BASIC KINETIC PARAMETERS,POSSIBLE CAUSES OF NON INDUCTION, NON-LINEAR BINDING, NON LINEARITY OF PHARMACOLOGICAL RESPONSES

By M. Priyanka

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CONTENTSI. Basic kinetic parameters

a) Absorption rate constantb) Elimination rate constantc) Volume of distributiond) Renal clearancee) Hepatic clearancef) Bioavailability fraction

II. Possible causes of non – inductiona) Drug absorptionb) Drug distributionc) Drug metabolismd) Drug excretion

III. Non linear bindingIV. Non linearity of pharmacological responses

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BASIC KINETIC PARAMETERS The main basic pharmacokinetic parameters in non–linear

pharmacokinetics are

Absorption rate constant(ka) Elimination rate constants(kE) Apparent volume of distribution(vd) Renal clearance(clR) Hepatic clearance(clH) Bioavailability fraction(F)

In non – linear pharmacokinetics these parameters will change depending upon its administered dose

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1. Absorption rate constant (ka):- It is expressed by ka

The rate of drug absorption can be zero order, first order, pseudo zero order, pseudo first order etc.,

For immediate release dosage form, ka is first order because of physical nature of drug diffusion

For IV infusion & certain controlled release drug products, ka will be zero order rate constant

ka can be determined by Method of residuals Flip flop method of ka & kE

Wagner – Nelson method Loo – Riegelman method

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Importance of ka :- Designing a multiple dosage regimen ka & ke helps to predict peak & through plasma drug

concentrations following multiple dosing It can be used in Bio – equivalence studies

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2. Elimination rate constant (kE):-kE is summation of rate constants for each process like urinary excretion, metabolism, biliary excretion, pulmonary excretion etc.,

= km+ kb+ kI +……..For zero order, rate of elimination is constant irrespective of plasma concentration

Er = kE

For first order, rate of elimination is proportional to plasma concentration. Constant fraction of drug eliminated per unit time

Er = dc/dt = - kE C

Importance of Elimination rate constant :- Determination of kE is important for selection of dose regimen Also in dose adjustment in renal impairment

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3. Volume of Distribution (Vd):-

It is also known as apparent volume of distribution, which is used to quantify the distribution of a medication between plasma & the rest of the body after oral or parental dosing.

It is defined as the volume in which the amount of drug would need to be uniformly distributed to produce the observed blood concentration

Volume of distribution may be increased by renal failure ( due to fluid retention) & liver failure (due to altered body fluid & plasma protein binding). Conversely it may be decreased in dehydration.

Vd is given by the following equation

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E.g:-

Importance of Vd :- The dose required to give a certain plasma concentration can be

determined if the Vd for that drug is known

Drug Vd

Warfarin

theophylline

Ethanol

8L

30L

30L

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4. Renal Clearance:-It is the volume of blood from which the drug is totally removed in

unit time through renal excretion. It is expressed as clR & the units are ml/min.

ClR is given by the following equation

physiologically,

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5. Hepatic Clearance (:- Hepatic clearance can be defined as the volume of blood perfusing

the liver that is cleared of the drug per unit time. can be given by the following equation

for certain drugs, the non renal clearance can be assumed as equal to hepatic clearance

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6. Bioavailability fraction (F):- The amount of drug that reaches the systemic circulation is called

as systemic availability or Bioavailability. The fraction of administered dose that enters the systemic

circulation is called as bioavailability fraction & is expressed as F

F can be given by the following equation

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POSSIBLE CAUSES OF NON-INDUCTIONThe term non – induction is used to represent non – linearity. Non linearity's can occur in drug absorption, distribution, metabolism & excretion

1. DRUG ABSORPTION :-Non linearity in drug absorption can arise from 3 sources –

When absorption is solubility or dissolution rate limited:-At higher doses, a saturated solution of the drug is formed in the GIT

or at any other extravascular site & the rate of absorption attains a constant value

E.g. Griseofulvin When absorption involves carrier mediated transport system:-

saturation of the transport system at higher doses of these vitamins results in non – linearity

E.g. absorption of riboflavin, ascorbic acid, cyanocobalamin

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When pre systemic gut wall or hepatic metabolism attains saturation:-

saturation of pre – systemic metabolism of these drugs at high doses leads to increased bioavailability E.g. propranolol, hydralazine & verapamil Other causes of non-linearity in drug absorption are

Changes in gastric emptying Changes in GI blood flow

The parameters effected will be F, Ka, Cmax, and AUC. A decrease

in these parameters is observed in the former two cases and an increase in the latter case.

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2. DRUG DISTRIBUTION:- Non-linearity in distribution of drugs administered at high doses may be due to Saturation of binding sites on plasma proteins:- there is a finite number of binding sites for a particular drug on plasma proteins & theoretically as the concentration is raised, so too is the fraction unbound E.g. Phenylbutazone, naproxen Saturation of tissue binding sites:-

with large single bolus doses or multiple dosing, saturation of tissue storage sites

can occur.E.g. Thiopental, Fentanyl

In both cases, the free plasma drug concentration increases but

Vd increases only in the former case whereas it decreases in the latter.

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3. DRUG METABOLISM :-Two important causes of non-linearity in metabolism are -

Capacity limited metabolism due to enzyme and/or co-factor saturation

E.g. Phenytoin, Alcohol, Theophylline Enzyme induction :-

decrease in peak plasma concentration has been observed on repetitive administration over a period of time. Auto induction characterized in this case is also dose-dependent. Thus, enzyme induction is a common cause of both dose & time dependent kinetics.

E.g. Carbamazepine Other causes of non-linearity in metabolism are -

saturation of binding sites Inhibitory effect of the metabolite on enzyme Pathological situations such as hepatotoxicity & changes in hepatic blood flow

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4. DRUG EXCRETION :-The two active processes in renal excretion of a drug that are saturable are –

Active tubular secretion :- after saturation of the carrier system, a decrease in renal clearance occurs E.g. Penicillin G

Active tubular reabsorption :- after saturation of the carrier system, an increase in renal clearance occurs E.g. water soluble vitamins, glucose

Biliary secretion :- which is also an active process, is also subject to saturation E.g. Tetracycline, Indomethacin

Other sources of non-linearity in renal excretion :- Forced diuresis Changes in urine Ph

Nephrotoxicity Saturation of binding sites

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DETECTION OF NON-LINEARITY :- Determination of steady state plasma concentration at

different doses :-If,Css is Xo (linear)Css is Xo (non-linear)

Determination of some important pharmacokinetic parameters :-

F, t1/2, C etc., are constant, any change in them will show non-linearity

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NON-LINEAR BINDINGA limited number of sites exist on plasma proteins. Average plasma concentration of albumin is 43g/L or 600 mm. the sites to which drugs bind in the tissue may be similarly limited. Consequently, the volume of distribution depends on drug concentrations, a concentrate-dependent behaviour.

Let us consider a hypothetical situation wherein 2 drugs are given by an I.V. bolus in equal doses. One drug is 90% protein bound whereas the other drug does not bind to the plasma protein and both are eliminated solely by glomerular filtration through the kidney.

B

Drug APlasma drug level

Time in hrsPlasma drug level – time profile of two drugs given in

equal doses

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In the above plot drug A represents 90% bound to plasma protein, curve B represents a drug not bound to plasma protein.

The protein bound drug is more concentrated in plasma than the drug that is not protein-bound. Free drug concentration of protein-bound drug is low and hence, its elimination rate will be slow when compared with the drug that does not bind to plasma protein. Further, the protein bound drug shows a non-linear elimination whereas the drug that is not bound to the plasma protein shows a linear elimination.

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A careful elimination of curve A reveals that the slope of the bound drug decreases gradually as the drug concentration decreases. It means that the free drug concentration decreases and bound drug concentration increases as the total drug concentration in plasma decreases. In other words, the ratio of the bound drug to free drug is not constant but increases at a low plasma concentration of the drug. Therefore, fitting the plasma concentration-time data of a protein-bound drug into a simple one compartment model without accounting for protein binding results in an erroneous estimation of volume of distribution & half life.

Drugs which are bound to plasma proteins will show non-linear kinetics compared to drugs which are not bound to plasma proteins.

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NON-LINEARITY OF PHARMACOLOGICAL RESPONSES

The empirical approach in optimization of drug therapy was based on relating pharmacological response to the dose administered. Given dose or dosing rate can result in large deviations in plasma drug concentration which in most cases are attributable to formulation factors, pharmacokinetics and pharmacological response.

Sometimes the pharmacological response may be non-linear due to – saturable absorption

saturable binding or reabsorption

Saturable elimination

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1. Saturable absorption: above a certain drug concentration at the absorption site, there is no further increase in the absorption rate. Therefore, absorption rate constant and possibly bioavailability decrease with doses leading to concentrations at the absorption site above the maximal absorption capacity.

2. Saturable binding or reabsorption: above a certain drug concentration, drug protein binding or drug reabsorption in kidney tubules tends to reach maximal capacity. This leads to a disproportionate increase in the rate of elimination with increasing drug concentrations (e.g. with high doses of vitamin).

3. Saturable elimination: above a certain drug concentration, the elimination rate tends to reach a maximal value. Once this maximum capacity is reached, there is no further increase in the elimination rate when plasma drug concentration increases. Therefore, in nonlinear elimination kinetics, the drug clearance decreases with increasing drug concentration.

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Example :- phenytoin

Phenytoin follows nonlinear (or zero-order) kinetics at therapeutic concentrations, because the rate of metabolism is close to the maximum capacity of the enzymes involved.

In nonlinear kinetics, clearance and half-life fluctuate with plasma concentration. As the rate of administration increases, the plasma concentration at steady state increases disproportionately. If the rate of absorption equals or exceeds the maximum rate of metabolism, steady state is never achieved.

This capacity-limited metabolism explains the inter-individual variability and the lack of predictability of the phenytoin plasma concentration-time profile, because the maximum capacity varies from patient to patient.

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REFERENCES

Biopharmaceutics and pharmacokinetics a treatise by D.M.Brahmankar and Sunil B. Jaiswal

Biopharmaceutics and pharmacokinetics by V. Venkateswarlu www.pharmaquest.weebly.com www.tmedweb.tulane.edu www.sepia.until.ch

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From

Priyanka