Pharmacokinetic parameters
PK parameters are mathematical values that, quantitatively, describe the
behavior of a drug in the body in relation to time (time course of a drug in
the body)
• Clearance (CL): the volume of plasma from which a drug is removed per unit
time
units of volume/time e.g. L/h
CL = Rate of elimination /plasma concentration
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Pharmacokinetic parameters
• Elimination half-life (t1/2): the time required for a concentration
(amount ) of a drug to decrease by half
units of time e.g. hours
• Volume of distribution (V): the apparent volume needed to
contain all the drug in the body
units of volume e.g. L
• First-order elimination rate constant (K): the fraction by
which the drug is eliminated per unit time
units of reciprocal of time e.g. 0.37 h-1
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Consider a drug having the following PK parameters:
will be
hour
off
trung
per
cleared
5L ofplasma
• CL: 5 L/h
The volume of plasma cleared of drug is 5 L in an hour i.e. 5 L of plasma is free
of drug in an hour
• V: 30 L
The amount of fluid need to contain all the drug to produce the observed
initial concentration is about 30 L
• t1/2: 5 h
The time required for the drug to drop to 50% of its initial concentration
within the body is 5 hours
• K: 0.25 h-1
About 0.25 (25%) of the drug is removed in an hour
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How pharmacokinetic parameters are derived?
Concentration versus Time Curve
ÑÑÉÉ
a
A drug plasma concentrations at various
times that sums up its movement in, around
and out of the body can be graphically
represented on a concentration versus time
graph
Distribution
Absorption
IV route
●---●
Other routes ●---●
Elimination
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Concentration versus Time Curve – Types of drug
movements in the body
Imost ofdray
high
hate ofeliminators is
concent
constant
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First order versus Zero order kinetics
The overall rate at which drug
movements in the body take place
and its changes due to various
factors are referred to as the order
of reaction or process
Time
First-order
(50 %)
Zero-order
(100 mg)
0
1000 mg
1000 mg
1
500 mg
900 mg
• First-order processes by which a
constant fraction of drug is
transported/metabolized in unit
time
2
250 mg
800 mg
3
125 mg
700 mg
4
62.5 mg
600 mg
• Zero-order processes by which a
constant amount of drug is
transported/metabolized in unit
time
5
31.25 mg
500 mg
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First-Order kinetics
• Most of drugs follow first-order
elimination kinetics
• The amount by which a drug plasma
concentration declines per unit time
is not constant but varies
Amount (mg)
1000 mg
2000 mg
3000 mg
Remaining in one half-life
(mg) (rate of elimination
is 50%)
500
1000
1500
• The higher the concentration, the
greater the rate of elimination
• The concentration declines
exponentially with time
Rate of elimination = CL* plasma concentration
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Zero-Order kinetics
• Few drugs follow zero-order
elimination kinetics
• The amount by which a drug plasma
concentration declines per unit time
is constant
Amount (mg)
1000 mg
2000 mg
3000 mg
Remaining in one half-life
(mg)
(elimination rate =100 mg)
900
1900
2900
• The change in concentration, has no
effect on the rate of elimination
• The concentration declines linearly
with time
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First-Order kinetics – Linear representation to
calculate PK parameters
order
The exponential decline at the eliminationfirst
phase (relationship
between concentration and time) can be transformed (log) to
produce a linear relationship describing the decline in
plasma concentration as
C = C0*e-Kt
ln C = ln C0-Kt
Where C is the concentration at a time (t)
C0 is the concentration at time zero
K is the elimination rate constant
Once C0 is known, the volume of distribution can be estimated
volume = amount (dose)/concentration -----V = dose /C0
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Pharmacokinetic parameters – Drugs obey first order kinetics
slope =
log y2 − log y1
x2 − x1
Slope=-K/2.303
then K = - slope *2.303
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First order
Zero order
↑ Cp → ↑rate of elimination
↑ Cp → NO ↑rate of elimination
Rate of elimination is
proportional to Cp
Rate of elimination is independent
of Cp
Half life is constant
Rate of metabolism is constant
Constant fraction is eliminated
Constant amount is eliminated
Most drugs follow this order
Few drugs follow this order
Cp vs time curve is exponential
Cp vs time curve is linear
90
Pharmacokinetic parameters
Time (h)
Example: The following pharmacokinetic
data are observed after an intravenous
dose of 1.5 g
1.0
1.5
2.0
3.0
4.0
6.0
8.0
10.0
Plasma
concentration
(mg/L)
324
255
210
157
129
95
74
57
91
Distribution phase
300
250
200
Elimination phase
150
100
50
0
0
2
4
6
Time (h)
8
10
12
Plasma concentration (mg/L) (log
scale)
Plasma concentration (mg/L)
350
1000
extrapolate line to time
zero give C0 = 232 mg/L
100
slope = -K/2.303
K = slope* 2.303
K= 0.13 /h
10
1
0
2
4
6
8
10
12
Time (h)
V = dose/C0 = 1500 mg/232 mg/L = 6 L
K= 0.13 /h
CL =V*K = 0.78 L/h
t1/2 = 0.693/K or
t1/2 = 0.693 * V/CL = 5.3 h
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Steady-state
8
Ii
If a drug is repeatedly administered at a constant-rate infusion, it will
accumulate in the body until input (administered amount) equals output
(eliminated amount) i.e. the drug blood concentration reaches a plateau i.e.
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steady-state concentration
Steady-state
• The time required to reach steady-state
No of
is about 4-5 half- lives. Why?
t
Amount
remaining
at one t1/2
1/2
• At steady-state:
Dose rate = Css*CL
ONE
important
Css: concentration at steady-state
After oral route only fraction (F) reaches
systemic circulation→ Dose rate = Css*CL/F
Starting
amount
%
achieved
0
-
100
-
1
50
150
50%
2
75
175
75%
3
87.5
187.5
87.5%
4
93.8
193.8
93.75%
5
97
-
96.76%
after 1 t½–50% drug is eliminated. 2 t½–75% (50 + 25) drug is
eliminated. 3 t½–87.5% (50 + 25 + 12.5) drug is eliminated. 4
t½–93.75% (50 + 25 + 12.5 + 6.25) drug is eliminated.
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Steady-state
Iiiii
Doubling the rate of infusion doubles steady state concentration but not
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the time to achieve it
Steady-state
• Time to reach steady state is dependent on the half-life (4-5 t1/2)
The longer the half-life the longer it takes to reach a steady state
• The concentration at SS is dependent on the dose and independent of
the t1/2
Thus, a loading dose is administered to reach the SS faster
• If the drug administration stops at any time, the plasma
concentration will decline at a rate dependent on the K and t1/2
PK parameters can be determined at such stage
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Loading dose and Maintenance dose
• For drugs with long t1/2 , initial large dose (loading dose) needed to
achieve target plasma concentration (Cp) quickly
• Maintenance dose is one that is to be repeated at specified intervals
after the attainment of target Cpss so as to maintain the same by
balancing elimination
Jose
bolusdose
dose to mumbree
to reachquicky
small
to thestadenstating furpatent
98
EXAMPLE
Drug x has long lifetime and only 10% cleared from the blood each day
Durg x works best when total amount in the body = 1g
241
So maintenance dose per day would be 100 mg
Maintenance dose approach
First day 100 mg and 10 mg cleared, leaving 90 mg
Second day 190 mg total, 19 mg cleared, leaving 171 mg
Third day 271 mg total, 27mg cleared, leaving 244 mg
IT TAKES MANY DAYS FOR THE TOTAL AMOUNT TO COME CLOSE TO 1G
Loading dose then maintenance dose approach
1 g taken the first day → full therapeutic effect
First day 1000 mg total , 100 mg cleared, leaving 900 mg
Second day 1000 mg total, 100 mg cleared, leaving 900 mg
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Loading dose and Maintenance dose
100
Pharmacokinetics calculations
Single dose calculation
Vd = D/C0
t1/2= 0.693/k → = 0.693*Vd/CL
CL =k*Vd
101
Case
A new cephalosporin antibiotic was given at a dose of 5mg/kg by a
single intravenous bolus injection to a 58-year-old man who weighs
75 kg. The antibiotic follows the pharmacokinetics for a onecompartment model and has an elimination half-life of 2 hrs. The
apparent volume of distribution is 0.28 L/kg.
1. What are the key pharmacokinetic parameters listed in this case?
2. What is the initial plasma drug concentration (Cop) in this patient?
3. What is the predicted plasma drug concentration (Cp) at 6hrs after the
dose is administered?
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