Pharmacokinetics VIII

Change in Elimination Characteristics
During Drug Therapy
With any drug taken regularly and accumulating
to the desired plasma level, it
is important to consider that conditions
for biotransformation and excretion do
not necessarily remain constant. Elimination
may be hastened due to enzyme
induction (p. 32) or to a change in urinary
pH (p. 40). Consequently, the
steady-state plasma level declines to a
new value corresponding to the new
rate of elimination. The drug effect may
diminish or disappear. Conversely,
when elimination is impaired (e.g., in
progressive renal insufficiency), the
mean plasma level of renally eliminated
drugs rises and may enter a toxic concentration
range.

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Pharmacokinetics VII

Accumulation: Dose, Dose Interval, and
Plasma Level Fluctuation
Successful drug therapy in many illnesses
is accomplished only if drug concentration
is maintained at a steady high
level. This requirement necessitates
regular drug intake and a dosage schedule
that ensures that the plasma concentration
neither falls below the therapeutically
effective range nor exceeds
the minimal toxic concentration. A constant
plasma level would, however, be
undesirable if it accelerated a loss of effectiveness
(development of tolerance),
or if the drug were required to be
present at specified times only.
A steady plasma level can be
achieved by giving the drug in a constant
intravenous infusion, the steadystate
plasma level being determined by
the infusion rate, dose D per unit of time
and the clearance
This procedure is routinely used in
intensive care hospital settings, but is
otherwise impracticable. With oral administration,
dividing the total daily
dose into several individual ones, e.g.,
four, three, or two, offers a practical
compromise.
When the daily dose is given in several
divided doses, the mean plasma
level shows little fluctuation. In practice,
it is found that a regimen of frequent
regular drug ingestion is not well
adhered to by patients. The degree of
fluctuation in plasma level over a given
dosing interval can be reduced by use of
a dosage form permitting slow (sustained)
release .
The time required to reach steadystate
accumulation during multiple
constant dosing depends on the rate of
elimination. As a rule of thumb, a plateau
is reached after approximately
three elimination half-lives (t1/2).
For slowly eliminated drugs, which
tend to accumulate extensively (phenprocoumon,
digitoxin, methadone), the
optimal plasma level is attained only after
a long period. Here, increasing the
initial doses (loading dose) will speed
up the attainment of equilibrium, which
is subsequently maintained with a lower
dose (maintenance dose).

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Pharmacokinetics VI

Time Course of Drug Plasma Levels
During Irregular Intake
In practice, it proves difficult to achieve
a plasma level that undulates evenly
around the desired effective concentration.
For instance, if two successive doses
are omitted, the plasma level will
drop below the therapeutic range and a
longer period will be required to regain
the desired plasma level. In everyday
life, patients will be apt to neglect drug
intake at the scheduled time. Patient
compliance means strict adherence to
the prescribed regimen. Apart from
poor compliance, the same problem
may occur when the total daily dose is
divided into three individual doses (tid)
and the first dose is taken at breakfast,
the second at lunch, and the third at
supper. Under this condition, the nocturnal
dosing interval will be twice the
diurnal one. Consequently, plasma levels
during the early morning hours may
have fallen far below the desired or,
possibly, urgently needed range.

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Pharmacokinetics V

Time Course of Drug Plasma Levels
During Repeated Dosing
When a drug is administered at regular
intervals over a prolonged period, the
rise and fall of drug concentration in
blood will be determined by the relationship
between the half-life of elimination
and the time interval between
doses. If the drug amount administered
in each dose has been eliminated before
the next dose is applied, repeated intake
at constant intervals will result in similar
plasma levels. If intake occurs before
the preceding dose has been eliminated
completely, the next dose will add on to
the residual amount still present in the
body, i.e., the drug accumulates. The
shorter the dosing interval relative to
the elimination half-life, the larger will
be the residual amount of drug to which
the next dose is added and the more extensively
will the drug accumulate in
the body. However, at a given dosing
frequency, the drug does not accumulate
infinitely and a steady state (Css) or
accumulation equilibrium is eventually
reached. This is so because the activity
of elimination processes is concentration-
dependent. The higher the drug
concentration rises, the greater is the
amount eliminated per unit of time. After
several doses, the concentration will
have climbed to a level at which the
amounts eliminated and taken in per
unit of time become equal, i.e., a steady
state is reached. Within this concentration
range, the plasma level will continue
to rise (peak) and fall (trough) as dosing
is continued at a regular interval.
The height of the steady state (Css) depends
upon the amount administered
per dosing interval and the
clearance (Cltot)

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Pharmacokinetics IV

Drug entry into hepatic and renal
tissue constitutes movement into the
organs of elimination. The characteristic
phasic time course of drug concentration
in plasma represents the sum of
the constituent processes of absorption,
distribution, and elimination,
which overlap in time. When distribution
takes place significantly faster than
elimination, there is an initial rapid and
then a greatly retarded fall in the plasma
level, the former being designated
the !-phase (distribution phase), the
latter the "-phase (elimination phase).
When the drug is distributed faster than
it is absorbed, the time course of the
plasma level can be described in mathematically
simplified form by the Bateman
function (k1 and k2 represent the
rate constants for absorption and elimination,
respectively).
B. The velocity of absorption depends
on the route of administration.
The more rapid the administration, the
shorter will be the time (tmax) required
to reach the peak plasma level (cmax),
the higher will be the cmax, and the earlier
the plasma level will begin to fall
again.
The area under the plasma level time
curve (AUC) is independent of the route
of administration, provided the doses
and bioavailability are the same (Dost’s
law of corresponding areas). The AUC
can thus be used to determine the bioavailability
F of a drug. The ratio of AUC
values determined after oral or intravenous
administration of a given dose of a
particular drug corresponds to the proportion
of drug entering the systemic
circulation after oral administration.
The determination of plasma levels affords
a comparison of different proprietary
preparations containing the same
drug in the same dosage. Identical plasma
level time-curves of different
manufacturers’ products with reference
to a standard preparation indicate bioequivalence
of the preparation under
investigation with the standard.

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Pharmacokinetics III

Time Course of Drug Concentration in
Plasma
A. Drugs are taken up into and eliminated
from the body by various routes. The
body thus represents an open system
wherein the actual drug concentration
reflects the interplay of intake (ingestion)
and egress (elimination). When an
orally administered drug is absorbed
from the stomach and intestine, speed
of uptake depends on many factors, including
the speed of drug dissolution (in
the case of solid dosage forms) and of
gastrointestinal transit; the membrane
penetrability of the drug; its concentration
gradient across the mucosa-blood
barrier; and mucosal blood flow. Absorption
from the intestine causes the
drug concentration in blood to increase.
Transport in blood conveys the drug to
different organs (distribution), into
which it is taken up to a degree compatible
with its chemical properties and
rate of blood flow through the organ.
For instance, well-perfused organs such
as the brain receive a greater proportion
than do less well-perfused ones. Uptake
into tissue causes the blood concentration
to fall. Absorption from the gut diminishes
as the mucosa-blood gradient
decreases. Plasma concentration reaches
a peak when the drug amount leaving
the blood per unit of time equals that
being absorbed.

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Pharmacokinetics II

The constancy of the process permits
calculation of the plasma volume
that would be cleared of drug, if the remaining
drug were not to assume a homogeneous
distribution in the total volume
(a condition not met in reality).
This notional plasma volume freed of
drug per unit of time is termed the
clearance. Depending on whether plasma
concentration falls as a result of urinary
excretion or metabolic alteration,
clearance is considered to be renal or
hepatic. Renal and hepatic clearances
add up to total clearance (Cltot) in the
case of drugs that are eliminated unchanged
via the kidney and biotransformed
in the liver. Cltot represents the
sum of all processes contributing to
elimination; it is related to the half-life
(t1/2) and the apparent volume of distribution
Vapp (p. 28) by the equation:
Vapp t1/2 = In 2 x ––––
Cltot
The smaller the volume of distribution
or the larger the total clearance, the
shorter is the half-life.
In the case of drugs renally eliminated
in unchanged form, the half-life of
elimination can be calculated from the
cumulative excretion in urine; the final
total amount eliminated corresponds to
the amount absorbed.
Hepatic elimination obeys exponential
kinetics because metabolizing
enzymes operate in the quasilinear region
of their concentration-activity
curve; hence the amount of drug metabolized
per unit of time diminishes
with decreasing blood concentration.
The best-known exception to exponential
kinetics is the elimination of alcohol
(ethanol), which obeys a linear
time course (zero-order kinetics), at
least at blood concentrations > 0.02 %. It
does so because the rate-limiting enzyme,
alcohol dehydrogenase, achieves
half-saturation at very low substrate
concentrations, i.e., at about 80 mg/L
(0.008 %). Thus, reaction velocity reaches
a plateau at blood ethanol concentrations
of about 0.02 %, and the amount of
drug eliminated per unit of time remains
constant at concentrations above
this level.

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Pharmacokinetics I

Drug Concentration in the Body
as a Function of Time. First-Order
(Exponential) Rate Processes
Processes such as drug absorption and
elimination display exponential characteristics.
As regards the former, this follows
from the simple fact that the
amount of drug being moved per unit of
time depends on the concentration difference
(gradient) between two body
compartments (Fick’s Law). In drug absorption
from the alimentary tract, the
intestinal contents and blood would
represent the compartments containing
an initially high and low concentration,
respectively. In drug elimination via the
kidney, excretion often depends on glomerular
filtration, i.e., the filtered
amount of drug present in primary
urine. As the blood concentration falls,
the amount of drug filtered per unit of
time diminishes. The resulting exponential
decline is illustrated in . The
exponential time course implies constancy
of the interval during which the
concentration decreases by one-half.
This interval represents the half-life
(t1/2) and is related to the elimination
rate constant k by the equation t1/2 = ln
2/k. The two parameters, together with
the initial concentration co, describe a
first-order (exponential) rate process.

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