School of Mathematics and Statistics
University of Glasgow
The United Kingdom
October 22, 2013
The Optimal Fibre Orientation in an Iliac Bifurcation Model
The distribution of collagen fibres is important to the mechanical properties of arterial walls. Experiments show that in most of the arterial walls, there are two (or more) distinct fibre families counter-rotating from the innermost to the outermost layers of the arterial wall. However, a recent investigation revealed that some arterial wall layers have only one preferred fibre direction; notably in the media layer of human common iliac artery . To explain this interesting observation, here we investigate this phenomenon using an idealised bifurcation model of an iliac artery. Material properties are characterised by a generalised structure-based constitutive model which incorporates a measured dispersion parameter of the collagen fibres. Inflation and extension numerical experiments are simulated with 100mmHg blood pressure loading in the lumen surface and a physiological axial pre-stretch at both ends. To separate the effects of the circumferential and axial residual stress from the geometric influences, we also consider a tube model as a comparison. Several approaches are used to determine the “optimal fibre angle” in the iliac artery model, including the uniform distribution of the transmural strain/stress, fibre stress remodelling, and optimisation of the total energy. Results from all three approaches support the hypothesis that the optimal fibre angle in the media layer of the iliac artery is closer to zero degree. That is, the two families of collagen fibers merge into one along the circumferential direction, as is observed by the experiment. The pre-stretch in the axial direction, in particular, is found to play an essential role in determining the optimal fibre angle in different sections of the arterial tree.
 A.J. Schriefl, G. Zeindlinger, D.M. Pierce, P. Regitnig, and G.A. Holzapfel. Determination of the layer-specific distributed collagen fibre orientations in human thoracic and abdominal aortas and common iliac arteries. Journal of the Royal Society Interface, 9(71):1275–1286, 2012.