Abstract

In [1] we developed a rotationally symmetric model to describe collagen fibre dispersion in soft biological tissues based on a generalized structure tensor. This has been highly successful, but recent experimental results [2] on the collagen fibre dispersion in human arterial layers have shown that the dispersion in the tangential plane is more significant than that out-of-plane. A rotationally symmetric dispersion model is not therefore able to capture this distinction. For this reason we introduce a new non-symmetric dispersion model, based on the bi-variate von Mises distribution, which is used to construct a new structure tensor. The latter is incorporated in a strain-energy function that accommodates both the mechanical and structures features of the material, extending our rotationally symmetric dispersion model [1]. Material and structural parameters were obtained by fitting predictions of the model to experimental data obtained from a human abdominal aortic adventitia. In a finite element example the non-homogeneous stress distribution is obtained for circumferential and axial strips under fixed extension. This work has been published in the recent paper [3].

[1] TC Gasser, RW Ogden, GA Holzapfel. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3:15-35, 2006.

[2] AJ Schriefl, G Zeindlinger, DM Pierce, P Regitnig, GA Holzapfel. Determination of the layer-specific distributed collagen fiber orientations in human thoracic and abdominal aortas and common iliac arteries. J. R. Soc. Interface 9:1275-1286, 2012.

[3] GA Holzapfel, JA Niestrawska, RW Ogden, AJ Reinisch, AJ. Schriefl. Modelling non-symmetric collagen fibre dispersion in arterial walls. J. R. Soc. Interface 12:2015.0188, 2015.