Basic Principles of Pharmacokinetics Betty Lee, Pharm.D. Lucile Packard Children’s Hospital Lucile Packard Children’s Hospital February 8, 2008

Basic Principles of Pharmacokinetics

Betty Lee, Pharm.D.Betty Lee, Pharm.D.

Lucile Packard Children’s HospitalLucile Packard Children’s Hospital

February 8, 2008February 8, 2008

Introduction of PharmacokineticsIntroduction of Pharmacokinetics

• Basic PrinciplesBasic Principles– Bioavailability (F)Bioavailability (F)– Volume of Distribution (V)Volume of Distribution (V)

– Administration Rate (RAdministration Rate (RAA))

– Clearance (Cl)Clearance (Cl)– Elimination Rate Constant (K) and Half-Life Elimination Rate Constant (K) and Half-Life

(t(t1/21/2))

– Creatinine Clearance (ClCreatinine Clearance (Clcrcr))

PharmacokineticsPharmacokinetics

• Dialysis of DrugsDialysis of Drugs– Continuous Venovenous Hemofiltration Continuous Venovenous Hemofiltration

(CVVH)(CVVH)

• Antimicrobial AgentsAntimicrobial Agents– AminoglycosidesAminoglycosides– VancomycinVancomycin

Bioavailability (F)Bioavailability (F)

• The percentage or fraction of the The percentage or fraction of the administered dose that reaches the systemic administered dose that reaches the systemic circulation of the patient.circulation of the patient.

• F = bioavailability factorF = bioavailability factor

• S = the fraction of the administered dose that S = the fraction of the administered dose that is the active drugis the active drug

• Amount of Drug Absorbed = (S) (F) (Dose)Amount of Drug Absorbed = (S) (F) (Dose)

Protein BindingProtein Binding

• fu = fu = Free Drug ConcentrationFree Drug Concentration Total Drug ConcentrationTotal Drug Concentration

• fu = fu = C freeC free C bound + C freeC bound + C free

• C free = (fu) (C total)C free = (fu) (C total)

• For example, gentamicin and vancomycin For example, gentamicin and vancomycin has fu value of 0.9.has fu value of 0.9.

Volume of Distribution (V)Volume of Distribution (V)

• The apparent volume of distribution, does The apparent volume of distribution, does not necessarily refer to any physiologic not necessarily refer to any physiologic compartment in the body.compartment in the body.

• V = (the total amt of drug in the body) / CV = (the total amt of drug in the body) / C• V is the major determinant of the loading V is the major determinant of the loading

dosedose• Loading dose = Loading dose = (V) (C)(V) (C) (S) (F)(S) (F)

Administration Rate (RAdministration Rate (RAA))

• The administration rate is the average rate at The administration rate is the average rate at which absorbed drug reaches the systemic which absorbed drug reaches the systemic circulation. circulation.

• This is usually calculated by dividing the amount This is usually calculated by dividing the amount of drug absorbed by the time over which the drug of drug absorbed by the time over which the drug was administered (dosing interval).was administered (dosing interval).

• RRAA = = (S) (F) (Dose)(S) (F) (Dose)

Clearance (Cl)Clearance (Cl)

• The intrinsic ability of the body or its The intrinsic ability of the body or its organs of elimination to remove drug from organs of elimination to remove drug from the blood or plasma.the blood or plasma.

• Clearance is expressed as a volume per unit Clearance is expressed as a volume per unit of time.of time.

• At steady state, the rate of drug At steady state, the rate of drug administration (Radministration (RAA) and rate of drug ) and rate of drug elimination (Relimination (REE) must be equal.) must be equal.


• Clearance (Cl) can best be thought of as the Clearance (Cl) can best be thought of as the proportionality constant that makes the proportionality constant that makes the average steady-state plasma level equal to average steady-state plasma level equal to the rate of drug administration (Rthe rate of drug administration (RA A ))

• RRAA = (Cl) (Css ave) = (Cl) (Css ave)• and Rand RAA = (S) (F) (Dose) / = (S) (F) (Dose) / • Cl = Cl = (S) (F) (Dose/ (S) (F) (Dose/ ) ) Css aveCss ave


• Factors that can alter clearance:Factors that can alter clearance:– Body weightBody weight– Body surface areaBody surface area– Cardiac outputCardiac output– Drug-drug interactionsDrug-drug interactions– Extraction ratioExtraction ratio

– GeneticsGenetics– Hepatic functionHepatic function– Plasma protein Plasma protein

bindingbinding– Renal functionRenal function

Elimination Rate Constant (K)Elimination Rate Constant (K)

• The elimination rate constant (K) is the fraction or The elimination rate constant (K) is the fraction or percentage of the total amount of drug in the body percentage of the total amount of drug in the body removed per unit of time and is a function of removed per unit of time and is a function of clearance and volume of distributionclearance and volume of distribution

• K = Cl / V K = Cl / V • First-order elimination– the amount or First-order elimination– the amount or

concentration of drug in the body diminishes concentration of drug in the body diminishes logarithmically over timelogarithmically over time

• CC22 = (C = (C11) (e) (e-Kt-Kt11))

Elimination Rate Constant (K)Elimination Rate Constant (K)

• CC22 = (C = (C11) (e) (e-Kt-Kt))

• CC22 / C / C11 = e = e-Kt-Kt

• ln (Cln (C22 / C / C11 )= -Kt )= -Kt

• ln (Cln (C11 / C / C22 )= Kt )= Kt

• K = K = ln (Cln (C11 / C / C22 ) ) tt

Half-Life (tHalf-Life (t1/21/2))

• Half-life is the time required to eliminate Half-life is the time required to eliminate one-half of the drugone-half of the drug

• tt1/21/2 = 0.693 / K = 0.693 / K• and K = Cl / V and K = Cl / V

• tt1/21/2 = = 0.693 (V)0.693 (V) ClCl• K and tK and t1/21/2 are dependent on clearance and the are dependent on clearance and the

volume of distributionvolume of distribution

Clinical Application of K and tClinical Application of K and t1/21/2

• Estimating the time to reach steady-state Estimating the time to reach steady-state plasma concentration after initiation or plasma concentration after initiation or change in the maintenance dosechange in the maintenance dose

• Estimating the time required to eliminate all Estimating the time required to eliminate all or a portion of the drug from the body once or a portion of the drug from the body once it is discontinuedit is discontinued


• Predicting nonsteady-state plasma levels Predicting nonsteady-state plasma levels following the initiation of an infusionfollowing the initiation of an infusion

• Fraction of Steady State Achieved at time tFraction of Steady State Achieved at time t11 = 1- e = 1- e-Kt1-Kt1

• CC11 = (Css ave) ( = (Css ave) (Fraction of Steady State Achieved at time tFraction of Steady State Achieved at time t11 ) )

• CC11 = = (S) (F) (Dose/ (S) (F) (Dose/ )) (1- e (1- e-Kt1 -Kt1 )) ClCl


• Predicting a steady-state level from a non-Predicting a steady-state level from a non-steady-state plasma level obtained at a steady-state plasma level obtained at a specific time following the initiation of an specific time following the initiation of an infusioninfusion

• Fraction of Drug Remaining at tFraction of Drug Remaining at t22 = e = e-Kt2-Kt2 • CC22 = (C = (C11) (e) (e-Kt2-Kt2))

• CC2 2 ==(S) (F) (Dose/ (S) (F) (Dose/ )) (1- e (1- e-Kt1 -Kt1 ) (e) (e-Kt-Kt22)) ClCl


• Given the degree of fluctuation in plasma Given the degree of fluctuation in plasma concentration desired within a dosing concentration desired within a dosing interval, determine that interval; given the interval, determine that interval; given the interval, determine the fluctuation in the interval, determine the fluctuation in the plasma concentrationplasma concentration

Dosing Interval (Dosing Interval ())

• If the goal of therapy is to minimize plasma If the goal of therapy is to minimize plasma fluctuations to no more than 50% between fluctuations to no more than 50% between doses, the dosing interval should be less than doses, the dosing interval should be less than or equal to the half-life.or equal to the half-life.

• Maintenance Dose = Maintenance Dose = (Cl)(Css ave) ((Cl)(Css ave) ()) (S) (F)(S) (F)

Creatinine Clearance (ClCreatinine Clearance (Clcrcr))

• ClClcrcr for Children = for Children = (0.48) (Height in cm) (BSA)(0.48) (Height in cm) (BSA) (ml/min) SCr(ml/min) SCrss ss (1.73m(1.73m22))

• ClClcr cr in ml/min= in ml/min= (U) (V)(U) (V) PP

• ClClcr cr in ml/min; U is the urine creatinine concentration in ml/min; U is the urine creatinine concentration in mg/dL, V is the volume of urine per time collection in mg/dL, V is the volume of urine per time collection in mL/min, and P the plasma creatinine concentration in mL/min, and P the plasma creatinine concentration in mg/dL. in mg/dL.

Dialysis of DrugsDialysis of Drugs

• ClClpatpat = Cl = Clmm + Cl + Clrr

• ClClpatpat is the patient’s drug clearance during is the patient’s drug clearance during

nondialysis periods and is the sum of the patient’s nondialysis periods and is the sum of the patient’s metabolic clearance (Clmetabolic clearance (Clmm) and residual renal ) and residual renal

clearance (Clclearance (Clrr).).

• Postdialysis Replacement Dose = Postdialysis Replacement Dose = [Amt of Drug in the Body Prior to Dialysis] [ Fraction of Drug [Amt of Drug in the Body Prior to Dialysis] [ Fraction of Drug

Lost during Dialysis]Lost during Dialysis]

Dialysis of DrugsDialysis of Drugs

• Postdialysis Replacement Dose = Postdialysis Replacement Dose =

(V) (Css ave) [(1-e (V) (Css ave) [(1-e ––((ClClpatpat + Cl + Cldialdial))(Td)(Td) ] ] VV

• Postdialysis Replacement Dose =Postdialysis Replacement Dose = (V) (Css ave) (1-e(V) (Css ave) (1-e-K-Kdialdial(Td) (Td) )) • Kdial is the elimination rate constant during

the dialysis; Td is the duration of dialysis.

Estimating Drug DialyzabilityEstimating Drug Dialyzability

• Divide the volume of distribution by fu or Divide the volume of distribution by fu or the usual free fraction to calculate the the usual free fraction to calculate the apparent unbound volume of distribution. If apparent unbound volume of distribution. If the unbound volume of distribution exceeds the unbound volume of distribution exceeds 3.5 L/kg, it is unlikely that the drug will be 3.5 L/kg, it is unlikely that the drug will be dialyzable.dialyzable.

• Unbound Volume of Distribution = V / fuUnbound Volume of Distribution = V / fu


• If patient’s clearance is > 10 ml/min/kg, it is If patient’s clearance is > 10 ml/min/kg, it is unlikely that hemodialysis will add unlikely that hemodialysis will add significantly to the patient’s intrinsic drug significantly to the patient’s intrinsic drug elimination process. This is because most elimination process. This is because most drugs have a hemodialysis clearance less drugs have a hemodialysis clearance less than 150 ml/min.than 150 ml/min.


• If the usual dosing interval is much less than If the usual dosing interval is much less than the drug’s tthe drug’s t1/21/2, it is unlikely that hemodialysis , it is unlikely that hemodialysis

will significantly alter the dosing regimen. will significantly alter the dosing regimen. The key is to schedule the drug The key is to schedule the drug administration shortly after rather than administration shortly after rather than shortly before dialysis, so that even if the shortly before dialysis, so that even if the drug is dialyzable, very little is remaining to drug is dialyzable, very little is remaining to be removed by dialysis.be removed by dialysis.


• Drugs with a low molecular weight are more Drugs with a low molecular weight are more likely to be removed significantly by likely to be removed significantly by dialysis. However, high-flux hemodialysis dialysis. However, high-flux hemodialysis can remove molecules with molecular can remove molecules with molecular weight > 1000 Daltons.weight > 1000 Daltons.

Continuous Venovenous Continuous Venovenous Hemofiltration (CVVH)Hemofiltration (CVVH)• Drug removal by means of CVVH is independent Drug removal by means of CVVH is independent

from drug molecule sizefrom drug molecule size

• ClClCVVHCVVH is clinically relevant for is clinically relevant for – drugs with dominant renal clearance, especially when drugs with dominant renal clearance, especially when

presenting a limited Vpresenting a limited Vdd and poor plasma protein binding and poor plasma protein binding

– most hydrophilic antimicrobial agents. (e.g. beta-most hydrophilic antimicrobial agents. (e.g. beta-lactams, aminoglycosides, glycopeptides)lactams, aminoglycosides, glycopeptides)

• The larger the VThe larger the Vdd, the less likely will be removed , the less likely will be removed

by CVVHby CVVH

Continuous Venovenous Continuous Venovenous Hemofiltration (CVVH)Hemofiltration (CVVH)

• Extent of drug removal is expected to be Extent of drug removal is expected to be directly proportional to the device’s surface directly proportional to the device’s surface area and to be dependent on the mode of area and to be dependent on the mode of replacement fluid administration (predilution replacement fluid administration (predilution or postdilution) and on the ultrafiltration or postdilution) and on the ultrafiltration and/or dialysate flow rates applied.and/or dialysate flow rates applied.


• ClClCVVHCVVH maximum = (fu) (CVVH flow rate) maximum = (fu) (CVVH flow rate)

• MaintenanceMaintenance = = (Cl(Clpatpat + C + CllCVVHCVVH)(Css ave) ()(Css ave) ()) DoseDose (S)(F)(S)(F)


• For time-dependent antimicrobialsFor time-dependent antimicrobials– Maintain the frequency of drug administration Maintain the frequency of drug administration

while modifying the amount of each single dosewhile modifying the amount of each single dose

• For concentration-dependent antimicrobialsFor concentration-dependent antimicrobials– Maybe more useful to change the dosing interval Maybe more useful to change the dosing interval

while maintaining a fixed dosagewhile maintaining a fixed dosage

AminoglycosidesAminoglycosides

• Volume of distribution is ~0.25 L/kg; pediatric Volume of distribution is ~0.25 L/kg; pediatric patients younger than 5 years tend to have a volume patients younger than 5 years tend to have a volume of distribution of 0.5 L/kgof distribution of 0.5 L/kg

• Aminoglycosides are eliminated almost entirely by Aminoglycosides are eliminated almost entirely by the renal route (Cl = Clthe renal route (Cl = Clcrcr).).

• tt1/21/2 = 2-3 hr = 2-3 hr• Peak level should be drawn 30 min. after a 30-min. Peak level should be drawn 30 min. after a 30-min.

infusion; trough level should be drawn within 30 infusion; trough level should be drawn within 30 min. before the next dosemin. before the next dose

Aminoglycosides—during CVVHAminoglycosides—during CVVH

• HydrophilicHydrophilic

• Low VLow Vdd

• Absence of plasma protein bindingAbsence of plasma protein binding

• Almost complete renal clearanceAlmost complete renal clearance

• Rapid and consistent extracorporeal removal Rapid and consistent extracorporeal removal during CVVHduring CVVH

AminoglycosidesAminoglycosides

• Bactericidal activity is concentration-dependentBactericidal activity is concentration-dependent• Also has postantibiotic effect that results in Also has postantibiotic effect that results in

depressed bacterial growth after plasma depressed bacterial growth after plasma concentrations have fallen below the MICconcentrations have fallen below the MIC

• Saturable uptake mechanisms within the renal Saturable uptake mechanisms within the renal cortex and inner ear indicate that extended interval cortex and inner ear indicate that extended interval dosing may also minimize the likelihood of dosing may also minimize the likelihood of developing nephrotoxicity and ototoxicity.developing nephrotoxicity and ototoxicity.

AminoglycosidesAminoglycosides• Conventional dosing:Conventional dosing:

– Gentamicin, Tobramycin:Gentamicin, Tobramycin:• Peak 5-8 mg/L, Trough <2 mg/LPeak 5-8 mg/L, Trough <2 mg/L

– Amikacin:Amikacin:• Peak 20-30 mg/L, Trough <10 mg/LPeak 20-30 mg/L, Trough <10 mg/L

• Once-daily dosing:Once-daily dosing:– Gentamicin, Tobramycin:Gentamicin, Tobramycin:

• Peak ~20 mg/L, Trough--UndetectablePeak ~20 mg/L, Trough--Undetectable

– Amikacin:Amikacin:• Peak ~60 mg/L, Trough--UndetectablePeak ~60 mg/L, Trough--Undetectable

Once-daily AminoglycosidesOnce-daily Aminoglycosides• Less intensive monitoring of serum concentrationsLess intensive monitoring of serum concentrations• Nomogram developed by Nicolau D et al. Nomogram developed by Nicolau D et al.

Antimicrob Agents Chemother 1995; 39:650-655.Antimicrob Agents Chemother 1995; 39:650-655.– Recommends a single level be drawn 6 to 14 hours after Recommends a single level be drawn 6 to 14 hours after

the dosethe dose

• With extended interval dosing there should be no With extended interval dosing there should be no significant accumulation with multiple dosing, significant accumulation with multiple dosing, therefore, measurements can be obtained after any therefore, measurements can be obtained after any dosedose

VancomycinVancomycin

• Volume of distribution: an average value of Volume of distribution: an average value of 0.7 L/kg or for patient older than 18 years:0.7 L/kg or for patient older than 18 years:V (L) = 0.17 (age in yr) + 0.22 (TBW in kg) + 15V (L) = 0.17 (age in yr) + 0.22 (TBW in kg) + 15

• Eliminated primarily by the renal route; Eliminated primarily by the renal route; approximately 5% of the dose is metabolized approximately 5% of the dose is metabolized (Cl ~ Cl(Cl ~ Clcrcr).).

• tt1/21/2 = 6 to 7 hours = 6 to 7 hours

Vancomycin—during CVVHVancomycin—during CVVH

• Low VLow Vdd

• HydrophilicHydrophilic

• Moderately protein-boundModerately protein-bound

• Short tShort t1/21/2

• Mainly renal clearanceMainly renal clearance

• Shown to be removed significantly removed Shown to be removed significantly removed during CVVH during CVVH


• Bactericidal for most gram-positive Bactericidal for most gram-positive organisms, except against enterococciorganisms, except against enterococci

• Synergistic with gentamicin against most Synergistic with gentamicin against most strains of strains of S. aureusS. aureus and enterococci and enterococci

• Therapeutic serum concentrations:Therapeutic serum concentrations:– Peak 30-40 mg/LPeak 30-40 mg/L– Trough 5-15 mg/LTrough 5-15 mg/L


• Some controversy about necessity for Some controversy about necessity for routinely monitoring plasma vancomycin routinely monitoring plasma vancomycin concentrations:concentrations:– Vancomycin exhibits concentration-independent killing, Vancomycin exhibits concentration-independent killing,

and specific peak plasma concentrations have not been and specific peak plasma concentrations have not been correlated with efficacy.correlated with efficacy.

– Monitor those at highest risk for therapeutic failure or Monitor those at highest risk for therapeutic failure or potential drug toxicity, which includes pediatric patients potential drug toxicity, which includes pediatric patients who have high clearances and short half-liveswho have high clearances and short half-lives


• As a general rule, vancomycin is dosed with As a general rule, vancomycin is dosed with an interval of approximately one half-lifean interval of approximately one half-life

• Peak level should be drawn 1 hour after a Peak level should be drawn 1 hour after a 1-hour infusion; trough level should be 1-hour infusion; trough level should be drawn within 1 hour before the next dosedrawn within 1 hour before the next dose

• Css max = [Css min] [Css max = [Css min] [(S)(F)(Dose)(S)(F)(Dose)]] VV


• Vancomycin-induced ototoxicity has been Vancomycin-induced ototoxicity has been primarily reported in patients with primarily reported in patients with vancomycin concentrations > 80 mg/L.vancomycin concentrations > 80 mg/L.

• As a single agent, vancomycin is associated As a single agent, vancomycin is associated with a low incidence of nephrotoxicity; with a low incidence of nephrotoxicity; however, when it is combined with however, when it is combined with aminoglycoside, the incidence may be as aminoglycoside, the incidence may be as high as 30%.high as 30%.

ReferencesReferences

• Winter, Michael. Basic Clinical Winter, Michael. Basic Clinical Pharmacokinetics, 4Pharmacokinetics, 4thth Ed. Baltimore: LWW, Ed. Baltimore: LWW, 2004.2004.

• Pea F, Viale P et al. Pharmacokinetic Pea F, Viale P et al. Pharmacokinetic Considerations for Antimicrobial Therapy in Considerations for Antimicrobial Therapy in Patients Receiving Renal Replacement Patients Receiving Renal Replacement Therapy. Clin Pharmacokinet 2007; 46 (12): Therapy. Clin Pharmacokinet 2007; 46 (12): 997-1038.997-1038.

Documents

Basic Principles of Pharmacokinetics Betty Lee, Pharm.D. Lucile Packard Children’s Hospital Lucile Packard Children’s Hospital February 8, 2008