Useful Pharmacokinetic Equations Symbols Trough (multiple dose) k e  Ce0  Cmin  D = dose 1 ek 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) FDk  e kte e kta  C  a     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 CCe0

Plasma concentration (multiple dose) Average concentration (steady state) FD Ce kte C  C  0 CL 1 ek e   Clearance Peak (multiple dose) Dose  F Cl  C0 AUC Cmax  1 ek e 

Cl  ke Vd

Equations/Useful_pharmacokinetic_equ_5127 1 Constant rate infusion Calculated peak  Cmax Cmax   Plasma concentration (during infusion) ekte 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 CCekte 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 eke T Vd     Short-term infusion k T ke T e [Cmax  (Cmin  e )]

Peak (single dose) Calculated recommended dosing interval D C  1 ekTe max(1 ) CL T   C  ln max(desired )  Trough (single dose)  C    min(desired )  T CCekTe  min(11 ) max( ) k e

Peak (multiple dose) Calculated recommended dose

kT D 1 e e 1 eke  C    max k  DCmax(desired ) kVT e CL T 1 e e 1 ekTe

Trough (multiple dose) Two-Compartment-Body Model

Caett  be CCekTe  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 = QClfuHbint

QCHb lint fu ClH = EQHH = QClfuHbint

QH FH = QH  Clint  fub

C in  C out Clren = RBFE = 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 VVP  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 k  V 1 e 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 ekeT  D keT C   If the dosing Cmax   1 e  max k  involves the use Vk T VkeT 1 e 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: k t k t F  D  ka ket kat F  D  k  e e e a C   e  e C  a    V ka  ke V k  k ke ka If the dosing a e 1 e  1 e involves oral administration: ka  1 tmax  ln   ke  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