3) Use the average steady-state equation to determine the dose. Note that only 100 mg tablets of aminophylline are available here.

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Dorthy Stokes
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1 PHA 5127 Dsigning A Dosing Rgimn Answrs provi by Jry Stark Mr. JM is to b start on aminophyllin or th tratmnt o asthma. H is a non-smokr an wighs 60 kg. Dsign an oral osing rgimn or this patint such that th thophyllin plasma lvls ar within th thraputic winow. Aum vry ast absorption o th tablt. Th ollowing inormation is provi: F(bioavailability) 1 V 0.5 L/kg Cl 40 ml/hr/kg Aminophyllin is 85% thophyllin by wight 100 mg aminophyllin tablts ar availabl thraputic winow is mg/l 1) Dtrmin V an Cl or this patint bas on th normal valus givn abov. Calculat k. 2) Dtrmin th osing intrval using th rlationship btwn τ an th luctuation actor F. Th osing intrval shoul b practical (i.. som actor o a 24-hour prio). 3) Us th avrag stay-stat quation to trmin th os. Not that only 100 mg tablts o aminophyllin ar availabl hr. 4) Calculat th stay-stat pak an trough lvls bas on this osing rgimn to vriy that th thophyllin lvls ar within th thraputic rang. 5) What inormation is n to bttr sign a osing rgimn or this patint? 6) How many oss will it tak to rach stay-stat plasma lvls? I th os or th osing intrval is chang, how long will it tak to again rach th stay-stat? 7) Suggst a loaing os to cras th amount o tim rquir to rach a thraputic lvl. What woul b th pak concntration atr this loaing os? Working through this problm shoul hlp you unrstan whr many o th quations w hav sn com into play. Disktt #2/Cas Stuis/Dsigning.. 1

2 Answrs by Jry Stark 1) V, Cl, an k may b stimat or this patint using th avrag valus givn as pr kilogram. V (0.5 L/kg)(60 kg) 30 L Cl (40 ml/hr/kg)(60 kg) x (1L/1000ml) 2.4 L/hr It is now poibl to calculat k : Cl k V Which rarrangs to giv k Cl 0.080hr V 30L 2.4L / hr 1 2) Th osing intrval τ can b trmin using th quation: ln F τ, k whr F is th luctuation actor that rlats th (pak) an th (trough) F (max) (min) Sinc w want th osing rgimn to prouc plasma lvls within th thraputic winow, w can us (max) 20 mg/l An (min) 10 mg/l 20mg Thn, F 2 10mg Th osing intrval shoul b: τ ln F k ln hr hr W can roun this numbr own to 8 in orr to os thr thims pr ay τ 8 hr Disktt #2/Cas Stuis/Dsigning.. 2

3 3) Th avrag stay-stat concntration or oral osing is givn by Cl D TOT This quation may b solv or th os, D D Cl TOT k V To us this quation, w must aum som avrag concntration within th thraputic winow. A sa avrag concntration btwn 10 an 20 mg/l is 15 mg/l. Howvr, is NOT th man o (max) an (min). W ar simply stating that 15 mg/l is a goo avrag concntration to rach. Thus, lt 15mg Th os rquir to obtain this avrag stay-stat lvl is (15mg )(2.4L / hr)(8hr) D 288mg thophyllin 1 Sinc w ar aministring aminophyllin an not pur thophyllin, w n to convrt this to th amount o aminophyllin. 100mg aminoph D ( aminoph) 288mg thoph 338 mg aminoph 85mg thoph I only 100 mg tablts ar suppli, this numbr must b roun own to 300 mg, i mg tablts. Thus th osing rgimn is 300 mg vry 8 hours 4) In trmining th osing rgimn, w ma two approximations: hours an mg (For rugs with narrow thraputic winows, it is always sar to roun own th os). It is a goo ia to calculat (max) an (min) bas on this osing rgimn to s how ths valus it in th thraputic winow. Disktt #2/Cas Stuis/Dsigning.. 3

4 W ar not givn a valu or k a. Thus, w can not us th oral osing quations or (max) an (min). I absorption taks plac vry ast, w may approximat ths lvls with th i.v. bolus quations. First, w must calculat th amount o thophyllin in th 300 mg os o aminophyllin: 85 mg thoph D (mg thoph) 300 mg aminoph 255mg thoph 100 mg aminoph Th i.v. bolus quation or (max) is (max) V D (1 k (30L)[1 τ ) 255mg 1 (0.08hr )(8hr) 17.98mg Th trough lvl is thn (min) (max) -k t (17.98 mg/l) -(0.08hr-1)(8hr) 9.48 mg/l 5) I w wr givn two concntration-tim points atr a singl os, w coul calculat k an V (i th i.v. bolus quations ar suicint) or this patint. Th actual paramtrs coul b us in ths calculations rathr than th population avrags. 6) It taks roughly 5-7 hal-livs o th rug to rach stay stat. t 1/2 may b calculat rom th k oun in part (1): t ln k 0.08hr 1 / hr Th tim rquir to rach stay-stat is approximatly 5 x t 1/2 (5)(8.7 hr) 43.5 hours Thus, or τ 8 hrs, 6 oss ar rquir to rach stay-stat lvls: Dos hours Disktt #2/Cas Stuis/Dsigning.. 4

5 Not: I any chang is ma in th osing rgimn, it will tak roughly 5 hal-livs to rach stay-stat again. That is, it taks about 43.5 hours to rach th point whr thr is no signiicant chang in th pak or trough concntrations. 7) Th purpos o a loaing os is to achiv stay-stat lvls with a singl os an thrby liminat th tim actor rquir or accumulation. To trmin th loaing os, w us th singl osing quation. This quation is solv or D (which will b th loaing os). This quation inclus (max), th sir pak lvl at stay-stat (s qustion 4). LD (max) V 100mg aminoph ( 17.99mg thoph)(30l)( ) 85 mg thoph 635 mg For practical purposs, this is roun own to 600 mg. Disktt #2/Cas Stuis/Dsigning.. 5

Multiple Short Term Infusion Homework # 5 PHA 5127

Multiple Short Term Infusion Homework # 5 PHA 5127 Multipl Short rm Infusion Homwork # 5 PHA 527 A rug is aministr as a short trm infusion. h avrag pharmacokintic paramtrs for this rug ar: k 0.40 hr - V 28 L his rug follows a on-compartmnt boy mol. A 300