**Non Compartment
Modelling**

__Session
objectives__

**By the end of this
session, students will be able to:**

• Define non-compartment modeling

• Discuss the advantages, disadvantages and applications of non-compartment
models

• Compute various pharmacokinetic parameters

__First
moment (Mean Residence Time):__

• It is referred to as MRT

• Explains plasma drug conc-time profile.

• Mathematically,

• Area under moment curve

**(****C _{1} x t) Vs time**

• Numerical value of AUMC is higher than AUC.

• AUMC is also calculated by trapezoid met

• Blood samples are collected for a long period to obtain
measurable conc. (c_{t}^{∗}).

• AUMC is calculated using,

• Terminal portion of curve – determines plasma elimination
rate constant (ƛ𝑍 ) of the drug.

__Second
moment (Variance of Mean Residence Time):__

• It is referred to as VRT.

• Explains plasma drug conc-time profile.

• Mathematically,

• A plot of (𝐶1 x 𝑡
2) Vs time is drawn.

• It is difficult to calculate area from time (𝑐1)
to infinity.

• Hence calculation is restricted to MRT.

AUC & MRT are generally used in the pharmacokinetic
analysis, because higher moments are prone to an unacceptable level of
computational errors.

__Non-compartment
Models – Pharmacokinetic Parameters__

**1. Mean Residence
Time (MRT)**

• It is defined as the average time that a drug resides in
the body before being eliminated.

• Units = hour.

• Represents time for elimination of 63.2 % of drug when
given by i.v. bolus injection

• It is the analogy of statistical moment to plasma drug
elimination half-life (50 %).

• Drug elimination from the body takes place by 1st order
phases,

Assumes that drug
follows one compartment open model

• k_{10} transformed to t_{1/2}
(ℎ−1 to h)

If drug follows two compartment open model:

• Drug equilibration takes place slowly into peripheral
compartment

• MRT can be used.

From urinary excretion data,

This is accurate if renal excretion is the major route of
elimination.

__2. Apparent
volume of distribution at steady state__

Vol. of distribution:
considered at steady state

â

Independent of
elimination

Solely reflects the anatomic space occupied by the drug
& relative degree of drug binding in blood & extravascular space.

For constant i.v. infusion:

R= infusion rate

T=duration of infusion

__3. Drug
clearance__

It is defined as the reciprocal of the zero moment of
conc-time curve after a single i.v. injection.

• Single i.v. injection:

• i.v. infusion at constant rate:

• Single oral dose:

• Multiple oral dosage regimen:

• Rearranging eq. 20:

Steady state plasma drug conc. (c_{1}^{ss}) is a function of
infusion rate (R) and total body clearance (Cl)

__4. Mean
Absorption Time (MAT)__

• Mean time required for drug to reach systemic circulation
from time of drug administration.

• In non-compartmental models, MAT is mathematically defined
as the differences in the MRT after different modes of administration.

• Absorption follows first order kinetics,

• If absorption follows zero order kinetics,

__5.
Bioavailability (F)__

• It is define as the ratio of zero moments of i.v. and
extravascular administration, normalized for doses.

• For i.v. bolus injection, F=1.

• Absolute bioavailability,

Where, AUC = zero moment curve, µg.h/ml

D = dose of drug administered

• Relative bioavailability, 𝐹*r* may be
expressed by comparing the zero moments of a product with a standard product.

__Summary__

• Non compartmental approach is to study the time course
changes of drug concentration in the body based on the statistical moment
theory and it is regarded as a model independent method

• It is highly applied in the evaluation of bioavailability
and bioequivalence

• The pharmacokinetic parameters mainly estimated by
non-compartment model are

- Peak plasma drug concentration, Cmax;- Time of peak plasma
drug concentration, tmax and Area under the curve, AUC

• It involves simple algebraic equations. So the derivation
of equations for obtaining pharmacokinetic parameters is easy

• The main disadvantage is that it applies only in linear
pharmacokinetics

• Statistical moments consider the time course changes of
plasma drug concentration as a statistical distribution phenomenon and terms
are mean area, mean residence time and variance of mean residence time and of
urinary excretion rate

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