Reliability of structure tensors in representing soft tissues structure

• Reliability of structure tensors in fiber network representation was investigated.
• Model simulation was compared with generated and measured data.
• Results show poor reliability except under approximately uniform orientation distribution.
• In contrast, Fourier series yields reliable structure representation.
• Structure tensors should thus be applied with extreme caution, only in few limited cases.

Structure tensors have been applied as descriptors of tissue morphology for constitutive modeling. Here the reliability of these tensors in representing tissues structure is investigated by model simulations of a few examples of generated and measured planar fiber orientation distributions. Reliability was evaluated by comparing the data with the orientation density distribution recovered from the structure tensor representation, and with a orientation density recovered from an alternative representation by Fourier series of spherical harmonics. The results show that except for the case of uniform or close to uniform orientation distributions, the distributions recovered from the structure tensor fit the data poorly. On the other hand, orientation distributions recovered from Fourier series of spherical harmonics converge to the data distributions provided sufficient terms are included in the truncated series. These results suggest that the structure tensor is a reliable descriptor of tissue structure only under very limited cases.