Principles of Pharmacokinetics Pharmacokinetics of IV Administration, 1-Compartment Karunya Kandimalla, Ph.D. Associate Professor, Pharmaceutics [email protected].

Principles of Pharmacokinetics

Pharmacokinetics of IV Administration, 1-Compartment

Principles of Pharmacokinetics

Pharmacokinetics of IV Administration, 1-Compartment

Karunya Kandimalla, Ph.D.Associate Professor, Pharmaceutics

[email protected]

Karunya Kandimalla, Ph.D.Associate Professor, Pharmaceutics

[email protected]

2

Pharmacokinetics & PharmacodynamicsPharmacokinetics & Pharmacodynamics

Target organ

Target organ

RR

RR

RR

RR

RR

RR

ADME

3

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

4

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.

5

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

6

Intravascular AdministrationIntravascular Administration

• IV administration (bolus or infusion):

• Drugs are injected directly into central compartment (plasma, highly perfused organs, extracellular water)

• No passage across membranes

• Population or individual elimination rate constants (kel) and volumes of distribution (Vd) enable us to calculate doses or infusion rates that produce target (desired) concentrations

• IV administration (bolus or infusion):

• Drugs are injected directly into central compartment (plasma, highly perfused organs, extracellular water)

• No passage across membranes

• Population or individual elimination rate constants (kel) and volumes of distribution (Vd) enable us to calculate doses or infusion rates that produce target (desired) concentrations

7

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

8

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

9

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

10

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

11

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

12

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)

13

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)

14

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

15

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)

16

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)

17

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]

18

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

19

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

20

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

21

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

el

KKt

tK

tKe

tKeCC

//2/1

2/1

2/10

0

693.02ln

2/12

1ln

2

12

ee

el

el

el

KKt

tK

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

22

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

23

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

24

Volume of Distribution—The ConceptVolume of Distribution—The Concept

•• •• ••

•• •• ••

• • • • • •

• • • • • •

• •

•

• • •

Plasma [C] Tissue [C] “Apparent” Vd

• • • • •• • • • •

• • • • •• • • • • •

• • • • •• • • •

• • •

• • •

• • •

• • •

NB: For lipid-soluble drugs, Vd changes with body size and age (decreased lean body mass, increased fat)

25

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

26

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

27

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

28

ORGANCinitial Cfinal

elimination

If Cfinal < Cinitial, then it is a clearing organ

Clearance -The ConceptClearance -The Concept

29

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

30

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)

31

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)

32

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

33

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

34

Home WorkHome Work

Determine AUC and

Calculate clearance from AUC

Determine AUC and

Calculate clearance from AUC

Principles of Pharmacokinetics

Pharmacokinetics of IV Administration, 2-Compartment

Principles of Pharmacokinetics

Pharmacokinetics of IV Administration, 2-Compartment

Karunya Kandimalla, [email protected]

Karunya Kandimalla, [email protected]

36

ObjectivesObjectives

• Be able to:• Describe assumptions associated with multi-

compartment models

• Describe processes that take place during distribution and terminal elimination

• Define and calculate , β, t½, Vi, VdSS, Cl and

AUC

• Understand influence of Volume of distribution on loading doses and toxicity

• Design appropriate experiments to determine proper modeling of drug disposition

• Be able to:• Describe assumptions associated with multi-

compartment models

• Describe processes that take place during distribution and terminal elimination

• Define and calculate , β, t½, Vi, VdSS, Cl and

AUC

• Understand influence of Volume of distribution on loading doses and toxicity

• Design appropriate experiments to determine proper modeling of drug disposition

37

Recommended ReadingsRecommended Readings

• Chapter 4, p. 73-92, 95-97• Multicompartment model assumptions (73-4)

• Two-compartment open model (75-9)

• Method of residuals (79-81)

• Digoxin simulation (81-84)

• Apparent volume of distribution (84-90)

• Drug in tissue compartment (90-91)

• Clearance and elimination constant (92)

• Determination of compartment models (95-7)

• Chapter 4, p. 73-92, 95-97• Multicompartment model assumptions (73-4)

• Two-compartment open model (75-9)

• Method of residuals (79-81)

• Digoxin simulation (81-84)

• Apparent volume of distribution (84-90)

• Drug in tissue compartment (90-91)

• Clearance and elimination constant (92)

• Determination of compartment models (95-7)

38

Physiological PerspectivePhysiological Perspective

Onecompartment

Twocompartments

k12

Quick

Quick Slow

39

Notes on Two-Compartment ModelingNotes on Two-Compartment Modeling

Blood or Plasma Pharmacokinetics

(2 compartment model) Blood or Plasma Pharmacokinetics

(2 compartment model)

Absorption (Input)Absorption (Input) DispositionDisposition

• Ideal model should mimic distribution and disposition

• Full set of rate processes seldom taken into account

• Tissue [C] often unknown

• Because tissue [C] correlates with plasma [C], response often (but not always) correlates with plasma [C]

• Invasive nature of tissue sampling limits sophistication

• Ideal model should mimic distribution and disposition

• Full set of rate processes seldom taken into account

• Tissue [C] often unknown

• Because tissue [C] correlates with plasma [C], response often (but not always) correlates with plasma [C]

• Invasive nature of tissue sampling limits sophistication

DistributionDistributionDistributionDistribution EliminationElimination

ExcretionExcretion MetabolismMetabolism

40

Vi Vt

ViVt3

Vt2

k12

k21

k12

k21

k31

k13

k10

k10

Two compartmentmodel

Three compartmentmodel

Vi = Volume of central compartment

Vt 2 or 3 = Volume of peripheral compartments

Multicompartment ModelingMulticompartment Modeling

41

Assumptions (Two-Compartment Model)Assumptions (Two-Compartment Model)

• Drug in peripheral compartment (bone, fat, muscle etc.) equilibrates with drug in central compartment

•Plasma, highly perfused organs, extracellular water

• [C] in a given compartment is uniform

• Two-compartment drugs distribute into various tissues at different, first order rates

• Elimination follows a single 1st order rate process only after distribution equilibrium is reached

• Drug in peripheral compartment (bone, fat, muscle etc.) equilibrates with drug in central compartment

•Plasma, highly perfused organs, extracellular water

• [C] in a given compartment is uniform

• Two-compartment drugs distribute into various tissues at different, first order rates

• Elimination follows a single 1st order rate process only after distribution equilibrium is reached

Vi Vt

k12

k21

k10

42

Two-Compartment Model (Mathematical Perspective)Two-Compartment Model (Mathematical Perspective)

• Ct is a bi-exponential decaying function that depends on 2 hybrid constants (A and B), which can be determined graphically, and the distribution () and elimination (β) rate constants

• Ct is a bi-exponential decaying function that depends on 2 hybrid constants (A and B), which can be determined graphically, and the distribution () and elimination (β) rate constants

Ct = A • e -t + B • e –βtCt = A • e -t + B • e –βt

A function of k10, k12 and k21

Because >> than β, this term goes to zero at greater t values

43Clinical Pharmacology and Therapeutics. 1993;53:6-14

2-Compartment Data (Linear Plot)2-Compartment Data (Linear Plot)

0.00

4.00

8.00

12.00

16.00

20.00

0.00 2.00 4.00 6.00 8.00 10.00

Time (hr)

Cp

(m

g/d

L)

Concentration-Time Course of Caffeine IV Bolus

44Clinical Pharmacology and Therapeutics. 1993;53:6-14

2-Compartment Data (Semi-log Plot)2-Compartment Data (Semi-log Plot)

1.00

10.00

100.00

0.00 2.00 4.00 6.00 8.00 10.00

Time (hr)

Cp

(m

g/d

L)

Concentration-Time Course of Caffeine IV Bolus

45

1.00

10.00

100.00

0.00 2.00 4.00 6.00 8.00 10.00

Time (hr)

Cp

(m

g/d

L)

2-Compartment Data (Semi-Log Plot)2-Compartment Data (Semi-Log Plot)

Distribution or Alpha Phase

Elimination or Beta Phase

Slope = β/2.303

Concentration-Time Course of Caffeine IV Bolus

Note the bi-exponential decline in drug concentration

A

B

Slope = /2.303

46

Calculation of Micro-constantsCalculation of Micro-constants

• k21 = • B + β • A

A + B

• k10 = • β

k21

• k12 = + β – k10 – k21

• k21 = • B + β • A

A + B

• k10 = • β

k21

• k12 = + β – k10 – k21

Vi Vt

k12

k21

k10

Note: Micro-constants cannot be calculated by direct means

47

Two-Compartment Elimination Rate ConstantsTwo-Compartment Elimination Rate Constants

• k10 represents elimination from central compartment only• Larger than β

• Not dependent on drug transfer into tissue compartment

• β represents elimination when distribution equilibrium attained• Influenced by drug transfer into deep tissues

• Clinically more useful than k10

• k10 represents elimination from central compartment only• Larger than β

• Not dependent on drug transfer into tissue compartment

• β represents elimination when distribution equilibrium attained• Influenced by drug transfer into deep tissues

• Clinically more useful than k10

48

Initial Concentration (Time = 0)Initial Concentration (Time = 0)

• Answer: The initial concentration at time = 0 is equal to the sum of the intercepts A and B

• Answer: The initial concentration at time = 0 is equal to the sum of the intercepts A and B

Question 1:

Based on the information gathered thus far, what is the drug

concentration at time Zero?

49

Half-LifeHalf-Life

• Compounds demonstrating two compartment kinetics will have t1/2 estimates for each exponential phases

• Distribution half-life

• t ½ Dist = ln2/

• Elimination half-life

• t ½ Elim = ln2/β

• Terminal Half life is the elimination half life for most of drugs

• Compounds demonstrating two compartment kinetics will have t1/2 estimates for each exponential phases

• Distribution half-life

• t ½ Dist = ln2/

• Elimination half-life

• t ½ Elim = ln2/β

• Terminal Half life is the elimination half life for most of drugs

50Clinical Pharmacokinetics Concepts and Applications, Third edition, Lippincott Williams & Wilkins, Media, PA 19063

What is the Elimination Half-Life (Aspirin Vs. Gentamicin)?What is the Elimination Half-Life (Aspirin Vs. Gentamicin)?

• Aspirin• Distribution phase accounts for 31% of the dose

• Elimination phase accounts for 69% of the dose

• Terminal half life is the elimination half-life for aspirin

• Gentamicin• Distribution phase accounts for 98% of the dose

• Elimination phase accounts for 2% of the dose

• Distribution half life is the appropriate half-life for gentamicin

• Aspirin• Distribution phase accounts for 31% of the dose

• Elimination phase accounts for 69% of the dose

• Terminal half life is the elimination half-life for aspirin

• Gentamicin• Distribution phase accounts for 98% of the dose

• Elimination phase accounts for 2% of the dose

• Distribution half life is the appropriate half-life for gentamicin

51

Volume of Distribution (Vd)Volume of Distribution (Vd)

• One compartment model Vd is constant:

• Two compartment model Vd changes with time and reaches a plateau at the distribution equilibrium

• One compartment model Vd is constant:

• Two compartment model Vd changes with time and reaches a plateau at the distribution equilibrium

0

DoseVd

C

0

DoseVd

C

52

Two Compartment Model (Vd vs. Time)Two Compartment Model (Vd vs. Time)

0

5

10

15

20

25

30

35

0 5 10 15 20 25

Time (hr)

Vo

lum

e d

istr

ibu

tio

n

Vi

Vdss

Vt

53

Determination of Vi, Vdss and Vd From Hybrid Constants

Determination of Vi, Vdss and Vd From Hybrid Constants

• Vi = Dose

A + B

• VdSS = Vi [1 + k12]

k21

• VdSS = Dose

β • AUC 0 ∞

• Vi = Dose

A + B

• VdSS = Vi [1 + k12]

k21

• VdSS = Dose

β • AUC 0 ∞

• Vt = Vi k12

k21

• Note that VdSS is a

function of transfer rate constants

• The more extensively a drug distributes (i.e., the higher k12) the larger the volume of distribution

• Vt = Vi k12

k21

• Note that VdSS is a

function of transfer rate constants

• The more extensively a drug distributes (i.e., the higher k12) the larger the volume of distribution

54

Vdss- The Concept Vdss- The Concept

• Vt is mostly influenced by the elimination rate and doesn’t reflect distribution

• Vdss is mostly influenced by distribution

• Volume term of the steady state when a drug is infused at a constant rate

• Lies between Vi and Vt

• Generally, difference between Vdss and Vt is small • Aspirin

• Vdss = 10.4 L, Vt = 10.5 L

• Gentamicin

• Vdss = 345 L, Vt = 56 L

• Substantially eliminated before distribution equilibrium achieved

• Vt is mostly influenced by the elimination rate and doesn’t reflect distribution

• Vdss is mostly influenced by distribution

• Volume term of the steady state when a drug is infused at a constant rate

• Lies between Vi and Vt

• Generally, difference between Vdss and Vt is small • Aspirin

• Vdss = 10.4 L, Vt = 10.5 L

• Gentamicin

• Vdss = 345 L, Vt = 56 L

• Substantially eliminated before distribution equilibrium achieved

55

Loading DosesLoading Doses

• Loading doses are designed to achieve therapeutic concentrations faster

• Loading doses are designed to achieve therapeutic concentrations faster

A: 45 mg/h constant IV infusion

B: Plasma [C]

C: Drug remaining from 530 mg IV loading dose

DL = Cp target • Vd

F

DL = Cp target • Vd

F

56

Two-Compartment Distribution, Loading Doses & Site of ActionTwo-Compartment Distribution, Loading Doses & Site of Action

• Some 2-compartment drugs exert their therapeutic and toxic effects on target organs located in the central compartment• Lidocaine, quinidine, procainamide

• Some 2-compartment drugs exert their therapeutic and toxic effects on target organs located in the central compartment• Lidocaine, quinidine, procainamide

Question 2:How should loading doses for these drugs be handled?

57

Loading Doses for Two-Compartment Drugs Acting in Vi

Loading Doses for Two-Compartment Drugs Acting in Vi

Answer:

Slow administration to allow for drug distribution into Vt

OR…Small bolus doses such that

Cp does not exceed predetermined concentrations

DL = VC • CSS

Answer:

Slow administration to allow for drug distribution into Vt

OR…Small bolus doses such that

Cp does not exceed predetermined concentrations

DL = VC • CSS

58

Two-Compartment Distribution, Loading Doses & Site of ActionTwo-Compartment Distribution, Loading Doses & Site of Action

• Some 2-compartment drugs exert their therapeutic and toxic effects on target organs located in Vt

• Digoxin has a myocardium distribution half-life of 35 min and requires 8 to 12 h to completely distribute

• Some 2-compartment drugs exert their therapeutic and toxic effects on target organs located in Vt

• Digoxin has a myocardium distribution half-life of 35 min and requires 8 to 12 h to completely distribute

Question 3:How should loading doses for these drugs be handled?

59

Loading Doses for Two-Compartment Drugs Acting in Vt

Loading Doses for Two-Compartment Drugs Acting in Vt

Answer:

Quick administration is fine sincethe initially observed high Cps are

not dangerous.These concentrations, however,

cannot be used to predicttherapeutic effects.

DL = VSS • CSS

Answer:

Quick administration is fine sincethe initially observed high Cps are

not dangerous.These concentrations, however,

cannot be used to predicttherapeutic effects.

DL = VSS • CSS

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Loading Doses: The Case of LidocaineLoading Doses: The Case of Lidocaine

• A: Loading dose + Infusion using Vi (volume of central compartment)

• B: Loading dose + Infusion using VSS

• Doted line: Constant infusion with no loading dose

• Dashed line: Loading dose using Vi, no infusion

• A: Loading dose + Infusion using Vi (volume of central compartment)

• B: Loading dose + Infusion using VSS

• Doted line: Constant infusion with no loading dose

• Dashed line: Loading dose using Vi, no infusion

Seizures

Hypotension

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TipTip

• If Vdss is unknown, use a value that falls between Vt and Vi

• If Vdss is unknown, use a value that falls between Vt and Vi

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Estimation of AUCEstimation of AUC

From hybrid constants:

• AUC0∞ = A + B

β

From hybrid constants:

• AUC0∞ = A + B

β

Area t2 t3 = ½ (t3 – t2)(C2 + C3)

AUC by Trapezoidal Method

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ORGANQ.CA Q.Cv

elimination

Clearance –Two Compartment ModelClearance –Two Compartment Model

• CA = arterial blood concentration; Cv= Venous blood concentration; Q = blood flow

• Clearance = Q(Ca-Cv)

Ca

• CA = arterial blood concentration; Cv= Venous blood concentration; Q = blood flow

• Clearance = Q(Ca-Cv)

Ca

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Clearance (Two Compartment Model)Clearance (Two Compartment Model)

• Answer: Clearance is model independent. However we need to use different rate constants depending on the choice of volume term

• Example: Cltotal = k10 • Vi

• Answer: Clearance is model independent. However we need to use different rate constants depending on the choice of volume term

• Example: Cltotal = k10 • Vi

Question 4:Clearance (1- compartment Model):

Vd • Kel

Clearance (2- compartment model):?

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Model-Independent Calculation of ClearanceModel-Independent Calculation of Clearance

• Cl = Dose

AUC 0 ∞

• No modeling consideration needed, but requires accurate measurement of AUC• Early & frequent sampling essential

• Units = Volume/time

• Theoretical volume of blood or plasma completely cleared of drug per unit time

• Cl = Dose

AUC 0 ∞

• No modeling consideration needed, but requires accurate measurement of AUC• Early & frequent sampling essential

• Units = Volume/time

• Theoretical volume of blood or plasma completely cleared of drug per unit time

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One vs. Two Compartment DilemmaOne vs. Two Compartment Dilemma

• Distribution phase may be missed entirely if blood is sampled too late or at wide intervals after drug administration

• Distribution phase may be missed entirely if blood is sampled too late or at wide intervals after drug administration

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Use of One Compartment Modeling for Two-Compartment DrugsUse of One Compartment Modeling for Two-Compartment Drugs

• If no concentration-time data points lie above back-extrapolated terminal line (semilog paper), assume one-compartment kinetics

• One-compartment modeling can be used in place of two-compartment modeling provided:

• Duration of distribution is small compared with elimination half-life

• Elimination is minimal during distribution• Referred to as “non-significant” 2-compartment kinetics

• Pharmacokinetic parameters must be computed after distribution is over

• If no concentration-time data points lie above back-extrapolated terminal line (semilog paper), assume one-compartment kinetics

• One-compartment modeling can be used in place of two-compartment modeling provided:

• Duration of distribution is small compared with elimination half-life

• Elimination is minimal during distribution• Referred to as “non-significant” 2-compartment kinetics

• Pharmacokinetic parameters must be computed after distribution is over

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Tips For Solving the Problem Set

Tips For Solving the Problem Set

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• Plot Cp against time on semilog paper

• Extrapolate terminal phase to t = 0• Intercept = B

• Slope = /2.303

• Read at least 3 extrapolated [C]s during distribution

• Calculate residual [C]s• Measured – extrapolated

• Plot residuals against time (semilog paper)• Intercept of “feathered” line = A

• Slope = /2.303

• Plot Cp against time on semilog paper

• Extrapolate terminal phase to t = 0• Intercept = B

• Slope = /2.303

• Read at least 3 extrapolated [C]s during distribution

• Calculate residual [C]s• Measured – extrapolated

• Plot residuals against time (semilog paper)• Intercept of “feathered” line = A

• Slope = /2.303