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Created 17/01/2021 at 02:20PM
We have heard many wonderful tales of skilled (and well equipped) nurses drawing a 6th or even 7th dosage from the vial, what kinda of sorcery is this? And how many dosages are there in a Pfizer vaccine?
According to this article there are 450µL in a vial, which is diluted in 1.8mL saline water, this gives a final volume of 2250µL, one dosage is 300µL, so a naive calculation is:
$$ \frac{2250\mu{}L}{300\frac{\mu{}L}{doses}} = 7.5 doses \Rightarrow 7 doses $$
Question: So There is 7.5 dosages in a vial, why can some only draw 5 and others up to 7?
Answer: Because there is a small dead volume in syringes, this volume depends on the quality of the syringe. Here is an image stolen from https://www.slowboring.com/p/dead-space
Let's redo the math with the 84µL dead space syringe which is what Pfizer expects to be used:
$$ \frac{2250µL}{300\frac{\mu{}L}{dose}+84\frac{\mu{}L}{dose}}=5.86 dose \Rightarrow 5 doses $$
So that gives the 5 doses that we all expected, let's try to redo the math with the 2µL syringe
$$ \frac{2250µL}{300\frac{\mu{}L}{dose}+2\frac{\mu{}L}{dose}}=7.45 dose \Rightarrow 7 doses $$
So with this vial we can potentially draw 7 doses, which is what Denmark is doing, how come most places are only banking on 6 doses?
I have two guesses.
Let's calculate the volume in the vial after 5 or 7 draws.
5 draws 84µL dead volume:
$$ 2250µL - 5dose \times (300\frac{\mu{}L}{dose} + 84\frac{\mu{}L}{dose}) = 330µL $$
So according to Pfizer they expect that nurses can draw 5 vials with only 330µL left (that's 0.3ml!) - there is a reason we call this skilled labor!
7 draws 2µL dead volume:
$$ 2250µL - 7dose \times (300\frac{\mu{}L}{dose} + 2\frac{\mu{}L}{dose}) = 136µL $$
So here there are 136µL left in the vial, for reference a drop of water is about 50µL, so if you have 2 drops of water stuck to the lid and one to the bottom of the vial, game over, if your hands shake more than the diameter of a water droplet, game over.
The fact that some can draw this 7th dose fills me with tremendous pride! Not all heroes wear cape, but a some wear scrubs or a lab coat.