship isn't linear, you can't just take the average of the PaO2 values. The PaO2 tells you what is dissolved in the liquid phase; the relationship to total O2 content is a different kettle of fish thanks to haemoglobin. If you tried to work it out by averaging the PaO2 values, you'd deceive yourself:

We can do a similar set of calculations to determine how well these lungs will blow off CO2 as well:

Figure 4: Effect of obstruction of the right bronchus on blood PaCO2 returning to the heart. The right lung returns what is effectively venous blood, unchanged after perfusing an unventilated lung. The left side returns arterial blood to the heart, but the mixture still has a high blood PaCO2 (5.6 pKa).

How does the body respond to this ventilation problem? On a breath to breath basis, you may remember that it isn't PaO2 that drives breathing but PaCO2 (although a PaO2 of 6.5 kPa is low enough to also trigger the sluggish hypoxic drive to breathe). Stimulation of carotid body and central chemoreceptors by increased CO2 should cause a reflex increase in the rate and depth of breathing. Let's say thatA doubles as a result. That should do the job, shouldn't it (Figure 5)?

Figure 5: Effect of doubling A on oxygenation of blood from lungs in which the right bronchus is blocked. Naturally, there is no improvement in the oxygen content from the right lung, because it doesn't see the increase in ventilation. On the left side, however, PaO2 increases to 17 kPa. Sadly, as haemoglobin is pretty well saturated on this side, this has almost no impact on improving oxygen content of the mixed blood returning to the heart. We need to get that peanut out if we are going to solve this problem.

If you can see from Figure 5 why increasing A hasn't helped at all, then skip the following calculation:

The problem here is that the blood in the left lung is pretty well saturated anyway; you can’t get any more O2 into it. The right lung will equilibrate with venous blood as there is no change in ventilation there. By increasing ventilation, all that is achieved is that the left lung is hyperventilated and will halve the CO2 content of the blood perfusing it:

Figure 6: The effect of increasing ventilation on the unobstructed side of the lung. This is hyperventilation, but it is the body's natural response to an unusual situation. You will see the same in patients with a significant degree of obstruction: increased total lung ventilation (to try to increase PaO2).  The result is hypocapnia due to hyperventilation of well-ventilated regions of the lung. You can always blow off CO2 in these regions, but you can't do more than saturate haemoglobin.

Consider the CO2 content of the two sides, and its impact:

Fetch the oxygen?
The lung that is ventilated is doing 100% of a job. You can't do more than saturate blood with O2. But, you can always blow CO2 off. That's the respiratory compromise that has to be balanced. What could we do to help such a patient? Increasing the fraction of inhaled O2 (FiO2; currently 0.21) won't help at all, because the working side of the lung can't take any more oxygen on, as it is saturating haemoglobin as it is. We need to get that nut out. The problem here is that blood is effectively shunted past the other half the lung, and returns to the heart unchanged. You see similar things in different types of shunts. In a newborn say, with a patent ductus arteriosus, some blood bypasses the lungs and the effect is largely the same. Supplemental O2 won't help.

Obstructive lung diseases
How does this compare with a respiratory disease such as asthma? In asthma airway obstruction isn't necessarily complete and is diffuse. This is a different situation, and one that will respond to supplemental oxygen. But why?

In an obstructive disease where airflow is limited, but not completely obstructed, the problem is one of getting adequate alveolar ventilation, rather than ventilation at all. Alveoli that are fed by bronchi which are completely obstructed (say, by mucus plugs) behave in much the same way as the peanut example described above, but on a smaller, local scale. Most airways in asthma are only partially obstructed and the alveoli that are fed by them behave differently.

Rather than equilibrating with venous blood, air in these alveoli just gets a bit stale: it accumulates too much CO2 and doesn't get enough fresh air to bring PaO2 up to where it belongs. If you increase the FiO2, you can increase the chances of PaO2 being closer to normal (or even better) and rectify the situation on the O2 front. Getting the CO2 out is a different story because it's going in the other direction. Like the peanut, the problem isn't solved until the partial obstruction is dealt with using a bronchodilator such as salbutamol.

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