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How many vial-days does a 15 mg vial give at 10 mg/mL on a weekly schedule?

Asked 13 Jun 2024Modified 23 months agoViewed 10k times
17

The specifics, since they change the answer: 15 mg · 10 mg/mL.

I would like the arithmetic checked rather than the conclusion asserted.

I have deliberately not used an online calculator because I want to be able to check the result.

Can someone walk through the arithmetic step by step?

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askedjonas_ekstrom18k2813 Jun 2024

2 Answers

Accepted answer first, then by votes
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Accepted answer

It helps to be literal here: the arithmetic only stops being confusing once you work it through once and see that it is straightforward.

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.

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 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.

edited 10 Aug 2024 by halvard_ness — fixed an arithmetic slip in the third paragraph

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answered · acceptedhalvard_ness42k386 Aug 2024
2I would add a sentence about sterility here, since it is the thing people skip. – micron22 29 days ago
The placebo-arm figure is the part everyone omits. – unit_math 9 months ago
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38

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

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.

Specifically, 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.

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.

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answeredtandem_gradient85k24817 Aug 2024
7The timing signature is the useful part. Everything else is confounded. – ahmed_zerouali 9 months ago
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