Download Non Linear Pharmacokinetics

UNIT 4
Non Linear Pharmacokinetics
S. SANGEETHA., M.PHARM., (Ph.d)
Department of Pharmaceutics
SRM College of Pharmacy
SRM University
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.
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
• 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, t1/2 , Cl etc. are constant, any change show nonlinearity.
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
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.
During Distribution
• Saturation of binding sites on plasma proteins eg. Phenylbutazone, naproxen.
• Saturation of tissue binding sites eg. Thiopental, fentanyl.
Causes………………….contd.
During Metabolism
• Capacity limited metabolism due to enzyme or cofactor saturation eg. Alcohol, Phenytoin.
• Enzyme induction eg. Carbamazepine
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
• 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.
• When Km = C
_ dC
dt Vmax 2
_ dC
dt Vmax.C Km
• When Km>>C
• When Km<<C
_ dC
dt Vmax
Vmax
dC/dt
Vmax
2
Zero order rate at high doses
Mixed order rate at intermediate doses
First order rate at low doses
Km
Concentration
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.
Log Co
Log Co
Log C
Terminal linear portion with slope= –Vmax/2.303 Km
Time (t)
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)
• 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
• Lineweaver Burke Plot
Km + 1 .
1 = DR Vmax.Css Vmax
1/DR
Slope = Km/Vmax
1/Vmax
1/Css
Km and Vmax (Steady state)....contd
• Direct Linear plot
DR
Vmax
DR1
DR2
Css1
Css2
Slope = Km/Vmax
Km
Css
Km
Km and Vmax (Steady state)....contd
• Graphical Method
DR = Vmax __ Km . DR
Css • Plot between DR and DR/Css yield straight line with slope: –Km, & y‐ intercept: Vmax