Case Study Vancomycin Answers Provided by Jeffrey Stark, Graduate Student
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1 Cas Stuy Vancomycin Answrs Provi by Jffry Stark, Grauat Stunt h antibiotic Vancomycin is liminat almost ntirly by glomrular filtration. For a patint with normal rnal function, th half-lif is about 6 hours. h volum of istribution is 0.9 L/kg. For systmic infctions, vancomycin is givn intravnously an shows a pronounc istribution phas (with a uration of up to on hour aftr aministration. Vancomycin is usually givn via short trm infusions (1 0 with a osing intrval of it 6 or 12 hours. Although, lik many ot antibiotics, vancomycin has a wi taputic margin, th sir stay-stat concntrations ar 20 mg/l (1 post-infusion an 5-10 mg/l at th n of th osing intrval. A 43 yar ol patint (70 kg vlops a woun infction (foun to b Staphylococcus aurus. Sinc this bactria is rsistant to pnicillins, th patint is bgun on vancomycin. Answr th following qustions concrning osag rgimns for this patint. Qustions 1 If vancomycin is givn as an i.v. bolus, which quation will bst scrib th concntration-tim profil? Do w hav sufficint information (givn abov to apply quations of this form? 2 Calculat an appropriat loaing os for this patint using both th i.v. bolus an short-trm infusion quations. Compar th rsults. Ar thy significantly iffrnt? Explain. 3 Using a osing intrval of 12 s, trmin a osing rgimn for this patint. How many o ar rquir to rach stay-stat lvls? What ar th pak (clarly inicat what "pak" rfrs to an trough valus at stay-stat? Disktt #2/Cas Stuis/Vancomycin 1
2 4 Consir th fact that this patint's cratinin claranc is only 30 ml/min an th osing rgimn is 500 mg vry 12 s. What ar th pak an trough valus at stay-stat? h limination rat constant may b calculat using th mpirically riv quation: k ( x (Cratinin Cl , which has units of If th actual pak an trough valus ar 23 mg/l an 14 mg/l (giving 500 mg vry 12 s, what ar k an V for this patint? Suggst a nw osing rgimn (os an osing intrval to provi pak an trough valus of 25 mg/l an 7 mg/l rspctivly. hs qustions ar bas on thos foun in Cas Stuis 9-12 in th whit book. Disktt #2/Cas Stuis/Vancomycin 2
3 1 Sinc vancomycin shows a pronounc istribution phas, a multicompartmnt mol is n. h gnral i.v. bolus quation for a two-compartmnt is: Cp(t a -αt + b -βt W ar not givn th hybri constants α & β; rat w ar givn a singl ovrall limination rat constant k (actually t 1/2. for, w cannot us th two compartmnt mol quation for th following calculations. W must "skip ovr" th istribution (α phas an iscu only plasma lvls on or two hours aftr aministration of th rug. 2 For a singl i.v. bolus os, th concntration is givn by Cp 0 Dos V Sinc w want to obtain stay-stat lvls with on loaing os (LD, Cp LD V which rarrangs to giv LD Cp V Hr, w can us 20 mg/l as th Cp valu, sinc w want to achiv th pak lvl (staystat with a singl os. If w ignor any short-liv paks (α-phas an consir vancomycin has a wi taputic winow, w choos th "pak" lvl for 1 post-infusion. h V (givn as a prkilogram valu can b foun using th patint's wight, 0.9L V 70kg 63L kg Disktt #2/Cas Stuis/Vancomycin 3
4 h loaing os is thn: Cp("pak" 20 mg/l Cp(0 -k t' D V k t ' In th quation abov, t' is th 1 allow for istribution. his quation must b solv for D which will b th loaing os: (20mg / L LD t' (20mg / L(63L 1414mg ( (1 For a singl short trm infusion, th pak lvl is givn by Cp( pak k Dos (1 w is th infusion tim. rcall that w shoul fin "pak" lvls as thos that occur on or two hours aftr th infusion is stopp. hus, w n to multiply th abov quation b -k t', w t' is th post-infusion tim (1. Cp(pak is 20 mg/l (th sir stay-stat lvl an V is 63L as just trmin. k may b foun from th half-lif (t 1/2 6 s; k ln s t 6s 1 / 2 Aftr th abov quation is multipli by -k t', it may b solv for os (or loaing os to giv Cp( pak k LD (1 t ' Disktt #2/Cas Stuis/Vancomycin 4
5 (20mg / L(0.1155(63L(1 ( (1 ( (1 [ mg his valu calculat with th infusion quation is somwhat largr than that calculat using th i.v. bolus quation. For a patint with normal rnal function, a significant amount may b liminat uring th infusion an also in th 1 post-infusion tim (istribution phas. In ths calculations, th infusion os in roughly 6% gratr than th i.v. bolus. 3 Sinc is givn as 12 hours, w n only to trmin th maintnanc os. his is asily on by solving th Cp (max short trm infusion quation for D, Cp ( pak D (1 (1 k t ' Again, w fin th "pak" lvl to b that at 1 hour post-infusion an hav multipli th multipl os pak quation by -k t' (w t' - 1 to account for this. Solving this quation for D givs, Cp D ( pak k (1 (20mg / L( D [1 (1 t ' ( (1 (63L(1[1 ( ( (1 ( mg 1123 mg For 1123 mg vry 12 hours, th "pak" an trough valus ar: Cp (pak 20 mg/l It is unncary to calculat this valu; this valu an th "pak" quation wr us to trmin th os. Disktt #2/Cas Stuis/Vancomycin 5
6 Sinc th osing intrval is 12 hours an 2 hours pa bfor our "pak" lvl (on hour for infusion an on hour for istribution, th trough occurs 10 s aftr th pak. Cp (trough Cp (pak -k t (t 10 s (20 mg/l -( ( mg/l Rcall that 5 half-livs ar n to rach stay-stat lvls. Sinc t 1/2 6 hours, (5 (6s 30 hours ar rquir to rach th stay-stat. With a osing intrval of 12 hours, 3 o will hav bn aministr, 4 Sinc glomrular filtration is th main limination pathway for vancomycin, rnal function is an important factor in trmining an optimal osing rgimn. Rcall that cratinin claranc rflcts GFR (normally 125 ml/min. Lowr cratinin claranc mans that GFR is lowr than normal. In this situation, th amount of os shoul b lowr sinc it is not bing liminat as rapily. o calculat xpct pak an trough lvls for th nw osing rgimn (500 mg vry 12 hours, w will n th actual k. Using th formula givn (Cas Stuy 11 k ( Cl crat ( (30 ml/min Disktt #2/Cas Stuis/Vancomycin 6
7 Disktt #2/Cas Stuis/Vancomycin 7
8 W can now apply th pak an trough xprions us in th prvious qustion. Cp ( pak (63L( D (1 (1 V k (500mg[1 ( (1[1 (1 ( t' (12 (0.0293( mg/l Cp (trough Cp (pak -k t with t 10 hours (25.6 mg/l -( ( mg/l Not how much hig th trough valu is than was calculat prviously whn w aum normal rnal function. 5 With actual ata points w can asily trmin th k (by th slop an V (by plugging th valus into th Cp (pak quation for this patint. k -m (ln 23 ln (2 2 V may b foun using th Cp (pak quation, Disktt #2/Cas Stuis/Vancomycin 8
9 Cp ( pak D (1 (1 k which may b rarrang to giv t' V D ( pak k (1 (1 Cp t ' (500mg [1 (23mg / L( L ( (1 (1 [1 ( ( (1 (12 Hr Dtrmin a nw osing rgimn to giv pak an trough valus of 25 mg/l an 7 mg/l. h first stp is to trmin th osing intrval. h xprion for u th fluctuation factor, F Cp (pak/cp (trough. 25mg / L F mg / L Now, ln F k ln Actually for a short trm infusion, w n to a in th infusion tim for trmining, ln F k 26.7 Sinc aministring mication vry 26.7 s is impractical, w roun th valu to 24 Disktt #2/Cas Stuis/Vancomycin 9
10 h nw maintnanc os can b calculat using an th Cp (pak xprion solv for D, Cp D ( pak k (1 (25mg / L( [1 (1 t ' ( (1 (45.0L(1[1 ( mg his may b roun to D 800 mg hus, th nw osing rgimn is 800 mg vry 24 s. ( (1 (24 Disktt #2/Cas Stuis/Vancomycin 10
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