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Basic Principles of
Pharmacokinetics
Betty Lee, Pharm.D.
Lucile Packard Children’s Hospital
February 8, 2008
Introduction of Pharmacokinetics
• Basic Principles
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Bioavailability (F)
Volume of Distribution (V)
Administration Rate (RA)
Clearance (Cl)
Elimination Rate Constant (K) and Half-Life
(t1/2)
– Creatinine Clearance (Clcr)
Pharmacokinetics
• Dialysis of Drugs
– Continuous Venovenous Hemofiltration
(CVVH)
• Antimicrobial Agents
– Aminoglycosides
– Vancomycin
Bioavailability (F)
• The percentage or fraction of the
administered dose that reaches the systemic
circulation of the patient.
• F = bioavailability factor
• S = the fraction of the administered dose
that is the active drug
• Amount of Drug Absorbed = (S) (F) (Dose)
Protein Binding
• fu = Free Drug Concentration
Total Drug Concentration
• fu =
C free
C bound + C free
• C free = (fu) (C total)
• For example, gentamicin and vancomycin
has fu value of 0.9.
Volume of Distribution (V)
• The apparent volume of distribution, does
not necessarily refer to any physiologic
compartment in the body.
• V = (the total amt of drug in the body) / C
• V is the major determinant of the loading
dose
• Loading dose = (V) (C)
(S) (F)
Administration Rate (RA)
• The administration rate is the average rate at
which absorbed drug reaches the systemic
circulation.
• This is usually calculated by dividing the amount
of drug absorbed by the time over which the drug
was administered (dosing interval).
• RA = (S) (F) (Dose)
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Clearance (Cl)
• The intrinsic ability of the body or its
organs of elimination to remove drug from
the blood or plasma.
• Clearance is expressed as a volume per unit
of time.
• At steady state, the rate of drug
administration (RA) and rate of drug
elimination (RE) must be equal.
Clearance (Cl)
• Clearance (Cl) can best be thought of as the
proportionality constant that makes the
average steady-state plasma level equal to
the rate of drug administration (RA )
• RA = (Cl) (Css ave)
• and RA = (S) (F) (Dose) / 
• Cl = (S) (F) (Dose/ )
Css ave
Clearance (Cl)
• Factors that can alter clearance:
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Body weight
Body surface area
Cardiac output
Drug-drug interactions
Extraction ratio
– Genetics
– Hepatic function
– Plasma protein
binding
– Renal function
Elimination Rate Constant (K)
• The elimination rate constant (K) is the fraction or
percentage of the total amount of drug in the body
removed per unit of time and is a function of
clearance and volume of distribution
• K = Cl / V
• First-order elimination– the amount or
concentration of drug in the body diminishes
logarithmically over time
• C2 = (C1) (e-Kt1)
Elimination Rate Constant (K)
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C2 = (C1) (e-Kt)
C2 / C1 = e-Kt
ln (C2 / C1 )= -Kt
ln (C1 / C2 )= Kt
K = ln (C1 / C2 )
t
Half-Life (t1/2)
• Half-life is the time required to eliminate
one-half of the drug
• t1/2 = 0.693 / K
• and K = Cl / V
• t1/2 = 0.693 (V)
Cl
• K and t1/2 are dependent on clearance and the
volume of distribution
Clinical Application of K and t1/2
• Estimating the time to reach steady-state
plasma concentration after initiation or
change in the maintenance dose
• Estimating the time required to eliminate all
or a portion of the drug from the body once it
is discontinued
Clinical Application of K and t1/2
• Predicting nonsteady-state plasma levels
following the initiation of an infusion
• Fraction of Steady State Achieved at time t1 = 1- e-Kt1
• C1 = (Css ave) (Fraction of Steady State Achieved at time t )
1
• C1 = (S) (F) (Dose/ ) (1- e-Kt1 )
Cl
Clinical Application of K and t1/2
• Predicting a steady-state level from a nonsteady-state plasma level obtained at a
specific time following the initiation of an
infusion
• Fraction of Drug Remaining at t2 = e-Kt2
• C2 = (C1) (e-Kt2)
• C2 =(S) (F) (Dose/ ) (1- e-Kt1 ) (e-Kt2)
Cl
Clinical Application of K and t1/2
• Given the degree of fluctuation in plasma
concentration desired within a dosing
interval, determine that interval; given the
interval, determine the fluctuation in the
plasma concentration
Dosing Interval ()
• If the goal of therapy is to minimize plasma
fluctuations to no more than 50% between
doses, the dosing interval should be less than
or equal to the half-life.
• Maintenance Dose = (Cl)(Css ave) ()
(S) (F)
Creatinine Clearance (Clcr)
• Clcr for Children = (0.48) (Height in cm) (BSA)
(ml/min)
SCrss
(1.73m2)
• Clcr in ml/min= (U) (V)
P
• Clcr in ml/min; U is the urine creatinine
concentration in mg/dL, V is the volume of urine
per time collection in mL/min, and P the plasma
creatinine concentration in mg/dL.
Dialysis of Drugs
• Clpat = Clm + Clr
• Clpat is the patient’s drug clearance during
nondialysis periods and is the sum of the patient’s
metabolic clearance (Clm) and residual renal
clearance (Clr).
• Postdialysis Replacement Dose =
[Amt of Drug in the Body Prior to Dialysis] [ Fraction of Drug
Lost during Dialysis]
Dialysis of Drugs
• Postdialysis Replacement Dose =
(V) (Css ave) [(1-e –(Clpat + Cldial)(Td) ]
V
• Postdialysis Replacement Dose =
(V) (Css ave) (1-e-Kdial(Td) )
• Kdial is the elimination rate constant during
the dialysis; Td is the duration of dialysis.
Estimating Drug Dialyzability
• Divide the volume of distribution by fu or
the usual free fraction to calculate the
apparent unbound volume of distribution. If
the unbound volume of distribution exceeds
3.5 L/kg, it is unlikely that the drug will be
dialyzable.
• Unbound Volume of Distribution = V / fu
Estimating Drug Dialyzability
• If patient’s clearance is > 10 ml/min/kg, it is
unlikely that hemodialysis will add
significantly to the patient’s intrinsic drug
elimination process. This is because most
drugs have a hemodialysis clearance less
than 150 ml/min.
Estimating Drug Dialyzability
• If the usual dosing interval is much less than
the drug’s t1/2, it is unlikely that hemodialysis
will significantly alter the dosing regimen.
The key is to schedule the drug
administration shortly after rather than
shortly before dialysis, so that even if the
drug is dialyzable, very little is remaining to
be removed by dialysis.
Estimating Drug Dialyzability
• Drugs with a low molecular weight are more
likely to be removed significantly by
dialysis. However, high-flux hemodialysis
can remove molecules with molecular weight
> 1000 Daltons.
Continuous Venovenous
Hemofiltration (CVVH)
• Drug removal by means of CVVH is independent
from drug molecule size
• ClCVVH is clinically relevant for
– drugs with dominant renal clearance, especially when
presenting a limited Vd and poor plasma protein binding
– most hydrophilic antimicrobial agents. (e.g. betalactams, aminoglycosides, glycopeptides)
• The larger the Vd, the less likely will be removed
by CVVH
Continuous Venovenous
Hemofiltration (CVVH)
• Extent of drug removal is expected to be
directly proportional to the device’s surface
area and to be dependent on the mode of
replacement fluid administration (predilution
or postdilution) and on the ultrafiltration
and/or dialysate flow rates applied.
Continuous Venovenous
Hemofiltration (CVVH)
• ClCVVH maximum = (fu) (CVVH flow rate)
• Maintenance = (Clpat + ClCVVH)(Css ave) ()
Dose
(S)(F)
Continuous Venovenous
Hemofiltration (CVVH)
• For time-dependent antimicrobials
– Maintain the frequency of drug administration
while modifying the amount of each single dose
• For concentration-dependent antimicrobials
– Maybe more useful to change the dosing interval
while maintaining a fixed dosage
Aminoglycosides
• Volume of distribution is ~0.25 L/kg; pediatric
patients younger than 5 years tend to have a volume
of distribution of 0.5 L/kg
• Aminoglycosides are eliminated almost entirely by
the renal route (Cl = Clcr).
• t1/2 = 2-3 hr
• Peak level should be drawn 30 min. after a 30-min.
infusion; trough level should be drawn within 30
min. before the next dose
Aminoglycosides—during CVVH
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Hydrophilic
Low Vd
Absence of plasma protein binding
Almost complete renal clearance
Rapid and consistent extracorporeal removal
during CVVH
Aminoglycosides
• Bactericidal activity is concentration-dependent
• Also has postantibiotic effect that results in
depressed bacterial growth after plasma
concentrations have fallen below the MIC
• Saturable uptake mechanisms within the renal
cortex and inner ear indicate that extended interval
dosing may also minimize the likelihood of
developing nephrotoxicity and ototoxicity.
Aminoglycosides
• Conventional dosing:
– Gentamicin, Tobramycin:
• Peak 5-8 mg/L, Trough <2 mg/L
– Amikacin:
• Peak 20-30 mg/L, Trough <10 mg/L
• Once-daily dosing:
– Gentamicin, Tobramycin:
• Peak ~20 mg/L, Trough--Undetectable
– Amikacin:
• Peak ~60 mg/L, Trough--Undetectable
Once-daily Aminoglycosides
• Less intensive monitoring of serum concentrations
• Nomogram developed by Nicolau D et al.
Antimicrob Agents Chemother 1995; 39:650-655.
– Recommends a single level be drawn 6 to 14 hours after
the dose
• With extended interval dosing there should be no
significant accumulation with multiple dosing,
therefore, measurements can be obtained after any
dose
Vancomycin
• Volume of distribution: an average value of
0.7 L/kg or for patient older than 18 years:
V (L) = 0.17 (age in yr) + 0.22 (TBW in kg) + 15
• Eliminated primarily by the renal route;
approximately 5% of the dose is metabolized
(Cl ~ Clcr).
• t1/2 = 6 to 7 hours
Vancomycin—during CVVH
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Low Vd
Hydrophilic
Moderately protein-bound
Short t1/2
Mainly renal clearance
Shown to be removed significantly removed
during CVVH
Vancomycin
• Bactericidal for most gram-positive
organisms, except against enterococci
• Synergistic with gentamicin against most
strains of S. aureus and enterococci
• Therapeutic serum concentrations:
– Peak 30-40 mg/L
– Trough 5-15 mg/L
Vancomycin
• Some controversy about necessity for
routinely monitoring plasma vancomycin
concentrations:
– Vancomycin exhibits concentration-independent killing,
and specific peak plasma concentrations have not been
correlated with efficacy.
– Monitor those at highest risk for therapeutic failure or
potential drug toxicity, which includes pediatric patients
who have high clearances and short half-lives
Vancomycin
• As a general rule, vancomycin is dosed with
an interval of approximately one half-life
• Peak level should be drawn 1 hour after a
1-hour infusion; trough level should be
drawn within 1 hour before the next dose
• Css max = [Css min] [(S)(F)(Dose)]
V
Vancomycin
• Vancomycin-induced ototoxicity has been
primarily reported in patients with
vancomycin concentrations > 80 mg/L.
• As a single agent, vancomycin is associated
with a low incidence of nephrotoxicity;
however, when it is combined with
aminoglycoside, the incidence may be as
high as 30%.
References
• Winter, Michael. Basic Clinical
Pharmacokinetics, 4th Ed. Baltimore: LWW,
2004.
• Pea F, Viale P et al. Pharmacokinetic
Considerations for Antimicrobial Therapy in
Patients Receiving Renal Replacement
Therapy. Clin Pharmacokinet 2007; 46 (12):
997-1038.