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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5849_Библиотеки_им_академика_М_И_Перельмана
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C
max
are the same as for determining T
max
. This parameter can be used qualitatively
to understand the mechanism of absorption and the associated kinetics (see discussion
in C
max
Section 5.4.2.1).
5.4.2.3 Absorption Rate The absorption rate constant (k
a
) is a first-order rate
constant that defines the absorption of the drug from the dosed compartment into the
systemic circulation as shown in the simplified Figure 5.16.
In most cases, the absorption rate constant k
a
> ke(rapid absorption) such that the
plasma level curves show a C
max
and the terminal phase (post-C
max
) reflects the
elimination phase with the elimination rate constant k
e
.
5.4.2.4 Bioavailability The probability of having the entire dose absorbed from
the dosing compartment is usually low. Moreover, the net dose that is available into
the systemic circulation is low with drugs having a low solubility or high clearance.
The fraction of the dose administered that enters the systemic circulation un-
changed is the fraction bioavailable.
By definition, the bioavailability is the rate and extent of absorption of a drug from
the dosing compartment.
The rate is determined by the time to C
max
,(T
max
) and also the absorption rate
constant (K
a
).
The extent is determined by estimating the fraction bioavailable (F) from
F ¼
AUC
EV
AUC
IV
Dose
IV
Dose
EV
ð5:42Þ
This equation assumes that the CL for both the IVand EV doses remains a constant.
It is important to recognize that if the EV dose is very high (such as in a toxicokinetics
study) and if there is a potential for this high dose to be in the nonlinear range, this
equation cannot be applied to calculate the fraction bioavailable.
When the AUC for EV is compared against the drug dosed as an IV, the
bioavailabilty is “absolute.” If the AUC for EV is compared against another EV
formulation (Equation 5.42), then the bioavailability is “relative.”
The bioavailability from an EV site can never exceed 100%. However, in many
instances the calculated value for the bioavailability shows an apparent value that
exceeds 100%. There are many reasons for this to occur and are to some degree an
error or misinterpretation of the data. Some instances when the percent bioavailability
exceeds 100% are as follows:
ka
ke
Dosed
Compartment
Plasma
Compartment
Figure 5.16 A one-compartment model with first-order absorption and first-order elimination.
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1. Measuring plasma conce ntrations with a nonspecific assay for the parent drug
and its metabolites. This can create an additive effect of the AUC values (AUC
of parent þ AUC of metabolite(s)) for the EV data as opposed to the IV data
particularly if the EV administration is a PO dose.
2. Estimating the bioavailability when the EV dose is much higher than the
IV dose, thereby resulting in a nonlinear kinetic profile for the EV dose and a
linear kinetic profile for the IV dose. This requires that the EV dose be similar to
the IV dose for comparisons.
3. Estimating the bioavailability of a prodrug by analytically measuring the drug
content released by hydrolysis of the prodrug. When such a prodrug is
administered via the PO route, it is almost completely converted to the drug
during the first pass through the liver, but the same prodrug injected into the vein
will take multiple cycles through the liver before it is completely converted.
The AUC (of the drug) from the PO route is inflated as compared to the
corresponding AUC from the IV route and the bioavailability is inflated.
4. In flip–flop kinetics (Section 5.4.2.5), the estimate of the AUC extrapolated to
infinity following IV administration may be smaller than when the same
extrapolation is done for the EV route. This may add on a large fraction of
area to the AUC following EV administration, thereby inflating the bioavailability calculat ions. Typically, the AUC values up to a time point (post-T
max
)
that is shared by both routes of administration should be compared.
5.4.2.5 Flip–Flop Kinetics In some cases, the absorption is slower than the
elimination (k
a
<<< ke) and the terminal phase represents the absorption. This is
“flip–flop kinetics” and simplest to confirm by dosing the drug via the IV route and
comparing the terminal phase of the IV curve with the terminal phase of the
extravascular curve. Typically in flip–flop kinetics, the curve acquires a “flatter”
0.001
0.01
0.1
1
10
6050403020100
TIME
CONCN
IV
Ka >> Ke
Terminal phase is elimination (parallel to
IV)
Ka << Ke
Terminal phase represents absorption (FlipFlop)
Figure 5.17 Absorption plots showing rapid absorption and flip–flop kinetics or slow
absorption.
DRUG ADMINISTRATION AND PK OBSERVATIONS 229
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shape and the C
max
is lower and T
max
is right-shifted (Figure 5.17). In many instances
(such as in toxicokinetic studies), the low doses will reflect the standard absorption
kinetics, while at higher doses a flip–flop kinetic situation might arise.
It is important for discovery teams to realize that the terminal phase observed via
EV dosing does not a priori reflect an elimination phase until the phase can be
confirmed by an IV formulation or another EV formulation that has a faster (or slower)
absorption profile.
5.4.2.6 First-Pass Effect Most drugs are designed for oral administration (PO)
and are meant to be absorbed into the systemic circulation from the membranes of
the GI tract. Following absorption, the drug has to pass through the hepatic-portal vein
through the liver and into the systemic circulation. If a drug is susceptible to
metabolism, it may not be able to enter the systemic circulation because it would
be metabolized in the GI tract or in the enterocytes or be completely destroyed by the
liver. The degradation of a drug as it passes through clearing organs for the first time
en-route to the systemic circulation is called the “first pass effect.”
The only way to protect the drug molecule from the first-pass effect is to modify the
metabolic “soft spots” on the molecule and if this is not feasible, the route of
administration should be changed (perhaps to an SC or IM, etc.) to bypass the firstpass metabolizing organ.
5.4.3 Analysis of Intravenous Infusion Data
In many instances, the drug cannot be delivered for some reason (e.g., poor solubility)
through an IV bolus. If dosing the drug to a steady-state level is desired, then an IV
infusion is optioned. Typically, the drug is infused into the vein for a fixed duration of
time using an infusion pump. Depending on the pharmacokinetic half-life of the drug,
a steady state is achieved, if the duration of the infusion is greater than 4–6 half-lives of
the drug (see Table 5.5 and Figure 5.18).
5.4.3.1 Steady State for Infusion As the drug is delivered into the body via a
continuous infusion, the plasma (or blood) levels of the drug rise. Correspondingly,
TABLE 5.5 Half-Life and Disposition of the Drug
No. of Half-Lives
Elapsed
Percentage of Initial
Concentration Eliminated
Percentage of Initial
Concentration Remaining
0 0 100
15050
27525
3 87.5 12.5
4 93.75 6.25
5 96.875 3.125
6 98.4375 1.5625
7 99.21875 0.78125
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as would be expected in a first-order process, the rate of elimination also increases.
When the rate of input (from the infusion) and the rate of elimination are the same,
then the resu ltant plasma levels remain unchanged as long as the infusion continues
at the same rate. Changing the rate of infusion will result in a new steady state to be
established (Figure 5.19).
Since kinetic processes are first order, the time to steady state is approximately six
half-lives (Table 5.5). By six half-lives, the drug has reached almost 99% of the true
steady state (the time to steady state is independent of any other criterion).
It takes approximately six half-lives to achieve 99% of steady state (Table 5.5),
and this time to steady state is independent of any other criterion. The steady-state
levels (C
ss
) depend on the rate of delivery and the CL of the compound such that
k
0
¼ Css CL
tot
ð5:43Þ
where k
0
is the drug input rate (zero order, like an infusion) and Cssis the steady-state
level.
If steady state is lost due to a missed dose or an overdose, it will take 6 t
1/2
to
reestablish the same steady state.
5.4.4 Analysis of PK Data after Multiple Dose Administrations
Most drugs are used for chronic therapy and hence are typically dosed at multiple
times during the day for many days (and sometimes are used for the lifetime of the
patient). Multiple dosing is most convenient for drugs that are administered via
noninvasive methods such as PO, INH, and TD.
Depending on the dosing frequency and the half-life of the drug, multiple dosing
usually is tailored to achieve an SS. By design, each dose administration results in
0
0.2
0.4
0.6
0.8
1
1.2
70
60
50
40
30
20
10
0
Time
Concentration
Non-Steady State
Steady State
Cmax
Cmax = Css
Same dose - therefore same AUC
Figure 5.18 A plasma PK profile after an IV infusion to a steady-state or a nonsteady-state
outcome.
DRUG ADMINISTRATION AND PK OBSERVATIONS 231
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an absorption followed by an elimination such that blood levels fluctuate in an
oscillatory manner. The impact of the frequency of dosing on the steady-state levels
as well as the fluctuation of the maximum and minimum response is shown in
Figure 5.20. As one doses closer to the half-life of a drug, the fluctuations (C
max
to
C
min
) reduce. It is for discovery teams to evaluate the right dosing frequency required
for maximum therapeutic benefit.
Figure 5.19 Time to steady state is six half-lives. The different steady-state levels are because
the infusion rate is different [20].
0.1
1
10
250200150100500
TIME (hours)
CONCN
QD
BID
TID
QID
Cl = 850 mL/hr/kg
V = 98 mL/kg
t1/2 = 6 hrs
Figure 5.20 Simulated plasma levels showing impact of various dosing frequency on the C
ss
and the degree of fluctuations for a drug with t
1/2 ¼
6 h. Blue ¼ QD (once a day); red ¼ BID
(twice a day); yellow ¼ TID (three times a day), and aqua ¼ QID (four times a day). See insert
for color representation of this figure.
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For any dosing scenario, an average steady-state concentration can be predicted by
C
ss
¼
AUC
t
ð5:44Þ
where the AUC is after a single dose and the “t” is the dosing interval (24 h for QD,
12 h for BID, and so on).
5.4.5 Analysis of PK Data after Escalating Dose Administrations
In all the above discussions, the PK of the drugs were assumed to be linear, that is, the
relationship between dose and AUC (as a measure of exposure) is proportional. This
means that if the dose is doubled, then the AUC must double and so on. In many cases,
and particularly at higher doses, this relationship fails and increasing dose results in
more than or less than proportional changes in AUC. This lack of proportionality
results in “nonlinear PK.”
Nonlinearity is considered a “problem situation in PK because the ability to
extrapolate and predict is lost. Since the PK now depends on the dose and the plasma
levels, PK parameters such as CL and V
d
are no longer constant and independent
of dose. Consequently, achieving a SS is difficult and the potential of increasing
plasma levels rapidly and in an uncontrolled and unpredictable manner can lead to
severe adverse events.
An initial discussion about recognizing nonlinearity was made in section “AUC in
Toxicology” and shown in Figure 5.21. Comparing AUCs at different doses to check
for proportionality will help to identify the nonlinearity.
0
10
20
30
40
50
60
70
80
90
100
10
8
6
4
2
0
Dose
AUC
Linear
Saturable protein binding or
saturable absorption
Saturable clearance
Figure 5.21 AUC versus dose plots are diagnostic on mechanisms.
DRUG ADMINISTRATION AND PK OBSERVATIONS 233
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5.4.5.1 Nonlinearity A linear first-order system demands that the concentrations
should change proportionally to the dose. If the dose is doubled, then the concentrations should double and so on. As long as this condition holds, extrapolations and
interpolations between such linear doses can be readily made as the PK parameters
such as CL and V
d
do not change as the dose changes. This linear assessment is best
made by comparing the AUC to the given dose or recognizing that in a linear system
the dose/AUC ¼ CL ¼ a constant.
When this condition is not met, the PK system is nonlinear and extrapolations
cannot be made. Depending on the type of nonlinea rity, there could be a safety issue
if drug concentrations following multiple administrations increase unbridled due to
a systemic nonlinearity.
Presystemic Absorption Nonlinearity If the AUC at higher doses increases in a less
than proportional manner, then absorption has become rate-limiting (Figure 5.21).
This rate-limited absorption could be due to a saturation of the absorption thro ugh the
biomembranes of the GI tract or for compounds with poor solubility, resulting in a
dissolution rate limit. Increasing the dose does not achieve a higher plasma level. A
possible approach to rectifying this problem may be to change the formulation (salt
form, dosage form, etc.).
Nonlinear Protein Binding Sometimes at higher plasma levels, all the binding sites
for the drug are saturated and the unbound fraction of the drug increases. Higher
concentrations of free drug are present resulting in an increase in the rate of CL.In
effect, the AUC decreases, as the dose and the correspo nding plasma levels increase,
result in the plateau effect seen in Figure 5.21. In a nonlinear protein-binding case, all
concentrations should be converted to the free levels, and the free plasma concentrations should be used for any further PK calculations.
Nonlinearity due to Saturable Clearance When the AUC increases more than
proportionally (see Figure 5.21), a CL pathway has become saturated. Typically, for
drugs that are metabolized by the cytochrome P450 enzymes, higher plasma levels
can result in concentrations in the liver that may saturate the capacity of the enzyme
to metabolize the drug. In this case, drug starts to accumulate in the system and if
unchecked, can increase alarmingly to levels that can cause toxicities. Some drugs
have the ability to inhibit or interact with the metabolizing enzyme or a transporter,
thereby making the enzyme unavailable for metabolism and CL. This can also be a
cause for the nonlinearity. If such a nonlinearity (green curve) is observed at very low
plasma levels, the only recourse is to change the molecule or increase potency to the
target and reduce the dose.
A nonlinearity can be caused if the drug induces an enzyme that is responsible for
the drugs own metabolism (autoinduction). This type of nonlinearity is not observed
after a single dose and it usually requires multiple doses of the drug to induce the
expression and synthesis of the enzyme. The blood levels measured (and the
corresponding AUCs) after multiple dosing for a week (usually) are much lower
(red curve) than expected despite the PK properties of the drug (adequate t
1/2
to
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expect accumulation and an increase in SS). This induction can be overcome by
adjusting the dose to a higher level.
5.5 HUMAN PK PROJECTION
The primary focus of accomplishing the PK studies in various laboratory animal
species is to have the ability to predict the human PK for the compound. Various
methods have been used to establish correlations of the PK properties between
animals and man; however, even if successful, these correlations work within a series
but do not translate across all compounds. There are two primary approaches in
scaling animal PK properties to humans, namely, allometric scaling and physiologically based pharmacokinetic (PBPK).
5.5.1 Allometric Scaling
Allometry is the study of the differential growth rates of different parts of the
organisms growth or behavior. In 1947, Max Kleiber [21] demonstrated that the
basal metabolic rate of an organism was related to the body weight in a power
function. This was quantified in an equation of the form
y ¼ a ðBWÞ
b
ð5:45Þ
where a ¼ allometric coefficient and is different for different relationships studied and
b ¼ power function. Kleiber described y ¼ P
met
, which is the basal metabolic rate of
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
70
60
50
40
30
20
10
0
TIME (hours)
CONCN (µM)
INDUCTION
STEADY STATE
ACCUMULATION/SATURATION
Figure 5.22 The impact of nonlinearities on the steady-state exposures of a hypothetical drug
undergoing saturable CL (green) and autoinduction (red). See insert for color representation of
this figure.
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the organism (measured in terms of heat in kilocalorie that the animal produces) and
a ¼ 73.3 (a constant) and b ¼ 0.75. Log transforming both sides of Equation 5.45 gives
Log y ¼ Log a þ b Log ðBWÞð5:46Þ
which can be plotted as a straight line for extrapolations. If a ¼ 1, then the growth is
considered isometric and if a > 1, the growth is positively allometric and if a < 1 then
the growth is negatively allometric.
.
Heart weight ðgÞ¼5 :8m
0:98
b
.
Long weight ðgÞ¼11:3m
0:98
b
.
Tidal volume ð mLÞ¼7:69m
1:04
b
.
Vital capacity ðmLÞ¼56:7m
1:03
b
.
Lung compliance ðmL=cmH2OÞ¼1:56m
1:04
b
.
Blood volume ðmLÞ¼65: 6 m
1:02
b
.
Muscle mass ¼ 0:40m
1:00
b
.
Skeletal mass ¼ 0:0608m
1:08
b
Using the above concept and applying it to pharmacokinetics the CL of a
compound measured in various animal species could be scaled and extrapolated to
humans (Figure 5.23).
Figure 5.23 Allometric scaling of 91 xenobiotics (red, proteins; green, drugs eliminated by
metabolism; blue, drugs eliminated by renal excretion; and black, drugs eliminated by both
renal excretion and metabolism [22]. See insert for color representation of this figure.
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The important PK parameters that are scaled are the CL, Vd, and by extension the
half-life. As mentioned before, the CL scales according to the following equation:
CL ¼ a ðBWÞ
0:75
ð5:47Þ
and the V
d
scales isometrically as
V
d
¼ a ðBWÞð5:48Þ
and recognizing that the half-life depends on both the CL and the V
d
(Equation 5.41),
it scales as
t
1=2
¼ a ðBW Þ
0:25
ð5:49Þ
where a is a constant (a is not the same constant for each relation).
Typically, these PK parameters are determined in three to four different laboratory
animal species such as mouse, rat, rabbit, dog, monkey, pig, and so on, and use the
allometric relationships mentioned above to scale the PK parameters to humans.
Many investigators have acknowledged that better correlations are obtained when
the CL of a compound are normalized to brain weight or in vitro intrinsic clearance,
or other physiological variables [23, 24]. These correlations are not based on any
scientific concepts but for a given compound can result in better est imates. The
practitioner is encouraged to try various approaches to establish a correlation and use
it for predictions to man.
5.5.1.1 Single-Species Scaling Recently, it has been shown that the rat alone
scales to human with an accuracy which is within twofold of the actual CL observed
in the clinic [25]. This level of accuracy is considered adequate by many clinicians
who cautiously study the PK of the investigational compound in first in human studies.
Taking the ratio of Equation 5.47 gives
CL
human
CL
rat
¼
BW
human
BW
rat
0:75
ð5:50Þ
where the BW
human
is usually assumed to be 70 kg and the BW
rat
is usually around
0.25 kg. The CL value used in Equation 5.50 is expressed in absolute units of volume
per time (e.g., mL/min or L/h, etc.).
Correspondingly, the volume of distribution scales linearly such that on an mL/kg
(or a L/kg) basis the value between species will remain the same.
5.5.2 Scaling by Physiologically Based Pharmacokinetic Modeling
Many investigators have suggested that a better method of scaling the pharmacokinetic parameters is based upon physiological processes, which in turn scale via
allometric equations such as shown before for various organ weights, volumes, blood
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