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NON COMPARTMENTAL ANALYSIS
SOBHA DEEPTHI KOMPELLA
Y10MPPC140015
M.PHARMACY(CEUTICS)
KVSRSCOPS
PHARMACOKINETIC MODELS
• Drug movement within the body is a complex process. The major objective is therefore to develop a generalized and simple approach to describe ,analyze and interpret the data obtained during in vivo drug disposition studies.• The 2 major approaches are Model approach Model independent approach ( non compartmental analysis)
MODEL APPROACH
MODEL INDEPENDENT APPROACH
COMPARTMENTAL MODEL
PHYSIOLOGICAL MODEL
DISTRIBUTED PARAMETER MODEL
MAMMILLARY MODEL
CATENARY MODEL
PERFUSION LIMITED MODEL
DIFFUSION LIMITED MODEL
NON COMPARTMENTAL ANALYSIS
METHODS FOR ANALYSIS OF PHARMACOKINETIC DATA
Deficiencies of compartmental analysis:
1. Lack of meaningful physiological basis for derived parameters.
2. Lack of rigorous criteria to determine # of compartments necessary to describe disposition.
3. Lack of ability to elucidate organ specific elimination.
4. Inability to relate derived parameters to quantifiable physiological parameters.
5. Inability to predict impact of pathophysiology.
6. Inability to provide insight into mechanism of drug-drug and drug-nutrient interactions.
7. Highly sensitive to sampling frequency.
NON COMPARTMENTAL ANALYSIS
• Also called as model independent method• Doesn't require the assumption of specific
compartment model to calculate the pharmacokinetic parameters.
• Based on assumption that drugs/metabolites follow linear kinetics.
• Thus it can be applied to any compartmental model
ADVANTAGES:• Ease of derivation of
pharmacokinetic parameters by simple algebraic equations.
• The same mathematical treatment can be applied to almost any drug/metabolite provided they follow 1st order kinetics.
• A detailed description of drug disposition characteristics is not required.
DISADVANTAGES:• It provides limited information
regarding the plasma drug concentration –time profile.
• More often it deals with averages.
• The method doesn't adequately treat non-linear cases.
APPLICATIONS:
• Non compartmental analysis is used to estimateMRT,MTT,MATBioavailabilityClearanceApparent volume of distributionHalf-life Fraction of drug eliminated from body
Key terms:• MEAN RESIDENCE TIME: The average total time molecules
of a given dose spend in the body before being eliminated out.
• MEAN TRANSIT TIME: The average time molecules of a given dose spend in the kinetic system.
• MEAN ABSORPTION TIME: The time taken for the drug to appear in systemic circulation.
• When determined after non-instantaneous administration, the MTT =MRT + MAT
• After I.V.bolus dose,MRT=MTT
MEAN RESIDENCE TIME:
• STATISTICAL MOMENT:: :A mathematical description of a discrete distribution of data. Statistical moments calculated from a set of conc.-time data represent an estimate of true moment.
MRT Mean residence time =
• MRT= first moment/zero moment
AUC
AUMC
0
0
)(
)(
dttC
dtttC
AUC
AUMC
AREA DETERMINATION• A. Integration of Specific Function
• B. Numerical Integration
1. Linear trapezoidal
2. Log trapezoidal
3. Extrapolation to infinity
A. Integration of Specific Function
• Must elucidate the specific function
• Influenced by the quality of the fit
2
2
1
1 :example CC
AUCC
AUCi
i
22
221
12
:example CC
AUMCC
AUMCi
i
B. Numerical Integration
1.LINEAR TRAPEZOIDAL:
))(( 2112212
1CCttArea
t
t
))((
...))(())((
1121
233221
122121
0
nnnn
t
ttCC
ttCCttCCArea n
1.Linear trapezoidalAdvantages: Simple (can calculate by hand)
Disadvantages:
• Assumes straight line btwn data points
• If curve is steep, error may be large
• Under or over estimate depends on whether curve is ascending of descending
2.Log trapezoidal
Advantages:• Hand calculator• Very accurate for mono-
exponential• Very accurate in late time
points where interval btwn points is substantially increased
Disadvantages:• Limited application• May produce large errors
on an ascending curve, near the peak, or steeply declining polyexponential curve
21
1221
lnln
))((2
1 CC
ttCCArea
t
t
IN GENERAL:
• Where = 2.303 x Ke
z
nt CAUCAUC n
00
z
nn
z
nt Ct
CAUMCAUMC n
200
z
16
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
AUC Determination
Area (mg-hr/L)-2.2753.131.831.130.9450.900
Total 10.21
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
LhrmgAUMC
LhrmgAUCt
t
/ 11.37
/ 21.10
2
0
0
18
18
17
LhrmgAUC
hr
LmgLhrmgAUC
CAUCAUC
z
t
/ 31.10
26.0
/ 025.0/ 21.10
0
10
1800
18
LhrmgAUMC
hr
Lmg
hr
LhrmgLhrmgAUMC
CCtAUMCAUMC
zz
t
/ 21.39
26.0
/ 025.0
26.0
/ 45.0/ 11.37
2
0
2112
0
2181818
00
18
Systemic availability:• The fraction of administered drug that reaches the
systemic circulation. Commonly used to measure the extent to which drug is available in the body after non-intravenous administration.
oraliv
ivoral
DAUC
DAUCF
CLEARANCE• Total (systemic) Clearance:
bloodin ion concentrat
raten Eliminatio
Cdt
dXCLT
0
0
0
0
0
Therefore
and
(Div) eliminatedamt total where,
,0 from gIntegratin
AUC
DCL
AUCCdt
dtdt
dX
Cdt
dtdtdX
CL
ivT
T
Additivity of clearance:
• Rate of elimination = Rate of Renal Excretion +
Rate of Hepatic Metabolism
• Dividing removal rate by incoming concentration:
• Total Clearance = Renal Clearance + Hepatic Clearance
CLT = CLR + CLH
aaa CCC
Metabolism Hepatic of RateExcretion Renal of RatenEliminatio of Rate
RTRiv
uR fCLCL
D
Xf
,
Riv
RTR
iv
uR
fAUC
DfCLCL
mg
mg
D
Xf
1.0 100
10
100 mg drug administered to a volunteer resultedin 10 mg excreted in urine unchanged:
APPARENT VOLUME OF DISTRUBUTION:
• Calculation via moment analysis• Vss = CL*MRT
• If administration via a short term infusion:
K0 = infusion rate
T = infusion duration
2AUC
AUMCDV iv
SS
AUC
TK
AUC
AUMCTKVSS 2
)( 20
20
HALF LIFE
• If drug declines via monoexponential decline
• MRT=AUMC = C0 /K2 = 1
AUC C0 /K K
• MRT I.V = 1/K
• t1/2 = 0.693* 1
k
• t1/2= o.693 * MRT I.V
CL
VMRT ss
:
Extraction Ratio:• Ratio of the rate of xenobiotic elimination and the rate at which
xenobiotic enters the organ.
a
va
a
va
C
CC
QC
CCQE
E
)(
Entry of Rate
nEliminatio of Rate
CONCLUSION:
• This overview of noncompartmental methods based on statistical moment theory permits a wide range of analysis, that in most instances, will be adequate to characterize the pharmacokinetics of a drug.
There are ofcourse,certain limitations like
• Nonlinear events are not adequately treated by SMT.
• Also SMT provides only limited information regarding time course of drug concentration ( averages are considered).