1 compartment model IV bolus administration equation

One compartment model bolus administration equation
Biopharmaceutics and Pharmacokinetics

1. One Compartment Open Model I.V Bolus Administration Dr. Prabhjot Singh (Associate Professor, Pharmaceutics) CH. DEVILAL COLLEGE OF PHARMACY, HARYANA, INDIA

2. Introduction The one-compartment open model offers the simplest way to describe the process of drug distribution and elimination in the body. This model assumes that the drug can enter or leave the body ( ie , the model is " open "), and the body acts like a single, uniform compartment. The simplest route of drug administration from a modeling perspective is a rapid intravenous injection (IV bolus). The simplest kinetic model that describes drug disposition in the body is to consider that the drug is injected all at once into a box, or compartment, and that the drug distributes instantaneously and homogenously throughout the compartment. Drug elimination also occurs from the compartment immediately after injection.

3. Depiction of model Pharmacokinetic model for a drug administered by rapid intravenous injection. D B (X) = drug in body; V D = apparent volume of distribution; k (K E ) = elimination rate constant. In the body, when a drug is given in the form of an IV bolus, the entire dose of drug enters the bloodstream immediately, and the drug absorption process is considered to be instantaneous. In most cases, the drug distributes via the circulatory system to potentially all the tissues in the body. Uptake of drugs by various tissue organs will occur at varying rates, depending on the blood flow to the tissue, the lipophilicity of the drug, the molecular weight of the drug, and the binding affinity of the drug for the tissue mass. Most drugs are eliminated from the body either through the kidney and/or by being metabolized in the liver.

4. Because of rapid drug equilibration between the blood and tissue, drug elimination occurs as if the dose is all dissolved in a tank of uniform fluid (a single compartment) from which the drug is eliminated. The volume in which the drug is distributed is termed the apparent volume of distribution, V D . The apparent volume of distribution assumes that the drug is uniformly distributed in the body. The V D is determined from the preinjected amount of the dose in the syringe and the plasma drug concentration resulting immediately after the dose is injected. The apparent volume of distribution is a parameter of the one-compartment model and governs the plasma concentration of the drug after a given dose. A second pharmacokinetic parameter is the elimination rate constant, k, which governs the rate at which the drug concentration in the body declines over time.

5. Derivation for one compartment open model I.V Bolus administration Rate change of drug in body = Rate of Input - Rate of output As there is no rate of input involved the equation becomes Rate change of drug in body= - Rate of output Integrating both sides  

6. Applying Limits LHS = X ----X, RHS = 0-----t This equation can now be converted into exponential or Common log form  

7. Converting to exponential form As X = V d C Since it is difficult to determine directly the amount of drug in body X advantage is taken of the fact that a constant relationship exists between drug concentration in plasma C (easily measurable) And as V d is constant equation can be written as The above equation shows that disposition of a drug that follows one-compartment kinetics is monoexponential .  

8. Transforming natural log to common log As X = V d C And as V d is constant equation can be written as This is equation of straight line (y = mx + c)  

9. Representation of equation on graph

10. Primary Parameters K E (Elimination Rate constant) is an additive property of rate constant for each of these processes and better called as overall elimination rate constant. K E = K e + K m + K b + ------ Units are per hour (h -1 ) or per minute (min -1 ) Elimination Half life t ½ It is defined as the time taken for the amount of drug in body as well as plasma concentration to decline by one half or 50% of its initial value. Unit is h (hours) or minutes  

11. Volume of distribution Clearance and Volume of distribution are two separate independent pharmacokinetic characteristics of a drug and as they are closely related with physiologic mechanism in body therefore called as primary parameters. Best way to estimate V d of a drug is to administer it as rapid I.V. injection.