# One Compartment IV Bolus

## 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