PH 5127 nswrs Homwork 2 Fall 2001 OK, bfor you rad th answrs, many of you spnt a lot of tim on this homwork. Plas, nxt tim if you hav qustions plas com talk/ask us. Thr is no nd to suffr (wll a littl suffring is good) hours and hours. On of us is always around and w do chck our mail and on to th answrs Givn information: CL 80 L/h UC 12.5 mg/l/h T 1/2 1.73 h for and 3.47 for 1 compartmnt body modl 0.60 (fb 0.40), Q H 90 L/hr What was th dos givn? Knowing th claranc and UC w can calculat a dos Dos CL UC 0 Dos CL UC 0 Dos (80 L/h)(12.5 mg/l/h) Dos 1000 mg Why is th initial plasma concntration diffrnt for ths two studnts? Provid a quantitativ xplanation (considr distribution and binding proprtis) for this diffrnc. Initial plasma concntrations can b calculatd for a dos administrd IV bolus, (0) D w know th dos, 1000 mg but w nd to know th volum of distribution which can b found by Cl (k)(vd) Cl k Th half-lif (t 1/2 ) is thn, ln 2 t 1 / 2 k 0.693 k t1/ 2 For studnt 0.693 1 k 0.40h 1.73 For studnt, 0.693 1 k 0.20hr 3.47 Know w know k and th claranc (80 L/h) D:\NEWDDRIVE\pha5127_Dos_Opt_I\Homworks\Homwork2\Fall-01\ans-hw2-01.doc 1
For studnt, Cl 80 200L k 0.40 For studnt, Cl 80 400L k 0.20 Going back to th original quation D (0) (0) for Studnt 1000mg / 200 L 5 mg/l (0) for Stdunt 1000 mg / 400 L 2.5 mg/l Sinc both studnts rcivd th sam dos and achivd diffrnt initial concntrations, must b diffrnt for ths two studnts. Rcall: For a drug that in lipophilic and unionizd it will most likly distribut wll into all tissus and cross mmbrans asily. Thrfor, th tissu volum into which a drug may distribut is 38 L (total tissu watr) and plasma volum is 3 L. Th volum of distribution may b rlatd to ths plasma and tissu volums by Vd V p + VT T is givn as 0.6 (actually w gav % bound to protin which was 40% so tofind fr concntration is 100%-40%). If w assum a tissu watr volum of 38L for both studnts, T must b diffrnt in ths studnts. Th xprssion abov may b rarrangd to giv. T V V ) T ( Vd p For studnt, (38L)(0.6) T (200L 3L) For studnt, (38L)(0.6) T (400L 3L) 0.116 0.057 Thus, th diffrnc in 's may b xplaind by th 2-fold diffrnc in tissu binding of th drug. What ar th fr drug concntrations in th plasma 1.5 hours aftr administration? This qustion is important bcaus only fr drug (drug not bound to plasma protin) is pharmacologically activ, its fr drugs that can pass through mmbrans in distribution procsss and its fr drug lvls that ar mtaboliz. First w nd to find (0) (which w did in qustion 2). Thn w nd to calculat total drug concntrations 1.5 h aftr w giv th drug. k C C 0 D:\NEWDDRIVE\pha5127_Dos_Opt_I\Homworks\Homwork2\Fall-01\ans-hw2-01.doc 2
For Studnt C 5mg/ L* C 2.75mg/ L For Studnt C 2.5mg/ L* (0.4)(1.5) 0.21.5 h C 1.86mg/ L Ths ar total drug concntration. Now w must multiply th valu by th fraction of drug unbound to protin (60%) For C 2.75 mg/l * 0.6 1.65 mg/l For C 1.86 mg/l * 0.6 1.12 mg/l t what tim post-injction (if any) will th plasma concntrations b qual in both studnts? Will th two studnts vr hav th sam plasma concntration at any givn tim? Studnt has a highr initial concntration but a largr limination rat constant (i.. stpr slop). ln? t So, at som tim t, concntration will b qual for both studnts. To find this tim, st th concntration xprssions qual to on anothr and solv for tim t. (This is similar to th drivation of t 1/2 prformd in class.) Th plasma concntration at any tim t is givn by ( t) (0) k t t som tim "t" aftr injction, th plasma concntrations for studnts and will b qual. Thus, ( t) ( t) D:\NEWDDRIVE\pha5127_Dos_Opt_I\Homworks\Homwork2\Fall-01\ans-hw2-01.doc 3
(gain, th tim "t" may b found by calculation or by plotting th concntrations (smilog) for both studnts.) Insrting th (t) xprssions for both studnts givs (0) k ( ) (0) k This quality must b solvd for t, (0) (0) k k ( ) k + k [ k ( ) k ]t Taking th natural log of both sids giv, (0) ln [ k ( ) k ] (0) and thus, t ln (0) (0) [ k ( ) k ] 5 ln 2.5 3.45 hr 1 (0.40 0.20) hr Th plasma concntrations for both studnts will b qual, roughly 3.5 hours aftr th IV bolus injction. Calculat claranc. What is th hpatic xtraction ratio? (NOTE: Whn givn a valu of claranc, it almost always rfrs to systmic claranc (Cl or Cl s or Cl TOT ). If hpatic claranc (Cl H or Cl Hp ) is givn or intrinsic claranc is givn (Cl INT ) it will b spcifically spcifid). Systmic claranc is th sum of all claranc procsss (Cl Cl Hp + Cl REN + Cl lood + tc). Sinc hpatic mtabolism is th only procss of drug limination, total claranc is qual to th hpatic claranc (CL hp ) and is thrfor 80 L/h To find th xtraction ratio, you know th hpatic claranc and you know hpatic blood flow so For hpatic claranc, D:\NEWDDRIVE\pha5127_Dos_Opt_I\Homworks\Homwork2\Fall-01\ans-hw2-01.doc 4
CL hp E Q H Whr E is th xtraction ratio. Solving for E givs CLhp E QH 80L / hr 90L / hr 0.89 This would b considrd a high xtraction drug If th hpatic claranc is rducd by 30%, tissu binding and plasma protin binding both rducd by 25% thn systmic claranc, volum of distribution, and half lif is now. Not: This qustion was not mant to b as difficult as it turnd out to b CL was rducd by 30% (rmmbr hpatic claranc total claranc) so 80 L/hr (0.70) 56 L/hr Volum of distribution is dtrmind by Vd V p + VT T so thr wr 2 ways in which you can approach this problm. Th first way was th way th qustion was attndd. To calculat th nw unbound concntrations in tissu and plasma assum a 25% rduction in protin binding is a 25% incras in tissu lvls plasma (0.6) (1.25) 0.75 tissu (0.116) (1.25) 0.145 using th nw valus 0.75 3L + 38L 200 L 0.145 so thr is no chang in volum of distribution. Notic th ratio (f u /f UT ) rmains th sam so V D will b th sam. Th scond way was to calculat th 25% rduction lik this Plasma: f u 1 (F b ) (0.75) F u 0.70 Tissu: f ut 1 (f b )(0.75) F ut 0.34 Using ths numbrs th ratio F u /f UT 2 This would man that V D 81 L Finally, on to half-lif. t 1/2 dpnds on both CL and sinc CL k V k d CL V d D:\NEWDDRIVE\pha5127_Dos_Opt_I\Homworks\Homwork2\Fall-01\ans-hw2-01.doc 5
Thus, Vd ln 2 t1/ 2 CL For studnt, th nw t 1/2 would b (200L)(0.693) t1 / 2 2. 5hr or (56L / hr) (81L)(0.693) t1 / 2 1hr (56L / hr) Th intntion of th qustion was to hav half-lif incras bcaus claranc dcrasd but volum of distribution rmaind th sam but as you can s it rally dpnds on th mannr in which you calculatd th nw fr fraction ( so sorry). Th corrct mthod of doing th problm would b th scond way, rducing th fraction bound by 25% and thn calculat th fr concntrations (again, sorry for th consion) D:\NEWDDRIVE\pha5127_Dos_Opt_I\Homworks\Homwork2\Fall-01\ans-hw2-01.doc 6