METHOD OF RESIDUALS

Method of residuals is a method to determine absorption rate constant and elimination rate constant

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 D ivided the body into central and peripheral compartment . C entral 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

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

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

7. Plotting the Cr versus time should give another straight line graph with a slope equal to -ka/2.303. The value of k a 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, x 1, x 2, x 3 , …). 4. Read the concentration values at x 1 and x ′1, x 2 and x ′2, x 3 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 - k a/2.303.

8. 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.

9. 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,

10. 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.

11. 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.

12. Lag time should not be confused with onset time. The previous curve can be described by two equations: In one, the lag time t 0 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

13. 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 k a and k .

14. 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.

15. 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.

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