Transcript ONE COMPARTMENT MODEL WITH IV INFUSION

CHAPTER 4
INTRAVENOUS INFUSION
1
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 equation
Zero-order Input (infusion rate, R)
First-order Output (elimination)
dCp
dt
 R  kelC p
By integration,
R
 k el t
Cp 
(1  e )
Vd k el
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Stopping the Infusion
Stopping the infusion before reaching steady
state
Infusion stops
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Stopping the Infusion
Equations
R
Cp 
(1  e kel t )
Vd k el
0  kel t
p
Cp  C e
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Steady State Concentration
IV Infusion until reaching Css
C ss
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R

Cl
Steady State Concentration (Css)
Theoretical SS is only reached after an infinite
infusion time
R

Cp 
(1  e )
Vd k el
R
R
C ss 

Vd k el Cl
Rate of elimination = kel Cp
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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
Loading
dose
IV
infusion
DL + IV
infusion
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C1  C  e

p
 kel t
DL kel t

e
Vd
R
 kel t
C2 
(1  e )
Vd kel
DL kel t
R
 kel t
Cp 
e

(1  e )
Vd
Vd kel
Loading Dose plus IV Infusion
DL is used to reach SS rapidly
DL kel t
R
 kel t
Cp 
e

(1  e )
Vd
Vd kel
DL kel t
R
R kel t
Cp 
e


e
Vd
Vd kel Vd kel
 DL kel t
R
R kel t 
Cp 
 
e

e 
Vd kel  Vd
Vd kel

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Reaching SS Immediately
Let , DL = CssVd
But, CssVd = R / kel
 DL kel t
R
R kel t 
Cp 
 
e

e 
Vd kel  Vd
Vd kel

Therefore, if a DL = R / kel is given SS will
be reached immediately
R
Cp 
Vd k el
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but
R
C ss 
Vd k el
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
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