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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5670_Библиотеки_им_академика_М_И_Перельмана
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Interfacial free energy plays an important role in the process of dissolution. The dissolution
of particles of different sizes can occur due to a change in interfacial free energy. It can
increase solubilization of the substance with decreasing particle size. This is indicated by the
following equation:
Where,
S = solubility of small particles of radius r,
S o = solubility of relatively larger particles,
γ = interfacial energy,
M = molecular weight of the solute,
ρ = density of the bulk solid (solute)
R = gas constant, and
T = thermodynamic temperature.
For storage of pharmaceutical suspensions this effect is important. In this type of
suspensions, the smaller particles would be more soluble than the larger particles. When the
small particles go into solution, they disappear, and the overall solubility of the suspended
drug particles will decrease. Thus, growth of larger particles in the suspensions would take
place. This growth of larger particles is called crystal growth . Occurrence of such crystal
growth by this mechanism is very important when the injectable suspensions are stored 4 .
When the radiuses of the particles are very small, the increase in solubility of the particles
with decrease in their sizes stops. Further decrease in size causes the decrease in solubility.
This is suggested that this change occurs due to the presence of an electrical charge on the
particles and that the effect of this charge becomes more significant as the size of the
particles further decreases’.
Type of solvent
The mechanism of solubilization has been discussed earlier and it has been known that the
solubility of a solid depends on the nature of the solvent. That is, the solubilities of a
particular solid in different solvents will be different. Changes in the properties of solvent
due to the presence of other substances may affect or influence the solubility of a solid.
Water is the most used solvent in pharmaceutical formulations; particularly in case of
preparations intended for internal use such as oral formulations and injections. The mixture
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of ethyl alcohol and water (hydro-alcohol) is also popular solvent. Simple organic liquids
such as ether, chloroform, acetone and different glycols and oils, are also used in addition to
water and alcohol in preparations prepared for external application. Therefore, different
types of solvents that can differently solubilize the solutes are there.
pH
This is a true that most of the drugs are either weakly acidic or weakly basic substances.
Thus, their solubilities would be affected by the pH of the aqueous solvent. For example, a
weakly acidic drug such as aspirin (acetylsalicylic acid) would be more soluble in alkaline
medium because during the process of dissolution, acetylsalicylic acid will dissociate into
sodium acetate and sodium salicylate (both are soluble salts). On the other hand, the drug
will be precipitated from aqueous solution, if the pH is lowered by the addition of a strong
acid. Similarly, weakly basic drug would be more soluble in aqueous solutions having low
pH (acidic) and will precipitate out from the solution by adding strong alkali to raise the pH.
Additional substances
Common Ion effect
Hydrochloric acid is a strong acid and readily dissociates in water. It can be made weak by
adding acetic acid to effect the common ion (hydronium ion). Thus, the solubility of a
sparingly soluble electrolyte can be reduced by addition of a second electrolyte containing
an ion common to that of first one. This effect is known as common ion effect.
In a saturated solution the undissolved solute (solid) remains in equilibrium in contact with
solution. The equilibrium condition can be written as:
If the salt is sparingly soluble, then the concentration of solute would not be sufficient to
represent complete dissociation into ions. The overall equilibrium may then be expressed as:
img
According to the Law of Mass Action, the equilibrium (K) for this reversible reaction can be
expressed as
img
Where, [A + ], [B – ] and [AB](s) represent the concentration of the respective components.
Moreover, the concentration of solid at equilibrium may be considered as being constant
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img
Where, K
′
s
is a constant and is known as the solubility product of the component, AB.
If each molecule of the salt contains more than one ion of each type such as AxBy, then in
the definition of the solubility product the concentration of each ion can be expressed to the
appropriate power: thus,
img
These equations for the solubility product are only applicable to solutions of sparingly
soluble salts. If [A + ][B – ], the product of concentration of ions, exceeds K
′
s
, then the
equilibrium shown in eqn.6.33 moves backward to restore the equilibrium and the solid AB
is precipitated (eqn. 6.34).
The product [A + ][B – ] will be increased by the addition of AX where more A + ions would
be produced by the dissociation of the compound, AX
img
Thus, A + is the common ion and the precipitation of solute (solid) along with the decrease in
solubility of the solute due to the common ion is called as common ion effect . The same
effect can be observed with addition of B – ion also. However, the precipitating effect of
common ions would be less than that predicted from eqn. 6.34.
Effect of indifferent electrolytes
Addition of a second electrolyte can increase the solubility of a sparingly soluble electrolyte,
if this electrolyte does not have any ion common to the first one. The solubility product of a
sparingly soluble electrolyte in terms of the concentration of ions produced at equilibrium
has been expressed by eqn. 6.34 which can be further expressed more thermodynamically as:
img
Where KS is the solubility product of the compound AB and a
A
+
and a
B
–
are called the
activities of the respective ions.
The activityof a particular ion may be considered as its effective concentration .Usually, the
value of this effective concentration is lower than the actual concentration; because some
ions obtained by dissociation of the electrolyte remain strongly associated with oppositely
charged ions. These ions do not contribute so effectively to the system. On infinite dilution,
no association of ions due to interaction between the ions could take place; as a result, wide
separation of ions and the molar concentration (c
A
+
) and activity coefficient ( a
A
+
) of a
particular ion (A + ) become equal; thus,
img
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When the ionic concentration increases, the effect of interionic association also increases and
the ratio of activity to molar concentration becomes less than one; that is,
img
Where, f A + is called activity coefficient of A + . If concentrations and activity coefficient are
used in place of activities, the eqn. 6.35 becomes
img
The product of the concentration terms, that is, (c
A
+
× c
B
–
) would be a constant (K
′
s
) as
shown in eqn. 6.35, and ( f
A
+
× f
B
–
) may be equal to ( f
2 A + B –
). The f
A + B
–
is called the
mean activity coefficient of the salt AB; thus,
img
Since f
A+B
–
varies with the overall concentration of ions present in the solution, called ionic
strength , and since, KS is a constant, it follows that K
′
s
must also vary with the ionic
strength of the solution in an inverse manner to the variation of f
A + B
–
. Therefore, in a
system containing a sparingly soluble electrolyte without a common ion, the ionic strength
will have an appreciable value and the mean activity coefficient f
A + B
–
will be less than one.
Effect of electrolyte on the solubility of non-electrolyte
The substances that do not dissociate into ions in aqueous solution are called nonelectrolytes. Thus, the dilute solutions of these substances consist of single molecules. These
substances dissolve in water depending on the formation of weak intermolecular bonds
(hydrogen bonds) between their molecules and the molecules of water. If a very soluble and
stronger electrolyte such as sodium chloride or ammonium sulphate is added to solution, the
solubility of non-electrolytes will reduce, because the affinity between the electrolyte and
water is high. The molecules of strong electrolyte will compete with the molecules of nonelectrolyte for water, the intermolecular bonds between the non-electrolyte and water will be
weakened. Such effect is very common to protein. According to this principle the proteins
are precipitated.
Effect of non-electrolyte on the solubility of electrolyte
The solubility of electrolytes depends on the dissociation of dissolved molecules into ions.
But the dielectric constant of the solvent plays an important role in this dissociation. The
dielectric constant of a solvent indicates the polarity of the solvent. For example, water and
formic acid possess high dielectric constant and are the most polar solvent. Due to this high
polarity, the solvent can reduce the attractive forces between the oppositely charged ions
produced by dissociation of the electrolyte.
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If alcohol, a water-soluble non-electrolyte is added to a solution of sparingly soluble
electrolyte, the solubility of that electrolyte would be reduced; because alcohol reduces the
dielectric constant of water (solvent), and thus, ionic dissociation of the electrolyte becomes
more difficult.
Effect of complex formation
The apparent solubility of a solute in a particular solvent (liquid) may change; either increase
or decrease, if a third substance is added, because this third substance may form complex
with the solute. The apparent change in the solubility of the original solute will be
established by solubility of the complex. For example, the complexes between m-amino
benzoic acid and various dicarboxylic acids have been found to increase the apparent
solubility of 3-aminobenzoic acid in water. The soluble and insoluble complexes can be
prepared by interaction between various amides and p-hydroxybenzoic acid, salicylic acid,
chloramphenicol, and phenol
7,8
.
img
Fig. 6.5 Schematic representation of absorption, distribution and elimination of drug
Effect of surface-active agent
These compounds can form large aggregates at some concentrations in aqueous solutions.
Organic compounds with low water solubilities when taken into the interior of these
aggregates, the apparent water solubilities of these organic compounds increase. This
phenomenon is called solubilization .
img
Fig. 6.6 Schematic representation of concentration-clearance relationship
Pharmacokinetic Parameters
Pharmacokinetics is a study of absorption, distribution, metabolism (biotransformation), and
elimination of drugs from the body of human beings and animals’. The passage of drug
molecules to the blood stream from the site of administration is called absorption, while
passage of drug molecules from the blood to tissues is called distribution. Elimination of
drug may take place through biotransformation and by the passage of drug molecules from
the blood to outside of the body through urine, bile, or other routes. Thus, there are four
fundamental processes– absorption, distribution, metabolism and elimination (ADME)
which influence the in vivo pharmacokinetics of a drug molecule in the body. The Fig 6.5
represents these processes schematically and k represents the rate constant of respective
process. Generally speaking, pharmacokinetics is what the body does to a drug and what
does the drug to the body is called pharmacodynamics. Pharmacokinetics has utility in
evaluating the time course of environmental (exogenous) toxicologic agents as well as
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endogenous compounds. A fundamental hypothesis of pharmacokinetics is that a
pharmacologic or toxic effect of a drug and the concentration of the drug are related to each
other, and it is readily available at site of the body such as blood. For many drugs this
hypothesis has been recorded
10,11
. However, for some drugs such clear relationship between
pharmacologic effect and plasma or blood concentrations has been found and noted as yet
12
.
Therefore, measurement of the amounts or the concentrations of drugs in blood, urines or
other body-fluids or tissues at different times after the administration, lot of information can
be collected on absorption of drug and on the passage of the drug molecules between blood
and tissues and ultimately on the drug elimination.
Importance of pharmacokinetics
Importance of pharmacokinetics are:
On the laboratory animals the studies conducted can give useful information for drug
research and development. For example, less powerful molecules in vitro can be found more
effective in vivo because of their favorable kinetics such as greater absorption, better
distribution, etc.
In animals, pharmacokinetics supports the studies of preclinical toxicology (toxicokinetics);
because in plasma or tissues the drug levels are often more predictive than the dose to
extrapolate the toxicity data too human being.
The knowledge about pharmacodynamic effects of drugs in man and of the drug-kinetics are
useful for correct use of drugs in therapy such as selection of the best route of
administration, selection of the best dose regimen, and the dose individualization.
Very often, the relationship between the drug levels and the effect do not depend on the
formulation. Formulations producing super imposable drug levels can be considered
interchangeable and based on this concept the bioequivalence stands. To plan for a
pharmacokinetic experiment the following conditions should be well defined:
The route of drug administration,
Dose regimen,
Tissues to sample,
Sample times,
Analytical methods,
The animal species, or clinical settings,
Inclusion and exclusion criteria of the subjects.
All these information and purposes of the experiment should always be mentioned when a
pharmacokinetic study is presented or being discussed. In many protocols the sampling
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•
•
•
•
•
•
•
•
times are kept equal for all the subjects or animals used in the investigation. It is a good
practice at the beginning for the analysis of data to plot not only the observations related to
every single subject, but also the mean concentration and standard deviation in the
population at each time. There are different pharmacokinetic parameters which are necessary
to be studied.
The pharmacokinetic parameters may be (1) Drug and formulation related, and (2) Patient
related
These are:
Peak plasma concentrations (C
max
),
Peak time (T
max
)
Biological half-life (t
1/2
),
Area under the curve (AUC),
Clearance,
Volume of distribution,
Plasma-protein binding,
Bioavailability,
When samples of urine are collected, the amount of drug excreted unchanged, or the
percentage of dose excreted in urine should also be noted. It should be noted that
concentration of drug in urine is very rarely of interest in pharmacokinetic study, although
the amount of drug excreted gives a mass balance of the fraction of the excreted dose. The
amount of drug can be calculated from the concentrations having the volumes; hence, the
volume of urine excreted during experiment should be recorded. A single kinetic profile may
be well summarized by C
max
, T
max
, t
1/2
and AUC.
Peak plasma concentration (C
max
)
Blood or plasma concentration of a drug depends on the degree of distribution and binding
of the drug. Again, the degree of distribution and binding of the drug depend on the
physicochemical property of the drug which varies considerably from one drug to another.
Therefore, the plasma concentration of equal doses of two drugs administered through
intravenous route can show two different concentrations just after administration on analysis
of blood samples.
Once a drug attains distribution equilibrium its plasma concentration indicates distribution
factors. A simple relationship between the amount of drug in the body and (A) and the
plasma concentration (C) can be expressed as:A = V× C
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•
•
•
•
•
Where, V is the apparent volume of distribution of the drug. The concentration of the drug in
the body is related to
Peak time (T
max
)
Biological half-life (t
1/2
)
The rate at which a drug disappears
Area under the curve (AUC)
Clearance
Clearance refers to the ability of the body to eliminate a drug. The drug can be eliminated
from the body through various organs. For example, blood clearance (CL b ), plasma
clearance (CL p ), urine clearance, etc. The drug eliminated may be free or unbound or in its
metabolites. Clearance is expressed as the volume eliminated in unit time. Concentration of
the drug in each fluid is measured. Elimination of a drug occurs because of processes that
occur in liver, kidney, and other organs. Clearance is additive in nature. Thus, total
clearance,
img
Other routes of elimination include saliva, sweat, etc. The Fig 6.8 shows how a drug is
removed from the systemic circulation after oral and intravenous administrations. The rate at
which a drug remains present to a drug-eliminating organ is the product of blood flow into
the organ (Q) and the concentration of the drug in the arterial blood entering the organ (C
A
). The rate at which a drug leaves the drug eliminating organ is the product of the organ
blood flow (Q) and the drug concentration in the venous blood (C V ) leaving the organ. By
mass balance, the rate of elimination (or extraction) of a drug by a drug-eliminating organ is
the difference between the rate of entry and the rate at which the drug leaves the body:
img
The extraction ratio (ER) of an organ can be defined as the ratio of the rate of elimination to
the rate of entry. Thus,
img
The maximum possible extraction ratio (ER) varies from 1.0 when no drug remains present
in the venous blood for elimination (C V = 0) to zero, when the entire drug passing through
the potential drugeliminating organ remains present in the venous blood; that is, C A = C V .
By convention, the drugs having extraction ration more than 0.7 are considered as high
extraction ration drugs and the drugs having extraction ratio of less than 0.3 are considered
as low extraction ratio drugs.
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The product of organ blood flow and extraction ratio of an organ stands for a rate at which a
definite volume of blood is completely free of drug. This is expressed as CL
organ
of the drug.
img
The eqn. 6.40 indicates that the clearance from an organ is controlled by the blood flow to
that organ; that is, ER = 1. Among the organs that can eliminate drugs, the liver possesses
the highest metabolic capability. The liver can excrete the drug into the bile, kidney
primarily excretes drugs into the urine, and for some drugs kidney is the main metabolite
site. In blood, drug can remain bound with blood cells and plasma proteins such as albumin,
glycoprotein, etc. Only unbound drug molecules can pass through hepatic membranes into
hepatocytes where the drugs are metabolized by hepatic enzymes or transported into bile.
Therefore, for elimination, the drug molecules must partition out of the RBCs and dissociate
from plasma proteins to become unbound or free. The fraction unbound (f u ) is the ratio of
the unbound drug concentration (C u ) to total drug concentration (C):
img
Volume of distribution
Generally, there is substantial difference between the apparent volume of distribution of a
drug and the actual volume in which the drug distributes itself. The apparent volume of
distribution is just a proportionality constant that relates the plasma concentration to the total
amount of drug present in the body. The apparent volume of distribution depends on the
degree of binding to plasma proteins and tissues. The apparent volume of distribution may
vary from 0.04lt/kg (plasma volume) to 20lt/kg or more. The actual volume of distribution of
a drug is related to the total volume of water present in the body; it never exceeds the total
weight of the body. It means that 42lt or 70% of the body weight, in a normal man having
body weight of 60kg, would be the apparent volume of distribution. The water remains
present in three compartments of the body– vascular fluid, extracellular fluid (ECF), and
intracellular fluid. The extracellular water, generally 19% of the body weight, includes water
present in plasma (4% of the body weight). The volume of blood (vascular) including
intracellular water of erythrocytes is about 8% of the total body weight.
Chloride and bromide ions can rapidly distribute throughout the extracellular fluid, do not
cross cell membranes; hence, these can be used to measure the extracellular water. The
volume of total body water can be approximately determined by determining the distribution
of heavy water (D 2 O) or certain poorly bound and lipid soluble substances such as
antipyrine. However, all these substances can provide an approximate result because these
can bind with plasma proteins and tissues. Few substances which can negligibly bind with
plasma proteins and tissues can be used to measure the true volume of distribution. The
equation describing the relationship between apparent volume of distribution, drug binding,
and anatomic volumes
13
is expressed as;
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img
Where,
V = apparent volume of distribution,
V B = blood volume,
V T = extravascular volume,
f B = free fraction of drug in the blood, and
f T = free fraction of drug in the tissues (extravascular space)
Since plasma proteins are not present in blood but are also present in extracellular fluid a
more physiologically correct expression to describe apparent volume of distribution
14
is:
img
Where,
V P = plasma volume
V E = extracellular space – plasma volume
V R = physical volume into which the drug distributes – extracellular space,
f P = free fraction of the drug in plasma,
f T = free fraction of the drug in tissue, and
R
E/L
= ratio of the amount of binding protein in the ECF outside the plasma to that in the
plasma.
Plasma-protein binding
Distribution, elimination, and the pharmacological effect of a drug can be affected by
binding of a drug to plasma protein. The high molecular weight of plasma proteins hampers
its passage across capillaries. Their low lipid solubility stops the passage across cell
membranes. Only the fraction of drug freely circulating or remaining unbound in
extracellular water can penetrate cell membranes and is subject to glomerular filtration.
The total drug concentration in plasma is usually higher than in lymph, cerebrospinal fluid
(CSF), synovial fluid, and other fluids of the extravascular space because the protein
concentration in extracellular fluid is less than in plasma. Normal CS fluid contains very
little amount of protein, it is often considered as the ultrafiltrate of the plasma. The plasma
protein binding of nortriptyline in man is almost 94%. The concentration of carbamazepine
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