# KINETICS

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### PRESENTED BY, AMRUTHA FELIX, M. PHARM 1st YEAR, PHARMACEUTICS.:

PRESENTED BY, AMRUTHA FELIX, M. PHARM 1 st YEAR, PHARMACEUTICS . 1

### WAGNER NELSON METHOD:

Determination of absorption rate constant k a from % unabsorbed Vs time plots. Better alternative to Curve-Fitting method. Applicable for one compartment open model disposition with first order absorption. Requires collection of blood samples at regular intervals of time, till the entire amount of drug is eliminated from the body. WAGNER NELSON METHOD 2

### PowerPoint Presentation:

After oral administration of a single dose of a drug at any given time, X A – amount of drug absorbed into the systemic circulation. X – amount of drug in the body. X E – amount of drug eliminated from the body. Then, X A = X + X E 1 3

### PowerPoint Presentation:

But, X = V d C X E = K E V d [AUC] 0-t Substituting the values of X and X E in equation 1, X A = V d C + K E V d [AUC] 0-t The total amount of drug absorbed into the systemic circulation from time zero to infinity X A ∞ = V d C ∞ + K E V d [AUC] 0-∞ 4

### PowerPoint Presentation:

At t = 0, C ∞ = 0, and therefore equation 2 reduces to, X A ∞ = K E V d [AUC] 0-∞ The fraction of drug unabsorbed at any time ‘t’, X A = V d C + K E V d [AUC] 0-t X A ∞ K E V d [AUC] 0-∞ X A = C + K E [AUC] 0-t X A ∞ K E [AUC] 0-∞ 5

### PowerPoint Presentation:

Percent drug unabsorbed at any time, % ARA = [1- X A ] x 100 X A ∞ % ARA = [1 - C + K E [AUC] 0-t ] x 100 K E [AUC] 0-∞ 6

### PowerPoint Presentation:

K E – obtained from ‘log C’ Vs ‘t’ plot. [AUC] 0-t and [AUC] 0-∞ - obtained from ‘C’ Vs ‘t’ plot. A semilog plot of ‘% ARA’ Vs ‘t’ yields a straight line whose slope is -Ka 2.303 If regular plot of the same is a straight line then absorption is zero order. 7

### PowerPoint Presentation:

Slope= -Ka log %ARA 2.303 t 8

### LOO-REIGELMAN METHOD:

Determination of K a from two compartment oral absorption data by plotting ‘% ARA’ Vs ‘t’. The method does requires that the drug be given intravenously as well as orally. Examples : pentaprazole and procainamide LOO-REIGELMAN METHOD 9

### PowerPoint Presentation:

X A = X C + X T + X E 1 X A – amount of drug absorbed into the body. X C – amount of drug in central compartment. X E – amount of drug in tissue compartment. Drug absorption & elimination occur from central compartment 10 Central Compartment Tissue Compartment Ka k 12 k 21 k E

### PowerPoint Presentation:

X C = V d C X T = V d C T X E = K E V d [AUC] 0-t Substituting values of X C , X T , X E in equation 1 X A = V d C + V d C T + K E V d [AUC] 0-t 2 Dividing equation 2 by V d X A = C + X T + K E [AUC] 0-t 3 V d V d 11

### PowerPoint Presentation:

At t = ∞ , equation 3 becomes (C = 0, X T = C T = 0) V d X A ∞ = K E [AUC] 0-t 4 V d 3 ÷ 4 X A = C + (X T ) + K E [AUC] 0-t X A ∞ V d K E [AUC] 0-∞ 12

### PowerPoint Presentation:

A plot of fraction of drug unabsorbed, 1- X A X A ∞ Vs time gives –K a /2.303 as the slope. C and K E [AUC] 0-∞ are calculated from the plot C Vs t. Values for X T can be approximated as follows; V d (C t ) tn = K 12 Δ C Δ t + K 12 (C) t(n-1) (1-e -K21 Δ t )+ (C) t(n-1) e -K21 Δ t 2 K 21 13

### PowerPoint Presentation:

C t - X t V d t - time of sampling for sample n t n-1 - time of sampling for the sampling point preceding sample n (C) tn-1 - conc. of drug at central compartment for sample n-1. 14

### MEAN RESIDENCE TIME:

MRT – the average amount of time spent by the drug in the body before being eliminated. MRT = AUMC AUC AUMC – area under first moment curve AUC – area under zero moment curve AUMC = 0 ∫ ∞ Ct.dt AUC = 0 ∫ ∞ C.dt MEAN RESIDENCE TIME 15

### PowerPoint Presentation:

16 From: Rowland M, Tozer TN. Clinical Pharmacokinetics – Concepts and Applications , 3 rd edition, Williams and Wilkins, 1995, p. 487. AUC AUMC AUC = Area Under the zero-order moment Curve AUMC = Area Under the first-order Moment Curve

### One Compartment Open Model-I.V Bolus:

The dug concentration in plasma following an IV bolus dose is given by, C = X 0 e - KEt V d X = X 0 e - KEt 1 One Compartment Open Model-I.V Bolus 17

### PowerPoint Presentation:

X 0 - IV bolus dose V d - volume of distribution C - plasma drug concentration X - amount of drug in body at any time t K E - first order rate constant By differentiating equation 1, dX /dt = - K E X 0 e - KEt The rate of drug molecules exiting at any time t is given by, dX E / dt = - dX /dt = K E X 0 e - KEt 2 18

### PowerPoint Presentation:

dX E - amount of drug being eliminated Equation 2 x t, gives the residence of the drug leaving with a residence time of t, dX E t = K E X 0 e - KEt t dt 3 Equation 3 on integration between the limits t=0 to ∞ gives total residence time for all drug molecules in the body and a division by total number of molecules (X 0 ) estimates the MRT. 0 ∫ ∞ dX E t / X 0 = 0 ∫ ∞ K E X 0 e - KEt t dt / X 0 4 19

### PowerPoint Presentation:

MRT = 0 ∫ ∞ K E e -KEt t dt In terms of concentration, equation 4 becomes, 0 ∫ ∞ dX E t / X 0 = 0 ∫ ∞ K E C 0 V d e - KEt t dt / C 0 V d then, MRT = 0 ∫ ∞ K E C 0 e -KEt t dt / C 0 6 Dividing the numerator and denominator by K E , in equation 6; 20

### PowerPoint Presentation:

MRT = 0 ∫ ∞ C 0 e -KEt t dt C 0 / K E But, C 0 . e - KEt = C , and C 0 / K E = [AUC] 0-∞ = 0 ∫ ∞ C.dt Therefore, MRT = 0 ∫ ∞ Ct.dt = AUMC 0 ∫ ∞ C.dt AUC 21

### REFERENCES:

Biopharmaceutics & Pharmacokinetics . A Treatise by D.M.Bramankar ; Page : 245-255, 280-282. Biopharmaceutics & Pharmacokinetics , 2 nd edition by V. Venkateswarlu ; Page: 364-373. Applied Biopharmaceutics & Pharmacokinetics , 5 th edition by Leon Shargel; Page : 176-178. Textbook of Biopharmaceutics and Pharmacokinetics by Dr. Shobha Rani R. Hiremath . Page : 85-89 REFERENCES 22

### PowerPoint Presentation:

Textbook of Biopharmaceutics & Pharmacokinetics Concepts & Applications by CVS Subrahmanyam; Page : 425, 437, 532. www.authorstream.com 23

### PowerPoint Presentation:

THANK YOU!!! 24 