A von Mises Mixture to Describe Experimentally-Derived Fiber Distributions From Soft Tissues

Collagen fibers strongly influence the biomechanical behavior of soft tissues [1], and constitutive models of such tissues should account for the characteristics of the fibers [2] and for their distribution. Such distributions can be measured using techniques such as small-angle light/X-ray scattering (SALS/SAXS; e.g. [3, 4]), diffusion tensor imaging [5] or 3D histology [6]. Fiber characteristics are often heterogeneous, so that measurements for entire organs or tissues typically yield large numerical data sets. Use of these raw data directly into biomechanical models is cumbersome and one may wish to parameterize them spatially for simplicity. This can be achieved through the use of a suitable mathematical function to fit the fiber distributions derived from experiment. Here we discuss how to choose such a function and optimize such a fit. We restrict our attention to thin tissue samples, where the fibers, assumed to be unimodally distributed, lie predominantly within a (tangent) plane, so that the problem is two-dimensional.