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CPD

Alison Thomson, PhD, MRPharmS, is areapharmacy specialist at Western Infirmary,Glasgow

For personal use only. Not to be reproduced without permission of the editor

(permissions@pharmj.org.uk)

Back to basics: pharmacokineticsIn the first article in a series intended to remind pharmacists about the basic principles of pharmacokinetics, pharmacodynamics and therapeutic

drug monitoring, Alison Thomson describes the principal pharmacokinetic parameters

As experts on medicines, pharmacistsshould be able to select the most appro-priate drug for an individual,recommend

the dosage regimen that is most likely toachieve the desired therapeutic response withminimum risk of toxic effects and monitorthe effects of a drug, if appropriate. In orderto do this, the principles of pharmacokineticsand pharmacodynamics need to be applied.Most pharmacists will remember learningthese at university but not all will have keptthem at their fingertips. It is important to ap-preciate that these principles are fundamentalto the current practice of clinical pharmacyand may become even more significant aspharmacists expand their roles into prescrib-ing.

Pharmacokinetic equations describe therelationships between the dosage regimenand the profile of drug concentration in theblood over time. Pharmacodynamic equa-tions describe the relationships between thedrug concentration-time profile and thera-peutic and adverse effects. By controlling theplasma concentration-time profile of a drug,we can ensure that the patient receives opti-mum treatment.

Initiating treatmentWhen a patient requires treatment with anew drug, a loading dose can be given so thattherapeutic concentrations are achievedquickly. Loading doses are commonly used inacute conditions, such as status asthmaticus or

status epilepticus, or if the drug has a longelimination half-life (eg, digoxin).

Volume of distribution In many respects,calculating a loading dose of a drug is similarto calculating the amount of drug required toachieve a desired concentration in a flask ofliquid (ie, dose = volume x concentration).Conversely, the volume of the flask can beestimated if the amount of drug andthe measured concentration are known(ie, volume = dose concentration).

In clinical practice,the volume of distribu-tion of a drug (V) can be estimated from aknown dose and measured concentrations.Because concentrations are typically analysedin blood,serum or plasma, the estimate repre-sents the apparent volume throughoutwhich the amount of drug would need todistribute in order to produce the measuredconcentration. For example, if two drugs, Aand B, are both given as 100mg intravenousbolus doses and the measured plasma concen-trations are 10mg/L and 1mg/L, the corre-sponding volumes of distribution would be10L and 100L, respectively.

Variability in apparent volume of distribu-tion between drugs reflects the proportion ofthe administered dose thatremains in the plasma.Drugs that are water-soluble or highly boundto plasma proteins have ahigh plasma concentrationrelative to the dose, hencesmall volumes of distribu-tion. In contrast, drugs

that are lipid soluble orbind extensively to tissuesare present in plasma inlow concentrations and,therefore, have largevolumes of distribution.

Variability in volume of distribution amongpatients is often also related to body weight.Table 1 shows weight-related averagevolumes of distribution for a range of drugswith different solubility and binding charac-teristics.

Target concentration An estimate of adrugs volume of distribution and the con-centration range that is associated with thedesired clinical response can be used to calcu-late the loading dose that would achieve the

Identify knowledge gaps1. What is a top-up loading dose and how

would you calculate it?2. How does drug clearance influence

maintenance dose requirements?3. What pharmacokinetic parameters influence

the elimination half-life of a drug in anindividual patient?

Before reading on, think about how this articlemay help you to do your job better. The RoyalPharmaceutical Societys areas of competencefor pharmacists are listed in Plan and record,(available at: www.rpsgb.org/education). Thisarticle relates to clinical pharmacy andtherapeutic drug monitoring (see appendix 4 ofPlan and record).

Drug % plasma protein Lipid solubility/ Volume of

binding tissue binding distribution (L/kg)

Warfarin 99 low 0.14

Gentamicin

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target concentration in a particular patient.The use of phenytoin to treat status epilepti-

cus illustrates this point.Phenytoin concentra-tions in the range 1020mg/L are associatedwith seizure control but, because statusepilepticus is a life-threatening condition, thetarget is usually at least 20mg/L. Using a typ-ical estimate of volume of distribution forphenytoin of 0.7L/kg (Table 1), the loadingdose can be calculated as follows:

Loading dose (mg) = 20mg/L x 0.7L/kg = 14mg/kg

This relationship can also be used to cal-culate top-up doses that may be required ifthe drug is already present but the concentra-tion is too low. Here, the measured concen-tration is subtracted from the targetconcentration (C), leading to the followinggeneral expression:

Loading dose = (Target C Measured C) x V

Salt correction factor Phenytoin is usuallyadministered as the phenytoin sodium salt,which contains 92mg phenytoin per 100mgsalt. Therefore, applying the salt correctionfactor (0.92) the loading dose of phenytoinsodium required is 15mg/kg (14mg/kg 0.92), as quoted in the British NationalFormulary. It follows that the loading dose fora 40kg patient would be 600mg whereas1,200mg would be required for an 80kgpatient.

Molar correction factor If the target concen-tration is expressed in molar units, the equa-tion must also include a molar correctionfactor, which is obtained from the molecularweight of the drug. For example, the molec-ular weight of phenytoin is 252.3 hence 1mole is contained in 252.3g of phenytoin. Inother words, 1g contains 0.004mol and 1mgcontains 4mol. A target phenytoin concen-tration of 80mol/L is, therefore, equivalent

to 20mg/L.

Continuing treatmentIf a treatment needs to be continued, furthercalculations can be performed to determinethe most appropriate maintenance dose.

Maintenance dose and clearance Insome respects, patients are like leaky flasks

because drugs start to be eliminated from thebody as soon as they are absorbed.Target drugconcentrations can, therefore, only be main-tained if doses are given at a rate that balancesthe clearance rate. Maintenance dosage regi-mens are designed to achieve this balance.

Figure 1 shows the serum concentration-time profile of a drug that is being adminis-tered by constant rate infusion, with noloading dose. Although the concentrationinitially increases with time, the increase getsprogressively smaller until the overall profileis flat.This is known as steady state and thesteady state concentration (Css) dependssolely on the balance between the infusionrate (IR) and the clearance rate (Cl), asfollows:

Css = (smIR) Cl

The salt (s) and molar (m) correction factors are used if appropriate

This relationship means that if a measuredsteady state concentration is too low or toohigh, a new dose can be determined by directproportion. For example, to double the Css,the infusion rate should be doubled, whereasto halve the concentration, the infusion rateshould be halved. Alternatively, the infusionrate required to achieve a target steady stateconcentration can be calculated as follows:

IR = (Target Css x Cl) (s m)

It is important that the units of these rela-tionships are consistent. If the dose is admin-istered in milligrams, the concentration willusually be in mg/L (mass units) or mol/L(molar units) but if the dose is administeredin micrograms, the concentration will be ing/L (mass units) or nmol/L (molar units).

Factors affecting clearance Clearance

represents the volume of blood, serum orplasma completely cleared of drug per unit oftime and therefore has units of volume/time.It is usually expressed in L/h or ml/min.Although clearance is often related to the sizeof the patient (eg, L/h/kg), it is also influ-

enced by a number of other clinical charac-teristics. Water-soluble drugs are generally

cleared by excretion into the urine, whereaslipid soluble drugs often have to bemetabolised to water-soluble metabolites bythe liver before they can be excreted. Somedrugs are cleared by a combination of renalexcretion and hepatic metabolism. Thesemechanisms mean that clearance and, there-fore, maintenance dose requirements can beaffected by a range of factors, including age,renal disease, hepatic disease and drug inter-actions.

Bioavailability and oral maintenancedosage regimens If a drug is given by aroute that requires absorption, such as oral,subcutaneous or intramuscular administra-tion, the amount that reaches the systemiccirculation is usually less than the adminis-tered dose. The proportion of the adminis-tered dose that reaches the systemiccirculation is known as the bioavailabilityand is usually denoted F (ie, the fractionabsorbed).

Many factors can influence bioavailability,including the physicochemical characteristicsof the drug and its formulation, the degree offirst-pass metabolism in the liver or intestine,the activity of gut transporters (such as P-glycoprotein), the co-administration of otherdrugs and gastrointestinal conditions (eg,mal-absorption syndromes, diarrhoea and vomit-ing). Drugs with a high first-pass metabolism,such as morphine,propranolol and verapamil,

Figure 1: Concentration-time profile for a drug given by aconstant rate infusion

Figure 2: Concentration-time profile for a drug given as aregular maintenance oral dose

Key for equationsC = concentrationCl = clearanceCss = steady state concentrationD = doseF = bioavailabilityIR = infusion ratek = elimination rate constant

s = salt correction factorm = molar correction factor = dosage intervalt1/2 = elimination half-lifeV = volume of distribution

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have a low oral bioavailability and oral dosesare, consequently, much higher than intra-venous doses. In contrast, other drugs (eg,diazepam, phenytoin and theophylline) have

bioavailabilities that are close to 100 per centand have similar oral and intravenous doses.When a maintenance oral dosage regimen

is started, the overall profile of accumulationto steady state parallels that observed with aconstant rate infusion. However, fluctuationsoccur within a dosage interval () as eachdose (D) is absorbed and eliminated, as illus-trated in Figure 2. The average steady stateconcentration (Css average), is the mean of allthe concentrations in the dosage interval,andagain depends on the ratio of dosing andclearance rate:

Css average =Dosing rate

=F D (s m)

Cl Cl.

Where F is the bioavailability, D is the dose, is the dosage

interval

Consequently, an oral maintenance dosecan be determined from the following rela-tionship:

Oral dose = (target Css average x Cl x ) F (s m)

Stopping treatmentWhen treatment is stopped, the time it takesfor the drug to be removed from the bodycan be of interest, particularly if the patient isexperiencing adverse effects.

Elimination rate constant and con-centration-time profile When druginput or absorption is complete, a constantproportion of the dose is usually cleared perunit time. Figure 3 illustrates the conse-quences of this first order elimination aftera single intravenous bolus dose. Initially, there

is a steep fall in the concentration then thedecline becomes shallower as the amount ofdrug remaining falls. The shape of the rela-tionship between concentration and time isdescribed by exponential function, and theconcentration at any time after the dose (Ct)can be calculated from:

Ct = (D/V) x exp-kt

Where D/V represents the maximum concentration that would be

achieved and exp-kt represents the fraction of this concentration

that would be left at time t hours after the dose

The elimination rate constant (k) is theratio of clearance to volume of distributionand is usually expressed in units of 1/h.Whenthis concentration-time profile is plotted on alog-linear scale, the decline is linear, with aslope of -k.

Elimination half-life The eliminationhalf-life (the time it takes for the concentra-tion of the drug to fall to half; t1/2) dependson the elimination rate constant and, conse-quently, on both clearance and volume ofdistribution. In that case, the proportionremaining is 0.5, therefore:

t1/2 = loge0.5 -k = 0.693 k

These relationships illustrate that drugs,themselves, do not have half-lives but patientshave half-lives. For example, gentamicin,which is cleared by renal excretion,has a half-life of two to three hours in a young adultwith normal renal function but as much as 24hours, or more, in a patient with severe renalimpairment. Similarly, a patient with fluidoverload may need to receive a higher doseless frequently due to an enlarged volume ofdistribution and longer elimination half-life.As shown in Table 2 and illustrated in Figures1 to 3, the elimination half-life determinesthe time it takes for a drug to be removed

from the body and thetime it takes to achievesteady state on a regularmaintenance dose.

For many drugs, theaim is to avoid large fluc-tuations in the concentra-tion-time profile and thisis normally achieved byusing a dosage intervalthat is shorter than thetypical elimination half-

life. However, this maydemand that some drugsare taken two or threetimes daily, which can re-duce adherence. This hasled to the development of

Figure 3 : Drug concentration vs time after a single

intravenous bolus, using a linear concentration scale

new formulations where the rate of drugrelease and therefore the rate of absorptionare reduced, thus allowing once daily dosing.This approach has been used successfully for anumber of drugs, including nifedipine, dilti-azem and verapamil.

SummaryDrug dosage regimens are determined by twobasic parameters, clearance,which determinesthe dosage rate to maintain an average steadystate concentration, and volume of distribu-tion, which determines the amount of drugrequired to achieve a target concentration.Related parameters, the elimination rate con-stant, k, (the ratio of clearance to volume ofdistribution), and elimination half-life (0.693/k) control the speed of elimination of drugsfrom the body. They are used to estimate thetime taken for a drug to be eliminated fromthe body and to achieve steady state onmultiple dosing.

Further reading

Begg E. Instant Clinical Pharmacology.Oxford: BlackwellPublishing Ltd; 2002.

Ritschel WA and Kearns GL. Handbook of Basic

Pharmacokinetics, 5th edition. Washington: American

Pharmaceutical Association; 1999.

Winter ME. Basic clinical pharmacokinetics, 3rd edition.

Vancouver: Applied Therapeutics Inc; 1994.

Action: practice pointsReading is only one way to undertake CPD and theSociety will expect to see various approaches in apharmacists CPD portfolio.1. Compile a list of commonly used drugs that

are cleared by excretion through the kidneysand require dosage adjustment in renalimpairment.

2. Compile a list of commonly used drugs thatare cleared by metabolism in the liver andrequire dosage adjustment in hepatic disease.

3. Compile a list of clearance and volume ofdistribution estimates for a list of commonlyused drugs and estimate the elimination half-life for patients with normal renal and hepaticfunction and for patients with severe renaland hepatic impairment.

EvaluateFor your work to be presented as CPD, you need toevaluate your reading and any other activities.Answer the following questions: What have youlearnt? How has it added value to your practice?(Have you applied this learning or had anyfeedback?) What will you do now and how will thisbe achieved?

Topics in this seriesFurther articles in this back to basics series willlook at: Inter-individual variability Therapeutic drug monitoring

Number of Dose Steady state

half-lives eliminated % achieved %

1 50 502 75 75

3 87.5 87.5

4 93.8 93.8

5 96.9 96.9

6 98.4 98.4

7 99.2 99.2

8 99.6 99.6

Table 2: Influence of elimination half-lifeon time to eliminate a drug and time toachieve steady state on regular dosing