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Principles of Pharmacokinetics
Pharmacokinetics of IV Administration, 1-Compartment
Principles of Pharmacokinetics
Pharmacokinetics of IV Administration, 1-Compartment
Karunya Kandimalla, [email protected]
Karunya Kandimalla, [email protected]
2
ObjectivesObjectives
• Be able to:• To understand the properties of linear models
• To understand assumptions associated with first order kinetics and one compartment models
• To define and calculate various one compartment model parameters (kel, t½, Vd, AUC and clearance)
• To estimate the values of kel, t½, Vd, AUC and clearance from plasma or blood concentrations of a drug following intravenous administration.
• Be able to:• To understand the properties of linear models
• To understand assumptions associated with first order kinetics and one compartment models
• To define and calculate various one compartment model parameters (kel, t½, Vd, AUC and clearance)
• To estimate the values of kel, t½, Vd, AUC and clearance from plasma or blood concentrations of a drug following intravenous administration.
3
Recommended ReadingsRecommended Readings
• Chapter 3, p. 47-62• IV route of administration
• Elimination rate constant
• Apparent volume of distribution
• Clearance
• Chapter 3, p. 47-62• IV route of administration
• Elimination rate constant
• Apparent volume of distribution
• Clearance
4
Kinetics From the Blood or Plasma DataKinetics From the Blood or Plasma Data
Pharmacokinetics of a drug in plasma or blood
Pharmacokinetics of a drug in plasma or blood
Absorption (Input)Absorption (Input) DispositionDisposition
DistributionDistribution EliminationElimination
ExcretionExcretion MetabolismMetabolism
5
Disposition Analysis (Dose Linearity)Disposition Analysis (Dose Linearity)
6
Disposition Analysis (Time Variance)Disposition Analysis (Time Variance)
0
5
10
15
20
25
30
35
40
0 5 10 15 20
Time (hr)
Pla
sm
a c
on
ce
ntr
atio
n (m g
/ml) 1st Adminitration
2nd Administration
3rd Administration
7
Linear DispositionLinear Disposition
• The disposition of a drug molecule is not affected by the presence of the other drug molecules
• Demonstrated by:a) Dose linearity
Saturable hepatic metabolism may result in deviations from the dose linearity
b) Time invariance
Influence of the drug on its own metabolism and excretion may cause time variance
• The disposition of a drug molecule is not affected by the presence of the other drug molecules
• Demonstrated by:a) Dose linearity
Saturable hepatic metabolism may result in deviations from the dose linearity
b) Time invariance
Influence of the drug on its own metabolism and excretion may cause time variance
8
Disposition ModelingDisposition Modeling
• A fit adequately describes the experimental data
• A model not only describes the experimental data but also makes extrapolations possible from the experimental data
• A fit that passes the tests of linearity will be qualified as a model
• A fit adequately describes the experimental data
• A model not only describes the experimental data but also makes extrapolations possible from the experimental data
• A fit that passes the tests of linearity will be qualified as a model
9
One Compartment Model (IV Bolus)One Compartment Model (IV Bolus)
• Schematically, one compartment model can be represented as:
Where Xp is the amount of drug in the body, Vd is the volume in which the drug distributes and kel is the first order elimination rate constant
• Schematically, one compartment model can be represented as:
Where Xp is the amount of drug in the body, Vd is the volume in which the drug distributes and kel is the first order elimination rate constant
Drug in Body
Drug in Body
Drug Eliminated
Drug Eliminated
Xp = Vd • C
kel
10
One Compartment Data (Linear Plot)One Compartment Data (Linear Plot)
0
5
10
15
20
25
30
35
0 5 10 15 20
Time (hr)
Pla
sm
a c
on
ce
ntr
atio
n (m g
/ml)
11
One Compartment Data (Semi-log Plot)One Compartment Data (Semi-log Plot)
0.1
1
10
100
0 5 10 15 20
Time (hr)
Pla
sm
a c
on
ce
ntr
atio
n (m g
/ml)
12
Two Compartment Model (IV Bolus)Two Compartment Model (IV Bolus)
• For both 1- and 2-compartment models, elimination takes place from central compartment
• For both 1- and 2-compartment models, elimination takes place from central compartment
Drug in Central
Compartment
Drug in Central
Compartment
Drug Eliminated
Drug Eliminated
Drug in Peripheral
Compartment
Drug in Peripheral
Compartment
kel
Blood, kidneys,
liver
Fat, muscle
K 12
K 21
13
Two Compartment Data (Linear Plot)Two Compartment Data (Linear Plot)
0
2
4
6
8
10
12
14
16
18
0 5 10 15
Time (hr)
Pla
sm
a c
on
ce
ntr
atio
n (m g
/ml)
14
Two Compartment Data (Semi-log Plot)Two Compartment Data (Semi-log Plot)
0.1
1
10
100
0 5 10 15
Time (hr)
Pla
sm
a c
on
ce
ntr
atio
n (m g
/ml)
15
One Compartment Model-AssumptionsOne Compartment Model-Assumptions
• 1-Compartment—Intravascular drug is in rapid equilibrium with extravascular drug• Intravascular drug [C] proportional to
extravascular [C]
• Rapid Mixing—Drug mixes rapidly in blood and plasma
• First Order Elimination Kinetics:• Rate of change of [C] Remaining [C]
• 1-Compartment—Intravascular drug is in rapid equilibrium with extravascular drug• Intravascular drug [C] proportional to
extravascular [C]
• Rapid Mixing—Drug mixes rapidly in blood and plasma
• First Order Elimination Kinetics:• Rate of change of [C] Remaining [C]
16
Derivation-One Compartment ModelDerivation-One Compartment Model
Bolus IV KelCentral Compartment (C)
303.2loglog
lnln
equation above thegLinearizin
tat time and 0 tat time
between equation above thegIntegratin
0
0
0
0
tKCC
tKCC
tKeCC
CC
dtKC
dC
CKdt
dC
el
el
el
el
el
303.2loglog
lnln
equation above thegLinearizin
tat time and 0 tat time
between equation above thegIntegratin
0
0
0
0
tKCC
tKCC
tKeCC
CC
dtKC
dC
CKdt
dC
el
el
el
el
el
17
IV Bolus Injection: Graphical Representation Assuming 1st Order KineticsIV Bolus Injection: Graphical Representation Assuming 1st Order Kinetics
• C0 = Initial [C]
• C0 is calculated by back-extrapolating the terminal elimination phase to time = 0
• C0 = Initial [C]
• C0 is calculated by back-extrapolating the terminal elimination phase to time = 0
C0 = Dose/Vd C0 = Dose/Vd
Slope = -K/2.303Slope = -Kel/2.303
Concentration versus time, semilog paper
18
Elimination Rate Constant (Kel)Elimination Rate Constant (Kel)
• Kel is the first order rate constant describing drug elimination (metabolism + excretion) from the body
• Kel is the proportionality constant relating the rate of change of drug concentration and the concentration
• The units of Kel are time-1, for example hr-1, min-1 or day-1
• Kel is the first order rate constant describing drug elimination (metabolism + excretion) from the body
• Kel is the proportionality constant relating the rate of change of drug concentration and the concentration
• The units of Kel are time-1, for example hr-1, min-1 or day-1
CKdt
dCel CK
dt
dCel
19
Half-Life (t1/2)Half-Life (t1/2)
//2/1
2/1
2/10
0
693.02ln
2/12
1ln
2
12
ee
el
el
KKt
tKel
tKe
tKeCC
//2/1
2/1
2/10
0
693.02ln
2/12
1ln
2
12
ee
el
el
KKt
tKel
tKe
tKeCC
• Time taken for the plasma concentration to reduce to half its original concentration
• Drug with low half-life is quickly eliminated from the body
• Time taken for the plasma concentration to reduce to half its original concentration
• Drug with low half-life is quickly eliminated from the body
t/t1/2% drug
remaining
1 50
2 25
3 12.5
4 6.25
5 3.125
20
Change in Drug Concentration as a Function of Half-LifeChange in Drug Concentration as a Function of Half-Life
0
20
40
60
80
100
120
t = 0 1 2 3 4 5 6 7
Number of Half-Lives
Pe
rce
nt
of
Dru
g R
em
ain
ing
% Remaining
21
Apparent Volume of Distribution (Vd)Apparent Volume of Distribution (Vd)
• Vd is not a physiological volume
• Vd is not lower than blood or plasma volume but for some drugs it can be much larger than body volume
• Drug with large Vd is extensively distributed to tissues
• Vd is expressed in liters and is calculated as:
• Distribution equilibrium between drug in tissues to that in plasma should be achieved to calculate Vd
• Vd is not a physiological volume
• Vd is not lower than blood or plasma volume but for some drugs it can be much larger than body volume
• Drug with large Vd is extensively distributed to tissues
• Vd is expressed in liters and is calculated as:
• Distribution equilibrium between drug in tissues to that in plasma should be achieved to calculate Vd
0
DoseV
C
0
DoseV
C
22
Area Under the Curve (AUC)Area Under the Curve (AUC)
• AUC is not a parameter; changes with Dose
• Toxicology: AUC is used as a measure of drug exposure
• Pharmacokinetics: AUC is used as a measure of bioavailability and bioequivalence•Bioavailability: criterion of clinical effectiveness
•Bioequivalence: relative efficacy of different drug products (e.g. generic vs. brand name products)
• AUC has units of concentration time (mg.hr/L)
• AUC is not a parameter; changes with Dose
• Toxicology: AUC is used as a measure of drug exposure
• Pharmacokinetics: AUC is used as a measure of bioavailability and bioequivalence•Bioavailability: criterion of clinical effectiveness
•Bioequivalence: relative efficacy of different drug products (e.g. generic vs. brand name products)
• AUC has units of concentration time (mg.hr/L)
elK V
Dose
Clearance
DoseAUC
d
elK V
Dose
Clearance
DoseAUC
d
23
CC
tt
1
2
1
2
Concentration
Time
))(( 2112212
1CCttArea
t
t
))((
...))(())((
1121
233221
122121
0
nnnn
t
ttCC
ttCCttCCArea n
Calculation of AUC using trapezoidal ruleCalculation of AUC using trapezoidal rule
24
Clearance (Cl)Clearance (Cl)
• The most important disposition parameter that describes how quickly drugs are eliminated, metabolized and distributed in the body
• Clearance is not the elimination rate
• Has the units of flow rate (volume / time)
• Clearance can be related to renal or hepatic function
• Large clearance will result in low AUC
• The most important disposition parameter that describes how quickly drugs are eliminated, metabolized and distributed in the body
• Clearance is not the elimination rate
• Has the units of flow rate (volume / time)
• Clearance can be related to renal or hepatic function
• Large clearance will result in low AUC
AUC
DoseCl AUC
DoseCl
25
Clearance Concepts
ORGANCinitial Cfinal
elimination
If Cfinal < Cinitial, then it is a clearing organ
26
Practical ExamplePractical Example
• IV bolus administration
• Dose = 500 mg
• Drug has a linear disposition
• IV bolus administration
• Dose = 500 mg
• Drug has a linear disposition
Time (hr)
Plasma Conc. (mg/L)
ln (PlasmaConc.)
1 9.46 2.25
2 7.15 1.97
3 5.56 1.71
4 4.74 1.56
6 3.01 1.10
10 1.26 0.23
12 0.83 -0.19
27
Linear PlotLinear Plot
0
1
2
3
4
5
6
7
8
9
10
0 2 4 6 8 10 12
Time (hr)
Pla
sm
a c
on
ce
ntr
atio
n (
mg
/L)
28
Natural logarithm PlotNatural logarithm Plot
y = -0.218x + 2.4155
R2 = 0.9988
-0.5
0
0.5
1
1.5
2
2.5
0 2 4 6 8 10 12
Time (hr)
Ln
(P
lasm
a c
on
ce
ntr
atio
n) Kel ln (C0)
29
Half-Life and Volume of DistributionHalf-Life and Volume of Distribution
t1/2 = 0.693 / Kel = 3.172 hrs
Vd = Dose / C0 = 500 / 11.12 = 44.66
ln (C0) = 2.4155
C0 = Inv ln (2.4155) = 11.195 mg/L
t1/2 = 0.693 / Kel = 3.172 hrs
Vd = Dose / C0 = 500 / 11.12 = 44.66
ln (C0) = 2.4155
C0 = Inv ln (2.4155) = 11.195 mg/L
30
ClearanceClearance
Cl = D/AUC
Cl = VdKel
Cl = 44.66 0.218 = 9.73 L/hr
Cl = D/AUC
Cl = VdKel
Cl = 44.66 0.218 = 9.73 L/hr
31
Home WorkHome Work
Determine AUC and
Calculate clearance from AUC
Determine AUC and
Calculate clearance from AUC