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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5948_Библиотеки_им_академика_М_И_Перельмана
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and its epoxide metabolite in CSF of epilepsy patients are closely related to free drug and
free metabolite concentrations in serum
15
.
Normal synovial fluid contains only 1-g albumin per 100 ml. Albumin levels may be
increased in synovial fluid from patients suffering from arthritis or other degenerative joint
diseases. The permeation of ampicillin and cloxacillin into synovial fluid has been measured
after oral administration of these drugs to patients suffering from osteoarthritis or
rheumatoid arthritis
16
. Although the drugs have been found to diffuse rapidly into synovial
fluid but their total concentrations in plasma are appreciably different. Ampicillin is not
highly bound to plasma proteins, only up to 10 – 15%; the total drug levels in synovial fluid
are like the plasma levels. In case of cloxacillin, it is highly bound to plasma proteins, about
95%; the total levels in synovial fluid are considerably lower than those in plasma.
Drug binding to plasma proteins may involve ionic, Van der Waals, hydrogen, and/or
hydrophobic bonds. The most important contribution to drug binding in plasma is made by
albumin which comprises about one half of the total plasma proteins. In healthy individuals,
albumin concentration in the plasma is about 4g per 100ml. During pregnancy lower levels
about 3.5g per 100ml are found particularly during the last trimester and in certain diseases.
A wide variety of drug molecules bind to albumin; but it plays important role in binding of
weak acids and neutral drugs. For basic drugs such as imipramine, lidocaine, propanolol,
quinidine, etc. greater affinity for binding is found with α1-Acid glycoprotein
(orosomucoid). This protein is having low molecular weight approximately 40000 Daltons.
Other proteins in plasma play a limited role in drug binding. There is a highly specific
interaction between some steroids, such as prednisolone, and corticosteroid-binding
globulin, also known as CBG or transcortin
17
. Transcortin also binds thyroxin and vitamin
B
12
. The γ-globulins react specifically with antigens, and negligibly with most drugs.
The protein-drug interaction can be represented by the law of mass action:
img
Where,
D F is the free drug,
D B is the bound drug,
k 1 is the rate constant for association reaction, and
k 2 is the rate constant for dissociation reaction.
img
Where,
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K is the equilibrium association constant, n is the number of binding sites per mole of
protein,
[D F ] is the molar concentrations of free drug,
[D B ] is the molar concentrations of bound drug, and
[P] is the molar concentrations of protein.
The binding rates k 1 and k 2 are large because the equilibrium is established almost
immediately. The equilibrium constant K varies from zero, where no drug is bound
essentially to the protein, to about 10‘ where almost all the drug molecules are bound to the
protein.
The fraction of drug in the plasma that is free or unbound, f P can be expressed as:
img
Where, [D T ] is the total concentration of drug in the plasma. In general, for a given amount
of drug in the body, the greater the binding of drug in the plasma protein, the larger is the
total drug concentration in plasma. Changes in binding usually affect blood levels of total
drug and play a role in pharmacokinetic variability.
The fraction of free drug in plasma depends on the amount of K, the total drug
concentration, and concentration of the protein. In fact, there is a limited number of binding
sites on the protein. With the increase in drug concentration in plasma, the number of free
sites decreases. Therefore, the fraction of free drug increases. However, for most of the drugs
administered in therapeutic doses, the fraction of unbound drug in plasma is essentially
constant over the entire drug concentration range.
Concentration-dependent changes in the fraction of free drug in the plasma are most
expected to occur with drugs having association constant of about 10 5 – 10 6 , and that are
given in large doses, such as certain sulphonamides and phenylbutazone. The fraction of
disopyramide unbound to plasma proteins varies from about 0.19 – 0.46 over the therapeutic
range of total drug concentration in plasma 2 – 8µg/ml
18
. That is, the concentration of free
drug increases 10-fold, when the concentration of total drug increases 4-fold.
Ceftriaxone is a third generation of cephalosporin drug. Its plasma protein binding depends
on concentration
19
.The relation between bioavailability and area under the drug
concentration-time curve (AUC) is nonlinear and depends on the rate of drug absorption
when the plasma protein binding of a drug depends on concentration
20
. Certain drugs show
a large degree of inter-subject variation in binding. Twenty-six patients who had been taking
phenytoin for more than two weeks were studied and found that concentration of free
phenytoin in plasma varied from 5.8 to 12.6% of total concentration of drug
21
. Similarly, the
amount of free warfarin concentration in plasma was found to vary from 0.4 to 1.9% of total
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concentration of drug, when 31 patients with cardiovascular disease who had been taking
regularly warfarin
22
.
The most appropriate methods of studying the plasma protein binding of drugs are
equilibrium dialysis and ultra-filtration. Although quick measurements are possible using
ultrafiltration, the equilibrium dialysis method provides more accurate result.
Since the concentration of protein in extravascular fluid is less than in plasma, the total
concentration of drug in plasma is commonly higher than in lymph, cerebrospinal fluid
(CSF), synovial fluid, and other fluids of the extravascular space. Normally, cerebrospinal
fluid contains so little amount of proteinthat it can be considered as an ultrafiltrate of the
plasma. Usually, synovial fluid contains only 1g albumin per 100 ml. The albumin level in
synovial fluid can be more in the patients with arthritis or other degenerative joint diseases.
Both ampicillin and cloxacillin can penetrate/diffuse rapidly into synovial fluid of patients,
suffering from osteoarthritis or rheumatoid arthritis, after oral administration. But their total
concentrations differed substantially from the total concentration in plasma
23
.About 10 –
15% of ampicillin is bound to plasma protein; the total drug levels in synovial fluid were
almost similar to the total plasma levels. About 95% of cloxacillin has been found to bind
with plasma proteins; total levels in synovial fluid were significantly lower than those in
plasma. Unbound levels of cloxacillin in synovial fluid and plasma were almost similar.
Various studies have showed that drug uptake by erythrocytes is a function of plasma protein
binding. Linear correlations have been reported between blood or RBC/ plasma
concentration ratio and the percent of unbound drug in the plasma for propanolol
24
,
phenytoin
25
, and haloperidol
26
.
It is believed that the concentration of free drug in plasma is responsible for drug effect. Of
course, limited experimental evidence is there. The relation between effect of anticoagulant
and concentration of free and total warfarin in rat plasma was investigated. The
concentration of total warfarin required for a defined anticoagulant effect varied widely
among animals. While required concentration of free warfarin showed much less variation.
This result shows that the anticoagulant effect of warfarin depends on free concentration
than the total concentration in plasma.
The rate of metabolism of some drugs is related to the extent of binding with protein in the
plasma. A strong correlation has been observed between total drug clearance of warfarin
from plasma and the free fraction of the drug in the serum of individual rats
27
.
For elimination, concentration of free drug acts as the driving force. If a drug or chemical is
neither secreted nor reabsorbed by the tubules and is not bound to protein, its renal clearance
is a measure of glomerular filtration rate. The clearance of many drugs from the blood is
directly proportional to free drug in the plasma, f P . The steady-state concentration of these
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drugs is inversely proportional to f P . Alternatively, the clearance of some drugs is largely
independent of plasma protein binding. These drugs are extensively metabolized in the liver.
Bioavailability
The bioavailability of a drug is defined as the rate and extent of absorption . For any drug
administered rapid and complete absorption is necessary. The more rapid the absorption, the
shorter is the onset and greater is the intensity of pharmacological action. The efficacy of a
single dose of a drug may be a function of both rate and extent of absorption. However, there
would be no assurance of the bioequivalence of two dosage forms of the same drug because
the amount of drug absorbed from each is equivalent; the rate of absorption of drug from
each drug product must also be comparable. When a drug is rapidly absorbed, the frequency
of oral administration of the drug and the severity of gastrointestinal problem would be
reduced with certain drugs. This is possible by reducing the contact time in the
gastrointestinal tract.
Generally, an estimate of the relative rate of absorption of a drug from different drug
products or under different conditions, such as with or without food, become useful to
compare the magnitude and time of occurrence of the peak drug concentrations in the plasma
after a single dose.
The extent or relative extent of absorption of a drug from a product can be measured by
comparing the total area under the drug concentration in plasma versus time curve (AUC) as
shown in Fig 6.7. The plot may be drawn between the total amount of unchanged drug
eliminated through urine after administration of the product to that found after
administration of a standard
28,29
. The standard may be an intravenous administration, or an
aqueous solution or water-miscible solution orally administered, or may be another product
of the same drug accepted as a standard. The absolute bioavailability can be determined by
administering the standard intravenously and the sample (test product) orally or through
some other extravascular route. In such case, if the doses of the drug are same in both the
cases and the AUC values are found same, it can be said that the drug in the test product is
completely absorbed and not pre-systemically metabolized.
However, sometime in bioavailability studies the standard used is the orally administered
solution of the drug or an established product of the same drug. If equal doses of the sample
productand the standardproduce the same AUC values, it can be said that the sample product
is 100% bioavailable, relative to the standard. Since, it is a comparison test; we should use
the term relative. If the same peak concentration of the drug in plasma and the same AUC
are produced by both sample and standard, the sample is called as bioequivalent .
img
Fig. 6.7 Typical plot of plasma concentration of drug vs. time
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The area, under a plasma concentration of drug vs. time curve, has the units of
concentration-time such as µg×hr/ml. This can be determined by several methods. One
method used is planimeter, an instrument used to measure the area of plane figures. Another
method used is cut and weigh method in which the area under the curve is cut and weigh.
The weight obtained is converted to the proper units by dividing it by the weight of a unit
area of the same paper. Most used method is by means of the trapezoidal rule. The area
bounded by the trapezoids approximates the area under the curve; if the numbers of data
points are more, the approximation would be closer. The area of a trapezoid is equal to one
half the product of the sum of the heights times the width. The area under the curve is
approximated by the following equation:
img
Where,
C = concentration of drug,
t = time, and subscript means the sample number.
Sample Time (hr) Concentration (μg/ml) Area
1 0 0.0 2.80
2 1 5.6 7.2
3 2 8.8 9.05
4 3 9.3 9.45
5 4 9.6 18.30
6 6 8.7 15.60
7 8 6.9 19.60
8 12 2.9 -
Let us understand with the help of the following example. After oral administration of a
drug, the data collected has been tabulated below:
Area (1) = ½(0 + 5.6)(1 – 0) = 2.80 µg.hr/ml
Area (2) = ½(5.6 + 8.8)(2 – 1) = 7.20 µg.hr/ml
Area (6) = ½(8.7 + 6.9)(8 – 6) = 15.6 µg.hr/ml
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1.
2.
3.
4.
5.
Area (7) = ½(6.9 + 2.9)(12 – 8) = 19.60 µg.hr/ml
The total area under the curve for drugs eliminated by first-order kinetics can be calculated
by:
img
Where, k is the overall elimination rate constant, and V is the volume of distribution.
It follows that the bioavailability, F of a drug from a formulation may be determined, when
equal doses of a drug are administered, from the equation given below:
img
When different doses of drug product and standard are administered, the area under the
curve should be scaled properly to allow the comparison under conditions of equivalent
doses, assuming that AUC is proportional to the dose.
The amount of drug excreted unchanged in the urine (A u ) after administration can be
expressed as:
img
Where, k is the overall elimination rate constant, and ku is the urinary excretion rate
constant.
Heckel Plots
Compaction of powder is a very important process of production in various types of
industries such as ceramic,food, and pharmaceutical industry. The structural and mechanical
properties of tablets depend on the properties of the input materials such granules or
powders. Although many scientific investigations have been done on this topic, but the
prediction of the properties of tablets based on the properties of input material remains
difficult or rather impossible. The most important reason for incomplete prediction lies on
the limited understanding of the processes involved and complexity of the powder
compaction process. The important parameters
30-35
those are responsible for this complexity
is:
Deformation behavior,
Particle size and shape,
Stress applied during compression,
Particle rearrangement,
Plastic and elastic deformation of particle,
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6. Particle fragmentation
Last three (4 – 6) parameters are called as micro-processing parameters
36-40
. The peculiarity
of these parameters is that they do not occur sequentially, but they take place simultaneously.
The role of a single mechanism depends on the properties of the input material and the
process used. Unfortunately, till today each mechanism remains difficult to be quantitatively
characterized. The number of inter-particulate bonds, the bonding forces and ultimately the
structural and mechanical properties
41,42
of the tablets compressed are influenced by the
deformation behavior. For prediction these reasons create the necessity for a systemic and
comprehensive characterization of the compression or compaction of raw materials to make
the process development and formulation a prerequisite and rational approach.
Most commonly, the out-of-die analysis method is used to determine the compression
curves, and the resulting compressibility is called out-of-die compressibility. In this method,
by applying different compression forces (stresses) the tablets are produced and stored under
different predefined conditions for a definite period, then solid (tablet) fraction/ porosity is
determined. This method can be successfully used only when tablet defects such as
lamination, capping, or chipping occurs during compression. This is also a limitation of this
method.
Tablet press fitted with instrument and displacement sensors, can determine the
compressibility characteristics. Based on the measured force-displacement curve, the weight
of the tablet, and its solid density, the solid fraction or porosity of the compressed tablet can
be calculated. This is called in-die analysis. The major advantage of indie analysis is that the
characteristics of the powder compressibility can be determined sufficiently even after single
compression. Moreover, even with the occurrence of the tablet defect, the in-die
compressibility can be used to determine the powder compressibility. Compared to out-ofdie compressibility, in-die compressibility can be shifted to higher solid fraction or lower
porosity. This can measure the different specific compression parameters, because the in-die
analysis takes elastic deformation into account. On the other hand, out-of-die analysis does
not consider the elastic deformation, because during and after unloading the compressed
powders relax. During compression, the molecular lattice deforms elastically inside the
individual particle, as a result, the specific volume of the solid decreases during
compression. Therefore, the density of solid increases with increasing stress, particularly if
the substance being compressed is organic compound. This phenomenon is known as solid
compressibility. For example, paracetamol when hydrostatically compressed at 400 MPa,
about 3% of its volume decreases.
Another influencing parameter may be diameter of the die used which is generally kept
unchanged. Till in the discussion the expansion of the die has not been considered.
Therefore, the out-of-die compressibility analysis is frequently used, although the in-die
method saves the material and time. Katz et al. proposed a new empirical approach using the
advantages of both the methods
43,44
. They calculated out-of-die compressibility based on in-
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die compressibility considering elastic and viscoelastic recovery. According to this method
only two compression experiments are to be done: one at relatively low compression stress
and other with maximum compression stress. This method is not suitable if there are tablet
defects. However, it is necessary to characterize the compression behavior that causes the
tablet defects for formulation and process development.
The theoretical concept of Heckel Model
For description of powder compressibility various mathematical models have been
developed. However, the Heckel model/equationis widely used in pharmacy.
It assumes that densification of a bulk powder under force follows the first-order kinetics as
expressed below:
img
Where,
ρ r is the relative density of the tablet (the ratio of tablet density to true density of powder) at
the appliedpressure,
P is the applied pressure (reciprocal of the yield pressure of the material),
K is the slope of the linear portion of the Heckel plot, and
A is a function of the original compact volume.
The value of Heckel plots is derived from their ability to identify the predominant form of
deformation in a given sample. Materials which are relatively soft and readily go through
plastic deformation retain different degrees of porosity, depending on the initial packing in
the die
45-48
. Subsequently this is influenced by the shape, size distribution, etc. of the
original powders. For such materials such as sodium chloride, Heckel plots are shown in Fig
6.8.
img
Fig. 6.8 Typical Heckel plots. The graphs a, b, and c represent decreasing particle size fraction of same material
img
Fig. 6.9 Typical Heckel plots. The plots indicate initial fragmentation of particles
On the other hand, harder materials with yield pressure values usually undergo compression
with initial fragmentation, then a denser packing (compression) which is shown in Fig.6.8 .
For example, lactose is the most common material of this type.
The plots shown in Fig 6.9 usually have a final slope (K y ) higher than those shown in Fig
6.8. This shows that the materials of former type have a lower yield stress. In general, hard,
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brittle materials are difficult to be compressed than soft and yielding materials because
fragmentation with subsequent percolation of smaller particles (fragments) is less efficient
than filling of voids by plastic deformation. However, for all materials the porosity
approaches are absent, plastic deformation may be prominent mechanism. It is generally
considered that Heckel plot has two regions– initial repacking and subsequent deformation.
The point of intersection indicates that at this point the lowest force would be required to
make a coherent tablet. Moreover, the crushing strength of tablets can be correlated with the
values of Ky of the Heckel plot. Usually, larger values of Kyindicate harder tablets. For
selection of binder in designing a tablet formulation this information should be used. Heckel
plots depend on the following factors:
The overall time of compression,
The degree of lubrication,
The size of the die,
Force-porosity relationship
The effects of these parameters should be studied. For many formulations, the relation
between force and porosity is important. There is a relatively narrow optimum residual
porosity range that is responsible for adequate mechanical strength, rapid water uptake, and
hence, good disintegration characteristics. Therefore, the formulator must identify this
optimum range and to predict the conditions at which compression should be done to prepare
the tablets of desired quality. In addition to the predictive ability to establish the behavioral
patterns for a given formulation (so-called “finger-printing”), the valuable diagnostic
information can be provided when a particular batch of the product causes problems.
This is important to note that the initial porosity can influence the process of compression
and application of slow force can develop low porosity for a given load applied.
Similarity Factors – f 2 and f
1
Out of these two factors f 2 is the similarity factor and f 1 is called difference factor. Both of
two factors are used to compare the dissolution profile of a generic oral, solid formulation
with that of an innovator formulation of same drug, same strength, and of same type. The
first method includes the determination of parameters such as Ratio of % dissolved, ratio of
area under the dissolution curves, and ratio of mean dissolution time. The second method
includes the determination of parameters such as Difference factor (f 1 ), and Similarity
factor (f 2 )
49
.
Similarity Factor – f
1
This method is model independent one.This is required for submission of the proposal before
US-FDA for approval of generic drugs. To compare the dissolution profiles the model
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•
•
independent concept can be categorized into two methods: (1) ratio tests, and (2) pair wise
procedures. These factors were first introduced by Moore and Flanner in the year 1996. The
Center for Drug Evaluation and Research (CDER) of US-FDA and the Human Medicine
Evaluation Unit of European Agency for Evaluation of Medicinal Products (EMEA) adopted
this method for assessment of similarity between two dissolution profiles. The difference
factor indicates the difference in percent dissolved between the test sample and reference
product at various time intervals
50
.
Difference factor (f 1 ) is defined by FDA as calculation of the % difference between two
curves at each time point and for measurement of the relative error between two curves . The
difference factor, f 1 is expressed as:
img
Where, n is the number of time points, R t is the % dissolved at time t of reference product
(pre change), T t is the % dissolved at time t of test product (post change).
The percent error is zero when the test and reference profiles are identical and increase
proportionally with the dissimilarity between two dissolution profiles. The US FDA
considers both the factors (f 1 and f 2 ) in various guidance documents. The US FDA states
different criteria for comparison of dissolution profile as:
When the numbers of dissolution units are equal to or more than 12, the dissolution
profiles can be used to compare. For comparison, the mean data can be used only
when the coefficient of variation at the first time-point is not more than 20%, and not
less than 10% at the rest of time intervals.
To determine whether the reference and test are statistically significant or not,
statistical approach to establish the confidence intervals may be used for accurate
calculation of similarity factor. In general, when the value of f 1 is found within a
range from 0 to 10, it ensures the similarity between the profiles.
The mean dissolution profiles from both the tests at each time interval are used to calculate
the fit factors.
Similarity factor (f 2 )
In pharmaceutical industry in-vitro dissolution test on solid dosage forms such as tablets,
capsules or pellets are performed on regular basis
51,52
. These dosage forms are orally
administered, and the test provides the information about the consistent quality of
medicines.The dissolution test results can also provide the information about in-vivo drug
release. The test measures the release of drug in-vitro at different time intervals under
standardized sink conditions such as dissolution medium, pH, speed of agitation, and
temperature. It is mandatory to perform the dissolution test of sample product and
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