This document discusses non-linear pharmacokinetics and pharmacodynamics. It begins by defining basic kinetic parameters like absorption and elimination rate constants, volume of distribution, and bioavailability fraction. It then explores possible causes of non-linearity, including saturation of absorption, distribution, metabolism and excretion processes. Non-linear binding due to saturation of plasma protein binding sites is also covered. The document concludes by giving an example of non-linear pharmacological responses with phenytoin, where capacity-limited metabolism leads to fluctuating clearance and half-life with changing plasma concentrations.

1. BASIC KINETIC PARAMETERS,
POSSIBLE CAUSES OF NON INDUCTION,
NON-LINEAR BINDING,
NON LINEARITY OF PHARMACOLOGICAL
RESPONSES
By M. Priyanka

2. CONTENTS
I. Basic kinetic parameters
a) Absorption rate constant
b) Elimination rate constant
c) Volume of distribution
d) Renal clearance
e) Hepatic clearance
f) Bioavailability fraction
II. Possible causes of non – induction
a) Drug absorption
b) Drug distribution
c) Drug metabolism
d) Drug excretion
III. Non linear binding
IV. Non linearity of pharmacological responses 2

3. 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 3

4. 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
4

5. 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
5

6. 2. Elimination rate constant (kE):-
kE is summation of rate constants for each process like urinary excretion, metabolism,
biliary excretion, pulmonary excretion etc.,
kE= 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 6

7. 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
𝑽 𝑫 =
𝑻𝒐𝒕𝒂𝒍 𝒂𝒎𝒐𝒖𝒏𝒕 𝒐𝒇 𝒅𝒓𝒖𝒈 𝒊𝒏 𝒕𝒉𝒆 𝒃𝒐𝒅𝒚
𝒅𝒓𝒖𝒈 𝒃𝒍𝒐𝒐𝒅 𝒄𝒐𝒏𝒄𝒆𝒏𝒕𝒓𝒂𝒕𝒊𝒐𝒏
7

8.  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
8

9. 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
𝑪𝒍 𝑹 =
𝑹𝒂𝒕𝒆 𝒐𝒇 𝒖𝒓𝒊𝒏𝒂𝒓𝒚 𝒆𝒙𝒄𝒓𝒆𝒕𝒊𝒐𝒏
𝑷𝒍𝒂𝒔𝒎𝒂 𝒅𝒓𝒖𝒈 𝒄𝒐𝒏𝒄𝒆𝒏𝒕𝒓𝒂𝒕𝒊𝒐𝒏
physiologically,
𝑪𝒍 𝑹 =
𝑹𝒂𝒕𝒆 𝒐𝒇 𝒇𝒊𝒍𝒕𝒆𝒓𝒂𝒕𝒊𝒐𝒏 + 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒔𝒆𝒄𝒓𝒆𝒕𝒊𝒐𝒏 − 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒓𝒆 𝒂𝒃𝒔𝒐𝒓𝒑𝒕𝒊𝒐𝒏
𝑷𝒍𝒂𝒔𝒎𝒂 𝒅𝒓𝒖𝒈 𝒄𝒐𝒏𝒄𝒆𝒏𝒕𝒓𝒂𝒕𝒊𝒐𝒏 (𝑪)
9

10. 5. Hepatic Clearance (𝒄𝒍 𝑯):-
 Hepatic clearance can be defined as the volume of blood perfusing the liver
that is cleared of the drug per unit time.
 𝑐𝑙 𝐻 can be given by the following equation
𝑐𝑙 𝐻 = 𝑐𝑙 𝑇 − 𝑐𝑙 𝑅
for certain drugs, the non renal clearance can be assumed as equal to
hepatic clearance 𝑐𝑙 𝐻.
10

11. 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
𝑭 =
𝑩𝒊𝒐𝒂𝒗𝒂𝒊𝒍𝒂𝒃𝒍𝒆 𝒅𝒐𝒔𝒆
𝒂𝒅𝒎𝒊𝒏𝒊𝒔𝒕𝒆𝒓𝒆𝒅 𝒅𝒐𝒔𝒆
11

12. POSSIBLE CAUSES OF NON-INDUCTION
The 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 12

13.  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.
13

14. 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.
14

15. 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 15

16. 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
16

17. 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
17

18. NON-LINEAR BINDING
A 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 hrs
Plasma drug level – time profile of two drugs given in equal
doses
18

19. 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.
19

20. 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.
20

21. 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 21

22. 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.
22

23. 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.
23

24. 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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