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The first lecture for Pharmacy students pharmacokinetics class
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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.
Anas Bahnassi PhD 2011 11
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.
Anas Bahnassi PhD 2011 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
Amount of Drug in the Urine
Anas Bahnassi PhD 2011 14
Sites of Drug Administration
Anas Bahnassi PhD 2011 15
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
Anas Bahnassi PhD 2011 16
Extra-vascular
Oral
Intra-mascular
Sub-cutaneous
Sub-lingual
Trans-dermal
Rectal
Inhalation
Important Features of
Extravascular Routes
Anas Bahnassi PhD 2011 17
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
Anas Bahnassi PhD 2011 18
• 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
Anas Bahnassi PhD 2011 19
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
Anas Bahnassi PhD 2011 20
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.
Anas Bahnassi PhD 2011 21
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.
Anas Bahnassi PhD 2011 22
Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009
Anas Bahnassi PhD 2011 23
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.
Anas Bahnassi PhD 2011 24
Niazi, S. 1979 Textbook of Biopharmaceutics and Clinical Pharmacokinetics, Appleton-Century-Crofts, New York, p142
IV Bolus Dose - One
Compartment
Anas Bahnassi PhD 2011 25
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
Anas Bahnassi PhD 2011 26
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
Anas Bahnassi PhD 2011 27
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
Anas Bahnassi PhD 2011 30
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
Anas Bahnassi PhD 2011 31
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
Anas Bahnassi PhD 2011 32
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
Anas Bahnassi PhD 2011 33
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
Anas Bahnassi PhD 2011 34
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
Anas Bahnassi PhD 2011 36
Rectilinear Paper
First-order Process
Anas Bahnassi PhD 2011 37
Rectilinear Paper
-dX/dt xX-1 =K,
where units are
mgh-1 x mg-1
K has unit is: h-1.
First-order Process
Anas Bahnassi PhD 2011 38
Rectilinear Paper
First-order Process
Anas Bahnassi PhD 2011 39
Rectilinear Paper Semilogarithmic
Paper
Comparison of Zero & First order
processes
Anas Bahnassi PhD 2011 40
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
abahnassi@gmail.com
http://www.linkedin.com/pub/anas-bahnassi/8/707/693
http://bahnassi.coursesites.com
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Anas Bahnassi PhD RPh
Pharmacokinetics
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