5 Quantitive Pharmacokinetics Flashcards
concentration =
mass/ volume
Volume of Distribution, VD
Used to estimate dose required to result in a certain [drug] in plasma
Volume of Distribution, VD
VD is the (apparent) volume of distribution.
The volume of plasma that would be required to contain the drug dose at the concentration measured in plasma.
Can be greater than total volume of a human due to tissue binding ! eg VD for amiodarone = 7000 L
Units: either L or can be expressed as L/Kg (to correct for different size patients)
Dose =
C VD
K is..
the elimination rate constant
Cl
clearance - the volume of plasma cleared of drug per unit time
Ca > Cv or Ca < Cv
The concentration of the drug in the blood leaving the liver will be lower
Ca > Cv
Amount of drug entering/minute =
QCa
Amount of drug leaving/minute =
QCv
Extraction ratio =
E = Ca-Cv/ Ca
E = 1 all eliminated E= 0 none eliminated
What is the extraction ratio
The extraction ratio is the fraction of drug entering a tissue that is eliminated
Rate of elimination =
blood flow rate x fraction of blood cleared of drug blood x Conc of drug in blood
Cl x C
Volume of distribution is..
volume that it appears the drug is dissolved in
Clearance varies with..
age and disease
Dose =
Cl x AUC∞
By measuring AUC∞ we can calculate Cl
Half life, t1⁄2
The time required for elimination of half of the absorbed drug
First order
– The Rate is proportional to “one variable” (hence “first”) – Here Rate depends on [Drug]
Rate α [Drug]
Rate = k [Drug]
(if [Drug] doubles, so does the rate)
Zero order
– The rate is constant
– It depends on “zero variables” (hence “Zero order”)
Rate is constant and doesn’t change with [Drug]
Rate = k
(if [Drug] doubles, rate stays the same)
First order drug elimination following intravenous bolus administration
C=C0e-kt
C0 = concentration of drug in plasma at t=0 (immediately after administration) k = elimination rate constant, fraction of drug eliminated per minute k = 0.1 min-1 10% of drug is eliminated per minute
k =
- slope x 2.303
kt1⁄2 =
ln2
VD =
Dose/ C0
ASSUMING: first order conditions, no non-linear PK, fast absorption and distribution
• Doubling the dose..
extends exposure above a certain concentration by t1⁄2
Relationship of Clearance and elimination rate constant
- k = elimination rate constant,
- k = fraction of drug eliminated per minute
k = Cl/ VD
K is the fraction of the drug thats eliminated per min
larger volume of distribution results in..
slower elimination
Half life depends on..
clearance and volume distribution
t1/2 =
0.693 x VD / Clearance
Effects on Volume of Distribution
- Ageing
- Obesity
- Pathologic fluid
How do these effect half-life
Aging (decreased muscle mass → decreased distribution)
Decreased
Obesity (increased adipose mass → increased distribution)
Increased
Pathologic fluid (increased distribution) increased
Effects on Clearance
- Cytochrome P450 induction
- Cytochrome P450 inhibition
- Cardiac failure
- Hepatic failure
- Renal failure
How do these effect half-life
Cytochrome P450 induction (increased metabolism)
Decreased
Cytochrome P450 inhibition (decreased metabolism)
Increased
Cardiac failure (decreased clearance) Increased
Hepatic failure (decreased clearance) Increased
Renal failure (decreased clearance) Increased
Intravenous Infusion
• Drug delivered over minutes-hours – allows precise and controlled exposure – adjust concentration – stop if required – short infusion sometimes used to reduce Cmax and adverse events following rapid bolus injection
Intravenous Infusion
• Drug concentration increases..
• Drug concentration increases to a plateau value Css
– rate of elimination = rate of infusion
C = Css(1-e-kt)
Intravenous Infusion
Calculation of infusion rate
•At plateau (“steady state concentration): Rate of elimination = Rate of infusion
•Rate elimination = Cl x Css
k = Cl VD
•so if we know Cl and the Css we wish to achieve we can calculate the required infusion rate
•Required rate of infusion Rinf = Cl x Css
Intravenous Infusion
Loading Dose
- Useful to quickly reach Css
- bolus iv dose
- Loading dose = CssVD
Intravenous Infusion
the longer the half life..
the longer it will take to get to the steady state
Intravenous Infusion
- Plateau concentration determined by..
- Plateau concentration determined by infusion rate and clearance
Rinf = Cl x Css Css = Rinf/Cl
Increasing the infusion rate will increase the final Css
Intravenous Infusion
- Time to reach plateau depends on..
- Time to reach plateau depends on the elimination constant (or t1/2).
Increasing the infusion rate will NOT REDUCE the time to reach Css because Css will be increased.
• Linear pharmacokinetics
– pharmacokinetic parameters don’t change with dose
– increasing dose increases exposure (AUC Css etc) proportionately
• Non-linear pharmacokinetics
– Pharmacokinetic parameters change with dose of drug
– increasing dose has a disproportionate effect on exposure
» eg exposure may be higher than expected because a metabolising enzyme is saturated
» eg exposure may be lower than expected because VD increases (eg drug accumulates in a different compartment at higher dose)
Rate of increase of drug in body =
Rate of absorption - Rate of elimination
Effect of dose & absorption rate on concentration profile
Increased dose results in
– increased Cmax and AUC
– no effect on Tmax
Effect of dose & absorption rate on concentration profile
Changing absorption kinetics results in
– eg different formulation, p.o. admin with food
– Cmax and Tmax altered
Effect of dose & absorption rate on concentration profile
Absorption can become..
rate-limiting
– usually elimination (disposition) is rate limiting
– but in some cases absorption is so slow that this becomes limiting:
» declining phase represents decrease absorption and elimination
» elimination rate = absorption rate
kel =
Clearance / VD
independent of dose
Bioavailability , F
• i.v. administration – all of the dose is bioavailable – F=1 (sometimes expressed as F=100% )
• Non i.v. – some drug may not reach systemic circulation
– incomplete absorption
» insufficient time, poor dissolution, poor permeability
– metabolism before absorption
» eg p.o. : gut flora, enzymes in gut wall, first pass metabolism
– F<1
• amount reaching systemic circulation = F x Dose
How can we measure bioavailability, F ?
Fpo =
Doseiv AUCpo/ Dosepo AUCiv
Repeated doses
2nd dose of drug is given before the 1st one has been eliminated. Thats why 2nd dose is higher
Repeated dose equation
dose =
Dose = t Cl Css,av/ F
Css,av depends on..
dose & frequency
Loading Dose
– an initial “high” dose of drug to quickly plasma drug concentration to the desired level
– particularly important for drugs with large VD
Doseloading = VD Css/ F
Maintenance dose
– once desired plasma drug concentration is achieved, them maintenance dose compensates for drug elimination
Dosemaintenance = t Cl Css, av/ F
