Pharmacokinetics: Lecture One

Introduction To Pharmacokinetics

Pharmacokinetics A Mathematical Tool

Anas Bahnassi PhD RPh

Lecture Objectives After completing this lecture, the student will be able

to:

1. Given patient data of the following types, the student will be able to

properly construct a graph and compute the slope using linear

regression: response (R) vs. concentration (C), response (R) vs. time

(T), concentration (C) vs. time (T)

2. Given any two of the above data sets, the student will be able to

compute the slope of the third by linear regression.

3. Give response vs. time and response versus concentration data, the

student will be able to compute the terminal (elimination) rate

constant and half life of the drug.

What is Pharmacokinetics?

The mathematical description

of drug behavior inside the human body

It is the study of factors affecting

the absorption, distribution,

metabolism and excretion of drug

As well as the quantitative description

of how these processes affect the

time course and intensity of response.

This powerful mathematical tool is used

to study the drug’s

• Fate in normal and

pathophysiological conditions

• Distribution / location /penetration

• Clearance / organs

• Conc vs. response

• Bioavailability

• It compares dosage forms and

different drug brands

• It quantitatively evaluate the

magnitude of drug interactions

• It provides the basics to make clinical

predictions

What is Pharmacokinetics?

What is Biopharmaceutics?

How the pharmaceutical formulation

variables affect drug availability and performance

(absorption)

in vivo

The use of these information helps optimizing

therapeutic outcomes of drug products

• IV

• PO

• IM

• MDI

Route of Administration

Dosage Regimen

Medication in

Circulation

Concentration Response

• Pharmacological

• Adverse Effect

Distribution

Elimination

Metabolites

The Pharmacokinetic Process

The Pharmacological Response

The intensity of a pharmacological

response (E) is proportional to the

concentration of a reversible drug-

receptor complex

The occupation theory

𝐸 =𝐷 𝐸𝑚𝑎𝑥

𝐾𝑅𝐷

where E is the intensity of the

pharmacological response, Emax is the

maximum attainable value of , [D] is the

molar concentration of free drug at the

active complex and KR is the dissociation

constant of the drug-receptor complex.

Drug must get into

blood

and blood is in

contact

with receptor.

Emax

Response vs. Drug

Concentration E=m.lnX+b

m:slope

X:dose = C.V V:volume

of

distribution

The Relationship Between The Administered

Dose and The Amount of the Drug in The Body

• The Fraction of the drug reaches the systemic

circulation is the amount available to elicit

pharmacologic effect.

• For iv administration, the amount of drug

reaches the general circulation is equal to the

dose administered.

9

(AUC)∞0 is the area under curve of plasma drug concentration versus time (AUC) from

time zero to time infinity

K is the first-order elimination rate constant

V (or Vd) is the drug’s volume of distribution.

𝐷𝑜𝑠𝑒 = 𝑋0 = (𝐴𝑈𝐶)0∞𝐾𝑉

Volume of Distribution

“The apparent volume into which a given mass

of drug would need to be diluted in order to give

the observed concentration.”

Anas Bahnassi PhD 2011 10

Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009

𝑉 =𝑋

𝐶

The Relationship Between The

Administered Dose and The Amount of the

Drug in The Body

For the extravascular route, the amount of

drug that reaches general circulation is the

product of the bioavailable fraction (F) and

the dose administered.


𝐹. 𝐷𝑜𝑠𝑒 = 𝐹𝑋0 = (𝐴𝑈𝐶)0∞𝐾𝑉

Previous equations suggest that we must know or determine

all the parameters (i.e. AUC, 0 , K, V, F) for a given drug;

therefore, it is important to know the concentration of a drug

in blood (plasma or serum) and/or the amount (mass) of drug

removed in urine (excretion data). Anas Bahnassi PhD 2011 12

Min. Toxic Conc.

Min. Effective Conc.


Onset of Action: The time at which the administered drug reaches the therapeutic range

and begins to produce effect.

Therapeutic Range: The plasma or serum concentration range within which the drug is

likely to produce the therapeutic activity or effect

Duration of Action: The time span from the beginning of the onset of action up to

termination of action

Termination of Action: The time at which the drug concentration in plasma falls below the

minimum effective concentration

Amount of Drug in the Urine


Sites of Drug Administration


Intravascular

Routes

Intra-

venous

Intra-

arterial

1. There is no absorption

phase.

2. There is immediate

onset of action.

3. The entire administered

dose is available to

produce pharmacological

effects.

4. This route is used more

often in life-threatening

situations.

5. Adverse reactions are

difficult to reverse or

control; accuracy in

calculations and

administration of drug

dose, therefore, are very

critical.

Sites of Drug Administration


Extra-vascular

Oral

Intra-mascular

Sub-cutaneous

Sub-lingual

Trans-dermal

Rectal

Inhalation

Important Features of

Extravascular Routes


1. An absorption phase is present.

2. The onset of action is determined by factors such as formulation and

type of dosage form, route of administration, physicochemical properties

of drugs and other physiological variables.

3. The entire administered dose of a drug may not always reach the

general circulation (i.e. incomplete absorption).

Review of the ADME Process


• The process by which a drug proceeds from the site of administration to the site of measurement

Absorption

• the process of reversible transfer of drug to and from the site of measurement Distribution

• the process of a conversion of one chemical species to another chemical species Metabolism

• The irreversible loss of drug from the site of measurement. It may occur by metabolism or excretion.

Elimination


The irreversible loss of a drug in a chemically unchanged or unaltered form.

Excretion Once a drug is in the systemic, it is distributed simultaneously to all tissues including the organ responsible for its elimination.

Disposition

Pharmacokinetic Models


The change in drug’s concentration after administration can be described

using certain equations mostly exponential. This suggests that ADME

processes follow a first order process and therefore drug transport is

mediated through passive diffusion mechanism. This means that there is a

direct relationship between the plasma concentration of the drug and the

amount eliminated in the urine and the original administered dose. This

identifies the term Linear Pharmacokinetics.

Compartment Concept in PK

• It is necessary to describe the pharmacokinetic

parameters adequately and accurately.

• The selection of the compartment model

depends solely on the distribution

characteristics of the drug administered.

• The corresponding equation depends on the

compartment model and the route of

administration.


The model selection process is highly

dependent upon the following factors.

1. The frequency at which plasma samples are collected. It is highly recommended that plasma samples are collected as early as possible, particularly for first couple of hours, following the administration of the dose of a drug.

2. The sensitivity of the procedure employed to analyze drug concentration in plasma samples. (Since inflections of the plasma concentration versus time curve in the low concentration regions may not be detected when using assays with poor sensitivity, the use of a more sensitive analytical procedure will increase the probability of choosing the correct compartment model.)

3. The physicochemical properties (e.g. the lipophilicity)of a drug.


Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009


Pharmacokinetic

Models

IV Bolus Dose - One

Compartment

Considering the body to behave as a single compartment. In order to simplify the mathematics it is often possible to assume that a drug given by rapid intravenous injection, a bolus, is rapidly mixed. This figure represents the uniformly mixed drug very shortly after administration.


Niazi, S. 1979 Textbook of Biopharmaceutics and Clinical Pharmacokinetics, Appleton-Century-Crofts, New York, p142

IV Bolus Dose - One

Compartment


Niazi, S. 1979 Textbook of Biopharmaceutics and Clinical Pharmacokinetics, Appleton-Century-Crofts, New York, p142

𝑋 = 𝑋0𝑒−𝑘𝑡 = 𝐷𝑒−𝑘𝑡 1

𝑙𝑛𝑋 = 𝑙𝑛𝐷 − 𝑘𝑡 (2)

E=m.lnX+b

𝐸 − 𝑏

𝑚=

𝐸0 − 𝑏

𝑚𝑘𝑡 (3)

E=E0-Rt

Basic Pharmacokinetics REV. 99.4.25 3-4 1996-1999 Michael C. Makoid

IV Bolus Two

Compartment Model


Often a one compartment model is not sufficient to represent the

pharmacokinetics of a drug. A two compartment model often has

wider application. Here we consider the body is a central

compartment with rapid mixing and a peripheral compartment

with slower distribution.

The central compartment

is uniformly mixed very

shortly after drug

administration, whereas

it takes some time for the

peripheral compartment

to reach a pseudo

equilibrium.

Niazi, S. 1979 Textbook of Biopharmaceutics and

Clinical Pharmacokinetics, Appleton-Century-

Crofts, New York, p175l.;l

Semi-log Graph


Rapid Distribution Slow Distribution

Absorption and Elimination

Anas Bahnassi PhD 2011

28 Semi-log Graph One Compartment with

absorption phase

Two Compartment with

absorption phase

29 Anas Bahnassi PhD 2011


A basic model for absorption and

Disposition

The model is based on mass

balance considerations:

1. The amount (e.g. mg) of

unchanged drug and/or

metabolite(s) can be measured in

urine.

2. Drug and metabolite(s) in the

body (blood, plasma or serum)

are measured in concentration

units (e.g. μgmL-1).

3. Direct measurement of drug at

the site of administration is

impractical; however, it can be

assessed indirectly.

At any time t, for the

extravascular route:

F(Dose) = absorbable amount at

the absorption site + amount in the

body + cumulative amount

metabolized + cumulative amount

excreted unchanged

For the intravascular route:

Dose = amount in the body +

amount metabolized + cumulative

amount excreted unchanged:

Characteristics of One

Compartment Model


1. Equilibrium between drug concentrations in

different tissues or organs is obtained rapidly

(virtually instantaneously), following drug input.

Therefore, a distinction between distribution and

elimination phases is not possible.

2. The amount (mass) of drug distributed in different

tissues may be different.

3. Following equilibrium, changes in drug concentra-

tion in blood (which can be sampled) reflect

changes in concentration of drug in other tissues

(which cannot be sampled).

Drug Concentration versus Time


From a graph such as this we can see the relationship between drug

concentration and drug effect. If a drug has to reach an effective

concentration at a receptor site this will be reflected as a required

blood concentration. Barr, W.H. 1968 Principles of

biopharmaceutics, Amer. J. Pharm. Ed., 32,

958

Drug Product Performance

Parameters


The figure shows

some of the bio-

pharmaceutic

parameters

which can be

used to measure

drug product

performance.

Later in the

semester we will

use the trap-

ezoidal method

of calculating

AUC. Dittert, L.W. and DiSanto, A.R. 1973 The bioavailability of drug

products, J. Amer. Pharm. Assoc., NS13, 421-432

Rate Processes


After administration, the drug

is subject to a number of

processes (ADME) whose rates

control the concentration of

drug in the elusive region

known as ‘‘site of action.’’

These processes affect the onset

of action, as well as the duration

and intensity of

pharmacological response.

Zero-order Process

Anas Bahnassi PhD 2011 35 Rectilinear Paper

Applications of zero-

order processes include

administration of a

drug as an intravenous

infusion, formulation

and administration of a

drug through

controlled release

dosage forms and

administration of drugs

through trans-dermal

drug delivery systems.

First-order Process


Rectilinear Paper

First-order Process


Rectilinear Paper

-dX/dt xX-1 =K,

where units are

mgh-1 x mg-1

K has unit is: h-1.

First-order Process


Rectilinear Paper

First-order Process


Rectilinear Paper Semilogarithmic

Paper

Comparison of Zero & First order

processes


Term Zero order First order

-dx/dt = K0 Rate remains

constant

KX Rate changes over time

Rate

constant

=K0

unit = mgh-1

=K

unit=h-1

X X=X0-Kt lnX=lnX0-Kt or

logX=logX0-kt/2.303

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Anas Bahnassi PhD RPh

Pharmacokinetics

Education

Pharmacokinetics: Lecture One