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What is the arithmetic to convert 40 mg in 2.5 mL into units on a U-100 scale?

Asked 3 Apr 2024Modified 2.0 years agoViewed 26k times
8

The case in front of me: 40 mg · 2.5 mL.

I want the working, not the result — I need to be able to redo it with different numbers.

I care about the precision as well as the value — I want to know how many figures are real.

Is my approach right even if my number is wrong?

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DL
askedDr_Otto_Lindqvist72k583 Apr 2024
Add whether the needle is fixed or detachable — the dead space differs by an order of magnitude. – triple_agonist_q 36 days ago
8How many draws are you planning from the vial? That decides which diluent to use. – gel_pack_warm 9 months ago
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3 Answers

Accepted answer first, then by votes
6

Accepted answer

16 mg/mL, so one unit carries 0.16 mg. 40 ÷ 2.5 = 16 mg/mL; one unit on a U-100 barrel is 0.01 mL; 16 × 0.01 = 0.16 mg per unit. To go the other way, divide your intended dose by 0.16: a 1.6 mg dose is 10 units, and a 3.2 mg dose is 20. Write both the concentration and the milligrams per unit on the vial.

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

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

ConfigurationDead volumeLoss at 5 mg/mLOver 20 draws
Fixed-needle insulin syringe3–5 µL15–25 µg0.3–0.5 mg
Low-dead-space, detachable<2 µL<10 µg<0.2 mg
Standard luer-lock + 30G35–60 µL175–300 µg3.5–6 mg
Luer-lock + 21G drawing needle70–100 µL350–500 µg7–10 mg

Concretely, 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.

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.

Worth noting: the concentration after reconstitution is not the same as the label claim, and most people do not account for the difference.

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

edited 16 Apr 2024 by u100_marks — added a caveat about sampling

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UM
answered · acceptedu100_marks52k376 Apr 2024
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70

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.

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.

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LS
answeredlow_dead_space37k3717 Apr 2024
52

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

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 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 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.

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.

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

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HP
answeredh_pergande71k15812 Jul 2024
8Minor: the filter membrane chemistry matters as much as the pore size for adsorption. – Dr_Yusuf_Adeyemi 3 days ago
7Reading the leading edge of the stopper rather than the shoulder is worth a sentence of its own. – bufferline42 8 months ago
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