1. Dosing Regimen Design
Infusion regimen

2. Why is a dosing regimen necessary?
To replace the drug that the body eliminates.
How can drug be replaced?
Continuously or intermittently.

3. Continuous Input Learning Objectives
input rate to achieve a desired plasma concentration.
kinetics of accumulation; i.e., how long to steady state.
loading dose.
determination of CL, V, KE and t1/2.

4. Examples of continuous input
i.v. drip
i.v. infusion
transdermal patch
sustained release oral dosage forms
Ocusert
Norplant

5. Kinetics of continuous input
A = amount of drug in body
Cp = plasma concentration
Ko = input rate (amt/time)
KE = elimination rate constant, (CL/V)
dA/dt = rate in - rate out
dA/dt = Ko - KEA
A = V x Cp and KEV = CL
dA/dt = Ko - CL•Cp v CL Ko
dA/dt = 0 at a plateau Cp
Rate In = Rate Out
Ko = CL •Cp,ss
Cp,ss = Ko/CL

6. Example: Diazepam Cp,t profile in young and old: DR adjustment? Ln Cp
Time
young
old
What’s different?
Vss CL
t1/2
fup
[L/kg]
[L/h/kg]
[h]
[%]
0.88
0.0174
44.5
2.49
1.39
0.0156
71.5
2.76
Herman and Wilkinson. Br. J. Clin. Pharmacol. 42:147, #2919

7. Principles
When infused at the same rate (one compartment model assumed):
all drugs with the same half life will have the same steady-state amount of drug in the body.
all drugs with the same clearance will have the same steady-state plasma concentration.

8. Accumulation Kinetics

9. Time to steady state 3.3 t1/2 is time to 90% of Cp,ss
t = nt1/2 where n = no. of half lives that have passed

10. Example
This drug has a V = 45 L and a CL = 12 L/h. What infusion rate is needed to achieve a Cp,ss of 25 mg/L?
Ko = CL x Cp,ss = 12 L/h x 25 mg/L = 300 mg/h
How long will it take to get to 90% of steady state?
t1/2 = ln 2 V/CL = (0.693)(45)/(12) = 2.6 h
t90% = 3.3 t1/2 = (3.3)(2.6) = 8.6 h
How much drug is in the body at steady state?
Ass = Cp,ssV = 45 L x 25 mg/L = 1,125 mg

11. Summary
Cp,ss
Ass
Time to SS
 Ko  
 CL 
 V

12. Diagram VP, VE, VR RE/I, fur, fup Ass Css Ko CL t90% V
QH, fup, CLint,u
GFR, etc.

13. Review With a constant rate of input, Ko Rate Out Rate In = _______ CL
Rate In = Css x ___
Rate In = Ass x ___ KE
All drugs with same CL will have same ____
Css
All drugs with same t1/2 will have same ____
Ass

14. Post-Infusion Cp Profile

15. Post-Infusion Cp Profile

16. Changing to a new Cp,ss
CL by 25%
Ko by 25%
V by 25% Cp
Time

17. Bolus and Infusion
A “loading dose” may be used to start at steady state immediately.
Loading Dose = Ass = Ko/KE = CssV

18. Rowland and Tozer, Figure 6-5. p. 74

19. Time to Steady State 3.3 t1/2 is time to 90% of Cp,ss.
When Cp,0 is 0, this is within ±10% of Cp,ss.
When Cp,0 is  0, the time to ±10% of Cp,ss differs from the t90%.
What is the appropriate endpoint for calculation of the time to steady state?

20. Calculation of time to ±10% Cp,ss
Plasma concentration at any time after bolus + infusion:
Given Cp,0 and Css, the time to reach any Cp can be calculated from:

21. Example
Cp,0 = 500 mg/L and Css = 100 mg/L, how long does it take to reach 110 mg/L? (i.e., 110% of Css)
(1/2)n = (100 – 110)/(100 – 500) = -10/-400 =
(n)[ln (0.5)] = ln (0.025)
n = ln (0.025) / ln (0.5) = half lives
140 mg/L
What would be the Cp after 3.3 half lives?

22. Assessment of PK parameters
1. CL = Ko / Cp,ss
Time
Log (Cp,ss - Cp)
-2.3 slope = KE
2. Get KE from the slope of a semilog plot of (Cp,ss – Cp) vs. t.
3. V = CL / KE