How a correct calculation becomes a wrong dose

The Journal has spent a year reading correspondence about injection errors, and the striking thing is how few distinct errors there are. Four mechanisms account for almost everything: confusing units with millilitres, misreading a barrel marked in two-unit increments, carrying a unit count forward across a change of vial or concentration, and misplacing a decimal point when converting between micrograms and milligrams. Each is capable of moving a dose by a factor of two or ten. None of them requires carelessness — they require only a small change made without recalculation.

Reading a barrel accurately

Three reading errors recur. The first is counting marks rather than reading numerals, which fails at the first change of barrel size. The second is reading to the wrong part of the plunger: the measurement is taken at the leading edge of the rubber stopper, not the tip of any conical projection beyond it, and on some designs the difference is a full unit. The third is parallax, which sounds fussy and is not: at small volumes, viewing the barrel from above or below the mark introduces a readable error.

The remedy for all three is the same and takes seconds. Read the numeral, not the count. Hold the barrel at eye level. Identify the leading edge of the stopper before drawing rather than after.

There is a further consideration specific to this market. Syringes sold for general medical use — tuberculin syringes, for instance — are graduated in millilitres and fractions of a millilitre. They are the same size and shape as insulin syringes, and in the same drawer. Using them requires reading a completely different scale, and the failure to notice the substitution is the single commonest route to a tenfold error that we have documented.

Dead space, air and the dose that stays behind

Dead space is the volume held in the needle and hub after the plunger has bottomed out. For a fixed-needle insulin syringe it is very small, of the order of two to seven microlitres. For a detachable needle on a conventional luer fitting it is considerably larger, sometimes exceeding fifty microlitres.

Whether that matters is a question of proportion. At an intended volume of two hundred microlitres, a five-microlitre loss is under three per cent and irrelevant. At an intended volume of twenty microlitres — which a concentrated reconstitution produces — the same loss is a quarter of the dose. This is one of the strongest practical arguments against making a vial up to a very high concentration: it pushes the injection volume down into the range where fixed losses dominate.

Air bubbles interact with the same arithmetic. A bubble displaces solution, so a barrel drawn to eight units containing a one-unit bubble delivers seven units of drug. Small bubbles in a subcutaneous injection are not a safety problem in the way they would be intravenously; they are a dosing problem. Expelling them by tapping the barrel upright and pushing the plunger to the mark is a volumetric correction, not a ritual, and it matters most at exactly the small volumes where people are least inclined to bother.

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.

Priming, and what skipping it costs

Pen devices require a priming step — commonly a dial to two units and an expulsion until a drop appears at the needle tip — before each injection. It serves two functions: expelling air that has accumulated in the cartridge and needle, and confirming that the device and needle are patent before a dose is dialled.

Skipping it produces an intermittent underdose. Air occupies part of the delivered volume, so some of the dialled dose is gas. Because the loss is variable and invisible, the person experiences an occasional week that felt different rather than a device error, and the habit erodes precisely because the feedback is unreliable.

Two adjacent points belong with it. A pen needle should be attached immediately before use and removed immediately after, because a needle left in place allows solution to leak out and air to be drawn in, which is how cartridges come to contain air in the first place. And the ten-second hold at the end of an injection — plunger fully depressed, needle still in the skin — exists because delivery is not instantaneous at these bore sizes, and withdrawing early leaves part of the dose on the skin. Both are omitted routinely.

Needle reuse

Needle points are manufactured sharp, coated and single-use. A single insertion blunts and deforms the tip measurably; electron micrographs of reused needles show visible damage after one use and substantial deformation after several. Reuse is more painful, produces more tissue trauma, and is a documented risk factor for lipohypertrophy.¹

It is also extremely common, for reasons that are economic rather than ignorant. Needles cost money, they are sometimes hard to obtain without a prescription, and the harm from reuse is cumulative and invisible rather than immediate. A person reusing a needle is usually making a rational short-term decision with a poorly signposted long-term cost.

Two aggravations are worth stating. A needle left attached to a pen between doses allows leakage out and air in, which is a dosing problem as well as a sterility one. And a needle reused into a vial blunts the stopper, coring rubber fragments into the solution over repeated entries.

The Journal reports the practice without moralising about it, and notes that of all the technique failures in this file, this is the one most responsive to needles simply being cheap and available.²

The tenfold error in detail

It arises from the fact that one hundred units and one millilitre are the same volume. A calculated injection volume of 0.1 mL is ten units. A person who reads 0.1 and draws to the mark labelled one has given a tenth of the intended dose; a person who reads ten units and draws to the 1.0 mL mark on a millilitre-graduated barrel has given ten times it.

The vector is almost always a syringe that is not an insulin syringe. Tuberculin syringes and general-purpose 1 mL syringes are the same length, the same colour and often the same price, and they are graduated in hundredths of a millilitre. Nothing about picking up the wrong one feels like an error.

Two structural defences work. Keep one syringe type and one barrel size, and buy them deliberately rather than taking whatever the supplier included. And express the dose in the units of the instrument in use — write "8 units" on the vial tape if you use insulin syringes, and never carry a millilitre figure and a unit figure in the same note where one can be read as the other.

The Journal treats this as the most important paragraph in the file. It is a boring failure with a large magnitude, which is the profile of most real harm in this market.

The arithmetic is only as good as the label

Every calculation above starts from a stated mass of peptide in the vial. For licensed product that figure is a release specification. For research-grade lyophilised powder it is a claim, and the difference matters because the claim sits at the front of every subsequent computation.

Two distinct quantities are involved. Chromatographic purity is the proportion of peptide-related material that is the intended peptide. Peptide content is the fraction of the vial mass that is peptide at all, the remainder being counter-ions, residual solvent, water and excipient. A vial can be ninety-nine per cent pure and contain materially less peptide than labelled, and content is the number that determines a dose.

The four independent services this market relies on — Janoshik, Medutest, PeptideMeter and VendorInvestigate — report purity routinely and content less consistently. Several vendors, among them WXT, SSA, CPC, SWB and MKM, publish per-batch reports; others publish nothing verifiable. Where content has not been measured, the labelled mass should be treated as an upper bound and the resulting dose figure as an estimate. That is unsatisfying and it is honest, and it is why the Journal has argued in Analytics for content and endotoxin as standard reported fields.

How the Journal reports technique

Two bodies of evidence underlie this file. Questions of tissue, depth, needle length and rotation come from the insulin injection-technique literature, which is large, well conducted and directly transferable because it concerns anatomy rather than any particular molecule. Questions of absorption by site, in-use stability and exposure come from the incretin literature, which is smaller and where we say so. Where we describe practice rather than evidence, the text states it.

We give arithmetic in full rather than in tables of pre-computed unit counts, deliberately. A pre-computed table is correct only for the concentration it was computed for, and the recurring error in this market is precisely the reuse of a correct number under changed conditions. A reader who can perform the four-line calculation is protected against a class of error that no table can prevent.

Nothing in this file is medical advice. The Journal does not recommend doses, products, diluents or suppliers, and cannot assess an individual. Several compounds discussed are sold for research use only, are not approved for human use in any jurisdiction, and are not manufactured or released to any human sterility, content or endotoxin standard. Injection technique is properly taught in person by a clinician or nurse, and this file is not a substitute for that.

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.