Structural identifiability analysis and reparameterisation (parameter reduction) of a cardiovascular feedback model

Abstract

Structural identifiability should be considered when developing mathematical models. A globally or at least locally identifiable model has to be obtained in order to have some chance of obtaining unique parameter estimates when real data are available. An indicator of structural unidentifiability may be that some unknown parameter estimates are found to be not well determined from parameter estimation of a model. An example is discussed in this paper to illustrate the procedures involved when such situations arise. Problems with parameter estimation were observed for a PKPD model for an α1A/1L-adrenoceptor partial agonist developed for the treatment of stress urinary incontinence The regulation of the side effects of the increased peripheral resistance, induced by the constriction of the blood vessels, was modelled by adapting a previous cardiovascular nonlinear PKPD model proposed by Franchetau and co-workers. Structural identifiability analysis confirmed that the model was unidentifiable. The model was then reparameterised (parameter list reduction) to obtain a globally identifiable model. Simulation studies confirm the superiority of the reduced parameterisation with respect to parameter estimation. The simulation study also confirms the models behave indistinguishably with respect to the input–output behaviour. The example demonstrates the importance of recognising an unidentifiable model and illustrates step by step identifiability analysis, reparameterisation and validation of reparameterised model against the original model.