Why syringe pump calculations are error-prone
Continuously administered drugs such as vasopressors, beta-blockers and sedatives often have a narrow therapeutic range. They are frequently prepared under time pressure, for example in the resuscitation room, during prehospital emergency care or at induction of anaesthesia. Calculating a syringe pump infusion requires three quantities to be combined:
- Dose, e.g. µg/kg/min or mg/kg/h
- Body weight
- Concentration in the syringe
Three different unit systems are involved: mass (µg, mg, g, mmol), time (min, h) and volume (ml). Most clinically relevant errors do not arise from the arithmetic itself. They arise when converting between these units.
The basic formula: calculating the infusion rate
A robust approach is to always calculate in the same order and to write out the units in full.
Step 1: Convert the concentration into the unit of the dose
If the dose is given in µg/kg/min, the syringe concentration is converted to µg/ml. Example: 5 mg in 50 ml gives 0.1 mg/ml, i.e. 100 µg/ml.
Step 2: Calculate the dose per hour
Dose (µg/kg/min) × body weight (kg) × 60 = µg/h
Step 3: Calculate the infusion rate
Infusion rate (ml/h) = dose × BW × 60 ÷ concentration
If the dose is already given per hour (mg/kg/h), the factor 60 is omitted.
Back-calculation as a check
Dose (µg/kg/min) = infusion rate (ml/h) × concentration (µg/ml) ÷ (BW × 60)
Back-calculating the dose from the set infusion rate is a simple and effective self-check. It should be performed before every start and after every change of infusion rate.
Worked examples for syringe pump dosing
Noradrenaline: 5 mg/50 ml = 100 µg/ml
The dose is titrated to a target blood pressure (e.g. MAP ≥ 65 mmHg), preferably via a central venous catheter (CVC). Example for 70 kg and 0.1 µg/kg/min:
- 0.1 × 70 × 60 = 420 µg/h
- 420 µg/h ÷ 100 µg/ml = 4.2 ml/h
This corresponds to the value in the syringe pump dosing table for 70 kg. At this standard concentration the formula can be simplified: ml/h = µg/kg/min × BW × 0.6.
The ampoule itself also matters. It contains 1 mg/ml and is therefore ten times more concentrated than the syringe pump solution. If the ampoule is mistaken for the syringe, a tenfold error results. According to the summary of product characteristics (SmPC), the following applies to noradrenaline:
- a dedicated lumen,
- no bolus administration via the same line.
Landiolol: 300 mg in 50 ml = 6 mg/ml (6000 µg/ml)
With normal left ventricular function, the dose is titrated to heart rate at 10–40 µg/kg/min. Example for 80 kg and 20 µg/kg/min:
- 20 × 80 × 60 = 96,000 µg/h
- 96,000 ÷ 6000 = 16 ml/h
For this preparation, the simplified formula is: ml/h = µg/kg/min × BW ÷ 100.
With impaired LV function, the SmPC recommends starting at 1 µg/kg/min and increasing slowly to a maximum of 10 µg/kg/min. For 80 kg this corresponds to 0.8 ml/h and 8 ml/h respectively. This illustrates a typical risk: a misplaced decimal point between 0.8 and 8 ml/h corresponds exactly to the difference between the starting dose and the maximum dose.
Midazolam: 1 mg/ml (50 mg/50 ml)
For sedation of mechanically ventilated patients, the SmPC states 0.03–0.2 mg/kg/h as a continuous infusion. As the dose is already given per hour and the solution contains 1 mg/ml, the following applies: ml/h = mg/kg/h × BW. For 80 kg and 0.1 mg/kg/h, this gives 8 ml/h.
However, midazolam is marketed in several concentrations (1, 2 and 5 mg/ml). If 5 mg/ml is drawn up inadvertently, the dose at the same infusion rate is five times higher.
In hypovolaemia, vasoconstriction or hypothermia, the loading and maintenance doses should be reduced.
Magnesium sulfate: grams, millimoles and percentages
For severe pre-eclampsia or eclampsia, the S2k guideline states a maintenance dose of 1–2 g/h via syringe pump. Three pitfalls should be noted:
- Reference quantity: The dose refers to g of magnesium sulfate heptahydrate. Some products instead declare mmol or mg of Mg²⁺. As a rule of thumb: 1 g ≈ 4 mmol Mg²⁺.
- Concentration: 10 % corresponds to 100 mg/ml, 50 % corresponds to 500 mg/ml. That is a factor of 5. The 50 % solution must be diluted before i.v. administration.
- Preparation: The infusion rate depends on the chosen dilution. It is calculated according to the SmPC or the local standard and not taken from memory.
Monitoring includes:
- patellar tendon reflex (it is the first to disappear in overdose),
- respiratory rate and SpO₂,
- urine output.
Typical sources of error in syringe pump calculations
Units and calculation
- µg instead of mg (or vice versa): factor of 1000.
- Factor 60 forgotten or applied twice: this concerns confusion between µg/kg/min and µg/kg/h.
- µg/kg/min confused with µg/min: the error is as large as the body weight.
- Decimal-point and order-of-magnitude errors: particularly dangerous at infusion rates below 1 ml/h and with pumps that display one decimal place.
Concentration and weight
- Wrong concentration: several marketed concentrations, inconsistent labelling (g of salt vs. mmol) or deviations from the ward standard.
- Uncertain body weight: an estimated weight is a source of error. The weight used should be documented.
Pump and line
- Pump operation: wrong entry selected from the drug library, wrong syringe type, unintended bolus function, clamps not removed.
- Line management: boluses or flushes via the catecholamine lumen wash the drug in uncontrollably. Interruptions during syringe changes can lead to drops in blood pressure.
- Low infusion rates: at very low infusion rates, dead space, start-up delay and height differences between syringe and patient have a greater effect. A more dilute standard solution may be appropriate, but must then be labelled consistently and uniformly.
Double-checking: making it effective
A double-check only provides protection if it is performed independently. If the second person merely reads through the completed calculation, they often adopt the same error. Practical elements include:
- Calculate separately: two people calculate the infusion rate independently and compare only afterwards.
- Check against a table: the result is compared with a validated syringe pump dosing table, provided one exists for the concentration used.
- Check plausibility: is the infusion rate in the expected order of magnitude? For 70 kg and the usual noradrenaline standard solution, 42 ml/h instead of 4.2 ml/h would be a warning sign.
- Back-calculate: calculate back from the set infusion rate to µg/kg/min or mg/kg/h.
- Closed-loop communication: order, read-back and confirmation including drug, concentration, dose and infusion rate. Units are always stated aloud.
- Label unambiguously: drug, total amount, volume, concentration, time and initials.
- Use standard concentrations: department-wide uniform preparations reduce the calculation burden. They work best together with a correspondingly configured pump drug library.
For reference, the web app "Notfall & Narkose" and the A6 pocket book contain syringe pump dosing tables for the standard preparation stated in each case. They apply only to exactly this concentration. If the preparation differs, the rate must be recalculated.
Practical conclusion
Calculating a syringe pump infusion safely requires less mental arithmetic skill than a fixed procedure:
- align the units,
- always calculate using the same formula,
- back-calculate the result,
- have it checked independently.
Standard concentrations and tables make syringe pump dosing considerably easier. However, they do not replace checking the label, the ampoule and the pump display. The dose itself is always titrated to clinical effect, e.g. blood pressure, heart rate or depth of sedation.
References
- Fachinformation Noradrenalin 1 mg/ml Konzentrat – aktuelle Fassung.
- Fachinformation Landiolol 300 mg Pulver zur Herstellung einer Infusionslösung (Landiololhydrochlorid) – aktuelle Fassung prüfen.
- Fachinformation Midazolam 1 mg/ml bzw. 5 mg/ml Injektionslösung – Standarddosierungstabelle; abgeglichen mit EU-SmPC Midazolam (UK).
- DGGG/OEGGG/SGGG. Hypertensive Schwangerschaftserkrankungen: Diagnostik und Therapie. S2k-Leitlinie, AWMF-Registernummer 015-018 – aktuelle Fassung prüfen.
This article does not replace clinical judgement in the individual case or the current summary of product characteristics and guidelines.