# Chapter 4

# One Compartment IV Bolus

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## Assumptions

We will start the course with a one compartment - linear model. Also, we will first consider drug kinetics after a rapid intravenous injection, an IV bolus injection. According to this model we will consider the body to behave as a single well-mixed container. To use this model mathematically we need to make a number of assumptions.
### 1. One compartment

The drug in the blood is in rapid equilibrium with drug in the extravascular tissues. The drug concentration may not be equal in each tissue or fluid however we will assume that they are proportional to the concentration of drug in the blood at all times. This is not an exact representation however it is useful for a number of drugs to a reasonable approximation.
### 2. Rapid Mixing

We also need to assume that the drug is mixed instantaneously in blood or plasma. The actual time taken for mixing is usually very short, within a few of minutes, and in comparison with normal sampling times it is insignificant. We usually don't sample fast enough to see drug mixing in the blood.
### 3. Linear Model

We will assume that drug elimination follows first order kinetics. First order kinetics means that the rate of change of drug concentration by any process is directly proportional to the drug concentration remaining to undertake that process. Remember first order kinetics is an assumption of a linear model not a one compartment model. If we have a linear if we double the dose, the concentration will double at each time point.

**Figure 4.2.1 Scheme for a One Compartment Model, Intravenous (IV) Bolus Administration**

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