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Clinical Pharmacokinetics
269
Now, for a drug substance being described by the ‘linear pharmacokinetics’, one may critically observe
that the ‘total body clearance (CL)’ remains absolutely independent of both the ‘dosage’ and ‘route of
administration’. Thus, we may have
FD
CL=
AUC
(al)
Equation (al), defi nes the ‘bioavailable dose’ immediately followed by an extravascular (EV) adminis-
tration as stated under:
EV EV
AUC .CLfD =
(am)
From Equation (am), it may be inferred that the respective ‘bioavailable dose ( f D
EV
)’ is directly pro-
portional to ‘area under the curve (AUC
EV
)’, by virtue of the fact that the ‘total body clearance (CL)’
remains almost constant.
In another situation, when the drug substance is duly administered via the IV route, f = 1 (by defi ni-
tion), because most of the administered dose of the drug substance gains entry to the blood. Now, as CL
remains constant, AUC
EV
is found to be directly proportional to the administered dose of the drug. Thus,
we have the following expression:
IV IV
DAUC.CL=
(an)
Figure 4.10 illustrates the blood concentration–time paths for a drug substance being administered by
fast and rapid IV doses of 2, 5 and 10 mg kg
−1
body weight.
As we know that the ‘total body clearance (CL)’ is a constant, the ratio of Equation (am) to Equation (an)
is given by the following expression:
EV EV
IV IV
AUC
AUC
fD
D
=
(ao)
Explanation
Interestingly, when ‘equal doses of drugs’ are duly administered by both extravascular (EV) and intrave-
nous (IV) routes, i.e.,
EV IV
= ,DD
we may have the following expression:
EV
IV
AUC
=
AUC
f
(ap)
Equation (ap), evidently shows that in a situation when an ‘equal doses are’ administered, the resulting
‘bioavailable fraction’ designates simply the ratio of the observed AUC values. Now, when the adminis-
tered ‘doses are not the same’, we may have the following modifi ed version of Equation (ao) being used
predominantly:
EV EV
IV IV
AUC /
=
AUC /
D
f
D
(aq)
Essentials of Biopharmaceutics and Pharmacokinetics
270
Thus, Equation (aq) exhibits that the ensuing ‘bioavailable fraction’ represents the ratio of the respec-
tive ‘dose-adjusted AUC-values’, and, therefore, may be expressed as the AUC dose
−1
for each individual
routes, viz. EV and IV.
Variants in AUC Value: In actual practice, the AUC-values are of three distinct types, such as:
∑ AUC value for extravascular route,
∑ AUC value estimated from reference plot and
∑ AUC value for an exponential concentration time course,
which would be discussed individually in the following:
1. AUC Value for Extravascular Route: There are several means and ways to calculate the AUC
value for the extravascular route, where we have already seen earlier:
0
AUC= .d
c
Ct
∫
(ar)
Importantly, the total AUC can be determined conveniently by making use of the well-known
‘trapezoidal rule’, as may be observed in the particular instance related to an intravenous administra-
tion of a drug.
,QVHUW
'RVH
7LPH+UV ∞
'UXJ&RQFHQWUDWLRQLQ%ORRG>PFJP/
±
@
$UHD
Figure 4.10 A plot showing blood concentration–time course for a drug substance via fast and rapid IV Doses
of 2, 5 and 10 mcg kg
−1
.
Clinical Pharmacokinetics
271
Figure 4.11 illustrates the total area under the typical concentration time-course following the
extravascular administration, which could be logically determined by summing up the areas per-
taining to the respective trapezoids and triangles that nearly comprise it.
'UXJ&RQFHQWUDWLRQLQ%ORRG
>PFJP/
±
@
7LPH+UV
;
<
G
F
D
D
E
$ DE
$ DFG
Figure 4.11 Graphic representation of total area under the concentration time course immediately following
extravascular administration duly determined by simply totalling up the areas of the trapezoids [X] and triangles
[Y] which nearly comprise it.
The various steps involved are as follows:
1. The curve in Figure 4.11 is critically divided into a series of ‘trapezoids’ and ending with a
‘triangle’ in each of them.
2. Each individual areas of the ‘trapezoids’, ½a(c + d); and also of the ‘triangle’, ½ab, are invari-
ably added up to determine the ‘total AUC’.
3. With a view to compare the attained AUC values for different curves, it is absolutely neces-
sary and important to make use of the
∑ same drug concentrations and
∑ same time units (viz. hrs).
4. However, it is not quite mandatory to make use of the same scales in plotting the data.
5. Importantly, both trapezoids and triangles may even be allowed to be expanded on a ‘full-
sheet of graph paper’.
Explanation
2. AUC Value Estimated from Reference Plot: In this particular instance, one may easily prepare
the ‘calibration plot’ by
∑ cutting carefully a number of squares from the graph paper and
∑ plotting their respective weights vs. their areas which can be calculated quite conveniently with
suffi cient accuracy. Subsequently, the curve to be determined may be estimated precisely:
_ fi rst, by cutting them out and weighing accurately and
_ secondly, by estimating the AUC value from the corresponding reference plot.
Essentials of Biopharmaceutics and Pharmacokinetics
272
3. AUC value for an Exponential Concentration Time Course: Importantly, the observed
‘drug blood concentration time profi les’ immediately following an oral administration may be
invariably expressed by the biexponential equation as given under:
..
ie ie
sz t si t
CC C
−−
=−
(as)
where
S
z
is the negative slopes of the fi rst-order plots for the terminal data,
S
i
is the negative slopes of the fi rst-order plots for the feathered data,
C
i
is the common intercept.
Note
1. One major advantage being that the irregularly shaped curves can also be assessed without
any diffi culty.
2. Necessary care must be taken for plotting the ‘squares’ and ‘curves’, which should be carried
out preferentially on the same concentration-time scale.
Note
S
z
designates the slower of the two exponentials.
Figure 4.12 represents the feathering of a biexponential drug–plasma concentration–time course as
described by Equation (as).
'UXJ&RQFHQWUDWLRQPJ
&
L
6
L
6
]
7LPH+UV
Figure 4.12 Designates the feathering of a biexponential drug–plasma concentration–time course as described
by Equation (at).
Clinical Pharmacokinetics
273
Important Points These essentially include
1. The ‘negative slope’ of the terminal log-linear plot is shown by S
z
.
2. The difference between the ensuing ‘S
z
line’ and the prevalent data points (•) are duly plotted (䊏)
so as to determine S
i
, i.e., the negative slope of the respective ‘log-linear difference plot’.
Figure 4.12 may be further expatiated as follows:
1. The appearance of an appreciable ‘lag time’ before the absorption actually comes into play,
one may observe these lines to meet at a negative time.
2. Lag period is given by the difference between the aforesaid time and zero time. Thus, the
observed intercepts for the two lines shall never be equal.
Explanation
Note
At this stage, it is absolutely not possible to assign an ‘absorption’ and an ‘elimination’ phase to an
‘oral curve’ unless and until additional information (S) are available.
Note
1. The competing gastrointestinal (GI) hydrolysis rates shall critically appear along with the
ensuing absorption rate constant, whereas the corresponding disposition rates may be an
integral component of the so-called elimination phase.
2. Importantly, for such a treatment, it may not be quite necessary to assign any specifi c rate
processes to the observed two slopes (viz. S
i
and S
z
), instead what we need is to describe the
data by the help of Equation (as).
3. Thus, S
z
represents the slower phase, and hence, shall duly correspond to the slower step accordingly.
Byron and Notari (1976)
24
and called this as the fl ip-fl ip phenomenon based on the fact that either S
i
or S
z
may eventually relate to the ensuing absorption process.
AUC for a Mono-Exponential Concentration Time Course: As the AUC for an observed mono-
exponential concentration time course could be expressed as
Intercept
AUC
Slope
=
−
(at)
From Equation (at), it follows that the actual area of a curve as given by Equation (as) denotes the pre-
vailing difference between two such terminologies:
ii
zi
AUC
CC
SS
=−
(au)
24
Byron PR and Notari RE: J Pharm. Sci., 65: 1140, 1976.
Essentials of Biopharmaceutics and Pharmacokinetics
274
Interestingly, the aforesaid principle can be successfully used to supplement the prevailing ‘trapezoid rule’
in a situation when such data are ended abruptly.
In Figure 4.12, when the ‘fi nal-data point’ is strategically located on the respective, ‘S
z
-line’
(i.e., O
i
.; O
ie
St
C
−
), one may determine the ‘missing area’ from the following expression:
i
z
AUC( )
C
t
S
−α =
(av)
3.12. Practice Problems
Problem 1 A 70 kg patient is administered with a 500 mg oral dose of a drug that behaves as per the linear
pharmacokinetics as described by the biexponential equation,
Sz.t Si.t
ie ie
CC C
−−
=−
, where S
z
= 0.087 hr
−1
,
1
i
= 0.72 hrS
−
and C
i
= 23 mcg mL
−1
. When a 250 dose was administered via rapid IV route to the same
patient, the corresponding concentration time course was duly described by C = (16.7 mcg mL
−1
)
1
(0.087 hr )
.
t
e
−
−
What is the bioavailable dose?
Solution We know the following relationship:
EV EV
IV IV
DAUC
DAUC
f
=
(aw)
Rearranging the above equation, we have
IV EV
EV
V
D.AUC
D
AUC
f
±
=
(ax)
Now,
ii
EV
zi
AUC
CC
SS
=−
(ay)
Putting the given values of C
i
, S
z
and S
i
in Equation (ay) we have:
EV
23 23
AUC
0.087 0.72
=−
= 264.36 – 31.94
= 232.42
But, AUC
IV
= 193.68, and putting these values in Equation (aw):
EV
250 232.42
D
193.68
f
×
=
= 299.81
⯝ 300 mg
Hence, the ‘Bioavailable Dose’ f D
EV
is 300 mg.
Problem 2
What does the ‘S
z
value’ stand for?
Solution Because ‘S
z
’, represents a value equivalent to the mono-exponential rate constant duly accom-
plished by IV administration of a drug substance, it grossly designates the elimination constant (K
E
) intimately
associated with the biological half-life (t
1/21
) which is equivalent to 0.693/S
z
= 8 hr s.
Clinical Pharmacokinetics
275
Problem 3 How would you determine the value of AUC from the data provided in Figure 4.12?
Solution Based on the following equation:
ii
zi
AUC
CC
SS
=−
(az)
Let us insert the values of C
i
= 15 mcg mL
−1
, S
z
= 0.082 hr
−1
and S
i
= 4.2 hr
−1
(as obtained from Figure
4.12) in Equation (az):
15 15
AUC
0.082 4.20
=−
= 188.27 – 3.58
= 179.31 mg% hr
or AUC ⯝ 180 mg% hr.
4. Pharmacokinetic Drug Interaction: Significance in Combination Therapy
Drug interaction usually refers to the pharmacological infl uence of one drug on another, which may
either prove to be benefi cial or harmful.
Pharmacists do have a major role to play in such critical and important activities, namely:
∑ examining for interactions,
∑ providing requisite advice to management when any interactions come into play and
∑ closely monitor such interactions at:
_ patients bedside,
_ segment of ‘dispensing process’ or
_ sale of a medicine at the pharmacists counter.
Mechanism of Interactions: An array of mechanisms are solely responsible for the ensuing phar-
macokinetic drug interactions, that may be classifi ed into two major categories, namely:
∑ Pharmacokinetic interactions and
∑ Pharmacodynamic interactions:
which will be treated individually in the following sections.
4.1. Pharmacokinetic Interactions
In general, the pharmacokinetic interactions are of four types, namely:
∑ drug absorption,
∑ interactions changing drug distribution,
∑ interactions affecting metabolism and
∑ interactions affecting renal excretion,
which would be discussed briefl y in the following sections:
4.1.1. Drug Absorption
Critically important and specifi c pharmacokinetic interactions which ultimately lead to the meaningful
modifi cation of drug absorption pattern appear to be intimately associated with the GI tract.
Essentials of Biopharmaceutics and Pharmacokinetics
276
Advantageous Interactions: There are quite a few advantageous interactions specifi cally with the
parenteral dosage forms, viz. IV, Im, SC etc.
Adrenaline—a vasoconstrictor—on being used in conjunction with a local anaesthetic, viz. xylocaine,
retards the absorption characteristics of the latter thereby prolonging the overall analgesic feature.
Example
Remarks: Instead of administering two drugs (e.g., xylocaine + adrenaline), it is advisable to use a single
long-acting molecule, e.g., bupivacaine, which eventually rules out the practice of using ‘two-drug-
combo’ to a patient.
Interactions in GI Tract: In true sense, such typical interactions may appreciably minimize the
quantum of a drug substance which gets absorbed into the body, and, therefore, cause reduction or
prevention in the overall ‘clinical action profi le’ duly exhibited by a host of medicines. These are usually
expatiated by such critically observed phenomena:
1. Chelation: Chelation is a phenomenon whereby a ‘claw’ type of metallic complex is formed in
which a ‘multi-ligand molecule’ produces a stable ring with a central metallic ion thereby render-
ing the ion inactive ultimately.
In particular, the heavy metal ions, viz. Fe
2+
, Ca
2+
, Mg
2+
, Zn
2+
, may get bound to the anionic drugs,
e.g., Tetracycline, Ciprofl oxacin, to yield poorly soluble salts which do not undergo dissolution, and,
hence, are not absorbed into the body.
Case Study 1
Mrs. SL is a young pregnant woman, who duly presents a prescription for ‘Tetracycline HCL’ to a phar-
macy to be fi lled. When handling over the medicine, the pharmacist checks whether Mrs. SL is taking
any other medicines. She clearly explains to the pharmacist that she regularly takes calcium and iron
tablets each morning under the advice of a physician.
Pharmacists Advice: The following was advised by the physician:
1. To take Tetracycline HCL (capsule) in the morning and at night, avoid milk and milk products at
these times; and must take iron at lunch time only.
Reason: Since the heavy metal ions, viz., Ca
2+
and Fe
2+
, may bind with Tetracycline (to form
chelates) to yield an insoluble salt which will neither
∑ get dissolved nor
∑ be absorbed
from the GI tract.
A word of caution suggests that such an ‘interaction’ might cause absolute therapeutic failure of
the recommended antibiotic.
2. The above anomaly may be intelligently circumvented by taking Tetracycline HCL at least 2 hrs
either before or after ingestion of calcium or iron.
3. The aforesaid ‘interaction’ by taking the iron tablets at lunch time, avoiding milk because that
contains Ca
2+
.
Avoiding Ion-Exchange Resins: The ion-exchange resins invariably get bound to certain
typical drug substances and thereby cause huge obstacle in their absorption.
Clinical Pharmacokinetics
277
Changes in GI Motility: It has been duly established that there are quite a few drugs that may enhance or
reduce the rate of passage of drugs via the GI tract. Importantly, such critical discourses may obviously afford
∑ rate of absorption of a drug and
∑ degree of drug absorbed.
Cholestyramine, an anionic resin, is recommended profusely to bind the respective bile salts (viz.
alkali salts of bile sodium glycocholate and sodium taurocholate), however, they can bind certain
drugs, e.g., Digoxin, Thyroxine and Warfarin.
Example
Metoclopramide, an anti-emetic drug, helps in relaxing the pyloric sphincter
25
at the base of the
stomach and enhances the GI motility appreciably. It critically minimizes the time for a drug,
paracetamol (acetaminophen), to gain access in the small intestine. It predominantly possesses an
enormous ‘clinical importance’ in migraine, in which case two processes occur sequentially:
∑ delayed gastric emptying phenomena and
∑ slowed action of paracetamol in reaching the requisite site of absorption (i.e., small intestine).
Examples
25
Pyloric Sphincter: It refers to a ring-like muscle which closes a natural passage pertaining to the pyloric part
of the stomach.
Remarks: Administering metoclopramide together with paracetamol reduces signifi cantly the required
on-set time for analgesia.
Bowel Flora Effects: There are certain drugs which may particularly change the normal bowel
fl ora, i.e., normal microbial population present in the colon (large intestine) that usually may possess a
major role to play in actual handling of a drug. Importantly, a number of broad-spectrum antibiotics, viz.,
Ciprofl oxacin, Penicillin Tetracyclines etc., do kill (destroy) a broad spectrum of microorganisms. Thus,
ultimately it may permit only a few selected unsusceptible bowel bacterial species to dominate prominently.
The administration of the ‘combined oral contraceptives’ (COCs) may critically help the bowel
microorganism to split literally the so-called ‘conjugated metabolic products of oestrogen (a hor-
mone)’ to permit the release profi le of ‘free oestrogen’ for being reabsorbed into the human body.
Example
Remarks: Therefore, in a situation when the population of bond
Clearing organisms gets reduced appreciably due to the low intake of oestrogen-containing COCs,
the prevalent ‘low levels of hormones’ may not be suffi cient enough to
∑ cause inhibition of ovulation phenomenon and
∑ prevent contraception effectively.
Essentials of Biopharmaceutics and Pharmacokinetics
278
4.1.2. Interactions Changing Drug Distribution
Importantly, certain typical interactions which specifi cally affect the distribution pattern of a drug sub-
stance are invariably related to such drugs which are bound more intimately to the plasma proteins and,
therefore, are being constantly displaced by another drug entity which gets bound rather more avidly.
Protein-Binding Displacement: As to date, the protein-binding displacement phenomena serves
as the realistic and acceptable mechanism for ‘drug interactions’ and appears to be scarcely having any
signifi cant clinical importance. Perhaps this could be duly explained by citing the example when a drug
is displaced by another drug. Thus, the ensuing concentration of the ‘free drug’ present in the plasma shall
rise appreciably while exposing the drug substance:
∑ to normal elimination phenomena and
∑ to lower the levels swiftly.
Methotrexate (an anti-neoplastic drug) and Warfarin (an anti-coagulant agent) get duly displaced
from proteins by ‘aspirin’ (acetylsalicylic acid) and other non-steroidal anti-infl ammatory drugs
(NSAIDs), viz. ‘ibuprofen’, which was primarily described as the probable mechanism for drug
interactions for these aforesaid displacements.
Examples
Note
Recently, it has been amply demonstrated that such ‘protein binding displacements’ comes into plays as
∑ an alteration in the actual metabolism of Warfarin and
∑ observed renal excretion profi le with methotrexate, that are defi nitely signifi cant in nature.
4.1.3. Interactions Affecting Metabolism
In the recent past, the most vital and overwhelmingly critical interactions do take place via the following
two modalities, namely:
∑ enhancement in the drug metabolism and
∑ blockade in drug metabolism.
Importance of Cytochrome Isoenzymes: The vigorous intensive and extensive research being
carried out on ‘Cytochrome P-450
26
(CYP 450)’—‘Isoenzymes’
27
—has more or less paved the way in:
∑ accurate identifi cation and
∑ augmenting the explicit understanding of mechanism with regard to several on-going interactions.
26
Cytochrome P-450: It refers to cytochrome of liver microsomes responsible for the non-specifi c oxidation of
drug substances and endogenous steroids.
27
Isoenzymes: An enzyme catalyzing the same biochemical reaction as another enzyme, but possesses an
altogether different electrophoretic mobility.