Pharmacokinetics lecture 5 Contents ...

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Pharmacokinetics lecture 5Contents ...

• Single i.v. bolus into a one
• compartment system
• Area Under the Curve

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Single i.v. bolus dose into one compartment
D
Dose 400 mg V 100 Litres K 0.3 h-1 Initial
conc (C0) 4 mg/L
V
K
3
D 400 mg V 100 L K 0.3 h-1
Mass 4 mg/L x 100 L 400 mg Rate of elim 400
mg x 0.3 h-1 120 mg/h
4 3 2 1 0
Mass 2 mg/L x 100 L 200 mg Rate of elim 200
mg x 0.3 h-1 60 mg/h
Conc (mg/L)
Mass 1 mg/L x 100 L 100 mg Rate of elim 100
mg x 0.3 h-1 30 mg/h
Exponential curve
0 2 4 6 8
10
Time (h)
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Half-life and K
4 3 2 1 0
C0 4 mg/L
Inefficiently eliminated
Efficiently eliminated
Conc (mg/L)
Low K / Long t ½
t ½ 2.3 h
t ½ 5.4 h
High K / Short t ½
0 2 4 6 8
10
Time (h)
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Predicting concentration at a given time point
C0
4 3 2 1 0
Ct C0.e-Kt
Conc (mg/L)
Ct
t
0 2 4 6 8
10
Time (h)
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Predicting concentration at a given time point
D 10 mg V 50 L K 0.05
h-1 What conc. after 12 hours? C0 D/V
10mg/50L 0.2mg/L 200µg/L Ct C0 .e-Kt
200µg/L . e-0.05h-1 x 12h 200µg/L .
e-0.6 200µg/L . 0.55 110 µg/L
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Predicting the time to reach a given concentration
C0 5 mg/L K 0.02h-1 How long until C 1
mg/L? Ct C0 .e-Kt Ct / C0 e-Kt 1/5
e-Kt 0.2 e-Kt (Take natural logs of both
sides) Ln(0.2) -Kt -1.609 -Kt (Drop minus
from both sides) 1.609 0.02h-1 x t t 1.609 /
0.02h-1 80.5 hours
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Area Under the Curve (AUC)
3 2 1 0

• Area under the concentration
• versus time curve
• Area Under the Curve
• AUC

Conc (mg/L)
0 2 4 6 8
10
Time (h)
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Units of AUC
3 2 1 0
Area is height x width Units are mg/L x h
mg.L-1.h Usually rearranged as
mg.h .L-1 In general Mass.Time.Volume-1
Conc (mg/L)
0 2 4 6 8
10
Time (h)
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AUC between time limits
3 2 1 0
AUC assumed to mean AUC 0- (The complete area
under the whole curve)
AUC2-4h
Conc (mg/L)
0 2 4 6 8
10
Time (h)
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Relationship between AUC, Dose and Clearance
Total amount of drug entering the body. (More
drug greater AUC)
AUC F.D Cl
Efficiency of removal. (Greater clearance
lower AUC)
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Calculation of AUC following single i.v. bolus
AUC F.D Cl e.g. D 5 mg Cl
4 L/h AUC 1.0 x 5mg 4
L/h 1.25 mg.h.L-1
Conc (mg/L)
0 2 4 6 8
10
Time (h)
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Example calculation
1mg of drug is administered (i.v) at time
zero. Vol Dis 50 L. Elim rate constant
0.015h-1 What will blood concentration be 2 days
later? Tip Calculate C0 first, then Ct.
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Answer
C0 D/V 1mg / 50L 0.02 mg/L
20 µg/L Ct C0.e-Kt 20µg/L x e-0.015h-1
x 2days 20µg/L x e-0.015h-1 x 48h
20µg/L x e-0.72 20µg/L x 0.487
9.7µg/L
Mixed units
2 calculator is no good. Need a good one!
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Terms with which you should be familiar ...
Area Under the Curve (AUC)
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What you should beable to do

• For a single i.v. bolus injection into a one
  compartment system ...
• Describe why the graph of concentration versus
  time adopts its distinctive shape
• Calculate remaining concentration from initial
  concentration, elimination rate constant and time
  elapsed (etc)
• Apply appropriate units to an AUC
• Calculate AUC following single i.v. injection