This document presents information on estimating the absorption rate constant using the method of residuals. It discusses absorption and compartment models, outlines the steps of the method of residuals for a one compartment model, and notes considerations like lag time, flip-flop phenomena, and applications and limitations of the method. The method involves plotting drug concentrations over time, obtaining slopes for the terminal and residual lines to determine the absorption and elimination rate constants. It is best suited for rapidly absorbed drugs following one-compartment kinetics.

1. PRESENTATION ON
ESTIMATION OF ABSORPTION RATE CONSTANT
METHOD OF RESIDUALS
PRESENTED BY
DIVYA PUSHP
REG. NO.-VP21PHAR0100004
M. PHARM[PHARMACEUTICS]

2. INTRODUCTION
ABSORPTION-
• Absorption can be defined as the process of movement of unchanged drug from
site of administration to site of measurement i.e. plasma.
• The actual drug absorption process may be zero order, first order, or a combination
of rate processes that is not easily quantitated.
ABSORPTION RATE CONSTANT-
It may be defined as a value describing how much drug is absorbed per unit of time.
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 multiple-dosage 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.

3. COMPARTMENT MODELS-
Compartmental modeling of pharmacokinetics describes the fate of a drug in the
body by dividing the whole body into one or more compartments. A compartment
involves several organs or tissues and is kinetically homogenous.
ONE COMPARTMENT OPEN MODEL
• Simplest form of model
• Depicts body as a single homogenous unit
TWO COMPARTMENT MODEL
• Divided the body into central and peripheral compartment.
• Central compartment (compartment 1)
- consists of the plasma and tissues
- where the distribution of the drug is practically instantaneous.
• The peripheral compartment (compartment 2)
-consists of tissues
- where the distribution of the drug is slower.

4. METHOD OF RESIDUALS
ONE COMPARTMENT MODEL
The technique is also known as feathering, peeling and stripping.
For a drug that follows one compartment kinetics and the time course of drug concentration in
plasma is expressed by a bi- exponential equation 1.
Equation 1 can be written as,
where, A is the hybrid comstant

7. During the elimination phase, when absorption is almost over,
Ka >>Ke and the value of second exponential
𝑒−𝐾𝑎𝑡approaches zero whereas the first exponential
𝑒−𝐾𝑒𝑡retains some finite value.
At this time the equation 2 reduces to
where C represents the back extrapolated plasma concentration
values.

8. Extrapolated plasma concentration- True plasma concentration i.e.,
equation 3 minus equation 2, gives residual concentration values

9. Plotting the Cr versus time should give another straight line graph with a slope equal
to -ka/2.303.
The value of ka is obtained by the following procedure:
1. Plot the drug concentration versus time on semi log paper with the concentration
values on the logarithmic axis.
2. Obtain the slope of the terminal phase (line BC,) by extrapolation.
3. Take any points on the upper part of line BC (eg, x′1, x′2, x′3, …) and drop vertically
to obtain corresponding points on the curve (eg, x1, x2,x3, …).
4. Read the concentration values at x1 and x′1, x2 and x′2, x3 and x′3, and so on. Plot
the values of the differences at the corresponding time points Δ1, Δ2, Δ3, … . A straight
line will be obtained with a slope of -ka/2.303.

10. Figure 4 Plasma level–time curve for a drug demonstrating first-order
absorption and elimination kinetics. The equation of the curve is
obtained by the method of residuals.

11. • When using the method of residuals, a minimum of three points
should be used to define the straight line.
• If drug absorption begins immediately after oral administration,

12. • In this method of calculation it is important to remember
that the following assumptions are made
It is assumed that ka is at least five times larger than kel, if
not neither constant can be determined accurately.
It is assumed that the absorption and elimination processes
both follow the first order, if not the residual line and,
perhaps, the elimination line will not be straight.

13. LAG TIME
In some individuals, absorption of drug after a single oral dose does not start immediately, due
to such physiologic factors as stomach-emptying time and intestinal motility.The time delay prior
to the commencement of the first order drug absorption is known as Lag time.
Figure 5 The lag time can be determined graphically if the two residual lines obtained
by feathering the plasma level–time curve intersect at a point where t > 0.

14. • Lag time should not be confused with onset time.
• The previous curve can be described by two equations:
In one, the lag time t0 is subtracted from each time point
This equation omits the lag time, as follows:
where A and B represent the intercepts on the y axis after extrapolation of the residual
lines for absorption and elimination, respectively.
The lag time, represents the beginning of drug absorption and should not be confused
with the pharmacologic term onset time, which represents latency, that is, the time
required for the drug to reach minimum effective concentration

15. FLIP FLOP OF ka AND kel
• The estimation of the rate constant for absorption and elimination by method of
residuals is based on the assumption that ka>>kel.
• If kel >>>> ka, then the values of k, from the terminal phase kel from the residual
line are obtained.
• This phenomenon is called flip-flop of the absorption and elimination rate constant.
• The only way to be sure of estimates is to compare Kel calculated from oral
administration with ka from intravenous data.
Figure 6 Flip-flop of ka and k.

16. • This technique works best when the difference between Ka and Kel is
large [Ka/Ke ≥ 3].
• In some instances, the Kel obtained after i.v. bolus of the same drug is
very large, much larger thean the Ka obtained by the method of
residuals [eg. Isoprenaline] and if Kel/Ka≥3 , then the terminal slope
estimates Ka and not Ke whereas the slope of the residual line gives
Ke and not Ka.
• This is called the flip-flop phenomenon since the slope of the two
lines have exchanged their meanings.

17. APPLICATIONS
• To calculate absorption rate constant for a drug administered orally ,absorbed by first
order kinetics and confer the characteristics of one and two compartment open model .
• This method is suited for drugs which are rapidly absorbed which are rapidly and
completely absorbed and follow one-compartment kinetics even when given i.v.
• This method enables resolution of the biexponential plasma level-time curve into its
two exponential components.
LIMITATIONS
• When the absorption is complex rather than a simple first order process.
• If the absorption of drug is affected in some way such as GI motility or enzymatic
degradation and if the drug shows multicompartment characteristics then the value of
ka that is obtained will be incorrect. Even if the drug is truly absorbed by first-order
kinetics.

18. THANK YOU