Revision of pharmacokinetic terms

• Therapeutic window• Bioavailability• Plasma half life• First, zero, pseudo-zero order elimination• Clearance• Volume of Distribution• Intravenous infusion• Oral dosing

• Plasma monitoring of drugs

time

Toxic level

Minimumtherapeutic levelCp

time

Therapeutic window

Narrow

Toxic level

Minimumtherapeutic levelCp

time

Therapeutic window

Wide

Bioavailability (F)

Measure of the amount of drug absorbed into the systemic circulation

Area under the curve (AUC)

obtained from the Cp versus time plot

gives a measure of the amount of drug absorbed

Foral = AUCoral

AUCiv

Clearance = F. doseAUC

iv bolus

oral dose

Cp

time

NB: same dose given iv and orally

Oral bioavailability

frusemide 0.61aspirin 0.68propranolol 0.26digitoxin 0.90digoxin 0.70diazepam 1lithium 1morphine 0.24

Same drug, same dose, different formulation• different amounts absorbed• different peak concentration• different AUCs

Cp

time

Oral bioavailability can be altered by formulation

Different routes of administration give different Cp versus time profiles (rates of absorption different)

Assume the bioavailability is the same (i.e. 1 for all routes)

iv

sc

oral

Cp

time

Different routes of administration give different Cp versus time profiles (rates of absorption different)

Assume the bioavailability is the same (i.e. 1 for all routes)

Slower the rate of absorption• time to peak longer• amplitude of peak is less• drug in body for longer

iv

sc

oral

Cp

time

Half life (t1/2)

time for plasma concentration to fall by 50%

Cp

time

time

Plasma half life

Cp

time

time

Plasma half life

Half life (t1/2)

time for plasma concentration to fall by 50%

Cp

time

First order elimination – majority of drugs

Rate of elimination depends on plasma concentration

C = C0e-kt (k= rate constant of elimination)

Drug elimination kinetics

Cp

time

First order elimination – majority of drugs

Half life independent of concentration

Rate of elimination depends on plasma concentration

C = C0e-kt (k= rate constant of elimination)

Drug elimination kinetics

Cp

time

Zero order elimination

rate of elimination is constant and independent of plasma concentration – elimination mechanism is saturated

Drug elimination kinetics

Cp

time

Zero order elimination

Half life varies with concentration

Drug elimination kinetics

Cp

time

Pseudo-zero order eliminationethanol, phenytoin

Drug elimination kinetics

Cp

time

Pseudo-zero order eliminationethanol, phenytoin

Drug elimination kinetics

Volume of distribution (Vd)

Vd = doseC0

Volume of water in which a drug would have to be distributed to give its plasma concentration at time zero.

Litres 70kg-1

Can be larger than total body volume (e.g. peripheral tissue accumulation)

frusemide 7 aspirin 14 propranolol 273 digitoxin 38

digoxin 640

Plasma clearance (Cl)Volume of blood cleared of its drug content in unit time (not

same as Rate of Elimination – for drugs eliminated by 1st order kinetics rate of eliminatiuon changes with Cp, value of clearance does not change)

Cp

time

Cp

time

Rate of elimination different, Clearance the same

Plasma clearance (Cl)Volume of blood cleared of its drug content in unit time (not

same as Rate of Elimination – for drugs eliminated by 1st order kinetics rate of eliminatiuon changes with Cp, value of clearance does not change)

Plasma clearance (ClP)

Litres hr-1 70kg-1

Vd (litres) Cl (L hr-1 70kg-1)

frusemide 7 8aspirin 14 39propranolol 273 50digitoxin 38 0.25digoxin 640 8

Plasma half life (t1/2) = 0.693 VdCl

Vd (litres) Cl (L hr-1 70kg-1) t1/2 (h)

frusemide 7 8 1.5aspirin 14 39 0.25propranolol 273 50 3.9digitoxin 38 0.25 161digoxin 640 8 39

Plasma half life (t1/2) = 0.693 VdCl

More complex pharmacokinetic models:The two compartment model

plasma tissues

elimination

Cp

time

Redistribution + elimination

elimination

e.g. thiopentone

At steady staterate of infusion = rate of elimination

= Css x Clearance

Css (plateau)

Intravenous infusion

Cp

time

At steady staterate of infusion = rate of elimination

= Css x Clearance

Css (plateau)

Time to >96 % of Css = 5 x t1/2

Intravenous infusion

Cp

time

Rate of infusion x mg min-1

Rate of infusion 2x mg min-1

Height of plateau is governed by the rate of infusion

Cp

time

At steady state rate of infusion = rate of elimination

= Css x Clearance

Lignocaine 2 10 hours

Valproate 6 30 hours

Digoxin 39 8.1 days

Digitoxin 161 33.5 days

Drug t1/2 (h) Time to >96% of steady state

rate of infusion x mg min-1

Height of plateau is governed by the rate of infusion

Cp

time

Use of loading infusion

Desired Css

rate of infusion x mg min-1

rate of infusion 2x mg min-1

Height of plateau is governed by the rate of infusion

Cp

time

Use of loading infusion

Desired Css

Followed by maintenance infusion x mg min-1

Initial loading infusion 2x mg min-1

Height of plateau is governed by the rate of infusion

Cp

time

Use of loading infusion

Switch here

Desired Css

Followed by maintenance infusion x mg min-1

Initial loading infusion 2x mg min-1

Height of plateau is governed by the rate of infusion

Cp

time

Use of loading infusion

timesaved

Switch here

Desired Css

At Steady State amount administered = amount eliminated between doses

Multiple oral dosing

time

Cp

Cssav = F . Dose Clearance. T F = oral bioavailability

T = dosing interval

Cssav

At Steady State amount administered = amount eliminated between doses

Multiple oral dosing

time

Cp

Cssav = F . Dose Clearance. T F = oral bioavailability

T = dosing interval

time

Cp

Loading doses

e.g. Tetracycline t1/2 = 8 hours

500mg loading dose followed by 250mg every 8 hours

Maintenance doses

Cssav = F . Dose Clearance. T

Cssav

F = oral bioavailabilityT = dosing interval

Cssav = F . Dose Clearance. T

Cssav

Reducing the dose AND reducing the intervalCssav remains the same but fluctuation in Cp is less

F = oral bioavailabilityT = dosing interval

Drug plasma concentration monitoring is helpful for drugs

• that have a low therapeutic index • that are not metabolised to active metabolites

• whose concentration is not predictable from the dose • whose concentration relates well to either the therapeutic effect or the toxic effect, and preferably both

• that are often taken in overdose

For which specific drugs is drug concentration monitoring helpful?

The important drugs are: • aminoglycoside antibiotics (e.g. gentamicin)• ciclosporin • digoxin and digitoxin • lithium• phenytoin • theophylline • paracetamol and aspirin/salicylate (overdose)

Other drugs are sometimes measured:• anticonvulsants other than phenytoin (eg carbamazepine, valproate)• tricyclic antidepressants (especially nortriptyline) • anti-arrhythmic drugs (eg amiodarone).

The uses of monitoring are

• to assess adherence to therapy

• to individualize therapy

• to diagnose toxicity

• to guide withdrawal of therapy

• to determine whether a patient is already taking a drug before starting therapy (e.g. theophylline in an unconscious patient with asthma)

• in research (e.g. to monitor for drug interactions)

Altered pharmacokinetic profile

• liver metabolismDiseasePharmacogenetics (cytochrome P450 polymorphisms)

• renal impairment (e.g. digoxin)DiseaseElderly