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

TL;DR

This paper demonstrates that for shear-thinning rheological models used in blood flow studies, parameter estimation from experimental data is fundamentally non-identifiable, leading to multiple parameter sets fitting data equally well but predicting different flow behaviors.

Contribution

The study reveals intrinsic non-identifiability issues in classical shear-thinning models, impacting their use in biomechanical and hemodynamic research.

Findings

Large flat likelihood regions allow multiple parameter fits.

Different parameters predict significantly different flow profiles.

Parameter non-identifiability is inherent to the models, not data quality.

Abstract

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 heamodynamics 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 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.