nonlinear pharmacokinetics

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Non Linear Pharmacokinetics:

Non Linear Pharmacokinetics Presented by: Lovenish Bhardwaj Department of pharmaceutical Technology, Meerut Institute of Information and Technology, Meerut

Difference between Linear and non linear pharmacokinetics:

Difference between Linear and non linear pharmacokinetics Linear pharmacokinetics Change in plasma concentration due to ADME process is proportional to dose of drug administered (single or multiple) Follow First order kinetics Semilog plot for concentration vs time is super imposable (Principle of superimposition) No change in F, Ka, Ke, Vd, Clearance etc.

Difference…………...contd.:

Difference…………...contd. Nonlinear Pharmacokinetics Rate process of ADME are dependent on carrier or enzymes having definite capacity and subjected to saturation. Change in concentration is no more proportional to dose administered during the total process of ADME. Follow First order + Zero order kinetics Change in different pharmacokinetic parameters.

Detection of non linearity:

Detection of non linearity Determination of steady state plasma concentration at different doses If: Css α Xo (Linear) Css α Xo (Non linear) Determination of some important pharmacokinetic parameters F, t 1/2 , Cl etc. are constant, any change show nonlinearity.

Stages at which Nonlinearity occur:

Stages at which Nonlinearity occur Non linearity can occur at any of the following stage during the fate of drug in body: Absorption Distribution Biotransformation/Metabolism Excretion

Causes of Nonlinearity:

Causes of Nonlinearity During absorption Absorption is solubility or dissolution rate limited eg. Griseofulvine Absorption involve carrier mediated transportation eg. Riboflavin, ascorbic acid Hepatic metabolism attain saturation eg. Propranolol, hydralazine

Causes………………….contd.:

Causes………………….contd. During Distribution Saturation of binding sites on plasma proteins eg. Phenylbutazone, naproxen. Saturation of tissue binding sites eg. Thiopental, fentanyl.

Causes………………….contd.:

Causes………………….contd. During Metabolism Capacity limited metabolism due to enzyme or cofactor saturation eg. Alcohol, Phenytoin. Enzyme induction eg. Carbamazepine

Causes………………….contd.:

Causes………………….contd. During Excretion Active tubular secretion eg. Penicillin G Active tubular re-absorption eg. Glucose, water soluble vitamins. Other sources: Forced Diuresis, change in urine pH, nephrotoxicity etc.

Michaelis Menten Equation:

Michaelis Menten Equation Nonlinear pharmacokinetics can be best described by Michaelis Menten Equation. _ dC Vmax . C dt Km + C Where: dC/dt : rate of decline in drug conc. with time Vmax : theoretical maximum rate of process Km : Michaelis constant

Equation………………contd.:

Equation………………contd. When Km = C _ dC Vmax dt 2 When Km>>C _ dC Vmax.C dt Km When Km<<C _ dC Vmax dt

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dC/dt Km Concentration Vmax Zero order rate at high doses Mixed order rate at intermediate doses First order rate at low doses Vmax 2

Estimation of Km and Vmax:

Estimation of Km and Vmax Integration of Michaelis Menten Equation log C = log Co + (Co – C) – Vmax 2.303Km 2.303Km Semilog plot of C vs t yields a curve with terminal linear portion, which on back extrapolation to time zero give y intercept log Co. log C = log Co – Vmax 2.303Km

Km and Vmax....……....contd.:

Km and Vmax....…….... contd. Log C Log Co Log Co Time (t) Terminal linear portion with slope= –Vmax/2.303 Km

Km and Vmax....……....contd.:

Km and Vmax....…….... contd. At low plasma concentration: (Co – C)/2.303 Km = log Co/Co So Km can be obtained from this equation while Vmax can be obtained from slope by putting value of Km.

Estimation of Km and Vmax (steady state):

Estimation of Km and Vmax (steady state) In case of I.V. infusion a steady state concentration is maintained by a suitable dosing rate (DR). This DR at steady state equals rate of elimination. So Michaelis Menten equation can be written: DR = Vmax . Css Km + Css

Km and Vmax (Steady state)....contd:

Km and Vmax (Steady state).... contd Lineweaver Burke Plot 1 = Km + 1 . DR Vmax.Css Vmax Slope = Km/Vmax 1/DR 1/Vmax 1/Css

Km and Vmax (Steady state)....contd:

Km and Vmax (Steady state).... contd Direct Linear plot Slope = Km/Vmax DR 1 Vmax Km DR 2 Css Km Css 1 Css 2 DR

Km and Vmax (Steady state)....contd:

Km and Vmax (Steady state).... contd Graphical Method Plot between DR and DR/Css yield straight line with slope: –Km, & y- intercept: Vmax DR = Vmax __ Km . DR Css

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Thank you