In recent years, advances have been made that improve understanding of the microstructure of fibrous tissues however, more information, such as the structure of the cross-linking of the collagen fibres and the effect this has on the mechanical response, is still needed to capture more details of the microstructure. To inform the modelling, it is important to have structural data from various imaging techniques in addition to data from mechanical tests. In this approach, the material is considered to be a fibre-reinforced composite with the fibres distributed within an isotropic matrix the models developed within this framework describe the effect of the structural arrangement of the fibres on the mechanical response very well. The continuum approach has been shown to be very successful in modelling the elastic behaviour of many types of fibrous tissues, including artery walls, cartilage, myocardiums, corneas and heart valves. Various models have been proposed to take account of different dispersion arrangements on the basis of continuum theory. In recent years, it has become apparent that in the modelling of fibrous soft biological tissues, the dispersion of the collagen fibres has a significant effect on the mechanical response compared with the case when no dispersion is assumed. 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. 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. 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. 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. 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.

Modelling of the dispersed structure is important for the prediction of the stress and deformation characteristics in (patho)physiological tissues under various loading conditions. It has recently been recognized that the dispersed orientation of these fibres has a significant effect on the mechanical response of the tissues. Collagen fibres within fibrous soft biological tissues such as artery walls, cartilage, myocardiums, corneas and heart valves are responsible for their anisotropic mechanical behaviour.

Mathematica 11.3 plot sphere