Transcript Pharmacokinetics lecture 10

Pharmacokinetics lecture 10
Contents ...
• Extravascular administration
• Determination of bioavailability
for extravascular doses
Extravascular
administration
Any route other than i.v.
• An absorption stage will be involved
• Bioavailability may not be 100%
Principally oral but also intramuscular,
subcutaneous etc
Aa
Ka
Ab
K
Body
Gut
Rate of change in body load
= Input - Output
= Ka.Aa - K.Ab
Extravascular
administration
Almost pure
elimination
Changing Ka
3h-1
Reduced Ka (Slower
release) causes peaks to be
lower and shifted to the right.
0.4h-1
Determination of F for
extravascular doses
Assume the same dose of a drug is
administered on two occasions to the same
individual. Either different dosage forms or
routes of administration are used on the two
occasions.
Determination of F
AUC = F.D
Cl
rearranges to
D = AUC
Cl
F
Drug administered on two occasions ...
D1 = AUC1
Cl1
F1
D2 = AUC2
Cl2
F2
Dose and clearance will be same on both occasions
D1 = D2 so
Cl1 Cl2
AUC1 = AUC2 and
F1
F2
F1 = AUC1
F2 AUC2
Absolute bioavailability
Absolute bioavailability can be calculated if
one of the doses is an i.v. injection.
Say the other dose is oral ...
Foral = AUCoral
Fiv
AUCiv
Fiv is always 1.0, so
Foral = AUCoral
AUCiv
Absolute oral bioavailability
Relative bioavailability
If neither of the doses is an i.v. injection, we can
only calculate a relative bioavailability.
If we give the same dose orally and by i.m.
injection ...
Foral = AUCoral
Fim
AUCim
This term is the bioavailability of the oral
dose relative to the i.m. dose.
i.v.
Oral
AUCoral = Absolute oral bioavailability
AUCiv
Capsule
Tablet
AUCtablet = Bioavailability of tablet
AUCcapsule
(Relative to capsule)
Practical methods for
determining AUC
• For an i.v. dose can use AUC = F.D
Cl
• For extravascular doses there is no
simple formula. Have to use graphical
methods.
Trapezoidal rule
Verticals dropped from each point.
Points joined by straight lines.
Conc
Divides the area into a series
of 6 trapezoids.
1 2
3
4
5
Time
Total area of the
trapezoids gives a
good approximation
of the AUC up to
the last blood
6
sample.
Area of each trapezoid
C2
C1
Mean height = C1 + C2
2
Width = t2 - t1
Area = C1 + C2 x (t2 - t1)
2
t1
t2
Area of
the ‘tail’
Conc
1.5
1.0
True AUC0- should include the
‘tail’ area beyond the last actual
measured concentration.
Calculate as:
Tail = Final measured conc
K
0.5
0.0
0
Time (h)
6
12
An example -
Determination of absolute
oral bioavailability
10mg of a drug have been administered on two
occasions to the same subject. One dose i.v., one
oral.
Plan
1 From i.v. data, get clearance and AUCiv
2 From oral data, get AUCoral up to last blood sample
3 Semi-log plot of oral data to get K and area of tail
4 Get total AUC oral
5 Get F as AUCoral / AUCiv
1: Determine clearance
and AUCiv
(Not dealt with in detail, as already covered in
Lecture 6.) Assume Clearance found to be 50 L/h.
AUC = F.D
Cl
AUC = 1.0 x 10mg
50 L/h
= 0.2 mg.h.L-1
= 200 µg.h.L-1
2: Use trapezoidal rule
to get oral AUC0-12h
Data from oral administration
Time (h)
Conc (µg/L)
1
9.6
2
11.0
4
12.0
6
9.4
8
5.0
10
2.5
12
1.25
Trap
AUC
----------------------------------------------------------------1
(0 + 9.6) / 2
x (1 - 0)
= 4.8 µg.h.L-1
2
(9.6 + 11.0) / 2 x (2 - 1)
= 10.3
3
(11.0 + 12.0) / 2 x (4 - 2)
= 23.0
4
(12.0 + 9.4) / 2 x (6 - 4)
= 21.4
5
(9.4 + 5.0) / 2
x (8 - 6)
= 14.4
6
(5.0 + 2.5) / 2
x (10 - 8) = 7.5
7
(2.5 + 1.25) / 2 x (12 - 10) = 3.75
-----------------------------------
Total
= 85.15 µg.h.L-1
3: Tail area
Tail area can be calculated from:
Tail = Final conc
K
• ‘Final conc’ is the last measured
concentration.
• To get K, need semi-log plot of data
Not C0, but can be used
to get t-half (85 µg/L)
Conc (µg/L)
50
By the later times,
absorption is
virtually complete
and we are seeing
almost pure
elimination.
42.5 µg/L
30
10
Identify the terminal
linear portion,
extrapolate back to
zero time and get
elimination half life.
5
3
t ½ = 1.9 h
1
0
2
4
6
8
Time (h)
10
12
Area of tail
K = 0.693
t½
= 0.693
1.9h
= 0.365h-1
Tail = Final conc
K
= 1.25 µg/L
0.365h-1
= 3.42 µg.h.L-1
4: Total AUCoral
Total area = AUC0-12h + Tail
= 85.15 + 3.42 µg.h.L-1
= 88.57 µg.h.L-1
5: Absolute oral
bioavailability
F = AUCoral
AUCiv
= 88.57 µg.h.L-1
200 µg.h.L-1
= 44.3%
Terms with which you
should be familiar ...
• Absolute bioavailability
• Relative bioavailability
• Trapezoidal rule
• ‘Tail’ area
What you should be
able to do
 Describe
and explain the characteristic shape of the
graph of concentration versus time following an
extravascular dose.
 Describe and explain the changes in this graph if a
slow-release dosage form is used.
 Describe the distinction between an absolute and a
relative bioavailabilty.
Continued ...
What you should be
able to do (continued)
 Calculate
AUC0- from a series of timed blood
samples following an extravascular dose.
 Calculate bioavailability from a a pair of AUCs