03-03-2011 1

MULTIPLE DOSING

K.PRADEEP KUMARM.PHARM (PHARMACEUTICS)

CONTENTS

Dosage regimen Drug accumulation Principle of superposition Multiple dosing with respect to I.V. Multiple dosing with respect to Oral route. Concept of loading dose, maintenance dose, References.

INTRODUCTION

• INTRODUCTIONA single dose may provide an effective

treatment. But the duration of illness is longer than the therapeutic effect produced by a single dose. In such cases drugs are required to be taken on a repetitive basis over a period of time.

The multiple dosing achieves and maintains drug concentration in plasma or at the site of action that are both safe and effective

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Two major parameters that can be adjusted in developing a dosage regimen are:

1. The dose size :- It is the quantity of the drug administered each time.

2. Dose frequency :- It is the time interval between doses.

DRUG ACCUMULATION

A) Drug accumulation during multiple dosing: following the 1st dose, if the 2nd dose is given early enough so that not the entire 1st dose is eliminated then the drug will start accumulating and we will get higher concentration with the 2nd and 3rd dose.

B) steady state during multiple dosing: The suitable amount of dose and identical dosing interval leads to steady state at which the mass of drug administered or absorbed is equal to the mass of drug eliminated

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Css max

Css min

Steady state

Time[h]

Plas

ma

drug

con

c.

1/2X0

X0+1/2X0

X0+1/4 X0

Accumulation Index

no.of ½ lives

1 2 3 4 5 6 7 8

0 100 max

1 50 min 150

2 75 175

3 87.5 187.5

4 93.8 193.88

5 96.88 196.88

6 98.44 198.44

7 99.22 192.22

8 99.6

No.of doses

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• The extent to which a drug accumulates in the body is a function of its dosing interval and elimination of half-life and is independent of dose size.

• The extent to which any drug accumulate with any dosing interval in a patient can be derived from information obtained with a single dose and is given by accumulation index Rac as :

• The extent to which a drug accumulates in the body is a function of its dosing interval and elimination of half-life and is independent of dose size.

• The extent to which any drug accumulate with any dosing interval in a patient can be derived from information obtained with a single dose and is given by accumulation index Rac as :

1(1 – e-KEt)Rac

=

Principle of superposition

• It assumes that the early doses of drug do not affect the pharmacokinetics of the sub sequent doses

• The basic assumptions are that the drug is eliminated by 1st order kinetics and that the pharmacokinetics of the drug after a single dose are not altered for multiple doses.

• Therefore, the blood levels after 2nd,3rd or nth dose will superimpose the blood levels attained after the (n-1)th

• [AUC]∞0 of single dose = [AUC]

t2

t1 during a dosing interval at

steady state

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• An equation for the estimation of the time to reach one half of the steady state plasma levels or the accumulation half life

accumulation t1/2 = t1/2 [1+3.3 log ka/ka-k]For iv administration, a is very rapid(approaches∞); k is

very small in comparison to ka

... t½=t½ [1+3.3 log ka/ka ]... log 1=0

Accumulation t½ = elimination t½

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Repetitive iv injection

On repeated drug administration, the plasma concentration will be added upon for each dose interval giving a steady state

Calculation of plasma drug concentration is done using superposition principle

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• Dose =Xo • Dosing interval of t hours• Cmax = Xo/Vd (1)• The concentration of drug in plasma at any time t is given by

C= Cmax .e-Kt (2)• K=overall rate constant• The concentration of drug in plasma at the end of first dosing

interval Ʈ , is given by C1t=C0

1. e-K Ʈ (3)

• Where C1 Ʈ =concentrtion of the drug in plasma at the end

of first dosing interval of Ʈ

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• C10 = zero time concentration for first dose

• The zero time concentration of the drug in plasma following the second dose will be

C20 =C1

Ʈ + C1

0 (4)

C1 Ʈ = C10 . e-K Ʈ (5)

C20 =C1

0 . eK Ʈ + C10 (6)

Let r = eK Ʈ then the above equation as be written asC2

0 =C10 r + C1

0 (7)

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• The drug concentration in plasma at the end of the second dosing interval is given by

C2Ʈ= C2

0 .e-K Ʈ = (C10r+C1

0)r (8)

Now this procedure can be used for finding zero time concentration & drug concentration at the end of dosing interval for each dose of the drug.

C30 = C2

Ʈ + C10 = (C1

0r+C10)r+C1

0 (9)

C3Ʈ = C3

0r=[(C10r+C1

0)r+C10]r (10)

... The plasma concentrations at the beginning & end of nth dosing interval are given by the fallowing series

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• Beginning= C10+C1

0r+C10r2+…………….+C1

0r(n-1) (11)

• End = C10r+C1

0r2+C10r3+…………+C1

0rn (12)• r<1, as n increases rn becomes smaller• When n=∞ equation 11,12,becomes

• Cmax =C1/1-r= X0/Vd(1- e-KƮ)(13)

• Cmin=Cmax.r

• An average study state concentration Cav is obtained by dividing AUC for dosing period by the dosing interval

• Cav=[AUC]t2t1/Ʈ

• Plasma drug concenration at any time tCn=C0(1-e-nkƮ/1-e-kƮ).e-kƮ

• N=no.of doses is time after nth dose. At steady state e-nkƮ approaches zero ...Cn

∞=C0(1/1-e-kƮ ) e-kƮ

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Repetitive extra vascular dosing

• Drug absorption and elimination processes follow first order kinetics• The pharmacokinetic parameters such as ka,k,vd & fraction of dose

absorbed(F) remain constant during multiple dosing• The plasma drug concentration time profile following a single dose

is given by C =kaFX0/Vd(ka-k) (e-KƮ - e-KaƮ) (14)

• If n fixed doses of drug X0are administered at fixed time intervals(t),the plasma concentrations fallowing the nth dose are given by

• Cn∞ = kaFX0/Vd(ka-k) [(1/1- e-KƮ ) e-KƮ (1/1- e-KaƮ )e-KƮ (15)

• The term tp (peak concentration of during in plasma after single dose) is

given by tp= (2.303/ka-k) log ka/k (16)

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• When t = tp

2.303 log [ Ka(1- e-kƮ)]

(Ka-k) [k(1- e-kƮ)]

If t=tp from the equation 15 the Cmax is given as

FX0 [( 1 ) e-ktp

Vd (1- e-kƮ )

If t =Ʈ from the equation 15 Cmin is given as

Cmin=KaFX0/Vd(Ka-k) [1 / 1-e-k ]e-kt

Cave =FX0/Vd.KƮ

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Loading Dose

• A drug dose does not show therapeutic activity unless it reaches the desired steady state.

• It takes about 4-5 half lives to attain it and therefore time taken will be too long if the drug has a long half-life.

• Therapeutic effect can be reached immediately by administering a dose that gives the desired steady state instantaneously before the commencement of maintenance dose X0.

• Such an initial or first dose intended to be therapeutic is called as priming dose or loading dose.

Calculation Of Loading Dose

I.VMaintenance dose X0 = X* (1-ekƮ)

Loading dose,

X* = X0/(1-e-kƮ)

Dose ratio = X*/X0

Extra vascular dosing maintenance dose

X* = cav . Vd /e-kƮ X0=X*(1-e-kƮ)

F

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Calculation Of Loading Dose

• When T > t1/2 dose ratio is smaller than 2.0• When T< t1/2 dose ratio is greater than 2.0

• If the loading dose is not optimum either too low or too high, the steady state is attained within a 4-5 half lives in a manner similar to when no loading dose is given.

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dosing interval in hrs

loading dose X0,L

X0

X0

X0

X0T T T T T

MEC

MSC

maintenance dose X0

Dose ratio >2

Dose ratio 2

Cp

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Conclusion

• The successive administration of an optimum dosing size and at an identical dosing frequency that shows minimum therapeutic concentration results in produces acute or required prolonged effect

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Reference

• Biopharmaceutics And Pharmacokinetics A Treatise, Brahmankar.

• “Text Book Of Biopharmaceutics & Pharmacokinetics”,

• By V.Venkateshwarlu• Different website sources , g books • ‘Applied Biopharmaceutics & Pharmacokinetics’ by Leon Shargel & Andrew B. C. Yu, 4th Edition

• ‘Clinical Pharmacokinetics, Concepts & Application’, 3rd Edition,

by Malcom Rowland & Thomas N. Tozer, Lea & Febiger

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THANK YOU