Answr omwork 5 PA527 Fall 999 Jff Stark A patint is bing tratd with Drug X in a clinical stting. Upon admiion, an IV bolus dos of 000mg was givn which yildd an initial concntration of 5.56 µg/ml. A fw days latr, th patint was startd on a rgimn of short trm insions of 000mg vry 8 hours. Insion tim was 30 minuts. h normal claranc (total of Drug X is 36L/hr; 50% is mtabolizd in th livr and th rmaindr is xcrtd (rnal unchangd. Normal plasma protin binding is 85%. Answr th following qustions showing all calculations. Givn information: Aftr IV bolus dos of 000mg, 0 5.56 µg/ml For short trm insion rgimn, D 000 mg, 0.5 hr, τ 8 hrs O 36 L/hr (50% hpatic, 50% rnal fb 0.85; thus, 0.5 Sinc no othr information or data is availabl, w aum this drug follows a oncompartmntal modl with first ordr limination. Is Drug X a high or low xtraction (hpatic drug? In ordr to dtrmin th valu of th xtraction ratio E, w must calculat th hpatic claranc, p. If 50% of th total claranc is du to mtabolism, p O 0.5 (36L/hr(0.5 8 L/hr Rcall th rlationship btwn claranc, xtraction ratio, and livr blood flow, p E Q Solving this xprion for E givs p E Q 8L 0.2 90L Sinc E 0.3, w conclud that Drug X is a low xtraction drug. 2 What rnal procs ar likly occurring in th xcrtion of th unchangd drug? D:\pha527_Dos_Opt_I\omworks\omwork5\Fall-99\ans-typ-hw5-99.doc
In ordr to dtrmin which rnal procs ar occurring, considr what th rnal claranc would b if only glomrular filtration taks plac: n GFR R 60min L (25ml / min(0.5 hr 000ml.25 L/hr his is much smallr than th Rn calculatd from th giv information, n O 0.5 8L R W must conclud that in addition to glomrular filtration, this drug is liminatd by activ tubular scrtion in th kidny. 3 Prdict th pak and trough concntrations aftr th first dos for th short trm insion rgimn. Aftr a singl ( st dos short trm insion, th pak plasma concntration is (max D ( k, whr tim of insion. In ordr to us this quation, w must calculat k. his may b don using O (givn and V d (from th IV bolus data. Aftr an IV bolus dos, 0 D V d D:\pha527_Dos_Opt_I\omworks\omwork5\Fall-99\ans-typ-hw5-99.doc 2
Solving this for V d givs D V d 0 000mg 000µ g L 5.56µ g / ml mg 000ml 80L From th gnral quation k V d w can find k : k Vd 36L 0.2hr 80L Rturning to th (max quation 000mg (max (36L (0.5hr 5.3 mg/l 5.3 µg/ml (0.5hr h trough plasma concntration (i.. th concntration just bfor th start of th 2 nd dos is asily found: (min (max k ( τ (max k t' whr t' is th post-insion tim. For this dosing rgimn th dosing intrval τ is 8 hours. At th bginning of ach dosing intrval thr is an insion lasting 30 minuts (0.5 hr. hus, thr is a tim span of (τ- 7.5 hr btwn th pak and trough lvls. (min (5.3µ g / ml (7.5hr.2 µg/ml D:\pha527_Dos_Opt_I\omworks\omwork5\Fall-99\ans-typ-hw5-99.doc 3
4 ow many doss ar rquird to rach stady-stat conditions? h tim rquird to rach stady-stat lvls in a multipl dosing rgimn is dpndnt solly on th t /2 of th drug: normally 3-5 half-lifs. (W will us 5 t /2 hr. h t /2 is calculatd dirctly from k, t / 2 ln 2 k 0.693 3.5hr 0.2hr hus, stady-stats ar rachd 5 x 3.5 hr 8 hr aftr th dosing rgimn is bgun. (If any changs ar mad in th rgimn, anothr 8 hours ar rquird to rach th nw stady-stat lvls. If dosing vry 8 hours, 0 8 6 24 st 2nd 3rd 4th stady-stat is rachd aftr th 3 rd dos 5 Prdict th pak and trough concntrations at stady-stat. At stady-stat, th pak plasma lvls ar obtaind using th xprion, D (max τ Putting in th givn and/or prviously calculatd paramtrs givs: 000mg (max (36L (0.5hr 6.6mg / L 6.6µ g / ml (0.5hr (8hr D:\pha527_Dos_Opt_I\omworks\omwork5\Fall-99\ans-typ-hw5-99.doc 4
h trough concntration at stady-stat is thn (min (max ( τ (6.6µ g / ml (8hr 0.5hr.5µg/ml 6 Dsign a short trm insion dosing rgimn which will maintain stady-stat concntrations within th thraputic window of 20-40ug/ml (total drug concntration rang for normal patints. Aum an insion tim of 30 minuts. o dsign a dosing rgimn which will maintain plasma lvls btwn 20-40 µg/ml, start by dtrmining an appropriat dosing intrval τ. For short trm insions, τ is calculatd as follows: τ ln (max k (min + whr (max and (min ar th dsird pak and trough valus, rspctivly, at stady-stat. τ ln(40 / 20 + 0.5hr 0.2hr 4 hr h appropriat dos may b found by solving th (max xprion for D and stting th valu of (max to th dsird pak lvl at stady-stat. (his quation is providd on your quation sht undr th hading "calculatd rcommndd dos". (max D Solving for dos (D givs D (max τ τ (4hr ( ( ( 000ml mg 40µ g / ml 36L 0.5hr (0.5hr L 000µ g D:\pha527_Dos_Opt_I\omworks\omwork5\Fall-99\ans-typ-hw5-99.doc 5
466 mg Not: If this wr an oral dosing rgimn, it would b ncary to round th dosag to on asily providd by availabl tablts. r, 466 mg 4000 mg. h dosing rgimn would b, for xampl, 4-000mg tablts vry 4 hours. For th short trm insions, it may or may not b ncary to round th dosag to a mor standardizd amount. Sinc this drug appars to hav a narrow thraputic rang, it may b safr to round down to a mor convnint dos. h dosing rgimn is thn 4000 mg insd ovr 30 minuts vry 4 hours. 7 Prdict th fr lvls (pak and trough at stady-stat for th dosing rgimn dtrmind in Qustion 6 auming normal plasma protin binding. For th dosing rgimn of 4000 mg vry 4 hours, th pak and trough valus at stadystat ar prdictd to b: D (max τ 4000mg (36L (0.5hr 38.4 µg/ml (0.5hr (4hr (min (max ( τ (4hr 0.5hr (38.4µ g / ml 9.µ g / ml (If dos wr lft at 466 mg, pak and trough lvls would hav bn 40 µg/ml and 9.9 µg/ml, rspctivly. Fr lvls ar found by multiplying total concntrations (calculatd abov by th fraction unbound. (max, fr (max (38.4 µg/ml(0.5 5.8 µg/ml (min, fr (min D:\pha527_Dos_Opt_I\omworks\omwork5\Fall-99\ans-typ-hw5-99.doc 6
(9. µg/ml(0.5 2.9 µg/ml 8 In Qustion 6, th thraputic window is statd in trms of total drug concntrations undr normal conditions. What ar th accptabl fr concntrations auming normal protin binding? Do th fr lvls prdictd in Qustion 7 fall in this rang? h thraputic rang may b xprd in trms of fr lvls by multiplying th xtrms of th thraputic window (hr, 40 µg/ml and 20 µg/ml by : (40 µg/ml(0.5 6 µg/ml (20 µg/ml(0.5 3 µg/ml for all practical purposs, th prdictd pak and trough lvls fall in th thraputic window. Not: his patint was found to hav lowr albumin lvls and th protin binding of Drug X was only 50%, lowr than normal. Us this nw information whn answring th following qustions. Nw information: protin binding for this patint is 50%, not 85% (th population avrag. D:\pha527_Dos_Opt_I\omworks\omwork5\Fall-99\ans-typ-hw5-99.doc 7
9 Prdict th half-lif of Drug X in this patint. Aum (i that th drug is lipophilic and distributs wll into all tius, (ii that tiu binding is th sam as that found in normal patints, and (iii that filtration is th only rnal proc affctd by a chang in protin binding. In ordr to prdict th half-lif, both O and V d must b r-addrd. aranc (hpatic: For a low xtraction drug, Q Q + int int int o stimat th hpatic claranc for this patint, w must dtrmin int for normal patints (i.. patints with normal protin binding and aum that int is rlativly constant from patint to patint. 8L 0.5 int 20L h hpatic claranc for this patint is thn: int (20L/hr(0.5 60 L/hr aranc (rnal: h rnal claranc calculatd in qustion 2 is th sum of that du to filtration and that du to othr rnal procs (mainly activ tubular scrtion for this drug. Rn (filtration + (othr procs h claranc du to scrtion is thn scrtion Rn - filtration 8 l/hr.25 L/hr 6.875 L/hr W will aum that scrtion is not affctd by a lowr protin binding. W now nd to calculat th claranc du to filtration and add it to 6.875 L/hr in ordr to find th ovrall rnal claranc. D:\pha527_Dos_Opt_I\omworks\omwork5\Fall-99\ans-typ-hw5-99.doc 8
filtration GFR 60 min L ( 25ml / min(0.5 hr 000ml 3.75 L/hr h ovrall rnal claranc for this patint is thn: Rn 6.875 L/hr + 3.75 L/hr 20.625 L/hr 20.6 L/hr otal claranc is thn, O p + Rn 60 L/hr + 20.6 L/hr 80.6 L/hr Volum of distribution (S Not blow: Sinc th drug is givn to b lipophilic and distributs wll into all tius, w will aum that V 38 L and that V p 3 L. h only paramtr that w nd to find to us th xprion. V d V p + V D:\pha527_Dos_Opt_I\omworks\omwork5\Fall-99\ans-typ-hw5-99.doc 9
W can solv for using th population avrag V d and normal : V d V p + V ( V d V V p V V ( Vd p (38L(0.5 (80L 3L 0.032 h V d for this patint ( 0.5 is thn V d V p + V 3L + 38L 0.5 0.032 596.75 L 597 L It is now poibl to calculat k and t /2 for this patint. k V d Solving for k givs k V d 80.6L 0.35hr 597L D:\pha527_Dos_Opt_I\omworks\omwork5\Fall-99\ans-typ-hw5-99.doc 0
h half-lif is thn t / 2 ln 2 k 0.693 5.3hr 0.35hr his t /2 is almost 50% gratr (actually, 47% than th population avrag half-li of 3.5 hr calculatd in Qustion 4. **Not** Du to th wording in th givn information, it may not b ncary to prdict a nw V d whn is not at a normal lvl. h actual V d for this patint can b calculatd from th dos and initial concntration providd. A V d calculatd from actual data would ncarily includ automatically. h dos and initial concntration should hav bn statd for a normal patint. hn, a normal V d could hav bn calculatd and from this, a nw V d may b prdictd basd on th abnormal protin binding for this patint. Eithr intrprtation will b accptd for grading purposs. If th V d (calculatd in Qustion 3 is aumd constant for this patint, th nw t /2 is dpndnt only on th chang in total claranc: k V d 80.6L 0.448hr 80L t / 2 ln 2 k 0.693.55hr 0.448hr D:\pha527_Dos_Opt_I\omworks\omwork5\Fall-99\ans-typ-hw5-99.doc
0 Rcalculat th fr lvls (pak and trough at stady-stat for th dosing rgimn dtrmind in Qustion 6. Is this dosing rgimn adquat or must it b adjustd (considr th accptabl fr concntration rang calculatd in Qustion 8? h valus of O, k, and from Qustion 9 ar usd to prdict th pak and trough lvls at stady-stat. If th dosing rgimn is 4000 mg vry 4 hr (from Qustion 6, D (max, fr τ (4000mg(0.5 (80.6L (0.5hr 7.8 mg/l 7.8 µg/ml (0.35hr (0.5hr (0.35hr (4hr (min, fr (max, fr ( τ t (7.8µ g / ml (0.35 hr (4hr 0.5hr 4.9 µg/ml h stady-stat fr plasma pak lvl of 7.8 µg/ml is outsid th thraputic fr rang of 3-6 µg/ml (s Qustion 8. It is, thrfor, ncary to radjust th dosing rgimn for this patint. A nw dosing rgimn is dtrmind blow. his was not rquird and is don for practic and illustration only. his tim, only fr lvls ar considrd. h dosing intrval is: τ ln (max k (min + ( 6 / 3 ln 0.5hr 0.35hr + 5.6 hr 6 hrs D:\pha527_Dos_Opt_I\omworks\omwork5\Fall-99\ans-typ-hw5-99.doc 2
h rcommndd dos is thn found using th quation, D (max τ Rcall that (max,fr (max. h quation for dos D may thn b writtn in trms of th dsird fr pak lvl as D 6µ g / ml 0.5 (max, fr τ (0.35hr (6hr ( ( 000ml mg 80.6L 0.5hr (0.35hr (0.5hr L 000µ g 43 mg 4000 mg th dosing rgimn is thn 4000mg insd ovr 30 minuts vry 6 hours. (Sinc th t /2 of th drug was longr in this patint, l frqunt dosing was ndd, i.. incras th dosing intrval τ. Whn calculations ar prformd and th dosing intrval and dos ar roundd to mor convnint valus, it is a good ida to calculat prdictd pak and trough lvls using th roundd valus (hr, 6 hr and 4000mg to b sur th concntrations ar within th bounds of th thraputic rang. ry this yourslf. It is good practic and grat n! D:\pha527_Dos_Opt_I\omworks\omwork5\Fall-99\ans-typ-hw5-99.doc 3