Cas Stuy 4 PHA 527 Aminoglycosis Answrs provi by Jffry Stark Grauat Stunt Backgroun Gntamicin is us to trat a wi varity of infctions. Howvr, u to its toxicity, its us must b rstrict to th thrapy of lif-thratning infctions an thos for which a l toxic antimicrobial agnt is inffctiv. Gntamicin follows a oncompartmnt boy mol with first-orr limination. Protin bining is low for gntamicin (pning on th tst prform, bining is rport to b -3%. Th volum of istribution is in th rang of -4L an th half-lif is aroun 2 hours (although thr may b consirabl variation in this paramtr. osag is normally. mg/kg vry 8 hours for 7- ays. Th thraputic rang is -6 mg/l. Gntamicin is commonly aministr via short-trm infusions. Howvr, for this cas stuy, aum that th infusions ar sufficintly short as to allow IV bolus quations to b us for any ncary calculations. (on t worry, w ll s all of th infusion xprions soon nough. Prhaps too soon for many of you, spcially th algbraically an xponntially challng. Patint information Mr. I.P. Littl (th nams hav bn chang to protct th innocnt is a 69 yar ol black mal with a history of iabts an hyprtnsion. H is bing trat with gntamicin for an infction in his lowr lg. Th infction was th rsult of a punctur woun which progr u to poor circulation an immun rspons. Aitional patint information is givn blow. hight 5 9 wight 7 lb SCr.3 mg/ml Not: Srum cratinin may also b xpr as.3 mg/l Whil th patint is most likly on othr mications as wll, aum no rug-rug intractions whn aring th following qustions. :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc
Qustions ( Prict th cratinin claranc of this patint. Is this in th normal rang? If not, xplain an propos a plausibl rason for any viation from th normal valu. Of what importanc is Cl crat in this cas stuy? Why is th ial boy wight (IBW us in th calculation rathr than th actual wight? Calculat Cl crat for this patint. This may b on with th quation, Cl crat (4 ag IBW ( mal 72 crat Not: this is an mpirically riv quation. Ag is in yars, IBW is in kg, an crat is in mg/ml. This rsults in Cl crat in ml/min. First, w must fin IBW: IBW (mal 5 kg + 2.3 kg for ach inch ovr 5 ft. 5 kg + (2.3kg(9 Sinc patint is 5 9 7.7 kg Rturning to th Cl crat calculation. (4 69(7.7 Cl crat ( mal 53.6ml / min (72(.3 Normal GFR 25 ml/min. sinc Cl crat rflcts GFR, w know that thr is som rnal ysfunction in this patint. This GFR is wll blow half th normal valu an coul b u to som unisclos isas stat or simply th ag of th patint. Cl crat is an important consiration in this cas stuy bcaus aminoglycosis ar liminat via glomrular filtration. Any chang in GFR will affct th claranc of gntamicin. W must us IBW in th calculation of Cl crat sinc cratinin is prouc by muscl mtabolism an not fat. Spcial quations ar mploy whn th patint is obs (th ajust boy wight. (2 Prict th k an t /2 of gntamicin starting with th quation which rlats k to cratinin claranc. Thn, calculat ths paramtrs bas on th xprion Clk *V auming a V of, say,5l (which falls within th normal rang. iscu any iffrnc btwn th two valus. Th quation rlating k to Cl crat is k (.293 Cl +.4 crat :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc 2
Again, this is an mpirically riv quation. Cl crat is in ml/min an k is in hr -. For this patint, k (.293(53.6 +.4.7hr This k woul giv a gntamicin half-lif of t ln 2.693 k.7hr / 2 4.hr Of cours, w may calculat k if Cl an V ar known (sinc ths two inpnnt paramtrs ictat th limination rat; Cl k V may b rarrang to giv Cl k V Using th cratinin claranc calculat in qustion ( an auming V 5L, w fin k 53.6ml / min L 6min.24hr 5L ml hr With this k, w woul xpct th gntamicin half-lif to b t ln 2.693 k.24hr / 2 3.2hr Th valus calculat from th two mthos ar rathr clos. A half-lif of 3.7 hr is not that iffrnt from on of 3.2 hr. sinc th first mtho is a rough stimat of k an w gu at th V in th scon mtho, w rally cannot commnt as to which is closst to th actual k. W n actual ata points (gntamicin concntration at iffrnt tim points in orr to calculat th prtinnt pharmacokintic paramtrs for this patint. :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc 3
(3 Using th kintic paramtrs foun in th part of qustion (2, calculat th pak an trough lvls for gntamicin xpct from a os of 7mg vry 8 hours. o this for th first os an for th stay-stat conitions. osing rgimn: 7 mg gntamicin vry 8 hrs. In this qustion, w ar ask to calculat pak an trough lvls for gntamicin following th osing rgimn abov. Although short-trm infusions ar us, w will aum th infusions ar short nough as to allow th IV bolus quations to b substitut for th mor complx infusion quations. This may not always b poibl. Howvr sinc you must first larn to walk bfor you bgin to run, w will mak things a bit asir. Start with a simpl sktch At stay stat, thr ar no changs btwn subsqunt paks or troughs. Calculating th pak an trough lvls aftr th first os is asy. Th pak is simply th initial concntration following an IV bolus os of 7 mg: V To us this quation, w n th valu of V. Using th Cl an k valus bas on srum cratin lvls calculat in qustion (2, w fin Cl k V Solving for V to giv V Cl k 53.6ml / min 6min L.7hr hr ml 8. 8 Not: If this is corrct, w unrstimat th V us in th prvious qustion. L :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc 4
Th is thus, 7mg ( pak 3.7mg 8.8L Th trough occurs 8 hours latr (just prior to th 2 n os ( trough ( pak k τ This is th xact quation w us prviously, ( t V kt kt Sinc w want th at th n of th osing intrval, w st t 8 hours τ. So, ( trough (3.7mg (.7hr (8hr.94mg Th quations for calculating concntrations at stay-stat ar asy to intify. Thy always inclu th accumulation factor ( k τ in th nominator. Th pak at SS is ( pak ( V ( kτ kτ [ 3.7mg (.7hr (8hr ] 4.96 ~ 5.mg Just as with th trough aftr th st os, th trough aftr a os at stay-stat is foun by multiplying th pak valu by a factor to account for limination uring th osing intrval (hr w hav 8 hours for limination. ( trough ( pak k τ (5.mg (.7hr (8hr.3mg :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc 5
(4 Plasma lvls wr rawn an gntamicin lvls trmin aftr th first os (7mg vry 8 hours. Th concntrations wr 5.8 mg/l an 3.8 mg/l at an 2 hours post infusion, rspctivly. Using this ata, rcalculat th k, t /2, V, an Cl for this patint. rug monitoring allows us to customiz a osing rgimn for a givn patint. Hr w ar givn two ata points following th first os. This will allow us to calculat th pharmacokintic paramtrs for this patint an bttr prict plasma lvls for rpat osing. Th ata points ar. (mg/l t(hr 5.8 3.8 2 From th ata givn, w can asily calculat k. k (ln 5.8 ln 3.8 m.2hr 2 t ln 2.693 k.2hr / 2 3.3hr Sinc th first ata point givn is at tim hr, w can fin V with qual as. V Solving this for V givs V 7mg 2. L 5.8mg :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc 6
W may now calculat claranc: Cl k V (.2hr (2.L 2.55L / hr (5 Using th kintic paramtrs foun in qustion (4, calculat th stay-stat gntamicin concntrations (pak an trough xpct for a osing rgimn of 7mg vry 8 hours. Ar ths lvls within th sir thraputic rang? If not, what changs in th osing rgimn woul you rcommn (kp th osing intrval at 8 hours? trmining pak an trough lvls using th paramtrs just calculat for this patint. Although not rquir in this problm, pak an trough lvls ar shown blow for th st os as wll as osing at stay-stat. pak 5.8mg (on of th ata points givn ( ( trough ( pak k τ (5.8mg (.2hr (8hr.7 ~.mg At stay-stat, ( pak ( ( trough 5.8mg (.2hr [ k τ (8hr ( pak ] (7.mg 7.mg k τ (.2hr (8hr /.3mg Ths ar a littl high. Whil th trough valu is in th thraputic rang of -6 mg/l, th prict pak of 7. mg/l may la to toxic si ffcts. W might rcommn crasing th os to giv a stay-stat pak of 6. mg/l (th uppr limit of th thraputic winow. To calculat this os, w must solv th appropriat quation for. ( pak k τ V ( which rarrang to yil (6.mg (2.L [ 59.2mg ~ 6mg ( pak V ( kτ (.2hr (8hr ] L :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc 7
A osing rgimn of 6 mg vry 8 hours woul provi stay-stat lvls of ( pak / V ( ( trough (6mg /2.L (.2hr (8hr [ ] k τ ( pak k 6.mg τ (.2hr (8hr (6.mg.mg This osing rgimn shoul b accptabl. Rcall that w ar using IV bolus quations vn though th aministration of th rug is actually via short-trm infusions. Ths IV bolus quations will ovrstimat th lvls. Th gr to which ths quations ovrstimat th concntrations is pnnt on th infusion rat an th rat of limination. :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc 8