Pharmacokinetics: Lecture two
-
Upload
anas-bahnassi- -
Category
Education
-
view
4.303 -
download
5
description
Transcript of Pharmacokinetics: Lecture two
Intravenous Bolus
Administration
One compartment Model
Anas Bahnassi PhD RPh
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
Anas Bahnassi PhD 2011 3
X
Xu • One-compartment model.
• 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.
Assumptions
Anas Bahnassi PhD 2011 4
IV Bolus Equations:
Anas Bahnassi PhD 2011 5
Pharmacokinetic Parameters
• Apparent volume of distribution (Vd).
• Elimination half-life (t1/2).
• Elimination rate constant (K0 or Kel).
• Systemic clearance (Cls).
Anas Bahnassi PhD 2011 6
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.
Anas Bahnassi PhD 2011 7
Vd Concept
Anas Bahnassi PhD 2011 8
The concentration of KI is different although the volume of water
in both beakers is the same.
Drug Concentration in Beaker Drug Concentration in Beaker
with charcoal
Dose = 10mg
Cp0 = 20mg/L
Vd= 500mL
Dose = 10mg
Cp0 = 2mg/L
Vd= 5000mL
Calculating Vd
Anas Bahnassi PhD 2011 9
𝑉 =𝑋
𝐶𝑝
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 amount) of unchanged drug becomes half (or 50%) of the initial mass of drug.
Anas Bahnassi PhD 2011 10
Semi-logarithmic Paper
Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009
Elimination Half life (t1/2)
Anas Bahnassi PhD 2011 11
When Cp = 0.5 (Cp)0
t = t1/2
Elimination Rate Constant (k)
Anas Bahnassi PhD 2011 12
Unit of k in first order process is reciprocal of time (h-1)
𝑘 = 𝑘𝑢 + 𝑘𝑚 Elimination
Rate
Constant
Excretion
Rate
Constant
Metabolism
Rate
Constant
X0=
250mg
M1=
75mg
M2=
50mg
Xu=
125mg
Elimination Rate Constant (k)
Anas Bahnassi PhD 2011 13
𝑘 =0.963
4= 0.173ℎ𝑟−1
%𝒆𝒙𝒄𝒓𝒆𝒕𝒆𝒅 =125
250𝑋100 = 50%
%𝒎𝒆𝒕𝒂𝒃𝒐𝒍𝒊𝒕𝒆𝟏 =75
250𝑋100 = 30%
%𝒎𝒆𝒕𝒂𝒃𝒐𝒍𝒊𝒕𝒆𝟐 =50
250𝑋100 = 20%
𝒌𝒖 = 𝟓𝟎%𝑿𝟎. 𝟏𝟕𝟑 = 𝟎. 𝟎𝟖𝟔𝟔𝒉𝒓−𝟏
𝒌𝒎𝟏 = 𝟑𝟎%𝑿𝟎. 𝟏𝟕𝟑 = 𝟎. 𝟎𝟓𝟏𝒉𝒓−𝟏
𝒌𝒎𝟐 = 𝟐𝟎%𝑿𝟎. 𝟏𝟕𝟑 = 𝟎. 𝟎𝟑𝟒𝟓𝒉𝒓−𝟏
Drawing a best-fit line through the
Data
Anas Bahnassi PhD 2011 14
Anas Bahnassi PhD 2011
15
X = 61.827e-0.526t
0
5
10
15
20
25
30
35
40
0 1 2 3 4 5 6 7 8 9 10
RL paper
Anas Bahnassi PhD 2011
16
From the SL graph
t½= 1.3h
Cp0= 63mg/mL.
𝑉𝑑 =𝑋0
𝐶𝑝0
𝑉𝑑 =600000
63= 9523.8𝑚𝑙
= 9.5238𝑙
𝑲 =𝟎. 𝟗𝟔𝟑
𝟏. 𝟑
Calculating PK Parameters
Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009
Anas Bahnassi PhD 2011
17
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.
Anas Bahnassi PhD 2011 18
Use of Urinary Data
X
Xu 𝑑𝑥𝑢
𝑑𝑡= 𝑘𝑢𝑋
𝑋𝑢 𝑡 = 𝑋0(1 − 𝑒−𝑘𝑢𝑡)
Cumulative amount In Urine at time (t)
Administered dose of drug
Excretion Rate Constant
𝒊𝒇 𝒕 = ∞
𝑋𝑢 = 𝑋0
Anas Bahnassi PhD 2011 19
Amount Remaining To be excreted
𝑿𝒖 ∞ − 𝑿𝒖 𝒕 = 𝐴𝑚𝑜𝑢𝑛𝑡 𝑅𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝑡𝑜 𝑏𝑒 𝑒𝑥𝑐𝑟𝑒𝑡𝑒𝑑 = 𝐴𝑚𝑜𝑢𝑛𝑡 𝑖𝑛 𝑡ℎ𝑒 𝑏𝑜𝑑𝑦
= 𝑿𝒕 Drug Totally Removed Unchanged
Can not calculate Volume of Distribution
Drug Totally Removed Unchanged
Anas Bahnassi PhD 2011 20
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.
An
as B
ahn
assi
Ph
D 2
011
21
Basic Pharmacokinetics: S. Jambhekar , Phillip Breen 2009
The plot represents the cumulative quantity of the medication from the collected urine
samples vs. the time.
Dose = 80mg
Drug Totally Removed Unchanged
An
as B
ahn
assi
Ph
D 2
011
22
The plot represents the amount remaining to be excreted of the medication vs. time
Drug Totally Removed Unchanged
Drug Totally Removed Unchanged
𝑘 = 𝑘𝑢
Can not calculate Volume of Distribution
Anas Bahnassi PhD 2011 23
Rate of Excretion
Method
𝒅𝒙𝒖
𝒅𝒕= 𝒌𝒖𝒙
𝒙 = 𝒙𝒐𝒆−𝒌𝒖𝒕
𝒅𝒙𝒖
𝒅𝒕= 𝒌𝒖𝒙𝒐𝒆−𝒌
𝒖𝒕
average rate of excretion
average time between
urine collection
Anas Bahnassi PhD 2011 24
The plot represents average rate of excretion within the time interval between
samples collection vs. average time between urine samples collection
An
as B
ahn
assi
Ph
D 2
011
25
An
as B
ahn
assi
Ph
D 2
011
26
𝑘 = 𝑘𝑢 =0.693
𝑡½=
0.693
1= 0.693ℎ𝑟−1
Anas Bahnassi PhD 2011 27
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
http://www.linkedin.com/in/abahnassi
http://bahnassi.coursesites.com
attribution – non-commercial – share alike
Anas Bahnassi PhD RPh
Pharmacokinetics
http://www.slideshare.net/abahnassi