non linear pharmacokinetics

1. Presentedby
MISS.JYOTIDIPAKMHOPREKAR
M Pharmacy(FirstYear,SemIi)
RollNo. 06
DEPARTMENTOF PHARMACEUTICS
SHREESANTKRUPACOLLEGEOF PHARMACYGHOGAON.

2. CONTENTS
Introduction
Linear and nonlinear pharmacokinetics
Detection of nonlinearity in pharmacokinetics
Causes of nonlinearity
Michaelis – Menten Equation
Estimation of Km and Vmax
Methods used to determine the Km and Vmax at a steady state

3. LINEAR PHARMACOKINETICS
At therapeutic doses, the change in amount of drug in the body or
the change in its plasma concentration due to absorption, distribution,
binding, metabolism or excretion is proportional to its dose, whether
administered as a single dose or as multiple doses.
In such situations, the rate process are said to follow first order or
linear kinetics and all semi log plots of C versus t for different doses,
when corrected for dose administered, are superimposable.
The important pharmacokinetic parameters is F, Ka , KE , Vd , ClR ,
ClH which describe the time course of a drug in the body remain
unaffected by the dose.
Pharmacokinetics is dose independent.

4. NON LINEAR PHARMACOKINETICS
The rate process of a drugs ADME are dependent upon carrier or
enzymes that are substrate specific, have definite capacities, and
susceptible to saturation at high drug concentration.
In such cases, an essentially first order kinetics transform into a
mixture of first order and zero order rate processes and the
pharmacokinetic parameters change with the size of the administered
dose.
Pharmacokinetics of such drugs are said to be dose dependent.
Other terms synonymous with it are mixed order, nonlinear and
capacity limited kinetics.

5. DETECTION OF NON LINEARITY IN PHARMACOKINETICS
There are several tests to detect non linearity in pharmacokinetics but
the simplest ones are :
1) Determination of steady state plasma concentration at different
doses.
2) Determination of some of the important pharmacokinetic
parameters such as friction bioavailable, elimination half life or
total systemic clearance at different doses of drug. Any change in
these parameters which are usually constant, is indicative of
nonlinearity.

6. CAUSES OF NON LINEARITY
Nonlinearities can occur in drug absorption, distribution, metabolism
and excretion.
Drug Absorption
Nonlinearity in drug absorption can arise from 3 important sources :
1) When absorption is solubility or dissolution rate limited e.g.
griseofulvin. At high concentration in intestine.
2) When absorption involves carrier mediated transport systems
e.g. absorption of riboflavin, ascorbic acid, cynacobalmin, etc.
3) When presystemic gut wall or hepatic metabolism attains
saturation e.g. propranolol, hydralazine and verapamil.
• These parameters affected F, Ka , Cmax , AUC.

7. Drug Distribution
Nonlinearity in distribution of drugs administered at high doses may
be due to :
1) Saturation of binding sites on plasma proteins e.g.
phenylbutazone and naproxen
2) Saturation of tissue binding sites e.g. thiopental and fentanyl.
• In both cases the free plasma drug concentration increases
• But Vd increases in (1)
• Clearance of a drug with high ER is greatly increased due to
saturation of binding sites.

8. Drug Metabolism
• The nonlinear kinetics of most clinical importance is capacity limited
metabolism, small changes in dose administered can produce large
variations in plasma concentrations at steady state.
Two important causes :
1) Capacity limited metabolism due to enzyme and/or cofactor
saturation. e.g. phenytoin, alcohol.
2) Enzyme induction - decrease in plasma concentration e.g.
carbamazepine.
• Autoinduction in dose dependent concentration.
• Saturation of enzymes decreases in ClH and increases in Css.

9. • Reverse is true for enzyme induction.
• Other causes of nonlinearity in biotransformation include
saturation of binding sites, inhibitory effect of the metabolite on
enzyme and pathological situations such as hepatotoxicity and
changes in hepatic blood flow.

10. Drug Excretion
• The two active processes in renal excretion of a drug that are
saturable .
1) Active tubular secretion e.g. penicillin G
2) Active tubular reabsorption e.g. water soluble vitamins and
glucose.
• Other sources of nonlinearity in renal excretion include forced
diuresis, changes in urine pH, nephrotoxicity, and saturation of
binding sites.
• Biliary secretion which is also an active process, is also subject to
saturation e.g. tetracycline and indomethacin.

11. Examples of drugs showing nonlinear pharmacokinetics
Causes
GI absorption :
Saturable transport in gut wall
Saturable GI decomposition
Intestinal metabolism
Distribution :
Saturable plasma protein binding
Tissue binding
Metabolism :
Saturable metabolism
Metabolite inhibition
Renal elimination :
Active secretion
Tubular reabsorption
Change in urine pH
Drugs
Riboflavin, Gabapentin, Penicillin
G, Omeprazole, Propranaolol,
Salicylamide
Phenylbutazone, Lidocaine,
Imipramine
Phenytoin, Salicylic acid,
Carbamazepine, Diazepam
P- aminohippuric acid, Ascorbic
acid, Riboflavin, Salicylic acid,
Dextroamphetamine.

12. MICHAELIS – MENTEN EQUATION
[E]+[P]
[E]+[S]

13. Three situations can now be considered depending upon the values
of Km and C :

14. ESTIMATION OF Kmax AND Vmax
V = reaction rate
C = substrate concentration
Method 1
By reciprocating equation

15. Method 2
Multiplying equation (ii) by C

16. Method 3
The equation can also be written as

17. Calculation of by steady state concentration Km and Vmax
If drug is administered for constant rate by IV infusion in a multiple
dosage regimen the steady state concentration is given in terms of
dosing rate [DR]

18. If the steady state is reached then
Dosing rate =rate of decline in plasma concentration
If decline is occurs due to a single capacity limited process then
equation (i) becomes,

19. METHODS USED TO DETERMINE THE KM AND VMAX AT
A STEADY STATE
1) Lineweaver Burk plot method
2) Direct linear plot method
3) Graphical method

20. 1) Lineweaver Burk plot method
If decline occurs due to a single capacity limited process the
equation (i) becomes

21. 2) Direct linear plot method

22. 3) Graphical method
If decline occurs due to a single capacity limited process then
equation (i) becomes