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Ability of hospital doctors to calculate drug doses

^a Department of Anaesthesia, Manchester Royal Infirmary, Manchester M13 9WL

Correspondence to: Dr Rolfe.

The contents of most drug ampoules are given as their mass concentration (mg or µg/ml), but a few drugs are traditionally given as a dilution or percentage concentration--for example, 1:1000 or 1% respectively. Many drugs used in resuscitation and acute medical emergencies are labelled in this way--for example, adrenaline 1:1000 and sodium bicarbonate 8.4% solution.

A survey showed that many junior doctors could not calculate the mass of lignocaine in ampoules of different concentrations.¹ We investigated further the ability of hospital doctors to convert between mass concentrations, dilutions, and percentage concentrations. We also asked which convention they preferred and the adequacy of their teaching on calculating drug doses.

Answers to questions on drug doses. Values are numbers (percentages) of hospital doctors
-------------------------------------------------------------------------------------------------------------
Question                                      Right                  Wrong                Don't know
-------------------------------------------------------------------------------------------------------------
1 How much noradrenaline
  (in mg) is there in 4 ml of a
  1:1000 solution?:
  All doctors (n=150)                               76 (51)              37 (24.5)               37 (24.5)
   Physicians (n=51)                   22 (43)                14 (27)               15 (30)
   Surgeons (n=70)                     26 (37)                22 (31.5)             22 (31.5)
   Anaesthetists (n=29)                28 (97)                 1 (3)                 0
2 How many mg of lignocaine are
  there in a 10 ml ampoule of
  lignocaine 1%?:
  All doctors (n=150)                               68 (45)              49 (33)                 33 (22)
   Physicians (n=51)                   20 (39)                16 (31)               15 (30)
   Surgeons (n=70)                     19 (27)                33 (47)               18 (26)
   Anaesthetists (n=29)                29 (100)                0                     0
3 How many mmol of sodium
  bicarbonate are there in 100 ml of
  an 8.4% solution?:
  All doctors (n=150)                               50 (33)              40 (27)                 60 (40)
   Physicians (n=51)                   17 (33)                12 (24)               22 (43)
   Surgeons (n=70)                      8 (11)                26 (37)               36 (51)
   Anaesthetists (n=29)                25 (86)                 2 (7)                 2 (7)
4 How many mg of adrenaline are
  there in a 10 ml ampoule of 0.25%
  bupivacaine with adrenaline in a
  1:200000 solution?:
  All doctors (n=150)                               46 (31)              39 (26)                 65 (43)
   Physicians (n=51)                    8 (16)                13 (25)               30 (59)
   Surgeons (n=70)                     16 (23)                19 (27)               35 (50)
   Anaesthetists (n=29)                22 (76)                 7 (24)                0
5 How many ml of a 1:10000
  solution would you need to
  obtain 1 mg of adrenaline?:
  All doctors (n=150)                               92 (61)              19 (13)                 39 (26)
   Physicians (n=51)                   32 (63)                 5 (10)               14 (27)
   Surgeons (n=70)                     31 (44)                14 (20)               25 (36)
   Anaesthetists (n=29)                29 (100)                0                     0

Subjects, methods, and results

We asked 150 teaching hospital doctors of all grades and from a representative spread of the major specialties to complete a written questionnaire comprising five questions about drug dilution and concentration (see table). One of us (SR) was present while the form was completed. Ten minutes was allowed. Unanswered questions were classified as "don't know" answers.

Completed forms were received from all doctors. The table shows the results. Questions 3 and 4 were the most difficult, having been answered correctly by only around a third of doctors. Proportionally more consultants and senior registrars than doctors in junior grades answered these questions correctly--for example, 58% (11/19) of consultants but only 4% (1/24) of preregistration house officers answered question 3 correctly.

Over two thirds of doctors (117) said that they would prefer ampoules to be labelled with the mass concentration rather than the dilution or percentage concentration. Thirteen expressed no preference, and nine thought that two conventions should be used. Of the 11 doctors who were satisfied with the current labelling arrangements, six were unable to answer any of the questions correctly and only two gave five correct answers.

Forty two doctors considered that they had received adequate teaching on calculating doses, but only 19 answered all the questions correctly.

Comment

Around half the doctors surveyed were unable to convert drug doses correctly from a percentage concentration or dilution to the more conventional mass concentration. Replies varied by as many as three orders of magnitude.

Those who correctly answered question 1 would be expected also to answer question 5 correctly since these questions are closely related: only 33 doctors gave answers that did not correlate. Twenty one of them could give the correct clinical dose of adrenaline (question 5); this might have been learnt by rote.

Many doctors thought that there was no need to be able to convert from one convention to another. One reason often cited was that the commonly available commercially packaged syringes of adrenaline and lignocaine for use in medical emergencies contain the appropriate dose. Many surgeons commented that they knew the safe maximum volume of a given lignocaine solution rather than its mass concentration, but this belief was not supported by previous findings.¹

Drug doses recommended in resuscitation protocols are confusing. The European Resuscitation Council's guidelines stipulate doses of adrenaline and sodium bicarbonate in mg and mmol.² Our results suggest that many doctors have little idea of what volume of drug is required when it is presented in commonly available ampoules.

In March 1991 the National Pharmaceutical Supply Group accepted a proposal for an NHS specification for ampoule labels.³ Initially the document specifies that units should be SI and "the amount/concentration [be] expressed as the amount 'x' or the concentration 'x' in 'y' ml, where 'y' is the total volume of the ampoule." The document later states, however, that when products (specifically local anaesthetic drugs) have been traditionally measured in another way they should continue to be measured that way. The European Drug Index also shows the coexistence of several conventions: adrenaline is listed as a dilution, mass concentration, and percentage concentration depending on the country in which it is used.

Our results suggest that all drugs, especially those used in medical emergencies, should be measured in a standard way, as a mass concentration, to avoid potentially hazardous confusion.

1. Scrimshire JA. Safe use of lignocaine. BMJ 1989;298:1497.
2. European Resuscitation Council Working Party. Adult advanced cardiac life support: the European Research Council guidelines, 1992 (abridged). BMJ 1993;306:1589-93.
3. National Pharmaceutical Supply Group. Ampoule labels: NHS specification London: HMSO, 1994.
4. Muller NF, Dessing RP, eds. European drug index. 2nd ed. Stuttgart: Deutscher Apotheke Verlag, 1992.

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