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 Death: a one-compartment drug model equation From CHEST, 10/1/05 by Terry Fagan PURPOSE: To find an easier way to estimate and use serum levels of vancomycin and aminoglycosides. METHODS: The one compartment model with volume of distribution (Vd) in liters, and drug clearance (CLd) in liters/day was examined with drug clearance approximated by creatinine clearance (CCR). This model generally gives a reasonable approximation for vancomycin and the aminoglycosides. The equation for serum level half-life (T1/2) = 0.693 * VD / CLd was used, along with peak serum level (P) and trough serum level (T), to give a useful one-compartment equation called DEATH. RESULTS: Define D as mg of drug given per day. Define H as number of drug half-lives between doses of the drug. Define E as drug excretion = CCR. Define the amplitude A as P-T. Define T = 2. Manipulation gives D = E*A*T/H. Example1: CCR = 40. You desire vancomycin P = 32 and T = 8. Then E = 40, A = 24, and the number of half-lives from 32 down to 8 is 2. D = 40*24*2/2 = 960. If vancomycin Vd = 40 L, each dose would be 40*(32-8) = 960. Hence your dosing would be 960 mg QD. Example2 CCR = 20, tobramycin 200 mg QD, estimated tobramycin VD = 20 L. Then E = 20, A = 10 and D = 200. Then 200 = 20*10*2/H. Hence H = 2 half-lives. Thus the trough T must be 1/4 of the peak P, and since P-T = 10, then P = 13.3 and T = 3.3. Example3: Amikacin 500mg Q 12h gives trough = 10. Amikacin Vd = 25 L. D = 1000, A = 20. The peak = T + 20 = 30. Peak of 30 to trough 10 requires 1.5 half-lives. Using the DEATH equation: 1000 = E*20*2/1.5 gives E = CCR = 38 ml/min. CONCLUSION: The DEATH equation D = E*A*T/H can be used to estimate dose, serum levels, and CCR. CLINICAL IMPLICATIONS: The DEATH equation is useful for vancomycin and aminoglycosides. DISCLOSURE: Terry Fagan, None. Terry Fagan MD * VA Medical Center, Wilkes-Barre, PA COPYRIGHT 2005 American College of Chest Physicians COPYRIGHT 2005 Gale Group Return to Amikacin
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