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1. NON - LINEAR
PHARMACOKINETICS
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2. Contents
Introduction
Definition
Saturable enzymatic elimination process
Drug elimination by capacity limited pk
Mixed drug elimination
Time dependent PK
Conclusion
References
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3. LINEAR PHARMACOKINETICS
• linear kinetics : In most cases, at therapeutic doses, the change in
the amount of drug in the body or change in plasma concentration
due to ADME is directly proportional to its dose, whether single or
multiple dose. In such situations, the rate process are said to follow
first order or linear kinetics.
• Plot on semilog paper C vs t for different doses, when corrected for
dose administered, are super impossible. This is called as principle
of superposition.
• It defines the relationship between the dose & the time course of
drug concentration in the body..
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4. NON LINEAR PHARMACOKINETICS2
• Synonyms: Capacity limited Kinetics, Mixed order Kinetics
(Dose Dependent Kinetics) ,Nonlinear
• Why it is known as Mixed order kinetics?
In some cases the kinetics of PK process changes from 1st
order to zero order with increase in dose or chronic
medication. So mixture of both 1st and zero order observed
in such cases.
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6. Causes of Non- Linearity
• Drug Absorption
– When absorption is solubility or dissolution is rate limited eg.
Griseofulvin
– When absorption involves carrier mediated transport system eg.
Riboflavin
– Hepatic metabolism attains saturation eg. Propranolol,Verapamil
• Drug Distribution
– Saturation of binding sites on plasma protiens eg. Phenylbutazone,
Naproxen
– Saturation of tissue binding site eg. Thiopental
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7. • Drug Metabolism
– Capacity limited metabolism due to enzyme and
cofactorsaturation. eg. Phenytoin, alcohol.
– Enzyme induction eg. Carbamazepine
• Drug Excretion
– Active tubular secretion eg. Penicilin G
– Active tubular reabsorption eg. Glucose, water soluble
vitamins
– Change in urine pH, nephrotoxicity & saturation of binding
sites
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8. CONDITIONS WHEN DRUG FOLLOWS
NON LINEAR PHARMACOKINETICS3
• Plasma concentration time profile is not linear.
• AUC is not proportional to administered dose after
administration of single dose.
• Steady state plasma concentration is not proportional to
administered dose during multiple drug administrations.
• Estimated PK parameters such as half- life and total body
clearance are different after administration of different doses.
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9. SATURABLE ENZYMATIC ELIMINATION
PROCESS2
• MICHAELIS MENTEN Equation –
- dc/dt = Vmax C/ Km +C----------(1)
Where,
-dc/dt = rate of decline of drug conc.with time
Vmax = theoretical maximum rate of the process
Km = Michaelis constant
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11. Now t
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12. 2) When Km >> C ,
Here Km + C = Km and the equation (1)
becomes ,
- dc/ dt = VmaxC/Km
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13. DRUG ELIMINATION BY CAPACITY LIMITED
PK
(Estimation of Vmax & Km )2
• Parameters of capacity limited processes like metabolism,
renal tubular secretion & billiary excretion defined by
assuming one compartment kinetics for the drug & that
elimination involves only a single capacity limited process.
• Parameters Km & V max can be assessed from plasma
concentration time data collected after I.V. bolus
administration of drug with non linear elimination
characteristics.
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14. Now rewriting Michaelis Menten equation,
-dc/dt =VmaxC/Km+c
Integrating above eqn to log base 10 yields ,
Logc=logCo+(Co-C)/2.303Km –(Vmax)/2.303Km
….. (2)
A semilog plot of C versus t yields a curve with a terminal linear
portion having slope -Vmax/2.303Km and when back extra
plotted to time zero gives Y intercept log Co
The equation that deascribes this line is
log C = log Co – Vmax/2.303 Km ….. (3)
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15. Fig.-semilog plot of A drug given as i.v. Bolus With non linear
elimination& that fits one compartmet kinetics.
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16. At low plasma concentration equation (2) & (3) are identical.
Equating the two and simplifying further we get
(Co- C) / 2.303 Km = log Co / Co
From above equation we can calculate Km and Vmax can be
obtained by substituting the value of Km in the slope value.
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18. Mixed Drug Elimination1
• Drugs may be metabolized to several different metabolites by
parallel pathways.
• At low drug doses corresponding to low drug concentrations at the
site of the biotransformation enzymes, the rates of formation of
metabolites are first order.
• However, with higher doses of drug, more drug is absorbed and
higher drug concentrations are presented to the biotransformation
enzymes.
• At higher drug concentrations, the enzyme involved in metabolite
formation may become saturated, and the rate of metabolite
formation becomes nonlinear and approaches zero order. Ex.
Sodium salicylate 18

19. The equation that describes a drug that is eliminated
by both first-order and Michaelis–Menten kinetics
after IV bolus injection is given by
where k is the first-order rate constant representing the
sum of all first-order elimination processes,
(V’maxCp/Km+Cp) = saturable process.
V'max is simply V max expressed as concentration by
dividing by V D.
-dCp/dt= kCp+(V’maxCp/Km+Cp)
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20. Time-dependent pharmacokinetics1
• Time-dependent pharmacokinetics generally refers to a
noncyclical change in the drug absorption or drug
elimination rate process over a period of time.
• Time-dependent pharmacokinetics leads to nonlinear
pharmacokinetics. Unlike dose-dependent
pharmacokinetics, which involves a change in the rate
process when the dose is changed.
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22. Conclusion
• Non linear pharmacokinetic is observed when absorption
,distribution or elimination processes can be saturated at a
high drug concentration.
• Drugs that behave non linearly within the therapeutic range
(Ex.-Phenytoin shows saturable metabolism ) yields less
predictable results in drug therapy & possesses greater
potential in precipitating a toxic effects.
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23. References
1) Shargel Leon, Susanna Wu-pong, Andrew B.C.YU, “Applied
Biopharmaceutics & Pharmacokinetics", 5thedition2005;
published by Mc Graw Hill page no-219-241
2) Biopharmaceutics and pharmacokinetics. D.M Brahmankar and
Sunil. B .Jaiswal, ,1st edition page no-305-313
3) Basic pharmacokinetics M.A.Hedaya CRC press first indian
reprint page no-169-180
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