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Clinical Pharmacokinetics
229
But AUC = Area under the plasma–drug concentration vs. the time curve after a single maintenance dose.
Therefore, Equation (d) may be written as
AUC
C
t
=
′
,
(e)
i.e., the ‘average steady-state plasma–drug concentration (C′) is equal to area under the plasma–drug
concentration vs. time curve (AUC) divided by the ‘dosing interval’ (τ).
2.2. Average Drug Concentration vs. Body Content from Multiple Dosing to Steady State
2.2.1. Preamble
It may be observed that the overall average drug concentration prevailing at a steady state (C
ss.av
) serves as
a function of the maintenance dose (X
0
), fraction of dose absorbed (F), dosing interval (τ) and clearance
(CL
R
) of the drug, that may be expressed as
0
ss.av
R
CL
FX
C
⋅
=
⋅τ
(f )
or
01/2
ss.av
d
1.44 t
AUC (single dose)
FX
C
V
⋅⋅
==
⋅τ τ
(g)
where
Factor 1.44 = Coeffi cient for the reciprocal of 0.693 in Equation (g).
AUC = Area under the curve following a ‘single maintenance dose’.
Hence, Equation (g) may be employed to calculate the maintenance dose of a drug substance to
accomplish its predetermined concentration. We already know that:
d
XVC=⋅
hence, the body content at a steady state is given by the following expression:
01/2
ss.av
1.44 tFX
X
⋅⋅ ⋅
=
τ
(h)
Interestingly, Equation (h) suggests clearly that the aforesaid average values do not represent the arith-
metic mean of C
ss.max
and C
ss.min
by virtue of the known fact that the ensuing plasma–drug concentration
declines exponentially.
In a broader perspective, there are three important aspects with particular reference to the average
drug concentration vs. body content from the multiple-dosing system to the steady state, namely:
∑ Loading and maintenance doses,
∑ Maintenance of drug level within the therapeutic range and
∑ Perfect design of dosage regimen based upon the plasma–drug concentration,
which will be discussed individually in the following sections.
Essentials of Biopharmaceutics and Pharmacokinetics
230
2.2.2. Loading and Maintenance Doses
Loading dose refers to the administration of a drug in a larger initial dose than the usual one to speed
entrance into the circulating blood. It is also known as the ‘bolus dose’ or ‘priming dose’.
Maintenance dose entails the periodic dose following the ‘loading dose’ given earlier to keep the
drug–plasma concentration very much within a therapeutic range.
Chloroquine phosphate [250 mg tablets: Lariago
®
]: The anti-malarial drug is fi rst administered
orally as four tablets (≡ to 1000 mg of drug) on the day 1 as the loading dose, which is followed
by two tablets each on the day 2, day 3 and day 4, respectively, as the maintenance doses.
Example
It actually takes almost fi ve plasma half-lives (t
1/2
) to attain the therapeutic activity level, and, therefore,
the time taken would be very long for such drugs having a long plasma half-life (see Accumulation
of Drug in Multiple Dosing in this section and Figure 4.4). Thus, it is quite feasible to obtain a pla-
teau immediately by giving a dose which provides the ultimate desired steady state almost instantane-
ously well before starting the respective maintenance doses (X
0
), i.e., the ‘loading dose’ (X
0.L
). It is duly
expressed by the following simple equation:
ss av d
0.L
CV
X
F
⋅
⋅
=
(i)
where
C
ss.av
is the average drug concentration at a steady state (C
ss
),
V
d
is the volume of distribution and
F is the fraction of dose absorbed.
Dose Ratio: The dose ratio may be defi ned as ‘the ratio of loading dose to maintenance dose, i.e., X
0.L
/X
0
⬘.
As a guiding rule, the dose ratio has three variants:
∑ X
0.L
/X
0
is equal to 2.0 when τ = t
1/2
,
∑ X
0.L
/X
0
is lesser than 2.0 when τ > t
1/2
and
∑ X
0.L
/X
0
is greater than 2.0 when τ < t
1/2
.
It may be observed critically that in a situation when the loading dose is not optimum, i.e., it either
remains too low or too high, the steady state (C
ss
) may be accomplished within nearly fi ve plasma half-
lives in a similar manner to when absolutely ‘no loading dose’ is being administered, as illustrated in
Figure 4.6.
Note
1. The above-mentioned Equations (f), (g) and (h) and the explanatory discussions so far are
applicable only to such drugs which predominantly follow up the ‘one-compartment open
model kinetics’ having the fi rst-order disposition.
2. However, the ‘multi-compartment models’ shall deal with more complex equations.
Clinical Pharmacokinetics
231
2.2.3. Maintenance of Drug Level Within the Therapeutic Range
In the overall case, convenience or diffi culty in the proper and adequate maintenance of drug level con-
centration within the therapeutic window (or range) depends exclusively on the following three critical
aspects, namely:
∑ therapeutic index of the drug,
∑ plasma half-life of the drug and
∑ convenience of dosing.
In usual practice, it is primarily a diffi cult task to maintain and sustain such a crucial ‘drug level’ particu-
larly for a drug possessing
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Figure 4.6 Diagrammatic representation of plasma–drug concentration–time profi les obtained when dose ratio
remains > 2 (A), ⯝ 2 (B) and < 2 (C).
Various important aspects of Figure 4.6 are as follows:
1. The plasma–drug concentration–time profi les of drugs having dose ratio either equal to 2
(shown by bold-line curves) or less than 2 (exhibited by dotted-line curves) are lying gener-
ously between minimum steady-concentration (MSC) and minimum effective concentra-
tion (MEC).
2. The plasma–drug concentration–time profi les of drugs having dose ratio more than 2
(shown by normal-line curves) usually are located between the maximum steady concen-
tration and minimum steady concentration.
3. The ‘loading dose’ (X
0.L
) is given duly at ‘zero’ hrs; whereas, the subsequent ‘maintenance
doses’ (X
0
) at the defi nite dosing intervals (τ).
Explanation
Essentials of Biopharmaceutics and Pharmacokinetics
232
∑ short plasma half-life (< 3 hrs) and
∑ narrow therapeutic index (e.g., Heparin),
On the basis of the fact that the ‘dosing frequency’ should necessarily be < t
1/2
.
Selected Examples: These consist of
1. Drugs with High Therapeutic Index: For drugs having a large therapeutic index (>> TD
50
/
ED
50
), e.g., penicillin (t
1/2
= 0.g hrs), it will be rather safe as well as common to administer doses
in excess (often nearly 10 time excess) of that which is needed minimally to obtain the desired
therapeutic response.
Note
In this specifi c instance, bioavailability fails to change the therapeutic index.
1. Importantly, penicillin can be administered ‘less frequently’, i.e., every 4–6 hrs; however, the main-
tenance dose should always be larger so that the plasma–drug concentration remains above the
minimum inhibitory level.
2. Drugs with Low Therapeutic Index: Drugs with a low therapeutic index, e.g., warfarin, may
be administered at dose intervals ranging between 1 and 3 plasma half-lives (t
1/2
). As the dose of
warfarin is increased, one may observe that a relatively larger segment of the patients respond
10
until almost all patients respond as shown in Figure 4.7.
Figure 4.7 Diagrammatic representation of the cumulative % of patients responding to plasma levels of warfarin.
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Note
When the ‘therapeutic index’ is low, it is quite possible to have a range of concentrations at
which point both the effective as well as toxic responses invariably overlap, e.g., certain patients
show a haemorrhage condition; whereas, others show the desired twofold prolongation of the
prothrombin time.
10
For ‘warfarin’, the desired response appears as a twofold increase in the prothrombin time.
Clinical Pharmacokinetics
233
Other Examples: Commonly used low therapeutic index drugs include hypoglycaemic agents, dig-
oxin, anti-arrhythmics, amino glycosides, xanthenes, cytotoxic and immunosuppressive drugs.
2.2.4. Perfect Design of Dosage Regimen Based Upon the Plasma–Drug Concentrations
Preamble Till late 1960s practically all patients were treated with the ‘same dosage of a specifi c drug’.
Obviously, there was absolutely no coveted status for the pharmacokinetic and pharmacodynamic vari-
ability in the introduction of drug therapy.
Koch-Weser (1975)
11
carried out an intensive and extensive survey, for a period of 3 years extending
from 1970 to 1972, with particular reference to the ‘phenytoin dosages’ recommended for the criti-
cal prevention of seizure in nearly 200 ambulatory patients; and duly observed that almost 92% of the
patients actually received the usual dose of 300 mg day
−1
.
Remarkable Observation: Koch-Weser’s observation was really remarkable in the sense, since
phenytoin designates a quintessential example of a specifi c drug substance having signifi cant inter-
patient variability quotient in the so-called clinical response.
Till date, clinician
12
while initiating a particular dosage regimen critically takes the following aspects
into consideration:
∑ patients age,
∑ size (body weight),
∑ disease condition and
∑ concomitant (connected) drug therapy.
Exceptional Examples: These essentially consist of
1. Theophylline (a diuretic) is normally prescribed at higher than ‘usual mg kg
−1
doses’ for children
and smokers; whereas, lower than ‘usual doses’ is recommended for patients with a history of con-
gestive heart failure (CHF).
2. There are certain specifi c drug substances that are mostly prescribed at a much reduced doses for
patients having a history of impaired renal function.
Antibiotics (Cephalosporins, Ofl oxacin, Norfl oxacin); Digoxin, Lithium etc.
Examples
11
Koch-Weser J: Eur. J. Clin. Pharmacol., 9: 1, 1975.
12
Clinician: A staff member providing technical medical services, especially a physician, also a pharmacist or nurse
associated with patient care system.
3. Elderly Patients: They are usually recommended with more conservation dosages of hypnotics
(barbiturates), anti-anxiety drugs (reserpine, chlorpromazine) etc.
Design of dosage regimen may be carried out effectively provided the following parameters are known:
∑ therapeutic range of the drug substance,
∑ apparent volume of distribution (V
d
),
∑ clearance (C
L
) and
∑ plasma half-life (t
1/2
) of drug substance.
Essentials of Biopharmaceutics and Pharmacokinetics
234
In fact, these parameters actually render a great help in maintaining the drug concentration within the
therapeutic range, that could be further expressed explicitly as:
∑ Upper limit designated as C
upper
, and
∑ Lower limit designated as C
lower
.
Thus, one may accomplish readily the maximum dosing interval (T
max
) that solely depends upon the following
two critical conditions:
∑ therapeutic index (C
upper
/C
lower
ratio) and
∑ elimination half-life of drug,
which may be expressed by the following equation:
()
upper lower
max
E
2.303log /
CC
K
τ=
(j)
As we know, K
E
= 0.693/t
1/2
, therefore, Equation (j) may be re-written as
()
upper lower
max
1/2
2.303log /
0.693/t
CC
τ=
or
()
max 1/2 upper lower
3.32 t log /CCτ= ⋅⋅
(k)
It may be argued logically from Equation (k) that the ensuing ‘dosing interval (τ)’ thus selected is invari-
ably of a smaller value in comparison to τ
max
. Hence, it follows that the anticipated maximum mainte-
nance dose [X
0.max
]
13
may be duly expressed as
()
d upper lower
0max
VC C
X
F
−
=
(l)
where,
V
d
is the apparent volume of distribution and
F is the fraction of drug absorbed.
On the basis of the above facts and observations, it is now possible to arrive at the maintenance dose (X
0
),
and the average steady-state condition (C
ss.av
) as follows:
0 max
0
max
X
X
⎛⎞
=τ
⎜⎟
τ
⎝⎠
(m)
()
()
upper lower
ss.av
upper lower
2.303log
CC
C
CC
−
=
−
(n)
13
That is, X
0.max
may be obtained from each and every τ
max
(maximum dosing interval).
Clinical Pharmacokinetics
235
2.3. Individualization
In a broader perspective, the drug dosing profi le and/or dosing adjustments are invariably based upon
the logistic calculations related to the population data.
Inter-Subject Var iability: It refers to the production of appreciably large differences in the pharma-
cologic response by using the ‘same dose of a drug’ in altogether different individuals. Alternatively, it
explicitly pronounces that the defi nite dose needed to cause a specifi c pharmacologic response dose
varies from one individual to another.
Individualization of a dosage regimen demands the rational drug therapy to fulfi ll the patients require-
ments specifi cally. Importantly, the clinical pharmacokinetics makes use of the underlying pharmaco-
kinetic principles in the skillful design of dosage regimens for the individual patients.
The inter-subject variability is essentially of two sources in the drug responses, namely:
1. Pharmacokinetic Var iability: It is generally caused due to the ensuing differences in the concentra-
tion of drug at the site of action. Besides, certain differences prevailing in the absorption, distribution,
biotransformation (metabolism) and excretion are also equally responsible for the pharmaco kinetic
variability.
2. Pharmacodynamic Variability: It is exclusively attributed to the actual pharmacological
response that predominantly varies from one individual to another at a given specifi ed dose.
2.3.1. Objectives of Individualization
First and foremost, an insuffi cient therapeutic response certainly demands a higher dosage regimen,
whereas, the inherent drug-related toxicity critically calls for a defi nite lower dosage regimen. Therefore,
in order to help the phenomenon of individualization, it is absolutely necessary to make the availability
of drug in the respective drug products (or dosage forms) with varying dose strengths, e.g., losartan potas-
sium [Tozaar
®
] an antihypertensive agent available as 25 and 50 mg tablets; azithromycin [Azibest
®
]—an
antibiotic—available in 100, 250 and 500 mg tablets.
Interestingly, the number of dose-strength availability of a drug depends exclusively on the following
two major criteria, namely:
∑ therapeutic index of the drug and
∑ extent of inter-subject variability.
Note
In reality, smaller therapeutic index and larger inter-subject variability shall lead to a greater
number of dose-strength dosage forms for a ‘drug’.
2.3.2. Important Steps for Individualization
Having assumed that practically ‘all subjects’ do essentially require the same plasma–drug concentration
range for the therapeutic effectiveness, the following are the three steps intimately involved in the desired
individualization of the dosage regimen:
∑ Determination of Pharmacokinetic Parameters: It is required to determine in an individual subject
_ pharmacokinetic parameters and
_ respective population values,
Essentials of Biopharmaceutics and Pharmacokinetics
236
in order to fi nd out the degree of variability observed. Evidently, greater the accountability of vari-
ations, better would be the probabilities of achieving the desired therapeutic objective.
∑ Variability vis-à-vis Measurable Characteristic Features: Such attributing characteristic fea-
tures comprise age factor, weight and above all the critical renal/hepatic ailment.
∑ New Dosage Regimen Designing: It is accomplished on a continuous basis from the available
‘collected data’.
Conclusively, the ‘design of never dosage regimens’ necessary implicates such adjustments as dosage pro-
fi le, dosage interval and a combination of both, i.e., dosage–dosage in val.
Drug Dosing Profi le in Obese Patients It is quite evident that the apparent volume of distribution
(V
d
) of the drug is solely dependent on the body weight, because the latter is directly related to the
volume of the body fl uids. Thus, the ‘ideal body weight’ (IBW) of either sex may be calculated from the
following expressions:
IBW
Men
= 50 kg ± 1 kg/2.5 cm
(o)
[Both above or below 150 cm in height]
IBW
Women
= 45 kg ± 1 kg/2.5 cm
(p)
[Both above or below 150 cm in height]
Note
A person is regarded as obese if the body weight is found to be more than the ‘ideal body weight’
(IBW).
Importantly, in obese people, the corresponding ratio between the lean to adipose tissue is signifi -
cantly small, since a major proportion of the body fat changes the apparent volume of distribution (V
d
)
of the drugs critically. Besides, the extracellular fl uid (ECF) present in the adipose tissue is found to be
appreciably small vis-à-vis the lean tissue of the obese subjects.
Important Generalizations: Following are some of the important generalizations pertaining to
both drug distribution and dose adjustment particularly in obese people:
1. Digoxin (a cardiac glycoside): It fails to cause an even distribution of the drug in the ‘excess
body space’ substantially. As there is no alteration in the V
d
, hence, the drug-dose to be given must
be calculated on the IBW basis.
2. Gentamycin (a polar antibiotic): The drug invariably gets distributed in the excess body space of
the obese patients to a limit that stands to be much less in comparison to the lean tissues. Therefore, the
drug dose must be relatively lesser based on per kg body weight, but more than that of the IBW basis.
3. Caffeine and Theophylline (Diuretics), Lidocaine (Local Anaesthetic), Lorazepam
(Anxiolytic): These drugs exhibiting similar degree of distribution for both adipose and lean tis-
sues certainly require that the dose to be administered must be calculated on the total body weight.
In this way, the apparent dose of the drug may appear to be higher. However, due to the inherent
higher V
d
, the administered dose will be the same based on per kg total body weight.
4. Diazepam (anti-skeletal muscle spasms), Phenytoin (antiepileptic agent): Importantly,
the lipid-soluble drugs like diazepam and phenytoin exhibit appreciable distribution particularly in
the adipose tissue (fat deposits) thereby registering higher V
d
for obese patients. The above expla-
nation suggests that relatively larger drug dose shall be needed on the basis of total body weight.
Clinical Pharmacokinetics
237
Drug Dose Calculations for Neonates, Infants and Children On a broader perspective, it should
be understood quite explicitly that the neonates, infants and children essentially require an altogether
different dosage regimen duly calculated, on population basis, for the adults. In reality, the glaring differ-
ences in the dosage regimen are on account of the following facts, namely:
∑ total body surface area (TBSA),
∑ total body weight (TBW) and
∑ extracellular fl uid (ECF),
duly calculated on per kg body weight basis.
It has been adequately established that in neonates, infants and children, the actual body surface
area shows a reasonably good correlation with the realistic dosage requirement with such physiological
aspects, namely:
∑ cardiac output,
∑ glomerular fi ltration rate (GFR) and
∑ renal blood fl ow.
Variants in Calculated Doses for Neonates, Infants and Children: Following are the four differ-
ent means generally adopted to calculate the respective doses for neonates, infants and children:
∑ Young’s rule,
∑ Clark’s rule,
∑ Fried’s rule and
∑ Mosteller’s equation (or square metre surface area)
which will be treated individually in the following sections:
1. Young’s Rule: It is applicable for children 2 years and above.
()
Age (yr)
adult dose child’s dose approx.
Age (yr) 12
⎡⎤
=
⎢⎥
+
⎣⎦
(q)
2. Clark’s Rule: It is also suitable for children 2 years and above.
()
Weight (lb)
adult dose child’s dose approx.
150
⎡⎤
=
⎢⎥
⎣⎦
(r)
3. Fried’s Rule: It is meant for infants up to 2 years age.
()
Age (months)
adult dose infant’s dose approx.
150
⎡⎤
=
⎢⎥
⎣⎦
(s)
4. Mosteller’s Equation (or Square Metre Surface Area): The surface area (SA) in square metres
may be calculated by the help of Mosteller’s equation:
()
1/2
2
(height weight)
SA in m
60
⋅
=
(t)
()
SA of child
adult dose child’s dose approx.
SA of child
⎛⎞
=
⎜⎟
⎝⎠
(u)
Essentials of Biopharmaceutics and Pharmacokinetics
238
The ‘average body SA’ of an adult is 1.73 cm
2
, therefore, Equation (u) may be written as
()
SA of child
adult dose child’s dose approx.
1.73
⎛⎞
=
⎜⎟
⎝⎠
(v)
In case the dose of the drug is prescribed clearly as the quantum of drug per body SA (m
2
), one may
calculate the individual dose as
Dose = (amount of drug m
−2
) × body SA (m
2
) (w)
In addition, a relationship also prevails between body SA and body weight, which may be expressed as
SA (m
2
) = body weight (kg)
0.7
Therefore, it is possible to calculate the child’s dose (approximately) as given by the following expression:
()
0.7
body wt. of child (kg)
Child’s dose approx. adult dose
70
⎡⎤
=⋅
⎢⎥
⎣⎦
(x)
Based on Equation (x) one may conclude that since the ‘total body weight (TBW)’ as observed in the
neonates is only 30% greater than the adults, one may observe that:
∑ apparent volume of distribution (V
d
) specifi cally for the water-soluble drug substances is relatively
much more vis-à-vis in infants and
∑ apparent volume of distribution (V
d
) particularly for the most fat-soluble drug substances remains
signifi cantly smaller in infants,
which actually determines the dose-adjustment most logically and methodically.
Haemodialysis Haemodialysis refers to the process of separating macromolecules from ions and low
molecular weight compounds in solution by the difference in their rates of diffusion via a semi-perme-
able membrane through which crystalloids pass readily but colloids pass slowly or not at all.
The haemodialysis is invariably carried out in severe cases of ‘renal failure’, i.e., in ‘uremic patients’,
in order to remove such substances as:
∑ urea
∑ creatinine
∑ uric acid
∑ phosphate
∑ other endogenous waste products.
Importantly, haemodialysis may also bring forth:
∑ drug loss from the body and
∑ essentially need ‘additional dose adjustments’.
Factors Infl uencing Haemodiazability of a Drug: There are fi ve important factors infl uencing
haemodiazability of a drug, namely:
1. Aqueous Solubility of Drug: The lesser the aqueous solubility of a drug, the lesser would be
its dialyzability profi le.