School of Mathematics, University of Birmingham, B15 2TT, UK; Institute for Metabolism and Systems Research, University of Birmingham, B15 2TT, UK.
John Tyndall Institute, School of Engineering, University of Central Lancashire, Preston PR1 2HE, UK; School of Medicine and Dentistry, University of Central Lancashire, Preston PR1 2HE, UK; Institute of Translational Medicine, University of Birmingham, B15 2TT, UK.
J Biomech. 2019 Mar 6;85:230-238. doi: 10.1016/j.jbiomech.2019.01.036. Epub 2019 Jan 29.
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.
选择合适的模型并根据实验数据确定其相关参数，对于生物力学中的许多问题来说是至关重要的。几十年来，Bird、Carreau、Cross 和 Yasuda 等人的剪切稀化复杂流体模型已被应用于高度引用的血液动力学计算研究中。在本文中，我们重新研究了这些模型，首先是为了突出文献中命名约定的某种不确定性，但更重要的是为了解决通过拟合流变实验推断模型参数的问题。通过重新拟合已发表的数据，以及通过模拟，我们发现似然面中有很大的平坦区域，这些区域产生了许多参数集，它们同样可以很好地拟合数据。尽管这些参数集对实验数据的拟合几乎没有区别，但它们可以预测非常不同的流动剖面，因此这些参数不能用于得出关于流体物理性质的结论，例如零剪切粘度或流体的松弛时间，或者实际上是流动行为。我们通过模拟验证了这些特征不是实验数据集的结果；通过从流变模型中采样点并添加少量噪声，我们创建了一个合成数据集，该数据集表明参数可识别性的问题是这些模型固有的。
