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# Pk lab 5

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2 compartments model

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### Pk lab 5

1. 1. Biopharmaceutics and PK Lab 5Calculation of PK parameters usingone and two compartment model: IV bolus. Dr Sameh Rabea
2. 2. Remember For 1st order kinetic one-compartment the equation will be: Cp= (Cp) 0 e –ktWhere: 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: I.V. Central Ke injection Compartment Out. AUC= Cp0/ Ke Vdc= Dose/ Cp0. t ½= 0.693/ Ke.
3. 3.  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.
4. 4.  The PK model: I.V. in Central K12 Peripheral Compartment Compartment inj. K 21 K2Cp0= A + BK2 = Cp0 / ( A/ α + B/ β )K12= A.B (β- α) 2 / Cp0 (A β + B α)K21= A β + B α / Cp0 .
5. 5.  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.
6. 6. Problem # 1 A patient received 500 mg cefepime I.V bolus injection and numerous blood samples were drawn as the following:
7. 7. Plotting DataTime (hr) Conc.( µ/ml) 0.5 38.2 1 21.6 2 11.6 4 5.0 8 1.4 12 0.2
8. 8.  A- Test the order of this data. B- Write your model Calculate as many PK parameter as possible.
9. 9. 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:
10. 10. Plotting DataTime (hr) Conc.( µ/ml) 0.2 5.6 0.4 4.6 0.6 3.8 0.8 3.2 1 2.8 2 1.8 3 1.35 4 1.2 5 1.06 24 0.0
11. 11.  Test the order of this data. Write the model. Calculate PK parameters.
12. 12. 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:
13. 13. Plotting DataTime (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
14. 14.  A- Draw diagrammatic presentation describing PK model , and write your equation.
15. 15.  Calculate the following PK parameters: A: B: α: β (Ke): t1/2 : AUC: Vdc: Vd area: