Aminoglycoside Kinetics Quiz
John Rotschafer, Pharm.D.
Karla Walker, Pharm.D.
Marnie Peterson, Pharm.D.
and Jeff Johnson
This module is constructed to help establish the student's competency in working with the Sawchuk-Zaske one-compartment first order pharmacokinetic model for aminoglycosides. Many of the situations depicted in these problems deviate from contemporary practice. Presently, current practice would attempt to produce trough concentrations of essentially zero using extended dosing intervals. The use of shorter dosage intervals and higher trough concentrations in these problems is done to provide the student with different challenges in manipulating data and in the use of the pharmacokinetic equations to gain mastery of the model.
A 17 year old woman is admitted with a diagnosis of pelvic inflammatory disease(PID). Antibiotic orders are as follows:
clindamycin, 900 mg IV q8hr, and gentamicin, 120 mg IV load, then 80 mg IV q8hr (doses to be infused over 1 hour).
The first dose of gentamicin was infused from 0800 to 0900.
Wt=60 kg SCr=0.8 mg/dl BUN=12 mg/dl
|TIME ||CONCENTRATION |
|0920 ||5.5 mg/L |
|1015 ||3.6 mg/L |
|1200 ||1.6 mg/L |
For this patient, graph the data and determine the maximum serum concentration (Cpmax).
A. 10.0 mg/L
B. 6.4 mg/L
C. 4.2 mg/L
D. 3.0 mg/L
Determine the elimination rate constant for this patient.
C. 0.495 hr
D. 1.5 hr
The correct answers are:
B. Cpmax = 6.4 mg/L, and
B. Kd = 0.495/hr (t1/2 = 1.4 hr).
If you did not get the correct answer, regraph the data and try again.
The formula to determine the Kd is:
x1 - x2
In this case:
ln 4.1 - 1n 2.5 = 0.495/hr
2 - 1
Given the pharmacokinetic parameters obtained from the graphical data for this patient, calculate the distribution volume (Vd) in liters and liters/kg.
dose = 120 mg given over 1 hr (first dose)
Kd = 0.495/hr Cpmax = 6.4 mg/L
A. 23 liters; 0.38 L/kg
B. 19 liters; 0.32 L/kg
C. 17 liters; 0.28 L/kg
D. 15 liters; 0.25 L/kg
The correct answer is D, 15 liters or 0.25 L/kg. This is calculated by substituting the following values into the formula for Vd.
Ko=120 mg/hr, Kd=0.495/hr
Cpmax=6.4 mg/L, Cpmin=0 mg/L (REMEMBER: Cpmin = 0 mg/L for first dose)
Kd [Cpmax - Cpmin x e(-Kdt')]
Vd = Ko [1-e(-Kdt')]
If you did not get the correct answer, try again. From the data that you have, calculate the patient's gentamicin clearance in milliliters/minute.
C. 150 ml/min.
D. 25 ml/min.
The correct answer is B, 124ml/min.
Clearance is calculated using the following equation:
Cl = Kd x Vd
Cl = 0.495/hr x 15 L x 1000 ml/1 L x 1 hr/60 min
Cl = 124ml/min
Calculate a dosing interval (hrs) and an infusion rate (mg/hr) that would obtain desired peaks of 6.5 mg/L and desired troughs of 1.0 mg/L or less.
A. 120 mg/hour every 6 hours.
B. 180 mg/hour every 6 hours.
C. 120 mg/hour every 4 hours.
D. 80 mg/hour every 8 hours.
The correct answer is A, 120 mg every 6 hours infused over one hour. This would give the patient 8 mg/kg/day of gentamicin. The following formulas were used to calculate the dosage regimen. Values are rounded to convenient dosage intervals and easily measurable doses.
T = (-1/Kd) x ln(Cpmin/Cpmax) + t'
Ko = Kd x Vd x Cpmax x [1 - e(-KdT)] / [1 - e(-Kdt')]
Because the dose and the dosing interval were rounded, the actual Cpmax and Cpmin will be different from those used to calculate the regimen. Calculate the estimated steady-state peak and trough concentrations for this patient on the new regimen (120 mg gentamicin q6hr).
A. 6.3 and 0.5 mg/L.
B. 7.2 and 1.6 mg/L.
C. 7.4 and 0.2 mg/L.
D. 7.7 and 0.6 mg/L.
The correct answer is A, Cpmax of approximately 6.3 mg/L and Cpmin of approximately 0.5 mg/L. The following formulas were used in calculating these values:
Cpmax = [Ko x (1 - e(-Kdt')] / [Kd x Vd x (1 - e(-KdT)]
Cpmin = Cpmax x e(-Kd(T-t')
If your calculations were wrong, carefully work through the calculations again. Common errors include forgeting minus signs on the exponents and confusing T with t'.
If this patient was obese, would a dosage adjustment be necessary at this time for this patient?
The answer is B, No.
The distribution volume that we have calculated for this patient is based on individualized pharmacokinetic data, and our calculation of total distribution volume does not change based on weight. However, if we were estimating volume in an obese patient with no knowledge of individual pharmacokinetics, we would expect a lower distribution volume expressed in L/kg (actual body weight) than is usually seen with non-obese patients. Obesity and fluid status are both important clinical considerations when attempting to estimate distribution volume in a given patient.
It is important to remember that there is significant variability in distribution volumes among a patient population.
A 45 year old diabetic woman with signs and symptoms of pyelonephritis (fever, nausea, vomiting, flank pain, dysuria) is admitted to your hospital. Urinalysis was significant for 23 RBC/hpf, 35 WBC, and many bacteria. Gram stain of the urine revealed Gram negative bacilli; culture and sensitivities are pending.
The physician wants to cover Gram negative rods, including Pseudomonas sp., until culture results are available. The physician has ordered ceftazidime, 1g IV q12hr, and tobramycin, 80 mg IV q8hr.
Wt=80 kg Ht=5'7 SCr=1.2 mg/dl BUN=38 mg/dl
You receive the consult before the first dose has been given. What is this patient's estimated creatinine clearance (using the method of Cockroft and Gault)?
A. 88.0 ml/min.
B. 74.8 ml/min.
C. 57.1 ml/min.
D. 67.2 ml/min.
The correct answer is C, 57.1 ml/min. The Cockroft-Gault equation for estimated creatinine clearance in women is:
Clcr = 0.85 x (140 - age) x LBW / (Scr x 72)
Common errors include forgeting to multiply by 0.85 for women and using the wrong weight. LBWwomen = 45 kg + 2.3 x (#in. > 5'); use ABW if ABW < LBW
IBW = ideal body weight
LBW = lean body weight
ABW = actual body weight
The physician feels that the patient has a very severe infection and may be septic. It is agreed that use of an aminoglycoside would be appropriate. You set goals of attaining steady state peak levels of approximately 7.0 mg/L and trough levels of approximately 1.0 mg/L.
Using the Dettli equation, calculate an estimated half-life for aminoglycosides in this patient. What is an appropriate first dose of tobramycin; and over what period of time should you collect levels for a first dose pharmacokinetic study?
A. 140 mg; collect levels over 8 hours.
B. 140 mg; collect levels over 24 hours.
C. 80 mg; collect levels over 24 hours.
D. 80 mg; collect levels over 8 hours.
The correct answer is A, give a 140 mg loading dose and collect serum samples over 8 hrs. The Dettli equation is as follows:
Kd = 0.0024 (Clcr) + .01/hr
For this patient, estimated Kd is 0.147/hr and estimated half-life is 4.7 hours. To obtain useful data, levels should be drawn over a period of time at least 1.5 x t1/2. Obtaining levels over 8 hours is reasonable in this patient. A loading dose of 2.0 mg/kg will provide levels of 6.5 to 7.5 mg/L in patients with usual distribution volumes.
A dosing weight (DBW = LBW + 0.4 (ABW - LBW)) should be used to calculate the dose in order to correct for the decreased distribution volumes (in L/kg) seen in the obese. (ABW > 30% over LBW)
DBW=dosing body weight
LBW=lean body weight
ABW=actual body weight
On your recommendation, the patient's dosing regimen was changed to 140 mg IV q12h over one hour. The initial dose of 140 mg tobramycin was infused from 2000 to 2100. The following levels were obtained.
|TIME ||CONCENTRATION |
|2136 ||7.0 mg/L |
|0200 ||3.3 mg/L |
|0530 ||1.8 mg/L |
Graph the data and calculate Kd and Vd.
A. 4.0/hr; 16.5 L.
B. 4.0 hr; 10.1 L.
C. 0.173/hr; 16.5 L.
D. 0.173/hr; 10.1 L.
The correct answer is C, Kd = 0.173/hr and Vd = 16.5 L.
If your answer was incorrect, try again.
Calculate an appropriate dosage schedule designed to provide steady state peak concentrations of approximately 7.0 mg/L and trough concentrations of approximately 1.0 mg/L.
A. 120 mg IV q 24 hr.
B. 110 mg IV q 12 hr.
C. 110 mg IV q 8 hr.
D. 140 mg IV q 12 hr.
The best answer is B, 110 mg IV q 12 hrs. This can be calculated using formulas for T and Ko.
Based on your consult, the physician changes the tobramycin order to 110 mg IV over 1 hour q12hr.
Calculate the expected steady state Cpmax and Cpmin for this patient on the prescribed regimen (110 mg tobramycin IV over 1 hour q12hr).
A. 7.4 mg/L, 1.6 mg/L
B. 7.0 mg/L, 1.0 mg/L.
C. 6.8 mg/L, 0.6 mg/L.
D. 8.3 mg/L, 1.1 mg/L.
The correct answer is B: Cpmax = 7.0 mg/L and Cpmin = 1.0 mg/L.
Do you expect this patient's status in regard to Vd and half-life to remain stable?
This patient was likely dehydrated when admitted (BUN/Cr > 20, had been vomiting and febrile) and hydration status will likely change as her infection is treated and she is given fluids.
Renal function may improve as the pyelonephritis and dehydration resolve.
Frequent levels to confirm status are indicated.
A 38 year old woman status post cesarean section, has a diagnosis of endometritis and has been receiving cefotetan, 2g IV q12hr, and gentamicin, 100mg IV q8hr for the past 2 days. She has gotten all doses on a regular schedule
Wt=70kg SCr=1.0 mg/dl BUN=10 mg/dl
Her 7th 100mg dose of gentamicin was infused from 1600 to 1700 and peak and trough gentamicin levels have been drawn.
|TIME ||CONCENTRATION |
|1545 ||1.0mg/L |
|1715 ||5.2 mg/L |
Graph the data.
NOTE: This patient is at steady state so the pre-infusion level can be plotted on the graph as the serum concentration 6.75 hr post infusion (15 minutes before the next scheduled dose).
From the graphed data determine the patient's volume of distribution.
A. 15.6 liters (0.22 L/kg).
B. 16.8 liters (0.24 L/kg).
C. 18.4 liters (0.26 L/kg).
D. 20.2 liters (0.29 L/kg)
The correct answer is C, 18.4 liters or 0.26 L/kg. This was calculated by substituting the following values into the formula for Vd:
Ko=100 mg/hr t'=1 hr Kd=0.257/hr
Cpmax=5.5 mg/L Cpmin=0.9 mg/L.
A 35 year old diabetic woman has a documented Pseudomonas aeruginosa bacteremia. Therapy is begun with ceftazidime and tobramycin and the physician requests a pharmacokinetic consult.
Wt=54 kg SCr=1.3 mg/dl BUN=26 mg/dl
Serum samples are drawn after the first dose of tobramycin of 80 mg which was infused from 1000 to
|TIME ||CONCENTRATION |
|1200 ||4.2 mg/L |
|1400 ||3.0 mg/L |
|1900 ||1.2 mg/L |
Graph the data and determine Cpmax.
The correct Cpmax is 5.1 mg/L. What is the calculated volume of distribution for this patient?
A. 14.3 liters.
B. 16.2 liters.
C. 17.4 liters.
D. 18.5 liters.
The correct answer is A, 14.3 liters or 0.26 L/kg. Values substituted into the equation for Vd to arrive at this answer are as follows:
Ko=80 mg/hr Kd=0.182/hr
t'=1 hr Cpmax=5.1 mg/L
Cpmin=0 mg/L (because this is the first dose).
Calculate a dosing regimen that will provide therapeutic peaks of 7.0 mg/L and troughs of 1.0 mg/L. Also calculate the actual expected values for Cpmax and Cpmin.
A. 100 mg IV given over 1 hr q8hr; 7.2/1.0 mg/L.
B. 100 mg IV given over 1 hr q12hr; 6.8/0.8 mg/L.
C. 80 mg IV given over 1 hr q12hr; 6.8/0.8 mg/L.
D. 100 mg IV given over 1 hr q12hr; 7.2/1.0 mg/L.
The optimal choice is D, 100 mg every 12 hours infused over one hour. This provides a peak of 7.2 mg/L and a trough of 1.0 mg/L. Pseudomonas aeruginosa is appropriately covered by two antibiotics in this patient. Tobramycin is a good aminoglycoside to use as it tends to have lower MICs than gentamicin for Pseudomonas aeruginosa.
MIC data becomes available for the P. aeruginosa isolated from blood culture.
|DRUG ||MIC |
|Tobramycin ||2.0 mg/L |
|Amikacin ||2.0 mg/L |
The physician would like to change the tobramycin to amikacin in order to provide better Cpmax/MIC ratios. Make a recommendation for an amikacin dosage regimen that will provide peak levels of 25 - 30 mg/L.
A. 800 mg amikacin IV q12hr.
B. 400 mg amikacin IV q8hr.
C. 400 mg amikacin IV q24hr.
D. 400 mg amikacin IV q12hr.
The best answer is D, 400 mg amikacin IV q12hr.
Amikacin is eliminated by the same pathways as tobramycin and half-life should be similar for both drugs. A 12 hour dosage interval is reasonable based on our previous data for tobramycin. Distribution volume would also be similar for both drugs. Amikacin doses are higher than gentamicin doses because desired levels are higher.
70 year old male, status post CVA, is diagnosed with severe aspiration pneumonia. He is to be treated with clindamycin, 600 mg IV q8hr, and gentamicin, 60 mg IV q8hr.
Wt=60 kg SCr=1.8 mg/dl BUN=32 mg/dl
The physician requests a pharmacokinetic consult. The first dose of gentamicin has been ordered but has not been infused. What is your initial recommendation?
A. Draw peak and trough levels after the patient is at steady state on the prescribed regimen.
B. Increase the initial dose to 2.0 mg/kg, increase the interval to q24hr, and draw 3 post infusion levels over at least 12 hours.
C. Draw 3 post infusion levels after the first prescribed dose.
D. Increase the dosing interval to q12hr; draw levels when patient reaches steady state.
The most correct answer is B.
The dose should be increased because aminoglycosides penetrate lung tissue poorly and aggressive levels are warranted. The dosing interval is also of concern in this patient with decreased renal function (estimated creatinine clearance = 32.4 ml/min). Because aspiration pneumonia can be a severe infection and aggressive levels are indicated, first dose kinetics should be performed in order to tailor this patient's regimen in a timely fashion.
The physician changes the dosing interval to q24hr but not the dose. The first dose of gentamicin, 60 mg, is infused from 1615 to 1700.
|TIME ||CONCENTRATION |
|1724 ||2.9 mg/L |
|2400 ||1.7 mg/L |
|0630 ||1.0 mg/L |
Graph the data and determine Cpmax.
The Cpmax is 3.0 mg/L. Calculate this patient's distribution volume in liters and in liters per kilogram (wt=60kg).
A. 18.2 liters; 0.30 L/kg.
B. 19.4 liters; 0.32 L/kg.
C. 23.3 liters; 0.39 L/kg.
D. 25.0 liters; 0.42 L/kg
The correct answer is B; 19.4 liters. A common error is assuming that the drug was infused over one hour when calculating the Vd. Actually, this patient was infused over 45 minutes and the infusion rate (Ko) is 80 mg/hr (60mg/0.75hr), not 60 mg/hr.
Substitute the following data into the equation and recalculate the Vd if you did not get the correct answer.
t'=0.75 hr Ko=80mg/hr (60mg/0.75hr)
Cpmax= 3.0 mg/L Cpmin=0 mg/L (first dose)
Calculate a dosing regimen that will provide desired peaks of 8.0 mg/L and troughs of 1.5 mg/L.
A. 60 mg IV q12hr.
B. 140 mg IV q12hr.
C. 60 mg IV q24hr.
D. 140 mg IV q24hr.
The best answer is D, 140 mg IV given over one hour q24hr.
Calculate the expected steady state Cpmax and Cpmin for this patient on a regimen of 140 mg gentamicin IV over one hour q24hr.
A. 7.6 mg/L, 1.9 mg/L.
B. 7.0 mg/L, 1.5 mg/L.
C. 8.7 mg/L, 0.9 mg/L.
D. 8.1 mg/L, 1.3 mg/L.
The correct answer is D, Cpmax=8.1 mg/L and Cpmin=1.3 mg/L.
You have completed this aminoglycoside tutorial. You can now
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