one-compartment model with oral drug administration

 

In a one-compartment model with oral drug administration, the drug is absorbed into the systemic circulation and eliminated from the body, assuming first-order kinetics. The integrated equation for

the plasma concentration-time profile is:

where:

C(t):  plasma concentration at time t

F:  bioavailability (fraction of the drug that reaches systemic circulation)

D:  dose of the drug administered

Ka: absorption rate constant (the rate at which the drug is absorbed from the site of

administration)

k: elimination rate constant (the rate at which the drug is eliminated from the body)

Vz: apparent volume of distribution (theoretical volume in which the drug is distributed)

t: time after administration

Explanation of Parameters:

Bioavailability (F): This is the fraction of the orally administered drug that reaches systemic

circulation unchanged. For intravenous administration, this value is 1, but for oral, it's usually

less due to incomplete absorption or first-pass metabolism.

Dose (D): The amount of drug administered.

Absorption Rate Constant (k,): The rate at which the drug is absorbed from the gastrointestinal tract into the bloodstream.

Elimination Rate Constant (x): The rate at which the drug is removed from the body, typically via liver metabolism and kidney excretion.

Volume of Distribution (Vz): A proportionality constant that relates the amount of drug in the

body to the concentration of the drug in the blood/plasma. A larger Vz means that the drug

distributes widely into body tissues.

Time (t): The time since the drug was administered.

Plot of Plasma Concentration-Time Profile

The plot above shows the plasma concentration-time profile for a one-compartment model with oral drug administration. Here's a breakdown of the key phases:

1. Absorption phase: Initially, the concentration increases as the drug is absorbed into the

bloodstream. This is represented by the rising part of the curve.

2. Peak concentration: After a certain time, the absorption and elimination rates balance, and the plasma concentration reaches its maximum (Cmax).

3. Elimination phase: As time progresses, the drug is eliminated from the body, and the plasma concentration declines exponentially.

The profile reflects the drug's journey from administration through absorption into the bloodstream, and finally, elimination from the body.