Biopharmaceutics and PK

Lab 5Calculation of PK parameters using one and two compartment model: IV

bolus.

Dr Sameh Rabea

Remember

For 1st order kinetic one-compartment the equation will be:

Cp= (Cp) 0 e –kt Where: Cp: Y ; (Cp) 0 : intercept; t: X; k: -slope x

2.303; Slope= (logC2 – logC1)/t2-t1.

Or Ke = ln (C1/C2)/t2-t1

The PK model:

Ke

Out.

AUC= Cp0/ Ke

Vdc= Dose/ Cp0.

t ½= 0.693/ Ke.

I.V. injection

Central Compartment

For 1storder kinetic two-compartment the equation will be:

Cp= A e –αt + B e –βt

Where A: intercept of line 1 and B intercept of line 2; α: distribution rate constant and β: elimination rate constant.

The PK model:

in K12

K 21

K2

Cp0= A + B

K2 = Cp0 / ( A/ α + B/ β )

K12= A.B (β- α) 2 / Cp0 (A β + B α)

K21= A β + B α / Cp0 .

I.V. inj.

Central Compartment

Peripheral Compartment

AUC= A/α + B/β . t ½= 0.693/ β.

Vd c= Dose/Cp0= Dose/ A+B.

Vd area= Dose/AUC. β

Vd ss = Vdc + (K12/K21) Vdc

Vd tissue= Vd area – Vdc.

Therefore: Vd area> Vd ss > Vdc> Vd tissue.

But Vd ss is not affected by elimination, so its represents true volume of distribution.

CL = Vdc. Ke or CL= Vdc. Β.

Problem # 1

A patient received 500 mg cefepime I.V bolus injection and numerous blood samples were drawn as the following:

Plotting Data

Time (hr) µ/ml) Conc(.

0.5 38.2

1 21.6

2 11.6

4 5.0

8 1.4

12 0.2

A- Test the order of this data. B- Write your model Calculate as many PK parameter as

possible.

Problem # 2

A patient received 300 mg I.V. dose of a drug. Several blood samples were collected and the following plasma concentrations were obtained:

Plotting Data

µ/ml) Conc(. Time (hr)

5.6 0.2

4.6 0.4

3.8 0.6

3.2 0.8

2.8 1

1.8 2

1.35 3

1.2 4

1.06 5

0.0 24

Test the order of this data. Write the model. Calculate PK parameters.

Problem # 3

A patient received 350 mg I.V bolus dose of drug. Several blood samples were collected and the following plasma concentrations were obtained:

Plotting Data

Time (hr) Conc. (µg/ml)

0.5 20.8

1 13.8

1.5 10

2 7.9

3 5.3

6 2.9

8 2

10 1.4

A- Draw diagrammatic presentation describing PK model , and write your equation.

Calculate the following PK parameters: A: B: α: β (Ke): t1/2 : AUC: Vdc:

Vd area: