Non-linear pharmacokinetics occurs when some aspect of a drug's absorption, distribution, metabolism, or excretion is saturable at higher doses. This can be caused by saturation of enzymes involved in drug metabolism or transporters involved in absorption. The Michaelis-Menten equation can be used to describe non-linear kinetics, where Vmax is the maximum rate and Km is the substrate concentration at half Vmax. Km and Vmax can be estimated from plasma concentration-time data after IV administration or by plotting steady-state concentration against dosing rate. Non-linear kinetics is usually due to saturation of protein binding, hepatic metabolism, or renal transport of the drug.
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NON-LINEAR PHARAMACOKINETICS
β’ It is a Dose Dependent Pharmacokinetics.
β’ Non-Linear pharmacokinetics models imply that some aspect of the
pharmacokinetic behaviour of the drug is saturable.
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CAUSES DRUG
When absorption involves
carrier mediated transport
systems
Riboflavin, ascorbic acid
When presystemic gut wall or
hepatic metabolism attains
saturation
Propranolol
When absorption is solubility or
dissolution rate limited
Griseofulvin,
GI absorption
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MICHAELIS MENTEN EQUATION
β’ Non linear pharmacokinetics can be best described by michaelis menten
equation.
β
π πͺ
π π
=
π½ πππ πͺ
π² π + πͺ
Where:
o -dC/dt = Rate of decline of drug concentration with time.
o Vmax = Theoretical maximum rate of the process.
o Km = Michaelis-Menten constant.
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1. When π² π= C
β
π πͺ
π π
=
π½ πππ
π
2. When π² π ΛΛ C
β
π πͺ
π π
=
π½ πππ πͺ
π² π
3. When π² π ΛΛ C
β
π πͺ
π π
= π½ πππ
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Estimation of Km and Vmax :-
β’ The parameters π² πand π½ πππ can be assessed from the plasma drug
concentration time data collected after i.v. bolus administration of the drug
with non-linear elimination characteristics.
β
π πͺ
π π
=
π½ πππ πͺ π
π² π + πͺ π
(π)
β’ Integration of above equation
π₯π¨π πͺ = π₯π¨π πͺ π +
(πͺ π β πͺ)
π. ππππ² π
β
π½ πππ
π. ππππ² π
(π)
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A semi log plot of C versus t yields a curve with a terminal linear portion having
slope β π½ πππ π. ππππ² π and when back extrapolated to time zero gives y-
intercept πππ
πͺ π
.
ππππͺ = πππ
πͺ π
β
π½ πππ
π. ππππ² π
(π)
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At low plasma concentrations, equation (2) and (3) are identical. Equating the two
and simplifying further, we get:
(πͺ π β πͺ)
π. ππππ² π
= πππ
πͺ π
πͺ π
(π)
Km Can thus be obtained from above equation. Vmax Can be computed by
substituting the value of Km in the slope value.
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π² π πππ π½ πππ from steady state concentration:-
When a drug is administered as a constant rate i.v. infusion or in a multiple
dose regimen, the steady-state concentration Cssis given in terms of βdosing
rateβ DR as:
π«πΉ = πͺ πΊπΊ πͺπ π» (π)
Where DR= R0when the dose is administered as zero order i.v. infusion and
it is equal to FX0/Ο when administered as multiple dosage regimen (F is
fraction bioavailable, X0is oral dosage and Ο is dosing interval).
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At steady state, the dosing rate equals rate of decline in plasma drug
concentration and if the decline (elimination) is due to a simple capacity
limited process (for e.g. metabolism), then;
π«πΉ =
π½ πππ πͺ πΊπΊ
π² π+πͺ πΊ
(2)
A plot of CSS versus DR yields a typical hockey-stickshaped curve as
shown in figure:
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β’ The rate process of drugβs ADME are depends upon carrier or enzyme that
are substrate specific, have definite capacities and are susceptible to
saturation at a high drug concentration
β’ Nonlinear kinetics is usually due to saturation occuring in one of the
pharmacokinetic mechanisms: protein binding, hepatic metabolism, or active
renal transport of the drug.
CONCLUSION:-
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REFERENCE:-
β’ D M Brahmankar, Sunil B. Jaiswal, Biopharmaceutics and
pharmacokinetics, 3rd edition, Delhi, Vallabh Prakashan,
2015, p. 307-317