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52 ESSENTIAL PHARMACOLOGY
Notice that the curve has two distinct portions. Initially the
decline follows a straight line as the rate of elimination is at its
maximum, constant value. Then, as the concentration falls below
the Km for the metabolizing enzyme (alcohol dehydrogenase), the
kinetics become linear, and the characteristic exponential decline is
seen. The linear portion of the curve represents the time that you
are following the “one drink an hour” rule for metabolizing alco-
hol at a constant rate. Note that there is not a constant half- time
in the nonlinear pharmacokinetic model because the clearance is
different at each plasma concentration of the drug. The half- time is
longer at higher plasma concentrations.
Be careful, as seen, the nomenclature can be confusing. The
linear model can generate curves (exponentials) while the nonlin-
ear model can generate straight lines!
6.5 Intermittent Oral Dosing
The pharmacokinetic models we have developed have assumed to
this point that the dosing rate is a constant. In practice this occurs
only when drugs are administered slowly in an intravenous line
0510
Time, Hours
15 20
25
Concentration
2.0
1.5
1.0
0.5
0.0
Linear portion of curve when drug
concentraion is > Km
Exponential part of curve when
drug concentration is < Km
Figure6.14 Decrease in the plasma concentration of ethanol initially following
Clinical Pharmacokinetics 53
or through slow absorption from a skin patch or intramuscular
depot. However, for maintenance therapy it is much more com-
mon to administer drugs by periodic injections or as pills that
are taken several hours apart. In this case the dosing rate fluctu-
ates over time, reflecting both the drug administration schedule
and the rate of absorption from, for example, the GI tract. These
fluctuations lead to fluctuations in the plasma concentration.
However, the models we have developed do accurately predict the
average drug concentration over time in the plasma.
In a therapeutic setting, we normally attempt to maintain the
average concentration at a given target level, providing the fluctua-
tions do not cause side effects (at the high end) or loss of therapy (at
the low end).
Although the rate of drug absorption will influence the mag-
nitude of fluctuations in plasma concentration between doses, it is
much more important to know what fraction of administered doses
reaches the systemic circulation (the extent of absorption minus the
extent of hepatic first- pass metabolism). Therefore, bioavailability,
expressed as F, has a value between 0 and 1, and must be factored
in for oral dosing.
The target concentration (Css) now becomes the average of peak
and trough values (see Figure6.15) and the dosing rate becomes:
FDoseDosage Interval hoursave CssCL
/.
The dosage interval that is chosen for a given drug usually repre-
sents a compromise and is determined by several factors, such as rate
of absorption and elimination and the size of fluctuations in plasma
concentration that can be tolerated, as well as convenience.
The dosage interval should be no greater than the half- life, if fluc-
tuations greater than twofold cannot be tolerated. However, some
drugs, like the antibiotic penicillin, have a very short half- life on the
order of 30 minutes, but have very few side effects at high plasma con-
centrations.Such a drug can be given in very high doses at intervals far
longer than the half- life, e.g., every four hours, and still provide thera-
peutic concentrations of the drug in plasma between doses.
54 ESSENTIAL PHARMACOLOGY
Alternatively, daily doses may be divided into several portions
even for drugs with half- lives of 24– 48 hours or more in order to avoid
side effects associated with peak plasma concentrations.
A key consideration is also the design of a convenient dosing
schedule. Patient compliance would probably be negligible if a drug
had to be taken every 17 hours!
6.6 Pharmacokinetics ofSingle Doses
In the pharmacokinetic characterization of a drug, a single dose may
be given and the resulting plasma concentration monitored over time
(Figure 6.16). The Area Under the Curve of plasma concentration
plotted versus time (see below) is a complex function of the absorption
rate, bioavailability, and clearance of the drug. This is referred to as the
A.U.C. and is a term that is frequently used to compare two different
2
1
0123
Time (multiples of elimination half-time)
456
C
Steady state
• Attained after approximately four half-times
• Time to steady state independent of dosage
Steady-state concentrations
• Proportional to dose/dosage interval
• Proportional to FICL
Fluctuations
• Proportional to dosage interval/half-times
• Blunted by slow absorption
Figure6.15 -
-
th
Clinical Pharmacokinetics 55
formulations of a drug or as a measure of the effectiveness of a single
dose of a drug in providing a therapeutic plasma drug concentration.
6.7 Recapitulation ofEquations (These are
the“Need- to- Know” Equations forPharmacokinetics)
1. Volume of distribution, loading dose group (where F=1):
Vd Dose Plasma concentrationDoseTargetconcentrationVd/;
2. Clearance and half- time relationships:
TVdCLCLVdT
12
12
0 693 0 693
//
./;. /
3. Rate of elimination, and steady state relationships:
Rate of elimination=C × CL (true at all times)
Dosing Rate=Css × CL (true only at steady state)
F × Dose=(ave.)Css × CL × Dosage Interval (equilibrium for
oral dosing)
Amount of drug in blood
Absorption Elimination
C
max
: Highest concentration of
drug in blood
AUC
(Area Under the Curve):
Overall drug exposure
t
½
(Half-life): Time at which drug has
lost half its maximum
concentration
C
min
: Lowest concentration
of drug in blood
Time
Drug is taken
Figure6.16 Schematic diagram of the area under the curve analysis of drug
56
Chapter 7
Pharmacodynamics I:
Determining Effects
in Intact Organisms;
Dose-Response
Relationships in Patients
7.1 Graded Responses: Plots of Dose (Dosage) Versus
Intensity of Effect
As introduced earlier, pharmacodynamics is the science of how
drugs act on the body. Here we will begin by defining some of the
terms we use in pharmacodynamics. In the “dose-response curve”
Pharmacodynamics I 57
below, the intensity of some effect of a drug is plotted versus the
concentration of the drug (Figure7.1).
The effect is any measurable parameter, such as an increase or
decrease in blood pressure or blood glucose, or an increase in vital
capacity of the lungs of an asthmatic patient.
The relationship may not be simple (i.e., not monotonic). In
some cases there may be peaks of effectiveness at intermediate con-
centrations.
Potency reflects the concentration of drug necessary to have
an effect. The "Kact" (K for activation) or "ED50” (Effective dose
for 50% activation) refers to the concentration that gives 50% of the
maximum effect.
Efficacy refers to the magnitude of the effect achieved and
is typically the most important drug characteristic in defin-
ing whether a drug is of utility. After all. If it does not have any
effect or very little effect, it is not useful to you. Potency is often
thought to be a very important characteristic of drugs, but it is
less important than efficacy. If the drug has low potency, it sim-
ply means you have to provide more of it to the patient to get the
Intensity of effect
Slope
Concentration
Potency
Variability
Maximal
effect
Figure7.1
SOURCE:
58 ESSENTIAL PHARMACOLOGY
same effect, and often that is not a problem. Although it can be
a problem if it is difficult to get enough drug absorbed into the
patient’s bloodstream due to poor absorption or bioavailability.
Also, sometimes more potent drugs have fewer nonspecific side
effects because they are acting at fairly low concentrations, but
that is not always the case.
The concentration axis is often a logarithmic axis so that we
can get several orders of magnitude of drug on the same graph.
Wewill see that drugs typically act over a couple of orders of mag-
nitude of concentration, and when different drugs are compared,
the relevant ranges can cover several orders of magnitude.
Variability may occur for pharmacokinetic, pharmacodynamic,
or unknown reasons.
Some patients will exhibit different, idiosyncratic dose-
response curves:
1. Hyperreactivity – indicates a response to unusually low
levels of drug.
2. Hypersensitivity– term often reserved for an allergic response.
3. Hyporeactive – indicates little response to a drug in the
expected dosage range. May be due to tachyphylaxis– a rapid
loss of response, e.g., depletion of a neurotransmitter results in
decreased response to a drug that acts by displacing or promot-
ing transmitter release.
4. Drug tolerance usually refers to a slower process, such as a
loss of receptors due to chronic treatment and downregulation
(removal) of receptor molecules.
7.2 Therapeutic Index andTherapeutic Window
The therapeutic index is a measure of the difference between
the concentration of a drug that promotes desired actions and the
concentration of the drug that causes toxic or undesirable side
effects. The therapeutic index was originally defined as the ratio of
the concentration of the drug equal to its LD50 (the concentration
Pharmacodynamics I 59
leading to 50% death of recipients (typically in experimental ani-
mals), and the ED50, the concentration giving 50% of the desired
action, or providing benefit to 50% of the recipients. Currently, for
practical or humane reasons, a less severe side effect, called the
“humane endpoint,” can be substituted for death in this determi-
nation. Defined this way, the therapeutic index is a measure of
drug safety, and the larger the numerical value it has, the better
(Figure7.2).
The therapeutic window is the range of concentrations of
a drug that can be safely used to have some desired therapeutic
effect. The maximum value of drug concentration within the ther-
apeutic window would be lower than foot of the toxicity curve as
shown in the figure. However, some flexibility may be exercised
in defining the upper end of the window if the side effect is not
severe and an important benefit is provided by administration
of the drug.
120
Therapeutic window
Therapeutic index = TD50/ED50
% of maximal effect
100
80
ED50
TD50
60
Effect
Toxicity
40
20
0
10
−10
10
−9
10
−8
10
−7
10
−6
10
−5
10
−4
[D], Molar
Figure7.2
60
Chapter 8
Pharmacodynamics II:
Determining Sites
and Mechanisms
of Action of Drugs
The concept that drugs achieve their effects in the body by binding
to specific target molecules evolved during the latter part of the nine-
teenth century. In Western science, this was a time when organic
chemistry was being developed, particularly in response to the need
for dyes in the textile industry. The availability of new synthetic dyes
allowed cell biologists at the time to better visualize tissues and cells
by light microscopy. Normally, thin tissue sections or individual cells
can be hard to visualize because they are essentially transparent.
Pharmacodynamics II 61
Certain dyes were found to be able to stain certain cell types or sub-
cellular organelles giving them a contrast readily observed in the
light microscope. In the medical field, this enabled one to stain for
infectious bacteria in blood or tissue samples, a step that was impor-
tant in confirming the germ theory of disease championed by Louis
Pasteur. The German scientist Paul Ehrlich, whom we may consider
one of the first modern pharmacologists, had the inspiration that
if certain dyes would bind to bacteria but not the surrounding tis-
sue, thus making them visible, it might be possible to use such dyes
or related compounds to selectively poison infectious microorgan-
isms without harming the host’s tissues. This was the concept of the
“magic bullet”– a toxic chemical that would enter the body but only
harm the disease- causing organisms.
Ehrlich experimented with dyes as chemotherapeutic agents,
even to the extent of clinical trials in human patients. In one case,
he extended the concept of selective toxicity to targeting certain cell
types in the body. He noticed that methylene blue strongly stained
nerve endings in tissues. He reasoned that if the dye blocked the
function of these nerve endings, he might be able to block pain
transmission; that is, the dye might be used as an anesthetic or
analgesic agent. He administered methylene blue intravenously to
hospitalized patients suffering from chronic pain. Sad to say, he suc-
ceeded only in turning his patients blue!
In spite of this setback, Ehrlich’s inspiration became one of the
important beginnings of modern pharmacology. After many years
of study of derivatives of the toxic element arsenic, he developed
the first useful chemotherapeutic agent, Salvarsan, for treating the
bacterium that causes syphilis. Since Ehrlich’s time, essentially all
of pharmacological research has focused on discovering or design-
ing chemical agents that enter the body and selectively interact with
particular molecular targets.
You will see in your study of pharmacology that many drugs in
use or being developed achieve their effectiveness by influencing
signaling systems in the body (human or parasite). They usually act
through one of two basic mechanisms:
1. Binding to receptors for endogenous signaling molecules in the
body, such as hormones and neurotransmitters. As examples,