Transcript Slide 1

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Determination of
Absorption-Rate Constant
By:
Arooj Khalid Alvi
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Drug Absorption
• “Absorption is defined as the appearance of
drug in the body fluids.”
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Kinetics of oral absorption of drug
ka
DGi
ke
DB VD
DE
dDB/dt = dDG/dt – dDE/dt
Graphically:
A plasma-level time curve showing drug absorption
and elimination can be made.
• Absorption phase:
Rate of drug absorption is greater than the rate of
drug elimination.
dDG/dt > dDE/dt
• Peak-drug concentration:
Rate of drug absorption equals rate of drug
elimination.
dDG/dt = dDE/dt
• Post-absorption phase:
Rate of drug elimination at this time is faster than the
rate of absorption.
dDG/dt < dDE/dt
• Elimination phase:
Drug absorption appears zero. The plasma level time
curve only represents the rate of drug
elimination.
dDB/dt =-kDB
Post-absorption phase
Absorption phase
Elimination phase
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ABSORPTION MODELS
Zero order absorption models
Zero-order drug absorption from the dosing site into the plasma occurs when
a zero-order controlled release delivery system is used.
Mathematically:
The rate of drug input is k0 and the rate of drug elimination is k. Therefore net
change per unit time in the body is:
dDB/dt = -kDB
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Contd…
• First-order absorption model
Normally absorption process in the body is assumed to follow firstorder kinetics. This model applies to the drugs those are in solution
form or rapidly dissolving dosage forms.
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Differential Equations:
The differential equations describing the
rates of change of the three components DG,
DB and DE are:
•
the rate of disappearance of drug from
the gut:
dDG/dt = -kaDGF (where F is the fraction
absorbed
the rate of drug eliminated:
dDE/dt = +kelDB
the rate of drug change in the body is the
rate of drug in – the rate of drug out of the
body:
dDB/dt =F kaDG - kelDB
dDB/dt =FkaDG-kelV.Cp (DB=V.Cp)
The first term, ka •DG, represents absorption and
the second term, kel.V.Cp, represents elimination.
Using Laplace transforms, our equation becomes:
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Absorption rate constant
DEFINITION:
“It may be described as a value describing how much drug is absorbed per
unit of time”.
DETERMINATION:
Absorption rate constant can be determined by the “Method of
residuals” by plotting the oral absorption data.
1. In One-Compartment Model
• by plotting amount of drug absorbed versus time
• by plotting the amount of drug unabsorbed versus time
2. In Two-Compartment Model.
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1. In One-Compartment Model
A. Amount of drug absorbed vs. time:
Using the equation
We can get the y-intercept. As with the passage of time, drug absorption is virtually
complete so exp(-kat)=0
As
So
•
=B
Cp=Be-kt
This equation representing the first-order drug elimination will yield a linear plot
on semi log paper. This slope is equal to –k/2.303.The value of ka can be obtained
using the method of residuals, or feathering technique
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Method of residuals:
Steps involved in method of residuals:
The value of ka can be obtained by the
following procedure:
1.Plot the drug-concentration versus time,
with time on x-axis and conc. on y-axis.
2.Obtain the slope of the terminal phase by
extrapolation
3.Take any points on the upper part of the
line(x1,x2,and x3) and drop vertically to
obtain corresponding points on the
curve(x’1,x’2,x’3)
4.Read the conc. values at x1 and x’1 and so
on and plot the difference at the
corresponding time point’s t1,t2,t3.a
straight line will be obtained with a slope
of –ka/2.303.
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1. In One-Compartment Model (Cont…)
Lag-time:
• In few individuals, the absorption of drug after a single oral-dose does not start
immediately
• the time delay prior to the commencement of first-order absorption is known as
lag-time.
Flip-Flop Of Ka And Kel:
• Using the method of residuals to estimate ka and kel, the terminal phase of the
absorption curve is usually represented by kel whereas steeper slope is
represented by ka .In few cases kel obtained from oral absorption does not agree
with that obtained after I/v bolus. Apparently the ka and kel obtained by this
method has been interchanged. This phenomenon is termed as “flip-flop” of ka
and kel.
• Drugs having flip-flop characteristics: are generally the one that have fast
elimination.(ke>ka).so for drugs with large kel, the chance of flip-flop is much
greater.
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1. In One-Compartment Model (Cont…)
B. Fraction of drug un-absorbed vs. time: (Wagner-Nelson Method)
From Blood-Data:
Let Ab = DB+DU (amount of drug absorbed) And Ab∞=amount of drug
absorbed at t∞
Ab= CpVD+ kVD[AUC]t 0
Ab∞=0+ kVD[AUC]∞ 0
as at t=∞,Cp∞=0
Ab/Ab∞= Cp+k[AUC]t 0/ k[AUC]∞ 0
The drug remaining in the GIT at any time t is:
DGI=D0e-kat
and
DGI/ D0= e-kat
log DGI/ D0=-kat/2.303 (taking log)
as
DGI/ D0is actually the fraction of drug unabsorbed that is (1-Ab/Ab∞),
so the plot of this fraction unabsorbed against t yields the slopeka/2.303.
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1. In One-Compartment Model (Cont…)
• Plot the fraction of drug unabsorbed vs.
time.
• find k from the terminal part of the
slope when the slope is –k/2.303.
• Find [AUC]0t by plotting Cp vs. t.
• Find k[AUC]0t by multiplying each
[AUC]0t with k.
• Find all [AUC]∞t by adding up all [AUC]0t
from t=0 to t=∞
• Determine (1- Ab/Ab∞)
• Plot this (1- Ab/Ab∞) vs. time on semi
log graph paper with (1- Ab/Ab∞) on yaxis.
• If this graph gives a linear regression.
Then the rate of drug absorption DGI/ Dt
is a first-order process.
1-(Ab/Ab∞)
Steps in determination of ka:
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1. In One-Compartment Model (Cont…)
Advantages
Disadvantages
• The absorption and elimination
processes can be quite similar and
still accurate determinations of ka • The major disadvantage of this method
can be made.
is that you need to know the
elimination rate constant, from data
• The absorption process doesn't have
collected
following
intravenous
to be first order. This method can be
administration.
used to investigate the absorption
process. This type of method has
been used to investigate data
obtained after IM administration and
it was found that two absorption
steps maybe appropriate. Possibly a
fast step from drug in solution and a
slower step from drug precipitated at
the injection site.
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1. In One-Compartment Model (Cont…)
From the Urinary Data
Absorption rate constant can also be determined from
urinary-excretion data using the plot of amount of drug unabsorbed vs. time.
And the fraction of drug absorbed is
Abt/ Ab∞=(dDU/dt)+k(DU)t /kDU∞
And a plot of the fraction of drug unabsorbed (1- Abt/Ab∞),
vs. t gives –k/2.3 as a slope from which the absorption rate
constant can be determined.
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2. In Two-Compartmental Model (LooRiegelman Method)
• Plotting the percent of drug unabsorbed vs. time can be used for
two-compartment model as well. This method requires that the
drug is given i/v and orally.
Total amount of drug in the body : Ab=Dp+Dt+Du
Ab/Ab∞=( Cp +Dt/Vp+ k[AUC]0t)/ k[AUC]0∞
Limitation:
For calculation of ka by this method, the drug must be given i/v to
allow evaluation of the distribution and the elimination rate
constants .For the drugs that cannot be given i/v, ka cannot be
calculated by Loo-Reiegelman Method. So for those drugs, WagnerNelson method may be used that assumes ka in one-compartment
model.
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Effects of Absorption-Rate Constant
• Higher the absorption rate constant, faster the absorption of the
drug. As the peak concentration is a function of both the rate of
absorption and the rate of elimination. If the elimination rate is the
same, as the absorption rate increases, the peak concentration
increases. And the product with highest peak conc, will exhibit
highest intensity of effects. so
• If the value for ka and kel are reversed ,tmax is same but Cmax and
AUC are different.
• If kel is constant and only ka is increased, then tmax becomes shorter
and Cmax is increased and AUC remains same.
• And if ka is kept constant but ke is increased, then tmax ,Cmax and
AUC decreases.
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Significance of Absorption-Rate
Constant
• For many immediate-release dosage forms, the absorption
process is first-order due to the physical nature of drug
diffusion.
• The calculation of ka is useful in designing a multipledosage regimen.
• Knowledge of ka and k allows for the prediction of peak and
trough plasma drug concentrations following multiple
dosing.
• In bio-equivalent studies, time of peak concentrations can
be very useful in comparing respective rates of absorption
of a drug from chemically equivalent drug products.
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References
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Applied Biopharmaceutics and Pharmacokinetics by Leon Shargel.Chapter no.7,page no.161.
Pharmacology and Experimental Therapeutics Department Glossary at Boston University School of
Medicine.
Journal of Pharmacokinetics and Pharmacodynamics, Volume 8, Number 2 / April, 1980, pages 203214.
Mayersohn, M and Gibaldi, M. 1970 Mathematical Methods in Pharmacokinetics. I Use of the
Laplace Transform for Solving Differential Rate Equations, Amer. J. Pharm. Education, 34, 608-614
http://www.boomer.org/c/p3/c17/c1704.html
Mosby's Medical Dictionary, 8th edition. © 2009, Elsevier.
http://mips.stanford.edu/public/classes/pharmacokinetics/2006/Lin_comp/MDR/RepDosing2ab.ht
ml
http://books.google.com.pk/books?id=cZa3DlaSTqIC&pg=RA1-PA433&lpg=RA1PA433&dq=method+of+residuals&source=bl&ots=2GnlCK55r&sig=TN8wTyJHRlJaor6K7aPtP8k7SYY&hl=en&ei=mjyKS6yoE8qHkQWi88D_Dw&sa=X&oi=
book_result&ct=result&resnum=5&ved=0CBMQ6AEwBA#v=onepage&q=method%20of%20residual
s&f=true
http://www.boomer.org/c/p1/Ch09/Ch0903.html
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THANKS FOR YOUR ATTENTION…
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