NONLINEAR PHARMACOKINETICS_ppt.pdf

NON LINEAR PHARMACOKINETICS

1. #
Ms. KIRTI GOEL
ASSISTANT PROFESSOR, MMCP, MM(DU)

2. CONTENTS
#
Introduction
Linear & Nonlinearity Pharmacokinetics
Detection of non-linearity in pharmacokinetics
Causes ofnonlinearity
Michaelis–Mentenequation
Estimation of K
m andV
max
Estimation of K
m and V
max at steady-stateconcentration

3. »Attherapeuticdoses,thechangeintheamountofdrugin
thebodyorthechangeinitsplasmaconcentrationdueto
absorption,distribution,binding,metabolismorexcretion,is
proportionaltoitsdose,whetheradministeredasasingledose
orasmultipledoses.
»Insuchsituationtherateprocessesaresaidtofollwfirst
orderorlinearkineticsandallsemilogplotsofCVstfor
differentdoseswhencollectedfordoseadministered,are
superimposable.
#
LINEARPHARMACOKINETICS

4. » The important pharmacokinetic
parameters viz. F, K
a, K
E, Vd, Cl
R, Cl
H which
describes the time course of a drug in the body remain
unaffected by thedose.
#
» Pharmacokinetics is doseindependent.

5. NONLINEARPHARMACOKINETICS
»Therateprocessofdrug’sADMEaredependuponcarrier
orenzymesthataresubstratespecific,havedefinitecapacities
andaresusceptibletosaturationatahighdrugconcentration.
»Insuchcases,anessentiallyfirst-orderkineticstransform
intoamixtureoffirst-orderandzero-orderrateprocessesand
thepharmacokineticparametersarechangedwiththesizeof
theadministereddose.
»Pharmacokineticsofsuchdrugsaresaidtobedose-
dependent.Termssynonymouswithitaremixed-order,
nonlinear and capacity-limitedkinetics.

6. DETECTION OF NON -LINEARITY IN
PHARMACOKINETICS
•There are several tests to detect non –linearityin
pharmacokinetics but the simplest onesare:
1)First test:-Determinationofsteadystateplasma
concentrationatdifferentdoses.
2)Second test:-Determinationofsomeimportant
pharmacokinetic parameterssuch as fraction
bioavailability, elimination half lifeor total systemic
clearanceat different doses of drug. Any change in these
parameters is indicative to non-linearity which are
usuallyconstant.

7. CAUSES OFNON-LINEARITY
•Threecauses:-I) Solubility / dissolution of drug is rate-limited;
Griseofulvin -at high concentration inintestine.
II)Carrier -mediated transport system; Ascorbic
acid -saturation of transportsystem.
III)Presystemic gut wall / hepatic metabolism
attains saturation; Propranolol.
•TheseparametersaffectedF, K
a, C
max and AUC.
•A decrease in these parameters is observed in former two causes
and an increase in latter cause.
Drugabsorption

8. At high doses non-linearity dueto
•Twocauses:-I) Binding sites on plasma proteins get
saturated; Phenylbutazone.
II) Tissue binding sites getsaturated.
•In both cases there is increase in plasma drug
concentration.
•Increase in V
d only in(I)
•Clearance with high ER get increased due to saturation of
bindingsites.
Drugdistribution

9. •Non-linearity occurs due to capacity limited metabolism, small
changes in dose administration -large variations in plasma
concentration at steady state -large intersubjectvariability.
•Two imp causes:-I) Capacity -limited metabolism -enzyme&/
cofactor saturation; Phenytoin, Alcohol.
II) Enzyme induction -decrease in plasma
concentration;Carbamazepine.
•Autoinduction in dose dependentconcentration.
•Saturation of enzymes -decrease inCl
H -increase inC
ss.
•In case of enzyme induction reversecondition.
•Other reasons includes saturation of binding sites, inhibitory
effects of the metabolites on the action ofenzymes.
Drugmetabolism

10. Drugexcretion
•Saturation of carrier systems -decrease in renal clearance in case of I
& increase in II. Half life alsoincreases.
•Other reasons like forced diuresis, change in urine pH,
nephrotoxicity & saturation of bindingsites.
•In case of biliary excretion non -linearity due to saturation -
Tetracycline &Indomethacin.
•Two active processes which aresaturable,
I)Active tubular secretion -Penicillin G
II)Active tubular reabsorption -Water soluble
vitamins &Glucose.

11. Examples of drugs showing nonlinearpharmacokinetics
Cause Drugs
GIabsorption:-
Saturable transport in gut wall
Saturable GI decomposition
Intestinal metabolism
Distribution:-
Saturable plasma protein binding
Tissuebinding
Metabolism:-
Saturablemetabolism
Enzyme induction
Metabolite inhibition
Renal elimination:-
Active secretion Tubular
reabsorption Change in
urinepH
Riboflavin, Gabapentin
Penicillin G, Omeprazole
Propranolol,Salicylamide
Phenylbutazone,Lidocaine
Imipramine
Phenytion, Salicylicacid
Carbamazepine
Diazepam
Para-aminohippuric acid
Ascorbic acid, Riboflavin
Salicylic acid,Dextroamphetamine

12. MICHAELIS MENTEN-ENZYME KINETICS
It is also called as Capacity-limited metabolism orMixed
orderkinetics.
E+ S ES E+M
Enzymes usually react with the substrate to form enzyme
substrate complexes; then the product is formed. The
enzyme can go back to react with another substrate to
form another molecule of theproduct.
#

13. MICHAELIS MENTENEQUATION
•The kinetics of capacity limited or saturable processes is best described by
Michaelis-Mentenequation.
-dC/dt = rate of decline of drug conc. with time
V
max = theoretical maximum rate ofthe
process
K
M = Michaelisconstant
•Three situation can now be considered depending upon the value of K
m and
C.
•
•
•
•
1)when K
M =C:
under this situation , eq I reducesto,
-dC/dt = V
max/2...................II
The rate of process is equal to half of its maximum rate.
This process is represented in the plot of dc/dt vs. C. shown in fig.1
dC
=
V
max .C
K
M+Cdt
Where,
……………….. I

14. #
2)If a drug at low conc. undergoes a saturable
biotransformation thenK
M>>C:
•here , K
M +C =K
M and eq. I reducesto,
-dC/dt =V
max C/K
M………………III
• above eq. is identical to the one that describe first order elimination of
drug, where V
max/K
M=K
E.
3)WhenK
M<<C:
•Under this condition ,K
M +C= C and eq. I willbecome,
-dC/dt =V
max…………….IV
above eq. is identical to the one that describe a zero order process i.e.
the rate process occurs at constant rate V
max and is independentof
drug conc.
E.g. metabolism ofethanol

15. Dc
dt
Zero order rate
at highdoses
Mixed order rate at
intermediateddoses
First order rate at lowdoses
C
Figure1
A plot ofMME
#

16. ESTIMATION OF V
max&K
m
•K
M +C
•where,V=reactionrate,
•C=substrateconc.
bothareusedto
determineVmax&
Km.
•Thevelocityofthereaction(V)atvariousconcentrationlevelsof
drug(C)aredeterminedeitherbyin-vitroexperimentsorin-vivo
experimentsatconstantenzymelevels.
In enzymatic kinetic work, the classic Michaelis-Menten
equation:
………..(1)
V=
Vmax .C
#

17. Method1
#
By reciprocating equation (1), we get:
1
=
Km.1
+
1……..(2)
VVmax.CVmax
When 1/V is plotted against 1/C, a straight line is
obtained with a slope of Km/Vmax and an Intercept of
1/Vmax.
E.g. : A plot of 1/ V vs 1/ C (shown in the fig.2)
gave an intercept of 0.33µmol and a slope of 1.65, Now,
calculate Vmax andK
M.

18. #
Figure2
Plot of 1/V vs 1/C for determining Km &Vmax
Now,Intercept= 1/ Vmax = 0.33 µmol.
Vmax = 3 µ mol/mlmin
Slope = Km/ Vmax So, 1.65 = Km/ Vmax
Km = 1.65 Х 3 = 4.95µmol/ml
X-axis intercept= -1/Km
Km/Vmax
1/Vmax
-1/Km

19. Multiplyingeq. 2 by C, we get:
CKm C
= + ……….....(3)
VVmaxVmax
A plot ofC /V vs C gives a straight line with 1 / Vmax as the slope and
Km / Vmax as the intercept (shown in the fig.3).
Method2
#

20. Figure3.
Plot of C/V vs C for determining Km &Vmax
ax
#
ax

21. …………(4)
#
The equation can also bewritten
as:
V=-KmV+Vmax
C
A plot ofVvsV / C gives a straight line with a slope of –Km & an Intercept
of Vmax. (shown in the fig.4)
Method3

22. Figure4
#
Plot of V vs V / C for determining Km &Vmax

23. CALCULATION OF K
M& V
MAX
STEADY-STATECONCENTRATION
•If drug is administered for constant rate IV infusion/ in a multiple
dosage regimen, the steady-state conc. is given in terms of
dosing rate(DR):
DR = C
ssCl
T
•If the steady-state is reached, then the dosing rate = the rateof
decline in plasma drug conc. & if the decline occurs due to a
single capacity-limited process then eq. I becomeas:
•From a plot of C
ssvs. DR, a typical curve having a shape of
hocky-stick is obtained which is shown in fig.5.
……………….. (1)
V
maxC
ss
#
M
K +C
ss
DR=
……………….. (2)

24. C
ss
K
m
V
max /2 V
max
DR (in mg/hr or mg/day)
#
Curve for a drug following nonlinear kinetics
By plotting the steady-state concentration against dosingrates
Figure5

25. METHODSUSEDTO
DETERMINETHE
K
M& V
MAXAT
STEADY-STATE
#

26. •There are three methods which are used to define the K
M
& V
maxat steady-state with appreciableaccuracy:
1)Lineweaver-Burk Plot:-the reciprocal of eq. (2) weget
•If 1/DR is plotted against 1/C
ss a straight line is obtained
having slope K
M/V
max & y-intercept1/V
max.
2)Direct linearplot:-
•Plotting a pair of C
ss, i.e.C
ss1,&C
ss2 against corresponding
dosing rates DR
1 & DR
2 we get following fig. 6 which
gives values K
M&V
max
DR
1
=
K
M
V
maxC
ss
1
+
V
max
……………….. (3)
#

27. #
C
ss
C
ss1 C
ss2
0 K
M
K
M
DR
DR
1
DR
2
V
max
Direct linear plot for
estimationof K
M & V
max
at steady-state conc. Of a drug, when it is
administered at different dosingrates
Figure6

28. Figure7
Plot of DRvs DR/C
ssfor determining Km &Vmax
DR
DR/C
ss
#
3)Graphical
method:-

29. 3)Graphicalmethod:-
•In this method by rearranging eq. (2) weget
•In graph DR is plotted against DR/Css, a straight line is
obtained with slope –K
M & y -interceptVmax.
•K
M & Vmax can be estimated by simultaneous eq.as
C
ss
K
MD
R ……………….. (4)
1
2
……………….. (6)
…………….…...(5)
DR=V
max-
DR=V
max
DR=V
max
-
-
K
MD
R1
#
C
ss1
K
MD
R2
C
ss2

30. •
On solving above
eq. 5 & 6 weget,
•
•By substituting values of DR
1, DR
2, C
ss1 & C
ss2 we get value of
K
M & from K
M we can found value of V
maxat steady-state
concentration.
From experimental observations, it shows that K
M is much
less variable than V
max.
M
K=
DR
2-DR
1
DR
1
-
DR
2
C
ss1C
ss2
……………….. (7)
#

31. QUESTIONS
#
1.Explain the non-linear pharmacokinetics of a drug giventhrough
I.V. bolus injection. (‘07)
2.Write Michaelis-Menten equation. How is V
max and K
M estimated.
(Sep’05)
3.Discuss Michaelis-Menten equation.(‘06)

32. REFERENCE
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1.Biopharmaceutics and Pharmacokinetics a treatise by
Brahmankar DM, JaiswalSB.
2.http://google.co.in
3.Biopharmaceutics & pharmacokinetics by Dr. ShobhaRani
R. Hiremath.

33. #