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).