Non-identifiability of parameters for a class of shear-thinning rheological models, with implications for haematological fluid dynamics

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Choosing a suitable model and determining its associated parameters from fitting to experimental data is fundamental for many problems in biomechanics. Models of shear-thinning complex fluids, dating from the work of Bird, Carreau, Cross and Yasuda, have been applied in highly-cited computational studies of hemodynamics for several decades. In this manuscript we revisit these models, first to highlight a degree of uncertainty in the naming conventions in the literature, but more importantly to address the problem of inferring model parameters by fitting to rheology experiments. By refitting published data, and also by simulation, we find large, flat regions in likelihood surfaces that yield families of parameter sets which fit the data equally well. Despite having almost indistinguishable fits to experimental data these varying parameter sets can predict very different flow profiles, and as such these parameters cannot be used to draw conclusions about physical properties of the fluids, such as zero-shear viscosity or relaxation time of the fluid, or indeed flow behaviours. We verify that these features are not a consequence of the experimental data sets through simulations; by sampling points from the rheological models and adding a small amount of noise we create a synthetic data set which reveals that the problem of parameter identifiability is intrinsic to these models.

Bibliographic note

Copyright © 2019 The Authors. Published by Elsevier Ltd.. All rights reserved.


Original languageEnglish
Pages (from-to)230-238
Number of pages9
JournalJournal of Biomechanics
Early online date29 Jan 2019
Publication statusPublished - 6 Mar 2019


  • Blood rheology, Identifiability, Non-Newtonian fluid dynamics, Parameter fitting