From milligrams in a vial to units in a barrel

The failure mode that recurs most often is not a miscalculation. It is a calculation that was correct and then became stale. A person establishes that their dose is eight units, uses that figure for months, receives a vial of a different strength or makes it up with a different volume of water, and continues to draw eight units. Nothing in the process announces the change. The syringe looks the same, the mark is in the same place, and the dose delivered may be double or half. The only defence is to recalculate at every vial and to write the result on something attached to the vial.

The arithmetic, in four lines

Concentration equals mass of peptide divided by volume of diluent. Injection volume equals intended dose divided by concentration. Units equal injection volume in millilitres multiplied by one hundred. Micrograms per unit equals concentration in micrograms per millilitre divided by one hundred.

Worked once: a 5 mg vial made up with 1.0 mL of diluent is 5 mg/mL, which is 5,000 micrograms per millilitre, which is 50 micrograms per unit. A 250 microgram dose is 0.05 mL, which is five units.

Worked again with a different diluent volume: the same 5 mg vial made up with 2.0 mL is 2.5 mg/mL, which is 25 micrograms per unit. The same 250 microgram dose is now ten units. The vial has not changed and the dose has not changed; the unit count has doubled because the concentration halved.

That pair of examples is the whole argument for recalculating at every vial. A person who established five units as their dose and then made the next vial up with twice the water, keeping five units, halved their dose without any step in the process appearing wrong. The Journal recommends writing the microgram-per-unit figure on the vial in permanent marker, because it is the number that changes and the one nobody remembers changing.

What the diluent changes, and what it does not

The diluent has no effect on the arithmetic and a substantial effect on everything else. Bacteriostatic water contains a preservative, conventionally benzyl alcohol at around nine tenths of a per cent, which inhibits microbial growth and is what makes repeated puncture of a multi-dose vial defensible. Sterile water for injection contains no preservative and offers no protection after the first puncture. Sodium chloride solution is isotonic and generally more comfortable on injection, and preserved and unpreserved presentations both exist.

The choice is therefore a sterility decision rather than a convenience one. A vial that will be entered more than once and kept for weeks is a different proposition from a single-use preparation, and the presence or absence of a preservative is the difference.

Two cautions belong here. Benzyl alcohol is not appropriate in all populations and is specifically avoided in neonates. And no preservative rescues poor technique: bacteriostatic means growth-inhibiting, not sterilising, and a stopper swabbed carelessly with a needle passed through a wet surface will introduce organisms that the preservative was never intended to handle. The diluent is a margin, not a permission.

Common vial strengths, worked

For a 2 mg vial: 1.0 mL of diluent gives 2 mg/mL and 20 micrograms per unit; 2.0 mL gives 1 mg/mL and 10 micrograms per unit. For a 5 mg vial: 1.0 mL gives 50 micrograms per unit; 2.0 mL gives 25; 2.5 mL gives 20. For a 10 mg vial: 1.0 mL gives 100 micrograms per unit; 2.0 mL gives 50; 5.0 mL gives 20.

Reading in the other direction: at 50 micrograms per unit, a 250 microgram dose is five units, a 500 microgram dose is ten, a 1 mg dose is twenty. At 100 micrograms per unit those become two and a half, five and ten. The half unit in that first case is not measurable on a barrel graduated in single units, which is a small illustration of how concentration choice constrains what doses can actually be given.

The general principle is to choose a diluent volume that puts your intended doses on whole, comfortably readable graduations across the whole escalation range you expect to use, and then to leave it alone. Choosing a concentration that makes the current dose convenient and the next three doses awkward is a common and avoidable annoyance.¹

The stale calculation

The commonest arithmetic failure in this market is not a miscalculation. It is a correct calculation that has quietly expired. Vials change strength between batches and between suppliers. Diluent volume changes because a different measuring device was used, or because the previous figure was not written down. Neither event produces any visible signal.

Three structural habits prevent it, and exhortations to care do not. Write the concentration and the microgram-per-unit figure on the vial, on tape, at the moment of reconstitution. Recalculate at every new vial from the stated mass and the measured diluent volume, rather than reusing the previous unit count. And do not change syringe barrel size and vial concentration in the same week, because if something then goes wrong there is no way to tell which change caused it.

The Journal notes that this is exactly the class of error a dispensing pharmacist exists to catch, and that in a market where material arrives as unlabelled powder there is no pharmacist. Structural checks are not a counsel of perfection here; they are the only remaining layer.

Four things about this that are genuinely unestablished

First, the in-use stability of home-reconstituted peptides. No sequence-specific, buffer-specific, container-specific stability study exists for the great majority of what is sold in this market, and the figures in circulation are extrapolations.

Second, whether the injection-site interchangeability established for licensed acylated agonists holds for material of uncertain formulation. The mechanism suggests it should; nobody has measured it.

Third, the real-world frequency of the errors catalogued above. Our ranking comes from correspondence, which is a self-selected sample that over-represents people who noticed. The denominator is unknown.

Fourth, whether any of the technique measures described here changes outcomes in this specific population. They are supported by anatomical evidence and by the insulin literature; a trial in incretin users has not been done and probably will not be.²

Readers who know of stability data or technique trials we have missed should write to standards@compoundjournal.com. This is one of the files where we would most like to be corrected, because the current state is that millions of injections a week are being given on the basis of transferred evidence and a four-line calculation.

This file sits between two others in the department. Titration decides what dose is intended; tolerability decides whether it can be sustained; technique decides whether the intended dose is the one delivered. All three have to be right, and the third is the only one that can be got right in full by a careful person with a calculator.