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AminoglycosidePharmacokineticsFirst Dose Kinetics!A 38 year old male with burns over 85% of total body surface area is admitted to the hospital. He weighs 75 kg and is 5’11’’ tall. He is empirically started on cefotaxime 1gm IV q8h and gentamicin 100 mg IV q8h. Tmax=101.1ºF, Scr=0.9, WBC=10,000. The following PK study is performed after the first gentamicin dose:PK study0.4 mg/L04301.2 mg/L02244.5 mg/L2230100 mg gentamicin infused2100-2200What is the trough?!As this is a first dose--the trough is zero!Important point to remember in understanding and calculating Vd!An estimation of Vd is dose/✁concentration"DO NOT apply this on the test: the equation for Vd with aminoglycosides is more complex to account for drug elimination during administration"When calculating the Vd after an initial dose, where no AG has previously been given, you are actually subtracting zero from the Cmax"When calculating the Vd for aminoglycosides after a first dose, don’t put anything in the denominator that would indicate there is drug on board when the first dose was given.At 2 hours post dose, concentration appears to be 2.5 mg/LAt time 5 hours post dose, concentration appears to be0.8 mg/LChange in y over change in x is (ln 2.5 - ln 0.8)/(5-2),which is 0.3798What is the Half-life!Change in y over change in x reveals an elimination rate constant of 0.3798 hr-1(half life = 1.83 hours)"Remember to use natural logs when calculating change in y--semi log paper only shows the relationship (and gives you the Cmax) but does not actually transform the data!By regression, elimination rate constant is 0.3953 hr-1What is the extrapolated peak!By reading graph, appears to be about 6!Can pick a point on the best fit line & extrapolate to peak"We’ll pick 2.5 mg/L at 2 hours post dose again"Use the equation C2=C1e-ktto move forward or back on the line#e-ktmoves forward in time#ektmoves back in time"2.5 e(0.3798*2)= 5.34 mg/L!By regression, is 5.8 mg/LC2 = C1e(-k✁✁✁✁t)What is the volume of distribution![100 (1-e-0.3798*1)]/[0.3798 (5.34 -0)] = 15.6 LWhat dose and interval will provide peak serum concentrations of 8 mg/L and troughs of 1 mg/L!Interval"[(-1/0.3798)*(ln1/8)] +1 = 6.5#Round to 8 hours!Infusion rate"[0.3798*15.6*8*(1-e-0.3798*8)]/[(1-e-0.3798*1)] = 142.8 mg/hr#Round to 140 mgWhat will the Cpmaxand Cpminbe on the regimen you have determined!Cmax"[140 (1-e(-0.3798*1))]/[0.3798*15.6*(1-e(-0.3798*8))] = 7.84 mg/L!Cmin"7.84e(-0.3798*7)= 0.55 mg/LSteady State Pharmacokinetics!MH is a 20 year old woman with an intra-abdominal infection who has been receiving ampicillin/sulbactam (Unasyn) 3 g IV q6h"Scr= 1.0 mg/dL"WBC = 13,000"Temp = 100oF"Wt = 52 kg"Ht = 5’3’’Pharmacokinetic study--around 0900 Dose, 3rdDay of therapy9.23 mg/L1015gentamicin 120 mg infused0900-10001.6 mg/L08451.69.239.231.6At steady state, Cpmaxand Cpmin remain the same, and given a time post dose, the concentration at that time remains the same. Here, the concentration is 1.6 mg/L at 0845 (0.25 hrs pre dose or 5.75 hours post previous dose). So, the concentration will be 1.6 mg/L at 1445 (0.25 hrs pre next dose or 5.75 hours post dose)1.69.231.6To arrive at the elimination rate constant, calculate ✁✁✁✁y over ✁✁✁✁x, or (ln9.23 - ln 1.6)/(5.75-1.25), or 0.3894 hr-1. This is the same as pluggingthe values into the formula C2=C1e-ktwhere C1is 9.23 mg/L, C2 is 1.6 mg/L and t is the difference in time between the 2 points, or 4.5 hours.1.69.231.6Here, there are only two data points. As two points define a straight line, there is no reason to pick any other points on the line you draw. That would only introduce error. Here, there is no real point ingraphing the data as long as you understand what is going on.9.231.61.6Remember, you can always calculate an elimination rate constant, given only two post-infusion data points. If you have three points, you should graph or use regression. In clinical practice, you will likely only very rarely have three data points.9.231.61.6A vertical line has been drawn in to represent the end of the infusion, and thus the intersection between the line describing the elimination and this vertical line is the Cmax. The Cmax appears to be slightlyabove 10 mg/L.Pre steady state kinetics$ In some of the problems, you are given two post infusion levels, and one pre-infusion level, and the patient is not yet at steady state. $ Here, calculate the elimination rate constant from the two post infusion levels and use that to get the trough by extrapolating forward from the pre-infusion level. $ Again, when calculating Vd, be sure to plug in the correct values for Cmax and Cmin (must be those immediately before and after the infusion that produced your two post-infusion levels)What is the half-life!Half life = ln (2)/elimination rate constant"Ln (2)/0.3894hr-1= 1.78 hoursWhat is the extrapolated peak concentration?!Recall from the graph, the peak appeared to be about 10 mg/L!Can calculate a more exact peak"Concentration 15 minutes post infusion end was 9.23 mg/L"Elimination rate constant is 0.3894 hr-1"Cmax = 9.23 e(0.3894*0.25)= 10.2 mg/LDetermine the extrapolated trough!Again, move down the “line” to get the trough"Can apply 10.2 mg/L (time to trough would be 5 hours), 9.23 mg/L (time to trough would be 4.75 hours) or 1.6 mg/L (time to trough of 0.25 hours)"1.6 e(-0.3894*0.25)= 1.45 mg/LDetermine the volume of distribution![120*(1-e(-0.3894*1))]/[0.3894 (10.2-(1.45e(-0.3894*1)))]= 10.8 LRecommend an appropriate gentamicin dose and interval that would result in peaks of 6-7 and trough<1.!Interval"[(-1/0.3894)*ln (1/7)] + 1 = 6 hours!Dose"[0.3894*10.8*7*(1-e(-0.3894*6))]/[(1-e(-0.3894*1)]= 82 mg, round to 80Calculate the peak and trough you expect on the new regimen!Cpmax"[80*(1-e(-0.3894*1))]/[0.3894*10.8*(1-e(-0.3894*6))]= 6.8!Cpmin"6.8e(-0.3894*5)= 0.97 mg/LInitial Dose!A 45 year old diabetic woman with signs and symptoms ofpyelonephritis (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, andtobramycin, 80 mg IV q8hr.!Wt=80 kg Ht=5'7 SCr=1.2 mg/dl BUN=38 mg/dlYou receive the consult before the first dose has been given.


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U of M PHAR 6124 - Aminoglycoside Pharmacokinetics

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