A SEMINAR ON ONE TWO COMPARTMENT OPEN MODEL

A SEMINAR ON ONE & TWO COMPARTMENT OPEN MODEL EXTRA VASCULAR ADMINISTRATION

Pharmacokinetic models are used to simplify all the processes that occur during drug administration that include drug distribution and elimination in the body. Compartment models – Classical pharmacokinetic models That stimulate the kinetic processes of drug A, D and E Compartment models broadly categorised into two types Single compartment model One compartment model Multiple compartment model which includes Two compartment model Three compartment model 2

3

4

5

6

One Compartment Open model extra vascular administration can be shown in a diagrammatic way by the following diagram 7

Normal and semi log plots depicting one compartment open model extra vascular administration 8

9

In One Compartment open model v EXTRAVASCULAR ADMINISTRATION When drug is administered by extravascular route, absorption is prerequisite for its therapeutic activity. The rate of absorption may be described mathematically as zero-order or first-order process. After e. v. administration, the rate of change in the amount of drug in the body is given by dx = Rate of absorption – Rate of elimination dt d. X = d. Xev - dxe dt dt dt 10

• During absorption phase, the rate of absorption is greater than elimination phase. d. Xev > dxe dt dt • At peak plasma concentration, d. Xev = dxe dt dt • During post absorption phase, d. Xev < dxe dt dt 11

ZERO-ORDER ABSORPTION MODEL R 0 Drug KE Blood Excretion This model similar to that of constant rate infusion and all equation which applies to it are applicable to this model. 12

FIRST-ORDER ABSORPTION MODEL Ka KE Drug Blood Excretion first order From equ. d. X = d. Xev - dxe dt dt dt Differentiating above equ. We get, d. X = Ka Xa – KEX, Ka= absorption rate const. dt Xa= amt of drug remaining to be absorbed. Integrating above equ. , X= 13

ABSORPTION RATE CONSTANT This can be calculated by METHOD OF RESIDUALS. Method is also known as Feathering, stripping and peeling. Drug that folllows one- compartment kinetics and administered e. v. , the concentration of drug in plasma is expressed by biexponential equation: Assuming A = Log Ka F X 0 Vd (Ka – KE) C = A e-k. Et – A e-Kat 14

During the elimination phase, when absorption is most over, Ka >>KE C = A e-Ket In log form above equation is Log C = Log A - Ket 2. 303 Where, C = back extraplotted plasma conc. Values. Substracting true plasma conc. From extraploted one, log(C – C ) =Cδ = Log A - Ket 2. 303 15

16

This method works best when difference between Ka KE is large (Ka/KE >3) If KE/Ka > 3 , the terminal slope estimates Ka and not KE whereas the slope of residuals line gives Ke and not Ka. This is called as flip-flop phenomenon since the slopes of the two lines have exchanged their meanings. 17

Wagner Nelson Method for Estimation of Ka The method involves determination of ka from percent un absorbed- time plots and does not required assumption of zero or first- order absorption After oral administration of single dose of drug at any given time , the amount of drug in the body X and the amount of drug eliminated from the body XE. Thus: X=Vd. C , The total amount of drug absorbed into systemic circulation from time zero to infinite can be given as : Since at t = ∞, , the above equation reduce to : 18

The fraction of drug absorbed at any time t is given as: Percent drug unabsorbed at any time is therefore: 19

20

Two compartment open model extra vascular administration 21

22

23

24

25

References: 1. D. M. Brahmankar, compartment model in Biopharmaceutics and Pharmacokinetics, Vallabh prakashan, second editon, 2009; p: 2. Applied Biopharmaceutics and Pharmaceutics sixth edition LEON SHARGEL 26