Identifiable pharmacokinetic models: The role of extra inputs and measurements

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Abstract
Single input, single output experiments can result in nonunique solutions for the rate constants of a linear compartmental model used to describe the pharmacokinetics. Where a finite number of solutions exists, a priori knowledge has to be used to distinguish between the solutions. Where there is an infinite number of solutions, assumptions have to be made about the values of some rate constants in order to obtain a unique solution for the others. This paper considers such experiments and determines whether either the addition of an extra input (simultaneously with the first input) or the taking of an extra measurement would result in a unique solution. It is found that perturbing a second input can be useful, but only if the perturbation is of different shape from the first input. Measurements of drug in urine and metabolite in plasma are generally not helpful in resolving identifiability of the drug dynamic model. If a radioactive tracer is used, though, the second measurement (for example, by externally scanning the radioactivity of the liver) can prove useful, but only if the gain of the measuring device is known.