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A SEMINAR ON
byV. Sandeep Kumar
M.Pharmacy, I Sem.
Department of PharmaceuticsUniversity College Of Pharmaceutical Sciences
Kakatiya UniversityWarangal
CONTENTS
Introduction Methods To Detect Absorption Rate Constant
Method of Residuals
Wagner-Nelson Method
Loo - Riegelman Method
Deconvolution Method
Estimation of ka from Urinary Data
• Significance of Absorption Rate Constants• Conclusion• References
INTRODUCTIONAbsorption can be defined as the process of movement ofunchanged drug from site of administration to site ofmeasurement i.e plasma.
The actual drug absorption process may be zero-order, first-order, or a combination of rate processes that is not easilyquantitated.
For a drug that follows one-compartment kinetics andadministered extra vascularlly, the time course of drugconcentration in plasma is expressed by a bi exponentialequation 1.
→Equation-1
METHOD OF RESIDUALSThe technique is also known as feathering, peeling and stripping.
Equation 1 can be written as
Cp = A.e-kel.t –A.e-ka.t →Equation- 2
where
Figure 1. Semi-logplot of Cp versusTime after OralAdministration
Cp
Time(hours)
True plasmaconcentrationvalues
During the elimination phase, when absorption is almost over,( Ka>> Kel ) and the value of second exponential approaches zero (e-kat) whereas the first exponentional (e-ket ) retains some finitevalue.
At this time, the equation 2 reduced to
Cp = A.e-kel.t →equation -3
where cp represents the back extrapolated plasma concentrationvalues.
A plot of log cp verses t gives terminal linear phase having slope =-kel /2.303.
Back extrapolation of this straight line to time zero yieldsy-intercept equals to=log A
Figure 2. Semi-log Plot of Cp versus Time after oraladministration of single dose
Cp
Time(hours)
Back extrapolation terminal portion ofcurve logCp
Intercept =
Slope =- kel /2.303
log log[( )
] / .CKaFX
Vd Ka KKt
02 303
Substracting of true plasma concentration values i.e.equation 2 from extrapolated plasma concentration values i.e.equation 3 yields a series of residual concentration values .
Cr = cp- cp
→equation 4
Plotting the Cr versus time should give another straightline graph with a slope equal to – ka/2.303 and the sameintercept as before, i.e. log A
Cr = A.e –ka t
Figure 3. Semi-log Plot of Cp versus Time
Cp
Time(hours)
Residual curve
True plasma concentration values
Back extrapolated terminal portion of curve
Slope= -kel/2.303Slope=- ka/2.303
Intercept=log log[( )
] / .CKaFX
Vd Ka KKt
02 303
From the slope, the absorption rate constant Ka can beestimated..
In this method of calculation it is important to rememberthat the following assumptions are made:
1. It is assumed that ka is at least five times larger than k el, if notneither constant can be determined accurately.
2. It is assumed that the absorption and elimination processesboth follow the first order, if not the residual line and, perhaps,the elimination line will not be straight.
LAG TIME
The time delay prior to the commencement of the first orderdrug absorption is known as Lag time( t 0 ). In some instances absorption of drug a single oral dose not
started immediately due to such physiological factors asstomach-emptying time and intestinal mobility or due toformulation itself.
where Fk aD 0/V D(k a–k) is the yvalue at the point of intersection ofthe residual lines in .
where A and B represents theintercepts after extrapolation of theresidual lines for absorption andelimination, respectively.
Plas
ma
drug
leve
l
Time(hours)Lag time t0
Back extrapolated terminal portion of curve
Residual curve
Figure 4. Determination of lag time by graphically
Flip-Flop of ka and kel
The estimation of the rate constant for absorption andelimination by method of residuals is based on the assumptionthat ka>>kel.
If kel >> ka, then the values of ka from the terminal phase andkel from the residual line are obtained .
This phenomenon is called flip-flop of the absorption andelimination rate constant.
The only way to be sure of estimates is to compare kel
calculated from oral administration with kel from intravenousdata
METHOD OF RESIDUALS FOR TWOCOMPARTMENT MODEL
There are three first order processes occurring simultaneouslyi.e. absorption, distribution and eliminationPlasma concentration of the drug depends initially on threeprocess (three exponents), then on two processes of distributionand elimination (two exponentials) and finally on eliminationprocess only ( mono exponential).
C = C0 e-kat + A e-αt + B e-βt
Time(hours)
True plasma concentration curve
Back extrapolated distribution curve
Back extrapolated elimination curve
First residual curveSecond residual curve
Log B
Log A
Log CO
Log C
Figure 5
Slope=-ka/2.303Slope=-α/2.303
Slope=-β/2.303
APPLICATIONS To calculate absorption rate constant for a drug administeredorally ,absorbed by first order kinetics and confer thecharacteristics of one and two compartment open model .
For a drug following intravenous administration and confermulty compartmental characteristics .
LIMITATIONS
When the absorption is complex rather than a simple first orderprocess .
WAGNER-NELSON METHOD
The Wagner-Nelson method of calculation does not require a modelassumption concerning the absorption process
The assumptions are(1) The body behaves as a single homogeneous compartment,
(2) Drug elimination obeys the first order kinetics.
For any e.v administration,
The amount administered = The amount absorbed (A)+ TheAmount unabsorbed (U)
The amount absorbed (A) to any time t = the amount of the drugin the body (X) + the amount of the drug eliminated from thebody to any time, t (Xe)
A = X + Xe 6
Taking the derivative with respective time
dA/dt = dX/dt + dXe/dt 7
but X = Vd. C ,hence
dX/dt = Vd. dC/dt
and dXe/dt = KX therefore,
dXe/dt = K.Vd.C
therefore,
dA/dt = Vd. dC/dt + K.Vd.C
dA = Vd.dC + K.Vd.C.dt 8
integrating equation 8 between limits of t = 0 to t = t gives,
dA Vd dC K Vd C dtttt
. . .000
A A Vd Ct C K Vd C dtt
t
0
0
0 . .
A Vd Ct KVd C dtt
t
. . .0
A0 = amount of drug absorbed at t = 0 is zero ,& C0 =0. so,
Rearranging the above equation At
VdCt K C dt
t
. .0
9
Where At/Vd is the amount of drug absorbed up to time t dividedby the volume of distribution
Ct = plasma concentration at time t
= AUC up to time t.
Integrating equation 8 between the limits of t = 0 to t = And rearranging the equation, give the following
10
dA Vd dC K Vd C dt
. . .000
A Vd C C K Vd C dt
. . . .00
At
VdCt K C dt
t
. .0
but C = 0, C 0= 0
Where, A/Vd = the total amount of drug absorbed from the dosageform up to infinity time divided by the volume of the distribution ofthe drug.
= AUC up to
The fraction of absorbed at any time is obtained when equation 9 isdivided by equation 10
11
the fraction of unabsorbed at any time t is
At A
Ct K C dt
K Cdt
t
/
.
0
0
C dt.0
12
figure 6 figure 7Pe
rcen
tof u
nabs
orbe
d
Time(hours)
Log
Perc
ento
f una
bsor
bed
Time(hours)
Slope=absorptionrate constant
Slope=-ka/2.303
Percent of unabsorbeddrug versus time plot-Zeroorder
Logarithm Percent ofunabsorbed drug versustime plot-First order
1. Plot log concentration of drug versus time.
2. Find K from the terminal part of slope when the slope is –K/2.303.
3. Find AUCt0 by plotting Cp versus time.
4. Find K.AUCtO by multiplying each AUCt
O by K.
5. Find AUC0 by adding up all the AUC pieces, from t = 0 to t= .
6. Determine the 1-(Ab/Ab) value corresponding to each timepoint using by the table.
7. Plot 1-(Ab/Ab) versus time on semi log paper, with 1-(Ab/Ab)on the logarithmic axis.
Wagner Nelson Method Procedure
For Example
k = 0.1 hr– 1
APPLICATIONS
To understand the absorption kinetics without prior assumption . Two formulations of a drug that differ substantially in terms of
how much of drug is eventually absorbed which is reflected in
Vs time plots
LIMITATIONS It applies rigorously only to the drugs with one compartmental
characteristics .
However , when conc vs time curve after oral administrationshows multi compartmental characteristics and on IVadministration shows one compartmental model, analysis bythis method gives incorrect result
At
VdCt K C dt
t
. .0
LOO-RIEGELMAN METHOD
Loo -Riegelman method is useful in determining the absorptionrate constant for a drug follows a two compartment model.
It requires the plasma concentration time data after i.v. bolusand oral administration to obtain all necessary kineticconstants.
This method can be applied to drug that can distributed by anynumber of compartments
Ab = Xc +Xt +X3 → Equation 3.1
Xc = Vc.Cp
Xt = Vt.Ct
X3 = Vc.k13 ∫ C.dt = Vc.k13 .[AUC]0t
Substituting of Xc and X3 into equation 3.1
Ab = Vc.Cp + Xt + Vc.k13 .[AUC]0t →Equation 3.2
Dividing the equation 3.2 by Vc, we getAb/ Vc= Cp + Xt/Vc + K13 [AUC]0
t →Equation 3.3
Setting the value of t = ∞, this equation becomesAb∞ /Vc = 0+ 0 + K13 [AUC]0
∞
Ab∞ /Vc = K13 [AUC]0∞ →Equation 3.4
Where, Ab∞ is the amount of the drug that will be ultimatelyabsorbed from the dosage form.
F = Ab∞ /X0 →Equation 3.5
The fraction of the dose absorbed at any time in comparison withAb∞ can be obtained by dividing the equation 3.3 by equation 3.4.
→equation3.6
Where, Xt /Vc = Ct = tissueconcentration
Slope= -Ka/2.303
Absorption rate constant byLoo- Riegelman method
figure 8
→Equation 3.7Where
Ct= Apparent tissue concentration
tn= time of sampling for sample n
tn-1 = time of sampling for the sampling point preceding sample n
(Cp) tn-1 = concentration of drug at central compartment forsample n-1
ΔCp = concentration difference at central compartment betweentwo sampling times.
= Time difference between two sampling times.t
Example To Calculate Ct values
K=0.16 hr– 1 ,k 12 = 0.29 hr– 1, k 21 = 0.31hr– 1.
APPLICATIONS Loo Riegelman method is applicable for the drugs that confers
multi compartmental characteristics .
LIMITATIONS It requires the concentration vs time data of both oral and IV
administration ofdrug to same subject.
An inherent limitation of this method is intra subject variabilitybetween oral and IV administration studies . The assumption bemade that kinetics of drug distribution and elimination remainunchanged in interval between doses.
DECONVOLUTION METHOD
It is a model independent method for determining theabsorption rate and its use has been limited.
It requires no assumptions regarding the no of compartmentsor kinetics of absorption .
Linear distribution and elimination are assumed.
It require both the data after oral and IV administration insame subject .
ESTIMATION Ka FROM URINARY DATA
Using a plot of percent of drug unabsorbed versus time.
For a one-compartment model
Ab =DB+DE 5.1
5.2
Assuming a one-compartment model,
Substituting V D C p into Equation 5.2
Rearranging Equation 5.35.4
Substituting for dC p/ dt into Equation 5.5 and kDu/ k e for D E,
5.6
Assuming first-order elimination kinetics with renal eliminationconstant k e
5.3
5.5
At t = ∞. The total amount of drug absorbed is Ab ∞and dD u/ dt = 0
D ∞u - total amount of
unchanged drug excreted in theurine.The fraction of drug absorbed atany time t
When the above expression is integrated from zero to time t,
Slope= -Ka/2.303
figure 9
LIMITATIONS
If the drug is rapidly absorbed, it may be difficult to obtainmultiple early urine samples to describe the absorption phaseaccurately.
Drugs with very slow absorption will have lowconcentrations.
The calculation of k a is useful in designing a multiple-dosageregimen. Knowledge of the k a and k allows for the predictionof peak and trough plasma drug concentrations followingmultiple dosing
The peak time (t max) in the plasma conc. versus time curveprovides a convenient measure of absorption rate.
With the increase in absorption rate constant, C max alsoincreases.
SIGNIFICANCE OF ABSORPTION RATE CONSTANT
Effect of a change in the absorption rate constant, k a, on theplasma drug concentration-versus-time curve.
To compare different formulations of same drug.
The method of residual is used for the drugs which follow oneor multi compartmental characteristics but the absorption processshould not be complex .
Wagner nelson method is used for the drug confers onecompartmental characteristics by orally.
Loo Riegelman method is applicable for the drug that confersmulti compartmental characteristics .
Deconvolution method has limited use due to its complexity.
When there is lack of sufficiently sensitive analytic techniquesto measure concentration of drugs in plasma, urinary excretiondata is used.
CONCLUSION
REFERENCES
1. Leon Shargel, Susanna, Wu Pong, Andrew B.C.Yu, Applied Biopharmaceutics andPharmacokinetics, Fifth Edition, Mc Graw Hill., pp.161-182.
2. Malcolm Rowland, Thomas N.Tozer, Clinical Pharmacokinetics,concepts andApplications, third edition,Waverly.,pp.119-130,478-484.
3. Milo Gibaldi and Donald Perrier, Pharmacokinetics; Second edition volume. 15,Marcel dekker., pp33-36,145-167,433-444.
4. V. Venkateshwarlu., Biopharmaceutics and pharmacokinetics, Pharma Booksyndicate.,pp.221-224,259-263,385-387.
5. D.M.Brahmankar, SunilB.Jaiswal, Biopharmaceutics and pharmacokinetics ,aTreatise,pp.222-224,244-268,
6. www.australianprescriber.com7. www.ncbi.nlm.nih.gov8. www.boomer.org9. www.medscape.com10. www.pharmainfo.net
