Nurse Education in Practice · lations why numeric and scientiﬁc knowledge and skills must be mastered to ensure safe dosage calculation and medicines management practice. The ﬁndings

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Nurse Education in Practice 13 (2013) e11ee22

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Nurse Education in Practice

journal homepage: www.elsevier .com/nepr

Safety in numbers 1: Essential numerical and scientific principles underpinningmedication dose calculation

Simon Young a, Keith W. Weeks a,*, B. Meriel Hutton b

a Faculty of Health, Sport & Science, University of Glamorgan, UKbKing’s College London, UK

a r t i c l e i n f o

Article history:Accepted 17 October 2012

Keywords:Medicines dosage calculationsHealthcare numeracyFundamental clinical pharmacokinetics

* Corresponding author.E-mail addresses: [email protected], kholland

(K.W. Weeks).

1471-5953/$ e see front matter � 2012 Published byhttp://dx.doi.org/10.1016/j.nepr.2012.10.012

a b s t r a c t

Registered nurses spend up to 40% of their professional clinical practice engaged in the art and science ofmedication dosage calculation problem-solving (MDC-PS). In advancing this patient safety criticaldiscipline it is our position that as a profession we must first situate MDC-PS within the context of thewider features of the nursing numeracy, medicines management and clinical pharmacokinetic domainsthat inform its practice. This paper focuses on the essential relationship between numeracy, healthcarenumeracy, medicines management, pharmacokinetics and MDC-PS. We present a taxonomy of genericnumerical competencies for the pre-registration curriculum, with examples of essential medicationdosage calculation requirements mapped to each skills domain. This is followed by a review of thesymbols and measurement units that represent essential components of calculation competence inhealthcare and medicines management practice. Finally we outline the fundamental pharmacokineticknowledge that explains how the body deals with medication and we illustrate through clinical corre-lations why numeric and scientific knowledge and skills must be mastered to ensure safe dosagecalculation and medicines management practice. The findings inform nurse education practice viaadvancing our understanding of a number of issues, including a unified taxonomy of generic numericalcompetencies mapped to the 42 revised UK Nursing and Midwifery Council (NMC) Essential SkillsClusters (NMC, 2010a; NMC, 2010b).

� 2012 Published by Elsevier Ltd.

Introduction and background

The potency of medication used in 21st century healthcarepractice requires registered nurses to have an up to date knowledgeof evidence-based interventions and the ability to effectively andaccurately apply numeracy as part of their medicines managementand wider clinical practice. From a regulation perspective, the UKNursing and Midwifery Council (NMC, 2010a) Essential Skills Clus-ters (ESC) andAdvice and Supporting Information for ImplementingNMC Standards for Pre-Registration Nursing Education (NMC,2010b) includes reference to a wide range of generic and field-specific numerical concepts and competencies that must bemastered to practice as a registered nurse. The medication dosagecalculation problem-solving (MDC-PS) component of theMedicinesManagement ESC was informed by a NHS Education for Scotlandcommissioned programme of research (see Sabin et al., 2013).

[email protected]

Elsevier Ltd.

Throughout this Safety in Numbers series we will explore theconstruct of conceptual competence (understanding themedicationdosage problem to be solved), calculation competence (computa-tion of an accurate numerical value for the dose to be administered)and technical measurement competence (accuratemeasurement ofthe medication dose and/or rate of administration). The masteryand integration of these competencies is necessary to demonstratethe essential knowledge and skills that underpin safe MDC-PSpractice. This paper commences the explication of the essentialapplied numerical knowledge and skills andwider pharmacologicalprinciples required to meet the MDC-PS requirements of profes-sional nursing practice. Within this context we aim to:

a. Provide a definition of numeracy.b. Articulate the relationship between numeracy, healthcare

numeracy, medicines management and medication dosagecalculation.

c. Present a unified taxonomy of generic numerical competenciesand examples of representative medication dosage calculationcomputation requirements mapped to the 42 NMC ESC.

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Fig. 1. An illustration of how competence in healthcare numeracy is a subset ofCoben’s wider definition of numeracy and medication dosage calculation is a subset ofboth healthcare numeracy and of a wider competency in medicines management.(Sabin et al., 2008).

S. Young et al. / Nurse Education in Practice 13 (2013) e11ee22e12

d. Review the esoteric symbols and measurement units thatrepresent important components of calculation competence inhealthcare and medicines management practice.

e. Outline the fundamental pharmacokinetic knowledge thatexplains how the body deals with medication; and illustratesthrough clinical correlations why numeric and scientificknowledge and skills must be mastered to ensure safe medi-cines management practice.

What is numeracy?

The Oxford English Dictionary (OED) defines being numerate asbeing ‘familiar with the basic principles of mathematics’.

This definition of numeracy provides a foundation for under-standing the concept and fundamental basis of numeracy. Howeverit provides little scope for considering numeracy in context, nordoes it define any of the boundaries that should be consideredwhen an educator assists a student in developing numeracy skills.In order to consider numeracy in its educational context a morerounded and functional definition of numeracy has been providedby Coben (2000, p. 35).

To be numerate means to be competent, confident, and comfortablewith one’s judgements on whether to use mathematics ina particular situation and if so, what mathematics to use, how to doit, what degree of accuracy is appropriate, and what the answermeans in relation to the context.

In order to develop and maintain calculation competence thisdefinition adds important detail for the educator. The definitionillustrates the importance of the type of mathematics to be used ina given context. A numerate structural engineer and numeratenurse both fall within the boundaries of the OED definition.However the definition provided by Coben (2000) specifies situa-tional and contextual comfort, competence and confidence. Thishighlights how the numerate engineer requires a different set ofnumeracy skills than the numerate nurse or healthcare profes-sional. The important features to consider in developing calculationcompetence is the context in which the calculations are used (Das,1988) and, secondly, in defining the boundaries of numeracy withinwhich the healthcare professional uses those calculations.

Defining medication calculation competence and its boundaries inmedication dosage calculation problem-solving (MDC-PS)

We have previously definedmedication calculation-competenceas ‘the need to undertake appropriate arithmetical operations andcomputations to calculate a numerical value that falls within anappropriate degree of accuracy for the required dose or rate (Cobenet al., 2010)’. This definition situates calculation competence asa keystone in developing MDC-PS within nursing practice. Theconcept of MDC-PS competence has been extended by Sabin et al.(2008) and Coben et al. (2010) through the use of illustrative settheory (see Fig. 1). This provides the context within which MDC-PSand calculation competence lies in the broader arena of numeracy,healthcare numeracy and medicines management. Within thisseries we draw on the Audit Commission definition of medicinesmanagement as encompassing ‘the entire way that medicines areselected, procured, delivered, prescribed, administered and reviewed tooptimize the contribution that medicines make to producing informedand desired outcomes of patient care’ (Audit Commission, 2001, p. 5).

These definitions illustrate two key education tenets that lie atthe core of supporting calculation competence development inprofessional practice: First, that of defining the context in whichcalculation competence is centred and the importance of situatedcognition, i.e., the learning and application of knowledge and skills

situated in the context of real life situations and practice environ-ments (Brown et al., 1989; Lave and Wenger, 1990; Weeks et al.,2013b); and second, the importance of supporting the construc-tion of accurate schemata (internal cognitive representations of ourworld) that reflect the ability to understand and use arithmeticaloperations, computations and symbols to competently solveauthenticmedication dosage problems. In essence, this requires thebridging of the theory-practice and knowledge-performance gapand to commence our advancement of this premise we nowpresent a taxonomy of essential nursing numeracy skills.

A taxonomy for nursing numeracy and essential medication dosagecalculation skills

Hutton developed a taxonomy of numeracy skills required bypractising nurses in the UK (Hutton, 1998). She substantiallydeveloped the inventories produced by Pirie (1987) and Roberts(1990), and reflected the major changes that had occurred in bothclinical practice and nurse education since their initial reporting.One critical contribution of Hutton’s study was to identify thenursing mathematics that was either specific to, or generally usedwithin the four current UK branches or fields of nursing, i.e., child,adult, mental health and learning disability (and that form the corecurricula of essential international general nursing programmes,e.g., USA Pre-Licensure KSA’s: Quality and Safety Education forNurses, 2011). This represented a substantial development ofPirie’s inventory, which while being a seminal piece of work at thetime, provided a rather general overview of nursing mathematics.Hutton interviewed clinical nursing staff and students from all fourbranches of nursing and relevant clinical settings, to identify theirperceptions of the mathematics used in those areas. These findingswere then confirmed and enhanced by the processes of observationand shadowing of clinical staff and students in clinical practice.Here we report how Hutton extended her original research intoa unified taxonomy of generic numerical competencies mapped tothe 42 revised NMC Essential Skills Clusters (NMC, 2010a). Thetaxonomy in Table 1 illustrates the numeracy skill required,examples of where the skill is utilised in nursing practice and thespecific branch or field of nursing practicewhere the numeracy skillis relevant. An addendum by Weeks and Young provides examplesof theminimum level of essential medication dosage & intra-venousinfusion calculation skills required at the point of registration andthat act as a foundation for development of more complex skills.

Table 1Taxonomy of essential numeracy skills required by nurses mapped against NMC (2010a) essential skills clusters.

Numeracy skill Examples Branch/field of practice mostcommonly using the skill

Essential skills clusters (NMC, 2010a, b) Examples of essential medication dosage& intravenous infusion calculation skills

For entry to branch/field For entry to register

Estimation All medication dosage & IVinfusion rate calculations

AllC ¼ ChildA ¼ AdultMH ¼ Mental HealthLD ¼ Learning Disability

Is competent in basicmedicines calculations (33i)

Makes a comprehensive assessment ofpatients/clients’ needs in relation to nutrition,identifying, documenting and communicatinglevel of risk (28v)Accurately calculates medicines frequentlyencountered within branch (33ii)Safely manages drug administration andmonitors effects (36iii)

Dose of medication or rate of infusionmay be estimated to provide a frameof reference or “ball park” figure priorto computing & checking thecalculation for accuracy, e.g.:Prescribed dose: 200 mgDispensed: 250 mg/10 mLEstimate: >5 mL & <10 mLAccurate computation: 8 mL

Addition of wholenumbers

Fluid balanceAddition of tablet dosesof varying formulations

All Accurately monitors dietaryand fluid intake and completesrelevant documentation (27ii)Accurately monitors andrecords fluid intake andoutput (29ii)

Documents progress against prescriptionand markers for hydration (32iii)

Prescribed dose 8 mg5 mg þ 2 mg þ 1 mg tablets

Subtraction of wholenumbers

Fluid balance All Accurately monitors dietaryand fluid intake and completesrelevant documentation (27ii)Accurately monitors and recordsfluid intake and output (29ii)

Documents progress against prescriptionand markers for hydration (32iii)

Multiplication of wholenumbers

Conversion of units, driprate calculation

All Is competent in basic medicinescalculations (33i)

Monitors and assesses patients/clientsreceiving intravenous fluids (32ii)Accurately calculates medicinesfrequently encountered withinbranch (33ii)Safely manages drug administrationand monitors effects (36iii)

25 � 150 � 2250 � 51000 � 20450 � 15

Division of wholenumbers

Conversion of units, driprate calculation



1000/81000/61000/12450/3450/4125/4167/3

Use of fractions Drip rate calculations,enteral feeding,conversion to SI units


.administers enteral feeds safelyand maintains equipment inaccordance with local policy (31iv)Monitors and assesses patients/clients receiving intravenous fluids (32ii)Accurately calculates medicinesfrequently encountered withinbranch (33ii)Safely manages drug administrationand monitors effects (36iii)

½ expressed as decimal equivalent¼ expressed as decimal equivalent1/3 expressed as decimal equivalent5/10 expressed as decimal equivalent125/250 expressed as decimal equivalent2/5 expressed as decimal equivalent200/250 expressed as decimal equivalent12.5/25 expressed as decimal equivalent6.25/12.5 expressed as decimal equivalent

Use of decimals Conversion of units,infusion pumps



12.5 � 26.25 � 5

Système Internationald’ Unités (S.I.) Units

Prescriptions, haematology& biochemistry blood results,patients’ weight measurement& conversion


Monitors and assesses patients/clients receiving intravenousfluids (32ii)Safely manages drug administrationand monitors effects (36iii)Applies knowledge of basicpharmacology, how medicines actand interact in the systems of thebody, and their therapeutic action. (36ii)

Understand the magnitude differencebetween SI unit mass (weight)expressed in:Litres (L)Millilitres (mL)Kilograms (Kg)Grams (g)Milligrams (mg)MicrogramsNanogramsUnderstand the difference between SI

(continued on next page)

S.Younget

al./Nurse

Educationin

Practice13

(2013)e11

ee22

e13

Table

1(con

tinu

ed)

Numeracyskill

Exam

ples

Branch

/fieldof

practicemost

common

lyusingtheskill

Essential

skillsclusters(N

MC,

2010

a,b)

Exam

plesof

essential

med

icationdosag

e&intrav

enou

sinfusion

calculation

skills

Foren

tryto

bran

ch/field

Foren

tryto

register

unitsof

massan

dIntern

ational

Units

(IU)of

biolog

ical

activity

oreffect

(e.g.u

sedin

themea

suremen

tof

Insu

lin)

Con

versionbe

twee

nunits

Paed

iatric

dosag

es,translation

toim

perialm

easu

resfor

patients/relatives

e.g.,

birthweigh

t

A,C

,MH

Take

san

dreco

rdsaccu

rate

mea

suremen

tsof

weigh

t,heigh

t/length,b

odymass

index

,andother

appropriate

mea

suresof

nutritional

status(28i)

Isco

mpeten

tin

basic

med

icines

calculation

s(33i)

Accurately

calculates

med

icines

freq

uen

tlyen

counteredwithin

bran

ch(33ii)

Safely

man

ages

drug

administrationan

dmon

itors

effects(36iii)

1.0�

1000

0.5�

1000

0.25

�10

000.62

5�

1000

1/10

0050

0/10

0025

0/10

0062

5/10

00Con

vert

220pou

ndto

Kg

Con

vert

6.6pou

ndto

Kg

Unde

rstanding

percentage

Distingu

ishbe

twee

npercentage

expressions,e.g.:

5%Dex

trose:

gram

s/10

0mL

98%ox

ygen

saturation

2%man

agem

entcu

ts

All

Administers

med

ication

safely

under

direct

supervision

,including

orally

andby

injection

insimulationan

d/or

practice(38iii)

Safely

andeffectively

administers

med

icines

viaroutesan

dmethod

sco

mmon

lyusedwithin

the

bran

chan

dmaintainsaccu

rate

reco

rds(38iv)

10%of

100

5%of

1000

0.9%

of10

00

Ratio

Prep

arationof

solution

sMed

icationsdosag

ecalculation

All

Isco

mpeten

tin

basic

med

icines

calculation

s(33i)

Accurately

calculates

med

icines

freq

uen

tlyen

counteredwithin

bran

ch(33ii)

Safely

man

ages

drugad

ministration

andmon

itors

effects(36iii)

Understan

dmea

suremen

tunitdosing

ratios,e

.g.,

Inmg/Kgdosinge.g.,a

10mg/kg

dose

represents

aratioof

10mgto

bead

ministeredforev

eryKgof

the

patient’sbo

dyweigh

t.Adrenaline(Epinep

hrine)1in

1000

¼1mg/mL.

Use

ofform

ulae

Dosag

ecalculation

Infusion

rate

calculation

Bod

ysu

rfacearea

(BSA

)estimation

BMIcalculation

All

Isco

mpeten

tin

basic

med

icines

calculation

s(33i)

Safely

man

ages

drugad

ministration

andmon

itorseffects(36iii)

Prescribed

Volumeðm

LÞ�DropFa

ctor

ðdropsper

mLÞ

Prescribed

Duration

ðhou

rsÞ�

Minutesper

hou

rBSA

:Sq

uareroot

of(heigh

t(cm)�

weigh

t(K

g)/360

0)

Use

oftables

Con

versiontables

(Imperial/SI

units)

Bod

ymassindex

tables

A,C

Take

san

dreco

rdsaccu

rate

mea

suremen

tsof

weigh

t,heigh

t/length,b

odymass

index

,andother

appropriate

mea

suresof

nutritional

status(28i)

Mak

esaco

mprehen

sive

assessmen

tof

patients/clie

nts’nee

dsin

relation

tonutrition,iden

tifying,

doc

umen

ting

andco

mmun

icatingleve

lofrisk

(28v

)

Understan

dingaseries

oftables

contained

intheBritish

National

Form

ulary(orintern

ational

equivalen

t)sp

ecifyingim

portantparam

eterssu

chas

idea

lbod

yweigh

tan

dco

nve

rsion

ofpou

ndsan

dston

esto

Kg

Use

ofch

arts/

grap

hs

Temperature

charts,g

rowth

charts,p

rescription

charts

A,C

,LD

Mea

suresan

ddoc

umen

tsvitals

ignsunder

supervision

andresp

ondsap

propriately

tofindings

outsidethe

normal

range

(9ix)

Usesprescription

charts

correctlyan

dmaintains

accu

rate

reco

rds(38i)

Mea

sures,doc

umen

tsan

dinterprets

vitalsign

san

dacts

appropriatelyon

findings

(9xx

iii)

Safely

andeffectivelyad

ministers

med

icines

viaroutesan

dmethod

sco

mmon

lyusedwithin

thebran

chan

dmaintainsaccu

rate

reco

rds(38iv)

Understan

dnom

ogram

dosingregimes

Appreciation

ofstatistics

Eviden

ce-based

practice

All

Question

s,critically

appraises

and

usesev

iden

ceto

supportan

argu

men

twhen

med

icines

may

ormay

not

bean

appropriate

choice

oftrea

tmen

t.(35iv)

Use

ofstatistics

such

asnnumbe

rs:

numbe

rnee

ded

toharm/treat

andin

understan

dingthefreq

uen

cyof

the

appea

rance

ofAdve

rseDrugRea

ctions

Budge

ting

Stoc

kco

ntrol

Orders,receives,storesan

ddisposes

ofmed

icines

safely.

(37ii)

Stoc

kco

ntrol

ofmed

icines

and

dressings

intheclinical

area

Basic

book

keep

ing

Helpingclients

withman

aging

theirmon

eyMH,L

DAssistingclients

withco

llecting

benefi

tsan

dpen

sion

ifunab

leto

doso

them

selves

Mea

suremen

tFluid

balance,v

ital

sign

s,preparing/drawing-upan

ddispen

singmed

icines

All

Accurately

undertake

san

dreco

rdsaba

selin

eassessmen

tof

weigh

t,heigh

t,temperature,

pulse,

resp

irationan

dbloo

dpressure(9ii)

Mea

sures,doc

umen

tsan

dinterprets

vitals

ignsan

dacts

appropriatelyon

findings

(9xx

iii)

Mak

esaco

mprehen

sive

assessmen

tof

patients/clie

nts’nee

dsin

relation

tonutrition,iden

tifying,

doc

umen

ting

Tech

nical

mea

suremen

tof

the

calculateddoseof

med

icationor

rate

ofIV

infusion

:Cou

ntingthenumbe

rof

tabletsor

capsu

lesto

bead

ministered.

Mea

suringthevo

lumeof

med

ication


Take

san

dreco

rdsaccu

rate

mea

suremen

tsof

weigh

t,heigh

t/length,b

odymass

index

,andother

appropriate

mea

suresof

nutritional

status(28i)

Administers

med

ication

safely

under

directsu

pervision

,includingorally

andby

injectionin

simulation

and/orpractice(38iii)

andco

mmunicatingleve

lof

risk

(28v

)Sa

fely

man

ages

drugad

ministration

andmon

itorseffects(36iii)

Safely

andeffectivelyad

ministers

med

icines

viaroutes

andmethod

sco

mmon

lyusedwithin

thebran

chan

dmaintainsaccu

rate

reco

rds(38iv)

tobe

administeredin

milliliters

ina

med

icinepot.

Mea

suringthevo

lumeof

med

ication

tobe

administeredin

milliliters

ina

syringe

&displacingalla

irbu

bbles.

Settingtherate

ofan

IVinfusion

ofcrystallo

idsolution

viaavo

lumetric

pump(m

Lper

hou

r).

Settingtherate

ofan

IVinfusion

ofcrystallo

idsolution

viaaman

ual

flow

meter

(dropsper

minute).

Neg

ative

numbe

rsFluid

balance,o

phthalmics

A,C

Accurately

mon

itorsan

dreco

rdsfluid

intake

and

output(29ii)

Iden

tifies

sign

sof

deh

ydration

andacts

toco

rrectthese(29v

i)

Recog

nition

ofindices

Blood

resu

lts

A,C

Applie

skn

owledge

ofba

sic

pharmacolog

y,how

med

icines

actan

dinteract

inthesystem

sof

thebo

dy,

andtheirtherap

eutic

action

.(36ii)

S. Young et al. / Nurse Education in Practice 13 (2013) e11ee22 e15

Following presentation of the taxonomy we explore the essentialmeasurement units employed in MDC-PS; and Weeks et al. (2013a)further explore the principles of diagnostic assessment of essentialcalculation skills.

The symbology of healthcare numeracy

Symbols are a ubiquitous and defining feature of mathematics.The symbols we call numbers are abstract representations ofsomething very concrete and real to humans (Bellos, 2010). Onechallenge that children face during the formative years of mathe-matical development is that the numerals we use to representnumbers bear no resemblance to the quantities they purport torepresent (Liston, 1994; Weeks et al., 2000, Weeks et al. 2001;Weeks et al., 2013b). For example, the symbolic representation ‘2’does not resonate with what we naturally associate with two asa numerical quantity (Ojose, 2008). One of the skills learned byhumans in mathematical development is the graduated shift fromconcrete/enactive to abstract/symbolic representation of quantifi-cation (see Fig. 2), and the semantic association of abstract symbolswith real concrete quantifications that are a part of everyday life(Piaget, 1983; Bruner, 1975, Bruner, 1978).

Symbols are important beyond the representation of numbers inthe context of numeracy. Algebra, for example, uses symbolicrepresentation to represent numbers or unknown quantities. Inscience (and everyday life) symbols representing units, universallydefine recognised quantities such as mass, length and time. Theseunits and their associated symbols were derived to measure thequantities that define the world in which we live. The majority ofunits used globally belong to the International System of Units,universally abbreviated SI (from the French Le Système Internationald’Unités) (National Institute of Standards & Technology [NIST],2008). The system was initially conceived in the late 18th centuryand was developed as an attempt to unify and rationalise systemsof measurement and highlights the introduction of metrificationinto scientific disciplines (NIST, 2008). The SI is founded on seven SIbase units for seven base quantities (See Table 2).

These seven units are the basic set of tools with which one candefine any other scientific measurement. The SI units for length (m)and time (s) are base defined standards and can be used to deriveunits of measurement such as speed (distance (m)/time(s)) andacceleration (distance (m)/time2(s2)). Dimensional analysis usingthe base units gives speed a derived SI unit of ms�1 and accelerationa derived SI unit of ms�2. In healthcare practice the first three baseunits are important because they are used in the calculationsassociated with medication, mass and volume and more complexcalculations involving infusion rates and syringe pump measure-ments and rates of administration. The SI base unit of temperature(K) is not used in healthcare practice but the degree Celsius scale(�c) is derived from and defined by the SI unit (NIST, 2008). Themole is also an important unit used in biochemistry and pharma-cology and can for example be found on infusion bag labelling andis used to define molar concentration and in biochemical conceptssuch as osmolarity.

In addition to the symbols derived to represent the SI units, thehealthcare professional will encounter the SI unit prefixes. Table 3illustrates twenty key prefixes used by the SI. The prefixes repre-sent decimal fractions and multiples of the SI unit (or derived unit)in question. The key units differ by a factor of 103 (1000), e.g.,a microgram (mg) is 103 (1000) times smaller than amilligram (mg).In medication dosage calculation, conversion of SI units is neces-sary, for example, when medicines are prescribed in microgramsand the medication is only available as a concentration in milli-grams. The knowledge that these conversions are necessary high-light that the healthcare professional needs to understand the

Fig. 2. Modes of representation in the construction of knowledge and quantification (Weeks et al., 2013b).


symbology of the SI unit and apply the knowledge as part of safeand effective medicines management practice.

Construction of accurate schemata for conversion between theSI units of grams, milligrams, micrograms and nanograms is criticalin avoiding errors of magnitude of up to 1000 times the requireddose. We illustrate in Fig. 3 a constructivist based ‘slide-rule’ tooldesigned to support nursing students’ schema construction fordividing and multiplying by magnitudes of 1, 10, 100 and 1000 (seethe animated process in the online paper). This construct lies in starkcontrast to the commonly taught, ‘rules without reason’ (Muelleret al., 2010) process of ‘moving the decimal point three places tothe left or to the right’, in the absence of additionally representingthe 1000 fold magnitude shift of the numerical quantity.

Supplementary data related to this article can be found online athttp://dx.doi.org/10.1016/j.nepr.2012.10.012.

In addition to the SI and derived SI units, the international unit(IU) is encountered in healthcare practice. The International Unit isa measurement of the amount of a substance based on its biologicalactivity or effect. The traditional way of measuring the amount ofa drug that is present in a medicinal product is by mass, e.g., mg ormg or by the amount of molecules it contains, e.g., molar solution.Many active drugs that originate from biological sources exist ina variety of forms. For example, Vitamin D is not one unitarysubstance; it is the name for a group of substances. The substancewe know as vitamin D is made up of compounds such as ergo-calciferol (Vitamin D2), cholecalciferol (Vitamin D3) and sitocalci-ferol (Vitamin D4). The aim of having an international unit for thesebiological products is to be able to pharmacologically compare eachform and produce a standard that produces the same biologicaleffect. The World Health Organisation (WHO) committee on Bio-logical Standardisation provides a reference preparation of givenagents, sets the number of IUs contained in that preparation andthen sets out an assay to compare other preparations to the refer-ence preparation. Examples of this principle for Insulin and VitaminA are illustrated in Table 4:

If a manufacturer wishes to produce an insulin preparation foruse in humans or animals the potency of the insulin is notmeasured by the amount (mg or micrograms of insulin per mL) of

Table 2The seven base SI units.

Base quantity Name Symbol

Length Meter mMass Kilogram KgTime Second sElectric current Ampere AThermodynamic temperature Kelvin KAmount of substance Mole MolLuminous intensity Candela Cd

the suspension but by comparing the activity of the insulinwith thebiological standard in Table 4.

Figs. 4 and 5 illustrate two examples of the fundamentaldifferences in technical measurement and administration vehicledesign for medications measured by SI unit (Prednisolone) andInternational Unit (IU) (Insulin). Understanding the essentialdifferences in both the characterisation and the measurement ofmedications expressed in these unit forms is critical to avoidingdosing errors and patient fatalities.

It is our position that the combined use of virtual representa-tions and diagnostic assessments such as that illustrated here,integrated with practice-based learning and competence assess-ments provide critical steps in constructing accurate schemata forunderstanding and competence in solving these variant dosageproblems (See Weeks et al., 2013b; Weeks et al., 2013c; Sabin et al.,2013; Macdonald et al., 2013; Weeks et al., 2013d).

In summary, it is critical to the safe administration of medicinesthat nursing students construct accurate schemata and competencein the conceptual, calculation and technical measurement knowl-edge and skills that underpin medication dosage calculationproblem-solving. Having articulated a taxonomy and the principleof a point of registration benchmark for the nursing mathematicsand measurement units employed in solving essential medicationdosage problems, we now turn to considering the fundamentalpathways taken by medicines as they pass through the humanbody, illustrating how important the accuracy of calculation anddosing is in safe and efficacious medicines management.

Why is getting the medication dose right so important?

In addition to defining the conceptual, calculation and technicalmeasurement competence mathematical influences required ingetting the dose right, there are other important efficacy and safetyconsiderations to be made when administering a medication toa patient. Some of these considerations extend beyond numeracyalone and need to be considered in the broader context of medi-cines management (Sabin et al., 2008).

Why is getting the dose correct so important? The questionposed is fairly simple and the answer seemingly obvious. Theoutcomes associated with mis-prescribed, mis-calculated, mis-prepared or mis-administered doses of a drug (the active thera-peutic agent contained in a medication) can range from, at theextremes, complete therapeutic failure due to under-dosing tooverdose and consequent toxicity and fatality. The importance ofaccurate dosing should be recognised at every stage of the medi-cine’s development and management chain of events. However,derivation of the data that is used by healthcare professionals indrug dosing in clinical practice is the result of complex scientificendeavour. The ‘correct dose’ is the result of several scientific and


Table 3The prefixes for the SI base units. The most commonly used are highlighted. The typical range used in healthcare practice are additionally italicised.


mathematical considerations that oblige those who prescribe,dispense and administer medications to take the utmost care whenperforming practice duties that relate to the safe management ofmedicines.

A great deal of time and effort invested by the pharmaceuticalindustry goes into ensuring that the dose (or dose ranges) sug-gested by their data is the safest and most efficacious for the range

Fig. 3. A constructivist ‘slide-rule’ tool for supporting mathematical conversion ofSI units.

of patients for whom it is intended (Cobert, 2012). Getting the doseright for a diverse population of patients is a phenomenallycomplex facet of pharmaceutical science. However, some basicprinciples can be considered to underpin the science and havea bearing on how nurses and educators consider developing safemedicationmanagement principles. One key premise to consider inthe broader context of medicines management is that in order fora drug to achieve its desired effect, a sufficient quantity of that drug(within a safe therapeutic range) must reach the drugs’ site ofaction (e.g., the target human cell or a bacterium). This concen-tration must be maintained, within certain limits, for the desiredperiod of treatment (Simonsen et al., 2006); i.e., the important end-point of all drug dosing is to attain the correct concentration of drugat the site(s) of action so that the desired therapeutic effect isachieved.

What influences the concentration of drug that reaches thesite of action?

Many factors can influence whether a drug reaches the site ofaction at the correct concentration. Key fundamental factors thatthe patient/healthcare professional are able to influence directlyinclude concordance, prescribing and administering the correctdrug to the correct patient; avoiding prescription and administra-tion of drugs to which the patient is allergic or sensitive; taking/administering the correct dose of the drug; taking/administeringthe drug via the correct route; and taking/administering the drug atthe correct dosing interval. Other factors, outside the direct controlof the patient/healthcare professional can also influence the final

Table 4Illustrative biological units standards for medicinal products.

Substance Biological equivalence

Insulin 1 IU is biologically equivalent to 45.5 mg of pure crystallineinsulin

Vitamin A 1 IU is equivalent to the standardised biological activityof 0.3 mg of retinol or 0.6 mg of beta carotene

Fig. 4. Example of the conceptual, calculation and technical measurement features for a SI unit based medication dosage calculation problem (Prednisolone).


concentration at the site of action: genetics; age (especially theextremes of life); coemorbidity; concurrent illness, e.g., dehydra-tion; and choice of pharmaceutical formulation. In order to betterunderstand how some of these influences are exerted, clinicalpharmacology should be studied and its influences on clinicalpractice considered. In particular an appreciation of the funda-mental aspects of clinical pharmacokinetics informs the practicinghealthcare professional of the science underpinning the safe andefficacious management of medicines. In this paper we focus onessential pharmacokinetic factors that the clinical nurse shouldconsider when considering and calculating a dose of medication foradministration to a patient.

Clinical pharmacokinetics

Clinical pharmacokinetics describes the influence that thehuman body has on drugs or foreign chemicals over a given time.The science of pharmacokinetics encompasses complex mathe-matical modelling of the movement of a drug through the body.When studying the subject for the first time, amore anatomical andless mathematical appreciation of pharmacokinetics can be made.The pharmacokinetics of a particular drug agent is best studied byconsidering four processes, known by the acronym ADME:

Fig. 5. Example of the conceptual, calculation and technical measurement features for

The four basic pharmacokinetic parameters (ADME)Absorption ADistribution DMetabolism MExcretion E

When a healthcare professional studies the Summary of ProductCharacteristics (SPC) of a drug (e.g., http://www.medicines.org.uk/emc/) it can be seen that each SPC illustrates pharmacokineticinformation using the ADME structure.

Absorption

Absorption describes the process of the drug agent moving fromits site of administration into the general circulation. Key essentialfactors influencing absorption include:

� The rate and extent of absorption of drugs is governed by manyfactors including route of administration, formulation, stage oflife, etc.

� Blood flow is an important factor in influencing the rate andextent of absorption of drugs.

� Dosing as per the manufacturers/prescribers instructionsensures that the plasma concentration of drugs is attained forthe most efficacious result. Deviating from these instructionsmay have a similar effect to not getting the dose right.

The majority of drugs are administered via a licensed route toenter the general circulation and from there to their site of action.Intravenous drugs (IV) are the only group of drugs that do notundergo absorption. Drug entities must cross various barriers to getto the general circulation (Neal, 2012). Many drugs move by passivediffusion, i.e., movement from an area of high concentration to oneof low concentration. Drugs administered via the oral route typi-cally move from the small intestine, through the gut wall, througha blood vessel wall into the hepato-portal circulation, to the liverwhere they undergo ‘first pass effect metabolism’ and eventually

an International Unit (IU) based medication dosage calculation problem (Insulin).

http://www.medicines.org.uk/emc/

http://www.medicines.org.uk/emc/


the systemic circulation. Some drugs utilise active transportmechanisms to reach the circulation, e.g., valaciclovir (Guo et al.,1999). Other drugs use both passive diffusion and active transportmechanisms, depending on factors such as their concentration inthe gut, e.g., vitamin B1 (Combs, 2008). Some of the factors thatinfluence absorption from the GI tract are described in ClinicalCorrelation 1 (Table 5).

Distribution

Distribution of a drug around the body occurs when the drugreaches the general circulation. The drug must then enter the tissueor interstitial fluid to exert its pharmacological effect. Factors thatinfluences drug distribution include:

� Blood flow� Drug - plasma protein binding� Blood brain/placental barrier� Storage sites� Disease states, e.g., hypoalbuminaemia

When a drug has been absorbed or introduced directly into theblood stream, it frequently needs to be transported and distributedto the site of action. The eminent pharmacologist, Paul Ehrlichcoined the phrase “magic bullet” to describe the selective targetingof bacterium with antibiotics without the antibiotic affectinganother organism. The majority of modern drug agents are not

Table 5Clinical correlation 1: Factors that may influence the absorption of drugs in thegastrointestinal (GI) tract.

Factor Explanation (examples)

Acidstability

Oral medication must be relatively acid stable to withstandthe pH of the stomach. Acid labile drugs are unsuitable fororal administration (without special formulation). Example:flucloxacillin is acid stable while insulin is not; this highlightsthe necessity to administer medications via their prescribed/ordered route.Age: Stomach pH is less acidic in both the very young: typicallypremature babies to 3 year olds (due to immature parietalcells); and the elderly (due to reduced production ofhydrochloric acid).

Surfacearea

The entire GI tract has a large surface area. Any condition thatreduces the functional absorptive surface area, e.g., damagedue to inflammatory bowel disease, or surgical removal oflarge segments of the bowel, may decrease the absorptionof the drug.Age: In the elderly both the absorptive surface of the gutvilli and the blood flow to the GI tract are reduced.

Gutmotility

The majority of drug absorption occurs in the small intestine;any factor that speeds up or slows gut motility can influenceabsorption. For example, diarrhoea or the administration ofthe anti-emetic drug metoclopramide, which speeds upgastric emptying may influence the rate and extent of drugabsorption.Age: Gastric emptying is reduced in both young children(due to irregular peristaltic movement) and the elderly(due to changes in smooth muscle tone and activity).

Lipidsolubility

Lipophilic drugs will pass more easily from the gut intothe cells of the gut and thence to the circulation.

Presenceof Food

Food may hinder the absorption of drugs from the GI tract.For example, food will decrease the absorption of flucloxacillinfrom the gut and decrease its bioavailability (the amount ofdrug available to the circulation). This is the reason thatflucloxacillin is administered half to 1 h before food or onan empty stomach. Calcium decreases the absorption ofcertain tetracyclines.

Otherdrugs

Antacid will increase stomach pH. This may influence thedissolution of the drug especially if it is enteric coated (EC).EC preparations are designed to dissolve further down theGI tract to avoid extensive contact with the stomach.

‘magic bullets’ and will travel indiscriminately in the circulation totheir site of action and elsewhere in the body. This indiscriminatebehaviour of drug agents leads to the most common adverseeffects experienced by patients when using pharmacologicallyactive agents.

Blood flow is an important factor in determining the exactdistribution of a drug agent. Organs that are well perfused, e.g., thekidneys and heart will generally receive a plentiful supply of mostdrug agents. Tissues such as fat and bone, which are poorlyperfused, will receive less of a drug in a given time and it may takea longer time period for the drug to reach an adequate concentra-tion for therapeutic effect in those tissues.

Barriers to distribution

The human body possesses natural structures that protect vitalorgans from the influences of foreign chemicals. The brain, forobvious reasons, must be protected from poisons and otherchemicals. The circulation of the brain possesses specific cellularformations (the bloodebrain barrier) that prevent the passage ofmany chemicals from the general circulation to the brain (Neal,2012). This protective mechanism is useful for survival, buta hindrance to pharmacological therapy. To exert their actionsantidepressants, antipsychotics, hypnotics and centrally actingagents must pass into the central nervous system in adequateconcentration. One key, common feature of these agents is thatthey are highly lipophilic. The placental barrier serves a similarpurpose in protecting the developing foetus.

Protein binding

For drugs to cross from the circulation into organs and tissuesthey must be dissolved in tissue fluids or plasma. Fig. 6 providesa highly simplified illustration of how in pharmacokinetic terms,a drug, which is dissolved in plasma and is able to diffuse from thecapillary into tissues where it can exert its effect on target cells iscalled free drug. Some drug agents, depending on their physico-chemical properties will bind to a greater or lesser extent to theprotein components of plasma, e.g., albuminora1-acid glycoprotein.

A delicate equilibrium is set up between bound and unbounddrug and drug that diffuses from the circulation to the tissue andcells. The dose of drug that should be administered takes account ofthis binding and is part of the consideration made in getting thecorrect concentration. Errors in medication dosing and adminis-tration can affect this delicate balance and can result in issues suchas increased prevalence of side effects and toxicity. Some of thefactors that may influence the distribution of drugs are described inClinical Correlation 2 (Table 6).

Competition at binding sites

The process of binding is usually competitive and some drugswill compete for binding sites with other drugs. If a highly proteinbound drug is added to an existing therapy which includes anotherhighly protein bound drug therewill be competition for the bindingto the plasma proteins. This results in changes in free drugconcentration of the initial drug and may result in an increase in itsactions.

Metabolism

Metabolism, in the pharmacological context, is concerned withthe biochemical transformation of chemicals (including drugs) todetoxify them and hasten their excretion from the body. Thefundamentals of metabolism include:

Fig. 6. Plasma binding of drugs, free drug and distribution of drugs to target cells.


� Altering the drug’s chemical composition� Removing/reducing pharmacological activity� Generating more water-soluble metabolites (products ofmetabolism)

� Most metabolism occurs in the liver, catalysed by hepaticenzymes

� Other sites important in metabolic processing include thekidneys, intestinal mucosa, lungs, plasma & placenta

If the human body possessed no capacity to metabolise andexcrete drug agents, a drug would never leave the body after itsadministration. A beta-blocker that was not metabolised orexcreted would continually circulate around the body unchangedand exert its effect continuously. In health and with maturity the

Table 6Clinical correlation 2: Factors that may influence the distribution of drugs.


Total bodywater

Age: The relative proportion of total body water in infants isgreater than in healthy young adults, however the absolutevolume of total body water is much less and over dosage ofdrug will have a smaller volume of water to be distributedwithin than in the adult. This in part explains the criticalrequirement for accurate body weight dependent dosagecalculation in children and ideal-body weight dependentdosage calculation in obese children. Similarly in the elderlythe total body water volume is decreased as the lean bodymuscle mass (which stores a relatively high percentage ofwater) decreases and the stored fat (which is relativelyanhydrous) to muscle ratio increases.

Proteinbinding

In disease states where there is either an increase or decreasein plasma protein, e.g., in cirrhosis of the liver (where theremay be a decrease in plasma albumin production andconcentration) the plasma-protein sites available for bindingare reduced and there will be more ‘free’ unbound drugavailable to the body.Age: Protein binding is decreased in infants (due to reducedsynthesis of protein by the immature liver) and in the elderly(due to decreased synthesis of protein by the aging liver). Thisin part explains the variation in dosing regimes observed inliver disease and in children.

body possesses efficient systems for biotransformation (metabo-lism) that serve many purposes. The most important, in the contextof medicines, is to break down chemicals with the primary aim ofmaking them less pharmacologically active, more water solubleand more easily excreted. The dose of drug administered is derivedand prescribed such that the dosing and dosage interval arebalanced against metabolism and excretion to maintain an appro-priate plasma concentration. For example first pass metabolism inthe liver or incomplete absorption can result in only a proportion ofthe administered drug reaching the systemic circulation: Fluclox-acillins’ oral bioavailability is approximately 79%. Only 395 mg ofa 500 mg oral dose reaches the general circulation after oral dosing(Actavis, 2010).

Drug metabolism is divided into two phases:

Phase I

The reactions catalysed in Phase I of metabolism are simplechemical changes that are made to the drug such as oxidation,reduction and/or hydrolysis. The most common group of enzymesconsidered when studying Phase I metabolism are the cytochromeP450 isoenzyme family (CYP450). The primary aim of this phase isto make the drug pharmacologically inactive and more water-soluble and to prepare the metabolite for Phase II metabolism.

Phase II

If the metabolites of Phase I are not sufficiently hydrophilic thenPhase II serves to conjugate (add) endogenous chemicals to thestructure to enhance the drug’s water solubility. Endogenouschemicals involved include glucuronates and sulphates. Thesemore water-soluble compounds are more easily excreted.

Certain drugs only undergo Phase I metabolism; others onlyPhase II metabolism; and some drugs undergo very little or nometabolism. Some drugs undergo Phase II metabolism and thenPhase I. Certain drugs, e.g., levodopa, are activated by the bodywhen biotransformation takes place (Joint Formulary Committee,2012). These drugs are known as pro-drugs. Certain drugs, e.g.,

Table 7Clinical correlation 3: Factors that may influence the metabolism of drugs.


Hepaticenzymes

Liver disease can damage and affect the capacity of the liverto synthesise hepatic enzymes and in liver disease the normaldosage range may need to be reduced.Age: Hepatic microsomal enzyme production is decreased ininfants (due to reduced synthesis of enzyme by the immatureliver) and in the elderly (due to decreased synthesis of enzymeby the aging liver). As the child’s metabolic pathways matureand hepatic enzyme synthesis increases, the age and weightdependent medication dose will increase.


fluoxetine, are transformed into metabolites that are also active,and these metabolites are partially responsible for the therapeuticactivity of the drug agent (Aurobindo, 2012).

The dosing of medication takes into account the metabolicpathways required for elimination of the agent. Accurate dosing isessential and inaccurate dosing, particularly in children and to anextent the elderly can result in significant toxicity and potentialfatality. Some of the factors that may influence the metabolism ofdrugs are described in Clinical Correlation 3 (Table 7).

Excretion

Renal excretion is the process that eliminates most drugs andxenochemicals from the human body:

� Most drugs and metabolites are excreted by the kidneys� In the glomerular filtrate, lipid-soluble drugs are readily reab-sorbed in the renal tubules by passive diffusion

� Ionization of weak acids & bases depends on the pH of urine� Manipulation of pH can increase renal excretion� Declining renal function, e.g., with aging directly influencesprescribing

The majority of drugs are excreted by the kidneys. The body hasthe capacity toexcretedrugs throughanypathbywhichwater leavesthe body, e.g., drugs are excreted into tears, breast milk, sweat andeven water vapour that is exhaled in breathing (Simonsen, 2006).

Drug agents are excreted either after undergoing metabolicprocessing or unchanged. To understand the process of renalexcretion of drugs it is necessary tounderstand thephysiologyof thekidneyandhowthe kidneysfilter plasma. It is beyond the capacityofthis paper to explore this, however, some basic principles apply.

Table 8Clinical correlation 4: Factors that may influence the excretion of drugs.


Renal disease or impairedrenal function

Some patients’ starting doses with impairedrenal function may be lower and the intervalbetween doses may differ from those innon-renally impaired patients.

Age Glomerular filtration rate (GFR) and tubularsecretion of drugs are decreased in infants andyoung children due to immaturity of the kidney.Drug dosing in children is sometimes tailoredin considering the immaturity of the kidneys.The half life of a drug like Gentamicin variesfrom 11.5 h in small premature infants(weighing less than 1.5 kg) down to 3 h ininfants greater than 6 months of age. In thecase of gentamicin the half life in the six monthold is comparable with that of an adult. Walkerand Whittlesea, 2010. In the elderly, as GFRdeclines, it is often necessary to adjust (reduce)doses of drugs with narrow therapeutic indicessuch as digoxin and the aminoglycosides.

Verywater soluble, unbounddrugswill freely diffuse from the bloodstream into the glomerulus of the kidney and be excreted (Neal,2012). Drugs bound to plasma proteins will not pass from theblood stream. More lipophilic drugs tend to get resorbed into theblood stream after initial excretion. Certain drugs that have certainphysico-chemical properties will be actively secreted by thekidneys. Some of the factors that may influence the excretion ofdrugs are described in Clinical Correlation 4 (Table 8).

Discussion & conclusion

This paper has illustrated the design of an essential skillsnursing numeracy taxonomy, a consideration of the context ofnumeracy in nursing practice, measurement unit knowledge usedin the calculation of dosage and rate computations and a briefreview of the pharmacokinetic principles that illustrate theimportance of accurate dosing.

This series highlights that the facilitation of teaching andlearning in calculation competence requires considerations anddemands from both the learner and facilitator whether the learningtakes place in practice or in the classroom. The context and scien-tific background that underpins accurate dosing is highlighted inorder that an appreciation of the complex nature of drug calcula-tions is not underestimated by teachers and students alike.

The literature remains replete with reports of medication errorsrelating to a lack of calculation competence in healthcare practice.In addressing this problem we have commenced our advancementof this discipline with an approach centred on:

a. A unified taxonomy of generic numerical competencies map-ped to the 42 NMC (2010a) ESC and examples of a sub-set ofembedded medication dosage calculation skills.

b. An understanding of the measurement units used in medicinesmanagement and the critical requirement for understandingboth appropriate conversion factors and appropriate use ofmeasurement vehicles.

c. An understanding of the basic science of pharmacokinetics andconditions when dose calculation and measurement must bealtered.

In the final analysis it is our position that key to construction ofMDC-PS competence is the need to dispense with reductionistapproaches that focus on calculation skill development in isolation.Critical to solving this ubiquitous problem is the need to co-locateconceptual, calculation and technical measurement competencedevelopment and assessment within a competency model andeducation structure.

Acknowledgements

Graphics & Animations �Authentic World Ltd: Matt Brown &Norman Woolley.

Conflict of interest statement

Professor Keith W. Weeks, Norman Woolley & Lester Lewis areDirectors of Authentic World Ltd, a spin-out company of theUniversity of Glamorgan & Cardiff University. safeMedicate andeDose are trademarks of the MDC-PS authentic web-based virtualenvironments distributed respectively by Authentic World Ltd (UKand Ireland) and CAE Healthcare (International).

Dr Simon Young has no commercial interest in Authentic WorldLtd or CAE Healthcare.

DrMeriel Hutton has no commercial interest in AuthenticWorldLtd or CAE Healthcare.


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