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CHAPTER 4

INTRAVENOUS INFUSION

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ONE COMPARTMENT MODEL WITH IV INFUSION

This can be obtained by high degree of precision by infusing drugs i.v. via a drip or pump in hospitals

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PK of Drug Given by IV Infusion

Zero-order Input (infusion rate, R)

First-order Output (elimination)

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Integrated equationZero-order Input (infusion rate, R)

First-order Output (elimination)

By integration,

pelp CkR

dt

dC

)1( tk

eldp

elekV

RC

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Stopping the Infusion Stopping the infusion before reaching steady state

Infusion stops

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Stopping the Infusion Equations

tkpp

eleCC 0

)1( tk

eldp

elekV

RC

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Steady State ConcentrationIV Infusion until reaching Css

Cl

RCss

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Steady State Concentration (Css)

Theoretical SS is only reached after an infinite infusion time

Rate of elimination = kel Cp

)1( ekV

RC

eldp

Cl

R

kV

RC

eldss

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Steady State Concentration (Css)

Rate of Infusion = Rate of Elimination

The infusion rate (R) is fixed while the

rate of elimination steadily increases

The time to reach SS is directly

proportional to the half-life

After one half-life, the Cp is 50% of the CSS, after 2 half-lives, Cp is 75% of the

Css .……

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Steady State Concentration (Css)

In clinical practice, the SS is considered to be reached after five half-lives

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Increasing the Infusion Rate If a drug is given at a more rapid infusion rate, a higher SS drug concentration is obtained but the time to reach SS is the same.

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Loading Dose plus IV Infusion DL with IV infusion at the same time

)1( tk

eld

tk

d

Lp

elel ekV

Re

V

DC

tk

d

Ltkp

elel eV

DeCC

1

)1(2tk

eld

elekV

RC

Loading dose

IV infusion

DL + IV infusion

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Loading Dose plus IV Infusion

DL is used to reach SS rapidly

)1( tk

eld

tk

d

Lp

elel ekV

Re

V

DC

tk

eldeld

tk

d

Lp

elel ekV

R

kV

Re

V

DC

tk

eld

tk

d

L

eldp

elel ekV

Re

V

D

kV

RC

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Reaching SS Immediately

Let , DL = CssVd But, CssVd = R / kel

Therefore, if a DL = R / kel is given SS will be reached immediately

tk

eld

tk

d

L

eldp

elel ekV

Re

V

D

kV

RC

eldp kV

RC

eldss kV

RC but

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Reaching SS Immediately IV DL equal to R /kel is given, followed by IV infusion at a rate R

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DL + IV Infusion