Principles of Pharmacokinetics

Pharmacokinetics of IV Administration, 1-Compartment

Principles of Pharmacokinetics

Pharmacokinetics of IV Administration, 1-Compartment

Karunya Kandimalla, Ph.Dkandimalla.karunya@mayo.edu

Karunya Kandimalla, Ph.Dkandimalla.karunya@mayo.edu

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

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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

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Disposition Analysis (Dose Linearity)Disposition Analysis (Dose Linearity)

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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

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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

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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

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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

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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)

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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)

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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

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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)

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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)

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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]

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Clearance Concepts

ORGANCinitial Cfinal

elimination

If Cfinal < Cinitial, then it is a clearing organ

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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

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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)

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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)

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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

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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

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Home WorkHome Work

Determine AUC and

Calculate clearance from AUC

Determine AUC and

Calculate clearance from AUC