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Page 1: Nonlinear pharmacokinetic

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Page 2: Nonlinear pharmacokinetic

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Mohi-ud-Din Islamic Institute ofMohi-ud-Din Islamic Institute ofPharmaceutical Sciences.Pharmaceutical Sciences.

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-:PRESENTED BY:-Muslim Khan

Class: 4th Year Pharm-DRoll No# 19

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CONTENTS

Introduction

Nonlinearity Pharmacokinetic

Causes of nonlinearity

Michaelis – Menten equation

Estimation of Km and Vmax

Estimation of Km and Vmax at steady-state concentration

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» Dose independent paharmacokineticPharmacokinetic paraméters dont change with increse or decrease in dose » In such situation the rate processes are follw first order or linear kinetics and all semilog plots of C Vs t for different doses are superimposable.

LINEAR PHARMACOKINETICS

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NONLINEAR PHARMACOKINETICS

» Dose dependent paharmacokinetic Pharmacokinetic paraméters change with increse or decrease

in dose

Pharmacokinetic paraméters(ADME ) are depend upon carrier or enzymes that are substrate specific, have definite capacities and are susceptible to saturation at a high drug concentration.

» In such cases, first-order kinetics transform into a mixture of first-order and zero-order rate processes

»

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Linear Pharmacokinetics Non Linear Pharmacokinetics

Pharmacokinetic parameters for a drug would not change with change in dose

Pharmacokinetic parameters for a drug can change with change in dose.

Dose Independent Dose dependent

First Order kinetics Also called as Mixed order, Saturated kinetics, capacity limited

All semilog plots of C vs t for diff. doses are superimposable.

Not superimposable

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CAUSES OF NON-LINEARITY

• Three causes:- • I) Solubility / dissolution of drug is rate-limited; Griseofulvin - at high concentration in intestine.

II) Carrier - mediated transport system; Ascorbic acid - saturation of transport system.

III) Presystemic gut wall / hepatic metabolism attains saturation; Propranolol.

Drug absorption

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At high doses non-linearity due to• Two causes:- • I) Binding sites on plasma proteins get saturated; Phenylbutazone.

• II) Tissue binding sites get saturated.

• In both cases there is increase in plasma drug concentration.

.

Drug distribution

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• Non-linearity occurs due to capacity limited metabolism, small changes in dose administration - large variations in plasma concentration at steady state.

• Two imp causes:-• I) Capacity - limited metabolism - enzyme &/ cofactor saturation; Phenytoin, Alcohol.

• II) Enzyme induction - decrease in plasma concentration; Carbamazepine.

Drug metabolism

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Drug excretion

• Two active processes which are saturable, I) Active tubular secretion - Penicillin G II) Active tubular reabsorption - Water soluble vitamins & Glucose.

• Saturation of carrier systems - decrease in renal clearance & increase in Half life.• Other reasons like forced diuresis, change in urine pH,

nephrotoxicity & saturation of binding sites.• In case of biliary excretion non - linearity due to saturation -

Tetracycline & Indomethacin.

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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.

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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).

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Saturable Enzymatic Elimination Processes

• Michaelis–Menten kinetics:

dCp/dt = rate of decline of drug concentration with time.Vmax = theoretical maximum rate of the process.Km = Michaelis constant.

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C p >> K m C p = K m C p << K m

• saturation of the enzymes occurs.•The value for K M is negligible.•The rate of elimination proceeds at a constant rate

•Rate of process is = one half of its max. rate

• -dc/dt = Vmax/2

•rate of drug elimination becomes a first-order process

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Drug Elimination by CapacityLimitedPharmacokinetics: One-Compartment Model, IV Bolus Injection:

• If a single IV bolus injection of drug (D 0) is given at t = 0, the drug concentration (C p) in the plasma at any time t may be calculated by an integrating equation,

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• Amount of drug in the body after IV Bolus ,

• Where, D 0 is the amount of drug in the body at t = 0.

• To calculate time for dose in the boy • Rearranging equation:

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Determination of K M and V max

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ESTIMATION OF Vmax & Km

In enzymatic kinetic work, the classic Michaelis-Menten equation:

Vmax . C ………..(1) KM + C where, V= reaction rate, C= substrate conc. both are used to determine Vmax & Km.The velocity of the reaction(V) at various concentration levels of drug(C) are determined either by in-vitro experiments or in-vivo experiments at constant enzyme levels.

V =

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Method 1

By inverting equation (1), we get : 1 Km . 1 1 ……..(2) V Vmax . C Vmax

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.

= +

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Figure 2Plot of 1/V vs 1/C for determining Km & Vmax

-1/ Km

Km/Vmax

1/ Vmax

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Multiplying eq. 2 by C, we get :

C Km C = + ………..... (3) V Vmax Vmax

A plot of C /V vs C gives a straight line with 1 / Vmax as the slope andKm / Vmax as the intercept (shown in the fig. 3).

Method 2

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Figure 3. Plot of C/V vs C for determining Km & Vmax

ax

ax

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The equation can also be written as :

V = - Km V + Vmax …………(4) C

A plot of V vs V / C gives a straight line with a slope of –Km & an Intercept of Vmax. (shown in the fig. 4)

Method 3

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Figure 4Plot of V vs V / C for determining Km & Vmax

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CALCULATION OF KM & VMAX STEADY- STATE CONCENTRATION

• 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 = Css

• If the steady-state is reached, then the dosing rate = the rate of decline in plasma drug conc. & if the decline occurs due to a single capacity-limited process then eq. I become as:

• From a plot of Css vs. DR, a typical curve having a shape of hocky-stick is obtained which is shown in fig. 5.

……………….. (1)

=Vmax Css

KM+ CssDR ……………….. (2)

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Css

Km

Vmax / 2 Vmax

DR (in mg/hr or mg/day )

Curve for a drug following nonlinear kineticsBy plotting the steady-state concentration against dosing rates

Figure 5

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METHODS USED TO DETERMINE THE

KM & VMAX AT STEADY-STATE

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• There are three methods which are used to define the KM & Vmax at steady-state with appreciable accuracy:

1) Lineweaver-Burk Plot:- the reciprocal of eq. (2) we get

• If 1/DR is plotted against 1/Css a straight line is obtained having slope KM/Vmax & y-intercept 1/Vmax.

2) Direct linear plot:- • Plotting a pair of Css, i.e.Css1,&Css2 against corresponding

dosing rates DR1 & DR2 we get following fig. 6 which gives values KM &Vmax

1DR

=KM

Vmax Css

1Vmax

+ ……………….. (3)

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Css

Css 1 Css 2

0 KM

KM

DR

DR1

DR2

Vmax

Direct linear plot for estimation of KM & Vmax

at steady-state conc. Of a drug, when it is administered at different dosing rates

Figure 6

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3) Graphical method:-• In this method by rearranging eq. (2) we get

• In graph DR is plotted against DR/Css, a straight line is obtained with slope –KM & y - intercept Vmax.

• KM & Vmax can be estimated by simultaneous eq. as

DRDR

Css

KM= Vmax……………….. (4)

=DR1

=DR2……………….. (6)

…………….…...(5)

-

Vmax

Vmax

-

-

KM

KM

DR1

DR2

Css1

Css2

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• On solving above eq. 5 & 6 we get,

• By substituting values of DR1, DR2, Css1 & Css2 we get value of KM & from KM we can found value of Vmax at steady-state concentration.

• From experimental observations, it shows that KM is much less variable than Vmax.

KM =DR2- DR1

Css 1 Css 2

DR1 DR2-……………….. (7)

DR

3) Graphical method:-

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