Design of optimal two-sample bolus injection tests for measuring low plasma clearance rates

The bolus injection technique is widely used for assessing plasma clearance rates of substances and is based on multiexponential data analysis of multiple concentration measurements. This approach can be simplified to a monoexponential description with only two measurements if intercompartmental mixing occurs at a much faster rate than elimination, i.e. with low plasma clearance rates. In this context initial transients must be ignored because the first measurement time instant affects the accuracy of clearance estimates if mixing is still incomplete. Moreover, measurement noise affects estimation precision which can be optimized by suitable choice of the sampling schedule and of the injected test dose. The aim of this study is to design two-sample bolus injection tests for measuring low plasma clearance rates with preassigned precision and with minimum amount of injected test substance. This paper provides equations for evaluating whether plasma clearance is sufficiently low to allow a monoexponential description of the plasma disappearance curve and for choosing the first sampling time instant. Closed form equations are proposed for determining the optimal test dose and the second sampling time. Result are derived for a particular heteroscedastic measurement noise description, and the problem of robustness with respect to interpatient variability of kinetic parameters is addressed.