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Pharmacokinetics
189
The various specifi c examples of drug substances having both low and high intrinsic clearances which
are duly eliminated via the hepatic metabolism are given in Table 3.14.
Importantly, the venous equilibrium model for hepatic clearance represents prominently an extremely
important and useful means to the precise assessment of the critical impact of all possible alterations in
the protein-binding phenomenon upon the so-called ‘hepatic clearance’. Reviewing Equation (ca) with
particular reference to a drug substance showing a distinctly low intrinsic hepatic clearance, one may
observe changes in the protein binding that would ultimately cause proportional changes in the hepatic
clearance. Interestingly, this kind of a ‘drug’ is believed to show restrictive clearance, which means the
unbound (or free) drug is largely available for clearance by the liver.
Likewise, the corresponding high intrinsic hepatic clearance drug substances are found to show non-
restrictive clearance.
6.4. Extra Hepatic/Non-Renal Elimination
Enough experimental evidences have mostly affi rmed the glaring fact that not only the drugs but also the
Xenobiotics and their respective metabolites are invariably excreted by such routes other than hepatic and
renal. Therefore, the aforesaid ‘other routes’ of elimination are usually termed as extra hepatic/non-renal (or
extra renal) routes of elimination. These are essentially represented by the following means of elimination:
∑ biliary excretion,
∑ exhalation,
∑ foecal excretion,
∑ intestinal excretion,
∑ excretion via saliva/skin and
∑ excretion via milk,
which will now be treated individually in the following sections.
6.4.1. Biliary Excretion
Biliary excretion may be defi ned as ‘elimination of intact drug molecules or this metabolites in the bile
secretions into the GI tract where either reabsorption and/or excretion in the faeces may take place.’
Table 3.14 Typical examples of drug substances having low and high intrinsic clearances which get eliminated
largely via hepatic metabolism*
S. No.
Drugs with low intrinsic clearance ( f
ub
.CL
u.int
< 0.2 L min
−1
)
S. No.
Drugs with high intrinsic clearance ( f
ub
.CL
u.int
> 5 L min
−1
)
1 Antipyrine 1 Chlorpromazine
2 Barbiturates 2 Encainide
3 Diazepam 3 Meperidine
4 Digoxin 4 Metoprolol
5 Phenytoin 5 Propafenone
6 Theophylline 6 Propranolol
7 Tolbutamide 7 Tricyclic Anti-depressants
8 Warfarin 8 Verapamil
* Adapted from: Gennaro AR. Remington: The Science and Practice of Pharmacy, 20th edn., Vol. II. New York: Lippincott
Williams & Wilkins.
Essentials of Biopharmaceutics and Pharmacokinetics
190
It is, however, pertinent to state here that the biliary excretion is usually regarded to be the most
important as well as a complementary route to both renal/hepatic elimination.
Mode of Action: The bile production takes place by the hepatic cell lining and bile canalaculi.
First of all, the blood emanated from GI tract passes via ‘liver’, which serves as the ‘predominant site of
metabolism’. Besides, ‘liver’ is responsible for the removal of
∑ drug substances and
∑ respective metabolites
that may be eventually excreted in the bile before they gain access right into the general circulation.
Salient Features: These essentially include
1. Transportation of drug substances and their respective metabolites from blood to bile happens to
an ‘active phenomenon’.
2. Invariably, relatively bigger drug molecules (MW > 250–300) are duly excreted via the biliary
excretion.
3. Biliary excretion designates an extremely vital route of elimination for the specifi c conjugated
chemical entities (or compounds).
Classifi cation of Substances Excreted via Biliary Excretion In fact, these specialized substances are
duly categorized into the following three classes that are solely based upon their ratio of concentration
present in bile vs. plasma:
Class A: Substances that belong to this particular class have a ‘ratio of 1’ (i.e., the ratio of concentra-
tion in bile vs. plasma stands at 1). Examples are Na, K, Cl
−
, glucose, Cs, Co, Hg and thallium (Th).
Class B: Substances that belong to the specifi c class have a ‘ratio > 1’, and it ranges between 10 and
1,000. Examples are bile acids, bilirubin, Pb, As and Mn.
Class C: Substances that belong to this class have a ‘ratio < 1’. Examples are Zn, Fe, Au, Cr, inulin
and albumin.
Note
1. The Class B compounds invariably designate a large segment of such drug substances
which are duly excreted by the ‘biliary excretion’.
2. In reality, these compounds are excreted exclusively by means of the ‘active transport mecha-
nism’. That is, mechanism by which such compounds belonging to either Class A and/or Class C
normally get excreted remains to be understood completely.
Important Features: There are two important features pertaining to the hepatic excretory mecha-
nisms, and biliary excretion pattern, which shall now be treated briefl y as under:
∑ Hepatic excretory mechanisms: It has been duly observed that in neonates,
45
the ensuing hepatic
excretory mechanisms are not found to be developed completely on account of which certain drug
invariably exhibit glaring ‘toxicity’.
Ouabain is a cardiotonic drug which clearly exhibits 40-folds more toxicity specifi cally in neonates
in comparison to the adult rats.
Example
45
Neonate: That is, newborn up to 4 weeks of age.
Pharmacokinetics
191
∑ Biliary excretion pattern: It distinctly shows appreciable variation in the biliary excretion pattern
due to species; and consequently, the extrapolation of data derived from animals to humans is rendered
extremely diffi cult to accomplish.
2
2
+
+
2
2
2+
2+
2+
2XDEDLQ
+2
+2
+2
+2
+2
&+
&+
The release pattern of indomethacin, an anti-infl ammatory, antipyretic and analgesic drug, usually
gets excreted up to 3.8% in dogs, whereas, monkeys excrete up to 33.6% to bile. Besides, 52.1%
gets excreted in dogs, whereas, monkeys excrete up to 33.6% in bile. Besides, 52.1% gets excreted
in dogs in the Phase II metabolite of indo-methacin; whereas, only 8.1% gets excreted in monkeys.
,QGRPHWKDFLQ
2
+
&2
&+
&O
&22+
1
Example
Enterohepatic Circulation of Bile Salts Generally, the drugs and their respective metabolites gain
entry into the duodenum via the common bile duct, and ultimately pass into the small intestine. In doing
so, the drugs may get reabsorbed into the body from the intestine. Importantly, there are certain drugs
that will be categorically reabsorbed right into the main blood steam and hence, return to the liver by
the so-called enterohepatic
46
circulation of the bile salts, as illustrated in Figure 3.20.
In this manner, the drug substance undergoes
∑ further extensive metabolism and
∑ ultimately secreted right into bile
46
Enterohepatic: It refers to the intestines and liver.
Essentials of Biopharmaceutics and Pharmacokinetics
192
And the above two, on-going phenomena are usually termed as ‘enterohepatic cycling’, which may
eventually help in a big way in extending the duration of action of a drug substance.
Consequences of Enterohepatic Circulation The two major consequences of entrohepatic circulation
are as follows:
1. The ‘drug’ soon after being secreted into the bile would be fi nally reabsorbed as an ‘active’ drug.
2. The ‘active’ drug may be re-eliminated into the bile and get reabsorbed.
As a consequence of aforesaid sequel of events, the ensuing ‘circulation’ of drug substances that get actively
secreted right into the bile may be eliminated primarily right from the human body via the kidneys.
6HFRQGDU\%LOH$FLGV
%LOH6DOWV
3RUWDO9HLQ
%LOH'XFW
*DOOEODGGHU
6\QWKHVL]HG
%LOH6DOWV
3ULPDU\%LOH$FLGV
&KROHVWHURO
6PDOO,QWHVWLQH /RZHU
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/RVW
LQ)DHFHV
Figure 3.20 Diagrammatic representation of the enterohepatic circulation of bile salts.
Ampicillin, penicillin, sulpha-drugs etc.
Example
Biliary function can be monitored and assessed by means of the drug sulphobromophthalein sodium
(a diagnostic aid for hepatic function) is found to be eliminated more or less completely as the parent
drug in bile.
(Adapted and Modifi ed from: Ward JPT et al. Physiology at a Glance. Oxford, U.K.: Blackwell Publishing LTD., 2005.)
Pharmacokinetics
193
6.4.2. Exhalation
47
In fact, exhalation (or pulmonary excretion) is solely responsible for the critical excretion of both gases
and volatile products via lungs. There are two prominent roles played mainly for the excretion of drug
substances via lungs, namely:
∑ plasma-drug concentration and
∑ blood-gas partition coeffi cient.
Nevertheless, the excretion of drug substances via lungs is caused exclusively due to the phenomenon
of ‘simple diffusion’.
Chloroform, ethanol (in alcoholic beverages), halothane.
Examples
Besides, it may also be observed critically that
∑ gases having low solubility exhibit rapid excretion and
∑ gases with high solubility in blood exhibit rather slow excretion.
Factors Infl uencing Exhalation: These essentially comprise the following:
1. pulmonary blood fl ow,
2. rate of respiration and
3. solubility.
6.4.3. Foecal Excretion
It has also been duly established that the foecal excretion designates as one of the most important routes
of elimination of drug substances, and their respective metabolites. Following are the several recognized
sources for the foecal excretion, for instance
∑ unabsorbed drug substances,
∑ biliary excretion and
∑ intestinal excretion.
Interestingly, the actual excretion via faeces is found to be absolutely of a direct nature for
∑ certain specifi c drugs or
∑ respective metabolites having little absorption or incomplete absorption.
Quaternary ammonium compounds, sucrose, polymers (polyesters), cholestyramine:
The aforesaid unabsorbed portion of drugs solely contribute to the actual foecal excretion due
to their inherent restricted intestinal absorption.
In short, the foecal excretion is by virtue of the on-going biliary excretion.
Examples
47
Exhalation: It refers to the phenomenon of breathing out (i.e., just opposite of inhalation).
Essentials of Biopharmaceutics and Pharmacokinetics
194
6.4.4. Intestinal Excretion
In a broader perspective, the intestinal excretion is mostly important for such drug substances that pre-
dominantly possess such aspects:
∑ low rates of metabolism,
∑ low renal clearance and
∑ low biliary clearance.
There are two vital types of drugs, namely:
Organic Acidic/Basic Drugs: They do exhibit an ‘active secretion’ specifi cally in the intes-
tine such as Quinine—an anti-malarial drug; Nicotine—an agent used for treatment of smoking-
withdrawal syndrome.
Drugs with Diverse Chemical Properties: They do exhibit ‘slow intestinal excretion’ into
the faeces, for instance Digitoxin—a cardiotonic drug; Hexachlorobenzene—an industrial antiseptic
(withdrawn since 1994 because of carcinogenicity. Dioxin (TCDD) as defoliant in Vietnam during
the 1960s, and since banned due to its carcinogenicity in 1994.)
Examples
6.4.5. Excretion via Saliva/Skin
The critical excretion of drug via saliva and skin (sweat) is largely due to the ‘passive diffusion’ of the
lipid-soluble drugs. It has been established beyond any reasonable doubt that both drug substances
and their respective metabolites that are solely excreted via sweat are believed to cause various types of
dermatological manifestations, such as:
∑ Urticaria—a vascular reaction of the skin duly characterized by transient eruption of slightly elevated
patches which appear to be more pale or more red than the surrounding areas.
∑ Dermatitis—infl ammation of the skin characterized by weeping vescicles and/or dry sealing.
∑ Allergic Disorders—relate to the skin rashes, severe itching (causing redness of the skin).
The typical examples of drug substances that are invariably excreted via skin (sweat) are Pb, Hg,
ethanol and antipyrene.
Examples
Drugs Excreted via Saliva: In true sense, the ‘basic drugs’ are usually excreted more abundantly in
saliva vis-à-vis the ‘acidic drugs’. Though most of the drug substances are duly excreted in saliva due to
the ‘passive diffusion’, yet quite a few of them are largely secreted in the saliva actively such as Penicillin,
Phenytoin and Lithium (Li).
Note
Drugs and their metabolites that are excreted mainly via saliva are swallowed frequently thereby
enabling the entire phenomenon of absorption of the drug to start afresh.
Pharmacokinetics
195
Sweat (skin) testing of drugs is carried out for the specifi c identifi cation of ‘drug abuse’.
Saliva testing of drugs is carried out for the ingestion of narcotics, e.g., cocaine, opiates, marijuana,
amphetamines, methamphetamines and phencyclidine.
6.4.6. Excretion via Milk
Generally, the excretion of drug substances and their metabolites into the milk proves to be of great
importance and concern due to the following vital reasons:
∑ Every possible danger of drugs to be transferred right from ‘mother’ to ‘infant’ is through breast
feeding and
∑ Drugs excreted in cow’s milk may be directly ingested by humans, e.g., Oxytocin.
Importantly, the critical transfer of drug substances from plasma to mother’s milk is mainly caused due to
the inherent passive diffusion process and, therefore, solely depends on such vital factors as
∑ pK
a
of the drug,
∑ pH partition existing between plasma (pH 7.4) and milk (pH 6.6),
∑ plasma concentration of the drug,
∑ lipoidal solubility profi le of the drug and
∑ molecular weight of the drug.
Important Points These essentially consist of the following:
1. The presence of Ca and fat in milk enable the ‘lipophilic drugs’ to undergo chelation with the
former and get excreted in the milk.
2. The inherent acidic nature of milk, in comparison to plasma, renders the weakly basic drugs to
concentrate more easily in milk.
3. Excessively high plasma protein drugs actually demonstrate relatively less secretion in milk, viz. diazepam.
Note
The actual quantum of drug substance being excreted in the breast milk is invariably in extremely
small amounts but it may possibly affect a ‘suckling infant’ who possesses
∑ lesser ability to metabolize the drug and
∑ allow it to be excreted from the infants body.
7. Non-Linear Pharmacokinetics
7.1. Preamble
A good number of therapeutically effective drugs vis-à-vis their ensuing ‘pharmacokinetics’ may be expati-
ated satisfactorily based upon its fi rst-order kinetics or linear kinetics. Nevertheless, one may come across
quite a few drugs that predominantly exhibit
∑ Non-linear absorption profi le, e.g., ascorbic acid,
∑ Non-linear distribution pattern, e.g., naproxen and
∑ Non-linear elimination trend, e.g., ribofl avin.
Essentials of Biopharmaceutics and Pharmacokinetics
196
As we know that in the specifi c instance of fi rst-order kinetics or linear kinetics, one may critically
observe changes in the prevailing plasma-drug concentration vs. time (hr),
48
and are invariably found to
be directly proportional to the dose of the drug administered. Therefore, such plots (see Figure 3.6), i.e.,
more appropriately ‘semi-log plots of plasma drug concentration’ vs. ‘time’ shall become superimposable
when necessary corrections have been duly incorporated for the ‘administered doses of the drug’. Thus,
the aforesaid phenomenon is invariably termed as the ‘principle of superimposition’.
Besides, it may be noted categorically that in such typical instances, the following pharmacokinetic
parameters, for instance
∑ volume of distribution (V
d
),
∑ elimination rate constants (K
E
),
∑ plasma half-life (t
1/2
) and
∑ hepatic clearance (CL
H
),
are generally found to be absolutely independent of the actual dose of drug being administered.
7.2. Michaelis–Menten Equation
The Michaelis–Menten equation is also termed as the dose-dependent kinetics. It has been duly observed
that several biological phenomena are precisely mediated by the following two vital aspects:
∑ enzyme systems and
∑ transport carrier system.
Obviously, the aforesaid two systems have restricted capacities and, therefore, are rendered to be quite
‘saturable’ in nature. Thus, the kinetic profi les of these undergoing phenomena are amply elaborated and
described by the Michaelis–Menten equation, which may be expressed as follows:
max
m
d
d
VC
C
tKC
×
−=
+
(cc)
where
−dC/dt is the rate of decline of drug concentration with regard to time,
V
max
is the theoretical maximum rate of the on-going process and
K
m
is the Michaelis–Menten constant.
7.2.1. Accounting for Deviation of Michaelis–Menten Equation
A survey of literature would reveal that fi rst and foremost the Michaelis–Menten equation was duly
employed in the investigative studies of ‘Enzyme Kinetics’.
1
3
2
Enzyme + Substrate Enzyme substrate complex Enzyme Product
K
K
K
⎯⎯→ +
Symbolically, the above expression may be represented as
[]
1
3
2
ES ES EP
K
K
K
+⎯⎯→+
(cd)
48
It is due to absorption, distribution, metabolism and elimination (ADME) of the drug administered.
Pharmacokinetics
197
At this particular point in time, we may have to ascertain three important assumptions, namely:
∑ ES represents a steady-state complex,
∑ At ‘saturation of an enzyme’, i.e., when the substrate concentration remains higher vis-à-vis enzyme
concentration, all enzymes generally found as ES-complex and
∑ Prevailing ‘saturated parameters’ the ultimate rate of formation of the product shall always be maxi-
mum i.e.,
max 3
[ES].VK=⋅
At equilibrium, i.e., at a steady state, we may have the following expression:
V
Formation of ES complex
= V
Cessation of ES complex
where
V
Formation of ES complex
=
[][]
1
ESK ⋅⋅
[] []
[]
()
Cessation of ES complex 2 3
23
ES E
ES
SVKK
KK
=⋅ +
=+
Hence, we may have
[][] [ ]
()
123
ES ESKKK×= +
(ce)
On dividing Equation (ce) K
1
, we have
[][] [ ]
23
1
ES ES
KK
K
⎡⎤
+
⋅=
⎢⎥
⎣⎦
(cf )
As we know that
23
m
1
KK
K
K
+
=
where K
m
is the Michaelis–Menten constant:
Equation (cf ) can now be written as
[] [ ]
m
[E] S ES K×= ×
or
[]
[]
[]
m
ES
E
S
K=×
(cg)
It is known that [E] is the concentration of free enzyme i.e., the quantum of enzyme actually available
for the ensuing reaction and hence, it may be expressed as
[E] = [E
t
] – [E
C
]
where
[E
t
] is the concentration of total enzyme and
[E
C
] is the concentration of enzyme present in [ES]-complex.
Essentials of Biopharmaceutics and Pharmacokinetics
198
In this manner, Equation (cg) may be written as
[][ ]
[]
[]
tCm
ES
EE
S
K−=×
(ch)
Equation (ch) may be divided by [ES] to obtain
[][ ]
[] []
tC
m
EE
ES S
K
−
=
or
[]
[]
[]
t
m
C
E
1
ES
K
−=
or
[]
[]
[]
t
m
C
E
1
ES
K
=+
or
[]
[]
[]
[]
t
m
C
E
S
ES
K+
=
(ci)
Interestingly, at this critical stage, two situations may arise namely:
Situation 1: When ‘Enzyme’ is saturated, it means that when the substrate concentration is higher than
the corresponding enzyme concentration. Thus, we may have
[E
t
] = [ES]
Besides, the rate of the reaction is maximum (V
max
). We have already seen earlier that
V
max
= K
3
. [ES]
Therefore, V
max
= K
3
. [E
t
]
or
[]
max
t
3
E
V
K
=
(cj)
Situation 2: When ‘Enzyme’ remains unsaturated, it indicates that the substrate concentration is lower in
comparison to the respective enzyme concentration.
Thus, we may have
[E
t
] ≠ [E
C
]
But, V = K
3
. [ES]
or
[]
3
ES
V
K
=
(ck)