Funtabulously Frivolous Friday Five 057

At LITFL we find figures and facts to be a font of funtabulousness, though we may have taken the frivolity out of the FFFF this week. While we agree with Reuben Strayer that the medical brain is prone to mathematical failure under stress (see his spectacular screencast on the pediatric airway for the non-pediatrician emergency physician) there are some fun figures well worth engraving on the surface of your encephalon if you’re an emergency or critical care doc.

Are you ready for them?


Q1. Why is the equation (age/4)+4 worth remembering?

Most people will know this equation as a guide to choosing the size of an uncuffed endotracheal tube in children. But it can be used for so much more:

  • it is also a guide to the expected A-a gradient in adults.
  • subtract 1 and you have the size of a cuffed ETT in children (some suggest subtracting 0.5, or using (age/3)+3 instead).
  • multiply by 2 and you have the size of an indwelling catheter in children.
  • multiply by 3 and you have the appropriate length at the teeth of an ETT in children (an alternative is to use (age/2)+12).
  • multiply by 4 and you have the appropriate size of an intercostal catheter in children.

Funtabulous, eh!

Q2. How can you calculate the A-a gradient at a glance of an ABG?

  • Just get really fast at using the equation: PAO2-PaO2 = (FiO2 x (PB – PH2O) – (1.25 x PCO2)) – PaO2 … yeah right.
  • You can quickly estimate the expected alveolar PO2 by using the equation: PAO2 = FiO2 x 500.
  • For instance, at sea level breathing air (21% oxygen), a person with normal lungs should have a PAO2 of 0.21 x 500, which is approximately 100 mmHg. To get the A-a gradient you just subtract the measured PaO2 from it.
  • But, what’s a normal A-a gradient? (see Q1 if you’ve already forgotten!)

Flippin’ funtabulous, eh!

Q3. How can you easily remember the expected HCO3 in acutely and chronically compensated respiratory acidosis or alkalosis?

  • Can you count 1-2-3-4-5? Can you put these numbers in 4 squares of a four square grid, with a 3 sitting on top? Can you remember that left is acute and chronic is right? Can you remember that the top row means the numbers go up, and the bottom row means the numbers go down? If so, then you can easily tell if there is appropriate metabolic compensation for a primary respiratory problem.
  • When you look at a gas either draw this little grid or visualise it with your mind’s eye:

  • For instance, if PaCO2 is 50 mmHg, that’s an increase of 10 mmHg from normal (PaCO2 40 mmHg). Thus in acute metabolic compensation the HCO3 should increase by 1 mmol/L from normal (HCO3 25 mmol/L) to 26 mmol/L, and in chronic compensation it should increase by 4 mmol/L from normal to 29 mmol/L.
  • Using the 4 square grid helps you remember which numbers correspond to what (acute comes before chronic, left before right), and whether they go up (top row) or down (bottom row).

OK, so that one might not suit everyone, but it works for my feeble mind!

Q4. How can 4 rules help you localise the lesion in patient with a possible brainstem lesion?

  • Gates’ Brainstem Rule of Fours is handy way of localising a lesion. The key things to know are:

In the rule of 4 there are 4 rules

  1. There are 4 structures in the ‘midline‘ beginning with M
  2. There are 4 structures to the ‘side‘ (lateral) beginning with S
  3. There are 4 cranial nerves in the medulla, 4 in the pons and 4 above the pons (2 in the midbrain)
  4. The 4 motor nuclei that are in the midline are those that divide equally into 12 except for 1 and 2, that is 3, 4, 6 and 12
    (5, 7, 9 and 11 are in the lateral brainstem)
  • The 4 medial structures and the associated deficits are:
  1. Motor pathway (or corticospinal tract):
    contralateral weakness of the arm and leg
  2. Medial Lemniscus:
    contralateral loss of vibration and proprioception in the arm and leg
  3. Medial longitudinal fasciculus:
    ipsilateral inter-nuclear ophthalmoplegia
    (failure of adduction of the ipsilateral eye towards the nose and nystagmus in the opposite eye as it looks laterally)
  4. Motor nucleus and nerve:
    ipsilateral loss of the cranial nerve that is affected (3, 4, 6 or 12)
  • The 4 ‘side’ (lateral) structures and the associated deficits are:
  1. Spinocerebellar pathway:
    ipsilateral ataxia of the arm and leg
  2. Spinothalamic pathway:
    contralateral alteration of pain and temperature affecting the arm, leg and rarely the trunk
  3. Sensory nucleus of the 5th cranial nerve:
    ipsilateral alteration of pain and temperature on the face in the distribution
    of the 5th cranial nerve
    (this nucleus is a long vertical structure that extends in the lateral aspect of the pons down into the medulla)
  4. Sympathetic pathway:
    ipsilateral Homer’s syndrome, that is partial ptosis and a small pupil (miosis)
  • According to Gates:

These pathways pass through the entire length of the brainstem and can be likened to ‘meridians of longitude‘ whereas the various cranial nerves can be regarded as ‘parallels of latitude‘. If you establish where the meridians of longitude and parallels of latitude intersect then you have established the site of the lesion.

For a fuller explanation check out the Brainstem Rules of 4 before testing yourself with Using the Brainstem 1 and Using the Brainstem 2.

Q5. What is an easy way to remember how much to increase the sodium by, and how much hypertonic saline to give, in a patient with symptomatic severe hyponatremia?

  • Remember two things:
    • the rule of Sixes
    • the rule of Threes
  • The rule of Sixes:
    • aim for a maximum increase in sodium of 6 mmol/L over 6 hours in the symptomatic severe hyponatremic patient.
    • in chronic hyponatremia, 6 mmol/L in the first 24 hours is a safe maximum increase to avoid osmotic demyelination syndrome — no further increase is necessary if the 6 hour target is met.
  • The rule of Threes:
    • treat the symptomatic severe hyponatremic patient with 3mL/kg of 3% NaCl over 30 mins.
    • This should raise Na by about 4 mmol/L – if the patient gets better (e.g. mental state returns to normal), stop the infusion!

Check out EMCrit Podcast 39 — Hyponatremia and ERCAST’s The Problem with Salt: How Low is Too Low? for more sensational saltiness.

Parting Piece of Funtabulous Wisdom

Wondered what it’s like being in prison? Wonder no more:


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  1. says

    while attempting (and failing) not to be a pedant… technically the spinal accessory nucleus is in the spinal cord not the medulla. the “cranial” accessory nucleus is in the medulla, but it’s thought it probably contributes entirely to the vagus and not to the accessory nerve anyhow

    i honestly don’t know if that makes the slightest bit of clinical difference. do things like wallenberg’s or vertebral artery lesions take out the spinal accessory too?

    • says

      Andy, I suspect Peter Gates anticipated such comments:

      “Any attempt to over simplify things runs the risk of upsetting those who like detail and I apologise in
      advance to the anatomists among us, but for more than 15 years this simple concept has helped numerous students and residents understand, often for the first time, brainstem anatomy and the associated clinical syndromes that result.”

      The original ‘Rule of Fours’ article is available as a fulltext pdf here:

      The motor function of CNXI is not an important feature of the brainstem rules of 4 -- probably because of the complexities that you’ve highlighted Andy. The Rule of Fours is really a tool for localising brainstem lesions, to one of three levels, either medial and/or laterally. I think its a great tool for the non-neurologist.


      • says

        cheers for the link chris

        to be perfectly honest my previous method for localising brainstem strokes was an MRI report so these rules are a big step up for me! i’ve been too lazy and confused on my neuro exam, and having a set of rules like this get me all excited about doing one!