# Non Compartment Modelling

Non Compartment Modelling

Session objectives

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

• Define non-compartment modeling

• 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

(C1 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. (ct).

• 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

• k10 transformed to t1/2  (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. (c1ss) 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, 𝐹r 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