Pharmacokinetics: Lecture two

Intravenous Bolus
Administration
Anas Bahnassi PhD RPh

One compartment Model

LECTURE’S OBJECTIVES

Upon the completion of this lecture the student should be able to:
• Describe the different pharmacokinetic parameters.
• Determine pharmacokinetic parameters from either plasma or
urinary data.
• State the equation for plasma drug concentration as a function of
time.
• Calculate the corresponding plasma drug concentration at time t
• Calculate the intravenous bolus dose of a drug that will result in
a target (desired) plasma drug concentration at time t.
Anas Bahnassi PhD 2011 2

X
Assumptions
• One-compartment model.
Xu
• First-order process.
• Passive diffusion.
• No metabolism takes place
(elimination is 100% via renal
excretion)
• The drug is being monitored in blood
(plasma/serum) and urine.
3
Anas Bahnassi PhD 2011

IV Bolus Equations:


Pharmacokinetic Parameters

• Apparent volume of distribution (Vd).
• Elimination half-life (t1/2).
• Elimination rate constant (K0 or Kel).
• Systemic clearance (Cls).


Apparent volume of distribution
(Vd)
• Concentrations are usually measured not
masses.
• Vd is a proportionality constant whose sole
purpose is to relate the plasma
concentration (Cp) and the mass of drug (X)
in the body at a time.
• It is not a physical volume.


Vd Concept
Drug Concentration in Beaker Drug Concentration in Beaker
with charcoal

Dose = 10mg Dose = 10mg
Cp0 = 20mg/L Cp0 = 2mg/L
Vd= 500mL Vd= 5000mL

The concentration of KI is different although the volume of water
in both beakers is the same.


Calculating Vd
�� Apparent volumes
�� = of distribution are
�� given in units of
volume (e.g. mL) or
units of volume on a
body weight basis
(Lkg-1 body weight).


Elimination Half life (t1/2)

The time (h, min,
day, etc.) at which
the mass (or Semi-logarithmic Paper
amount) of
unchanged drug
becomes half (or
50%) of the initial
mass of drug.

Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009
10

Elimination Half life (t1/2)

When Cp = 0.5 (Cp)0
t = t1/2


Elimination Rate Constant (k)

Unit of k in first order process is reciprocal of time (h-1)

�� = �� + ��
Elimination
Rate
Constant
Metabolism
Rate
Excretion Constant
Rate
Constant


Elimination Rate Constant (k)
X0=
0.963
�� = = 0.173ℎ�� −1 250mg
4
125
%�� = ��100 = 50%
250 M1=
75 75mg
%�� = ��100 = 30%
250
50
%�� = ��100 = 20%
250 M2=
50mg
�� = ��%��. �� = ��. ��−��
�� = ��%��. �� = ��. ��−��

�� = ��%��. �� = ��. ��−�� Xu=
125mg

Drawing a best-fit line through the
Data


40

X = 61.827e-0.526t
35

30

25

20

15

10
RL paper
5

15
0
0 1 2 3 4 5 6 7 8 9 10 Anas Bahnassi PhD 2011

Calculating PK Parameters

From the SL graph ��0
t½= 1.3h �� =
��0
Cp0= 63mg/mL.
600000
�� = = 9523.8��
63
= 9.5238��

��. ��
�� =
��. ��


16

Use of Urinary Data

Amount remained
to
be excreted Rate of
Excretion
1. Urine collection is a non-invasive technique.
2. More convenient sample collection
3. Sample size is not restricting.
4. The sampling time reflects cumulative drug concentration
in urine collected over a period of time, rather than a drug
concentration at a discrete time.
5. Urinary data allows direct measurement of bioavailability,
both absolute and relative, without the need of fitting the
data to a mathematical model. 17

Use of Urinary Data
X
Cumulative amount ��
Xu
= ��
In Urine at time (t) ��
�� = ��0 (1 − �� −�� )

Administered dose
of drug
Excretion Rate
�� = ∞ Constant
�� = ��0

Amount Remaining
To be excreted
�� ∞ − �� = ��
= �� ℎ��
= �� Drug Totally
Drug Totally
Removed Unchanged
Removed Unchanged

Can not calculate
Volume of Distribution
19

Limitations
1. Keep obtaining urine samples until no
additional drug practically appears in the urine,
(t = 7 t½)
2. Urine samples can not be lost, or urine from
any samples used in the determination of Xu
(the exact volume of urine at each time interval
must be known)
3. A time-consuming method for a drug with a
long elimination half life.
4. There is a cumulative build up of error.


Dose = 80mg

The plot represents the cumulative quantity

of the medication from the collected urine
Drug Totally
Removed Unchanged
samples vs. the time.

21

The plot represents the amount remaining
to be excreted of the medication vs. time

Drug Totally
Removed Unchanged

�� = ��
Can not calculate

Volume of Distribution

22

Rate of Excretion
Method
��
= ��
�� = �� −��
��
�� = �� −��
average time
between
urine
collection
average rate
of excretion


The plot represents average rate of
excretion within the time interval between
samples collection vs. average time
between urine samples collection


0.693 0.693
�� = �� = = = 0.693ℎ�� −1

��½ 1

26

Questions:
What is the concentration of drug 0, 2 and 4 hours after a dose of 500
mg. Known pharmacokinetic parameters are apparent volume of
distribution, Vd is 30 liter and the elimination rate constant, kel is 0.2
hr-1 ?

From the plot seen calculate all
pharmacokinetic parameters that
you can calculate


Pharmacokinetics

Anas Bahnassi PhD RPh

abahnassi@gmail.com

http://www.linkedin.com/in/abahnassi

http://www.slideshare.net/abahnassi

http://bahnassi.coursesites.com

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Pharmacokinetics: Lecture two

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