Useful Pharmacokinetic Equations Symbols Trough (multiple dose) k e Ce0 Cmin D = dose 1 ek e = dosing interval CL = clearance Average concentration (steady state) Vd = volume of distribution D ke = elimination rate constant Cp ss CL ka = absorption rate constant F = fraction absorbed (bioavailability) K0 = infusion rate T = duration of infusion Oral administration C = plasma concentration Plasma concentration (single dose) FDk General a ktea kt C ee Vd kae k Elimination rate constant C Time of maximum concentration (single ln 1 dose) CL C2 lnCC12 ln k e Vd tt tt ka 21 21 ln k e tmax Half-life kkae 0.ln(). 693 Vd 2 0 693 t12/ CL kee k Plasma concentration (multiple dose) kte kta FDka e e C Vd k k 11 e ke e ka Intravenous bolus ae Initial concentration Time of maximum concentration (multiple D dose) C k 0 e Vd kea 1 ln k a kee 1 Plasma concentration (single dose) tmax kte kkae CCe0 Plasma concentration (multiple dose) Average concentration (steady state) FD Ce kte C C 0 CL 1 ek e Clearance Peak (multiple dose) Dose F Cl C0 AUC Cmax 1 ek e Cl ke Vd Equations/Useful_pharmacokinetic_equ_5127 1 Constant rate infusion Calculated peak Cmax Cmax Plasma concentration (during infusion) ekte k * 0 kte with Cmax = measured peak, measured at time C 1 e * CL t after the end of the infusion Plasma concentration (steady state) Calculated trough k CCekte C 0 min min CL * with Cmin = measured trough, measured at Calculated clearance (Chiou equation) time t* before the start of the next infusion 2 k 2 Vd C C CL 0 12 CC CC tt Calculated volume of distribution 12 1221 D 1 eke T Vd Short-term infusion k T ke T e [Cmax (Cmin e )] Peak (single dose) Calculated recommended dosing interval D C 1 ekTe max(1 ) CL T C ln max(desired ) Trough (single dose) Cmin(desired ) T CCekTe min(11 ) max( ) k e Peak (multiple dose) Calculated recommended dose kT D 1 e e 1 eke C max k DCmax(desired ) kVT e CL T 1 e e 1 ekTe Trough (multiple dose) Two-Compartment-Body Model Caett be CCekTe min max AUC a// b Calculated elimination rate constant Vd Vd Vc C area ss ln max C k min Creatinine Clearance e t with C * = measured peak and C * = ()140 age weight max min CL() male measured trough, creat 72 Cp creat measured over the time interval t ()140 age weight CL() female creat 85 Cp creat With weight in kg, age in years, creatinine plasma conc. in mg/dl and CLcreat in ml/min Equations/Useful_pharmacokinetic_equ_5127 2 Ke for aminoglycosides Ke = 0.00293(CrCL) + 0.014 Metabolic and Renal Clearance Clint fub EH = QClfuHbint QCHb lint fu ClH = EQHH = QClfuHbint QH FH = QH Clint fub C in C out Clren = RBFE = GFR C in rate of excretion Clren = plasma concentration Rate of secretion - Rate of reabsorption Clren = fu GFR Plasma concentration Urine flow urine concentration Cl = ren Plasma concentration Ideal Body Weight Volume of Distribution VVP VT K P Male fu V V V IBW = 50 kg + 2.3 kg for each inch over 5ft in P T fuT height Female Clearance IBW = 45.5 kg + 2.3 kg for each inch over 5ft in Dose height Cl AUC Obese ABW = IBW + 0.4*(TBW-IBW) Cl ke Vd Equations/Useful_pharmacokinetic_equ_5127 3 For One Compartment Body Model For a single I.V. bolus administration: For multiple I.V. bolus administration: D nke C D 1 e k t 0 Cn(t) e e V V ke 1 e ket C C e at peak: t = 0; at steady state n If the dosing 0 involves the use at trough: t = of I.V. bolus administration: D 1 Cmax ss k V (1 e e ) ke Cmin ss Cmax ss e For a single short-term I.V. infusion: For multiple short-term I.V. infusion at steady state: Since = t for C max D 1 ekeT D k T If the dosing C 1 e e Cmax max Vk T ke involves the use Vk T e 1 e of I.V. infusion: e ke ( T ) ke ( T ) Cmin Cmax e Cmin Cmax e Last modified 2010 C:\Current Data\pha5127_Dose_Opt_I\equations\5127-28-equations.doc D keT ket Ct e 1 e (most general eq.) during infusion t = T so, VkeT If the dosing D k t e (during infusion) at steady state t , e-ket, t 0 so, involves a I.V. Ct 1 e infusion (more VkeT equations): D k0 k0 D Cpss (steady state) remembering k0 and VkeT Vke CL T CL V ke For a single oral dose: For multiple oral doses: F D ka k t k t ket kat C e e e a F D ka e e V k k C a e V k k ke ka If the dosing a e 1 e 1 e involves oral administration: ka 1 t ln ke max k k k ka 1 e 1 e a e tmax ln ka k k ke 1 e a e Last modified 2010 C:\Current Data\pha5127_Dose_Opt_I\equations\5127-28-equations.doc .