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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5195_Библиотеки_им_академика_М_И_Перельмана.pdf
mL per kg. In multicompartment models, various methods can be used to
calculate Vd. A common approach is to estimate Vd from the terminal β phase
as follows:
where AUC is the area under the concentration–time curve after a single
dose. An alternative method used to calculate Vd is the noncompartmental
approach. With this method, Vd is defined as Vd at a steady state, V
dss
; this is
calculated using the following equation:
where AUMC is the area under the first moment curve (concentration ×
time vs. time). The related fraction AUMC/AUC equals the mean time that
drug molecules remain in the body and is referred to as the mean residence
time (MRT). From a theoretical basis, V
dss
= Vdc + Vdp, where c and p are the
central and peripheral compartments, respectively. Although this method has
the advantage of being relatively independent of terminal slope determination,
it requires a much longer sample collection duration to characterize the
AUMC from the first moment curve (because this curve is less “steep” than
the concentration vs. time curve, Fig. 2.4). It also requires estimating an
absorption input parameter (mean absorption time, MAT) as a correction
factor when estimating Vd for drugs that are not administered as an intravenous
bolus.
Figure 2.2 Basic one-compartment model.
Figure 2.3 Basic two-compartment model. Drug distributes between central and peripheral
compartments and is eliminated from the central compartment.
Figure 2.4 Concentration-versus-time and first moment curve (concentration × time vs. time) for a
drug exhibiting pronounced multicompartment pharmacokinetics. Ninety percent of the area under the
concentration-versus-time curve (AUC) can be captured with sampling out to 36 hours. To characterize
the same portion of the first moment curve (AUMC) requires collecting samples nearly twice as long.
Although the volume of distribution does not represent a true physical
space, changes in body composition seen throughout infancy and childhood
can have a predictable impact on the volume of distribution based on a drug’s
chemical and physical properties. Newborn infants have a higher proportion
of extracellular and total body water than older populations, and thus drugs
that are distributed freely in water have larger volumes of distribution in
newborns. Accordingly, aminoglycoside antibiotics, which are highly polar
and hydrophilic and are distributed primarily into extracellular fluid, have
approximately double the volume of distribution in newborns as in adults.
Preterm newborns have a reduced percentage of total body fat. Thus, for
lipophilic drugs, the volume of distribution may be reduced compared to that
in adults.
Differences in drug binding across age groups can affect its Vd. Whereas
drugs can bind to tissue components and plasma proteins, only the free
(unbound) drug equilibrates. Thus, with newborns and certain diseases in
which albumin and α-1-acid glycoprotein levels are low, highly bound drugs
will have a greater free fraction (unbound/total drug concentration) in plasma,
and more drug will distribute out of the plasma compartment into tissues. This
will have the net effect of a higher Vd for total drug, although the Vdu may be
similar. While unbound drug concentrations may be more representative of the
“effective” concentration seen at the site of action, they are not routinely
measured because their measurements require more sensitive, timeconsuming, and expensive assays. In most clinical situations, alterations in
protein binding will not have a significant impact on therapy but can greatly
impact the interpretation of measured (total) drug concentrations.
DISTRIBUTION INTO SPECIFIC TISSUES
When acute drug effects are of critical importance, such as in induction of
anesthesia or in treatment of shock, the distribution characteristics of a drug
are integral to its therapeutic utility. In general, distribution characteristics for
drugs used in the treatment of chronic diseases are of lesser clinical
importance. One important exception relates to target sites that a drug may not
access easily. Whereas most distribution is based on concentration gradients
and passive diffusion, in some tissues drug access is limited by tight junctions
in the endothelium and active drug transport. For many drugs, free
concentrations do not come into true equilibrium within the central nervous
system due to these processes. P-glycoprotein and other active transporters
pump various drugs out of the central nervous system and greatly reduce the
overall effective penetration into this site.
CLEARANCE
Drug clearance (CL) is a measure of drug elimination. It represents the
volume of blood or plasma from which the drug is completely removed per
unit of time. It is analogous to creatinine clearance as an assessment of renal
function. It is the ratio of the rate of elimination or extraction divided by the
drug concentration and can be mathematically defined as
At steady state, whereby definition drug input equals drug elimination, this
equation can be rearranged to
Dose (rate in) = CL · C
pave
Thus, CL dictates the average steady-state concentration, C
pave
, that will be
achieved from a given dosing regimen. It can also be expressed in terms of
mass balance for the organ of elimination. The rate of drug clearance from an
eliminating organ is the product of the blood flow, Q, and the extraction ratio
(ER) from arterial blood of that organ. An organ’s ER is determined from
arterial concentration, CpA, reaching the organ and venous concentration, CpV,
leaving the organ of elimination and can be expressed as
It can range from 0 (no extraction) to 1 (complete extraction). An important
mathematical property regarding CL is that it can be separated into its
individual components. The two most common organs of drug elimination are
the liver and the kidney. The liver metabolizes drugs and can also excrete
drugs and drug metabolites in bile. The kidney filters and excretes drugs and
drug metabolites. Occasionally, other tissues contribute significantly to a
drug’s clearance. Therefore, overall CL can be expressed as
CL
total
= CL
hepatic
+ CL
renal
+ CL
other
For most drugs, CL is constant over the range of concentration encountered
clinically. When a drug’s CL is independent of concentration, the elimination
is referred to as first order. In this setting, there is a linear relationship
between the logarithm of drug concentration and time during drug elimination.
With first-order elimination, changes in dosing lead to proportional changes in
drug concentrations. Clearance can be estimated by model-based methods
through fitting the observed concentration-versus-time profile to an
appropriate PK model. Following intravenous administration, CL (and Vd)
can be determined using a one-compartment model through iterative fitting of
drug concentrations to the following equation:
Alternatively, CL can be estimated using noncompartmental methods from
AUC. The AUC can be approximated following intensive sampling using the
trapezoidal method. This is the summation of the area of trapezoids estimated
from sequential, intensively collected plasma concentrations with the area of
each individual trapezoid equal to [(Cpi + C
pi+1
)/2] ∙ (t
i+1
− ti), and the final
area after the last trapezoid can be estimated as C
p-last/λz
, where λz is the
terminal slope of the log plasma concentration-versus-time curve. From the
AUC, the CL following a single intravenous dose can be calculated as
Clearance may also be defined with respect to unbound drug concentrations.
For drugs with protein binding, unbound drug concentrations are always less
than the total drug concentrations, and thus AUC for unbound drug
concentration is always lower than AUC for total drug concentration. Because
clearance is inversely related to AUC, the calculated clearance for unbound
drug is greater than that for total drug.
RENAL CLEARANCE
Many drugs undergo elimination into the urine by the kidneys. This occurs via
filtration through the glomerulus and active secretion of acids and bases,
which occurs primarily in the proximal tubule. Typically, only free or
unbound drugs are filtered by the glomerulus into the urine; thus, renal
elimination via filtration equals glomerular filtration rate (GFR) ∙ fu, where f
u
is the unbound fraction of the drug in serum. Separate active transport systems
exist for acid (anion) and base (cation) secretion by the kidneys. Drug
elimination by filtration and active secretion can be mitigated by reabsorption
of the drug along the proximal and distal tubules as well as the collecting
duct. Reabsorption is primarily a passive process; however, its impact can be
pronounced. Because the great majority of water that is filtered by the
glomerulus is reabsorbed, drugs with favorable physical–chemical properties
(small, nonpolar) will follow the water and be reabsorbed as well. The
reabsorption of drugs with pKa values in the range of urinary pH can be
markedly influenced by acidification or alkalinization of urine.
Mathematically, renal clearance equals renal excretion rate divided by
average plasma concentration and can be determined from serial blood and
urine collections using the equation:
where Ae is the cumulative drug excreted unchanged in the urine and AUC
is derived from the plasma concentration-versus-time profile.
GFR can be estimated from serum creatinine or cystatin C in adults and is
used to individualize dosing of drugs eliminated by renal mechanisms.
Although GFR can also be estimated from serum creatinine in children, the
relationship between measured serum creatinine and GFR is different
between pediatric and adult populations. Age-specific equations have been
developed for estimating GFR in pediatric populations; however, lower
serum creatinine concentrations in children reduce the precision of these
equations. In newborn infants, estimating the GFR from serum creatinine is
confounded by the transplacental creatinine that infants receive from their
mothers in utero. This additional maternally derived creatinine may bias
estimates of GFR in newborns during the first few days of life.
HEPATIC CLEARANCE
The liver is the primary site of drug metabolism. Drug biotransformation is
influenced by a drug’s chemical and structural properties, which determine its
affinity to various drug-metabolizing enzymes in the liver. Drug metabolism
may also be influenced by hepatic blood flow and protein binding. Drugs with
a great affinity for metabolizing enzymes are highly extracted and their
metabolism is limited primarily by hepatic perfusion. Their hepatic clearance
approaches and parallels hepatic blood flow. Changes in hepatic blood flow
have much less impact on the clearance of those drugs with lower affinity for
metabolizing enzymes or low hepatic extraction. However, for low-hepaticextraction drugs, their total hepatic clearance is sensitive to changes in protein
binding. Hepatic clearance of unbound drug can be used as a measure of the
liver’s overall ability to metabolize that drug. Hepatic clearance of unbound
drug is also frequently referred to as intrinsic clearance, CLhu. It is
mathematically related to total hepatic clearance, CLh, by multiplying with the
fraction unbound:
CLh = CLhu ∙ f
u
Understanding the hepatic extraction of a compound aids in determining
the impact that patient-specific factors, including age, genotype, drug–drug
interactions, liver disease, and cardiac status, may have on hepatic clearance.
Although it is easiest to think of hepatic extraction as fixed in an individual,
drugs may impact their own metabolism either by autoinduction or by
autoinhibition. In these settings, the hepatic extraction and CLh will increase
or decrease with exposure to the drug of interest; thus, single-dose PK studies
will not accurately predict steady-state concentrations.
SATURABLE ELIMINATION
In some instances, CL is not independent of drug concentration, as the
metabolizing enzyme or secretory pump gets overwhelmed by excessive drug.
This is often referred to as nonlinear or Michaelis–Menten elimination. It is
mathematically expressed as
where V
max
is the maximum capacity of drug metabolism and Km is the
concentration at which metabolism is half of maximal. This equation is
analogous to equations describing enzyme kinetic behavior. An important
characteristic of this equation is that as drug input approaches V
max
, small
increases in dose can lead to very large increases in steady-state drug
concentrations. Another category of nonlinear PK is zero-order elimination,
where metabolism is constant regardless of drug concentration. This
represents an extreme version of Michaelis–Menten kinetics where the drug
concentration greatly exceeds Km such that elimination is essentially equal to
V
max
at all experienced concentrations. This PK behavior is seen with ethanol.
PHARMACOKINETICS OF BIOLOGICS
The development of biologics as drugs has gained increased interest in the
past 10 years. Most notably monoclonal antibodies (mAbs) are becoming
important therapies for use in adults with oncology, inflammatory bowel
disease, and other disorders. These agents are typically administered
intravenously because of the volume. However, the injection volume of infant
doses is much smaller and can be administered subcutaneously. Adults may
also be able to receive larger doses subcutaneously in conjunction with
hyaluronidase. mAb metabolism follow the metabolic fate of endogenous
immunoglobulin s (IgGs) and are governed by different processes than typical
standard small molecule drugs and are relatively slow. IgGs are not
metabolized by typical drug-metabolizing enzymes (cytochrome P450 [CYP]s
or uridine diphospho-glucuronosyltransferases [UGTs]) in the liver, nor are
they eliminated renally or exhibit blood flow dependent PK. Instead their
elimination is through the reticuloendothelial system (RES) where they are
taken up via endocytosis. Within the endosome, they develop into lysosome
where they undergo proteolysis. Of interest during this process is the fact that
mAbs can bind to FcRn intracellularly, which protects them from metabolism,
and a portion of these protected mAbs are returned intact to the circulation.
Another unique characteristic of mAb PK is that they can be affected by the
relative concentration of their antigen (Ag) target with a saturable elimination
pathway because of mAb–Ag interactions. So, at mAb concentrations that
greatly exceed the target Ag concentrations (high mAb/Ag ratio), the
elimination of mAb is primarily dictated by the linear, nonspecific RES
uptake and metabolism. However, at low mAb or high Ag concentrations, the
mAb–Ag-mediated elimination may play a more prominent role and the PK
will appear very nonlinear. This phenomenon is referred to as target-
mediated drug disposition (TMDD).
DRUG ABSORPTION
Whereas drugs that are administered intravenously are completely available
to the systemic circulation, drugs administered by other routes may not enter
into the systemic circulation intact. The proportion of a dose that enters into
the systemic circulation intact is defined as the drug’s bioavailability. By
definition, the bioavailability following intravenous administration equals 1.
Absolute bioavailability F is calculated as the ratio of exposures from an
extravenous dose to an intravenous dose, or