A SEMINAR ON ONE & TWO COMPARTMENT OPEN MODEL

EXTRA VASCULAR ADMINISTRATION

PRESENTED BY SANKAR DASARI

M PHARM ,PHCETS ,1 YR 2 SEMMALLAREDDY COLLEGE OF PHARMACY

GUIDED BY Dr. SATYA BRATA BHANJA sir

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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 modelsThat stimulate the kinetic processes of drug A,D and E

Compartment models broadly categorised into two typesSingle compartment model One compartment model Multiple compartment model which includes Two compartment model Three compartment model

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One Compartment Open model extra vascular administration can be shown

in a diagrammatic way by the following diagram

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

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In One Compartment open model EXTRAVASCULAR ADMINISTRATIONWhen 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

dX = dXev - dxe dt dt dt

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• During absorption phase, the rate of absorption is greater than elimination phase.

dXev > dxe dt dt

• At peak plasma concentration,

dXev = dxe dt dt

• During post absorption phase,

dXev < dxe dt dt

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ZERO-ORDER ABSORPTION MODEL R0 KE

Drug Blood Excretion

This model similar to that of constant rate infusion and all equation which applies to it are applicable to this model.

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FIRST-ORDER ABSORPTION MODEL Ka KE

Drug Blood Excretion first order

From equ. dX = dXev - dxe dt dt dtDifferentiating above equ. We get, dX = Ka Xa – KEX, Ka= absorption rate const. dt Xa= amt of drug remaining to be absorbed.Integrating above equ.,

X =

[ ]tKTK

Ea

oa aE eeKK

FXK −− −− )(

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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-kEt – A e-Kat

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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

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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.

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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=VdC ,

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 :

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The fraction of drug absorbed at any time t is given as:

Percent drug unabsorbed at any time is therefore:

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Two compartment open model extra vascular administration

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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