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Pharmacokinetics Homework: Calculating Drug Concentrations and Doses, Assignments of Health sciences

University of Florida (UF)Health sciences

Solutions to homework problems related to pharmacokinetics, including calculating cmax, cmin, accumulation factors, loading doses, maintenance doses, and steady state reach times.

Typology: Assignments

Pre 2010

Uploaded on 09/17/2009

koofers-user-f1x
koofers-user-f1x 🇺🇸

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Homework 5
1. Given the following equation give the portion which represents (1.5 pts)
tke
tauke e
e
Vd
Dose
C*
**
1
1
*min −
−⎟
⎠
⎞
⎜
⎝
⎛
−
=
A. The Cmax
B. The accumulation factor
C. Elimination
A=Dose/Vd
B=1/(1-e^(-ke*tau))
C=e^(-ke*t)
2. Drug X was given via IV bolus. The pharmacokinetics of Drug X can be described by
linear one-compartment model. Volume of distribution of this drug is 18 L, and its half-
life is 4 hr. If AB was administrated this drug twice a day (BID).
A. Calculate the accumulation factor at steady state (1pt).
ke= 0.693/T1/2=0.693/4= 0.173/hr
Rss=1/(1-e^(-ke*12)=1/(1-e^(-0.173*12))=1.14
B. Calculate the average concentration for a dose of 500 mg (1pt).
Cpss=D/(CL*τ)=D/(ke*Vd*τ)=500mg/(0.173hr-1*18L*12hr)=13.36mg/L
C. Calculate the maximum and minimum plasma concentrations (Cmax, Cmin) in the body
at steady state if dose of 500mg (2pts).
Cmax=D/Vd*Rss=500/18*1.14=24.37 mg/L
Cmin=Cmax*e^(-ke*τ)=24.37mg/L*exp(-0.173*12)=3.06 mg/L
3. A 60-kg patient is to be started on a continuous intravenous infusion. To achieve an
immediate effect, a loading dose is administered as an IV bolus. The continuous infusion
is started immediately after the loading dose. The desired average steady state
concentration is 15mg/L. The volume of distribution 30L and the clearance is 7 L/hr.
A. Calculate the loading dose (1pt).
Loading dose=Concentration*Vd=15mg/L*30L=450mg
pf2

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Homework 5

  1. Given the following equation give the portion which represents (1.5 pts)

ke t

ke tau

e

Vd e

Dose

C

min *

A. The Cmax B. The accumulation factor C. Elimination

A=Dose/Vd B=1/(1-e^(-ketau)) C=e^(-ket)

  1. Drug X was given via IV bolus. The pharmacokinetics of Drug X can be described by linear one-compartment model. Volume of distribution of this drug is 18 L, and its half- life is 4 hr. If AB was administrated this drug twice a day (BID).

A. Calculate the accumulation factor at steady state (1pt).

ke= 0.693/T1/2=0.693/4= 0.173/hr Rss=1/(1-e^(-ke12)=1/(1-e^(-0.17312))=1.

B. Calculate the average concentration for a dose of 500 mg (1pt).

Cpss=D/(CLτ)=D/(keVd*τ)=500mg/(0.173hr -1^ 18L12hr)=13.36mg/L

C. Calculate the maximum and minimum plasma concentrations (Cmax , C min ) in the body at steady state if dose of 500mg (2pts).

Cmax=D/VdRss=500/181.14=24.37 mg/L Cmin=Cmaxe^(-keτ)=24.37mg/Lexp(-0.17312)=3.06 mg/L

  1. A 60-kg patient is to be started on a continuous intravenous infusion. To achieve an immediate effect, a loading dose is administered as an IV bolus. The continuous infusion is started immediately after the loading dose. The desired average steady state concentration is 15mg/L. The volume of distribution 30L and the clearance is 7 L/hr.

A. Calculate the loading dose (1pt).

Loading dose=ConcentrationVd=15mg/L30L=450mg

B. Calculate the maintance dose (infusion rate) (1pt).

R0=ConcentrationCL=15mg/L7L/hr=105mg/hr

C. How long until steady state is reached? (0.5pt)

Steady state=5 half-lives=5(0.693/(Cl/Vd))=5(0.693/(7L/hr/30L))=14.85hr

D. The patient remains on the constant infusion for 5 days and it is then stopped. Predict the concentration 5 hours after the infusion is stopped (1pt).

Once the infusion has stopped, the concentration at any given time can be calculated using the iv bolus equation.

Css=R0/CL=105mg/hr/7L/hr=15mg/L C=C0e^(-ket)=15mg/Le(-7L/hr/30L5hr)=4.67mg/L

E. It is decided that the infusion should be restarted when the concentration equals 2mg/L. How long after the stop of the infusion should it be restarted (1pt)?

C=C0e^(-ket)= Ln(C/C0)=-ke*t Ln(C/C0)/-ke=t Ln(2mg/L/15mg/L)/-(7L/hr/30L)=8.63hr