multiple dose regimen

8/9/2019 Multiple Dose Regimen

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MULTIPLE DOSE REGIMENMULTIPLE DOSE REGIMEN


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INTRODUCTION Drugs are rarely used in single doses to produce an acute

effect

But, drugs are administered in successive doses to produce achronic or prolonged effect The goal in the design of dosage regimens is to achieve and

maintain drug concentrations in plasma or at the site of actionthat are both safe and effective

That is to maintain the drug concentration with in thetherapeutic window (Below the minimum toxic concentrationand above the minimum effective concentration)

Toxicity would result if doses are administered too frequently,

whereas, effectiveness would be lost if the dosage rate are tooinfrequent The two parameters important in dosage regimen are

The size of the dose of the drug

The frequency of drug administration (time interval betweendoses)


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INTRODUCTIONEffect of frequency of administration of a drug on plasma drug

level

PlasmaDrugC

oncent r

ation

Time

Minimum toxic concentration

Minimum toxic concentration

A

B

C

Therapeutic

Window

A Too frequent dosing B Proper dosing C Inadequate

frequency


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DRUG ACCUMULATION When drugs are administered on multiple dose regimen, each

dose (after first dose) is administered before the preceding

doses are completely eliminated This results in a phenomenon known as drug accumulation,

where the amount of the drug in the body (represented by

plasma concentration) builds up as successive doses are

administered But, after seven doses of the drug at an interval equal to the

drug half-life, the maximum and minimum amounts in the body

becomes fairly constant

This is called Steady State Condition At this stage, the amount of the drug lost during dosing interval

is equal to the administered dose


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DRUG ACCUMULATIONDrug Accumulation during Multiple Dose Regimen

Dose =100 mg Dosing interval = t1/2

of the drug

No. of halflives

(Frequencynumber)

No. of doses

1 2 3 4 5 6 7 8

0 100 Max -

1 50 Min 150

2 75 175

3 87.5 187.5

4 93.8 193.8

5 96.88 196.88

6 98.44 198.44

7 99.22 199.22 Max

8 99.61 Min

This prediction of the amount of the drug in the body following repeated doses of a drug

in the above example is based on the assumption that its elimination half-life is constantthroughout the dosage regimen


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PRINCIPLE OF SUPERPOSITION An accepted plasma concentration profile at the steady state

can be devised with the aid of pharmacokinetic parameters

derived from single dose experiments based on the principle ofsuperposition

The principle of superposition assumes that early doses of a

drug do not affect the pharmacokinetic of subsequent doses

The basic assumptions are that the drug is eliminated by firstorder kinetics and that the pharmacokinetics of the drug after a

single dose (first dose) are not altered for multiple doses

Therefore, the blood level after the second, third, or nth dose will

overlay orsuperimpose the blood level attained after n-1

th

dose In addition, AUC (0 ) following the administration of a single

dose equals the AUC (t1 t2) during a dosing interval at

steady state


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PRINCIPLE OF SUPERPOSITIONSimulated date showing blood level after administration of multiple

doses and accumulation of blood level when equal doses are

given at equal time intervals

PlasmaDrug

Concent r

ation

Time (hours)

AUC (t1 t2)


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PRINCIPLE OF SUPERPOSITION

Thus, the drug levels in plasma versus time data obtained witha single dose is used to predict the drug levels in plasma after

multiple doses

As the superposition principle is an overly method, it may beused to predict drug concentrations after multiple doses givenat equal and unequal dosage intervals

The predicted plasma concentration would be the total drugconcentration obtained by adding the residual drugconcentration obtained after each previous dose

The principle of superposition can not be used in certainsituations, including, changing pathophysiology, saturation ofthe drug carrier system, saturated protein binding, saturated

active secretion, enzyme induction and enzyme inhibition


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. . OPEN MODEL Calculation of plasma drug concentrations following repetitive doses of a

drug using superposition principle requires preparation of a list of plasma

drug concentrations for each dose as shown in table

Dose No. Time

(hours)

Plasma drug doses level (mg/ml) Total

1 2 3 4 5

1 0123

021.022.319.8

021.022.319.8

2 4567

16.914.312.010.1

021.022.319.8

16.935.334.329.9

3 89

1011

8.57.156.015.06

16.914.312.010.1

021.022.319.8

25.442.540.335.0

4 12131415

4.253.583.012.53

8.57.156.015.06

16.914.312.010.1

021.022.319.8

29.746.043.337.5

5 1617

1819

2.131.79

1.511.27

4.253.58

3.012.53

8.57.15

6.015.06

16.914.3

12.010.1

021.0

22.319.8

31.847.8

44.838.8


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. . OPEN MODEL.

Let us consider that a drug was repeatedly injected intravenously at a doseof X0 with a dosing interval of t hours

The maximum concentration of the drug in plasma following a rapid i.v.injection is equal to the dose divided by Vd of the drug

The concentration of the drug in plasma at any time t is given by

Where K is the overall elimination rate constant

The concentration of the drug in plasma at the end of the first dosing

interval, , is given by

dVXC /00 =

KteCC

= .0

KeCC

= .01

1


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. . OPEN MODEL.

Where is the concentration of the drug in plasma at the end of the firstdosing interval

is zero time concentration for first dose

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

be

But,

Therefore,

Let R = then, the above equation can be written as

1C

01C

0

11

0

2CCC +=

KeCC

= .0

1

1

0

1

0

1

0

2 . CeCCK

+=

Ke

0

1

0

1

0

2. CRCC +=


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. . OPEN MODEL.

The drug concentration in plasma at the end of the seconddosing interval is given by

Now, this procedure can be used for finding zero time

concentration (maximum drug concentration in plasma) and drug

concentration at the end of dosing interval (minimum drugconcentration in plasma) for each dose of the drug

RCRCeCC K )(. 0101

022 +==

0

1

0

1

0

1

0

12

0

3 )( CRCRCCCC ++=+=

RCRCRCRCC ])[( 010

1

0

1

0

33 ++==


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. . OPEN MODEL.

Since the plasma concentration at the beginning and end of the n th dosing intervalare given by the following series

Beginning =

End =

Since, R is always smaller than 1, Rn becomes smaller as n increases

Therefore, the high power terms in the above equations become negligible as n

increases and additional doses do not change the value of or significantly

This explains why the plasma concentrations reach a plateau instead of continuing

to rise as more doses are given

)1(01

201

01

01 .............

++++nRCRCRCC

nRCRCRCRC ............. 01

30

1

20

1

0

1 ++++

0

nC

nC


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. . OPEN MODEL.

When n = , the above equations become

Hence, Cmax and Cmin are defined as the plasma concentration at the beginning and end,respectively, of the nth dosing interval after the plateau has been reached (i.e., n = )

Thus, the maximum and minimum plasma concentrations on the plateau of a repetitive i.v.

dosing regimen can be calculated if the dosing interval ( ), the overall elimination rate

constant (K), and the initial plasma concentration (C0) are known

RCC =1/

0

1max

RRCRCC == 1/. 01maxmin


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. . OPEN MODEL.

An average steady state plateau drug concentration Cave , is obtained by dividingAUC for a doing period by the dosing interval

it should be remembered that Cave is not the arithmetic mean of Cmax and Cmin

because plasma drug concentrations decline exponentially

The AUC (t1-t2) is related to the dose X0 divided by the total body clearance (Vd. K)

Therefore,

/][ 21

t

taveAUCC =

KVXAUC dt

t ./][ 02

1 =

../0 KVXC dave =


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. . OPEN MODEL.

Equations can also be expressed in terms of the amont of the drug inthe body

Where, Xmax , Xmin , and Xavg are the maximum , minimum and average

amount of the drug in the body at the steady-state

It is sometimes desirable to know the plasma drug concentration atany time after the administration of n doses of a drug

The general expression for calculating this plasma drug concentration

is

RXX = 1/0max RRXRXX == 1/. 0m a xm i n

./0

KXXave

=

KtKKnt

n eeeCC

= )1/1(0


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. . OPEN MODEL. Where n is the number of doses given and is the time after the nth dose

At steady state approaches zero and equation reduces to

Repetitive Extravascular Dosing One Compartment Open

Model Although the equations become considerably more complex than for the

i.v. case, Cmax , Cmin , Cave can be calculated when the drug is administered

by an extravascular route

The basic assumptions made in developing the equations for the

extravascular route are

Drug absorption and eliminated processes follow first order kinetics

The pharmacokinetic parameters such as Ka, K, Vd, and the fraction of the dose

absorbed (F) remain constant during multiple - dosing

nK

e

KtK

neeCC

= )1/1(0

REPETITVE EXTRAVASCULAR DOSING ONE


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COMPARTMENT OPEN MODEL. The equation describing the plasma drug concentration time profile

following a single dose of extravascular administration of the drug is given by

If n fixed doses of the drug (X0) are administered at fixed time intervals (t), the

plasma drug concentrations following the nth dose are given below

Whereas is the concentration of the drug at time t, after nth dosing

When n is large (i.e., when the plasma concentrations reach a plateau), the

terms and becomes negligible

))]((/[ 0tkKt

ada

aeeKKVFXKC

=

]})1/1[(

])1/1){[((/0tKKnK

KtKnK

ada

t

n

aaa

eee

eeeKKVFXKC

=

t

nC

nKe anKe



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COMPARTMENT OPEN MODEL.

The above equation can be used to calculate the Cmax and Cmin valueson the plasma concentration plateau by substituting values for t which

correspond to the peaks and troughs in the C versus t curve

Thus if t = tp (the time of peak concentration of drug in plasma),

If t = 0 (the time at which another dose is to be given) the equation gives

Cmin

)]1/(

)1/)[((/0

aa KtK

KKt

adan

ee

eeKKVFXKC

=

)]1/(

)1/)[((/0max

aa KtpK

KKtp

ada

ee

eeKKVFXKC

=

)]1/1()1/1)[((/0maxaKKada eeKKVFXKC

=



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COMPARTMENT OPEN MODEL. The mean plasma level at steady state Cave is obtained by applying the similar

method used for repeated i.v. injections

or

since

Multiple Dose Regimen Loading Dose The time required for the drug to accumulate to a steady state plasma level is

dependent mainly on its elimination half-life

The time need to reach 95% Cave is approximately 5 half-lives of the drug

for a drug with a half-life of 5 hours, it would take approximately 25 hours to reach

95% of Cave

/][ 21

t

taveAUCC = KVFXC

dave/0=

KVFXAUCd

t

t /][ 02

1=



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COMPARTMENT OPEN MODEL. In order to initiate a immediate therapeutic effect, an initial dose

also called loading dose or primary dose is administered to

achieve Cave

i.v. injections: As we know

Where X0 is i.v. dose, is dosing interval, Vd is the volume of

distribution of the drug and k is the elimination rate constant

Therefore we should administer a loading dose X* just before the

administration of the maintenance dose X0 The amount present in the body is equal to X0/

The amount of the drug present in the body after t

= following and an i.v dose of X* is X ave

./. 0 KXVCX daveave ==

K

K

ave eXX

= .*



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COMPARTMENT OPEN MODEL. The amount of the drug eliminated during this period must besupplied in the form of a maintenance dose X

0

The amount of a the drug eliminated from a loading dose intime , is equal to the difference between the loading dose

(X*) and the amount remained in the body after (Xave)

Amount of the drug eliminated

The amount of the drug eliminated should be equal to the

maintenance dose, X0, to maintain the steady-state level

Therefore, Maintenance dose,

aveXX = *K

eXX

= **

)1(*

KeX

=

)1(*0K

eXX

=



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COMPARTMENT OPEN MODEL. And loading dose,

In practice, the Cave, value for a particular drug is known

The elimination rate constant (K), Volume of distribution (Vd)

and dosing interval are taken from the literature to calculate the

loading dose (X*), using the following equation

The ratio of loading to maintenance dose depends on the

dosing interval and the half-life of the drug and is equal to the

accumulation index, Rac

)1/(* 0KeXX =

Kdave

Kave eVCeXXLodingDose

== //*

Kac eXXR

== 1/1/* 0



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COMPARTMENT OPEN MODEL.

Extravascular Dosing In case of extravascular dosing, the fraction of the dose absorbed, F,

should be taken into consideration while calculating the loading dose Loading Dose

Maintenance Dose

Multiple dose regimen Two Compartment Open Model

One compartment equations modified in minor ways apply to two

compartment systems with reasonable accuracy, when the distributionphase after one dose is approximately complete before the next dose is

administered

FeVCX

K

dave /)/.(*

=

FeXX K /)1(*0

=



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COMPARTMENT OPEN MODEL. Under these conditions, may be substituted for K and Vd

area for

Vd, to adopt one compartment equations to two compartment

systems for rough approximations of the two compartmentparameters and plasma concentrations

For i.v. injections:

Loading Dose

For extravascular dosing:

Loading Dose

The accumulation ratio of the drug Rac

is the ratio of loading

and maintenance doses

areadave VXC /0=

= eVC areadave /.

areadave VFXC /0=

FeVC areadave /)/.(

=

)1/1()/*( 0

= eXXRac

multiple dose regimen

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