The first lecture for Pharmacy students pharmacokinetics class

1. Introduction
To Pharmacokinetics
Pharmacokinetics A Mathematical Tool
Anas Bahnassi PhD RPh

2. 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.

3. 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.

4. What is Pharmacokinetics?
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

5. 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

6. Distribution
Elimination
Metabolites
• IV Medication
• PO in
Circulation
• IM
• MDI Dosage
Regimen
Concentration
Response
Route of
Administration
• Pharmacological
• Adverse
Effect
The Pharmacokinetic Process

7. The Pharmacological Response
Drug must get into
The occupation theory blood
The intensity of a pharmacological and blood is in
response (E) is proportional to the contact
concentration of a reversible drug- with receptor.
receptor complex
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.

8. m:slope Response vs. Drug
E=m.lnX+b
Concentration
X:dose = C.V V:volume
of
Emax
distribution

9. 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.
∞
������������������������ = ������0 = (������������������)0 ������������
(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. 9

10. 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.”
������
������ =
������
Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009
Anas Bahnassi PhD 2011 10

11. 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.
∞
������. ������������������������ = ������������0 = (������������������)0 ������������
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12. Min. Toxic Conc.
Min. Effective Conc.
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

13. 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
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14. Amount of Drug in the Urine
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15. Sites of Drug Administration
1. There is no absorption
phase.
Intra- 2. There is immediate
Intravascular venous onset of action.
3. The entire administered
Routes dose is available to
Intra- produce pharmacological
arterial 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
Anas Bahnassi PhD 2011 dose, therefore, are very
15
critical.

16. Sites of Drug Administration
Oral
Inhalation
Intra-
mascular
Extra-
vascular Sub-
Rectal cutaneous
Trans- Sub-
dermal lingual
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17. 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).
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18. Review of the ADME Process
• The process by which a drug proceeds from
Absorption the site of administration to the site of
measurement
• the process of reversible transfer of drug to
Distribution and from the site of measurement
• the process of a conversion of one chemical
Metabolism species to another chemical species
• The irreversible loss of drug from the site of
Elimination measurement. It may occur by metabolism
or excretion.
Anas Bahnassi PhD 2011 18

19. Excretion Disposition
The irreversible loss of Once a drug is in the systemic,
a drug in a chemically it is distributed simultaneously
unchanged or unaltered to all tissues including the organ
form. responsible for its elimination.
Anas Bahnassi PhD 2011 19

20. 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.
Anas Bahnassi PhD 2011 20

21. 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.
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22. 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
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23. Pharmacokinetic
Models
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24. 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
Anas Bahnassi PhD 2011 24

25. IV Bolus Dose - One
Compartment
������ = ������0 ������ −������������ = ������������ −������������ 1
������������������ = ������������������ − ������������ (2)
E=m.lnX+b
������ − ������ ������0 − ������
= ������������ (3)
������ ������
E=E0-Rt
Basic Pharmacokinetics REV. 99.4.25 3-4 1996-1999 Michael C. Makoid
Niazi, S. 1979 Textbook of Biopharmaceutics and Clinical Pharmacokinetics, Appleton-Century-Crofts, New York, p142
Anas Bahnassi PhD 2011 25

26. 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
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27. Semi-log Graph
Rapid Distribution Slow Distribution
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28. Absorption and Elimination
One Compartment with Two Compartment with
absorption phase Semi-log Graph absorption phase
28
Anas Bahnassi PhD 2011

29. Anas Bahnassi PhD 2011 29

30. A basic model for absorption and
Disposition
The model is based on mass
balance considerations:
At any time t, for the
1. The amount (e.g. mg) of
extravascular route:
unchanged drug and/or
F(Dose) = absorbable amount at
metabolite(s) can be measured in
the absorption site + amount in the
urine.
body + cumulative amount
2. Drug and metabolite(s) in the
metabolized + cumulative amount
body (blood, plasma or serum)
excreted unchanged
are measured in concentration
units (e.g. μgmL-1).
For the intravascular route:
3. Direct measurement of drug at
Dose = amount in the body +
the site of administration is
amount metabolized + cumulative
impractical; however, it can be
amount excreted unchanged:
assessed indirectly.
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31. 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).
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32. 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 Anas Bahnassi PhD 2011 32
biopharmaceutics, Amer. J. Pharm. Ed., 32,
958

33. 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
Dittert, L.W. and DiSanto, A.R. 1973 The bioavailability of drug
of calculating
products, J. Amer. Pharm. Assoc., NS13, 421-432 AUC.
Anas Bahnassi PhD 2011 33

34. 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.
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35. Zero-order Process
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.
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Rectilinear Paper

36. First-order Process
Rectilinear Paper
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37. First-order Process
-dX/dt xX-1 =K,
where units are
mgh-1 x mg-1
 K has unit is: h-1.
Rectilinear Paper
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38. First-order Process
Rectilinear Paper
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39. First-order Process
Rectilinear Paper Semilogarithmic
Paper
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40. Comparison of Zero & First order
processes
Term Zero order First order
-dx/dt = K0 Rate remains KX Rate changes over time
constant
Rate =K0 =K
constant unit = mgh-1 unit=h-1
X X=X0-Kt lnX=lnX0-Kt or
logX=logX0-kt/2.303
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41. Pharmacokinetics
Anas Bahnassi PhD RPh
abahnassi@gmail.com
http://www.linkedin.com/pub/anas-bahnassi/8/707/693
http://bahnassi.coursesites.com
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