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?

## Volume Left in Vial

I have two guesses.

- They have slightly worse syringes, a dead space of 22µL will make the 7th
dose impossible to draw
- It requires highly skilled personal to draw the 7th dose

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.