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`Pharmacokinetics made easy 11 Designing dose regimens - Australian Prescriber
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`Pharmacokinetics made easy 11
`Designing dose regimens
`
`Aust Prescr 1996;19:76-8 1 1 July 1996
`
`D.J. Birkett, Professor of Clinical Pharmacology, Flinders University of South Australia, Adelaide
`Key words: parenteral dosing, oral dosing, dosing intervals, sustained release
`
`Information from previous articles in this series can be used to design dose regimens.
`
`1. Intravenous infusion and intermittent intravenous bolus dosing
`Continuous intravenous infusions and intermittent intravenous boluses are common ways of administering
`drugs such as gentamicin, lignocaine and theophylline. Fig. 1 illustrates the plasma concentration time
`course of theophylline given intravenously. Given as a continuous infusion, the drug accumulates to a
`steady state concentration (C„) determined only by the dose rate and clearance (CL) (see Article 1
`'Clearance' Aust Prescr 1988;11:12-3). The maintenance
`dose rate to achieve a desired concentration can be calculated if the clearance is known.
`
`equation 1
`
`Desired concentration (Css) = maintenance dose rate / CL
`The time to reach steady state is determined by the half-life (3-5 half-lives, see Article 3 Half-life' Aust
`Prescr 1988; 11:57-9). If intermittent bolus doses are given every half-life (8 hours in this case for
`theophylline), half the first dose is eliminated over the first dosing interval. Therefore, after the second dose
`there are 1.5 doses in the body and half of this amount is eliminated before the third dose. The drug
`continues to accumulate with continued dosing until there is double the dose in the body, at which point the
`equivalent of one dose is eliminated each dosing interval (half-life). The plasma concentration is then at
`steady state (rate of administration equals rate of elimination where each is one dose per dosing interval).
`At steady state with a dosing interval equal to the half-life:
`
`the plasma concentration fluctuates two-fold over the dosing interval
`the amount of drug in the body shortly after each dose is equivalent to twice the maintenance dose
`the steady state plasma concentration averaged over the dosing interval is the same as the steady
`state plasma concentration for a continuous infusion at the same dose rate (see Fig. 1).
`
`2. Use of a loading dose
`The effect of a loading dose before an intravenous infusion has been discussed in Article 2 (Volume of
`distribution' Aust Prescr 1988;11:36-7). The loading dose to achieve a desired concentration is determined
`by the volume of distribution (VD).
`
`equation 2
`
`Loading dose = desired concentration x VD
`
`Fig.lntravenous infusion (a) Continuous intravenous Parameters used in the simulations were: CL = 2.6
`/ or intermittent dosing infusion at a dose rate of
`L/hour, VD = 30 L, t112 = 8 hours. At steady state,
`of a drug such as
`37.5mg/hour
`the average plasma concentration over the dosing
`theophylline.
`(b) Intermittent bolus dosing interval is the
`300 mg 8-hourly (dose rate same as that during a continuous infusion (14.4
`(dose/dosing interval) is 37.5 mg/L in this case). The therapeutic range for
`mg/hour)
`theophylline is 10-20 mg/L (55-110 mmol/L).
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`Pharmacokinetics made easy 11 Designing dose regimens - Australian Prescriber
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`(c) As for (b) but with a
`loading dose of 600 mg,
`twice the maintenance dose
`
`--- (a) cortinucus irfusbn
`(b) intErmittent bolus dosing
`(c) %Ali initial !co:ling.:lose
`
`0
`
`8
`
`le
`
`32
`24
`Time (hr)
`
`40
`
`48
`
`56
`
`If the loading dose achieves a plasma drug concentration the same as the steady state concentration for
`the maintenance infusion (see equation 1), steady state will be immediately achieved and maintained. If
`the loading dose over- or under -shoots the steady state concentration, it will still take 3-5 half -lives to
`reach Css (see Article 2), but the initial concentration will be closer to the eventual steady state
`concentration.
`
`With intermittent bolus dosing, Fig. 1 shows that where the dosing interval is equal to the half-life of the
`drug, a loading dose of twice the maintenance dose immediately achieves steady state. Half the loading
`dose (one maintenance dose) is eliminated in the first dosing interval (one half-life) and is then replaced by
`the first maintenance dose and so on.
`
`The use of a bolus loading dose may sometimes cause problems if adverse effects occur because of the
`initial high plasma drug concentrations before redistribution occurs. This is the case for example with
`lignocaine, where CNS toxicity occurs if too high a loading dose is given too rapidly. In this situation, a
`loading infusion or series of loading infusions can be used to allow redistribution to occur while the loading
`dose is being given. (A common regimen for lignocaine is to give an initial intravenous dose of 1 mg/kg,
`followed by up to 3 additional bolus injections of 0.5 mg/kg every 8-10 minutes as necessary, and a
`maintenance infusion of 2 mg/minute.)
`
`Another example is digoxin, where it is common for the loading dose to be divided into 3 parts given at 8-
`hourly intervals. Digoxin is slowly distributed to its site of action so the full effect of a dose is not seen for
`about 6 hours (see Article 2). Giving the loading dose in parts allows the full effect of each increment to be
`observed before the next is given so that potential toxicity can be avoided.
`
`3. Effects of varying the dose interval
`So far we have considered a dosing interval equal to the half -life of the drug. Fig. 2 shows the plasma
`concentration time profile for once daily intravenous bolus dosing of drugs with half-lives of 6 hours, 24
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`Pharmacokinetics made easy 11 Designing dose regimens - Australian Prescriber
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`hours and 96 hours (0.25, 1 and 4 times the dosing interval of 24 hours). For the drug with a half-life of 6
`hours (characteristic of theophylline), the concentration is virtually at steady state shortly after the first dose,
`but there is a large fluctuation (94%) over the dosing interval ((Cmax - Cmin) divided by Cmax = 0.94). The
`drug with a half-life of 24 hours (characteristic of amitriptyline) takes 3-5 half-lives to reach steady state and
`the fluctuation over the dosing interval is 0.5. For the drug with a half-life
`of 96 hours (characteristic of phenobarbitone), it takes 12-20 days (3-5 half-lives) to reach steady state, and
`with once daily dosing (4 doses per half-life), the extent of fluctuation over the dosing interval is small
`((Cmax - Cmin) divided by
`Cmax = 0.16).
`
`A dosing interval of about a half-life is appropriate for drugs with half-lives of approximately 8-24 hours
`allowing dosing once, twice or three times daily. It is usually not practicable to administer drugs with shorter
`half-lives more frequently. If such a drug has a large therapeutic index, so that a large degree of fluctuation
`over the dosing interval does not result in toxicity due to high peak concentrations (e.g. many antibiotics
`and beta-blocking drugs), it can be given at intervals longer than the half-life. For example, the plasma
`concentration time profile shown in Fig. 2A is similar to that for gentamicin when intravenous doses are
`given 8-hourly (half-life is 1-2 hours).
`
`Fig.Plasma concentration time profiles for drugs with half -lives (A) Half-life is 6 hours (e.g. See text for
`2 of 6, 24 or 96 hours administered once daily
`theophylline)
`explanation.
`(B) Half-life is 24 hours
`(e.g. amitriptyline)
`(C) Half-life is 96 hours
`(e.g. phenobarbitone)
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`Pharmacokinetics made easy 11 Designing dose regimens - Australian Prescriber
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`A
`
`Half Ife = 6 hrs
`
`0
`
`1
`
`2
`
`3
`
`4
`
`5
`
`Days
`
`B
`
`25
`
`20
`
`15
`
`10
`
`5
`
`20
`
`15
`
`10
`
`5
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`0
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`15
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`5
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`
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`3
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`Half Ife = 24 rrs
`
`4
`
`5
`
`C
`
`\\\
`
`\N\
`
`\\N
`
`Ha f life = 4 days
`
`5
`
`10
`
`15
`
`20
`
`25
`
`Days
`
`Drug coricellration (roll
`
`Drug concTikation (rot)
`
`Drug coricellration (roll
`
`By contrast, if the drug has a low therapeutic index and plasma concentrations need to be maintained in a
`narrow therapeutic range (e.g. theophylline with a therapeutic range of 10-20 mg/L (55-110 rrirnol/L)), use
`of a sustained release formulation will be necessary.
`
`If the drug has a very long half-life (e.g. phenobarbitone with a half-life of 4 days), once daily administration
`may still be appropriate and convenient. The fluctuation over the dosing interval will be small, but it should
`be remembered that it will still take 3-5 half-lives (12-20 days in this example) to reach steady state. A
`loading dose could be used, but may not be feasible if tolerance to adverse effects occurs as the drug
`gradually accumulates to steady state. For example, from equation 2, the loading dose of phenobarbitone
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`Pharmacokinetics made easy 11 Designing dose regimens - Australian Prescriber
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`to reach a plasma concentration of 30 mg/L (in the middle of the therapeutic range for anticonvulsant
`activity) would be about 1.5 g - a lethal dose for a non-tolerant individual
`(loading dose = C x VD = 30 mg/L x 50 L).
`
`Fig. 3
`
`Effect of absorption rate and bioavailability on plasma concentration time profile. The example is
`characteristic of theophylline in children who metabolise the drug more quickly than adults. Note the effect
`of the sustained release preparation in reducing the degree of fluctuation over the dosing interval and
`allowing 12-hourly dosing for a drug with a short half-life and narrow therapeutic index (therapeutic range
`10-20 mg/L (55-110 mmol/L)). The ka is the absorption rate constant (a measure of the rate of absorption in
`the same way that the elimination rate constant is a measure of rate of elimination).
`
`Parameters used in the simulations were:
`
`Dose rate = 13 mg/kg/12 hours (1.08 mg/kg/hour),
`VD = 0.5 L/kg, t112 = 4 hours, CL = 0.086 L/hour/kg,
`F = 1
`
`(a) instantaneous absorption (intravenous bolus dosing)
`(b) ka = 1.5/hour similar to a rapidly absorbed oral formulation
`(c) ka = 0.15/hour similar to a sustained release formulation
`(d) as for (c) except that bioavailability (F) = 0.5
`
`From equation 3:
`
`for (a), (b) and (c), Css is 12.6 mg/L and
`for (d), Css is 6.3 mg/L due to reduced bioavailability
`
` (a) intra'vencus tolus dosing
`--
` (b) rapidly absorbed or
`formulation
`
`- — — (0) sustained release formulation
`(d) wi th tioavailatility reduced to 0.5
`
`I
`
`I
`
`I
`
`I
`
`I
`
`12
`
`24
`Hours
`
`36
`
`I
`
`48
`
`40
`
`30
`
`20
`
`10
`
`Drug concentration (mg/L)
`
`0
`
`0
`
`4. Oral dosing
`The principles applying to intermittent intravenous dosing also apply to oral dosing with two differences
`(Fig. 3):
`
`the slower absorption of oral doses 'smooths' the plasma concentration profile so that fluctuation
`over the dosing interval is less than with intravenous bolus dosing. This smoothing effect is
`exaggerated with sustained release formulations (see Article 3 and Fig. 3), allowing less frequent
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`06/01/2016
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`Pharmacokinetics made easy 11 Designing dose regimens - Australian Prescriber
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`administration for drugs with short half- lives.
`the dose reaching the systemic circulation is affected by the bioavailability so that at steady state
`
`equation 3
`
`Desired concentration (Css) = F x oral dose rate / CL
`where F is the bioavailability (compare with equation 1 and see Article 5 'Bioavailability and first pass
`clearance' Aust Prescr 1991;14:14-6). The relationship between oral and intravenous dose rates to
`achieve the same Css then (combining equations 1 and 3) is
`
`equation 4
`
`Oral dose rate = intravenous dose rate / F
`For example, the oral bioavailability of theophylline is close to complete (F = 1) so that oral and intravenous
`dose rates are about the same. Morphine has an oral bioavailability of about 0.2 due to extensive first pass
`metabolism, so to achieve similar plasma concentrations and clinical effects, oral dose rates need to be
`about 5 times intravenous dose rates (intravenous dose rate/0.2).
`
`Other routes of administration and special dose forms also need to be considered. Parenteral dosing by
`the intramuscular or subcutaneous routes will give absorption profiles similar to those seen with oral
`dosing. Absorption from intramuscular sites can be very slow for some drugs such as phenytoin and
`diazepam, and can be erratic if tissue blood flow is disturbed as in shock. Sustained release parenteral
`formulations, of antipsychotic drugs for example, are used to give slow (but sometimes variable) absorption
`over weeks to months from an intramuscular depot injection allowing infrequent dosing and ensuring
`compliance.
`
`Percutaneous administration of drugs such as glyceryl trinitrate or oestrogens avoids first-pass metabolism
`and provides a slow absorption rate imposed by the rate of transfer through the skin or the release rate of
`the patch formulation.
`
`5. Summary
`The intravenous loading dose is determined by the volume of distribution:
`
`Loading dose = desired concentration x VD
`The oral maintenance dose rate is determined by the clearance and bioavailability and the desired steady
`state plasma concentration:
`
`Maintenance dose rate = CL x Css / F
`The time to reach steady state is determined by the elimination half-life:
`
`Time to steady state = 3-5 half-lives
`The degree of plasma concentration fluctuation over the dosing interval is determined by:
`
`the half-life
`the absorption rate
`the dosing interval
`
`First published online 1 July 1996
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