Week 3D Infusion model

Question 1

Post-Infusion if Css Has Been Achieved

Answer 1

• concentration at any time after infusion is stopped (Ct) is Ct=Css x e^-kt; t is the time since the END of infusion

Question 2

A patient is started on theophylline constant rate
infusion of 35 mg/hr. The infusion is stopped after
48 hours. What is the steady state theophylline
concentration and level 12 hours after the end of
infusion? (Vd = 40L, k = 0.10 h-1)

Answer 2

first find Css
Css = ko/k x V = 35/0.1 x 40 = 8.8 mg/L

Ct= Css ⋅ e^−k⋅t = 8.8e^−(0.1•12) = 2.6mg / L

Question 3

Post-Infusion if Css Has Not Been Achieved (Short Infusion model)

Answer 3

most common method of iv drug administration

• concentration at any time after infusion is stopped (Ct) is: Ct=Ctin x e^-kt (Tin = infusion duration)

Question 4

A patient received a constant rate IV infusion of 45 mg/h theophylline until steady-state was achieved. The infusion was terminated and the plasma concentration measured 2 and 10 hours after stopping the infusion were 12.3
and 5.5 mg/L respectively. Calculate the revised k and Vd of theophylline.

Answer 4

k=(ln(C1) - ln(C2))/t2-t1 = ln (12.3) - ln(5.5)/10-2
k=0.1 h^-1
Back-extrapolate to end of infusion
(t=0) to determine Css: (in order to find it at time zero):
C2 = Css ⋅ e^−k⋅t
Css =12.3e^(0.1⋅2)
Css = 15mg / L
Calculate clearance from Css
Cl = k0/Css = 45/ 15 = 3L / h
Calculate volume of distribution
V =CL/k=3/0.1 = 30L

Question 5

• consider how to achieve steady-state sooner if a drug that requires termination of an acute symptom, but has a long half-life such as theophylline
• the average half-life of theophylline in healthy
adult nonsmokers is approx. 6-8 h

Answer 5

if a patient of this type has an acute asthma attack, we do not want to wait 4 t1/2 (28 hrs) to achieve 94% of Css

so a loading dose is given

Question 6

an IV bolus and maintenance infusion is one
way to achieve a steady-state plasma
concentration rapidly and maintain it.
• we may not be able to give an IV bolus dose rapidly, and a short infusion may be necessary.

Answer 6

can give a loading dose by short infusion and then give a constant maintenance infusion once the Ctarget is achieved

Question 7

Example: Theophylline
example of loading dose short infusion on pp slides
for theophylline, k = 0.1 h-1, V = 30L; with a desired C = 15 mg/L
• if we wish to give a loading infusion over 30 min we need to give the infusion at a rate which will produce

Answer 7

C = 15 mg/L at 0.5 hr

rearrange the Cp equation to solve for k0

Question 8

to maintain the plasma concentration at 15

mg/L, next we need a maintenance dose:

Answer 8

M.D. =Css ⋅ k ⋅V
M.D. = 15 (0.1)(30) = 45 mg/h
– a maintenance IV infusion of 45 mg/h
– a loading dose by short infusion of 459 mg administered over 30 mins

Question 9

Bolus vs. Short Infusion Model

The choice of the bolus or short infusion model
depends on infusion duration (Tin) relative to the half-life of the drug (t1/2).

Answer 9

– Tinfusion < 1/6 half-life, then drug loss during the short infusion is insignificant (< 10%) and the bolus model is sufficient
–Tinfusion ≥ 1/6 half-life, then drug loss during the short infusion is significant (≥ 10%) and the short infusion model is necessary

Question 10

Use IV infusion model to solve for the concentration after:

Answer 10

– a long infusion, which reached steady state

– a short infusion, which did not reach steady state

Question 11

• Calculate loading doses by infusion using

Answer 11

• bolus model

- short infusion model