How many units on a U-40 insulin syringe is a 15 mg dose at 10 mg/mL?

What I am working with: a U-40 insulin syringe · 15 mg · 10 mg/mL.

I have worked this out and I would like someone to find the error, because I suspect there is one.

My working so far, for the record, is below, and I am fairly sure the error is in the unit conversion rather than the algebra.

How many significant figures are actually justified here?

Put another way, the distinction that resolves most of these questions is understanding what concentration actually means and why it is not the same as label claim.

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.

The concentration you actually work with is label claim times content fraction divided by actual diluent volume, which is usually not the same as the nominal concentration because content is usually not 100 per cent and you rarely measure the diluent volume to 0.1 mL precision.

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.

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

More usefully, the answer depends on exactly which dose and which vial you are asking about, but the method is always the same.

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.

Concretely, 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.

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.

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

Put another way, work in the order concentration, then volume, then units, and the arithmetic stops being confusing. Concentration is milligrams per millilitre and comes from the vial contents and the diluent volume. Volume per dose is dose divided by concentration. Units on a U-100 syringe are volume in millilitres multiplied by one hundred.

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.

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.

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

edited 14 Jun 2024 by coldpack_88 — added the citation requested in comments

Stated carefully, this is arithmetic, so let us do the arithmetic rather than argue about it.

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.

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.

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 26 Sept 2024 by ilaria_bertone — added the method parameters