Useful Pharmacokinetic Equations - University of Florida

1 Equations /Useful_pharmacokinetic_equ_512 7 1 Useful Pharmacokinetic Equations Symbols D = dose = dosing interval CL = clearance Vd = volume of distribution ke = elimination rate constant ka = absorption rate constant F = fraction absorbed (bioavailability) K0 = infusion rate T = duration of infusion C = plasma concentration General Elimination rate constant kCLVdCCttCCtte lnlnln12211221 Half-life tVdCLkkee120 69320 693/.ln(). Intravenous bolus Initial concentration CDVd0 Plasma concentration (single dose) CCekte 0 Plasma concentration (multiple dose) CCeektkee 01 Peak (multiple dose) CCekemax 01 Trough (multiple dose) CCeekkeemin 01 Average concentration (steady state) CpDCLss Oral administration Plasma concentration (single dose) CFDkVd kkeeaaektktea Time of maximum concentration (single dose) tkkkkaeaemaxln Plasma concentration (multiple dose) CFDkVd kkeeeeaaektkktkeeaa 11 Time of maximum concentration (multiple dose) tkekekkakekaeeamaxln 11 Average concentration (steady state) CFDCL Clearance AUCFDoseCl deVkCl Equations /Useful_pharmacokinetic_equ_512 7 2 Constant rate infusion Plasma concentration (during infusion) CkCLekte 01 Plasma concentration (steady state)

2 CkCL 0 Calculated clearance (Chiou equation) CLkCCVd CCCC t t 22012121221 Short-term infusion Peak (single dose) CDCL TekTemax( )11 Trough (single dose) CCekTemin( )max( )11 Peak (multiple dose) CDCL TeekTkeemax 11 Trough (multiple dose) CCekTeminmax Calculated elimination rate constant kCCte lnmaxmin with Cmax* = measured peak and Cmin* = measured trough, measured over the time interval t Calculated peak CCektemaxmax with Cmax* = measured peak, measured at time t* after the end of the infusion Calculated trough CCekteminmin with Cmin* = measured trough, measured at time t* before the start of the next infusion Calculated volume of distribution )]([1minmaxTekTekeeCCeTkDVd Calculated recommended dosing interval lnmax()min()CCkTdesireddesirede Calculated recommended dose DCkVTeedesiredekkTee max()11 Two-Compartment-Body Model Caebett AUCab // VdVdVcareass Creatinine Clearance CLmaleageweightCpcreatcreat()() 14072 CLfemaleageweightCpcreatcreat()() 14085 With weight in kg, age in years, creatinine plasma conc.

3 In mg/dl and CLcreat in ml/min Equations /Useful_pharmacokinetic_equ_512 7 3Ke for aminoglycosides Ke = (CrCL) + Metabolic and Renal Clearance EH = ClfuQClfubHbintint ClH = EQHH = QClfuQClfuHbHb intint FH = bHHfuClQQ int Clren = RBF E = inoutinCCCGFR Clren = ionconcentrat plasmaexcretion of rate Clren = ionconcentrat Plasmaonreabsorpti of Rate -secretion of RateGFRfu Clren = ionconcentrat Plasmaionconcentrat urineflow Urine Ideal Body Weight Male IBW = 50 kg + kg for each inch over 5ft in height Female IBW = kg + kg for each inch over 5ft in height Obese ABW = IBW + *(TBW-IBW) Volume of Distribution PTPKVVV TTPfufuVVV Clearance AUCDoseCl deVkCl Last modified 2010 C:\Current data \pha5127_Dose_Opt_I\ Equations \ For One Compartment Body Model If the dosing involves the use of bolus administration: For a single bolus administration: VDC 0 tkeeCC 0 For multiple bolus administration: tkknkeeeeeeVDtCn 11)( at peak: t = 0; at steady state n at trough: t = )e(VDCekss 11max eksssseCC maxmin If the dosing involves the use of infusion: For a single short-term infusion: Since = t for Cmax TkeeeTVkDC 1max )(maxminTkeeCC For multiple short-term infusion at steady state: eekTkeeeTVkDC 11max )(maxminTkeeCC Last modified 2010 C:\Current data \pha5127_Dose_Opt_I\ Equations \ If the dosing involves a infusion (more Equations ): tkTketeeeeTVkDC 1(most general eq.)

4 During infusion t = T so, tketeeTVkDC 1(during infusion) at steady state t , e-ket, t 0 so, CLkVkkTVkDCpssee00 (steady state) remembering TDk 0and ekVCL If the dosing involves oral administration: For a single oral dose: tktkeaaaeeekkVkDFC eaeakkkkt 1lnmax For multiple oral doses: aaeektkktkeaaeeeekkVkDFC11 eakekakkekektae 111lnmax