Concept of non linear and linear pharmacokinetic model

CONCEPT OF LINEAR &
NONLINEAR COMPARTMENT
MODELS
Submitted by:-
Nitin Rawat
M.Pharm (Pharmacology)
Submitted to:-
Prof. Anil Kumar
Professor of Pharmacology
UINVERSITY INSTITUTE OF PHARMACETICAL SCIENCES,PANJAB UNIVERSITY CHANDIGARH

CONTENT
• Introduction to pharmacokinetics
• Introduction to pharmacokinetic models
• Approaches of pharmacokinetic models
Model approach
• Compartment model
• Physiological model
• Distributed parameter model
Non-model approach
• Non-linear pharmacokinetics
• Comparisons between linear and non linear pharmacokinetics

PHRMACOKINETICS
Pharmacokinetics is defined as the kinetics of drug absorption, distribution,
metabolism and excretion (KADME) and their relationship with the
pharmacological, therapeutic or toxicological response in man and animals.

 There are two aspects of pharmacokinetic studies –
1. Theoretical aspect – which involves development of pharmacokinetic
models to predict drug disposition after its administration. Statistical methods
are commonly applied to interpret data and assess various parameters.
2. Experimental aspect – which involves development of biological sampling
techniques, analytical methods for measurement of drug (and metabolites)
concentration in biological samples and data collection and evaluation.
 Use of pharmacokinetic principles in optimizing the drug dosage for
individual patient in order to achieving maximum therapeutic utility is
called as clinical pharmacokinetics.

• Models are used to describe changes in drug concentration in the body with time.
• Model is a hypothesis that employs mathematical terms to concisely describe quantitative
relationships of drug(s)(w.r.t time) throughout the body and compute meaningful
pharmacokinetic parameters.
• Applications of Pharmacokinetic Models
• Characterizing the behavior of drugs in patients.
• Predicting the concentration of drug in various body fluids with any dosage regimen.
• Calculating the optimum dosage regimen for individual patients.
• Evaluating the risk of toxicity with certain dosage regimens.
• Estimating the possibility of drug and/or metabolite(s) accumulation in the body.
• Determining the influence of altered physiology/disease state on drug ADME.
• Explaining drug interactions.
PHARMACOKINETIC MODELS

Types of pharmacokinetic models

Compartmental Models
• Compartment is not a real physiologic or anatomic region but a fictitious or virtual one and
considered as a tissue or group of tissues that have similar drug distribution characteristics
(similar blood flow and affinity).
• It is the traditional and commonly used approach to pharmacokinetic characterization of a drug.
These models simply interpolate the experimental data and allow an empirical formula to estimate
the drug concentration with time.
Assumptions
• Compartment is not a real physiologic or anatomic region but a fictitious or virtual one and
considered as a tissue or group of tissues that have similar drug distribution characteristics
(similar blood flow and affinity).
• The body is represented as a series of compartments arranged either in series or parallel to each
other, that communicate reversibly with each other.
• Within each compartment, the drug is considered to be rapidly and uniformly distributed i.e. the
compartment is well-stirred.

Types of compartmental models
• Compartment models are divided into two categories
• Depending upon arrangement of compartments
Mammillary model
Catenary model.
• Depending upon number of compartment assumed
One-compartment or one-compartment open model
Two compartment
Multiple compartment

Mammillary model
Central compartment (comprises of plasma and highly perfused tissues such as lungs, liver,
kidneys) joined parallel to the peripheral compartment(comprises of less perfused organ) like
connection of satellites to a planet.
Catenary model
Compartments are joined to one another in a series like compartments of a train. This is however
not observable physiologically/anatomically as the various organs are directly linked to the
blood compartment.

One-compartment open model
Body is considered as a single, kinetically
homogeneous unit that has no barriers to the
movement of drug
Open indicates that the input (availability) and
output (elimination) are unidirectional and that
the drug can be eliminated from the body.

One-compartment open model, i.v. bolus administration.
One-compartment open model, continuous i.v. infusion.
One-compartment open model, e.v. administration, zero-order
absorption
One-compartment open model, e.v. administration, first-order
absorption
Types One-compartment open model

TWO-COMPARTMENT OPEN MODEL
body tissues are broadly classified into 2 categories –
Central Compartment or Compartment 1
 Comprising of blood and highly perfused tissues like liver, lungs,
kidneys, etc. that equilibrate with the drug rapidly.
 Elimination usually occurs from this compartment.
Peripheral or Tissue Compartment or Compartment 2
 Comprising of poorly perfused and slow equilibrating tissues such as
muscles, skin, adipose, etc. and considered as a hybrid of several functional physiologic units.
Classification of a particular tissue, for example brain, into central or peripheral compartment depends upon the
physicochemical properties of the drug.
Depending upon the compartment from which the drug is eliminated, the two-compartment model can be categorized into
3 types:
1.Two-compartment model with elimination from central compartment.
2.Two-compartment model with elimination from peripheral compartment.
3.Two-compartment model with elimination from both the compartments.

Also known as Physiological based pharmacokinetic model.
• They are drawn on the basis of known anatomic and physiological data and thus present a
more realistic picture of drug disposition in various organs and tissues.
Two types
• Perfusion rate-limited models
lipophilic drugs
• Diffusion-limited models
hydrophilic drugs
Physiological models

Distributed Parameter Model
• Useful for assessing regional differences in drug concentrations in tumours
or necrotic tissues.
• It take into account –
 Variations in blood flow to an organ, and
 Variations in drug diffusion in an organ.

Nonlinear Pharmacokinetics
In some cases, the rate process of a drug’s ADME are dependent upon carrier or enzymes
that are substrate-specific, have definite capacities, and susceptible to saturation at high drug
concentration. In such cases, an essentially first-order kinetics transform into a mixture of
first-order and zero-order rate processes and the pharmacokinetic parameters change with
the size of the administered dose. The pharmacokinetics of such drugs are said to be dose-
dependent. Other terms synonymous with it are mixed-order, nonlinear and capacity-
limited kinetics.
Drugs exhibiting such a kinetic profile are sources of variability in pharmacological
response.

CAUSES OF NONLINEARITY
Nonlinearity in drug absorption can arise from 3 important sources –
1. When absorption is solubility or dissolution rate-limited e.g. griseofulvin. At higher
doses, a saturated solution of the drug is formed in the GIT or at any other extravascular
site and the rate of absorption attains a constant value.
2. When absorption involves carrier-mediated transport systems e.g. absorption of
riboflavin, ascorbic acid, cyanocobalamin, etc. Saturation of the transport system at higher
doses of these vitamins results in nonlinearity.
3. When presystemic gut wall or hepatic metabolism attains saturation e.g. propranolol,
hydralazine and verapamil. Saturation of presystemic metabolism of these drugs at high
doses leads to increased bioavailability.
1. Drug Absorption

Nonlinearity in distribution of drugs administered at high doses may be due to –
1. Saturation of binding sites on plasma proteins e.g. phenylbutazone and naproxen. There is
a finite number of binding sites for a particular drug on plasma proteins and, theoretically, as
the concentration is raised, so too is the fraction unbound.
2. Saturation of tissue binding sites e.g. thiopental and fentanyl. With large single bolus doses
or multiple dosing, saturation of tissue storage sites can occur.
Drug Distribution

The nonlinear kinetics of most clinical importance is capacity-limited metabolism since small
changes in dose administered can produce large variations in plasma concentration at steady-
state. It is a major source of large intersubject variability in pharmacological response.
Two important causes of nonlinearity in metabolism are –
1. Capacity-limited metabolism due to enzyme and/or cofactor saturation. Typical examples
include phenytoin, alcohol, theophylline, etc.
2. Enzyme induction e.g. carbamazepine, where a decrease in peak plasma concentration has
been observed on repetitive administration over a period of time. Autoinduction characterized
in this case is also dose-dependent. Thus, enzyme induction is a common cause of both dose-
and time-dependent kinetics.
Drug Metabolism

The two active processes in renal excretion of a drug that are saturable are –
1. Active tubular secretion e.g. penicillin G. After saturation of the carrier system, a decrease
in renal clearance occurs.
2. Active tubular reabsorption e.g. water soluble vitamins and glucose. After saturation of the
carrier system, an increase in renal clearance occurs.
Drug Excretion

MICHAELIS MENTEN EQUATION
The kinetics of capacity-limited or saturable processes is best described by Michaelis- Menten equation:
−
𝑑𝑐
𝑑𝑡
=
𝑣 𝑚𝑎𝑥 𝐶
𝐾𝑚 + 𝐶
–dC/dt = rate of decline of drug concentration with time
Vmax = theoretical maximum rate of the process
Km = Michaelis constant
Three situations can now be considered depending upon the values of Km and C:
1. When Km = C
−
𝑑𝐶
𝑑𝑡
=
𝑉 𝑚𝑎𝑥
2
2. When Km >> C
Here, Km + C = Km
−
𝑑𝑐
𝑑𝑡
=
𝑣 𝑚𝑎𝑥 𝐶
𝐾𝑚
means that the drug concentration in the body that results from usual dosage regimens of most drugs is
well below the Km of the elimination process with certain exceptions such as phenytoin and alcohol.
3. When Km << C
Here, Km + C = C −
𝑑𝑐
𝑑𝑡
= 𝑉𝑚𝑎𝑥

Concept of non linear and linear pharmacokinetic model

Concept of non linear and linear pharmacokinetic model

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