1. Pharmacokinetic Models
One Compartment Model
IV Bolus
Absorption

2. One Compartment Model v Simplest compartmental model
Body is assumed to behave as if it were a single, well stirred fluid. v CL
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 bolus V = 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) =
KE = (-2.303)( ) = h-1

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

7. One Compartment Model KEY 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. KE
t1/2 CL V

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

10. Calculation of AUC Trapezoidal Method, R&T, p.469 Cp
mg/L
Time [h]
AUC = = 23.3 mg•h/L

11. CL for individual pathwaysMB
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 Model Absorption 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. v CL ka
Tmax
At the peak Cp, dCp/dt = 0

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

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

32. v CL ka
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.