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Noncompartmental analysis and The Mean Residence Time approach. A BousquetMélou. Synonymous. Mean Residence Time approach Statistical Moment Approach Noncompartmental analysis. Standard deviation. Random variable values. Mean. Statistical Moments.
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A BousquetMélou
Mean Residence Time approach
Statistical Moment Approach
Noncompartmental analysis
Standard deviation
Random variable values
Mean
Stochastic interpretation of drug disposition
Statistical Moment Approach
Statistical Moment Approach
Statistical moments in pharmacokinetics.
J Pharmacokinet Biopharm. 1978 Dec;6(6):54758.
Yamaoka K, Nakagawa T, Uno T.
Statistical moments in pharmacokinetics: models and assumptions.
J Pharm Pharmacol. 1993 Oct;45(10):8715.
Dunne A.
Principle of the method: (1)
MRT =
Entry : time = 0, N molecules
t1 + t2 + t3 +...tN
N
Exit : times t1, t2, …,tN
Principle of the method : (2)
Principle of the method: (3)
Only one exit from the measurement compartment
Firstorder elimination : linearity
Entry (exogenous, endogenous)
Central compartment (measure)
recirculation
exchanges
Exit (single) : excretion, metabolism
C
C1
AUCDt
C(t1) x t
(t)
t1
X N
X N
n1 =
=
AUCtot
AUCtot
Principle of the method: (4)
Consequence of linearity
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
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
Mean Residence Time
AUMC
AUC
From: Rowland M, Tozer TN. Clinical Pharmacokinetics – Concepts and Applications, 3rd edition, Williams and Wilkins, 1995, p. 487.
Mean Residence Time
Limits of the method:
Central
compartment (measure)
Computational methods
Trapezes
Area
calculations
Equation parameters : Yi, li
Computational methods
Area calculations by numericalintegration
AUC
AUMC
Computational methods
Area calculations by numericalintegration
Advantages: Simple (can calculate by hand)
Computational methods
Area calculations by numericalintegration
2. Loglinear trapezoidal
AUC
AUMC
Computational methods
Area calculations by numericalintegration
2. Loglinear trapezoidal
< Linear trapezoidal
Computational methods
Extrapolation to infinity
Assumes loglinear decline
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
Noncompartmental analysis
Dose x AUMC
AUC2
Computational methods
Trapezes
Area
calculations
Equation parameters : Yi, li
Area
calculations
Fitting with a polyexponential equation
Area calculations by mathematicalintegration
For one compartment :
Fitting with a polyexponential equation
For two compartments :
Computational methods
Trapezes
Area
calculations
Equation parameters : Yi, li
Area
calculations
Direct MRT
calculations
Analysis with a compartmental model
Example : Twocompartments model
k12
1
2
k21
k10
Analysis with a compartmental model
Example : Twocompartments 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
Analysis with a compartmental model
Then the matrix ( K1) gives the MRT in each compartment
Dosing in 1
Dosing in 2
MRTcomp1
MRTcomp1
Comp 1
(K1) =
MRTcomp2
MRTcomp2
Comp 2
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
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%
The Mean Absorption Time
MAT and bioavailability
!
solution
tablet
solution
The Mean Dissolution Time
absorption
dissolution
digestive tract
blood
MDT = MRTtablet  MRTsolution
Mean Residence Time in the Central Compartment (MRTC) and in the Peripheral (Tissues) Compartment (MRTT)
MRTC
MRTT
Entry
MRTsystem = MRTC + MRTT
Exit (single) : excretion, metabolism
The Mean Transit Time(MTT)
The Mean Residence Number(MRN)
MRT
MRN =
MTT
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
MRTC
MRTT
MTTT =
MTTC
R
R + 1 =
Computation : intravenous administration
MRTsystem = AUMC / AUC
MRTC = AUC / C(0)
MRTT = MRTsystem MRTC
MTTC =  C(0) / C’(0)
Digoxin
Determinist vs stochastic
21.4 e1.99t + 0.881 e0.017t
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 h1
VT : 551L
Vc : 33.7 L
MRTsystem = 48.8 h
0.095 h1
0.338 h1
t1/2 = 41 h
Determinist vs stochastic
Gentamicin
y =5600 e0.281t + 94.9 e0.012t
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 h1
MRTsystem = 23 h
VT : 40.8L
Vc : 14 L
0.016 h1
0.17 h1
t1/2 = 57 h