Displacement smoothing for the precise MRI-based measurement of strain in soft biological tissues

Displacement and strain are fundamental quantities that describe the normal and pathological mechanical function of soft biological materials. Non-invasive imaging techniques, including displacement-encoded magnetic resonance imaging (MRI), enable the direct calculation of biomaterial displacements during the application of extrinsic mechanical forces. However, because strain is derived from measured MRI-based displacements, data processing must be accomplished to minimise the propagation and amplification of errors. Here, we evaluate smoothing methods (including averaging filters, splines, finite impulse response filters and wavelets) that enable the calculation of strain in biomaterials from MRI-based displacements for minimal error, defined in terms of bias and precision. Displacement and strain precisions were improved using all smoothing methods studied. Precision generally increased with the number of smoothing iterations (i.e. repeated applications) of a chosen smoothing method. The bias depended on the smoothing method and tended to increase with the number of smoothing iterations. A Gaussian filter characterised complex and heterogeneous strain fields with maximum precision and minimum bias. The results suggest that the optimal choice of smoothing method to compute strain for a given biomaterial or tissue application depends on a careful consideration of trade-offs between the improved precision (with increased data smoothing) and the trending increase in bias.