# Chapter 4

# One Compartment IV Bolus

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## Linear Model - First Order Kinetics

**First-order kinetics**
To illustrate first order kinetics we might consider what would happen if we were to give a drug by iv bolus injection, collect blood samples at various times and measure the plasma concentrations of the drug. We might see a steady decrease in concentration as the drug is eliminated, as shown in Figure 4.3.1.

**Figure 4.3.1. Concentration ***versus* time

**Rate ***versus* Cp

If we measure the slope of this curve at a number of times we are actually measuring the **rate of change of concentration at each time point**, ΔCp/Δt, represented by the straight line tangents in Figure 4.3.2.

Figure 4.3.2 Same as Figure 4.3.1 with Tangents shown

Now if we plot this rate of change *versus* the plasma concentration, for each data point, we will get a straight line when first order kinetics are obeyed. This is shown in Figure 4.3.3.

**Figure 4.3.3 Plot of ΔCp/Δt ***versus* Cp for first order process

This behavior can be expressed mathematically as:-

**Equation 4.3.1**

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