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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5195_Библиотеки_им_академика_М_И_Перельмана.pdf
If extravenous and intravenous doses are of different sizes, then
When PK data following intravenous administration are not available, the
relative bioavailability between various formulations and routes of
administration can be compared. PK parameters estimated exclusively from
oral data are confounded by not knowing the dose of drug absorbed intact.
Thus, the relative contribution of bioavailability in estimating CL and V
d
cannot be determined. PK parameters from oral data are typically presented
as apparent or oral parameters, specifically CL/F and Vd/F. Bioavailability
less than 100% following oral administration can occur for a number of
physiologic and drug formulation–related issues, including problems with
drug dissolution or solubility and instability in gastric acid. In addition,
gastrointestinal transit time, gastric acid secretion, and biliary and pancreatic
exocrine function all can affect drug absorption. These are dynamic processes
during the first years of life and can result in age-dependent bioavailability
differences. Oral drugs may also undergo metabolism in the gut and liver
before reaching the systemic circulation. Blood from the intestinal tract that
contains the absorbed drug is carried to the liver by the portal vein, where it
can be metabolized before reaching the general systemic circulation. The
combined drug metabolism in the gut and in the liver via portal circulation
before the drug has reached the systemic circulation is termed first-pass
metabolism. Therefore, drugs exhibiting first-pass metabolism, such as
morphine, may have excellent absorption but low bioavailability. Whereas
most drug absorption from the gut is passive, active transport of drugs in
enterocytes back into the lumen of the gut may also limit bioavailability. Other
routes of drug administration, including intramuscular, subcutaneous, rectal,
and inhaled, may have bioavailability less than 1.
Bioavailability characterizes the extent of absorption but drug entry into
the body can also be characterized by the rate of drug absorption. Absorption
rate is sometimes confused with bioavailability, as it can be influenced by
some of the same formulation and physiologic processes that affect
bioavailability. Intuitively, the rate of absorption dictates the onset of effect
for rapidly acting drugs, but it can also determine the duration of effect for
drugs that are also rapidly eliminated (Fig. 2.5). Absorption rate is most
commonly characterized by peak time, t
max
. Although this is relatively easy to
obtain graphically, it reflects both absorption and elimination processes and is
different following single-dose and multiple-dose administration. The most
common mathematical model used to characterize oral drug absorption is the
first-order absorption. This model is characterized by an absorption rate
constant KA, with the amount of drug absorbed per unit of time equal to K
A
times the amount of drug remaining in the gut. Because very little drug
absorption occurs in the stomach, a delay in the detection of drug in the
systemic circulation is often observed during the first few minutes after oral
drug administration. In this setting, a lag time can be utilized in conjunction
with a first-order absorption model to describe this absorption pattern.
Alternative absorption models with multiple first-order absorption
compartments in serial (transit compartments), constant drug absorption (zero
order), and convoluted functions with multiple rate constants affecting various
fractions of the dose can also be used to describe drug input.
Figure 2.5 The impact of absorption rate on duration of action for drugs with rapid elimination. The
slower absorption (KA = 0.9 hour−1) results in later and much lower peak than the rapidly absorbed
formulation (KA = 6.5 hour−1). However, the more slowly absorbed formulation maintains higher
concentrations later in the dose interval (the area under the curve [AUC]s are identical). This results in a
longer total time above the minimum effective concentration.
The rate and extent of oral drug absorption are dependent on a drug’s
chemical properties and formulation as well as physiologic characteristics of
the patient and administration circumstances. Oral drug administration to
infants and young children requires either liquid or chewable product
formulations. These pediatric formulations may have significantly different
absorption properties than solid oral dosage forms used in older populations.
Extemporaneous compounding liquid pediatric formulations from adult
dosage forms may also alter drug stability and thus limit the intended dose
administered. The bioavailability of a drug may also be altered by the
presence and composition of coadministered food. A true fasting state is
difficult to achieve for drug administration in infants and the limited variety in
their dietary intake can limit bioavailability of compounds that require highfat meals for optimal absorption. Based on these factors, large, unanticipated
differences between oral absorption in young pediatric and adult populations
can be encountered.
HALF-LIFE
The elimination half-life, t
1/2
, is defined as the time necessary for the drug
concentration to decrease by 50%. After one half-life, 50% of the initial
concentration remains; after two half-lives, 25% of the initial concentration
remains; and so on. A related parameter is the elimination rate constant, K,
that is related to t
1/2
by K = 0.693/t
1/2
. During the elimination phase, K can be
used to predict concentrations at any time t from the following equation (Fig.
2.6):
C
piδt
= Cpi ∙ e−K ∙
Δt
where Δt is the time between the two concentrations Cpi and C
pi+1
measured during the elimination phase. Half-life can also be used to describe
drug accumulation. After one half-life, the drug concentration will be 50% of
the ultimate steady-state value; after two half-lives, 75% of the steady-state
value; and so on (Fig. 2.7 and Table 2.1). Drug accumulation approaches
steady state asymptotically; after 3.3 to 5 half-lives on a constant-dosage
regimen, drug concentrations are 90% to 97% of final steady-state values and
can be effectively considered steady state. The exact proportion of steadystate concentration at any time t can be determined from
Proportion of steady state = 1 − e
−K∙t
Figure 2.6 Concentration-versus-time profile for one-compartment drug, plotted as log concentration
versus time, with the slope representing the elimination rate constant (−K).
TABLE 2.1
Figure 2.7 Symmetry and relationship between half-life and portion of drug remaining and
accumulation with continuous infusion to steady state. After one half-life, the drug concentration is 50%
of its initial value and the drug has accumulated to 50% of the steady-state level.
Relationship Betwee n Half-Life and Portion of Drug Re maining and
Accumulation
Half-Lives Percentage Remaining Percentage Accumulation
0.5 71 29
1 50 50
2 25 75
3.3 10 90
4 6 94
5 3 97
6.6 1 99
For drugs exhibiting first-order elimination (which includes most drugs),
t
1/2
is independent of dose. It is mechanistically dependent on CL and Vd and
can be described as
For drugs with saturable or Michaelis–Menten elimination, t
1/2
has limited
utility as a PK parameter because it is dynamic, increasing at higher drug
concentrations. Whereas the general concept of half-life is easily grasped, it
is often assumed that any change in half-life reflects a change in drug
elimination. This is not necessarily true, as half-life alterations may be
entirely due to changes in drug distribution. It is clear from the above equation
that clinical situations that reduce a drug’s CL or increase its Vd will be
associated with an increase in that drug’s t
1/2
. Whereas t
1/2
does not indicate
what drug concentrations will result from a given dosage, it is used to
determine dosing intervals. Half-life dictates the peak/trough ratio and needs
to be considered when constructing an appropriate dosing regimen for a drug.
The elimination t
1/2
is most commonly determined from the terminal slope
or “washout” portion of the concentration–time profile. For drugs that exhibit
multicompartment PK, t
1/2
and the apparent elimination rate constant (λz or β
for a two-compartment model) can also be determined in this manner (Fig.
2.8). However, care must be taken in estimating β to ensure that a sufficiently
long portion of the log-linear concentration-versus-time profile is captured
and that concentrations influenced by ongoing absorption or distribution are
not included. The elimination rate constant and half-life can also be estimated
from drug accumulation or urinary excretion profiles as well as derived from
the area under the first moment curve (K = 1/MRT and t
1/2
= 0.693 ∙ MRT).
Figure 2.8 Concentration-versus-time profile for a two-compartment drug, plotted as log
concentration versus time. The initial slope represents the distribution phase and rate constant, α, and the
terminal, linear portion of the curve represents the elimination phase and rate constant β.
APPLICATION OF PHARMACOKINETIC
PRINCIPLES TO MULTIPLE-DOSE REGIMENS
In most clinical situations, drugs are administered repeatedly at fixed
intervals rather than as single doses. The goal is to maintain drug
concentrations above a minimum effective target concentration associated
with clinical benefit and below concentrations that are likely to result in
toxicity, keeping drug concentrations in this “therapeutic range” throughout the
dosage interval. For drugs that exhibit linear or dose-independent PK, the PK
parameters from a single dose can be used to predict drug concentrations that
will result from various multiple-dose regimens. The contribution of each
individual dose can be calculated and summed to determine the total
concentration following multiple doses. This method of superposition can be
used to determine non–steady-state and steady-state concentrations but
becomes cumbersome if the number of doses included for steady-state
determination is large. However, because the AUC during a dosing interval at
steady state equals the sum of AUCs contributed from single doses at dosing
intervals of τ (AUC
0−τ
, + AUC
τ−2τ
+ AUC
2τ−3τ
+ ···), the total AUC
0−τ
(at steady
state) is equal to AUC
0−inf
for a single dose. Thus, steady-state clearance can
be calculated from the following equation:
Once steady state is achieved, an accumulation factor can determine
concentrations at various times in the dosing interval. The rate of
accumulation is independent of the dosing interval, but the magnitude of the
peak/trough ratio increases with increasing dosing intervals (Fig. 2.9). Peak,
trough, and average steady-state concentrations following repeated
intravenous boluses can be easily determined using a one-compartment model
from the following equations:
Figure 2.9 Impact of various dosing intervals on concentration-versus-time profile following multiple
doses and same total daily dose. Average concentrations for all three regimens are identical, with
peak/trough differences increasing with larger dose intervals.
For example, for a drug with Vd = 2.0 L per kg and CL = 0.10 L per hour
per kg (K = 0.05 hour−1), a bolus dose of 100 mg per kg every 8 hours yields
the following steady-state peak and trough concentrations: