How do I get 10 units out of a vial reconstituted to 6.67 mg/mL without guessing?

Numbers first: 10 units · 6.67 mg/mL.

I can find plenty of assertions about this and almost no reasoning, which is usually a sign that nobody has checked.

Assume no laboratory access beyond what I can pay a third party for.

Concretely, what should I do, and how would I know afterwards whether I did it right?

To be exact about it, the single most useful thing to do is write the arithmetic on the vial label, because you will reconstruct it from memory at an inconvenient moment if you do not.

Worked example, because the general form is easier to trust once you have seen it once. Take a 10 mg vial and add 2 mL of diluent: the concentration is 10 ÷ 2 = 5 mg/mL. A 0.5 mg dose is 0.5 ÷ 5 = 0.1 mL. On a U-100 syringe, where 1 unit = 0.01 mL, that is 0.1 ÷ 0.01 = 10 units. Change the diluent to 1 mL and the same dose becomes 5 units — same dose, half the resolution.

Rotation of injection site is a tolerability measure, not a pharmacokinetic one, but if you are going to do it you might as well do it right.

Published data on syringe dead space quantifies low-dead-space designs as retaining under 2 µL against 35 µL or more for conventional detachable-needle syringes.

Do the arithmetic twice, ideally with someone else doing it independently.

Mechanically, two people working through the same arithmetic independently should get the same answer, and if they do not, someone has made a unit error.

The rounding error accumulates if you round too many times — rounding concentration to 5.0, rounding the dose volume to 0.1 mL, rounding the unit reading to 10 — and the safest approach is to work the full precision and round only the final answer.

Air bubbles at these volumes are a measurement problem rather than a safety one. A 2 mm bubble in a 0.3 mL syringe is roughly 4 µL, which at 10 units drawn is a four per cent error.

If in doubt, use more diluent and accept the shorter usable window.

More usefully, rounding to the nearest whole syringe unit is usually the right error to make, but understanding which direction it is and why matters.

Do not use the same needle to pierce the stopper and to administer. The tip is blunted by the stopper, and the hub now contains a dose you are about to lose to dead space anyway.

The insulin-unit standard U-100 means 100 units per millilitre, so one unit is 0.01 mL — this is the conversion that trips up more people here than any other single piece of arithmetic.

Write the arithmetic on the vial label. It costs nothing and removes the step where you reconstruct it from memory.

edited 23 Jun 2024 by petra_hovland — clarified the distinction between purity and content

It helps to be literal here: this is arithmetic, so let us do the arithmetic rather than argue about it.

Number of stopper piercings matters less than the gauge doing the piercing. A 30G or 31G needle through a butyl stopper leaves a track that reseals; a 21G or 18G drawing needle punches a core and can drop it into the solution.

Do the arithmetic twice, ideally with someone else doing it independently.