MODELS OF DRUG ADMINISTRATION AND DISPOSITION

In the following image , the effect of drug added via intravenous drug administration is shown by adding a known amount of the drug into the beaker and the graph besides shows the time course of the amount of drug in the beaker. 

(CR : Basic and Clinical Pharmacology, Katzung, Lange, 12th Edition) 

• Example (A):  no movement of drug out of the beaker -->  a steep rise to maximum followed by a plateau. 
• Example (B): a route of elimination is present --> a slow decay after a sharp rise to a maximum; level of material in the beaker falls --> “pressure” driving the elimination process also falls --> slope of the curve decreases : Exponential decay curve. 
• Example (C) : drug placed in first "blood" compartment - equilibrates rapidly with second "extravascular" compartment -->  amount of drug in “blood” declines exponentially to a new steady state. 
• Example (D): model for a more realistic combination of elimination mechanism and extravascular equilibration -->  an early distribution phase followed by the slower elimination phase. 

COMPARTMENTAL MODELS

(Cr. : Malcolm R., & Thomas N, Clinical Pharmacokinetics and Pharmacodynamics)

Here, the ADME terms used in pharmacokinetics schematically defined relative to the process of moving from the site of administration into the body, absorption, moving between locations within the body, distribution, or moving out of the body, elimination. All of the processes are defined relative to the site of measurement, usually plasma. 

Disposition : 

The combined processes of distribution and elimination. Compounds are eliminated from the body by both excretion and metabolism.

• A solid encounters several barriers and sites of loss in its sequential movement through gastrointestinal tissues and the liver. 
• Incomplete dissolution or metabolism in the gut lumen or by enzymes in the gut wall is a cause of incomplete input into the systemic circulation. 
• Removal of drug as it first passes through the liver may further reduce systemic input.

VOLUME OF DISTRIBUTION AND CLEARANCE

We are going to understand the terms of volume of distribution and clearance using a model 

If we consider the volume of the reservoir in the model same as that of volume of  the drug in all the compartments of the body then , then we can term it as volume of distribution

To know the amount of drug which is eliminated by the body , we need to consider the following factors

              

   

 

1. INITIAL CONCENTRATION 

    Initial concentration in the reservoir depends on the amount introduced and the volume of the reservoir 

      

   C = Dose                                                                                              --- Equation 1

          volume 

 

2. RATE OF ELIMINATION

    Since the fluid passes with a certain flow , Q  with a concentration C  , Extractor removes certain fraction E ,  which can be measured by the difference between concentration entering the extractor and the concentration leaving the extractor, then the speed at which a drug is eliminated is given by

Rate of elimination = Q . C . E =  Q. ( C - COUT  )                                  --- Equation 2   

 where Q = volume/time     

3. EXTRACTION RATIO

     It is determined by taking the difference between the concentrations entering and leaving the extractor to the entering concentration

 E  = Q . ( C - COUT  )

               Q . C

     

  E  =   ( C - COUT  )                                                                                --- Equation 3

                  C

 where  E  has no unit 

4. CLEARANCE

      Rate of elimination can be related to the measured concentration in the systemic circulation (here it is the reservoir)

Rate of elimination = CL . C                                                               --- Equation 4

By comparing  equations under 2 & 4 

     Rate of elimination = CL . C  - (4)

                             CL   = Rate of elimination                                     --- Equation 5

                                                  C

     Rate of elimination = Q . C . E  - (2)

                           Q . E  =  Rate of elimination                                   ---  Equation 6

                                                  C

  Therefore we can clearly state that,

                             CL    =   Q . E                                                        ---  Equation  7