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Pharmacokinetic Models

Pharmacokinetic Models. One Compartment Model IV Bolus Absorption. v. CL. One Compartment Model. Simplest compartmental model Body is assumed to behave as if it were a single, well stirred fluid. I.V. Bolus Dose -dX/dt = CL •C p -d(X/V)/dt = ( CL/V) •C p = -dC p /dt

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Pharmacokinetic Models

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  1. Pharmacokinetic Models One Compartment Model IV Bolus Absorption

  2. v CL One Compartment Model • Simplest compartmental model • Body is assumed to behave as if it were a single, well stirred fluid. • I.V. Bolus Dose • -dX/dt = CL•Cp • -d(X/V)/dt = (CL/V)•Cp = -dCp/dt • Cp = Cp,oe-(CL/V)t

  3. Example: Dose = 300 mg, as iv bolusV = 35 L and CL = 2 L/h Cp,o = Dose/V = 300 mg ÷ 35 L = 8.57 mg/L

  4. One Compartment Model Cp = Cp,oe-(CL/V)t log Cp = log Cp,o – (CL/V)t/2.3 Slope = -(CL/V)/2.3 -2.3Slope = CL/V = KE V = Dose ÷ Cp,o V = 300 mg ÷ 8.56 mg/L = 35 L CL = KEV

  5. One Compartment Model -2.303 x Slope = KE Slope = (y2 – y1)/(x2 – x1) = (log Cp2 – log Cp1)/ ( t2 – t1) = log (Cp2/Cp1)/(t2 – t1) = log (7.65/1.10)/(2 – 36) = -0.0248 KE = (-2.303)(-0.0248) = 0.0571 h-1

  6. One Compartment Model CL = KEV = (0.0571 h-1)(35 L) = 2 L/h • Half Life: • t1/2 = ln 2/KE = 0.693/0.0571 h-1 • = 12 h • t1/2 = 0.693 V/CL • = 0.693•35L/2L h-1 • = 12 h

  7. KE t1/2 CL CL V V One Compartment ModelKEY CONCEPT! • Half Life and KE depend on both CL and V; a change in either CL or V will cause a change in t1/2 and KE.

  8. Area Under the Curve • AUC = the area under the Cp,t profile, from time = 0 to time = , usually for a single dose. • AUCt1-t2 = the area under the curve from time = t1 to time = t2.

  9. v KE t1/2 CL CL V V CL Summary of Wednesday I.V. Bolus Dose Cp = Cp,oe-(CL/V)t - 2.3 x Slope = CL/V = KE V = Dose ÷ Cp,o CL = KEV

  10. Calculation of AUCTrapezoidal Method, R&T, p.469 2 3 2.4 1.8 Cp mg/L 1 2 4 8 Time [h] AUC = 1+2.5+5.4+8.4+6 = 23.3 mg•h/L

  11. CL for individual pathways MB Murine CL = CLH + CLR + CLP CLH CLR DB Durine CLP Expired air

  12. One Compartment Model • A two-fold change in CL:

  13. One Compartment Model • A two-fold change in V:

  14. One Compartment ModelAbsorption Input • Drug enters body by a first-order, monoexponential process. ka • dX/dt = kaXg - CL•Cp v CL

  15. Absorption The slope of the log-linear phase reflects the smaller of ka and KE.

  16. Absorption • Shape parameters • Cmax • Tmax • AUC • t1/2 Use shape parameters to deduce changes in PK parameters: ka, CL, V, F

  17. ka v CL Tmax At the peak Cp, dCp/dt = 0

  18. ka v CL Cmax

  19. AUC

  20. ka • ka  ___Cmax ___Tmax ___t1/2 ___AUC

  21. CL • CL  ___Cmax ___Tmax ___t1/2 ___AUC

  22. F•Dose • F•Dose  ___Cmax ___Tmax ___t1/2 ___AUC

  23. V • V  ___Cmax ___Tmax ___t1/2 ___AUC

  24. Shape parameters as functions of PK parameters

  25. Peak Shape Analysis

  26. Peak Shape Analysis

  27. PK Parameters from single-dose plasma concentration profile Uncertainty in ‘F’ is transmitted to CL. The ratio Dose/AUC gives the true value of CL only when F=1. If F1, then the calculation gives a CL value that is larger than the true value.

  28. PK Parameters from single-dose plasma concentration profile -2.3 x slope = KE (usually)

  29. Pharmacokinetic Models One Compartment Model Absorption Rate Bioavailability

  30. ka v CL Absorption Rate XG = Dose•e-kat How can the value of ka be determined from the Cp,t profile?

  31. ka v CL Determination of ka XGI XB XE X = amount XGI cannot be measured; ka must come from Cp,t profile

  32. ka v CL Determination of ka 1. Computer fit of equation using software such as WinNonlin. 2. Graphical analysis; aka “method of residuals”, “feathering”, “peeling”

  33. Method of Residuals When ka > 4KE, e-kat goes to 0 before e-KEt does. After e-kat goes to 0:

  34. Method of Residuals Subtract the Cp,t profile from the line:

  35. Method of Residuals What if KE > 4ka?

  36. Bioavailability - F

  37. Bioavailability - F When AUCstd is from an i.v. dose, Fstd = 1.00 and the “absolute bioavailability” of the test is determined. When AUCstd is somethingelse such as the innovator’s product or a solution, “relative bioavailability” is determined.

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