Multiple dosing: intravenous bolus administration Dr Mohammad Issa Saleh.

Multiple dosing: intravenous bolusadministration

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


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:1. The half life

hr hr K

t 93.61.0

)2ln()2ln(2/1

3


2. The concentration 2 hrs after the dose


mg/L 5.46D

)2( )2( tKeV

tC

mg/L 2.45D

)10( )10( tKeV

tC

4



mg/L 10.1D

)18( )18( tKeV

tC

5


5. 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)(1 tC

8

Conc. After the second dose)(2 tC

9

Conc. After the third dose)(3 tC

10

Total Conc.)'(3 tCn

11

)2()10()18()2'( 3213 tCtCtCtCn

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

12


5. 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?

mg/L 01.9)2'(

46.545.210.1)2'(

)2()10()18()2'(

3

3

3213

tC

tC

tCtCtCtC

n

n

n

13


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 0 0 0

1 21.0 21.0

3 19.8 19.8

2 4 16.9 0 16.9

5 14.3 21.0 35.3

7 10.1 19.8 29.9

3 8 8.50 16.9 0 25.4

9 7.15 14.3 21.0 42.5

11 5.06 10.1 19.8 35.0

4 12 4.25 8.50 16.9 0 29.7

13 3.58 7.15 14.3 21.0 46.0

15 2.53 5.06 10.1 19.8 37.5

Multiple IV bolus administration

Concentration after n doses:

where r:

n: number of doses, T: dosing interval

)(D tK

n eV

rC

KT

nKT

ee

r

11

Multiple IV bolus administration

Concentration at steady state:

where R is the accumulation ratio:

T: dosing interval

)(D tK

ss eV

RC

KTeR

1

1

Multiple IV bolus administration: useful equations

Maximum concentration after n doses:

Maximum concentration at steady state:

VRC

SS

Dmax

VrC

N

Dmax


Minimum concentration after n doses:

Minimum concentration at steady state:

KTe

VRC

SS

Dmin

KTe

VrC

N

Dmin

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)

AUC for a single dose is:

As explained in the previous slide,


Average concentration at steady state:

0

.dtC

CSS

average

SS

KVd

XC average

SS

0

0

τ

0

SS dose).dt C(single.dtC

KVd

X 0

0

dose).dt C(single

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

)1ln(44.1 5.0 fsstn

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

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

clearance

rate Dosing0 KVd

KC average

SS

clearance

rate dosing0 KVd

XC average

SS

Example 1

To a patient 250 mg penicillin with t½ of 1 h and Vd of 25 L is administered every 6 h intravenously

1. Estimate Cmax, Cmin and Cav at steady state

2. Has the objective of maintaining concentration above minimum inhibitory concentration (4 mg/L) been achieved in this therapy? Elaborate!

3. How long did it take to reach 95% of Css? 4. Is the idea of giving a bolus dose to

achieve Css in a shorter time feasible with regard to this drug?

Example 1

016.11

11

16*693.0

ee

RKT

1

0.5

hr 0.6931

0.693

t

0.693K

mg/L 10.1625

2501.016

V

DRCmax

SS

mg/L 0.16e25

2501.016e

V

DRC *60.693KTmin

SS

mg/L 2.416*25*0.693

250

KVdτ

XC 0average

SS

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)

hr 4.30.95)ln(1*1.44

fss)ln(1t1.44

*1

0.5

nτnτ

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

T

CC

tt

CCK SSSS )ln()ln()ln()ln( minmax

12

21

1hr 0.05912

ln(40)ln(81.5)K

97.11

11

112*059.0

eeR

KT

L 24.281.5

10001.97

C

DRV

V

DRC

max

max

SS

SS

Multiple dosing: intravenous bolus administration Dr Mohammad Issa Saleh.

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