13. Volume of distribution, Clearance and Half-life Flashcards
Define volume of distribution. >
How can it be measured
What are the units
Volume of distribution (VD) is
the theoretical volume
into which a drug must disperse
in order to produce the
measured plasma concentration.
> It cannot be measured directly but instead it is derived from a log concentration–time graph where VD = Dose/C0
(see Chapter 10,
‘Exponential function’).
> Its units are typically mL.
What factors determine the volume of distribution of Drug
- > Lipid solubility of the drug.
2.
> Percentage plasma protein binding of the drug.
3.
> Percentage tissue protein binding of the drug.
4.
> Blood flow to the various tissues.
Define clearance
Constant / varied over time
What components take part
Sites
Derived
units
described
Clearance (Cl) is the
volume of plasma
completely cleared of
a substance per unit time.
> It is usually constant over
the therapeutic concentration range
because drug elimination systems
are not saturated (i.e. first-order kinetics).
> It is additive,
a function of elimination
by all participating organs such as
liver or kidney:
Cl systemic = Cl renal + Cl hepatic + Cl other.
> Kidney and liver are the
two most important sites for
drug elimination, but other sites
can include the
lungs,
muscle
and plasma.
> It can be derived from a concentration–time graph where Cl = Dose/AUC
(AUC = area under curve).
> Other equations used to calculate clearance include:
- Cl = rate of elimination/plasma concentration
- Cl = VD × k
- Cl = VD × (0.693/t½) (where 0.693 = ln2)
> It is used to describe elimination in first-order kinetics.
> Its units are typically mL/min.
Define half-life.
Derived from
Equations to calculate
How much elim after 5 t 1/2
what is reached after 5
> Half-life (t½) is the time taken
for the plasma concentration
of a substance to
reduce to half its original value.
> It can be derived from a
concentration–time graph.
> Equations used to calculate t½ include:
- t½ = 0.693 × VD/Cl
- t½ = 0.693/k
- t½ = 0.693τ
> After five half-lives,
elimination is 96.875% complete.
Steady-state conditions are typically
quoted to occur after five half-lives
(or three time constants).
> Used to calculate dosing schedules.
> Its units are typically minutes (min).
How are VD, Cl and t½ interrelated?
VD ∝ t½ × Cl
t½ ∝ VD/Cl
Cl ∝ VD/t½
How can VD, Cl and t½ be used to explain the different clinical effects of fentanyl and alfentanil?
> Fentanyl is significantly more
lipid soluble than alfentanil
(i.e. more potent)
and is therefore used in much smaller doses.
> Being more lipid soluble also
accounts for the higher VD of fentanyl
because the drug can better penetrate tissues.
> The differences in the onset
of effect can be explained
by the pKa values.
Both fentanyl and alfentanil are basic compounds, which means that they become increasingly ionised below their pKa.
At physiological pH 7.35
(which is above the pKa of alfentanil)
90% of alfentanil is in the un-ionised form
and
can therefore penetrate tissues easily
to produce a rapid effect.
For fentanyl, physiological pH is below its pKa and therefore the majority of this drug gets ionised such that only 9% remains in the un-ionised form and this explains its longer onset of effect.
> The clearance of alfentanil
is a lot slower than that of
fentanyl but despite this
it has a shorter duration of action
because its smaller VD ensures a
shorter t½.
Table 13.1 Pharmacokinetic comparison of fentanyl and alfentanil
Drug Fentanyl Alfentanil
Dose (μg/kg) 1 10
Onset (min) 5 1–2
Duration of action (min) 30 10
Lipid solubility +++ +
pKa 8.4 6.4
Percentage un-ionised 9 90
VD (L/kg) 4 0.8
Cl (mL/min) 500–1500 300–500
t½ (min) 360 120
