elementary pharmacokinetics jap
TRANSCRIPT
Learning Objectives
Following this lecture, students should be able to:
Define what is meant by a minimum effective concentration (MEC),
maximum tolerated concentration (MTC) and the therapeutic ratio (TR)
Understand what is meant by ‘first order’ elimination and the half-life (t½) of
a drug
Define what is meant by the clearance (Cl) of a drug
Appreciate that the rate of elimination of a drug (showing first order
kinetics) is the product of its plasma concentration (Cp) and clearance
Understand the principles of dosing to steady state by i.v. and oral
administration
Define what is meant by the volume of distribution (Vd) and appreciate its
important in calculating a loading dose (LD)
Understand what is meant by zero order elimination
Drug Efficacy and Safety
To achieve an effect, a drug must reach a critical concentration
in the plasma (i.e. Minimum Effective Concentration; MEC) but
ideally be well below that causing significant unwanted effects
(i.e. Maximum Tolerated Concentration)
MTC
MEC
Pla
sm
a c
on
ce
ntr
ati
on
(Cp
)
t
‘Safe’ drug
‘Therapeutic window’
t
MTC
MEC
Cp
‘Unsafe’ drug
‘Therapeutic window’
The Therapeutic Ratio (or Index): TR =MTC
MEC
‘Unsafe’ drugs (low ratio)‘Safe’ drugs (high ratio, in
most individuals, or situations)
• Penicillins
• Benzodiazepines
• Cardiac glycosides
• Barbiturates
A simple starting point is to consider the human body as a single,
well-stirred, compartment of volume Vd. Drug is added to the
compartment by absorption at rate Kabs and removed by elimination
at rate Kel
Single well stirred
compartment of
volume, Vd
absorption Kabs
elimination Kel
Dose, D
(Oral)
Dose, D
(iv)
absorption is by-passed
• the initial concentration (Co) =
D/Vd (concentration = mass / volume)
• the concentration at a later
time t (Ct) will depend upon Kel
If drug at dose D is added
rapidly by intravenous (iv)
injection
Pharmacokinetics is the mathematical
analysis of all drug disposition factors
(absorption, distribution, metabolism and
excretion)
The half-life (t½) is the time
taken for Ct to fall by 50%.
It is inversely related to Kel,
i.e.
t½ = 0.69/Kel
Time (half-lives)
t½ t½ t½
Pla
sm
a c
on
ce
ntr
ati
on
(C
p)
(arb
un
its
)
C0 = D/Vd
100
75
25
50
Ct = C0e-Kel.t
Most drugs exhibit first-order kinetics
where the rate of elimination is directly
proportional to drug concentration
Drug concentration falls exponentially
according to the equation:
1 2 3
For drugs that exhibit first order kinetics, the dose administered changes Cp in direct proportion, but does not affect Kel or t½
Time (h)
0 2 4 6 8 10 12 14 16 18 20 22
Cp (
Arb
. u
nit
s)
0
10
20
30
40
50
60
70
80
90
100
Dose X
Dose 2X
Clearance (Cl) Probably the single most important pharmacokinetic parameter
‘The volume of plasma cleared of drug in unit time’
‘A constant relating the rate of elimination to plasma concentration’
Applies only to drugs that exhibit first order kinetics (the majority)
Rate of elimination Cp
Time (half-lives)
t½ t½ t½
Pla
sm
a c
on
ce
ntr
ati
on
(C
p)
100
75
25
50
1 2 3
Time (half-lives)
t½ t½ t½
Pla
sm
a c
on
ce
ntr
ati
on
(C
p)
100
75
25
50
1 2 3
t½ t½ t½
Pla
sm
a c
on
ce
ntr
ati
on
(C
p)
100
75
25
50
1 2 3
Rate of elimination = constant x Cp
Clearance is the constant
Rate of elimination = Cl x Cp
Units are l/hr
Cl determines the
maintenance dose rate
(dose per unit time
required to maintain a
given plasma
concentration)
Dosing to Steady State (i.v.)
At steady state (ss): rate of drug administration = rate of drug
elimination
Rate of elimination at steady state = Cl x CpSS
rate of administration must also = Cl x CpSS
Time
Cp
MTC
MEC
Cpss
Constant IV infusion
Rate of administration and
elimination are equal
CpSS =maintenance dose rate
Cl
Cl is the sum of all clearance processes
Cl (total) = Cl (renal) + Cl (hepatic) + Cl (other)
Input Output
Time (h)0 4 8 12 16 20 24
Cp (
ng
ml-1
)
0
50
100
150
200
Clp = 20 ml min-1
Vd = 6.95 l
240 g h-1
120 g h-1
60 g h-1
Infusion rate (g h-1)
0 60 120 180 240
Css (
ng
ml-1
)
0
50
100
150
200
Drug Dosing (i.v. continued)
For drugs that exhibit first order kinetics, the steady state (ss)
plasma concentration (Css) is linearly related to the infusion rate
The time to reach Css is determined by t½, but not the infusion
rate. Css is reached after approximately 5 half-lives
t½
Dosing to steady state with intermittent oral administration involves
the same principles as continuous infusion, but plasma concentration
fluctuates about an average steady state value (Css (average))
Cp
t
Drug Dosing (Oral, or per os)
MTC
MEC
Css(average) =F x Dose
Clp x dosage interval
where F = the oral bioavailability
i.e. the fraction of the drug
administered that enters the
systemic circulation
Do
se
Steady state(Css (average))
Rate
of
dru
g e
nte
rin
g p
las
ma
>
rate
le
avin
g p
las
ma
Rate
of
dru
g e
nte
rin
g p
las
ma
<
rate
le
avin
g p
las
ma
Ra
te o
f d
rug
en
teri
ng
pla
sm
a =
rate
le
avin
g p
las
ma
Therapeutic
range
Solid line i.v. 50 mg per hour
Dashed line po 300 mg 6 hourly (= 50 mg per hour)
The half life of theophylline is 6 hr (range 4 – 8 hr)
It takes five half lives to reach steady state
Example of IV and Oral Administration of the Same DrugSteady state pharmacokinetics for theophylline
The Volume of Distribution (Vd)
‘The volume into which a drug appears to be distributed with a
concentration equal to that of plasma’
‘A proportionality constant relating the plasma concentration
(Cp) to the amount of drug in the body (Ab)’
Ab = Vd x Cp
Lo
gC
p
Time
DeterminationCpo
At time zero Ab = dose
then Cpo = dose/Vd
and Vd = dose/ Cpo
units Volume (l) or Volume (I)/kg
Nb. This is no more than a restatement of: concentration (Cp) = mass (Ab) / volume (Vd)
The Volume of Distribution (Vd) and Loading Dose
A loading dose (LD) is an initial higher dose of a drug given at the
beginning of a course of treatment before stepping down to a lower
maintenance dose
Employed to decrease time to steady state for drugs with long half
lives (e.g. digoxin, phenytoin)
Can be estimated from the Vd of the drug
For i.v. administration For oral adminstration
LD = Vd x Target Cp LD = Vd x Target Cp
F
N.B. Vd does not correspond to a real anatomical compartment
Vd can change in disease (e.g. heart failure, liver disease).
Adjustment of dosage may be necessary, particularly for drugs
with a low TR
Digoxin With and Without Loading Dose
Marcus et al. (1966) Circulation 34: 1864-875
Digoxin t½ 36 hr
Time to Cpss without loading dose 6 to 7.5 days
Half Life (t½)
‘The time for the concentration of drug in plasma
(or the amount of drug in the body) to halve’
Time (half-lives)
t½ t½ t½
Pla
sm
a c
on
ce
ntr
ati
on
(C
p)
100
75
25
50
1 2 3
Time (half-lives)
t½ t½ t½
Pla
sm
a c
on
ce
ntr
ati
on
(C
p)
100
75
25
50
1 2 3
t½ t½ t½
Pla
sm
a c
on
ce
ntr
ati
on
(C
p)
100
75
25
50
1 2 3
t½ gives an index of: the time course of drug accumulation
the time course of drug elimination
choice of dose interval
t½ Vd
Cl
t½ =0.693 x Vd
Cl
(In 2)
• t½ is dependent upon Vd and
Cl
• Vd and Cl are the independent
variables
Zero Order (or Saturation) Kinetics
A few drugs of clinical significance (e.g. ethanol, phenytoin) are
initially eliminated at a constant rate, rather than at a rate that is
proportional to their concentration (this can occur, for example,
when the plasma concentration of a drug is greater than the Km of an
enzyme that metabolises it)
Elimination is initially zero order,
converting to first order at low
concentration
Time (h)0 2 4 6 8 10 12 14 16 18
Cp (
mg
l-1
)
0
20
40
60
80
100
120zero order
first order
Plasma steady-state concentration
is not simply linearly related to
dose rate
Dose rate (mg day-1
)
0 100 200 300 400 500 600
Css (
mg
l-1
)
0
10
20
30
40
50
60
70saturation