Non linear Pharmacokinetics

Non linear Pharmacokinetics

1. Nonlinear Pharmacokinetics
•Most of the rate processes discussed in this course,
except for the infusion process, follow first order
kinetics.

•For a few drugs it is observed that the elimination of
the drug appears to be zero order at high
concentrations and first order at low concentrations.

•That is 'concentration' or 'dose' dependent kinetics are
observed. At higher doses, which produce higher
plasma concentrations, zero order kinetics are
observed, whereas at lower doses the kinetics are
linear or first order.

2. Nonlinear Pharmacokinetics
•This occurs especially with drugs which are
extensively metabolized.

•A typical characteristic of enzymatic reactions and
active transport is a limitation on the capacity of
the process.

•There is only so much enzyme present in the liver,
and therefore there is a maximum rate at which
metabolism can occur.

3. Nonlinear Pharmacokinetics
•A further limitation in the rate of metabolism can
be the limited availability of a co-substance or co-
factor required in the enzymatic process.

•This might be a limit in the amount of available
glucuronide or glycine, for example.

•Drug concentrations in the blood can increase
rapidly once an elimination process is saturated.

•This nonlinear pharmacokinetic behavior is also
termed dose-dependent pharmacokinetics.

4. Nonlinear Pharmacokinetics
•A number of drugs demonstrate saturation
or capacity-limited metabolism in humans.

•Examples of these saturable metabolic
processes include:
– glycine conjugation of salicylate.
–sulfate conjugation of salicylamide.
–acetylation of p-aminobenzoic acid.
–The elimination of phenytoin.

5. Nonlinear Pharmacokinetics
•Drugs that demonstrate saturation kinetics usually
show the following characteristics:

1)Elimination of drug does not follow simple first-order
kinetics—that is, elimination kinetics are nonlinear.

2)The elimination half-life changes as dose is increased.
Usually, the elimination half-life increases with
increased dose due to saturation of an enzyme
system. However, the elimination half-life might
decrease due to "self"-induction of liver
biotransformation enzymes, as is observed for
carbamazepine.

6. Nonlinear Pharmacokinetics
3)The area under the curve (AUC) is not proportional
to the amount of bioavailable drug.

4)The saturation of capacity-limited processes may be
affected by other drugs that require the same
enzyme or carrier-mediated system (ie, competition
effects).

5)The composition and/or ratio of the metabolites of
a drug may be affected by a change in the dose.

7. Nonlinear Pharmacokinetics
•When a large dose is given, a
curve is obtained with an initial
slow elimination phase followed
by a much more rapid
elimination at lower blood
concentrations (curve A).

•With a small dose of the drug,
apparent first-order kinetics are
observed, because no saturation
kinetics occur (curve B).
Plasma level–time curves for a drug
that exhibits a saturable elimination
process. Curves A and B represent high
and low doses of drug, respectively,
given in a single IV bolus.

8. Nonlinear Pharmacokinetics
•If the pharmacokinetic data
were estimated only from the
blood levels described by
curve B, then a two fold
increase in the dose would
give the blood profile
presented in curve C, which
considerably underestimates
the drug concentration as well
as the duration of action.
Plasma level–time curves for a drug
that exhibits a saturable elimination
process. The terminal slopes of curves
A and B are the same. Curve C
represents the normal first-order
elimination of a different drug.

9. Nonlinear Pharmacokinetics
•In order to determine whether a drug is following
dose-dependent kinetics, the drug is given at
various dosage levels and a plasma level–time
curve is obtained for each dose.

•The curves should exhibit parallel slopes if the
drug follows dose-independent kinetics.
Alternatively, a plot of the areas under the plasma
level–time curves at various doses should be
linear.

10. Nonlinear Pharmacokinetics
Area under the plasma level–time curve versus dose
for a drug that exhibits a saturable elimination process.
 Curve A represents dose-dependent or saturable
elimination kinetics.
 Curve C represents dose-independent kinetics.

11. Saturable Enzymatic Elimination
Processes
•The elimination of drug by a saturable enzymatic
process is described by Michaelis–Menten kinetics.

•If C
p is the concentration of drug in the plasma,
then:


•Where:
–V
max is the maximum elimination rate.
–K
M is the Michaelis constant that reflects the capacity of
the enzyme system. PM
PP
CK
CV
dt
dC


max
raten Eliminatio

12. Saturable Enzymatic Elimination
Processes
•K
M is not an elimination constant, but is actually a
hybrid rate constant in enzyme kinetics,
representing both the forward and backward
reaction rates and equal to the drug concentration
or amount of drug in the body at 0.5V
max.

•The values for K
M and V
max are dependent on the
nature of the drug and the enzymatic process
involved.

13. Saturable Enzymatic Elimination
Processes
•When the drug concentration C
p is large in relation to
K
M (C
p >> K
m), saturation of the enzymes occurs and
the value for K
M is negligible.


•The rate of elimination proceeds at a fixed or
constant rate equal to V
max. Thus, elimination of drug
becomes a zero-order process and Eq. becomes: max
max
- raten Eliminatio V
C
CV
dt
dC
P
PP


14. Saturable Enzymatic Elimination
Processes
•When the drug concentration C
p is small in
relation to the K
M, the rate of drug elimination
becomes a first-order process.
PP
MMP
PP
CkC
K
V
KC
CV
dt
dC



maxmax

Where: k' is a first-order rate constant for a saturable process

15. Saturable Enzymatic Elimination
Processes
•When given in therapeutic doses, most drugs
produce plasma drug concentrations well below K
M
for all carrier-mediated enzyme systems affecting
the pharmacokinetics of the drug.

•Therefore, most drugs at normal therapeutic
concentrations follow first-order rate processes.

16. Saturable Enzymatic Elimination
Processes
•Only a few drugs, such as salicylate and
phenytoin, tend to saturate the hepatic mixed-
function oxidases at higher therapeutic doses.

•With these drugs, elimination kinetics are first-
order with very small doses, mixed order at
higher doses, and may approach zero-order with
very high therapeutic doses.

17. Saturable Enzymatic Elimination
Processes
Linear Plot of Cp Versus Time
Showing High Cp and Low Cp –
Zero Order and First Order Elimination

18. Saturable Enzymatic Elimination
Processes
Semi-Log Plot of C
p Versus Time
Showing High C
p and Low C
p

19. Nonlinear Pharmacokinetics
•As the concentration increases we would expect the
clearance to decrease.

•Calculations based on an assumption of constant
clearance, such as the calculation of AUC are no
longer valid.

•A simple increasing of dose becomes an adventure.

•No longer can we increase the dose by some fraction,
for example 25%, and expect the concentration to
increase by the same fraction. The calculations are
more complex and must be done carefully.

20. Nonlinear Pharmacokinetics
•When we talked about linear kinetics we talked about
the time it takes to get to steady state concentrations.
With linear kinetics this time was independent of
concentration and could be calculated as 3, 4 or 5
half-lives.

•With non-linear kinetics, this time will increase with
concentration just as this psuedo half-life increases
with concentration.

21. •The relationship between elimination half-life
and drug concentration is shown in Equation
10.16. The elimination half-life is dependent
on the Michaelis–Menten parameters and
concentration

22. Nonlinear Pharmacokinetics
•This is very important when we use steady state
concentrations to make parameter estimates. If
we don't wait long enough our determination of
steady state concentration will be in error and so
will the parameter estimates.

•This time to steady state might change from a few
days to weeks as the dose is increased.

23. Nonlinear Pharmacokinetics
•The presence of saturation
kinetics can be quite important
when high doses of certain
drugs are given, or in case of
over-dose.
•In the case of high dose
administration the effective
elimination rate constant is
reduced and the drug will
accumulate excessively if
saturation kinetics are not
understood.

24. Nonlinear Pharmacokinetics (Phenytoin)
•Phenytoin is an example of a drug which commonly
has a K
m value within or below the therapeutic range.
–The average K
m value is about 4 mg/L.
–The normally effective plasma concentrations for phenytoin
are between 10 and 20 mg/L.
•Therefore it is quite possible for patients to be
overdosed due to drug accumulation.
•At low concentration the apparent half-life is about 12
hours, whereas at higher concentration it may well be
much greater than 24 hours.

25. •Dosing every 12 hours, the normal half-life, can rapidly
lead to dangerous accumulation.
•At concentrations above 20 mg/L elimination maybe
very slow in some patients. Dropping for example from
25 to 23 mg/L in 24 hours, whereas normally you
would expect it to drop from -25> -12.5> 6 mg/L in 24
hours.
•Typical V
m values are 300 to 700 mg/day. These are the
maximum amounts of drug which can be eliminated
by these patients per day. Giving doses approaching
these values or higher would cause very dangerous
accumulation of drug.
Nonlinear Pharmacokinetics (Phenytoin)

26. C
p
ss
profile following different doses of
Phenytoin.

27. Determination of K
M and V
max
•When an experiment is performed with solutions
of various concentration of drug C, a series of
reaction rates (v) may be measured for each
concentration. maxmax
max
11
VCV
K
CK
CV
M
M






28. Determination of K
M and V
max
•A plot of 1/v versus 1/C is
linear.

•The y-intercept for the line
is 1/V
max.


•The slope is K
M/V
max.
Plot of 1/v versus 1/C
for determining K
M and V
max.

29. Linear & Nonlinear
Linear Nonlinear

30. Linear & Nonlinear
Linear

Nonlinear

31. Linear & Nonlinear
Linear

Nonlinear