PHA 5128
Homework 3,
Spring 2009 (10pts)
1. A 69 year old male who is being treated for a gram negative wound infection with
gentamicin. He is 5’4” tall and weighs 172 lbs. His SCr is 1.3 mg/dL (8pts).
a) Calculate his gentamicin clearance (1pt).
Weight in kilograms: 172/2.2=78 kg
Determine if the patient is obese (TBW > 120% of his IBW):
IBW= 50 + 2.3(4) = 59.2 kg
Since the patient is obese (TBW = 78 kg > 120%*IBW = 72 kg), we use the ABW for
the CL calculation:
ABW = IBW + 0.4(TBW-IBW) = 59.2 + 0.4(18.8) =66.72 kg
∴ CL = CLcr =
(140 − 69) ⋅ 66.72
= 50.61 mL / min
72 ⋅ 1.3
b) Calculate the volume of distribution (Vd) and elimination half-life (T1/2) (1pts)
Vd = 0.25 × 66.72 = 16.7 L
CL 50.61ml / min
ke =
=
= 0.18/ hr
Vd
16.7 L
T 1 / 2 = 3.8 hr
orby ( Dettli ) : ke = 0.00293 • CLcr[ml / min] + 0.014[/ hr ] = 0.16/ hr
T 1 / 2 = 4.3hr
c) Calculate the dose and dosing interval if 10 mg/L (clinical peak) and 1 mg/L
(clinical trough) of a half-hour infusion treatment are desired (2pts).
CL
Vd
*
⎛ Cmax
ln ⎜ *
⎝ Cmin
use ke =
= 0.18/ hr
τ=
⎞
⎟
⎠ + T + t * + t * = 14.3 hr ≈ 12 hr
max
min
ke
assume one − compartment :
*
• e ke•tmax = 10.9 mg / L
Cmax = Cmax
*
(1 − e − ke•τ )
(1 − e −0.18•12 )
= 10.9 • 0.18 • 16.7 • 0.5 •
D = Cmax • CL • T •
(1 − e − ke•T )
(1 − e −0.18•0.5 )
≈ 170mg
d) For Once-a-day strategy (Q24h), calculate the steady state concentration C11 (11
hour after the start of infusion) with 7 mg/kg (for dosing weight) gentamicin in a 30minute-infusion (assume one-compartment as in class) (1pt).
Dose = 7 × 66.72 = 467 mg
D
(1 − e − ke•T )
467
(1 − e −0.18•0.5 )
Cmax =
•
=
•
CL • T (1 − e − ke•τ ) CL • T (1 − e −0.18•14.3 )
= 27 mg / L
C11 = Cmax • e − ke•10.5 = 4.01 mg / L
e) Assume C11 calculated in d) is the real observation, how should we adjust dosing
interval according to ODA nomogram below (1pt).
No dosing interval adjustment is needed, i.e., Q24h.
2. Discuss why the sampling time is important to monitor aminoglycoside
administration. When and why clinical peak and trough levels should be drawn.
(2pts)
The sampling time is of importance in aminoglycoside administration since
aminoglycosides have a small but significant distribution phase. The most widely
accepted method is to sample 1 hour after the maintenance dose has been initiated
(for a 30 min infusion that would mean 30 min after the infusion is stopped).
Trough concentrations are usually obtained in the half hour before the next
maintenance dose. It is important to record the exact sampling time, so the clinical
peak and trough (sampled 30 after ending the infusion and 30 min before the next
maintenance dose) concentrations can be extrapolated to the true peak and trough
concentrations.
3. K. T., a 42-year old, 50-kg, non-obese woman with a serum creatinine of 1.5
mg/dL. What is the dosing regimen according to the nomogram below?
Following the recommended treatment, what is the expected peak vancomycin
concentration for her at steady state (assume i.v. bolus)? (2pts).
Vd = 0.17 ( 42 ) + 0.22 ( 50 ) + 15 = 33 L
(140 − 42)(50)
= 38.6ml / min = 2.3L / hr
72 ⋅ 1.5
∴ we will use 500q 24h
CL = CLcr = 0.85 ⋅
ke = CL / Vd = 2.3 / 33 = 0.07 h −1
Dose
1
(500)
1
•
=
•
= 18.6mg / L
Css max =
− k ⋅τ
Vd 1 − e
(33) 1 − e −0.07⋅24