On fibre dispersion modelling of soft biological tissues: a review

Collagen fibres within fibrous soft biological tissues such as artery walls, cartilage, myocardiums, corneas and heart valves are responsible for their anisotropic mechanical behaviour. It has recently been recognized that the dispersed orientation of these fibres has a significant effect on the mechanical response of the tissues. Modelling of the dispersed structure is important for the prediction of the stress and deformation characteristics in (patho)physiological tissues under various loading conditions. This paper provides a timely and critical review of the continuum modelling of fibre dispersion, specifically, the angular integration and the generalized structure tensor models. The models are used in representative numerical examples to fit sets of experimental data that have been obtained from mechanical tests and fibre structural information from second-harmonic imaging. In particular, patches of healthy and diseased aortic tissues are investigated, and it is shown that the predictions of the models fit very well with the data. It is straightforward to use the models described herein within a finite-element framework, which will enable more realistic (and clinically relevant) boundary-value problems to be solved. This also provides a basis for further developments of material models and points to the need for additional mechanical and microstructural data that can inform further advances in the material modelling.