# Relationship between half life and steady state

### Drug Half-Life, Steady State, and Recommended Sample Collection Time

As repeated doses of a drug are administered its plasma concentration builds up and reaches what is known as a steady state. This is when the. We call this "steady state." It takes somewhere between 5 and 6 half-lives for a medication to reach steady state. Thus, medications with short half-lives reach. This test guide provides the drug half-life and time to steady state for many plasma at one rate then exchanged between plasma and tissues at a different rate).

### Understanding Steady State Pharmacokinetics – Certara

Someone in your house notices the empty spots in the carton of eggs and purchases 2 more eggs and places them in the carton. So when you wake up the next morning, the carton is full of eggs. If this process repeats itself over many days, it would appear that the eggs never change … there are always 12 eggs in the carton even though you use them for various meals and recipes.

In this hypothetical scenario, the eggs are at steady state because the rate of elimination is equal to the rate of input. The eggs represent individual drug molecules in the body.

## REPEATED ADMINISTRATION

Using the eggs represents the variety of clearance mechanisms that eliminate drug molecules from circulation. And the replenishment of eggs represent taking new doses of medication.

PK parameters associated with steady state There are several special PK parameters associated with steady state kinetics. These parameters are not necessarily more important; however, they are useful because of the unique situation when drug input rate and elimination rate are equivalent.

The first is the average plasma concentration at steady state, or Css. By solving for Cp, you get the following: As a further simplification, we know that there is a relationship between dose, clearance, and bioavailability shown by the following equation: By rearranging terms we can get the following: Then replacing terms from the equation for Css above with AUC, we get the following: When the rate of drug elimination compensates the rate of drug administration, the average drug concentration reaches steady state or plateau.

At steady state, the amount of drug lost in each interval equals the amount gained, that is the dose multiplied by the bioavailability. Therefore, the plasma concentration fluctuates between doses similarly from one dosing interval to another.

The factors affecting the average steady state concentration are: Rate of dose administration unit dose divided by dosing intervalwhich affects proportionally the steady state plasma concentration. Bioavailability, which modulates rate of dose administration.

**Loading Dose vs. Maintenance Dose**

Reduced clearance will lead to higher steady state concentration, and vice-versa, making clearance inversely related to steady state concentration. During the dosing interval, the factors affecting the fluctuation of plasma concentration around the average concentration are: Frequency of drug administration: For a similar dosing rate, the greater the relative frequency of administration, the smaller the plasma fluctuation.

The longer the half-life, the smaller the plasma fluctuation Rate of absorption: The time required to reach steady state is determined by the drug's half-life, as is the time it takes to reach a new plateau after a change in regimen.