1. Multiple dosing: intravenous bolus administration
Dr Mohammad Issa Saleh

2. Multiple dosing calculations using Superposition
Let:
Dose 1  Conc. 1
and:
Dose 2  Conc. 2
then the response system behaves according to the superposition principle if:
Dose 1 +Dose 2  Conc. 1 + Conc. 2
and in that case the response system is a linear response system 2

3. Multiple dosing calculations using Superposition
A patient is to be given 100 mg of a drug intravenously. Assuming that K = 0.10 hr-1 and a V = 15 L, estimate the following:
The half life 3

4. Multiple dosing calculations using Superposition
The concentration 2 hrs after the dose
The concentration 10 hrs after the dose 4

5. Multiple dosing calculations using Superposition
The concentration 18 hrs after the dose 5

6. 6

7. Multiple dosing calculations using Superposition
Assuming that 100 mg of the drug is administered every 8 hrs, estimate the concentration 2 hrs after the third dose using the values calculated in parts 2-4. What property of the linear systems did you use to answer this question? 7

8. Conc. After the first dose8

9. Conc. After the second dose9

10. Conc. After the third dose10

11. Total Conc. 11

12. t = 2 hrs after third dose = 10 hrs after second dose
= 18 hrs after first dose 12

13. Multiple dosing calculations using Superposition
Assuming that 100 mg of the drug is administered every 8 hrs, estimate the concentration 2 hrs after the third dose using the values calculated in parts 2-4. What property of the linear systems did you use to answer this question? 13

14. Multiple dosing calculations using Superposition
The principle of superposition assumes that early doses of drug do not affect the pharmacokinetics of subsequent doses.
Therefore, the blood levels after the second, third, or nth dose will overlay or superimpose the blood level attained after the (n – 1)th dose

15. Multiple administration every 4 hrs
Dose Number
Time
(hr)
Dose 1
Dose 2
Dose 3
Dose 4
Total 1
21.0 3
19.8 2 4
16.9 5
14.3
35.3 7
10.1
29.9 8
8.50
25.4 9
7.15
42.5 11
5.06
35.0 12
4.25
29.7 13
3.58
46.0 15
2.53
37.5

16. Multiple IV bolus administration
Concentration after n doses:
where r:
n: number of doses, T: dosing interval

17. Multiple IV bolus administration
Concentration at steady state:
where R is the accumulation ratio:
T: dosing interval

18. Multiple IV bolus administration: useful equations
Maximum concentration after n doses:
Maximum concentration at steady state:

19. Multiple IV bolus administration: useful equations
Minimum concentration after n doses:
Minimum concentration at steady state:

20. Conc time profile:

21. The AUC during a dosing interval at steady state is equal to the total AUC following a single dose (For linear PK)

22. Multiple IV bolus administration: useful equations
Average concentration at steady state:
As explained in the previous slide,
AUC for a single dose is:

23. Predicting average Css using single dose data

24. Time to reach steady state conc.
The time required to reach to a certain fraction of the steady-state level is given by:
Time required to achieve steady-state depends on the half-life and is independent of the rate of dosing and the clearance
To get to 95% of the steady-state: 5 half-lives are needed
To get to 99% of the steady-state: 7 half-lives are needed

25. Different doses regimen have the same average steady state conc: The same dosing rate (Dose/ T)

26. Multiple IV bolus dosing compared to IV infusion

27. Multiple IV bolus dosing compared to IV infusion
For IV infusion:
For multiple IV bolus (dosing rate = dose/ dosing interval):
The steady-concentration depends on the rate of dosing and the clearance

28. Example 1
To a patient 250 mg penicillin with t½ of 1 h and Vd of 25 L is administered every 6 h intravenously
Estimate Cmax, Cmin and Cav at steady state
Has the objective of maintaining concentration above minimum inhibitory concentration (4 mg/L) been achieved in this therapy? Elaborate!
How long did it take to reach 95% of Css?
Is the idea of giving a bolus dose to achieve Css in a shorter time feasible with regard to this drug?

29. Example 1

30. Example 1
Drug concentration cannot be maintained above the MIC if it is being administered every 6 h (6 x t½). Because almost 98% of the dose is out of the body at the time of the next administration. However, conventionally penicillins are given q.i.d. and it is known that they are effective. Therefore, there is no need for keeping the concentration above MIC during the entire therapy.
 4.3 hrs are needed to get to 95% of Css (i.e. Css was obtained as a result of the first dose)

31. Example 1
The steady-state is achieved very rapidly (after the first dose). Since there is no need for accumulation, there is little justification for giving a loading dose.

32. Example 2
A patient is receiving 1000 mg of sulfamethoxazole iv every 12 hours for the treatment of severe gram-negative infection. At steady state the maximum and minimum serum sulfamethoxazole concentrations were 81.5 mg/L and 40 mg/L, respectively. Estimate the values of K and VD

33. Example 2