On fibre dispersion modelling of soft biological tissues: a review

Abstract

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.

Effect of myofibre architecture on ventricular pump function by using a neonatal porcine heart model: from DT-MRI to rule-based methods

“…To incorporate fibre dispersion in material constitutive law, Gasser et al [26] introduced a structural tensor to account for collagen fibre dispersion in arterial tissue, they assumed a rotational symmetry for fibre distribution and a compact form of characterizing fibre dispersion was then given with one dispersion parameter, the so-called κ-model. In a series of studies [27,28], Holzapfel and coworkers used this generalized structural tensor to characterize the passive response of fibre-reinforced soft tissues. Later on, Pandolfi and co-workers [29][30][31] extended Gasser's general structural tensor approach by including the second-order term of the Taylor expansion on the mean invariant along the fibre direction, to improve the accuracy of a structural tensor with large dispersions.…”

General method for classification of fiber families in fiber-reinforced materials: application to in-vivo human skin images

“…Furthermore, the analysis of N fiber families in the fiber image is realized by modeling the COD as a sum of N sigmoid functions [Eq. (8)]. The number N of fiber families is iteratively determined by the FINE algorithm.…”

“…indicates the presence of at least one fiber family, and the first sigmoid function (Eq. (8) with N = 1) is fitted to the COD. The resulting fit of a single fiber family is shown in Fig.…”

Mechanical Considerations of Bioprinted Tissue

“…Additionally, decades of work examining biomechanical processes, too many to cite here, is relevant to bioprinting-based strategies for tissue fabrication. Modeling of collagen fibril dispersion within soft tissues to predict stress and deformation characteristics (Holzapfel et al, 2019) coupled with finite element modelbased simulations of growing neovessel and collagen fibril dynamics during angiogenesis, (Edgar et al, 2014a;Edgar et al, 2014b;Edgar et al, 2015), for example, could be useful in designing final microvascular topologies. An understanding of the cellular aggregate fusion process and tissue environment dynamics could provide a design framework to fabricate tissue microarchitectures that are beyond bioprinting resolution (Sun et al, 2014;Robu et al, 2019).…”