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`Pharmacokinetics
`A new Continuing
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`Vol 272 No 7304
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`CPD Mf}
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`lie
`
`Back to basics: pharmacokinetics
`
`Inthefirst article in a series intended to remind pharmacists aboutthe basic principles of pharmacokinetics, pharmacodynamics and therapeutic
`drug monitoring, Alison Thomson describes the principal pharmacokinetic parameters
`
`
`
`
`
`CallieStewart
`
`Evaluate
`
`
`
`ue knowledge gaps
`
`1. Whatis a “top-up” loading dose and how
`would you calculate it?
`. How does drug clearanceinfluence
`maintenance dose requirements?
`3. What pharmacokinetic parametersinfluence
`the elimination half-life of a drug in an
`individual patient?
`
`|
`
`Beforereadingon,thinkabouthowthisarticle
`
`may help you to do yourjob better. The Royal
`Pharmaceutical Society's areas of competence
`for pharmacists are listed in “Plan and record”,
`(available at: www.rpsgb.org/education), This
`article relates to “clinical pharmacy”and
`“therapeutic drug monitoring” (see appendix 4 of
`“Plan and record’).
`
`Variability in volume ofdistribution among
`patients is often also related to body weight.
`Table
`1
`shows weight-related average
`volumes of distribution for a range of drugs
`with different solubility and binding charac-
`teristics.
`
`Target concentration An estimate of a
`drug’s volume ofdistribution and the con-
`centration range that is associated with the
`desired clinical response can be used to calcu-
`late the loading dose that would achieve the
`
`39
`at
`18
`40
`90
`99
`25
`95
`61
`
`low
`ba
`low
`jow/medium
`medium
`high
`high
`high
`high
`
`0.14
`ee
`0.30
`0.48
`0.70
`1.10
`7.00
`15.00
`115.00
`
`Volumeof distribution In many respects,
`calculating a loading dose of a drug is simular
`to calculating the amountof drug required to
`achieve a desired concentration in a flask of
`liquid (ie, dose = volume x concentration).
`Conversely, the volume of the flask can be
`estimated if
`the amount of drug and
`the measured concentration are known
`(ic, volume = dose + concentration).
`Inclinical practice, the volume ofdistribu-
`tion of a drug (V) can be estimated from a
`known dose and measured concentrations.
`Because concentrations are typically analysed
`in blood, serumor plasma, the estimate repre-
`sents
`the “apparent” volume throughout
`which the amount of drug would need to
`distribute in order to produce the measured
`concentration. For example, if two drugs, A
`and B, are both given as 100mg intravenous
`bolus doses and the measured plasma concen-
`trations are 10mg/L and 1mg/L,the corre-
`sponding volumes ofdistribution would be
`10L and 100L, respectively.
`Variability in apparent volumeof distribu-
`tion between drugs reflects the proportion of
`the administered dose that
`|Tabi¢ 1:Examplesofvolumeofdistribution estimates
`remains
`in the plasma.
`Drugs
`that are water-
`
`
`
`soluble or highly bound % plasma protein_—Lipid solubility/“Drug. Volume of
`Initiating treatment
`
`to plasma proteins have a
`binding
`tissue binding
`distribution (L/kg)
`When a patient requires treatment with a
`new drug, a loading dose can be given so that
`:
`high plasma concentration
`relative to the dose, hence
`Warfarin .
`therapeutic
`concentrations
`are
`achieved
`small volumes of distribu-
`Sentanicin
`quickly. Loading doses ate commonly used in
`.
`:
`,
`Amoxicillin
`acute conditions, such as status asthmaticus or
`tion.
`In contrast, drugs
`Theophylline
`that are lipid soluble or
`Phenytoin
`status epilepticus, or if the drug has a long
`bind extensively to tissues
`Diazepam
`elimination half-life (eg, digoxin).
`are present
`in plasma in
`Digoxin
`low concentrations and,
`Amitriptyline
`therefore,
`have
`large
`Chloroquine
`volumes of distribution.
`
`A: experts on medicines, pharmacists
`
`should be able to select the most appro-
`priate drug for an individual, recommend
`the dosage regimen that
`is most
`likely to
`achieve the desired therapeutic response with
`minimum risk of toxic effects and monitor
`the effects of a drug, if appropriate. In order
`to do this, the principles of pharmacokinetics
`and pharmacodynamics need to be applied.
`Most pharmacists will
`remember learning
`these at university but not all will have kept
`them at their fingertips. It is important to ap-
`preciate that these principles are fundamental
`to the current ‘practice of clinical pharmacy
`and may become even more significant as
`pharmacists expand their roles into prescrib-
`
`Pharmacokinetic equations describe the
`relationships between the dosage regimen
`and the profile of drug concentration in the
`blood over
`time. Pharmacodynamic equa-
`tions describe the relationships between the
`drug concentration-time profile and thera-
`peutic arid adverse effects. By controlling the
`plasma concentration-time profile of a drug,
`we can ensure that the patient receives opti-
`mum treatment.
`
`Alison Thomson, PhD, MRPharmsS,is area
`pharmacyspecialist at Western Infirmary,
`Glasgow
`
`www.pjonline.com
`
`19 June 2004
`
`The Pharmaceutical Journal (Vol 272) 769
`
`Apotex v. Cellgene - IPR2023-00512
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`
`
`
`Concentration(%ofsteadystate}
`
`
`
`0
`
`4
`
`2
`
`3
`
`4
`Time(half-lives)
`
`5
`
`Steady 'state
`
`
`
`
`
`Concentration(4ofCssaverage)
`
`
`
`
`100
`120
`110
`90
`100
`80
`30
`70
`80
`60
`70
`60
`50
`§0
`40
`40
`30
`30
`20
`20
`10
`10
`
` 3
`
`Average steady state
`cancentration
`
`8
`a
`6
`5
`4
`Time(elimination half-lives)
`
`Figure 1: Concentration-time profile for a drug given by a
`constantrate infusion
`
`Figure 2: Goncentration-time profile for a drug given as a
`regular maintenance oral dose
`
`target concentration in a particular patient.
`The use of phenytoin to treat status epilepti-
`cusillustrates this point. Phenytoin concentra-
`tions in the range 10-20me/L are associated
`with seizure control but, because status
`epilepticus is a life-threatening condition, the
`target is usually at least 20mg/L. Using a typ-
`ical estimate of volume of distribution for
`phenytoin of 0.7L/kg (Table 1), the loading
`dose can be calculated as follows:
`
`Loading dose (mg) = 20mg/L x 0.7L/ke = l4mg/kg
`
`This relationship can also be used to cal-
`culate “top-up” doses that may be required if
`the drug is already present but the concentra-
`tion is too low. Here, the measured concen-
`tration is
`subtracted from the
`target
`concentration (C), leading to the following
`general expression:
`
`Loading dose = (Target C— Measured C) x V
`
`Salt correction factor Phenytoin is usually
`administered as the phenytoin sodiumsalt,
`which contains 92mg phenytoin per 100mg
`salt. Therefore, applying the salt correction
`factor (0.92) the loading dose of phenytoin
`sodium required is 15mg/kg (14mg/kg +
`0.92),
`as quoted in the British National
`Formulary. It follows that the loading dose for
`a 40kg patient would be 600mg whereas
`1,200mg would be required for an 80kg
`patient.
`
`Molar correction factor If the target concen-
`tration is expressed in molar units, the equa-
`tion must also include a molar correction
`factor, which is obtained from the molecular
`weight of the drug. For example, the molec-
`ular weight of phenytoin is 252.3 hence 1
`mole is contained in 252.3g of phenytoin. In
`other words, 1g contains 0.004mol and Img
`contains 4umol. A target phenytoin concen-
`tration of 8Oumol/L is, therefore, equivalent
`to 20mg/L.
`
`Continuing treatment
`If a treatment needs to be continued, further
`calculations can be performed to determine
`the most appropriate maintenance dose.
`
`Maintenance dose and clearance [In
`some respects, patients are like leaky flasks
`because drugs start to be eliminated from the
`body as soon as they are absorbed. Target drug
`concentrations can, therefore, only be main-
`tained if doses are given at a rate that balances
`the 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 no
`loading dose. Although the concentration
`initially increases with time, the increase gets
`progressively smaller until the overall profile
`is flat. This is known as “steadystate” and the
`steady state concentration (C,.) depends
`solely on the balance between the infusion
`rate (IR) and the clearance rate (Cl),
`as
`follows:
`
`Css = (smiR) = Cl
`
`Thesalt (s) and molar (m) correction factors are used if appropriate
`
`This relationship means that if a measured
`steady state concentration is too low or too
`high, a newdose can be determined bydirect
`proportion. For example, to double the Css,
`the infusion rate should be doubled, whereas
`to halve the concentration, the infusion rate
`should be halved. Alternatively, the infusion
`rate required to achieve a target steadystate
`concentration 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 adinin-
`istered in milligrams, the concentration will
`usually be in mg/L (mass units) or pmol/L
`(molar units) but if the dose is administered
`in micrograms, the concentration will be in
`pe/L (mass units) or nmol/L, (molar units).
`
`Factors affecting clearagce Clearance
`represents the volume of blood, serum or
`plasma completely cleared of drug per unit of
`time and therefore has units of volumie/time.
`It
`is usually expressed in L/h or ml/min.
`Althoughclearanceis often related to the size
`of the patient
`(eg, L/h/kg), it is also influ-
`
`enced by a number ofother clinical charac-
`teristics. Water-soluble drugs are generally
`cleared by excretion into the urine, whereas
`lipid soluble
`drugs often have
`to be
`metabolised to water-soluble metabolites by
`the liver before they can be excreted. Some
`drugs are cleared by a combination of renal
`excretion and hepatic metabolism. These
`mechanisms mean that clearance and, there-
`fore, maintenance dose requirements can be
`attected by a range of factors, including age,
`renal disease, hepatic disease and drug inter-
`actions.
`
`Bioavailability and oral maintenance
`dosage regimensIf a drug is given by a
`route that requires absorption, such as oral,
`subcutaneous or intramuscular administra-
`tion,
`the amount that reaches the systemic
`circulation is usually less than the adminis-
`tered dose. The proportion of the adminis-
`tered
`dose
`that
`reaches
`the
`systemic
`circulation is known as
`the bioavailability
`and is usually denoted “F” (ie,
`the fraction
`absorbed).
`Manyfactors can influence bioavailability,
`including the physicochemical characteristics
`of the drug and its formulation, the degree of
`first-pass metabolism in theliver or intestine,
`the activity of gut transporters (such as P-
`glycoprotein), the co-administration of other
`drugs and gastrointestinal conditions (eg, mal-
`absorption syndromes, diarrhoea and vomit-
`ing). Drugs with a high first-pass metabolism,
`such as morphine, propranolol-and verapamil,
`
`
`
`Cl
`
`Key for equations
`=
`concentration
`Clearance
`Steady state concentration
`dose
`bioavailability
`infusion rate
`elimination rate constant
`salt correction factor
`Molar correction factor
`dosageinterval
`elimination half-life
`Volume of distribution
`
`770=The Pharmaceutical Journal (Vol 272) 19 June 2004
`
`
`www.pjonline.com
`
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`

`
` andtime
`achieve:esteadystateonesdesing
`\ Number of
`Dose
`Steaty state
`half-lives
`eliminated % achieved %
`
`/Action: practice points
`
`Elimination rate constant and con-
`centration-time profile When drug
`input or absorption is complete, a constant
`Readingis only one way to undertake CPD and the
`proportion of the dose is usually cleared per
`Society will expect to see various approaches ina
`unit mg. Figure 3
`illustrates the conse-
`pharmacist's CPD portfolio.
`|
`quences ofthis “first order” elimination after
`1. Compile alist of commonly used drugs that
`a single intravenous bolusdose.Initially, there
`are cleared by excretion throughthe kidneys
`is a steep fall in the concentration then the
`50
`50
`1
`decline becomes shallower as the amount of
`15
`i
`2
`_
`and require dosage adjustmentin renal
`87.5
`87.6
`3
`impairment.
`drug remaining falls. The shape ofthe rela-
`93.8
`93.8
`4
`2. Compilealist of commonly used drugs that
`tionship between concentration and ume is
`5
`96.9
`96.9
`_
`are cleared by metabolism in the liver and
`described by exponential function, and the
`6
`98.4
`98.4
`|__Tequire dosage adjustment in hepatic disease.
`concentration at any time after the dose (Ct)
`7
`99.2
`99.2
`can be calculated from:
`
`_ 3. Compilealist of clearance and volumeof |
`8
`99.6
`99.6
`distribution estimatesfor a list of commonly
`used drugs and estimate theelimination half-
`__
`life for patients with normalrenal and hepatic
`|
`function and for patients with severe renal
`and hepatic impairment.
`
`}i ; (
`
`Evaluate
`| For your work to be presented as CPD, you need to
`evaluate your reading and anyother activities.
`_ Answerthefollowing questions: What have you
`|
`learnt? How hasit added value to your practice?
`|
`(Have you applied this learning or had any
`|
`feedback?) What will you do now and how will this
`be achieved?
`
`Topics in this series
`Further articles in this back to basics series will
`look at:
`© Inter-individual variability
`a Therapeutic drug monitoring
`
`—
`
`|
`
`= (DA)x exp*
`
`Where D/V represents the maximum concentration that would be
`achieved and exp"representsthefraction of this concentration
`that would be left at time “t” hours after the dose
`
`is the
`(k)
`The elimination rate constant
`ratio of clearance to volume ofdistribution
`and is usually expressed in units of 1/h. When
`this concentration-timeprofile is plotted on a
`log-linear scale, the decline is linear, with a
`slope of -k.
`
`Elimination half-life The elimination
`half-hfe (the time it takes for the concentra-
`tion of the drug to fall to half; ty2) depends
`on the elimination rate constant and, conse-
`quently, on both clearance and volume of
`distribution.
`In that case,
`the proportion
`remainingis 0.5, therefore:
`
`tz = loge0.5 + -k = 0.693 = k
`
`
`
`
`new formulations where the rate of drug
`release and therefore the rate of absorption
`are reduced, thus allowing once daily dosing.
`This approach has beenused successfully for a
`number ofdrugs, including nifedipine, dilti-
`azem and verapamil.
`
`Summary
`Drug dosage regimens are determined by two
`basic parameters, clearance, which determines
`the dosage rate to maintain an average steady
`state concentration, and volume of distribu-
`tion, which determines the amount of drug
`required to achieve a target concentration.
`Related parameters, the elimination rate con-
`stant, k, (the ratio of clearance to volume of
`distribution), and elimination half-life (0.693/
`k) control the speed of elimination of drugs
`from the body. Theyare used toestimate the
`time taken for a drug to be eliminated from
`the body and to achieve steady state on
`multiple dosing.
`
`Further reading
`Begg E, Instant Clinical Pharmacology.Oxford: Blackwell
`Publishing Ltd; 2002.
`” Ritschel WA and Kearns GL. Handbookof Basic
`Pharmacokinetics, 5th edition. Washington: American
`Pharmaceutical Association; 1999.
`Winter ME;Basicclinical pharmacokinetics, 3rd edition
`Vancouver: Applied Therapeutics Inc; 1994,
`
`19 June 2004
`
`The Pharmaceutical Journal (Vol 272) 771
`
`|
`
`have a loworal bioavailability and oral doses
`are, consequently, much higher than intra~
`venous doses. In contrast, other drugs (eg,
`diazepam, phenytoin and theophylline) have
`bioavailabilities that are close to 100 per cent
`and havesimilar oral and intravenous doses.
`Whena maintenanceoral dosage regimen
`is started, the overall profile of accumulation
`to steadystate parallels that observed with a
`constant rate infusion. However, fluctuations
`occur within a dosage interval (t) as each
`dose (D) is absorbed and eliminated, as ilus-
`trated in Figure 2. The average steady state
`concentration (Csg average), is the mean ofall
`the concentrations in the dosage interval, and
`again depends on the ratio of dosing and
`clearance rate:
`
`Css average = Dositerate _ _FD(sm)
`F
`Cl
`Ct
`
`WhereF is the bioavailability, D is the dose, tis the dosage
`interval
`
`Consequently, an oral maintenance dose
`can be determined from the following rela~
`tionship:
`
`Oral dose = (target Cg average X Clxt) =F fs m)
`Stopping treatment
`When treatmentis stopped, the timeit takes
`for the drug to be removed from the body
`can be ofinterest, particularly if the patientis
`experiencing adverse effects.
`
`These relationships illustrate that drugs,
`themselves, do not have half-lives but patients
`have half-lives. For example, gentamicin,
`whichis cleared byrenal excretion,hasa half-
`life of two to three hours in a young adult
`with nornial renal function but as much as 24
`hours, or more, in a patient with severe renal
`impairment. Similarly, a patient with fluid
`overload may need to receive a higher dose
`less frequently due to an enlarged volume of
`distribution and longer elimination half-life.
`As shownin Table 2 andillustrated in Figures
`1
`to 3, the chimination halflife determines
`the time it takes for a drug to be removed
`from the body and the
`time it
`takes
`to achieve
`steady state on a regular
`maintenance dose.
`the
`For many drugs,
`aim is co avoid large fluc-
`tuations in the concentra-
`tion-time profile and this
`is normally achieved by
`using a dosage interval
`that
`is shorter than the
`typical elimination half
`life. However,
`this may
`demand that some drugs
`are taken two or
`three
`times daily, which can re-
`duce adherence. This has
`led to the development of
`
`Time(elimination half-lives)
`
`E3
`—x&
`
`—3x¢
`
`ts}
`
`£=v9<3
`
`o
`
`5
`4
`3
`
`
`Figure 3 : Drug concentrationvs time after a single
`intravenous bolus, using a linear concentration scale
`
`www.pjonline.com
`
`Apotex v. Cellgene - IPR2023-00512
`Petitioner Apotex Exhibit 1018-0005
`
`Apotex v. Cellgene - IPR2023-00512
`Petitioner Apotex Exhibit 1018-0005
`
`