Transcript 510-08Pkin - dan

Pharmacokinetics
• Introduction
– Describes quantitatively the rates of the steps of drug
disposition (i.e.- absorption, distribution, elimination)
– encompasses ADME plus clearance
– clearance: the removal of a drug in units of volume/time
– quantitative data important to detail fate of the drug, but
also to be able to predict doses, routes, etc.
– allows individual adjustment based on individual
pharmacokinetic assessment
Pharmacokinetics
• Relation of dose, plasma drug concentration,
and effect
– a specific dose of a drug should produce a specific
effect:
• Dosage  Conc. in plasma water  Conc. At site of action 
Intensity of effect
– Intensity of effect related to drug conc. at receptor sites
– Duration of action related to how long drug conc. at
receptor site remains high enough to provide response
–Conc. at receptor sites changes as drug enters,
distributes, and is eliminated
Pharmacokinetics
• Difficulty in Quantitation
– Due to the difficulty of properly modeling so many
processes occurring simultaneously
– Often make certain assumptions which do not greatly
affect the data such as:
• Intensity of effect is correlated to the concentration of free drug
in plasma
– not always true – may be very difficult with irreversibly acting
drugs, drugs which develop tolerances, or drugs which act
synergistically
Pharmacokinetics
• Modeling
– Used whenever the fate of a drug is described either
qualitatively or quantitatively.
– Mathematical model encompassing known factors about
drug (such as distribution, etc) hypothesized first, then
proven (or modified) by real-life observation.
– One-compartment model easiest to use, and many
drugs follow this scheme.
• Assumes a single compartment which is in equilibrium which
accounts for drug in plasma, and various tissues.
– Two (or more) compartment models more difficult to
model.
• Seen when drug moves into tissues and is handled at different
rates than central plasma compartment.
Drug Fate in Body
One Compartment Model
One Compartment Model
• Mathematics
– Assuming first-order disposition (rate at any time is
proportional to concentration of the drug)
– Therefore, after IV administration, plasma concentration
(Cp) decreases at a rate proportional at all times (t) to the
concentration at that time:
• -dCp/dt = kCp (where k = rate constant)
• solving, Cp = C0 e-kt (where C0 is the initial
concentration, e is the natural log base, and Cp is the
concentration in plasma at any time t).
• OR, log Cp = logC0 – kt/2.303
One Compartment Model
One Compartment Model
• Mathematics
– From the dose given, the volume of distribution can also
be calculated:
• Vd = D0/C0
– The elimination half-life would then be:
• t1/2 = 0.693/k ( 0.693 = ln 2)
Two Compartment Model
• Involves both distributive and elimination
phases normally.
• Log plot does not give a single straight line,
but instead shows two phases.
• So now have a central compartment (ex.plasma), and another compartment (ex.tissue).
• Can be described mathematically by two
differential equations.
Two Compartment Model
Two Compartment Model
Absorption and Elimination
Absorption Curve
Absorption and Elimination
Rates of Processes
• Have been assuming first-order rate kinetics
so far.
• This is usually ok, but what happens if a
process (ex.- elimination) is dependant on a
carrier or enzyme that may become
saturated?
– Rate now no longer dependant on concentration, but
instead becomes constant, at least until concentration falls
below saturation.
– This is termed zero-order kinetics, where the rate is
independent of the concentration.
Rates of Processes
Repeated Drug Administration
Bioavailability
• Definitions:
–Bioavailability – percentage of a drug or drug product
that enters the general systemic circulation.
•Includes not only amount entering body, but also rate of entry
–Bioequivalence – comparable bioavailability between
drugs.
–Therapeutic equivalence – comparable clinical
effectiveness and safety between similar drugs.
• Mathematics
–Bioavailability = F = AUC (oral) / AUC (IV)
Bioavailability
Volume of Distribution
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Vd = D/C0
D = amount of Drug in the body
C0 = initial plasma concentration
The volume of distribution, Vd, is the
apparent or “virtual” volume into which a
drug distributes.
Volume of Distribution
• Can Vd be larger than the total plasma
volume in the body?
– heparin = 5 liters (plasma only)
– chlordiazepoxide = 28 liters
(extracellular water)
– imipramine = 1600 liters
(highly lipid soluble)
•Note: knowledge of the Vd is also important
in estimating the loading dose.
Clearance
• Introduction
– Quantitative measure of the removal of endogenous or
exogenous substances from the body or a specific organ.
– Examples include:
•Hepatic biotransformation
•Renal excretion
•Fecal excretion
•Lung exhalation
– Can be mathematically modeled to help define proper
dosing regimes.
Total Body Clearance
• Cltot = k Vd , where:
– Cltot = total body clearance
– k = first order elimination rate constant
– Vd = apparent volume of distribution
• Cltot = D / AUC
– Assumes drug is completely absorbed (IV)
– D = dose of drug
– AUC = area under plasma conc. (y) vs time curve (x)
– If not completely absorbed, Cltot = F D / AUC, where F is
the fraction ‘absorbed’ (bioavailability)
IV AUC
Dosage for IV Infusion
• Goal is to provide a constant plasma level
while supplying drug at the same rate as
elimination.
• Q = k Vd Cpss , where:
– Q = amount of drug supplied per unit time
– k = elimination rate constant
– Vd = apparent volume of distribution
– Cpss = plasma concentration at steady state
• Since Cltot = k Vd, then Q = Cltot Cpss
Loading Dose
• Used to reach steady state plasma
concentration (Cpss) immediately, instead of
waiting the normal 5 half-lives.
• L = Vd Cpss , where:
– L = loading dose (amount of drug)
– Vd = apparent volume of distribution
– Cpss = plasma concentration desired at steady state
Repeated IV Dosing
• Can not maintain a constant Cpss, but
instead maintain an average Cpss.
• Dosing interval will determine severity of
fluctuation above and below average Cpss.
• Cpss = (Dm / Tm) / Cl , where:
– Dm = maintenance dose (amount)
– Tm = maintenance dose interval
• Dm = k Vd Cpss Tm (rearranging by Cl = k Vd)
Ideal Dosing Regimen
• Determine the maintenance dose which will
keep plasma level in therapeutic window:
– Dm = (Cptox – Cpther) Vd
– Tm = (ln Cptox – ln Cpther) / k
= (2.3 / k) log (Cptox / Cpther)
= 3.32 t1/2 log (Cptox / Cpther)
• To determine a loading dose:
– L = Vd Cptox
IV AUC
Practical Dosing Regimen
• Maintenance doses are frequently given at
intervals equal to their t1/2 , but must also be
given at manageable times (ex. – q4h, q6h,
q12h, qd).
•Mathematically, giving a dose at intervals of
it’s t1/2 yields a Cpmax = 2Cpmin, which is a
100% fluctuation.
• Obviously more frequent dosing would be
preferred to diminish fluctuations, but may not
be critical.
Practical Dosing Regimen
• Drugs with a t1/2 less than 6 hours require a
very wide therapeutic window to use them in
repeated doses.
• Drugs with narrow therapeutic windows
should be given by continuous infusion.
•To utilize repeated oral dosing, one must take
bioavailability (F, the fraction entering general
systemic circulation) into all calculations.
Clearance By Specific Organs
• Clearances are additive.
– Cltot = ClH + ClR + …
• Amount of drug removed by an organ
dependant on perfusion and extraction ratio:
– E = (Ca – Cv) / Ca , where:
•E = extraction ratio
•Ca = concentration in arterial inflow
•Cv = concentration in venous outflow
Clearance By Specific Organs
• By taking blood flow into account,
– Cltissue = Qtissue E , where Q = tissue blood flow
– Then, ClH = QH (Ca – Cv) / Ca
• First pass effect can also be described as:
– FH = 1 – E , where:
•FH = the bioavailability fraction due to first pass
• First pass may be saturable, and like all
liver metabolism may increase due to enzyme
induction.
Clearance By Specific Organs
• High Extraction Ratio
–ClH controlled by blood flow rate
–Strong first-pass effect
–Plasma protein binding may facilitate clearance
• Low Extraction Ratio
–ClH controlled by intrinsic clearance
–Biotransformation limited by diffusion
–Plasma protein binding reduces clearance
–Sensitive to enzyme inhibition and induction
Clearance By Specific Organs
• For Kidneys:
–Rate of renal excretion = Rate of filtration + Rate
of secretion – Rate of reabsorption
–ClR = (Excreted amount / Time Interval)
Plasma Concentration
• For Biliary Excretion:
–ClB = (Conc. in bile / Conc. In plasma) Bile flow
–Bile flow normally 0.5 – 0.8 ml/min.