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
Random variable values
Mean
Statistical MomentsStochastic interpretation of drug disposition
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
C1
AUCDt
C(t1) x t
(t)
t1
X N
X N
n1 =
=
AUCtot
AUCtot
Mean Residence TimePrinciple 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
AUMC
AUC
From: Rowland M, Tozer TN. Clinical Pharmacokinetics – Concepts and Applications, 3rd edition, Williams and Wilkins, 1995, p. 487.
Limits of the method:
Central
compartment (measure)
Trapezes
Area
calculations
Equation parameters : Yi, li
Area calculations by numericalintegration
Advantages: Simple (can calculate by hand)
Area calculations by numericalintegration
2. Loglinear trapezoidal
< Linear trapezoidal
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 noncompartmental analysis
Trapezes
Area
calculations
Equation parameters : Yi, li
Area
calculations
Fitting with a polyexponential equation noncompartmental analysis
Area calculations by mathematicalintegration
For one compartment :
Fitting with a polyexponential equation noncompartmental analysis
For two compartments :
Computational methods noncompartmental analysis
Trapezes
Area
calculations
Equation parameters : Yi, li
Area
calculations
Direct MRT
calculations
Analysis with a compartmental model noncompartmental analysis
Example : Twocompartments model
k12
1
2
k21
k10
Analysis with a compartmental model noncompartmental analysis
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 noncompartmental analysis
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 noncompartmental analysis
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 noncompartmental analysis
MAT and bioavailability
!
solution noncompartmental analysis
tablet
solution
The Mean Dissolution Time
absorption
dissolution
digestive tract
blood
MDT = MRTtablet  MRTsolution
MRT noncompartmental analysisC
MRTT
MRTcentral and MRTtissueEntry
MRTsystem = MRTC + MRTT
Exit (single) : excretion, metabolism
MRT noncompartmental analysis
MRN =
MTT
The Mean Residence Number (MRN)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
MRT bodyC
MRTT
MTTT =
MTTC
R
R + 1 =
Stochastic interpretation of the drug disposition in the bodyComputation : 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