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Choosing a suitable model and determining its associated parameters fromfitting 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 ofheamodynamics for several decades. In this manuscript we revisit these models,first to highlight a degree of uncertainty in the naming conventions in theliterature, but more importantly to address the problem of inferring modelparameters by fitting rheology experiments. By refitting published data, andalso by simulation, we find large, flat regions in likelihood surfaces thatyield families of parameter sets which fit the data equally well. Despitehaving almost indistinguishable fits to experimental data these varyingparameter sets can predict very different flow profiles, and as such theseparameters cannot be used to draw conclusions about physical properties of thefluids, such as zero-shear viscosity or relaxation time of the fluid, or indeedflow behaviours. We verify that these features are not a consequence of theexperimental data sets through simulations; by sampling points from therheological models and adding a small amount of noise we create a syntheticdata set which reveals that the problem of parameter identifiability isintrinsic to these models.

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