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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_6000_Библиотеки_им_академика_М_И_Перельмана.pdf
Clinical Pharmacokinetics
219
1.1. Scope of Pharmacokinetics
The scope of pharmacokinetics relates to the time course of drug concentration in a human body after
its administration due to an array of its parameters. In true sense, the information obtained from the
pharmacokinetics of a drug (D
1
) helps in anticipating (predict) the pharmacokinetics of another drug
(D
2
). A survey of literature pertaining to the pharmacokinetic behavioural pattern of a particular drug
substance amalgamated with certain critical and vital pharmacodynamic parameters, e.g., the ‘therapeutic
index’
2
of the same may be effectively put to several meaningful applications.
Following are the ten important applications of the pharmacokinetic principles:
1. Development and design of ‘Newer Drug Molecules’ showing excellent inherent features,
such as:
∑ extensively modifi ed therapeutic effi cacy,
∑ lesser side effects and
∑ fewer toxic effects.
2. Design and development of an ‘Optimized Formulation’ for better and usefulness of the drug
product (or dosage form).
3. Effective development and design of such unique formulations as
∑ controlled-release formulation,
∑ targeted-release formulation,
∑ ocular-release formulation,
∑ transdermal-release formulation,
∑ iontophoretic-release formulation,
∑ mucoadhesive-release formulation,
∑ supramolecular-release formulation and
∑ oral-transmucosal-release formulation.
4. Proper selection of the most appropriate and preferred route for drug administration, e.g., IM, IV,
oral, transdermal, subcutaneous.
5. Choice of most suitable drug for an individual by a physician.
6. Predict and clearly explain the following two undesired aspects:
∑ drug–drug interactions
3
and
∑ drug–food interactions.
4
7. Perceptive design of the most suitable ‘multiple-dosage regimen’, i.e., sustained-release formula-
tions (usually a tablet or capsule) wherein the release pattern of the drug is duly extended over a
stipulated span of time.
8. Most precise and classical ‘therapeutic drug monitoring’ in specifi c individual patients, e.g., time-
controlled secondary pharmaceutical products (dosage forms) vs. chronopharmacology.
2
Therapeutic Index: It refers to the quantitative comparison of a therapeutic effect and an untoward effect of a
drug in the human body. Alternatively, the ratio of the maximum tolerated dose of a drug to its minimum curative
dose is termed as the therapeutic index.
3
Such as Ca
2+
and tetracyclines cause chelation of the bivalent cation.
4
Grape fruit juice (containing xenobiotics) inhibit drug-metabolism, thereby leading to prolonged drug action
plus serious adverse effects [Murray M: Clin Pharmacokinetics, 23: 132, 1992.]
Essentials of Biopharmaceutics and Pharmacokinetics
220
1.2. Therapeutic Objective
The therapeutic objective is invariably referred to such cardinal factors that predominantly
∑ control and manage or
∑ cure the disease condition
in the least possible time-frame with bare minimum side effects by the careful and judicious usage of the
‘least quantum of drug’. As to date, tremendous thrust and effective research-oriented efforts are geared
towards
∑ new drug development and/or
∑ structural modifi cations
so as to afford an improved pharmacokinetic characteristic features and enhanced glaring effi cacy.
Besides, there are quite a few well-recognized and widely accepted ‘drug product design’ endeavours
across the globe that are solely aimed at
∑ an optimized bioavailability of ‘active drug’ and
∑ improved control/cure of human ailments via targeted or controlled-release formulations.
Following are certain aspects that meet the ‘therapeutic objectives’ in an effi cient and effective manner:
1. Correct choice of route of administration of ‘drug’ to allow the ‘active drug’ to have an access to
the ‘site of action’ in both suffi cient quantum and faster mode.
2. Choice of an appropriate ‘drug substance’ is solely dependent upon attaining an ‘optimum therapy
level’ by striking a proper balance between the desired and undesired effects.
3. Co-administration of many drugs simultaneously to a patient may ultimately cause perceptive
change in the observed ‘pharmacokinetic profi le of a drug’, that could be due to the drug–drug
interactions taking place.
Time-released formulation of theophylline [Theo-24
®
]:
The drug product duly attained the requisite therapeutic drug concentrations during the night,
and remarkably avoided toxic effects during the day (when the drug was administered at 1500 hrs).
5
1. Effective and preventive dosage adjustments in the event of an observed
∑ changed physiology and
∑ drug interactions.
2. Mainly aimed at accomplishing the utmost desirable therapeutic objective(s).
Example
5
Smolensky et al.: Chronobiol. Intl., 4(3): 435–437, 1987.
Note
Therefore, a proper judicious understanding of the interaction makes easier the appropriate
and rational usage of drugs that are intended to be co-administered to a patient (under the close
supervision of a physician).
Clinical Pharmacokinetics
221
2. Dosage Regimens: Design, Modalities and Implementation
Dosage regimen strictly regulated the amount of drug and schedule for administration to a patient.
Dosage form (or drug product) refers to the pharmaceutical preparation intended for use by or
administration to a patient with a minimum of further processing, e.g., tablet, capsule, elixir, suspen-
sion, injectables etc.
Dosage range represents the maximum and minimum dose to achieve a therapeutic benefi t without
any toxic effects.
Dosage rules essentially consist of the following aspects:
∑ Rules for calculating dosage—especially for children,
∑ Clark’s Rule—weight in pounds times adult dosage divided by their age plus 12 times the adult dos-
age equals the respective child dose,
∑ Young’s Rule—age in years divided by the age plus 12 times the adult dosage equals the child dose,
∑ Body Surface Area (BSA) Rule—BSA in m
2
(of child) divided by the average adult BSA (1.73 m
2
)
multiplied by the adult dosage equals the child dose.
The design, modalities and implementation of dosage regimens shall now be discussed appropriately in
the following sections.
2.1. Design of Dosage Regimens
In actual practice, the dosage regimens could be categorized into the following two types:
∑ optimal single dosage regimen and
∑ optimal multiple dosage regimen,
which will be discussed briefl y in the following.
2.1.1. Optimal Single Dosage Regimen
An optimal single dosage regimen may invariably provide an ‘effective treatment’. Nevertheless, the
actual prevalent illnesses in most cases are found to be longer enough vis-à-vis the ensuing therapeutic
effect caused by an optimal single dose.
1. Albendazole (an ‘anthelmintic’) is given once only to children for deworming.
2. Antiemetics, hypnotics and analgesics are given in a single dose to produce an effective treatment.
Examples
2.1.2. Optimal Multiple Dosage Regimen
In certain specifi c instances, viz. prolonged illness (tuberculosis, pernicious anaemia, chronic diabetes,
essential hypertension etc.), it becomes almost mandatory to have drugs on a repetitive basis stretched
duly over a certain stipulated length of time which depends solely on the critical ‘nature of ailment’.
Therefore, to accomplish a successful therapy, the design of an ‘optimal multiple dosage regimen’ is
an absolute necessity. Hence, an optimal multiple dosage regimen may be defi ned as ‘a predetermined
protocol wherein the drug is required to be administered in appropriate doses having enough frequency
Essentials of Biopharmaceutics and Pharmacokinetics
222
level, which precisely ensures adequate maintenance of the plasma concentration very much well within
the proposed therapeutic window
6
during the entire period of therapy’.
6
Therapeutic Window: It refers to a defi nite protocol devoid of any excessive fl uctuation and drug accumulation
in the body.
7
C
ss.max
: It refers to the maximum steady-state plasma–drug concentration (mcg mL
−1
).
8
C
ss.min
: It designates the minimum steady-state plasma–drug concentration (mcg mL
−1
).
The following are a few prominent examples:
1. Antibiotics, Antihypertensive, Antibacterials, Antituberculosis: These drugs do
essentially require a minimum level of effective concentration to be maintained at all times,
so as to accomplish the best therapeutic effi cacy (i.e., drugs with broad-therapeutic indices).
2. Phenytoin, Cephalosporin, Xylocaine: These drugs with narrow therapeutic indices
must be administered in such a manner that their toxic concentration (level) is not exceeded.
Examples
Designing a Dosage Regimen In designing a dosage regimen, the following two important aspects
should be taken into consideration:
∑ Pharmacokinetic parameters of the ‘drug’: It is largely found to remain constant in the course
of therapy, i.e., when the dosage regimen gets duly established. However, if one observes any type of
change during therapy, the dosage regimen is rendered ‘invalid’.
∑ Basic of calculations for dosage regimen: These typical calculations are solely based upon
_ open one-compartment model and
_ two-compartment model,
in case, one makes use of ô (i.e., dosage interval) instead of K
E
(elimination constant), and V
d.ss
, i.e.,
apparent volume of distribution at steady state, instead of V
d
(apparent volume of distribution).
Dose Size Dose size usually refers to the quantity or volume of a medicinal agent intended to be taken
at one time (unit dose) or in a given time interval, e.g., daily dose.
In a broader perspective, it may be ascertained that the actual apparent magnitude of
∑ therapeutic response and
∑ toxic response
depends exclusively on the ‘dose size’.
Important Points
1. Dose size calculations mostly need a comprehensive knowledge for the critical ‘quantum of drug’
being absorbed effectively soon after the administration of each dose.
2. Greater variations between C
ss.max
7
and C
ss.min
8
may be observed with greater dose size in the course of
∑ each and every dosing period and
∑ ultimately causing probability in ‘toxicity’.
Figure 4.2 shows the diagrammatic representation of the direct infl uence of dose size upon the ensuing
plasma–concentration–time profi le soon after the following two events:
Clinical Pharmacokinetics
223
∑ oral administration of ‘drug’ and
∑ administration at ‘fi xed schedules of time’.
Figure 4.2 Diagrammatic representation of dose size infl uence upon plasma–drug concentration vs. time profi le
soon after administration of a drug at fi xed dosing intervals (T) of time (hrs).
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The various steps involved are as follows:
1. The plot between the observed plasma–drug concentration (mcg mL
−1
) vs. time (hrs) at dif-
ferent dosing intervals (T) clearly shows three zones marked by X, Y and Z (see Figure 4.2).
2. The X-zone relates to the longer-dose profi le with matching longer variations that critically
exhibits the ensuing therapeutic and toxic responses.
3. The Y-zone represents the optimum dose profi le with therapeutically successful and effec-
tive responses.
4. The Z-zone designates the particular smaller dose profi le with minimum variations while
showing almost ineffective therapeutic responses.
Explanation
Dosing Frequency It is known that the ‘dosing interval’ refers to the time elapsed between the
administration of the consecutive doses of a drug. Importantly, the dosing interval (which is the inverse
of the dosing frequency) is usually calculated based on the plasma half-life (t
1/2
) of the drug. In a situ-
ation where the specifi c ‘dose interval’ is enhanced while the dose remains unchanged, one may criti-
cally observe the following values:
C
max
—decreases,
C
min
—decreases,
C
av
—decreases and
C
max
/C
min
ratio—increases.
Essentials of Biopharmaceutics and Pharmacokinetics
224
In addition, the reduced dose interval profi le may result in a signifi cant accumulation of drug in the
human body leading to toxicity status.
Figure 4.3 illustrates the diagrammatic profi le pertaining to the infl uence of the ‘dosing frequency’
upon the plasma–drug concentration-time profi le duly obtained soon after the oral administration of
the ‘fi xed doses of a drug’.
Note
When the specifi c ‘dose interval’ is reduced (i.e., dosing frequency increased), the above values of
C
max
, C
min
, C
av
and C
max
/C
min
ratio become just the ‘opposite’.
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Figure 4.3 Diagrammatic representation of dosing frequency infl uence upon plasma–drug concentration–time
profi le obtained soon after the oral administration of fi xed doses of a drug.
The following are the different sequential steps:
1. The graphic plot between plasma–drug concentration(mcg mL
−1
) vs. time (hrs) at varying
dosing frequency explicitly shows three distinct zones marked by X, Y and Z (see Figure 4.3).
2. The X-zone designates the high-dosing frequency (τ < t
1/2
) with lesser variations that exhib-
its both therapeutic and toxic responses.
3. The Y-zone relates the optimum-dosing frequency (τ = t
1/2
), and proves to be successful
therapeutically.
4. The Z-zone represents the low-dosing frequency (τ > t
1/2
) with large variations and turns
out to be unsuccessful therapeutically.
Explanation
Salient Features: It is quite necessary to sustain a proper balance between the two components, namely:
∑ dose size and
∑ dosing frequency,
Clinical Pharmacokinetics
225
in order to accomplish the two most sought after requirements, viz., safety and effi cacy. However, one may
not obtain such a status simply by administering relatively ‘higher doses at a less frequency’. Importantly,
the administrations of rather smaller doses at frequent intervals do produce defi nitely lesser variations.
Digoxin, a cardiac glycoside, has a narrow therapeutic index and, therefore, is administered most
preferably in a small doses only at frequent intervals (normally < t
1/2
of the drug) so as to accomplish
∑ a therapeutic profi le having the least variations and
∑ very much similar to the profi le obtained with either
_ controlled-drug release system or
_ constant rate infusion.
Example
Accumulation of Drug in Multiple Dosing In order to understand the intricacies associated with the
accumulation of drug in multiple dosing system, accomplished after IV multiple dosing with the dosing
interval equivalent to one plasma half-life (t
1/2
) of the drug, one may consider the amount of drug duly
present in the body–time profi le as depicted in Figure 4.4.
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Figure 4.4 Diagrammatic representation showing accumulation of drug in the body with multiple dosing
regimen of IV bolus having dosing interval equivalent to one plasma half-life of the drug.
Essentials of Biopharmaceutics and Pharmacokinetics
226
Note
Approximately fi ve plasma half-lives are essentially required for accomplishing the ‘steady state’.
The various cardinal steps involved in Figure 4.4, showing the accumulation of drug in a multi-
ple-dosing system, are as follows:
1. Immediately after the administration of the very fi rst dose, X
0
, at τ = 0, the quantum of drug
available in the body shall be X = 1 X
0
.
2. Now, at the next dosing-interval, will be the quantum of drug remaining in the body, i.e.,
X = ½ X
0
.
3. Likewise, the administration of the subsequent IV dose helps to raise the body content to
a level equivalent to X = X
0
+ ½ X
0
, i.e., accumulation of drug takes place in the body. Thus,
it suggests explicitly that the phenomenon of ‘accumulation’ comes into play due to the
fact that drug from the corresponding previous doses has not yet been removed completely.
4. Since the quantum of drug in the body slowly gets enhanced because of accumulation, the
respective elimination rate also increases in a proportionate manner until it accomplishes
∑ a steady state or
∑ reaches a plateau state
in a critical situation when the rate of drug gaining adequate entry into the body almost
equals to the rate of exit of drug.
5. Consequently, at the steady state, the observed maximum values (X
ss.max
) and minimum val-
ues (X
ss.min
) do show a tendency to approach the respective asymptotes strategically located
at the plateau, viz. ‘upper asymptote’ and ‘lower asymptote’.
6. Importantly, at the plateau, X
ss.min
= 1 X
0
, and X
ss.max
= 2 X
0
, which means that X
ss.min
equals the
quantum of drug present in the body soon after the administration of the fi rst-dose, whereas,
X
ss.max
clearly equals twice the fi rst dose. Besides, we may have the following two expressions:
X
ss.max
− X
ss.min
= X
0
and X
ss.max
/X
ss.min
= 2
7. The above observations hold good only in a situation when τ = t
1/2
, and the drug is admin-
istered via the IV route.
8. When τ < t
1/2
, the extent of accumulation is greater and vice versa.
Explanation
Remarks: The concluding remarks include:
1. The degree up to which a drug gets accumulated duly in the body in the course of multiple-
dosing designates a function of
∑ dosing interval,
∑ elimination half-life and
∑ independent of dose-size.
2. The degree up to which a drug shall get accumulated irrespective of any dosing interval in a
subject may be duly derived based upon the relevant information (S) obtained with a single dose.
Clinical Pharmacokinetics
227
It is invariably represented by the so-called ‘Accumulation Index’ (Rac) as given by the following
expression:
E
1
Rac
1
K
e
τ
−
=
−
(a)
Reachable Time for Achieving Steady State in Multiple Dosing It has been established beyond
any doubt that the reachable time needed for a steady state solely depends on the plasma half-life (t
1/2
)
of the drug substance. In fact, the desired plateau is accomplished in nearly fi ve plasma half-lives in a
specifi c situation when
aE
KK>>
(i.e., the fi rst order rate constant is greater than the elimination rate
constant). In other words, the rate at which the ‘multiple-dose steady-state’ is attained satisfactorily may
be estimated by K
E
(i.e., the elimination rate constant).
Interestingly, the time taken to reach the above-cited multiple-dose steady state is found to be abso-
lutely independent of the following three critical aspects:
∑ dose size,
∑ dosing interval and
∑ number of doses.
Multiple Dosing Profi le The most fundamental objective of the therapeutic treatment by a drug is to
attain rapidly and maintain reasonably the ensuing plasma–drug concentration within the limits of the
‘therapeutic range’ with least possible observed fl uctuations.
Oral Multiple Dosing Regimens: In this typical instance, after the administration of the fi rst dose
one may notice an enhancement in the plasma–drug concentration level which is immediately
followed by a distinct peak level, and fi nally a decline in the plasma–drug concentration.
Example
The administration of the second dose further increases the level of plasma–drug concentration and
attains a level higher than in the fi rst-dose. Nevertheless, there shall be a continuous increase unless and
until a steady-state plasma–drug concentration is duly accomplished, as depicted in Figure 4.5.
Evidently, one may prominently observe a ‘steady state’ as and when the input and output of the drug
substance stands to be ‘equal’.
Calculation of Drug Accumulated in Human Body after the First Dose: It may be calculated
easily by using the following expression:
( 0.693 )
1/2
1
=
1/t
R
e
−τ
−
(b)
where,
R is the accumulation factor
9
and
τ the dosing interval.
9
Accumulation Factor: It solely depends on two vital parameters, viz. dosing interval and plasma half-life (t
1/2
).
Essentials of Biopharmaceutics and Pharmacokinetics
228
First-Order Kinetics: On the basis of the fi rst-order kinetics, nearly 90% of the average steady-state
plasma–drug concentration shall be attained very much within the four plasma half-lives. Importantly,
the realistic time span needed to actually approach the ‘steady state’ shall depend solely upon the plasma
half-life of the drug. However, it has been observed from various experimental investigative studies that
the ‘average steady-state plasma–drug concentration (C
′
)’ would depend exclusively on the following
important factors:
∑ X
0
, i.e., the ‘maintenance dose’,
∑ F, i.e., the fraction of the ‘absorbed dose’,
∑ τ, i.e., the ‘dosing interval’ and
∑ C
L
, i.e., the ‘clearance’.
Thus, we may have the following expression for C′:
0
L
FX
C
C
=
′
τ
(c)
We also know that
d
0
1/2
1.44 t
CV
X
F
τ
′
=
Putting the value of X
0
in Equation (c), we have
01/2
d
1.44 t
FX
C
V
⋅⋅ ⋅
=
′
⋅τ
(d)
where V
d
is the volume of distribution.
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Figure 4.5 Schematic representation of the plasma–drug concentration–time profi le soon after multiple dosing
regimen.
Note
From Equation (b) it may be inferred that smaller the ratio τ/t
1/2
greater will be the quantum of
drug being accumulated in the human body.