The alveolar gas equation

A patient is in respiratory distress, SaO2 deteriorates and you wonder how to turn round the situation. Apart from other diagnostics, you get an arterial blood gas and analyse pH, pCO2 and elytes. Yet the core value is pO2 and this is the hardest to analyse. There are no normal values for pO2, unless you know the FiO2, the temperature and the age of the patient. The one most important medical equation for intensive care is the alveolar gas equation (AGE), which is actually quite easy to derive:

1. O2 streams into the alveolus with the breathing gas, which consists of ambient air (possibly enriched with O2) and water vapor (saturated by the nose, trachea and bronchi) – so it comes with a partial pressure of

  •  (atmospheric pressure – water pressure) x inspiratory O2 quotient


  • Now we are used to getting atmospheric pressure as hPa and not in Torr, but our BGA values tend to be in Torr (aka mmHg), so you have to convert the units. In Augsburg, atmospheric pressure is about 1020 hPa, which amounts to 768 mmHg. Water pressure is 47 mmHg.
  • The inspiratory O2 quotient is easy, if no O2 is supplied (21%), but gets problematic if nasal prongs or a mask without reservoir are used, because they don’t provide a predictable FiO2. Nasal prongs deliver from 30% to at most 40% (the latter only if you turn up the flow to ridiculous levels). Normal face masks deliver between 40% und 60%, again depending on the flow. Non-rebreather (reservoir) masks can deliver 100% only, if you (can) close both inlet valves, otherwise you end up with (about) 80%.

2. Now O2 not only streams into the alveolus through breathing, but also is taken up by the blood, but the amount is hard to measure (we don’t know much about our own work, so we can’t  know how much the patient works either, so we cannot compute how much oxygen he needs). But we get that information from the CO2 in the alveolus, because every CO2 has to have been metabolized from O2 through glycolysis. Depending on what we burn with O2, we get between 1,2 and 0,7 CO2 for every O2 (this is the respiratory quotient), but it is usually taken as 0,8 in intensive care. So we spend O2 in an amount proportional to

  • alveolar CO2 / respiratory quotient

The funny thing is that CO2 diffuses exceptionally well through the various alveolar layers, so we may assume that alveolar CO2 is roughly equal to arterial CO2, so that O2 spent is proportional to

  • arterial CO2 / respiratory quotient

Since dividing by 0,8 is about as good as multiplying by 1,25 or maybe 1,2, the latter expression reads

  • 1,2 * PaCO2

[Here comes the mathematician: we talked about income and spent O2 being proportional to these expressions, but not about the real values. That you can still compute with pressures rather than volumes is not completely obvious – but follow the complete math here.]

3.The whole AGE reads

  • P_alveolar O2 = FiO2 * (P_atm – P_H2o) – 1,2 * PaCO2 = FiO2 * 721 – 1,2 * PaCO2    [values for Augsburg, 11th floor, stroke unit]

This, of course, holds only under steady state conditions (O2 and CO2 have time to diffuse, be metabolized and so on; no change in diet) and proper ICU diets.


  • I find it not too hard to do the math in my head, but ICU docs usually just ignore the CO2-part, using FiO2 * 600 as a rough estimate for expected alveolar PO2. In fact, the Horowitz index is a very crude simplification of the AGE. If you know that high CO2(as in COPD) and low atmospheric pressures (such as on Mount Everest)  obscur things, you may actually use these simplifications in practice.
  • How do you use the AGE? You compare your arterial PO2 to the expected, i.e., alveolar PO2, subtract the higher from the lower (forming the alveolar-arterial oxygen difference PAaO2) and use this as a marker for the severity of your lung problem. Note that real hypoventilation (as in being sedated) should not really increase your PAaO2.
  • Nowadays, we know that advanced lung disease may interfere with a lot of the assumptions of the AGE, so beware with ARDS and COPD patients.

End-of-life care on the ward

Since stroke care is care for very sick patients, we face this situation at least every week: to withdraw “life support” and let the patient die. So assume a patient (in our case a terminal mitochondriopathy patient with resistant status epilepticus) that eyeryone (including – by advance directive – the patient) has agreed will, may and should die. We discuss the practical aspects of care in these end-of-life situations.

Some certain goals in this terminal phase of care are:

  • The patient should not suffer (too much) hunger, thirst, pain, dyspnea
  • The relatives should not suffer (too much)
  • The team should not suffer (too much)
  • It should not take too long (this pertains to all three previous goals)
  • Religious and personal final requests should be met.

There is some controversy about whether the patient should be kept from fear, should remember the experience (or get some benzos to forget), should be allowed to be awake at all.

How do patients actually die? Of course, that depends, but in Neurology, most of them aspirate continuously until pneumonia takes over and then (through infection) some cardiovascular complication does it (like pulmonary embolism, arrhythmia, CHF decompensation). If you want to let this take it’s course, you will reduce your respiratory care, not suctioning to often, giving Morphine and Oxygen ad libitum. Take your time to increase the MSI dose until the patient breathes peacefully, pupils are small and the heart rate shows that stress is under control. If anxiety is predominant add benzodiazepines. As for liquids, the problem is not dehydration (this actually promotes the dying process) but thirst and dry mouth is – so you should add mouth rinses and morphine so that thirst is under control. If the process takes longer than expected (or hoped), lack of nutrition becomes important through it’s effect on immune reaction, but hunger should not appear (again, Morphine does the trick).

You cannot hope to predict the time of death, since you never know the precise pathophysiology, so call religious services, relatives and everyone else required by the patient as early as possible. Leave room and time for all the people to be able to tend to the patient. Show up from time to time, but don’t keep them from suffering – the death of a loved one is something you cannot make a pretty experience through empathy. Tears, moans and crises are normal and should be met with empathy and professionalism.


Gait demonstrations

Age-old wisdom has it that, as a Neurologist, you should be able to recognize the major gait abnormalities. Unfortunately, I find it quite hard to categories the average pedestrian zone pathologies you can see. Perhaps a good way to learn some of the pathological gait forms is to simulate them and this is what we are going to do…

Camptocormia and Parkinson’s

Starting with a patient with “bent spine syndrome” aka camptocormia we go through the fascinating duality

  • peripheral (myogenic) causes
  • central (mostly degenerative) causes
Of course, the most important diagnosis is Parkinson’s (where camptocormia tends to appear later rather than earlier), but other classical neurodegenerative diseases such as MSA-P, PSP may also cause camptocormia.
Even more interesting is what happens in PD with camptocormia. It is really unclear how myopathic and myositic findings can occur (such as elevated CK, myodegeneration in MRI, myopathic EMG, inflammatory changes on muscle biopsy of the erector spinae) in a disease that we all believe happens in the CNS…
As for treatment, you can try
  • change from dopamine agonists to L-Dopa (or vice versa)
  • BoTox of the abdominal muscles
  • steroids or IVIGs (if a lot of inflammation can be seen on MRI or biopsy)
  • DBS (although camptocormia can also be caused by DBS)
Here are two recent references

The canadian C-spine rule and competitors

You cannot always rely on a trauma surgeon to clear the cervical spine of your epilepsy patient that wears the infamous collar. Having worked as a paramedic here for about 20 years, I concede that the c-collar is way easier to install than to get rid off.

  • If you have a coherent (e.g., non-neurological :-)) patient, you can use the canadian c-spine rule, which requires you first to consider clear high-risk signals (age > 65, dangerous mechanisms, paresthesias), then find a good reason not to image your patient (a so-called low-risk factor).
  • For our average patient (stroky, somnolent, febrile, confused, nursing home resident), you still have to get an image of the cervical spine, if the trauma is only slightly relevant.

Reading uptodate’s article on cervical spine injuries and this review of 2009, I was surprised to learn that MRI really doesn’t add to the management of simple cervical spine injury (which means that ligament trauma doesn’t change the treatment). What I still don’t understand is how plain 3-view-films of the cervical spine is really worse than CT (of course CT is what we do).

Interpreting CT and MR angiographies with IMPAXX

Impaxx is our image-viewing system and, despite the fact that it is Java-based, it is pretty good (even if we are not allowed to use some of the more advanced features).

We run through the basics of interpreting a stroke MRI

  • DWI – is there a stroke?
  • ADC – what stage is it in?
  • FLAIR – what other strokes are there (and what non-stroke lesions?)?
  • HEME (T2*, SWI, or – if nothing better is available – the b0 pictures of the DWI sequence, which is pretty susceptible to heme artifacts as well)
  • MRA

Next, we concentrate on how to reconstruct angiographies using the 3d-modelling tool, how to do a curved MPR and what is the difference between average and MIP reconstructions.