What is the arithmetic to convert 20 mg in 2 mL into units on a U-100 scale?

Setup, so nobody has to ask: 20 mg · 2 mL.

The units are where I keep going wrong, so please be explicit about them.

I have sanity-checked the order of magnitude and it seems right, which is not the same as being right.

How many significant figures are actually justified here?

Write the units at every step, because units errors are the failure mode that catches everyone eventually.

Dead space quantified: a fixed-needle insulin syringe holds roughly 3 to 5 µL in the hub and needle after the plunger bottoms out. A luer-lock syringe with a detachable needle holds 35 to 100 µL depending on the hub design. At 5 mg/mL that is 15 to 25 µg lost per draw on the insulin syringe and 175 to 500 µg on the luer-lock — which over ten draws is the difference between losing a rounding error and losing half a milligram.

Dead space by syringe type

Put another way, breaking it down further: if a 10 mg vial has 96.5 per cent content, you have 9.65 mg of peptide. Divide that by 2.00 mL and your concentration is 4.825 mg/mL, not 5.00 mg/mL, which is a 3.5 per cent systematic error in every dose calculation.

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.

One qualification: if your arithmetic and someone else's disagree by a factor of ten, one of you has made a unit error, and writing out the units at every step is the diagnostic.

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

Mechanically, the arithmetic only stops being confusing once you work it through once and see that it is straightforward.

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.

On filtration: a 0.22 µm syringe filter will remove particulates and organisms, and it will also adsorb a fraction of your peptide onto the membrane — with a low-binding PVDF or PES membrane the loss is typically a few per cent.

The limitation is that technique reduces risk, it does not remove it, and nothing you can do outside a controlled environment makes a non-sterile preparation sterile.

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

edited 23 Oct 2024 by Dr_Nadia_Farsi — clarified the distinction between purity and content

The part that matters: the common error is getting the concentration right but then misreading the syringe scale, which is why checking the barrel marking rather than your memory matters.

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.

Specifically, 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.

The Arrhenius relationship for drawing kinetics means that cold solution takes noticeably longer to draw than room-temperature solution.

The caveat is that this assumes the vial contains what the label says, and if the content assay has not been done, the arithmetic is precise about an unknown quantity.

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

Put another way, dose arithmetic has three parts: concentration from vial content and diluent, volume from dose and concentration, and units from volume and syringe scale.

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.

The content assay results from major testing services show that nominal vial claim and measured content differ by one to ten per cent, making content a driver of dose error.

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

The part that matters: this is one of those calculations where checking your work takes two minutes and prevents a very consequential error.

Room temperature before drawing is worth the ten minutes. Cold solution is more viscous, draws slower, and condensation on a cold barrel makes it harder to read the meniscus.

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 24 Aug 2024 by lyoph_cake — expanded the table to cover the lower concentration