Non compartmental analysis and the mean residence time approach l.jpg
This presentation is the property of its rightful owner.
Sponsored Links
1 / 47

Non-compartmental analysis and The Mean Residence Time approach PowerPoint PPT Presentation


  • 405 Views
  • Uploaded on
  • Presentation posted in: General

Non-compartmental analysis and The Mean Residence Time approach. A Bousquet-Mélou. Synonymous. Mean Residence Time approach Statistical Moment Approach Non-compartmental analysis. Standard deviation. Random variable values. Mean. Statistical Moments.

Download Presentation

Non-compartmental analysis and The Mean Residence Time approach

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Non compartmental analysis and the mean residence time approach l.jpg

Non-compartmental analysisandThe Mean Residence Time approach

A Bousquet-Mélou


Synonymous l.jpg

Synonymous

Mean Residence Time approach

Statistical Moment Approach

Non-compartmental analysis


Statistical moments l.jpg

Standard deviation

Random variable values

Mean

Statistical Moments

  • Describe the distribution of a random variable :

    • location, dispersion, shape ...


Statistical moment approach l.jpg

Statistical Moment Approach

Stochastic interpretation of drug disposition

  • Individual particles are considered : they are assumed to move independently accross kinetic spaces according to fixed transfert probabilities

  • The time spent in the system by each particule is considered as a random variable

  • The statistical moments are used to describe the distribution of this random variable, and more generally the behaviour of drug particules in the system


Slide5 l.jpg

Statistical Moment Approach

  • n-order statistical moment

  • zero-order :

  • one-order :


Slide6 l.jpg

Statistical Moment Approach

Statistical moments in pharmacokinetics.

J Pharmacokinet Biopharm. 1978 Dec;6(6):547-58.

Yamaoka K, Nakagawa T, Uno T.

Statistical moments in pharmacokinetics: models and assumptions.

J Pharm Pharmacol. 1993 Oct;45(10):871-5.

Dunne A.


The mean residence time l.jpg

The Mean Residence Time


Mean residence time l.jpg

Mean Residence Time

Principle of the method: (1)

  • Evaluation of the time each molecule of a dose stays in the system: t1, t2, t3…tN

  • MRT = mean of the different times

    MRT =

Entry : time = 0, N molecules

t1 + t2 + t3 +...tN

N

Exit : times t1, t2, …,tN


Mean residence time9 l.jpg

Mean Residence Time

  • Under minimal assumptions, the plasma concentration curve provides information on the time spent by the drug molecules in the body

Principle of the method : (2)


Mean residence time10 l.jpg

Mean Residence Time

Principle of the method: (3)

Only one exit from the measurement compartment

First-order elimination : linearity

Entry (exogenous, endogenous)

Central compartment (measure)

recirculation

exchanges

Exit (single) : excretion, metabolism


Mean residence time11 l.jpg

C

C1

AUCDt

C(t1) x t

(t)

t1

X N

X N

n1 =

=

AUCtot

AUCtot

Mean Residence Time

Principle of the method: (4)

Consequence of linearity

  • AUCtot is proportional to N

  • Number n1 of molecules eliminated at t1+ t is proportional to AUCDt:

  • N molecules administered in the system at t=0

  • The molecules eliminated at t1 have a residence time in the system equal to t1


Mean residence time12 l.jpg

Mean Residence Time

Principle of the method: (5)

Cumulated residence times of molecules eliminated during t at :

C

C1

C(1) x t

AUCTOT

t1 : t1 x x N

tn : tn x x N

Cn

n1

C(n) x t

AUCTOT

(t)

tn

t1

Cn x t x N

C1 x t x N

MRT = t1x   tn x N

AUCTOT

AUCTOT


Mean residence time13 l.jpg

Mean Residence Time

Principle of the method: (5)

Cn x t x N

C1 x t x N

MRT = t1x   +tn x  N

AUCTOT

AUCTOT

MRT = t1xC1 x t  +tn x Cn x t AUCTOT

 ti x Ci x t

 t C(t) t

AUMC

MRT = =

=

AUC

AUCTOT

 C(t) t


Slide14 l.jpg

Mean Residence Time


Slide15 l.jpg

  • AUC = Area Under the zero-order moment Curve

AUMC

  • AUMC = Area Under the first-order Moment Curve

AUC

From: Rowland M, Tozer TN. Clinical Pharmacokinetics – Concepts and Applications, 3rd edition, Williams and Wilkins, 1995, p. 487.


Slide16 l.jpg

Mean Residence Time

Limits of the method:

  • 2 exit sites

  • Statistical moments obtained from plasma concentration inform only on molecules eliminated by the central compartment

Central

compartment (measure)


Slide17 l.jpg

Computational methods

  • Non-compartmental analysis

    Trapezes

Area

calculations

  • Fitting with a poly-exponential equation

    Equation parameters : Yi, li

  • Analysis with a compartmental model Model parameters : kij


Slide18 l.jpg

Computational methods

Area calculations by numericalintegration

  • Linear trapezoidal

AUC

AUMC


Slide19 l.jpg

Computational methods

Area calculations by numericalintegration

  • Linear trapezoidal

Advantages: Simple (can calculate by hand)

  • Disadvantages:

    • Assumes straight line between data points

    • If curve is steep, error may be large

    • Under or over estimation, depending on whether the curve is ascending of descending


Slide21 l.jpg

Computational methods

Area calculations by numericalintegration

2. Log-linear trapezoidal

AUC

AUMC


Slide22 l.jpg

Computational methods

Area calculations by numericalintegration

2. Log-linear trapezoidal

< Linear trapezoidal

  • Disadvantages:

    • Produces large errors on an ascending curve, near the peak, or steeply declining polyexponential curve

  • Advantages:

    • Hand calculator

    • Very accurate for mono-exponential

    • Very accurate in late time points where interval between points is substantially increased


Slide23 l.jpg

Computational methods

Extrapolation to infinity

Assumes log-linear decline


Slide24 l.jpg

Computational methods

AUC Determination

AUMC Determination

C x t

(mg/L)(hr)

0

2.00

3.39

3.50

3.01

2.00

0.45

Area

(mg.hr2/L)

-

1.00

5.39

6.89

6.51

7.52

9.80

37.11

Time (hr)C (mg/L)

0 2.55

1 2.00

3 1.13

5 0.70

7 0.43

10 0.20

18 0.025

Area (mg.hr/L)

-

2.275

3.13

1.83

1.13

0.945

0.900

Total 10.21


The main pk parameters can be calculated using non compartmental analysis l.jpg

The Main PK parameters can be calculated using non-compartmental analysis

Non-compartmental analysis

  • MRT = AUMC / AUC

  • Clearance = Dose / AUC

  • Vss = Cl x MRT =

  • F% = AUC EV / AUC IVDEV = DIV

Dose x AUMC

AUC2


Slide26 l.jpg

Computational methods

  • Non-compartmental analysis

    Trapezes

Area

calculations

  • Fitting with a poly-exponential equation

    Equation parameters : Yi, li

Area

calculations

  • Analysis with a compartmental model Model parameters : kij


Slide27 l.jpg

Fitting with a poly-exponential equation

Area calculations by mathematicalintegration

For one compartment :


Slide28 l.jpg

Fitting with a poly-exponential equation

For two compartments :


Slide29 l.jpg

Computational methods

  • Non-compartmental analysis

    Trapezes

Area

calculations

  • Fitting with a poly-exponential equation

    Equation parameters : Yi, li

Area

calculations

  • Analysis with a compartmental model Model parameters : kij

Direct MRT

calculations


Slide30 l.jpg

Analysis with a compartmental model

Example : Two-compartments model

k12

1

2

k21

k10


Slide31 l.jpg

Analysis with a compartmental model

Example : Two-compartments model

K is the 2x2 matrix of the system of differential equations describing the drug transfer between compartments

X1

X2

dX1/dt

K =

dX2/dt


Slide32 l.jpg

Analysis with a compartmental model

Then the matrix (- K-1) gives the MRT in each compartment

Dosing in 1

Dosing in 2

MRTcomp1

MRTcomp1

Comp 1

(-K-1) =

MRTcomp2

MRTcomp2

Comp 2


The mean residence times l.jpg

The Mean Residence Times

Fundamental property of MRT : ADDITIVITY

The mean residence time in the system is the sum of the mean residence times in the compartments of the system

  • Mean Absorption Time / Mean Dissolution Time

  • MRT in central and peripheral compartments


The mean absorption time mat l.jpg

The Mean Absorption Time(MAT)


Slide35 l.jpg

The Mean Absorption Time

Definition : mean time required for the drug to reach the central compartment

IV

EV

Ka

1

A

K10

F = 100%

!

because bioavailability = 100%


Slide36 l.jpg

The Mean Absorption Time

MAT and bioavailability

  • Actually, the MAT calculated from plasma data is the MRT at the injection site

  • This MAT does not provide information about the absorption process unless F = 100%

  • Otherwise the real MAT is :

!


Slide37 l.jpg

solution

tablet

solution

The Mean Dissolution Time

  • In vivo measurement of the dissolution rate in the digestive tract

absorption

dissolution

digestive tract

blood

MDT = MRTtablet - MRTsolution


Slide38 l.jpg

Mean Residence Time in the Central Compartment (MRTC) and in the Peripheral (Tissues) Compartment (MRTT)


Mrt central and mrt tissue l.jpg

MRTC

MRTT

MRTcentral and MRTtissue

Entry

MRTsystem = MRTC + MRTT

Exit (single) : excretion, metabolism


The mean transit time mtt l.jpg

The Mean Transit Time(MTT)


The mean transit times mtt l.jpg

The Mean Transit Times (MTT)

  • Definition :

    • Average interval of time spent by a drug particle from its entry into the compartment to its next exit

    • Average duration of one visit in the compartment

  • Computation :

    • The MTT in the central compartment can be calculated for plasma concentrations after i.v.


The mean residence number mrn l.jpg

The Mean Residence Number(MRN)


The mean residence number mrn43 l.jpg

MRT

MRN =

MTT

The Mean Residence Number (MRN)

  • Definition :

    • Average number of times drug particles enter into a compartment after their injection into the kinetic system

    • Average number of visits in the compartment

    • For each compartment :


Stochastic interpretation of the drug disposition in the body l.jpg

Stochastic interpretation of the drug disposition in the body

Mean number

of visits

R+1

R

IV

Cldistribution

MRTT

(for all the visits)

MTTT

(for a single visit)

MRTC

(all the visits)

MTTC

(for a single visit)

R

number

of cycles

Clredistribution

Clelimination


Stochastic interpretation of the drug disposition in the body45 l.jpg

MRTC

MRTT

MTTT =

MTTC

R

R + 1 =

Stochastic interpretation of the drug disposition in the body

Computation : intravenous administration

MRTsystem = AUMC / AUC

MRTC = AUC / C(0)

MRTT = MRTsystem- MRTC

MTTC = - C(0) / C’(0)


Interpretation of a compartmental model l.jpg

Interpretation of a Compartmental Model

Digoxin

Determinist vs stochastic

21.4 e-1.99t + 0.881 e-0.017t

Cld = 52 L/h

0.3 h

MTTC : 0.5h

MRTC : 2.81h

Vc 34 L

MTTT : 10.5h

MRTT : 46h

VT : 551 L

4.4

41 h

ClR = 52 L/h

stochastic

Cl = 12 L/h

Determinist

1.56 h-1

VT : 551L

Vc : 33.7 L

MRTsystem = 48.8 h

0.095 h-1

0.338 h-1

t1/2 = 41 h


Interpretation of a compartmental model47 l.jpg

Interpretation of a Compartmental Model

Determinist vs stochastic

Gentamicin

y =5600 e-0.281t + 94.9 e-0.012t

Cld = 0.65 L/h

t1/2 =3h

MTTC : 4.65h

MRTC : 5.88h

Vc : 14 L

MTTT : 64.5h

MRTT : 17.1h

VT : 40.8 L

0.265

t1/2 =57h

ClR = 0.65 L/h

stochastic

Clélimination = 2.39 L/h

Determinist

0.045 h-1

MRTsystem = 23 h

VT : 40.8L

Vc : 14 L

0.016 h-1

0.17 h-1

t1/2 = 57 h


  • Login