Multiple dosing: intravenous bolus administration Dr Mohammad Issa Saleh

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

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

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

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

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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

Conc. After the first dose 8

Conc. After the second dose 9

Conc. After the third dose 10

Total Conc. 11

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

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

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

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

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

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

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

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

Conc time profile:

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

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

Predicting average Css using single dose data

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

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

Multiple IV bolus dosing compared to IV infusion

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

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?

Example 1

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)

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.

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

Example 2