Structural identifiability of physiologically based pharmacokinetic models

When starting a project in drug kinetics it is necessary to test a priori whether there is sufficient information in the experimental input-output design to estimate unique values of internal rate constants. This is an important test if the pharmacokinetics of a drug are to be characterised in some way by the parameter values estimated from the observed plasma or blood concentration profile. Various modifications of the well-perfused Physiologically Based Pharmacokinetic model (PBPK) are considered here. More complex PBPK models can be considered to consist of subsystems, representing groups of tissues, which are connected in parallel to the central compartment. A novel method of structural identifiability analysis is presented here that considers these subsystems individually. This makes analysis of subsequently modified models much simpler. It is found in a number of cases that these more complex systems remain globally identifiable and at worst reduce to locally identifiable for the additional parameters. A caveat is added about having more than one eliminating peripheral tissue.