Drug distribution typically refers to the process of getting pharmaceutical products from manufacturers or wholesalers to pharmacies, hospitals, clinics,
2. • ELIMINATION RATE CONSTANT
• As stated in the previous section, the elimination rate
constant (K) represents the fraction of drug removed per unit
of time and has units of reciprocal time (e.g., minute-1, hour-1,
and day-1). These units are evident from examination of the
calculation of K. For example, C0 is the first plasma drug
concentration, measured just after the dose is given, and C1 is
the second plasma drug concentration, measured at a later
time (t1).
• From our previous discussion, we know that the equation for
this line (y = mX + b) is:
• ln C1 = -Kt + ln C0
• Furthermore, we know that the slope of the line equals -K,
and we can calculate this slope:
5/7/2024 2
4. • HALF-LIFE
• Another important parameter that relates to the rate
of drug elimination is half-life (T1/2). The half-life is the
time necessary for the concentration of drug in the
plasma to decrease by half. A drug's half-life is often
related to its duration of action and also may indicate
when another dose should be given.
• One way to estimate the half-life is to visually examine
the natural log of plasma drug concentration versus
time plot and note the time required for the plasma
concentration to decrease by half
5/7/2024 4
5. • The half-life and the elimination rate constant
express the same idea. They indicate how quickly a
drug is removed from the plasma and, therefore,
how often a dose has to be administered.
• If the half-life and peak plasma concentration of a
drug are known, then the plasma drug concentration
at any time can be estimated
5/7/2024 5
7. • The equation represents the important relationship
between the half-life and the elimination rate constant
shown by mathematical manipulation. We already know
that:
ln C = ln C0-Kt
By definition, the concentration (C) at the time (t) equal to
the half-life (T1/2) is half the original concentration (C0).
Therefore, at one half-life, the concentration is half of
what it was initially. So we can say that at t = T1/2, C =
1/2C0. For simplicity, let's assume that C0 = 1.
Therefore:
• ln 0.5C0 = ln C0 - K(T1/2) ln 0.5 = ln 1 - K(T1/2)
5/7/2024 7
8. • The AUC is determined by drug clearance and the
dose given
• When clearance remains constant, the AUC is directly
proportional to the dose administered. If the dose
doubled, the AUC would also double. Another way to
think about this concept is that clearance is the
parameter relating the AUC to the drug dose
5/7/2024 8
9. • With a one-compartment model, first-order
elimination, and intravenous drug administration, the
AUC can be calculated easily:
• C0 has units of concentration, usually milligrams per
liter ( ), and K is expressed as reciprocal time (usually
hour-1), so the AUC is expressed as milligrams per liter
times hours ( ).
• These units make sense graphically as well, because
when we multiply length times width to measure area,
the product of the axes (concentration, in milligrams
per liter, and time, in hours) would be expressed as
milligrams per liter times hours.
5/7/2024 9
11. • AUC can be calculated by computer modeling of the
above AUC equation, or by applying the "trapezoidal
rule".
• The trapezoidal rule method is rarely used, but
provides visual means to understand AUC. If a line is
drawn vertically to the x-axis from each measured
concentration,
• Because we are using the determined
concentrations rather than their natural logs, the
plasma drug concentration versus time plot is curved
5/7/2024 11
12. • Application of Pharmacokinetics to Clinical
Situations:
• The success of drug therapy is highly dependent
on the choice of the drug and drug product and
on the design of the dosage regimen.
• The choice of the drug and drug product, eg,
immediate release versus modified release, is
based on the patient's characteristics and the
known pharmacokinetics of the drug.
5/7/2024 12
13. • A properly designed dosage regimen tries to achieve
a specified concentration of the drug at a receptor
site to produce an optimal therapeutic response with
minimum adverse effects
• Individual variation in pharmacokinetics and
pharmacodynamics makes the design of dosage
regimens difficult. Therefore, the application of
pharmacokinetics to dosage regimen design must be
coordinated with proper clinical evaluation of the
patient and monitoring.
5/7/2024 13
14. • Pharmacokinetics
• After a drug is released from its dosage form, the drug
is absorbed into the surrounding tissue, the body, or
both. The distribution through and elimination of the
drug in the body varies for each patient but can be
characterized using mathematical models and
statistics.
• Pharmacokinetics is the science of the kinetics of drug
absorption, distribution, and elimination (ie, excretion
and metabolism). The description of drug distribution
and elimination is often termed drug disposition.
5/7/2024 14
15. • Characterization of drug disposition is an important
prerequisite for determination or modification of
dosing regimens for individuals and groups of
patients.
• The study of pharmacokinetics involves both
experimental and theoretical approaches. The
experimental aspect of pharmacokinetics involves
the development of biologic sampling techniques,
analytical methods for the measurement of drugs
and metabolites, and procedures that facilitate data
collection and manipulation
5/7/2024 15
16. Pharmacokinetics and Pharmacodynamics
Pharmacokinetics Pharmacodynamics
Design
of dosage regimen
•Where?
•How much?
•How often?
•How long?
Plasma
Concentration
Effects
Plasma refers to the clear
supernatant fluid that results
from blood after the cellular
components have been
removed
5/7/2024 16
17. • During the drug development process, large numbers
of patients are tested to determine optimum dosing
regimens, which are then recommended by the
manufacturer to produce the desired pharmacologic
response in the majority of the anticipated patient
population.
• However, intra- and interindividual variations will
frequently result in either a subtherapeutic (drug
concentration below the MEC) or toxic response
(drug concentrations above the minimum toxic
concentration, MTC), which may then require
adjustment to the dosing regimen.
5/7/2024 17
18. • Clinical pharmacokinetics is the application of
pharmacokinetic methods to drug therapy. Clinical
pharmacokinetics involves a multidisciplinary
approach to individually optimized dosing strategies
based on the patient's disease state and patient-
specific considerations
5/7/2024 18
19. Pharmacogenetics
• Science of assessing genetically determined
variations in patients and the resulting affect
on drug pharmacokinetics and
pharmacodynamics
• Useful to identify therapeutic failures and
unanticipated toxicity
5/7/2024 19
20. • Pharmacodynamics
• Pharmacodynamics refers to the relationship
between the drug concentration at the site of action
(receptor) and pharmacologic response, including
biochemical and physiologic effects that influence
the interaction of drug with the receptor.
• The interaction of a drug molecule with a receptor
causes the initiation of a sequence of molecular
events resulting in a pharmacologic or toxic
response.
5/7/2024 20
21. • Efficacy
– Degree to which a drug is able to produce the
desired response
• Potency
– Amount of drug required to produce 50% of the
maximal response the drug is capable of inducing
– Used to compare compounds within classes of
drugs
5/7/2024 21
22. • Effective Concentration 50% (ED50)
– Concentration of the drug which induces a
specified clinical effect in 50% of subjects
• Lethal Dose 50% (LD50)
– Concentration of the drug which induces death in
50% of subjects
5/7/2024 22
23. • Therapeutic Index
– Measure of the safety of a drug
– Calculation: LD50/ED50
• Margin of Safety
– Margin between the therapeutic and lethal doses
of a drug
5/7/2024 23
24. • . Pharmacokinetic-pharmacodynamic models are
constructed to relate plasma drug level to drug
concentration in the site of action and establish the
intensity and time course of the drug.
5/7/2024 24
25. • Pharmacodynamics and Pharmacokinetics
• As we have discussed the importance of using
pharmacokinetics to develop dosing regimens that
will result in plasma concentrations in the
therapeutic window and yield the desired
therapeutic or pharmacologic response.
• The interaction of a drug molecule with a receptor
causes the initiation of a sequence of molecular
events resulting in a pharmacodynamic or
pharmacologic response.
5/7/2024 25
26. • The term pharmacodynamics refers to the
relationship between drug concentrations at the site
of action (receptor) and pharmacologic response,
including the biochemical and physiologic effects
that influence the interaction of drug with the
receptor.
• Early pharmacologic research demonstrated that the
pharmacodynamic response produced by the drug
depends on the chemical structure of the drug
molecule.
5/7/2024 26
27. • Pharmacokinetic models allow very complex
processes to be simplified. The process of
pharmacokinetic modeling continues until a model is
found that describes the real process quantitatively.
• The understanding of drug response is greatly
enhanced when pharmacokinetic modeling
techniques are combined with clinical pharmacology,
resulting in the development of pharmacokinetic–
pharmacodynamic models
5/7/2024 27
28. • Pharmacokinetic– pharmacodynamic models use
data derived from the plasma drug concentration-
versus-time profile and from the time course of the
pharmacologic effect to predict the
pharmacodynamics of the drug.
• Pharmacokinetic–pharmacodynamic models have
been reported for antipsychotic medications,
anticoagulants, neuromuscular blockers,
antihypertensives, anesthetics, and many
antiarrhythmic drugs (the pharmacologic responses
of these drugs are well studied because of easy
monitoring).
5/7/2024 28
29. • Basic Pharmacokinetics and Pharmacokinetic Models
• Drugs are in a dynamic state within the body as they
move between tissues and fluids, bind with plasma
or cellular components, or are metabolized.
• The biologic nature of drug distribution and
disposition is complex, and drug events often happen
simultaneously. Yet such factors must be considered
when designing drug therapy regimens.
• The inherent and infinite complexity of these events
require the use of mathematical models and
statistics to estimate drug dosing and to predict the
time course of drug efficacy for a given dose.
5/7/2024 29
30. • A model is a hypothesis using mathematical terms to
describe quantitative relationships concisely. The predictive
capability of a model lies in the proper selection and
development of mathematical function(s) that
parameterize the essential factors governing the kinetic
process.
• The key parameters in a process are commonly estimated
by fitting the model to the experimental data, known as
variables. A pharmacokinetic parameter is a constant for
the drug that is estimated from the experimental data.
• For example, estimated pharmacokinetic parameters such
as k depend on the method of tissue sampling, the timing
of the sample, drug analysis, and the predictive model
selected.
5/7/2024 30
31. • Such mathematical models can be devised to
simulate the rate processes of drug absorption,
distribution, and elimination to describe and predict
drug concentrations in the body as a function of
time. Pharmacokinetic models are used to:
• 1. Predict plasma, tissue, and urine drug levels with
any dosage regimen
• 2. Calculate the optimum dosage regimen for each
patient individually
5/7/2024 31
32. • 3. Estimate the possible accumulation of drugs
and/or metabolites
• 4. Correlate drug concentrations with pharmacologic
or toxicologic activity
• 5. Evaluate differences in the rate or extent of
availability between formulations (bioequivalence)
• 6. Describe how changes in physiology or disease
affect the absorption, distribution, or elimination of
the drug
• 7. Explain drug interactions
5/7/2024 32
33. • Simplifying assumptions are made in
pharmacokinetic models to describe a complex
biologic system concerning the movement of drugs
within the body.
• For example, most pharmacokinetic models assume
that the plasma drug concentration reflects drug
concentrations globally within the body.
• A model may be empirically, physiologically, or
compartmentally based. The model that simply
interpolates the data and allows an empirical formula
to estimate drug level over time is justified when
limited information is available.
5/7/2024 33
34. • Empirical models are practical but not very useful in
explaining the mechanism of the actual process by
which the drug is absorbed, distributed, and
eliminated in the body
5/7/2024 34
35. • Compartment Models
• If the tissue drug concentrations and binding are
known, physiologic pharmacokinetic models, which
are based on actual tissues and their respective
blood flow, describe the data realistically.
• Physiologic pharmacokinetic models are frequently
used in describing drug distribution in animals,
because tissue samples are easily available for assay.
• On the other hand, tissue samples are often not
available for human subjects, so most physiological
models assume an average set of blood flow for
individual subjects.
5/7/2024 35
36. • In contrast, because of the vast complexity of the
body, drug kinetics in the body are frequently
simplified to be represented by one or more tanks,
or compartments, that communicate reversibly with
each other.
• A compartment is not a real physiologic or anatomic
region but is considered as a tissue or group of
tissues that have similar blood flow and drug affinity.
Within each compartment, the drug is considered to
be uniformly distributed.
5/7/2024 36
37. • Mixing of the drug within a compartment is rapid
and homogeneous and is considered to be "well
stirred," so that the drug concentration represents
an average concentration, and each drug molecule
has an equal probability of leaving the compartment
• Rate constants are used to represent the overall rate
processes of drug entry into and exit from the
compartment. The model is an open system because
drug can be eliminated from the system.
Compartment models are based on linear
assumptions using linear differential equations
5/7/2024 37
38. • Mammillary Model
• A compartmental model provides a simple way of grouping
all the tissues into one or more compartments where drugs
move to and from the central or plasma compartment.
• The mammillary model is the most common compartment
model used in pharmacokinetics.
• The mammillary model is a strongly connected system,
because one can estimate the amount of drug in any
compartment of the system after drug is introduced into a
given compartment. In the one-compartment model, drug
is both added to and eliminated from a central
compartment.
5/7/2024 38
39. • The central compartment is assigned to represent
plasma and highly perfused tissues that rapidly
equilibrate with drug.
• When an intravenous dose of drug is given, the drug
enters directly into the central compartment.
Elimination of drug occurs from the central
compartment because the organs involved in drug
elimination, primarily kidney and liver, are well-
perfused tissues
5/7/2024 39
40. • In a two-compartment model, drug can move
between the central or plasma compartment to and
from the tissue compartment.
• Although the tissue compartment does not represent
a specific tissue, the mass balance accounts for the
drug present in all the tissues.
• In this model, the total amount of drug in the body is
simply the sum of drug present in the central
compartment plus the drug present in the tissue
compartment.
5/7/2024 40
41. • Knowing the parameters of either the one- or two-
compartment model, one can estimate the amount
of drug left in the body and the amount of drug
eliminated from the body at any time.
• The compartmental models are particularly useful
when little information is known about the tissues.
5/7/2024 41
42. • Several types of compartment models are described in .
The pharmacokinetic rate constants are represented by
the letter k. Compartment 1 represents the plasma or
central compartment, and compartment 2 represents the
tissue compartment. The drawing of models has three
functions.
• The model (1) enables the pharmacokineticist to write
differential equations to describe drug concentration
changes in each compartment,
• (2) gives a visual representation of the rate processes,
and
• (3) shows how many pharmacokinetic constants are
necessary to describe the process adequately
5/7/2024 42
43. • Catenary Model
• In pharmacokinetics, the mammillary model must be
distinguished from another type of compartmental
model called the catenary model. The catenary
model consists of compartments joined to one
another like the compartments of a train.
• In contrast, the mammillary model consists of one or
more compartments around a central compartment
like satellites. Because the catenary model does not
apply to the way most functional organs in the body
are directly connected to the plasma, it is not used as
often as the mammillary model.
• .
5/7/2024 43
44. • Physiologic Pharmacokinetic Model (Flow Model)
• Physiologic pharmacokinetic models, also known as blood
flow or perfusion models, are pharmacokinetic models
based on known anatomic and physiologic data.
• The models describe the data kinetically, with the
consideration that blood flow is responsible for distributing
drug to various parts of the body. Uptake of drug into
organs is determined by the binding of drug in these
tissues.
• In contrast to an estimated tissue volume of distribution,
the actual tissue volume is used. Because there are many
tissue organs in the body, each tissue volume must be
obtained and its drug concentration described.
5/7/2024 44
45. • The model would potentially predict realistic tissue
drug concentrations, which the two-compartment
model fails to do. Unfortunately, much of the
information required for adequately describing a
physiologic pharmacokinetic model are
experimentally difficult to obtain.
• In spite of this limitation, the physiologic
pharmacokinetic model does provide much better
insight into how physiologic factors may change drug
distribution from one animal species to another.
Other major differences are described below
5/7/2024 45
46. • The primary purpose of rigorous pharmacokinetic
data analysis, compartmental or model-independent,
is to determine the pharmacokinetic parameters
useful in dosing drugs for patients.
• Consequently, multiple plasma drug concentrations
are obtained at specific time points in healthy and
diseased persons to assess a drug's population
pharmacokinetic parameters.
5/7/2024 46
47. • In clinical practice, it may be difficult to obtain
multiple plasma samples after the first dose to
determine a patient's pharmacokinetic parameters.
• Consequently, clinicians use population parameters
from the literature to make individual patient dosage
calculations.
5/7/2024 47
48. • Model-independent pharmacokinetic data analysis
provides the opportunity to obtain pharmacokinetic
values that do not depend on a compartmental
model.
• Total body clearance, mean residence time (MRT),
volume of distribution at steady state, and formation
clearance are four of the most frequently used
model-independent parameters and are the focus of
this section
5/7/2024 48
49. • The use of model-independent data analysis
techniques to generate model-independent
parameters offers several advantages over traditional
compartmental approaches.
• First, it is not necessary to assume a compartmental
model. Many drugs possess complex distribution
patterns requiring two, three, or more exponential
terms to describe their elimination.
5/7/2024 49
50. • As the number of exponential terms increases, a
compartmental analysis requires more intensive
blood sampling and rigorous data calculations.
• Second, several drugs (e.g., gentamicin) can be
described by one, two, or more distribution
compartments, depending on the characteristics of
the patients evaluated or the aggressiveness of the
blood sampling.
5/7/2024 50
51. • Therefore, a compartmental approach would require
that pharmacokinetic parameters be obtained for
each distribution pattern, making it difficult to
compare one data set to another.
• Third, calculations are generally easier with model-
independent relationships and do not require a
computer with sophisticated software.
• One drawback of using model-independent
parameters is the inability to visualize or predict
plasma concentration versus time profiles. This may
result in the loss of specific information that provides
important insight regarding drug disposition
5/7/2024 51
52. • Mean Residence Time
• MRT is defined as the average time intact drug
molecules transit or reside in the body.
• For a population of drug molecules, individual
molecules spend different times within the body.
Following the principles of statistical probability,
specific drug molecules may be eliminated quickly
whereas others may remain in the body much longer.
• Consequently, a distribution of transit times can be
characterized by a mean value. In other words,
elimination of a drug can be thought of as a random
process.
5/7/2024 52
53. • Residence time reflects how long a particular drug
molecule remains or resides in the body. The MRT
reflects the overall behavior of a large number of
drug molecules.
• This parameter is not used frequently in clinical
practice to monitor patients. However, it is useful
when comparing the effect of disease, altered
physiologic state, or drug-drug interaction on the
pharmacokinetics of a specific drug. MRT can be
calculated with the following equation
5/7/2024 53
55. Nonlinear Pharmacokinetics:
• Introduction
• . These linear models assumed that the
pharmacokinetic parameters for a drug would not
change when different doses or multiple doses of a
drug were given.
• With some drugs, increased doses or chronic
medication can cause deviations from the linear
pharmacokinetic profile previously observed with
single low doses of the same drug. This nonlinear
pharmacokinetic behavior is also termed dose-
dependent pharmacokinetics.
5/7/2024 55
56. • Many of the processes of drug absorption,
distribution, biotransformation, and excretion involve
enzymes or carrier-mediated systems.
• For some drugs given at therapeutic levels, one of
these specialized processes may become saturated.
• Besides saturation of plasma protein-binding or
carrier-mediated systems, drugs may demonstrate
nonlinear pharmacokinetics due to a pathologic
alteration in drug absorption, distribution, and
elimination.
5/7/2024 56
57. • Pharmacokinetic parameters, such as elimination
half life (t1/2), the elimination rate constant (K), the
apparent volume of distribution (V), and the systemic
clearance (Cl) of most drugs are not expected to
change when different doses are administered
and/or when the drug is administered via different
routes as a single dose or multiple doses
• The kinetics of these drugs is described as linear, or
dose-independent, pharmacokinetics and is
characterized by the first-order process
5/7/2024 57
58. • The term linear simply means that plasma
concentration at a given time at steady state and the
area under the plasma concentration versus time
curve (AUC) will both be directly proportional to the
dose administered
5/7/2024 58
59. 59
Nonlinear
• For some drugs, however, the above situation may
not apply
• For example, when the daily dose of phenytoin is
increased by 50% in a patient from 300 mg to 450
mg, the average steady-state plasma concentration,
(Cp)ss, may increase by as much as 10-fold
• This dramatic increase in the concentration (greater
than directly proportional) is attributed to the
nonlinear kinetics of phenytoin
5/7/2024
61. • Saturable Enzymatic Elimination Processes:
• The elimination of drug by a saturable enzymatic
process is described by Michaelis–Menten
kinetics. If C p is the concentration of drug in the
plasma, then
• where V max is the maximum elimination rate and
K M is the Michaelis constant that reflects the
capacity of the enzyme system. It is important to
note that K M is not an elimination constant,..
5/7/2024 61
62. • but is actually a hybrid rate constant in enzyme
kinetics, representing both the forward and
backward reaction rates and equal to the drug
concentration or amount of drug in the body at 0.5V
max. The values for K M and V max are dependent on
the nature of the drug and the enzymatic process
involved
5/7/2024 62
63. • Determination of K M and V max
• When an experiment is performed with solutions of
various concentration of drug C, a series of reaction
rates (v) may be measured for each concentration.
Special plots may then be used to determine K M and
V max.
5/7/2024 63
64. • At steady state, the rate of drug metabolism (v) is
assumed to be the same as the rate of drug input R
(dose/day). However, steady state will not be
reached if the drug input rate, R, is greater than the
V max; instead, drug accumulation will continue to
occur without reaching a steady-state plateau.
• where R = dose/day or dosing rate; C ss = steady-state
plasma drug concentration, V max = maximum
metabolic rate constant in the body, and K M =
Michaelis–Menten constant of the drug in the body
5/7/2024 64
65. • Determination of K M and V max by Direct Method
• When steady-state concentrations of phenytoin are
known at only two dose levels, there is no advantage
in using the graphic method. K M and V max may be
calculated by solving two simultaneous equations
formed by substituting C SS and R with C 1, R 1, C 2,
and R 2. The equations contain two unknowns, K M
and V max, and may be solved easily.
• where C 1 is steady-state plasma drug concentration
after dose 1, C 2 is steady-state plasma drug
concentration after dose 2, R 1 is the first dosing rate,
and R 2 is the second dosing rate.
5/7/2024 65
66. 66
Nonlinear
Administration of different doses
of drugs with nonlinear kinetics
may not result in parallel plasma
concentration versus time
profiles expected for drugs with
linear pharmacokinetics
5/7/2024
67. 67
Nonlinear kinetics
• Nonlinearity may arise at any one of the
pharmacokinetic steps, such as absorption,
distribution and/or elimination
• For example, the extent of absorption of amoxicillin
decreases with an increase in dose
• For distribution, plasma protein binding of
disopyramide is saturable at the therapeutic
concentration, resulting in an increase in the volume
of distribution with an increase in dose of the drug
5/7/2024
68. • As for nonlinearity in renal excretion, it has been
shown that the antibacterial agent dicloxacillin has
saturable active secretion in the kidneys, resulting in
a decrease in renal clearance as dose is increased
• Both phenytoin and ethanol have saturable
metabolism, which means that an increase in dose
results in a decrease in hepatic clearance and a more
than proportional increase in AUC
68
5/7/2024
69. 69
Nonlinearity in metabolism
Capacity-limited metabolism
• Capacity-limited metabolism is also called saturable
metabolism, Michaelis–Menten kinetics
• Nonlinearity in metabolism, is one of the most
common sources of nonlinearity
5/7/2024
70. 70
Nonlinearity in metabolism
Capacity-limited metabolism
• The rate of metabolism, or the rate of elimination if
metabolism is the only pathway of elimination, is
defined by the Michaelis–Menten equation:
• where Vmax is the maximum rate (unit:
amount/time) of metabolism; Km is the Michaelis–
Menten constant (unit: same as the concentration
[amount/volume]), and C is the drug concentration
C
K
C
V
rate
Metabolism
m
max
5/7/2024
75. 75
Estimation of Michaelis–Menten parameters from
administration of a single IV bolus dose
Drug amount in the
Body (X)
IV bolus
administration
(dose = X0)
Elimination process
Based on the assumption of nonlinear elimination process:
C
K
C
V
rate
n
Eliminatio
m
max
5/7/2024
76. 76
Estimation of Michaelis–Menten parameters from
administration of a single IV bolus dose
C
K
C
V
-
dt
dX
m
max
Divide by Vd
C
K
C
Vd
V
dt
dC
m
max
Assume that
Vd
V
V max
max
C
K
C
V
-
dt
dC
m
max
Rearrangement
dC
dC
C
K
dt
V
- m
max
Derivation of observed concentration equation
5/7/2024
77. 77
Estimation of Michaelis–Menten parameters from
administration of a single IV bolus dose
Integration
dC
dC
C
K
dt
V
- m
max
m
max
0
m
0
K
t
V
lnC
K
C
C
lnC
Previous equation represent the observed conc
5/7/2024
78. 78
Estimation of Michaelis–Menten parameters from
administration of a single dose
Terminal line
(C<< Km)
Observed conc
m
max
0
m
0
K
t
V
lnC
K
C
C
lnC
5/7/2024
79. 79
Estimation of Michaelis–Menten parameters from
administration of a single IV bolus dose
m
max
m
max
K
C
V
-
C
K
C
V
-
dt
dX
Divide by Vd
C
K
V
dt
dC
m
max
Derivation of terminal concentration equation
When C>>Km: Km+C ≈ C
First order elimination
t
K
V
lnC
lnC
m
max
*
0
This equation represent the
terminal concentration
equation
5/7/2024
80. 80
Estimation of Michaelis–Menten parameters from
administration of a single dose
Observed conc
m
max
0
m
0
K
t
V
lnC
K
C
C
lnC
t
K
V
lnC
lnC
m
max
*
0
Terminal line
(C<< Km)
5/7/2024
81. 81
Estimation of Michaelis–Menten parameters from
administration of a single dose
0
0
0
m
C
*
C
ln
C
K
m
max
K
303
.
2
V
Slope(log)
5/7/2024
82. 82
Estimation of Michaelis–Menten parameters from
administration of a single IV bolus dose
• Steps:
1. Plot log(conc)-time profile
2. Get the initial conc (C0)
3. Extrapolate the terminal line to get an initial
terminal conc (C0
*)
4. Calculate the slope of the terminal line using the
log
0
0
0
m
C
*
C
ln
C
K slope
K
2.303
V m
max
0
Dose
Vd
C
Vd
V
V max
max
5/7/2024
83. 83
Example 1
• The following concentration time profile was
constructed after administration of 300 mg dose of
drug A to an adult patient.
find
1. Vm
2. Km
3. Vd
4. The dose required to produce a steady-state conc of 20
mg/L in this patient.
5/7/2024
86. 86
Example 1
• The dose required to produce a steady-state
concentration of 20 mg/L in this patient:
hr
mg
C
Km SS
/
340
20
65
.
6
20
*
453
VmC
rate
Dosing SS
gm
mg 16
.
8
8160
24
*
rate
Dosing
Dose
Daily
5/7/2024
87. 87
Estimation of Michaelis–Menten parameters from
two steady-state drug concentrations arising from
two dosing rates
• At steady state:
Input rate = output rate
Dosing rate = Elimination rate
C
K
C
V
R
m
max
R is the input rate that is described as:
D
F
R
5/7/2024
88. 88
Estimation of Michaelis–Menten parameters from
two steady-state drug concentrations arising from
two dosing rates
• Two dosing rates resulted in the following
steady state conc:
• Estimate Vmax and Km
Dosing rate Css
R1 Css1
R2 Css2
5/7/2024
89. 89
Estimation of Michaelis–Menten parameters from
two steady-state drug concentrations arising from
two dosing rates
Css1
R1
K
R1
Css1
V
Css1
K
Css1
V
R1 m
max
m
max
Css2
R2
K
R2
Css2
V
Css2
K
Css2
V
R2 m
max
m
max
Two equations with two unknowns
5/7/2024
90. 90
Example 2
• RM is a 32 year old, 80kg male who is being seen in the
Neurology Clinic. Prior to his last visit he had been taking
300mg of Phenytoin daily; however, because his seizures
were poorly controlled and because his plasma
concentration was only 8mg/L, his dose was increased to
350mg daily. Now he complains of minor CNS side effects
and his reported plasma Phenytoin concentration is 20mg/L.
Renal and hepatic function are normal. Assume that both of
the reported plasma concentrations represent steady state
and that the patient has compiled with the prescribed
dosing regimens. Calculate RM’s apparent Vm and Km and a
new daily dose of Phenytoin that will result in a steady state
level of about 15mg/L.
5/7/2024
92. 92
Example 2
• Calculate RM’s a new daily dose of Phenytoin
that will result in a steady state level of about
15mg/L
day
mg
C
Km SS
/
5
.
337
15
5
.
2
15
*
75
.
393
VmC
rate
Dosing SS
5/7/2024
93. • Chronopharmacokinetics and Time-Dependent
Pharmacokinetics
• Chronopharmacokinetics broadly refers to a temporal
change in the rate process (such as absorption or
elimination) of a drug.
• The temporal changes in drug absorption or
elimination can be cyclical over a constant period
(e.g., 24-hour interval), or they may be noncyclical, in
which drug absorption or elimination changes over a
longer period of time.
• Chronopharmacokinetics is an important
consideration during drug therapy.
5/7/2024 93
94. • Time-dependent pharmacokinetics generally refers to
a noncyclical change in the drug absorption or drug
elimination rate process over a period of time. Time-
dependent pharmacokinetics leads to nonlinear
pharmacokinetics.
• Unlike dose-dependent pharmacokinetics, which
involves a change in the rate process when the dose
is changed, time-dependent pharmacokinetics may
be the result of alteration in the physiology or
biochemistry in an organ or a region in the body that
influences drug disposition .
5/7/2024 94
95. Drug distribution
• INTRODUCTION
• Once a drug begins to be absorbed, it undergoes
various transport processes, which deliver it to body
areas away from the absorption site. These transport
processes are collectively referred to as drug
distribution and are evidenced by the changing
concentrations of drug in various body tissues and
fluids.
• Information concerning the concentration of a drug
in body tissues and fluids is limited to only a few
instances in time (i.e., we know the precise plasma
drug concentration only at the few times that blood
samples are drawn)
5/7/2024 95
96. • Drug distribution means the reversible transfer of
drug from one location to another within the body
• Once a drug has entered the vascular system it
becomes distributed throughout the various tissues
and body fluids in a pattern that reflects the
physiochemical nature of the drug and the ease with
which it penetrates different membranes
5/7/2024 96
97. Drug distribution patterns
The drug may remain largely within the vascular
system, ex: Plasma substitutes such as dextran and
drugs which are strongly bound to plasma protein
Some are uniformly distributed throughout the body
water, ex: low molecular weight water soluble
compounds (ethanol) and a few sulfonamides
5/7/2024 97
98. Distribution patterns (Contd.)
A few drugs are concentrated specifically in one or
more tissues that may or may not be the site of
action, ex: Iodine (in the thyroid gland), chloroquine
(in the liver even at conc 1000 times those present in
plasma), tetracycline (irreversibly bound to bone and
developing teeth) and highly lipid soluble
compounds (distribute into fat tissue)
5/7/2024 98
99. Most drugs exhibit a non-uniform distribution in the
body (largely determined by the ability to pass
through membranes and their lipid/water
solubility). The highest concentrations are often
present in the kidney, liver, and intestine.
Distribution patterns (Contd.)
5/7/2024 99
100. Table 1. Apparent Volumes of Distribution
of Some Drugs
Drug Liters/Kg Liter/70 Kg
Chloroquine 94 - 250 94 - 250
Nortriptyline 211 500
Digoxin 7 500
Lidocaine 1.7 120
Theophylline 0.5 35
5/7/2024 100
101. Factors affecting drug distribution
Rate of distribution - Membrane permeability
Blood perfusion
Extent of Distribution - Lipid Solubility
pH - pKa
Plasma protein binding
Intracellular binding
5/7/2024 101
102. Factors Affecting Rate of distribution
A. Membrane permeability
• The capillaries are typically lined with endothelium
whose cells overlap, though to a lesser degree than
epithelial cells. Also, the junctions between cells are
discontinuous. Capillary walls are quite permeable. Lipid
soluble drugs pass through very rapidly. Water soluble
compounds penetrate more slowly at a rate more
dependent on their size. Low molecular weight drugs
pass through by simple diffusion. For compounds with
molecular diameter above 100 Å transfer is slow.
• For drugs which can be ionized the drug's pKa and the pH
of the blood will have a large effect on the transfer rate
across the capillary membrane.
5/7/2024 102
103. Two deviations to the typical capillary structure which
result in variation from normal drug tissue
permeability:
Permeability is greatly increased in the renal capillaries by
pores in the membrane of the endothelial cells, and in
specialized hepatic capillaries, known as sinusoids which
may lack a complete lining. This results in more extension
distribution of many drugs out of the capillary bed.
On the other hand brain capillaries seem to have
impermeable walls restricting the transfer of molecules
from blood to brain tissue. Lipid soluble compounds can
be readily transferred but the transfer of polar substances
is severely restricted. This is the basis of the "blood-
brain" barrier.
5/7/2024 103
104. Factors Affecting Rate of distribution (Cont.)
B. Blood perfusion rate
: The rate at which blood perfuses to different organs
varies widely
5/7/2024 104
106. Total blood flow is greatest to brain, kidneys, liver,
and muscle with highest perfusion rates to brain,
kidney, liver, and heart. It would be expected that
total drug concentration would rise most rapidly in
these organs. Certain organs such as the adrenals
(1.2/0.2%) and thyroid (2.4/1%) also have large
perfusion rates.
5/7/2024 106
107. Factors affecting extent of
distribution
• PROTEIN BINDING
• Another factor that influences the distribution of
drugs is binding to tissues (nucleic acids, ligands,
calcified tissues, and adenosine triphosphatase) or
proteins (albumins, globulins, alpha-1-acid
glycoprotein, and lipoproteins).
• It is the unbound or free portion of a drug that
diffuses out of plasma. Protein binding in plasma can
range from 0 to >99% of the total drug in the plasma
and varies with different drugs.
• The extent of protein binding may depend on the
presence of other protein-bound drugs and the
concentrations of drug and proteins in the plasma.
5/7/2024 107
108. • Theoretically, drugs bound to plasma proteins are
usually not pharmacologically active. To exert an
effect, the drug must dissociate from protein
• Although only unbound drug distributes freely, drug
binding is rapidly reversible (with few exceptions), so
some portion is always available as free drug for
distribution.
• The association and dissociation process between
the bound and unbound states is very rapid and, we
assume, continuous
5/7/2024 108
109. • Extensive plasma protein binding will cause more
drug to stay in the central blood compartment.
Therefore drugs which bind strongly to plasma
protein tend to have lower volumes of distribution.
• Of these plasma proteins, albumin, which comprises
50 % of the total proteins binds the widest range of
drugs. Acidic drugs commonly bind to albumin, while
basic drugs often bind to alpha1-acid glycoproteins
and lipoproteins. Many endogenous substances,
steroids, vitamins, and metal ions are bound to
globulins.
5/7/2024 109
110. Table 4. Proteins with Potential Binding Sites for
Various Drugs
Drugs Binding Sites for Acidic
Agents
Bilirubin, Bile acids, Fatty Acids,Vitamin C,
Salicylates, Sulfonamides,Barbiturates,
Phenylbutazone,Penicillins, Tetracyclines,
Probenecid
Albumins
Binding Sites for Basic
Agents
Adenisine, Quinacrine,
Quinine,Streptomycin,
Chloramphenicol,Digitoxin, Ouabain,
Coumarin
Globulins, alpha1, alpha2,
beta1, beta2, gamma
5/7/2024 110
111. Forces involved in protein binding
• electrostatic interactions between groups on the protein
molecules with drugs i.e.
- the –NH3
+ of lysine and N- terminal amino acids,
- the –NH2
+- of histidine,
- the - S- of cysteine
- the - COO- of aspartic and glutamic acid residues.
• van der Waal's forces (dipole-dipole; dipole-induced
dipole; induced dipole-induced dipole)
• hydrogen bonding.
5/7/2024 111
112. • Agents which denature protein may cause the
release of bound drug.
• Often there may be competition between drugs, in
which agents that are bound very tightly, such as
coumarin anticoagulants, are able to displace less
tightly bound compounds from their binding sites.
5/7/2024 112
113. • Slight changes in the binding of highly bound drugs
can result in significant changes in clinical response
or cause a toxic response.
• Since it is the free drug in plasma which equilibrates
with the site of pharmacological or toxic response, a
slight change in the extent of binding, such as 99 to
98 % bound, which can result in an almost 100 %
change in free concentration, can cause very
significant alteration in response.
5/7/2024 113
114. • For a large number of drugs, including warfarin and
phenytoin, drug response will be dependent on free
drug concentration. Alteration of free concentration
by drug interaction or disease state can alter the
intensity of action of these drugs. Examples include
phenylbutazone and salicylates displacing
tolbutamide to give an increased effect,
hypoglycemia.
5/7/2024 114
115. • The degree of drug binding to plasma proteins is
usually expressed as a percentage or as a fraction ()
of the bound concentration (Cb) to the total
concentration (Ct), bound plus unbound (Cu) drug:
=Cb/(Cu+Cb)=Cb/Ct
• Drugs having an alpha value of greater than 0.9 are
considered highly bound (90%); those drugs with an
alpha value of less than 0.2 are considered to be little
protein bound
5/7/2024 115
116. • Bound drug is neither exposed to the body’s
detoxication (metabolism) processes nor is it filtered
through the renal glomeruli.
• Bound drug is therefore referred to as the inactive
portion in the blood, and unbound drug, with its
ability to penetrate cells, is termed the active blood
portion
5/7/2024 116
117. • The bound portion of drug serves as a drug reservoir
or a depot, from which the drug is released as the
free form when the level of free drug in the blood no
longer is adequate to ensure protein saturation.
• For this reason a drug that is highly protein bound
may remain in the body for longer periods of time
and require less frequent dosage administration than
another drug that may be only slightly protein bound
and may remain in the body for only a short period
of time.
5/7/2024 117
118. • For most drugs, distribution throughout the body
occurs mainly by blood flow through organs and
tissues. However, many factors can affect
distribution, including:
• · differing characteristics of body tissues,
• · disease states that alter physiology,
• · lipid solubility of the drug,
• · regional differences in physiologic pH (e.g., stomach
and urine), and
• · extent of protein binding of the drug.
5/7/2024 118
119. • BODY TISSUE CHARACTERISTICS
• To understand the distribution of a drug, the
characteristics of different tissues must be
considered. Certain organs, such as the heart, lungs,
and kidneys, are highly perfused with blood; fat
tissue and bone (not the marrow) are much less
perfused. Skeletal muscle is intermediate in blood
perfusion.
• The importance of these differences in perfusion is
that for most drugs the rate of delivery from the
circulation to a particular tissue depends greatly on
the blood flow to that tissue. This is called perfusion-
limited distribution. .
5/7/2024 119
120. • Perfusion rate limitations occur when the
membranes present no barrier to distribution. The
rate-limiting step is how quickly the drug gets to the
tissue.
• If the blood flow rate increases, the distribution of
the drug to the tissue increases. Therefore, drugs
apparently distribute more rapidly to areas with
higher blood flow
5/7/2024 120
121. • Highly perfused organs rapidly attain drug
concentrations approaching those in the plasma; less
well-perfused tissues take more time to attain such
concentrations. Furthermore, certain anatomic
barriers inhibit distribution, a concept referred to as
permeability-limited distribution.
• This situation occurs for polar drugs diffusing across
tightly knit lipoidal membranes. It is also influenced
by the oil/water partition coefficient and degree of
ionization of a drug.
5/7/2024 121
122. • DISEASE STATES AFFECTING DISTRIBUTION
• Another major factor affecting drug distribution is
the effect of various disease states on body
physiology.
• In several disease states, such as liver, heart, and
renal failure, the cardiac output and/or perfusion
of blood to various tissues are altered.
5/7/2024 122
123. • A decrease in perfusion to the tissues results
in a lower rate of distribution and, therefore, a
lower drug concentration in the affected
tissues relative to the plasma drug
concentration.
• When the tissue that receives poor perfusion
is the primary eliminating organ, a lower rate
of drug elimination results, which then may
cause drug accumulation in the body.
5/7/2024 123
124. • LIPID SOLUBILITY OF THE DRUG
• The extent of drug distribution in tissues also
depends on the physiochemical properties of the
drug as well as the physiologic functions of the
body.
• A drug that is highly lipid soluble easily
penetrates most membrane barriers, which are
mainly lipid based, and distributes extensively to
fat tissues.
5/7/2024 124
125. • Drugs that are very polar and therefore hydrophilic
(e.g., aminoglycosides) do not distribute well into fat
tissues. This difference becomes important when
determining loading dosage requirements of drugs in
overweight patients.
• If total body weight is used to estimate dosage
requirements and the drug does not distribute to
adipose tissue, the dose can be overestimated.
5/7/2024 125
126. • REGIONAL DIFFERENCES IN PHYSIOLOGIC PH
• Another factor affecting drug distribution is the
different physiologic pHs of various areas of the
body. The difference in pH can lead to localization of
drug in tissues and fluids.
• A drug that is predominantly in its ionized state at
physiologic pH (7.4) does not readily cross
membrane barriers and probably has a limited
distribution.
• An example of this phenomenon is excretion of drugs
in breast milk..
5/7/2024 126
127. • Only un-ionized drug can pass through lipid
membrane barriers into breast milk. Alkaline drugs,
which would be mostly un-ionized at pH 7.4, pass
into breast tissue Once in breast tissue, the alkaline
drugs ionize because breast tissue has an acidic pH;
• therefore, the drugs become trapped in this tissue.
This same phenomenon can occur in the urine.
• Due to the nature of biologic membranes, drugs that
are un-ionized (uncharged) and have lipophilic (fat-
soluble) properties are more likely to cross most
membrane barriers.
5/7/2024 127
128. DISTRIBUTION
Storage (Concentration-Sequestration) of the
Drugs in Tissues
– Stored drug molecules in tissues serve as drug
reservoir.
– The duration of the drug effect may get longer.
– May cause a late start in the therapeutic effect
or a decrease in the amount of the drug effect.
Redistribution:
– Some drugs (especially general anesthetics)
which are very lipophilic, following the injection,
firstly (initially) distributes to the well-perfused
organs like central nervous system...
5/7/2024 128
129. – Later, the distribution occurs to less perfused
organs like muscles.
– At last, distribution of these drugs shifts to the
very low-perfused tissues like adipose (fat) tissue.
– Redistribution results with the running away of
the drugs from their target tissue and last their
effect
5/7/2024 129
130. DISTRIBUTION
Passage of the drugs to CNS:
– A blood-brain barrier exists (except some
areas in the brain) which limits the passage of
substances.
– Non-ionized, highly lipophilic, small molecules
can pass into the CNS and show their effects.
– Some antibiotics like penicillin can pass through
the inflamed blood-brain barrier while it can’t
pass through the healthy one.
5/7/2024 130
131. Passage of the drugs to fetus:
– Placenta doesn’t form a limiting barrier for the
drugs to pass to fetus.
– The factors that play role in simple passive
diffusion, effect the passage of drug molecules to
the fetus.
Placental blood flow
Molecular size
5/7/2024 131
132. Drug solubility in lipids
Fetal pH (ion trapping): fetal plasma pH: 7.0 to
7.2; pH of maternal plasma: 7.4, so according to
the ion trapping rules, weak basic drugs tend
to accumulate in fetal plasma compared to
maternal plasma
5/7/2024 132
133. Metabolism
• Drugs and toxins are seen as foreign to patients
bodies
• Drugs can undergo metabolism in the lungs, blood,
and liver
• Body works to convert drugs to less active forms and
increase water solubility to enhance elimination
5/7/2024 133
134. . Drug metabolism
• Biotransformation is a term used to indicate the
chemical changes that occur with drugs within the
body as they are metabolized and altered by various
biochemical mechanisms.
• The process of biotransformation is commonly
referred to as the “detoxification” or “inactivation”
process.
5/7/2024 134
135. • BIOTRANSFORMATION
• Biotransformation processes are affected by many
factors. The functioning of metabolic enzyme
systems may be quite different at the extremes of
age. Neonates are at risk of toxicity from
chloramphenicol because they do not conjugate this
drug efficiently.
• Also, the social habits of a patient may affect drug
elimination. Alcohol use and smoking may increase
hepatic clearance of some drugs by inducing
metabolic enzymes..
5/7/2024 135
136. The biotransformation of a drug results in its
conversion to one or more compounds that are
• more water soluble,
• more ionized,
• less capable of being stored in fat tissue,
• less able to penetrate cell membranes,
• less active pharmacologically,
• less toxic and is more readily excreted
5/7/2024 136
137. There are four principal chemical reactions involved
in the metabolism of drugs:
• oxidation
• reduction
• hydrolysis
• conjugation
Other metabolic processes, including methylation,
and acylation conjugation reactions, occur with
certain drugs to foster elimination.
5/7/2024 137
138. Metabolism
• Liver - primary route of drug metabolism
• Liver may be used to convert pro-drugs
(inactive) to an active state
• Types of reactions
– Phase I (Cytochrome P450 system)
– Phase II
5/7/2024 138
139. Phase I reactions
• Cytochrome P450 system
• Located within the endoplasmic reticulum
of hepatocytes
• Through electron transport chain, a drug
bound to the CYP450 system undergoes
oxidation or reduction
• Enzyme induction
• Drug interactions
5/7/2024 139
141. • Drug metabolism or biotransformation refers to the
biochemical conversion of a drug to another chemical form.
• The process of biotransformation is usually enzymatic but
drugs may undergo non-enzymatic transformation e.g.
ester hydrolysis.
• Metabolizing enzymes of the endoplasmic reticulum are
called microsomal enzymes and are abundantly found in
Liver.
5/7/2024 141
142. • Phase I reactions are also called as Synthetic or
Functionalization Reactions.
• Biotransformation usually results in the metabolites that
are more polar and considerably less active than the parent
compounds.
• Metabolites are excreted in the urine more rapidly than
their precursors because often they are not subjected to
tubular reabsorption.
• Hence the apparent volume of distribution of a metabolite
is usually less than that of the parent drug.
5/7/2024 142
146. Phase I reactions
(microsomal)
• Oxidation reactions : Two types of oxidation reactions:
Oxygen is incorporated into the drug molecule (e.g.
hydroxylation)
– Oxidation causes the loss of part of the drug molecule
(e.g. oxidative deamination, dealkylation)
5/7/2024 146
147. o Aromatic hydroxylation :
e.g. lignocaine → 3 – hydroxy lignocaine
o Aliphatic hydroxylation : Hydroxylation of aliphatic side chain of
pentobarbitone.
OH
OH
5/7/2024 147
148. o Epoxidation :
e.g. carbamazepine dihydroxy – carbamazepine.
o N-Dealkylation
5/7/2024 148
150. • N-Oxidation :
e.g. N-Oxidation of 3-methylpyridine
S-Oxidation : S-Oxidation of sulfides to sulfoxides is one of the most common
metabolic transformations of sulfur-containing drugs.
5/7/2024 150
151. Non microsomal
• Oxidation :
o Alcohol dehydrogenase :
e.g.
H2
C
CH3
HO
ethanol
H
C
CH3
O
acetaldehyde
5/7/2024 151
152. • Aldehyde oxidation :
e.g. acetaldehyde to acetic acid
H
C
CH3
O
acetaldehyde
C
H3C
O
OH
acetic acid
OH
• Xanthine oxidase :
NH
C=O
N
N
O
N
O
NH
N
N
O
N
O
theophylline
5/7/2024 152
153. • Aromatases : cyclohexane benzoic acid to benzoic acid
O
OH
cyclohexane carboxylic acid
O
OH
benzoic acid
5/7/2024 153
155. • Azo reduction :
e.g. azo dyes used as colouring agents in pharmaceutical products and food are reduced to form
amines both in the liver and the Intestine.
Hydrolysis :
o ester hydrolysis :
5/7/2024 155
159. Phase II reactions
• Polar group is conjugated to the drug
• Results in increased polarity of the drug
• Types of reactions
– Glycine conjugation
– Glucuronide conjugation
– Sulfate conjugation
5/7/2024 159
160. Several examples of biotransformations occuring within
the body are as follows:
• Acetaminophen Acetaminophen glucuronide
• Amoxapine 8-hydroxy-amoxapine
• Procainamide p-Aminobenzoic acid
• Nitroglycerin 1-2and 1-3 dinitroglycerol
5/7/2024 160
161. It is important to mention that several factors influence
drug metabolism.
• species differences
• age of the patient
• diet
• presence of disease states
5/7/2024 161
162. DRUG ELIMINATION
• The liver and kidneys are the two major organs
responsible for eliminating drugs from the body.
Although both organs share metabolic and excretory
functions, the liver is principally responsible for
metabolism and the kidneys for elimination.
• The importance of these organs cannot be
overestimated in determining the magnitude and
frequency of drug dosing. Additionally, an
appreciation of the anatomy and physiology of these
organs will provide insight into the impact of disease
and altered physiologic states, as well as concomitant
drug administration, on the clearance and dosing of
drugs..
5/7/2024 162
163. • The physical and chemical properties of a drug are
important in determining drug disposition. For
example, lipophilic drugs (compared with hydrophilic
drugs) tend to be:
• · bound to a greater extent to plasma proteins,
• · distributed to a greater extent throughout the body,
and
• · metabolized to a greater extent in the liver
5/7/2024 163
164. • Finally, concomitant drug use may affect drug
metabolism. Certain drugs, such as
phenobarbital, induce hepatic enzymes; others,
such as cimetidine, may inhibit them.
• Even in healthy individuals, in the absence of
hepatic enzyme inducers or inhibitors, the
ability to metabolize drugs may vary
considerably.
• For example, investigators have shown that two
distinct subpopulations have varying capacities
for drug acetylation (phase II reaction).
5/7/2024 164
165. • These differences are the result of genetic variations.
"Fast acetylators" have a greater rate of elimination
for drugs such as isoniazid and hydralazine. For "slow
acetylators," the usual doses of these agents may
result in excessive plasma concentrations and,
therefore, increased drug toxicities.
5/7/2024 165
166. • RENAL ELIMINATION
• . The fraction of drug metabolized is different for
various agents. The overall elimination rate is the
sum of all metabolism and excretion processes and is
referred to as total body elimination:
• total body elimination = drug excreted unchanged +
drug metabolized
Excretion is the process that removes a drug from
tissues and the circulation. A drug can be excreted
through urine, bile, sweat, expired air, breast milk, or
seminal fluid
5/7/2024 166
167. • Excretion may occur for a biotransformed drug or for
a drug that remains unchanged in the body. For
example, penicillin G is primarily excreted unchanged
in the urine. Elimination of this drug is thus
dependent on renal function. Renal excretion is the
net effect of three distinct mechanisms within the
kidneys:
• · glomerular filtration,
• · tubular secretion, and
• · tubular reabsorption.
5/7/2024 167
169. RENAL EXCRETION
• Drugs and metabolites are excreted from the
kidneys by 2 ways.
a) Glomerular filtration
b) Tubular secretion
• Tubular reabsorption is not an excretion way;
however there is no doubt that it effects the
excretion of drugs from the body by the kidney.
a.
5/7/2024 169
170. ) Glomerular filtration:
Simple passive diffusion play role in glomerular
filtration.
The filtration rate is 110-130 ml/min.
They are filtered from the glomerulus into
proximal tubules except the bound fraction of
drug molecules to the plasma proteins. Because
albumin cannot be filtered from the glomerulus,
the drugs cannot pass through into the proximal
tubules
5/7/2024 170
171. RENAL EXCRETION
b) Tubular secretion:
• There are 3 important points about the tubular
secretion mechanism of the drugs:
Tubular secretion occurs mainly in the proximal
tubules.
Active transport is the main mechanism for
tubular secretion.
The efficiency (performance) of the excretion
by tubular secretion is higher than glomerular
filtration route. Clearance maximum in
glomerular filtration is approximately 120
ml/min, whereas the clearance maximum of
tubular secretion is about 600 ml/min.
5/7/2024 171
172. RENAL EXCRETION
• Tubular reabsorption:
This mechanism works in an opposite (counter)
way by reducing the drug or metabolite
excretion.
Tubular reabsorption occurs mainly in distal
tubules and partially in proximal tubules.
It occurs by simple passive diffusion generally
5/7/2024 172
173. Changing the pH value of the urine (making the
urine acidic or basic) is going to change the
ionization degree and the simple passive diffusion
of the drug or the metabolite and lastly affect the
excretion from the kidney.
If we make the urine acidic, the reabsorption of the
weak acid drug from the renal tubules into the
blood will increase, thus the excretion will
decrease.
In the opposite way, making the urine basic will
cause an increase in the excretion of weak acid
drugs
5/7/2024 173
174. • These substances are
generally secreted into
the biliary ducts from the
hepatocytes by active
transport and finally they
are drained into the
intestines.
• Especially, highly ionized
polar compounds
(conjugation products)
can be secreted into the
bile in remarkable
amounts.
BILIARY EXCRETION
5/7/2024 174
175. • After biotransformation,
metabolites are drained
into the small intestine by
biliary duct.
• Drug metabolites in the
small intestine are broken
down again in the small
intestine and reabsorbed
back reaching the liver by
portal vein again.
• This cycle between the
liver and small intestine is
called the enterohepatic
cycle.
ENTEROHEPATIC CYCLE
5/7/2024 175
176. • Especially the drugs which are metabolized by the
conjugation reactions go under enterohepatic
cycle.
• This is important, because enterohepatic cycle
prolongs the duration of stay of the drugs in our
body which leads an increase in the duration of
their effect.
• Drug examples that go under the enterohepatic
cycle in remarkable amounts.
Chlorpromazine
Digitoxin
5/7/2024 176
177. ARTIFICIAL EXCRETION WAYS
• Hemodialysis is one of the options among
the artificial excretion way for the drugs.
5/7/2024 177
178. ARTIFICIAL EXCRETION WAYS
• For the achievement of this system, there
are some requirements:
Plasma protein binding of the drug should be
low (bound fraction should be low).
Drug should not be stored in tissues (apparent
volume of the drug should be low)
The main elimination route of the drug should
be from kidneys in unchanged (without
biotransformation) form.
5/7/2024 178
179. CLEARANCE
• It can be described as the volume of plasma
cleared from the drug per unit time (ml/min).
• Total Body Clearance: It is the plasma volume
cleared from the drug per unit time via the
elimination of the drug from all biotransformation
and excretion mechanisms in the body.
5/7/2024 179
180. • Renal Clearance: It can be described as the rate of
the excretion of a drug from kidneys. So in other
words, renal clearance is the volume of plasma
cleared from the non-metabolized (unchanged) drug
via the excretion by kidneys per minute.
• There are four important factors that affect the renal
clearance of the drugs:
Plasma protein binding of the drug.
Tubular reabsorption ratio of the drug.
Tubular secretion ratio of the drug.
Glomerular filtration ratio of the drug.
5/7/2024 180
181. CL renal = [(Glomerular filtration rate + Tubular secretion rate) – Tubular reabsorption rate] / Cp
If the renal clearance of the drug is higher than the physiological creatinine clearance (120-130 ml/m
that time we can say that the tubular secretion helps and contributes the elimination
of the drug additionally to filtration.
In early newborns and newborns, glomerular filtration and tubular secretion mechanisms
are immature and not sufficient.
Renal Clearence (CLR) =
V x CU
t x CP
V= collected urine volume
t= duration to collect the urine
CP= plasma concentration of the drug
CU= urine concentration of the drug
5/7/2024 181
182. From the Site of Delivery to Elimination…
steps in drug delivery, absorption, distribution and elimination
• Distribution
– Drugs must reach the site of action
• Tissue
• Plasma
• Elimination
• Metabolism
– Liver, kidneys, cells
• Excretion
– Kidneys
– Feces
Depends upon drug binding capabilities
5/7/2024 182
184. Mathematical Modeling of Drug
Disposition
• Single compartment
• Single compartment with absorption
• Two compartments
• Two compartments with absorption
• Physiological Models
5/7/2024 184
185. Single Compartment Model
• Assumptions:
– Body as one compartment characterized by a
volume of distribution (Vd)
– Drug is confined to the plasma (small V)
C, Vd
absorption
elimination
k, C
t
C/C0
5/7/2024 185
186. One-Compartment Model with Absorption
• Low absorption occurs
• Absorption is the rate-
limiting step
• Slow absorption may
represent drug entry
through GI tract or leakage
into circulation after SC
injection
• Drugs require multiple
doses to maintain drug
concentration within
therapeutic window
t
M/D0
t
M/D0
5/7/2024 186
187. The simplest
pharmacokinetic model is
the single compartment
open-model system.
This model depicts the
body as one compartment
characterized by a certain
volume of distribution (Vd)
that remains constant.
5/7/2024 187
189. For drugs whose
distribution follows first-
order, one-compartment
pharmacokinetics, a plot
of the logarithm of the
concentration of drug in
the plasma (or blood)
versus time will yield a
straight line.
5/7/2024 189
190. • The equation that describes the plasma decay
curve is
• Cp=C0e-kelt
• where Kel is the first-order rate of elimination
of the drug from the body,
• Cp is the concentration of the drug at time
equal to t,
• C0 is the concentration of drug at time equal
to zero.
5/7/2024 190
191. LogCp = LogC0-Kel/2.303(t)
• Most drugs administered orally can be adequately
described using a one-compartment model.
• Drugs administered by rapid intravenous infusion
are usually described by a two-compartment or
three compartment model system.
5/7/2024 191
192. Half life
• The half-life (T1/2) of a drug describes the time
required for a drug’s blood or plasma
concentration to decrease by one half.
• The biological half-life of a drug in the blood
may be determined graphically off of a
pharmacokinetic plot of a drug’s blood-
concentration time plot, typically after
intravenous administration to a sample
population.
5/7/2024 192
193. The half-life can also be mathematically determined.
Kelt/2.303=log C0 -logCp=log C0 /Cp
If it assumed that Cp is equal to one-half of C0
p, the
equation will become:
Kelt/2.303= log C0/0.5C0=log2
Thus,
t1/2=2.303log2/Kel=0.693/Kel
Kel=0.693/t1/2
5/7/2024 193
194. • Data on a drug’s biologic half-life are useful in
determining the most appropriate dosage regimen to
achieve and maintain the desired blood level of drug.
• Such determinations usually result in such
recommended dosage schedules for a drug, as the
drug to be taken every 4 hours, 6 hours, 8 hours, etc.
5/7/2024 194
195. Two-Compartment Model
• Drug rapidly
injected
• Drug distributed
instantaneously
throughout one
compartment and
slowly throughout
second
compartment
• Describes drug
concentration in
plasma injected IV
C1, V1
C2, V2
k2, C2
k12 k21
k1, C1
Compartment 1
Compartment 1
Compartment 2 Compartment 2
t t
Concentration after ingestion Concentration with slow absorption
C/C0
C/C0
5/7/2024 195
196. • In the two-compartment
system, a drug enters into
and is instantaneously
distributed throughout the
central compartment.
• Its subsequent distribution
into the second or
peripheral compartment is
slower.
5/7/2024 196
197. The central compartment
is usually considered to
include the blood, the
extracellular space, and
organs with good blood
perfusion, e.g., lungs, liver,
kidneys, heart.
5/7/2024 197
198. • Note the initial steep
decline of the plasma drug
concentration curve.
• This typifies the
distribution of the drug
from the central
compartment to the
peripheral compartment.
5/7/2024 198
199. A semi-logarithmic plot of
the plasma concentration
versus time after rapid
intravenous injection of a
drug which is best described
by a two-compartment
model system can often be
resolved into two linear
components.
5/7/2024 199
200. • The slope of the feathered line (-a/2.303) and the
extrapolated line (-b/2.303) and the intercepts, A and
B, are determined.
Cp=Ae-at+Be-bt
• This is a bi-exponential equation which describes the
two-compartment system.
5/7/2024 200
201. Intravenous Bolus Administration
• INTRODUCTION
• In clinical practice, most pharmacokinetic dosing is performed
with one-compartment, intermittent infusion models at
steady state. Using these models, we can obtain an
elimination rate constant (K) and then calculate volume of
distribution (V) and dosing interval (t) based on this K value.
• So far, our discussion has been limited to a single intravenous
(IV) bolus dose of drug. Most clinical situations, however,
require a therapeutic effect for time periods extending
beyond the effect of one dose. In these situations, multiple
doses of drug are given.
• The goal is to maintain a therapeutic effect by keeping the
amount of drug in the body, as well as the concentration of
drug in the plasma, within a fairly constant range (the
therapeutic range).
5/7/2024 201
202. • INTRAVENOUS BOLUS DOSE MODEL
• Although not used often clinically, the simplest
example of multiple dosing is the administration of
rapid IV doses (IV boluses) of drug at constant time
intervals, in which the drug is represented by a one-
compartment model with first-order elimination.
• Clinical Correlate
• This lesson describes a one-compartment, first-order,
IV bolus pharmacokinetic model. It is used only to
illustrate certain math concepts that will be further
explored with the more commonly used IV intermittent
infusion
5/7/2024 202
203. • The first dose produces a plasma drug concentration
versus time curve like the one. C0 is now referred to
as Cmax, meaning maximum concentration, to group
it with the other peak concentrations that occur with
multiple dosing.
• If a second bolus dose is administered before the
first dose is completely eliminated, the maximum
concentration after the second dose (Cmax2) will be
higher than that after the first dose (Cmax1) The
second part of the curve will be very similar to the
first curve but will be higher (have a greater
concentration.
5/7/2024 203
204. • The time between administration of doses is the
dosing interval. The dosing interval, symbolized by
the Greek letter tau (t), is determined by a drug's
half-life. Rapidly eliminated drugs (i.e., those having
a short half-life) generally have to be given more
frequently (shorter t), than drugs with a longer half-
life
5/7/2024 204
205. • If a drug follows first-order elimination (i.e., the
fraction of drug eliminated per unit of time is
constant), then plasma drug concentrations after
multiple dosing can be predicted from concentrations
after a single dose.
• This method uses the principle of superposition, a
simple overlay technique. If the early doses of drug do
not affect the pharmacokinetics (e.g., absorption and
clearance) of subsequent doses, then plasma drug
concentration versus time curves after each dose will
look the same; they will be superimposable. The only
difference is that the actual concentrations may be
higher at later doses, because drug has accumulated
5/7/2024 205
206. • A second IV bolus dose is administered after
the dosing interval (t), but before the first
dose is completely eliminated.
• Because Ct = C0e-Kt at any time (t) after the first
dose, it follows that:
• Cmin1 = Cmax1e-Kt
5/7/2024 206
207. • where Cmin1 is the concentration just before the
next dose is given and t, the dosing interval, is the
time from Cmax to Cmin.
• Cmax2 is the sum of Cmin1 and Cmax1, as the same
dose is given again:
• Cmax2 = Cmax1 + Cmin1
• We showed that:
• Cmin1 = Cmax1e-Kt
• so:
• Cmax2 = Cmax1 + Cmax1e-Kt
5/7/2024 207
209. • Above equation ,where n is the number of
doses given. This equation can be simplified
by mathematical procedures to a more useful
form
5/7/2024 209
211. • INTRAVENOUS BOLUS EQUATIONS AT STEADY STATE
• As successive doses of a drug are administered, the drug
begins to accumulate in the body. With first-order elimination,
the amount of drug eliminated per unit of time is proportional
to the amount of drug in the body. Accumulation continues
until the rate of elimination approaches the rate of
administration:
• rate of drug going in = rate of drug going out
• As the rate of drug elimination increases and then approaches
that of drug administration, the maximum (peak) and
minimum (trough) concentrations increase until an
equilibrium is reached. After that point, there will be no
additional accumulation; the maximum and minimum
concentrations will remain constant with each subsequent
dose of drug .
5/7/2024 211
212. • When this equilibrium occurs, the maximum (and minimum)
drug concentrations are the same for each additional dose
given (assuming the same dose and dosing interval are used).
When the maximum (and minimum) drug concentrations for
successive doses are the same, the amount of drug eliminated
over the dosing interval (rate out) equals the dose
administered (rate in) and the condition of "steady state" is
reached.
• Steady state will always be reached after repeated drug
administration at the same dosing interval if the drug follows
first-order elimination. However, the time required to reach
steady state varies from drug to drug, depending on the
elimination rate constant. With a higher elimination rate
constant (a shorter half-life), steady state is reached sooner
than with a lower one (a longer half-life)
5/7/2024 212
213. • Steady state is the point at which the amount of drug
administered over a dosing interval equals the amount of drug
being eliminated over that same period and is totally
dependent on the elimination rate constant.
• Therefore, when the elimination rate is higher, a greater
amount of drug is eliminated over a given time interval; it
then takes a shorter time for the amount of drug eliminated
and the amount of drug administered to become equivalent
(and, therefore, achieve steady state). If the half-life of a drug
is known, the time to reach steady state can be determined. If
repeated doses of drug are given at a fixed interval, then in
one half-life the plasma concentrations will reach 50% of
those at steady state.
5/7/2024 213
214. • ACCUMULATION FACTOR
• Equations can describe the plasma concentrations
and pharmacokinetics of a drug at steady state.
Remember, steady state will be reached only after
four or five half-lives.
• Recall that with an IV bolus injection of a drug fitting
a one-compartment model and first-order
elimination, the drug concentration at any time (t)
after any number of doses (n), not necessarily at
steady state,
5/7/2024 214
216. • To predict the plasma concentration of a drug
at any time t after n number of doses, we
therefore need to know four values:
• · drug dose (X0),
• · volume of distribution (Vd),
• · elimination rate constant (K), and
• · dosing interval (t).
5/7/2024 216
217. • AVERAGE STEADY-STATE CONCENTRATION WITH
INTRAVENOUS BOLUS DOSING
• We now have examined both the maximum and
minimum concentrations that occur at steady state.
Another useful parameter in multiple IV dosing
situations is the average concentration of drug in the
plasma at steady state. Because is independent of
any pharmacokinetic model, it is helpful to the
practicing clinician (model assumptions do not have
to be made). is not an arithmetic or geometric mean.
5/7/2024 217
218. • Several mathematical methods may be used
to calculate the average drug concentration, but only
one is presented here. A plasma drug concentration
versus time curve, after steady state has been
achieved with IV dosing By knowing the dose given
(X0) and the dosing interval (t), we can determine the
average concentration if we also know the area
under the plasma drug concentration versus time
curve (AUC) over t.
5/7/2024 218
220. • Continuous Infusion
• As stated previously, repeated doses of a drug (i.e.,
intermittent infusions) result in fluctuations in the plasma
concentration over time. For some drugs, maintenance of a
consistent plasma concentration is advantageous because of a
desire to achieve a consistent effect. To maintain consistent
plasma drug concentrations, continuous IV infusions are often
used. Continuous IV infusion can be thought of as the
administration of small amounts of drug at infinitely small
dosing intervals. If administration is begun and maintained at
a constant rate, the plasma drug concentration versus time
curve will result.
• The plasma concentrations resulting from the continuous IV
infusion of drug are determined by the rate of drug input (rate
of drug infusion, K0), volume of distribution (V), and drug
clearance (Clt). The relationship among these parameters is:
5/7/2024 220
222. • where t is the time since the beginning of the drug
infusion. This equation shows that the plasma
concentration is determined by the rate of drug
infusion (K0) and the clearance of drug from the body
(remember, VK = Clt). The equation is used to find a
concentration at a time before steady-state is reached.
• The term (1 - e-Kt) gives the fraction of steady-state
concentration achieved by time t after the infusion is
begun. For example, when t is a very low number, just
after an infusion is begun, K0(1 - e-Kt) is also very small.
When t is very large, (1 - e-Kt) approaches 1, so K0(1 - e-
Kt) approaches K0 and plasma concentration
approaches steady state
5/7/2024 222
224. • Loading Dose
• As stated previously, after a continuous IV infusion of
drug is begun, five drug half-lives are needed to
achieve steady state. If an immediate effect is
desired, that may be too long to reach the
therapeutic range. Sometimes a "loading dose" is
administered at the initiation of the infusion so that
the therapeutic range is maintained from the outset.
This loading bolus IV dose is usually relatively large
and may produce immediate therapeutic plasma
concentrations.
5/7/2024 224
225. • Note that a loading dose should not be used if
substantial side effects occur with large doses
of the drug. Also, sometimes clinicians desire
for drugs to accumulate slowly rather than to
achieve therapeutic concentrations
immediately so that the patient may have
adequate time to develop tolerance to the
initial side effects (e.g., tricyclic
antidepressants).
5/7/2024 225
226. • The desired loading dose for many drugs can be
derived from the definition of the volume of
distribution. As shown previously, V = X0/C0 for a
drug described by a one-compartment model.
Rearranging this equation, we see that the
loading dose equals the desired concentration
multiplied by the volume of distribution:
• X0 = C0(desired)V
• Note that C0 in this case is equivalent to the
desired steady-state concentration.
5/7/2024 226
227. • Loading doses usually are given as short
infusions (often 30 minutes). Taking this
procedure into account, we can further
modify the above equations to predict plasma
concentrations.
• For the loading dose:
5/7/2024 227
231. Extravascular routes of drug
administration
• Please note that a similar approach may be applied
to determine pharmacokinetic parameters of drugs
when any other extravascular route is used.
• The following assumptions are made:
• drug exhibits the characteristics of onecompartment
model
• absorption and elimination of a drug follow the first-
order process and passive diffusion is operative at all
the time
5/7/2024 231
234. • where dX/dt is the decrease in the amount of
absorbable drug present at the site of administration
per unit time.
• Ka is the firstorder absorption rate constant
• (Xa)t is the mass or amount of absorbable drug at
the site of administration (e.g. the gastrointestinal
tract) at time t.
5/7/2024 234
235. • Monitoring drug in the blood (plasma/serum)
or site of measurement
• The differential equation that follows relates
changes in drug concentration in the blood with
time to the absorption and the elimination rates
5/7/2024 235
237. • where dX/dt is the rate of change of amount of drug
in the blood;
• X is the mass or amount of drug in the blood or body
at time, t;
• Xa is the mass or amount of absorbable drug at the
absorption site at time t;
• Ka and K are the firstorder absorption and
elimination rate constants, respectively
• KaXa is the first-order rate of absorption
• and KX is the first-order rate of elimination
5/7/2024 237
238. • Determination of elimination half life (t1/2)
and elimination rate constant (K or Kel)
when written in concentration (Cp) terms, takes
the following form:
5/7/2024 238
240. • where KaFX0
• VðKa KÞ is the intercept of plasma drug
concentration versus time plot
• When time is large, because of the fact that
KaK, eKat approaches zero,
5/7/2024 240
242. • The apparent volume of distribution (V) For a
drug administered by the oral, or any other
extravascular, route of administration,
• the apparent volume of distribution cannot be
calculated from plasma drug concentration data
alone.
• The reason is that the value of F (the fraction of
• administered dose that reaches the general
circulation) is not known.
5/7/2024 242
244. • If we can reasonably assume, or if it has been
reported in the scientific literature, that F¼1.0
(i.e. the entire administered dose has reached the
general circulation), only then can we calculate
the apparent volume of distribution
• Following the administration of a drug by the oral
or any other extravascular route.
• In the absence of data for the fraction of
administered dose that reaches the general
circulation, the best one can do is to obtain the
ratio of V/F:
5/7/2024 244
245. • to obtain the peak plasma concentration
• There are three methods available for
determining peak plasma concentration (Cp)max.
Two are.
• Method 1. Peak plasma concentration obtained
• from the graph of plasma concentration versus
time
• Method 2. Peak plasma concentration obtained
by using an equation. shows that
5/7/2024 245
247. • Flip-flop kinetics
• Flip-flop kinetics is an exception to the usual case
in which the absorption rate constant is greater
than the elimination rate constant (Ka>K).
• For a drug absorbed by a slow first-order process,
such as certain types of sustainedrelease
formulations,
• the situation may arise,where the elimination
rate constant is greater than the absorption rate
constant (K>Ka).
5/7/2024 247
249. Goals
• Optimum therapeutic response with minimum
adverse effects
• Individualization of drug dosage regimen, esp drugs
with a narrow therapeutic window
5/7/2024 249
251. Dosage regimen design
Dosage
Regimen
Activity-toxicity
-Therapeutic window
-Side effects
-Toxicity
-conc-response rel
Pharmacokinetics:
ADME
Clinical Factors
-Patients (age, weight, patophysiologic cond
-Management of ther (multiple drug ther,
convenience of regimen, compliance of patient)
Other factors:
-Route of adm
-Dosage form
-Tolerance-dependence
-Drug interaction
-Cost
5/7/2024 251
252. Dosage regimen design
• The most accurate approach to dosage regimen
design is to calculate the dose based on the
pharmacokinetics of the drug in the individual
patient (not for initial dose; only for readjustment of
the dose).
• The initial dose was estimated using average
population pharmacokinetic parameters obtained
from literature. Clin pharm softwares for drugs with
narrow ther window are available (Datakinetics etc)
5/7/2024 252
253. 3 methods
1. Dosage regimens based on population averages:
(a) the fixed model
(b) the adaptive model
2. Dosage regimens based on partial pharmacokinetic
parameters
3. Empirical dosage regimens
5/7/2024 253
254. Dosage regimens based on population
averages
• Obtained from clinical studies published in the drug
literature
• (a) the fixed model, assumes that population
average pharmacokinetic parameters may be used
directly to calculate a dosage regimen for the patient
without any alteration.
5/7/2024 254
255. • Parameters such as : ka, F, VD apparent, and ke are
assumed to remain constant; follow a one-
compartment model. The practitioner may use the
usual dosage suggested by the literature and/or
make small adjustment based on the patient’s weight
and/or age
5/7/2024 255
256. (b) the adaptive model
dosage regimen was calculated by using patient
variables such as: weight, age, sex, body surface
area, and known patient patophysiology such as
renal disease as well as the known population
average pharmacokinetic parameters of the drug.
This model assumes that drug clearance do not
change from one dose to the next.
5/7/2024 256
257. Dosage regimens based on partial
pharmacokinetic parameters
• For drugs with unknown or unavailable
pharmacokinetic profile, the pharmacokineticist
needs to make some assumptions to calculate the
dosage regimen. Exp: to let F equal 1 or 100%.
the risk of undermedicated or
overmedicated. Assumptions will depend on the
safety, efficacy and therapeutic range of the drug.
5/7/2024 257
258. Empirical dosage regimens
• Not based on pharmacokinetic variables, but on
empirical clinical data, personal experience and
clinical observations.
5/7/2024 258
259. Dosage regimens for continuous
maintenance of therapeutic conc
• Half-lives < 30 minutes
low TI drugs : must be infused ex:
heparin
high TI : may be given less frequently
(than t1/2) but with higher MD
ex: Penicillin, 4 – 6 hr interval (t1/2 = 30
min)
5/7/2024 259
260. Dosage regimens for continuous
maintenance of therapeutic conc
• 30 min < t1/2 < 8 hr
- low TI drugs: must be given every
half- life or more frequently or by
infusion
ex: lidocain (90min) infusion,
theophylline (3-6 doses/day)
- high TI drugs: once every 1 – 3 t1/2
ex: cephalosporins (30min-3hr) 3 – 6
halflives
5/7/2024 260
261. Dosage regimens for continuous
maintenance of therapeutic conc
• 8 < t1/2 < 24 hr
- the most convenience
- a dose is given every half life, LD
must be twice MD to achieve Css
immediately
ex: sulfamethoxazole (high TI) and
clonidine (low TI)
5/7/2024 261
262. Dosage regimens for continuous
maintenance of therapeutic conc
• T1/2 > 24 hr
administration once daily is convenient
and promotes patient compliance
Ex: Chloroquine (high TI), Digitoxin (low TI)
5/7/2024 262
263. When one considers the development of a dosage
regimen, a number of factors that should be
considered
1) Inherent activity, i.e., pharmacodynamics, and
toxicity, i.e., toxicology of the drug.
2) The pharmcokinetics of the drug, which are
influenced by the dosage form in which the drug is
administered to the patient, e.g., biopharmaceutical
considerations.
5/7/2024 263
264. 3) The patient to whom the drug will be given and
encompasses the clinical state of the patient and
how the patient will be managed.
4) A typical factors may influence the dosage regimen.
5/7/2024 264
266. • The dosage regimen of a drug may simply involve the
administration of a drug once for its desired
therapeutic effect, e.g. pinworm medication, or
encompass the administration of drug for a specific
time through multiple doses.
• The objective of pharmacokinetic dosing is to design a
dosage regimen that will continually maintain a drug’s
therapeutic serum or plasma concentration within the
drug’s therapeutic index, i.e., above the minimum
effective concentration but below the minimum toxic
level.
5/7/2024 266
269. INTRODUCTION
Drugs are rarely used in single doses to produce an acute effect
But, drugs are administered in successive doses to produce a chronic
or prolonged effect
The goal in the design of dosage regimens is to achieve and maintain
drug concentrations in plasma or at the site of action that are both
safe and effective
That is to maintain the drug concentration with in the therapeutic
window (Below the minimum toxic concentration and above the
minimum effective concentration)
Toxicity would result if doses are administered too frequently,
whereas, effectiveness would be lost if the dosage rate are too
infrequent
The two parameters important in dosage regimen are
The size of the dose of the drug
The frequency of drug administration (time interval between
doses)
5/7/2024 269
270. INTRODUCTION…
Effect of frequency of administration of a drug on plasma drug level
Plasma
Drug
Concentration
Time
Minimum toxic concentration
Minimum toxic concentration
A
B
C
Therapeutic
Window
A – Too frequent dosing B – Proper dosing C – Inadequate frequency
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271. DRUG ACCUMULATION
• When drugs are administered on multiple dose regimen, each dose
(after first dose) is administered before the preceding doses are
completely eliminated
• This results in a phenomenon known as ‘drug accumulation’, where
the amount of the drug in the body (represented by plasma
concentration) builds up as successive doses are administered
• But, after seven doses of the drug at an interval equal to the drug
half-life, the maximum and minimum amounts in the body becomes
fairly constant
• This is called ‘Steady State Condition’
• At this stage, the amount of the drug lost during dosing interval is
equal to the administered dose
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272. DRUG ACCUMULATION…
Drug Accumulation during Multiple Dose Regimen
Dose =100 mg Dosing interval = t1/2 of the drug
No. of half
lives
(Frequency
number)
No. of doses
1 2 3 4 5 6 7 8
0 100 Max -
1 50 Min 150
2 75 175
3 87.5 187.5
4 93.8 193.8
5 96.88 196.88
6 98.44 198.44
7 99.22 199.22 Max
8 99.61 Min
This prediction of the amount of the drug in the body following repeated doses of a drug in the
above example is based on the assumption that its elimination half-life is constant throughout
the dosage regimen
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273. PRINCIPLE OF SUPERPOSITION
• An accepted plasma concentration profile at the steady state can be
devised with the aid of pharmacokinetic parameters derived from
single dose experiments based on the ‘principle of superposition’
• The principle of superposition assumes that early doses of a drug do
not affect the pharmacokinetic of subsequent doses
• The basic assumptions are that the drug is eliminated by first order
kinetics and that the pharmacokinetics of the drug after a single dose
(first dose) are not altered for multiple doses
• Therefore, the blood level after the second, third, or nth dose will
overlay or superimpose the blood level attained after n-1th dose
• In addition, AUC (0 – α) following the administration of a single dose
equals the AUC (t1 – t2) during a dosing interval at steady state
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274. PRINCIPLE OF SUPERPOSITION…
Simulated date showing blood level after administration of multiple
doses and accumulation of blood level when equal doses are given at
equal time intervals
Plasma
Drug
Concentration
Time (hours)
AUC (t1 – t2)
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